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admin:main admin:copilot/add-clang-tidy-scan-pipeline admin:copilot/update-mkdocs-and-fonts admin:feature/rotation_improved admin:feature/example-simplegame admin:develop
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..
compare: admin:v4.3.0
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admin:copilot/add-clang-tidy-scan-pipeline admin:main admin:copilot/update-mkdocs-and-fonts admin:feature/rotation_improved admin:feature/example-simplegame admin:develop
admin:v4.8.0 admin:v4.7.1 admin:v4.7.0 admin:v4.6.1 admin:v4.6.0 admin:v4.5.1 admin:v4.5.0 admin:v4.4.0 admin:v4.3.0 admin:v4.2.0 admin:v4.1.0 admin:v4.0.1 admin:v4.0 admin:v3.10.1 admin:v3.10 admin:3.10 admin:v3.9.4 admin:v3.9.3 admin:v3.9.2 admin:v3.9.1 admin:v3.9.0 admin:v3.8.2 admin:v3.8.1 admin:v3.8.0 admin:v3.7.1 admin:v3.7.0 admin:v3.6.2 admin:v3.6.1 admin:v3.6.0 admin:v3.5.3 admin:v3.5.2 admin:v4.0rc admin:v3.5.1 admin:v3.5.0 admin:v3.4.0 admin:v3.3.1 admin:v3.3.0 admin:v3.2.3 admin:v3.2.2 admin:v3.2.1 admin:v3.2.0 admin:v3.1.0 admin:v3.0.5 admin:v3.0.4.2 admin:v3.0.4.1 admin:v3.0.4 admin:v3.0.3.1 admin:v3.0.3 admin:v3.0.2.1 admin:v3.0.2 admin:v3.0.1 admin:v3.0.0 admin:v2.6.1 admin:v2.6.0 admin:v2.5.1 admin:v2.5.0 admin:v2.4.0 admin:v2.3.3 admin:v2.3.2.1 admin:v.2.3.3 admin:v2.3.2 admin:v2.3.1 admin:v2.3.0 admin:v2.2.1 admin:v2.2.0 admin:v2.1.1 admin:v2.1.0 admin:v2.0.1.1 admin:v2.0.2 admin:v2.0.1 admin:v2.0.0 admin:v1.3.0 admin:v1.2.0 admin:v1.1.3 admin:v1.1.2 admin:v1.1.1 admin:v1.1.0 admin:v1.0.1 admin:v1.0.0

479 Commits
v2.2.0 ... v4.3.0

Author SHA1 Message Date
Orange++
9efabd8fb2 Merge pull request #102 from orange-cpp/feature/gjk_algorithm 
Feature/gjk algorithm
 2025-11-09 23:27:03 +03:00
Orange
8f225c5f8e forgot keyname 2025-11-09 23:23:13 +03:00
Orange
44682b6f2c added other collision types 2025-11-09 22:39:09 +03:00
Orange
a6cf043d79 style fix 2025-11-09 22:27:04 +03:00
Orange
3968d13a19 removed redundant headers 2025-11-09 22:25:29 +03:00
Orange
a3f45628aa fixed formating 2025-11-09 22:22:02 +03:00
Orange
6da44a5a51 added mesh class, added mesh trair 2025-11-09 22:10:56 +03:00
Orange
e5d8e1c953 add mesh class 2025-11-09 21:28:00 +03:00
Orange
e2378bfa8b Refactors Simplex class for GJK algorithm 
Simplifies Simplex initialization and accessors.

Ensures correct handling of collinearity within the simplex calculation, preventing issues when colliders share the same origin. This improves stability and reliability of the GJK algorithm.
 2025-11-09 17:29:50 +03:00
Orange
ca3dab855b Corrects transform order for collider 
Reorders the transform application to translation, scale, then rotation.

This ensures the collider’s world matrix is constructed correctly, preventing potential scaling or rotation issues in the GJK algorithm being developed on this branch.
 2025-11-09 17:15:01 +03:00
Orange
79482d56d1 fix 2025-11-09 17:09:46 +03:00
Orange
c4024663bb Auto stash before checking out "origin/feature/gjk_algorithm" 2025-11-09 17:08:57 +03:00
Orange
b2a512eafe Adds mesh scaling to mesh collider 
Updates the mesh collider to include a scale parameter, allowing for non-uniform scaling of the collision mesh.

This provides more flexibility in defining collision shapes and supports a wider range of scenarios.
 2025-11-09 17:02:07 +03:00
Orange
7b0e2127dc Adds GJK collision test with equal origins 
Implements a new test case for the GJK algorithm
to verify collision detection when colliders share the same origin.
This enhances the robustness of collision detection in scenarios
where objects are positioned at the same location.
 2025-11-09 16:57:52 +03:00
Orange
0b663b73d5 Handles collinear cases in simplex collision 
Adds helper functions to address near-zero vectors and find perpendicular directions.

This prevents potential crashes and improves robustness when the origin lies on the line defined by the simplex edges during GJK collision detection.
 2025-11-09 16:56:38 +03:00
Orange
afc0720f08 Refactor: Simplify GJK simplex handling 
Removes the separate `Simplex` class and integrates its functionality directly into the `GjkAlgorithm`. This simplifies the code and reduces unnecessary overhead.

Updates tests to align with refactored implementation.
 2025-11-09 16:02:13 +03:00
Orange
015fc9b1e7 made final 2025-11-09 15:51:28 +03:00
Orange
62d1a615ae fix 2025-11-09 15:50:07 +03:00
Orange
043b5c588d updated 2025-11-09 15:39:11 +03:00
Orange
cd18b088cb updated test 2025-11-09 15:38:38 +03:00
Orange
ebfdd0b70e Refactors simplex handling in GJK algorithm 
Updates simplex handling to use references for vertex access, avoiding unnecessary copies. This improves performance and clarity within the GJK algorithm.
 2025-11-09 14:40:22 +03:00
Orange
e7b82f441c patch 2025-11-09 14:23:34 +03:00
Orange
6e59957247 Adds mat_scale function 
Introduces a utility function to create a scaling matrix from a Vector3.
This simplifies the creation of scale transformations, particularly useful for the GJK algorithm implementation.
 2025-11-09 14:19:08 +03:00
Orange
1e540862a0 Refactors GJK tetrahedron handling 
Updates the `handle_tetrahedron` function to use const references for simplex points, improving efficiency and readability.

Corrects a potential bug where the `simplex` variable wasn't being correctly updated when recursively calling `handle_triangle`.

Also, const-qualifies `point_to_same_direction` for better safety.
 2025-11-09 14:15:32 +03:00
Orange
31cc1116ae Updates simplex iterator and size access 
Changes the index type for accessing simplex points to `std::size_t` for consistency and safety.

Adds `[[nodiscard]]` attribute to `size()` and iterator functions to signal potential misuse and enable static analysis.

These updates are part of the GJK algorithm implementation.
 2025-11-09 14:05:46 +03:00
Orange
338246a618 Implements GJK collision detection 
Adds GJK algorithm implementation for detecting collisions between mesh colliders.

Includes mesh collider definition and unit tests for basic collision detection.

Provides a foundation for more complex collision handling and physics interactions.
 2025-11-09 14:04:01 +03:00
Orange++
10ebf6ed04 Merge pull request #101 from orange-cpp/feature/added_pe_scan_example 
Adds PE signature scanner example
 2025-11-08 14:38:17 +03:00
Orange
ec9a15927a Adds PE signature scanner example 
Implements a basic example demonstrating how to scan for a given pattern within a PE file.

The example takes a file path, section, and signature as input and utilizes the `omath::PePatternScanner` to locate the signature within the specified section of the PE file.
 2025-11-08 14:34:14 +03:00
Orange++
1a0e55b4cf Merge pull request #100 from orange-cpp/feature/improved_scree_to_world 
Improves screen to world conversion accuracy
 2025-11-08 13:54:44 +03:00
Orange
b48160e1b7 Improves screen to world conversion accuracy 
Adds support for different screen origin configurations.

This change allows for more accurate conversion from screen coordinates to world coordinates by correctly handling different screen origin positions (top-left and bottom-left). Includes new unit tests to verify the functionality with both configurations.
 2025-11-08 13:51:56 +03:00
Orange++
d4a16a94e6 Update documentation links from HTTPS to HTTP 2025-11-08 07:43:28 +03:00
Orange
07c0eebf21 removed old banner 2025-11-03 17:17:54 +03:00
Orange++
9ed18f27c3 Merge pull request #99 from luadebug/macosx 
Add macOS CI workflow and update CMake presets for vcpkg integration
 2025-11-01 16:53:27 +03:00
Saikari
86b1e8a00d Add macOS CI workflow and update CMake presets for vcpkg integration 2025-11-01 16:44:40 +03:00
Orange
db9200d7b5 upgraded version 2025-11-01 14:07:06 +03:00
Orange
d894b62773 patch 2025-11-01 13:39:13 +03:00
Orange
ade281cdd2 Adds const version of rev_bar method 
Adds a const overload for the `rev_bar` virtual method.
This allows calling the method on const instances of the reverse engineered class.
 2025-11-01 13:28:51 +03:00
Orange++
9bb94ee33b Merge pull request #96 from orange-cpp/feature/docs 
Feature/docs
 2025-11-01 13:07:58 +03:00
Orange
754b370d8b Renames documentation titles for consistency 
Updates several documentation titles to a more consistent format.
Changes include renaming "Frequently Asked Questions (FAQ)" to "FAQ",
"Getting Started with OMath" to "Getting Started",
"Troubleshooting Guide" to "Troubleshooting", and
"OMath Tutorials" to "Tutorials".
```
 2025-11-01 13:00:32 +03:00
Orange
d3e379e71b Removes dark overrides CSS file 
Deletes the `dark-overrides.css` file.

This file appears to have been superseded by other theming mechanisms and is no longer needed. Its presence was causing potential conflicts.
 2025-11-01 12:57:33 +03:00
Orange++
6ed40a7bc1 Merge pull request #98 from orange-cpp/copilot/sub-pr-96 
Comprehensive documentation overhaul with guides, tutorials, and cross-references
 2025-11-01 12:56:05 +03:00
copilot-swe-agent[bot]
f3d5f84d2c Improve documentation with cross-references and README enhancements 
Co-authored-by: orange-cpp <59374393+orange-cpp@users.noreply.github.com>
 2025-11-01 09:54:08 +00:00
copilot-swe-agent[bot]
0b89c1d36d Add comprehensive documentation improvements 
Co-authored-by: orange-cpp <59374393+orange-cpp@users.noreply.github.com>
 2025-11-01 09:51:38 +00:00
copilot-swe-agent[bot]
b8ed0bd5a5 Initial plan 2025-11-01 09:40:43 +00:00
Orange++
b9ae356e57 Merge pull request #97 from orange-cpp/copilot/sub-pr-96 
Add documentation for game engine math modules
 2025-11-01 12:40:09 +03:00
copilot-swe-agent[bot]
e351b64355 Add comprehensive documentation for all game engines 
Co-authored-by: orange-cpp <59374393+orange-cpp@users.noreply.github.com>
 2025-11-01 09:37:11 +00:00
copilot-swe-agent[bot]
f4df88bb7a Initial plan 2025-11-01 09:22:33 +00:00
Orange
8142d800c7 Styles navbar for wider display and consistent spacing 
Widens the navbar container to accommodate more content.
Adjusts padding of navbar items for tighter spacing.
Prevents line wrapping and enables horizontal scrolling on smaller screens.
 2025-11-01 12:14:36 +03:00
Orange
95c0873b8c Documents view angle struct and related API 
Adds documentation for the `omath::ViewAngles` struct,
clarifying its purpose, common usage patterns,
and the definition of the types of pitch, yaw and roll.

Also, adds short explanations of how to use ViewAngles and what tradeoffs exist
between using raw float types and strongly typed Angle<> types.
 2025-11-01 09:12:04 +03:00
Orange
d12a2611b8 Moves images to improved documentation structure 
Moves various image files demonstrating libomath’s usage and featuring artwork from showcases to the improved `docs/images` structure to reorganize the project's documentation in a logical and maintainable fashion.

This change ensures consistency and simplifies updating documentation assets.
 2025-10-31 16:47:28 +03:00
Orange
9212b1f51f Documents pattern scanning API 
Adds comprehensive documentation for the pattern scanning API.

Details parsing behavior, complexity, and usage examples.
Includes troubleshooting tips and minimal test sketches.
Clarifies edge-case handling and implementation notes.
 2025-10-31 16:25:56 +03:00
Orange
56505cf3e1 Adds documentation for ray-triangle intersection 
Documents the `omath::collision::Ray` and `LineTracer` types, detailing their purpose, usage, and API.

Includes a description of the Möller–Trumbore algorithm
and provides usage examples for segment-triangle
and infinite ray intersection tests.

Relates to feature/docs
 2025-10-31 16:17:32 +03:00
Orange
0510dd8328 Adds documentation for Vector4 and incorporates ImGui integration 
Adds comprehensive documentation for the `Vector4` class, outlining constructors, operators, and utility functions. Includes detailed notes on `clamp` functionality and potential ImGui integration caveats. Incorporates optional ImGui integration with explanations for correct usage and potential improvements.
 2025-10-31 16:14:20 +03:00
Orange
ce9758c86b Adds dark theme support to the OM documentation 
Applies a dark theme to the documentation site using the `darkly` theme.
Provides a visually appealing dark mode option.
Configures colors to ensure readability and aesthetic consistency.
 2025-10-31 16:06:03 +03:00
Orange++
7d194a5c36 Merge pull request #95 from orange-cpp/pathfinding_improvement 
removed brackets
 2025-10-30 05:44:00 +03:00
Orange
eec34c1efb removed brackets 
Initial plan

Initial exploration and analysis complete

Co-authored-by: orange-cpp <59374393+orange-cpp@users.noreply.github.com>

Optimize performance: A* pathfinding, Vector3 hash, pattern scanner, AVX2 code, and serialization

Co-authored-by: orange-cpp <59374393+orange-cpp@users.noreply.github.com>

Add bounds check for navigation mesh serialization

Co-authored-by: orange-cpp <59374393+orange-cpp@users.noreply.github.com>

Document serialization limitation for large neighbor counts

Co-authored-by: orange-cpp <59374393+orange-cpp@users.noreply.github.com>

Add _codeql_build_dir to gitignore

Co-authored-by: orange-cpp <59374393+orange-cpp@users.noreply.github.com>

Removes codeql detected source root

Eliminates the automatically generated file that was causing issues.

This file was added by codeql and no longer needed.

revert
cleaned up gitignore

moved to anon namespace

Improves navigation mesh serialization and clamping

Ensures correct serialization of navigation meshes by clamping neighbor counts to prevent data corruption when exceeding uint16_t limits.

Updates data types to `std::uint8_t` and `std::size_t` for consistency.
Uses `std::copy_n` instead of `std::memcpy` for deserialization.
 2025-10-30 05:38:58 +03:00
Orange
765d5e7216 fixed typo 2025-10-30 05:37:34 +03:00
Orange
7cb8a4de52 Clarifies release process for stable builds 
Explains that changes merged into master won't reach stable users unless the `stable` tag is updated.
 2025-10-28 01:21:41 +03:00
Orange++
d2fbc286b1 Merge pull request #93 from orange-cpp/feaure/small_improvement 
removed useless option
 2025-10-28 01:19:21 +03:00
Orange
64385757af fix 2025-10-28 01:15:36 +03:00
Orange
ea7b812645 removed 2025-10-28 01:11:02 +03:00
Orange
b214cdf3a1 removed useless option 2025-10-28 01:09:47 +03:00
Orange
dccc12ee30 added some comments 2025-10-27 11:25:31 +03:00
Orange
60e744978c force disabled tests 2025-10-27 11:22:24 +03:00
Orange++
495a2a80e4 Merge pull request #92 from orange-cpp/feature/projection_utility 
added vcpkg integration
 2025-10-27 11:11:28 +03:00
Orange
6fbc010fa1 considered to switch to v4 2025-10-27 11:05:55 +03:00
Orange
c8f77de4f2 updated version 2025-10-27 10:59:30 +03:00
Orange
5c2d09b175 patch 2025-10-27 10:58:26 +03:00
Orange
b3646ab708 Adds default and artifact registries 
Configures the default Vcpkg registry and adds an artifact registry
for the microsoft catalog. This enables the tool to find and use
pre-built packages from the Microsoft catalog.
 2025-10-27 10:57:57 +03:00
Orange
d751eaf132 Adds Darwin build presets with Vcpkg support 
Adds new CMake presets for Darwin platforms, including debug and release configurations with optional Vcpkg integration.
This allows for easier builds on Darwin systems utilizing pre-built libraries from Vcpkg.
 2025-10-27 09:57:12 +03:00
Orange
62e7ccb054 Update CMake configuration for Vcpkg integration and feature enablement. 
Enables features and sets build configurations via Vcpkg manifest.
Adds new presets for Windows and Linux debug/release builds using Vcpkg.
Conditionally enables features (imgui, avx2, tests, benchmark) based on Vcpkg manifest features.
 2025-10-27 09:55:49 +03:00
Orange
4d9e055bb3 Fixes invalid NT header check in variant 
Ensures the NT header signature check uses a capture to avoid potential issues with variable scope.
 2025-10-27 09:22:00 +03:00
Orange
9be7ca886d Disables Vcpkg build override 
Disables the automatic override of build options by Vcpkg.

This prevents unintended consequences when using Vcpkg and allows for more control over the build process.
 2025-10-27 09:19:51 +03:00
Orange
30568f3633 Disables tests and benchmarks by default for VCPKG 
Changes the default state of `OMATH_BUILD_TESTS` and `OMATH_BUILD_BENCHMARK` to OFF when built via VCPKG.

Previously, these flags were inherited from the project's top level. This change ensures that these are explicitly enabled via VCPKG manifest features, providing better control over build configuration.
 2025-10-27 09:19:09 +03:00
Orange
5f22499b66 Links tests to gtest when available 
Conditionally links the test target to gtest when it is available,
rather than requiring the OMATH_BUILD_VIA_VCPKG flag to be false.
This allows for a more flexible test setup.
 2025-10-27 09:05:40 +03:00
Orange
f75afb8354 fix 2025-10-27 08:59:42 +03:00
Orange
e38df8bd23 Removes baseline from omath vcpkg.json 
Eliminates the `builtin-baseline` setting from the omath vcpkg.json file.
This setting is no longer necessary.
 2025-10-27 08:56:37 +03:00
Orange
ae347c8509 fix 2025-10-27 08:51:58 +03:00
Orange
ee40979a2d fix 2025-10-27 08:41:22 +03:00
Orange
69d0b7b829 fix 2025-10-27 08:37:55 +03:00
Orange
490ccfe983 fix 2025-10-27 08:36:48 +03:00
Orange
5630c2708e Update build system and enable VCPKG 
Migrates to CMake presets and enables VCPKG to manage dependencies.
Removes explicit submodule configuration.
Updates benchmark and googletest to be integrated or linked properly.
The goal is to ease the build process and reduce complexity related to linking and dependency management.
 2025-10-27 08:34:05 +03:00
Orange
ed7220dc9c Configures CMake for Vcpkg integration 
Sets up CMake presets to utilize the Vcpkg toolchain.

Specifies the Vcpkg root directory and manifest features.

Defines the installation directory for Vcpkg packages.

Forces the usage of Ninja as the make program.
 2025-10-27 08:11:13 +03:00
Orange
5e4fae9e42 Enables Vcpkg usage for CMake builds 
Configures CMake to utilize vcpkg for dependency management on both Linux and Windows platforms.
This ensures consistent build environments across different operating systems and simplifies the integration of external libraries.
 2025-10-27 08:07:25 +03:00
Orange
063f43e74c fix 2025-10-27 08:03:42 +03:00
Orange
171b4ca3da Adds Vcpkg setup to CI workflows 
Adds vcpkg setup for Arch Linux and Windows CI jobs.

This ensures consistent dependency management and builds via Vcpkg for both platforms and enables OMath to build via vcpkg.
Clones the vcpkg repository and bootstraps it during the job execution.
 2025-10-27 08:00:53 +03:00
Orange
878e3358c0 Adds vcpkg integration and updates build configuration 
Configures CMakePresets.json to utilize vcpkg for dependency management.
Adds support for building with vcpkg.

Adds error message for missing VCPKG_ROOT environment variable.
Adds explicit VCPKG_MANIFEST_FEATURES and VCPKG_INSTALLED_DIR to CMakePresets.json.
Adds benchmark dependency to vcpkg.json.
 2025-10-27 07:53:53 +03:00
Orange
81aef68143 Adds support for tests and benchmarks via Vcpkg features 
Enables building unit tests using GTest and benchmarks using Benchmark,
through Vcpkg features.

Adds `tests` and `benchmark` features to `vcpkg.json`,
and adds corresponding CMake logic to control their build based on
Vcpkg manifest features.
 2025-10-27 06:42:43 +03:00
Orange++
e2a37f2c81 Fix formatting and spacing in LICENSE file 
Corrected formatting and removed extra spaces in the LICENSE file.
 2025-10-27 02:32:06 +03:00
Orange
69575c1cb3 added additional check 2025-10-23 06:43:09 +03:00
Orange
8adf5db409 added vcpkg manifest file 2025-10-23 06:35:22 +03:00
Orange
2c7e443f52 added contained type alias 2025-10-23 06:26:57 +03:00
Orange
6ad4ef29e9 fix 2025-10-23 01:08:19 +03:00
Orange++
8feb805067 Remove 'future' from affiliation clause in LICENSE 2025-10-23 01:00:40 +03:00
Orange
816da38987 added frostbite into global header 2025-10-23 00:55:49 +03:00
Orange
0ba795c767 added Frostbite into readme 2025-10-23 00:50:35 +03:00
Orange
88b709f531 deleted not needed header 2025-10-23 00:49:54 +03:00
Orange
a7eacb529e updated comments 2025-10-23 00:48:54 +03:00
Orange++
5a4026a4fc Merge pull request #91 from orange-cpp/feature/frostbite_engine 
Defines constants for Frostbite engine
 2025-10-23 00:18:07 +03:00
Orange
404c7de594 added frostbite sources 2025-10-23 00:08:17 +03:00
Orange
f26f48cc53 Defines constants for Frostbite engine 
Introduces a constants header file for the Frostbite engine,
including common vectors, matrices, and angle types.
This provides a centralized location for defining and accessing
essential mathematical constants used throughout the engine.
 2025-10-21 04:56:49 +03:00
Orange++
ed8afb02a1 Merge pull request #90 from orange-cpp/feature/ndc_invalid_calc_fix 
Fixes NDC calculation and updates formulas
 2025-10-21 04:45:07 +03:00
Orange
d86695fad7 nuked not needed test 2025-10-21 04:38:43 +03:00
Orange
570c035f27 added second method of w2s 2025-10-21 04:38:43 +03:00
Orange
5657282577 Fixes incorrect NDC calculation and updates formulas 
Corrects the NDC calculation in `world_to_screen` to improve accuracy.
Replaces custom perspective projection matrix calculation with `omath::mat_perspective_right_handed` for correctness and consistency.
Updates test cases and provides debugging information by printing view and projection matrices.
Addresses an issue in the feature/ndc_invalid_calc_fix branch.
 2025-10-21 04:38:43 +03:00
Orange
551ac62075 Added TF2 into gallery 2025-10-19 04:00:20 +03:00
Orange++
1b1be48ee6 Merge pull request #89 from luadebug/wasm 
Fix pattern scan range check to use end() instead of cend()
 2025-10-17 15:27:03 +03:00
Saikari
1f9ea136b0 Fix pattern scan range check to use end() instead of cend() 2025-10-16 19:47:27 +03:00
Orange
8dadb22e75 Removes ReSharper disable comments 
Removes the `ReSharper disable CppInconsistentNaming` comments
from the header file.
 2025-10-14 13:23:09 +03:00
Orange
8dd9860aa1 Adds PE pattern scan utility 
Includes a new utility for scanning PE patterns.
 2025-10-14 13:20:14 +03:00
Orange++
9a0470f781 Merge pull request #88 from orange-cpp/feaute/more_support_for_hash 
Adds hash support for Vector2, Vector3, and Vector4
 2025-10-14 13:08:28 +03:00
Orange
eb8688c90c Unifies orthographic matrix generation 
Consolidates the generation of left-handed and right-handed orthographic matrices into a shared implementation to reduce code duplication.
 2025-10-14 13:06:23 +03:00
Orange
9f2f619a21 Adds hash support for Vector2, Vector3, and Vector4 
Implements `std::hash` specialization for `omath::Vector2`, `omath::Vector3`, and `omath::Vector4` with float components.

This enables usage of these vector types as keys in hash-based containers, such as `std::unordered_map` and `std::unordered_set`.
 2025-10-14 13:00:28 +03:00
Orange++
568883ff1c Merge pull request #87 from orange-cpp/feature/no_win_api 
Removes Windows-specific API dependencies for pattern scanning
 2025-10-13 14:25:03 +03:00
Orange++
97003b953a Update README.md 2025-10-13 14:24:53 +03:00
Orange
5646654317 Removes Windows-specific API dependencies for pattern scanning 
Replaces calls to Windows API functions (GetModuleHandleA) with a void pointer parameter.

Simplifies pattern scanning for loaded modules by removing Windows-specific code and replacing it with a generic approach.
 2025-10-13 14:17:30 +03:00
Orange++
ee54e3de34 Merge pull request #86 from orange-cpp/feature/improved_pe_scanner_interface 
Feature/improved pe scanner interface
 2025-10-12 20:20:28 +03:00
Orange
7b0af9cf66 Removes unnecessary code in PE scanner 
Simplifies the PePatternScanner class by removing extraneous code.
This cleans up the codebase and improves readability.
 2025-10-12 20:00:52 +03:00
Orange
563ae0a656 Moves namespace declaration to end of file 
Refactors the source file layout to improve readability and consistency.
Moves the namespace declaration to the end of the file.
 2025-10-12 19:59:47 +03:00
Orange
b9e2307d7a Organizes PE scanner code into namespaces 
Refactors the PE scanner implementation to group related definitions and functions within namespaces.

This improves code organization and readability, particularly for internal PE handling and scanning logic.

The included link to the `linux-pe` repository served as a reference during this refactoring.
 2025-10-12 19:57:47 +03:00
Orange
cd0a864e7c Refactors PE scanner to eliminate redundant section extraction 
Simplifies the PE pattern scanner by removing the redundant `extract_section_from_pe_file` function.

The extracted data is now returned directly from a new `ExtractedSection` struct within the main scanning function, streamlining the code and reducing duplication. This improves readability and maintainability of the PE scanner.
 2025-10-12 19:53:41 +03:00
Orange++
5c30f57c4c Merge pull request #85 from orange-cpp/feature/hide_pe_defs 
Feature/hide pe defs
 2025-10-12 19:46:22 +03:00
Orange
3dcd033616 Removes redundant NtHeaderVariant field declarations 
Simplifies NtHeaderVariant structure by removing redundant field declarations.
This improves code readability and reduces unnecessary code duplication.
 2025-10-12 19:43:29 +03:00
Orange
f10dc60772 Removes redundant NtHeaderVariant declaration 
Moves the `NtHeaderVariant` definition outside the unnamed namespace,
to avoid repetition and improve code consistency.
This change is part of the ongoing work on feature/hide_pe_defs.
 2025-10-12 19:42:53 +03:00
Orange
37f624956b Removes PE definition files 
Removes the PE definition files and related functions as they are no longer needed.
 2025-10-12 19:41:18 +03:00
Orange
20dc4e6730 Updates omath version to 3.9.2 2025-10-11 17:22:16 +03:00
Orange
f6c607d84c Uses source engine camera trait for view angle calculation 
Replaces the custom `view_angle_to` function with `omath::source_engine::CameraTrait::calc_look_at_angle` for vector3 view angle calculations.
This change aligns with source engine conventions and improves code consistency.
 2025-10-11 15:46:52 +03:00
Orange++
81ed5f80d7 Merge pull request #84 from luadebug/patch-1 
internal_rev_object.hpp: do not use __fastcall for non-Windows platforms
 2025-10-10 07:47:25 +03:00
Saikari
e385686323 Update internal_rev_object.hpp 2025-10-09 21:34:19 +03:00
Orange++
086eda4ee3 Merge pull request #82 from orange-cpp/feature/pe_scanner 
Updates PE header structure for x64
 2025-10-09 20:45:21 +03:00
Orange
9419e390da Allows specifying target section for file scan 
Enables users to specify the target section name when scanning a PE file for a pattern.
This provides more flexibility in locating patterns within a PE file, as it's not limited to the ".text" section.
 2025-10-09 20:42:03 +03:00
Orange
d919600ac2 Removes unused path parameter from function. 
Simplifies `extract_section_from_pe_file` by removing the unused path parameter.
This clarifies the function's purpose and improves readability.
 2025-10-09 20:36:10 +03:00
Orange
11681ac601 Refactors PE header parsing for improved robustness 
Simplifies PE header reading and validation logic, extracting common functionality into helper functions.

Introduces `get_nt_header_from_file` to handle both x86 and x64 PE headers.

Adds validation checks for both DOS and NT headers to ensure file integrity.

Improves code readability and maintainability by reducing redundancy in header parsing.

Relates to feature/pe_scanner
 2025-10-09 20:32:36 +03:00
Orange
6c5152297a Uses correct calling convention for virtual methods 
Adjusts the virtual method calling convention based on the compiler (_MSC_VER).
This ensures compatibility and correct behavior on different platforms.
 2025-10-09 20:08:04 +03:00
Orange
547f64e4c4 Removes platform-specific error handling 
Simplifies pattern scanner logic by removing conditional compilation for non-Windows platforms.

The error handling previously thrown on non-Windows platforms was unnecessary as this functionality is not intended for those systems. This change streamlines the code and removes a misleading error message.
 2025-10-09 20:03:43 +03:00
Orange
3129e32f0c Uses std::uint16_t for SubsystemId enum 
Ensures consistency by using `std::uint16_t` instead of `uint16_t` for the `SubsystemId` enum.

Relates to feature/pe_scanner
 2025-10-09 20:01:34 +03:00
Orange
72b54e9673 Removes PE scanner test code 
Eliminates the PE scanner test code from the unit tests.

This removes a test that appears to be broken or no longer relevant, since the test directly references a file path.
 2025-10-09 19:58:58 +03:00
Orange
2ff291b255 Supports broader architectures in PE scanner 
Updates the PE scanner implementation to support both 32-bit and 64-bit architectures.
Leverages `std::variant` and a generic `ImageNtHeaders` to abstract architecture-specific details.
Simplifies the logic for retrieving section data, generalizing the process for improved maintainability.
 2025-10-09 19:58:19 +03:00
Orange
8eda1ce4bc Adds PE scanner infrastructure and data structures 
Initializes infrastructure for PE file scanning.

Adds data structures for PE headers (DOS, optional, section),
including user-defined types for section characteristics.

Refactors existing pattern scanning code to utilize new PE data structures.

Adds basic parsing of PE headers.
 2025-10-08 19:22:20 +03:00
Orange
e1b4375621 fixed for mac improved readability 2025-10-08 19:22:20 +03:00
Orange
d84259fdcc Adds PE file header definitions 
Defines `DosHeader` and `FileHeader` structures to represent PE file header information.
Includes definitions for `MachineId` enum and `FileCharacteristics` union.
These definitions are prerequisite for PE file parsing and analysis.
 2025-10-08 19:22:20 +03:00
Orange
d64c7ad756 Adds PE section extraction and pattern scanning 
Adds functionality to extract a specific section from a PE file and scan for a given pattern within that section.

Introduces `extract_section_from_pe_file` to isolate a section, enabling more targeted pattern searches.
Overhauls `scan_for_pattern_in_file` to utilize extracted section data and improve accuracy.
 2025-10-08 19:22:20 +03:00
Orange
710f91999f Adds scan functionality for PE files 
Introduces a method to scan for patterns within specified PE files.
This facilitates searching for patterns outside of loaded modules.
 2025-10-08 19:22:20 +03:00
Orange
f3fe0e3cee added pe pattern scan 2025-10-08 19:22:20 +03:00
Orange
c5c5c2e972 Clarifies build preset usage in INSTALL.md 
Rephrases the explanation regarding build presets for clarity in the INSTALL.md file.
The text now more explicitly advises users on selecting appropriate presets.
 2025-10-08 19:22:20 +03:00
Orange
a7cb056ce7 Moves PE headers file to omath directory 
Organizes the project by relocating the PE headers file to the omath directory structure.
This improves code organization and maintainability.
 2025-10-08 19:22:20 +03:00
Orange
dae1555ec4 added mkdoc 2025-10-08 19:22:19 +03:00
Orange
2c6ef1b8cc Defines PE header structure for x64 
Introduces a structure for representing the DOS header
within a PE (Portable Executable) file for x64 architectures.
This definition enables easier parsing and manipulation of PE header information.
 2025-10-08 19:22:19 +03:00
Orange++
d70e8853e8 Add Kaspersky LLC to license restrictions 2025-10-08 17:48:24 +03:00
Orange
e35d64b486 Disables rvalue overload of scan_for_pattern 
Prevents implicit conversions and unexpected behavior by deleting the rvalue overload of `scan_for_pattern`.
 2025-10-06 15:05:04 +03:00
Orange
9868c832a1 Corrects function signature 
Adjusts the `scan_for_pattern` function signature to correctly use `const std::string_view&`.
 2025-10-06 14:46:40 +03:00
Orange
42e46f9921 added global header 2025-10-06 14:36:00 +03:00
Orange
e7ccc2ead0 added concept for iterators, reworked interface 2025-10-06 14:25:52 +03:00
Orange
170f969697 improved scanner interface 2025-10-06 14:21:52 +03:00
Orange
131fd891b0 added unlikely 2025-10-06 14:04:43 +03:00
Orange++
a5396b72cb Merge pull request #81 from orange-cpp/feature/pattern_scan 
Improves pattern scanning functionality and adds corner case tests
 2025-10-05 15:59:59 +03:00
Orange
ec876ea292 Includes header for fixed-width integer types 
Adds `#include ` to ensure platform-independent use of fixed-width integer types.
 2025-10-05 15:56:35 +03:00
Orange
8021050fad Uses std::ranges::find for pattern scanning 
Replaces `std::find` with `std::ranges::find` for improved code consistency and potentially better performance when dealing with ranges.
 2025-10-05 15:54:54 +03:00
Orange
bd585b5412 Uses parsed pattern size in pattern scan 
Updates the pattern scan loop to iterate over the size of the parsed pattern, ensuring correct iteration when using parsed patterns.
 2025-10-05 14:14:31 +03:00
Orange
06f9a8c9ee Adds pattern scanning functionality and corner case tests 
Implements a pattern scanning feature that allows searching for byte patterns within a byte range.

Adds `scan_for_pattern` method to `PatternScanner` to locate a pattern within a byte span.

Adds corner case tests to verify functionality and handle invalid inputs.
 2025-10-05 06:37:20 +03:00
Orange
160b51da94 Adds corner case tests for pattern scanning 
Adds new test cases to cover additional scenarios for pattern scanning, including tests for leading/trailing whitespace and spacing variations to ensure robustness.
 2025-10-04 18:43:05 +03:00
Orange
064edf9ef1 Handles empty pattern strings 
Skips processing when encountering an empty string slice during pattern scanning.
This prevents unexpected behavior and potential errors when the pattern string contains sections that result in an empty byte string.
 2025-10-04 18:33:57 +03:00
Orange
f17d36dcd3 Adds pattern scanning functionality 
Implements a pattern scanner for byte sequence parsing.

Introduces `omath::PatternScanner` to parse pattern strings, which represent byte sequences.
Adds support for wildcard characters ('?' and '?') to represent optional bytes in the pattern.
Includes unit tests for basic read operations to ensure proper functionality.
 2025-10-04 18:30:43 +03:00
Orange++
ec4f9f6c90 Merge pull request #80 from orange-cpp/feature/rev_eng 
Feature: Reverse Engineering classes
 2025-10-04 10:09:07 +03:00
Orange
cbee8c2c95 finished test 2025-10-04 10:04:34 +03:00
Orange
dc6edbb67f update global header 2025-10-04 09:52:14 +03:00
Orange
74381eda5c added external class 2025-10-04 09:47:48 +03:00
Orange
1ef7833bd9 reordored omath headers 2025-10-03 13:51:53 +03:00
Orange
c10386f3f6 added rev_object 2025-10-03 13:43:47 +03:00
Orange
413cef4f23 version update 2025-10-03 13:16:48 +03:00
Orange
867cee41c3 femoved useless file 2025-10-03 13:14:11 +03:00
Orange
990fe78a33 fixed wrong spam of command option into build log 2025-10-03 12:40:18 +03:00
Orange++
1efdb50f73 Merge pull request #78 from luadebug/patch-1 
CMakeLists.txt: support AVX2 detection
 2025-10-01 03:10:24 +03:00
Saikari
86fea065e7 CMakeLists.txt: do not use /ARCH:AVX since we have /ARCH:AVX2 already 2025-09-30 23:40:07 +03:00
Saikari
ac046aae6c Update CMakeLists.txt 2025-09-30 23:18:00 +03:00
Saikari
9646054877 CMakeLists.txt: support AVX2 detection for https://github.com/xmake-io/xmake-repo/pull/8277 2025-09-30 21:40:25 +03:00
Orange
6334002639 forgot linux macos 2025-09-29 11:23:28 +03:00
Orange
72e0c0c90b removed useless fields of C compiler 2025-09-29 11:21:43 +03:00
Orange
2f2a5a00c4 added another clangformat 2025-09-27 10:55:05 +03:00
Orange++
c394993418 Add documentation link to README 2025-09-27 10:40:54 +03:00
Orange
476048583d added version file update cmake version 2025-09-27 10:38:31 +03:00
Orange++
76ae67c968 Revise features and clean up README 
Updated features section and removed usage examples.
 2025-09-27 10:35:14 +03:00
Orange++
d1d95d2f36 Merge pull request #77 from orange-cpp/feature/formating_improvement 
Feature/formating improvement
 2025-09-25 22:03:47 +03:00
Orange
6409568334 added plane header 2025-09-25 21:59:59 +03:00
Orange
83ba339eb5 fix 2025-09-25 21:57:05 +03:00
Orange
c49c93d542 decomposed formatter 2025-09-25 21:55:56 +03:00
Orange
92dab52d66 improvement 2025-09-25 21:43:33 +03:00
Orange
dac3d8e43f improved encoding for formating 2025-09-25 21:06:46 +03:00
Orange
fb0b05d7ef imprvoed code style 2025-09-25 19:33:06 +03:00
Orange++
993212e7ab Merge pull request #76 from orange-cpp/bugfix/projectile_pred 
projectile pred look at fix
 2025-09-22 02:43:04 +03:00
Orange
380a9f0a16 fix 2025-09-22 02:41:12 +03:00
Orange
ba7bce5502 ooops 2025-09-22 02:39:50 +03:00
Orange
ce40891e37 added targets specification to ci cd build 2025-09-22 02:38:25 +03:00
Orange
c4d10f8872 disable benchmark build for CI/CD 2025-09-22 02:34:52 +03:00
Orange
2bb0c82c30 added source engine benchmark 2025-09-22 02:29:36 +03:00
Orange
a4dcf8dc3b unreal engine fix 2025-09-22 02:12:20 +03:00
Orange
17eaddbc8c fix unity 2025-09-22 02:10:33 +03:00
Orange
9005c02499 opengl fix 2025-09-22 02:08:58 +03:00
Orange++
e7380b5eb6 Merge pull request #75 from orange-cpp/bugfix/fix_look_at 
Bugfix/fix look at
 2025-09-20 17:12:16 +03:00
Orange
f8d6e4b544 unified look at for source iw_engine 2025-09-20 17:09:13 +03:00
Orange
893eca296b improved tests 2025-09-20 17:00:49 +03:00
Orange
b0bd58ccb2 improved opengl tests stability 2025-09-20 16:36:05 +03:00
Orange
44a42d39d0 improved test stability 2025-09-20 16:34:44 +03:00
Orange
a8c7e8eb54 fixed test 2025-09-20 16:22:24 +03:00
Orange
cef22919a4 added more iterations 2025-09-20 16:08:04 +03:00
Orange
f79350e609 style fix 2025-09-20 16:00:30 +03:00
Orange
1102cad390 fixed unreal 2025-09-20 15:59:43 +03:00
Orange
df4e999c82 fixed unity 2025-09-20 15:54:48 +03:00
Orange
3baeb182f0 fixed opengl 2025-09-20 15:48:59 +03:00
Orange
5539bbad0d reverted 2025-09-20 15:46:21 +03:00
Orange
4d4dfae8f2 fix 2025-09-20 15:44:33 +03:00
Orange
03c514104e fixed rotation matrix 2025-09-20 15:44:33 +03:00
Orange
792db7a673 added new mat function 
more tests
 2025-09-20 15:44:33 +03:00
Orange
bfd399e631 fixed test 2025-09-20 15:44:33 +03:00
Orange
7fef690f5e fixed iw engine 
fixed source

revert
 2025-09-20 15:44:33 +03:00
Orange++
3df7d65ac1 Update README.md 2025-09-18 19:39:11 +03:00
Orange
e1a1164136 fixed warning 2025-09-18 19:06:56 +03:00
Orange
23216279dc fix 2025-09-18 18:42:02 +03:00
Orange
9e082f7dfa now its ref 2025-09-18 18:39:28 +03:00
Orange
7750819e83 improved naming 2025-09-18 18:38:07 +03:00
Orange++
2ec0e2f93f Update CREDITS.md to include Billy O'Neal 
Added acknowledgment for Billy O'Neal's contributions.
 2025-09-18 06:08:49 +03:00
Orange++
9170ffb1a9 Merge pull request #74 from BillyONeal/fmodf 
Don't name std::fmodf.
 2025-09-18 06:04:43 +03:00
Orange
e05f9ef5a9 Removes FMA check for matrix multiplication 
Removes preprocessor check for FMA instructions in matrix multiplication functions.
This simplifies the code and relies on the compiler's ability to optimize the
code based on available hardware support. The assumption is that modern
compilers will automatically utilize FMA instructions if available, and fall
back to alternative implementations if not.
 2025-09-18 06:02:37 +03:00
Orange
89bb4aa625 Guards AVX2 usage with a preprocessor definition 
Ensures that AVX2 intrinsics are only included when the
OMATH_USE_AVX2 preprocessor definition is set. This prevents
compilation errors when AVX2 support is not available or
explicitly disabled.
 2025-09-18 05:22:22 +03:00
Billy Robert O'Neal III
9b0845593d Don't name std::fmodf. 
The C standard library function fmodf is not guaranteed to be in namespace std, and in fact is not with a default Ubuntu 24.04 installation, leading to the following compile error:

```console
Change Dir: '/vcpkg/buildtrees/vcpkg-ci-orange-math/x64-linux-dbg'

Run Build Command(s): /vcpkg/downloads/tools/ninja/1.12.1-linux/ninja -v -v -j33
[1/2] /usr/bin/c++ -DOMATH_SUPRESS_SAFETY_CHECKS -DOMATH_VERSION=\"3.5.0\" -isystem /vcpkg/installed/x64-linux/include -fPIC -g -std=gnu++23 -MD -MT CMakeFiles/main.dir/main.cpp.o -MF CMakeFiles/main.dir/main.cpp.o.d -o CMakeFiles/main.dir/main.cpp.o -c /vcpkg/scripts/test_ports/vcpkg-ci-orange-math/project/main.cpp
FAILED: CMakeFiles/main.dir/main.cpp.o
/usr/bin/c++ -DOMATH_SUPRESS_SAFETY_CHECKS -DOMATH_VERSION=\"3.5.0\" -isystem /vcpkg/installed/x64-linux/include -fPIC -g -std=gnu++23 -MD -MT CMakeFiles/main.dir/main.cpp.o -MF CMakeFiles/main.dir/main.cpp.o.d -o CMakeFiles/main.dir/main.cpp.o -c /vcpkg/scripts/test_ports/vcpkg-ci-orange-math/project/main.cpp
In file included from /vcpkg/installed/x64-linux/include/omath/omath.hpp:22,
                 from /vcpkg/scripts/test_ports/vcpkg-ci-orange-math/project/main.cpp:1:
/vcpkg/installed/x64-linux/include/omath/color.hpp: In member function ‘constexpr omath::Hsv omath::Color::to_hsv() const’:
/vcpkg/installed/x64-linux/include/omath/color.hpp:98:45: error: ‘fmodf’ is not a member of ‘std’; did you mean ‘modf’?
   98 |                 hsv_data.hue = 60.f * (std::fmodf(((green - blue) / delta), 6.f));
      |                                             ^~~~~
      |                                             modf
ninja: build stopped: subcommand failed.
```

Only the 'sufficient additional overloads' of `fmod` are guaranteed to be in `std`. Since this is clearly intended to call the (float, float) overload, explicitly cast `((green - blue) / delta)` (which is a `double`) to `float` and call the name in `std` as suggested by the diagnostic.
 2025-09-17 19:15:10 -07:00
Orange++
617ded2dd4 Merge pull request #73 from orange-cpp/featore/performance_tests 
added performance folder
 2025-09-17 20:53:11 +03:00
Orange
e882a224d2 fix 2025-09-17 20:50:30 +03:00
Orange
e04f6573c0 patch 2025-09-17 20:46:00 +03:00
Orange
791e3b2313 improved bench 2025-09-17 20:40:03 +03:00
Orange
26b56d757c fix 2025-09-17 20:25:22 +03:00
Orange
fbb77b9925 patch 2025-09-17 20:22:42 +03:00
Orange
7b671dbd90 added benchmark submodule 2025-09-17 20:14:33 +03:00
Orange
5875930f1a added benchmark 2025-09-17 19:56:50 +03:00
Orange
d773985822 added avx mutiplication 2025-09-17 19:47:29 +03:00
Orange
a2de6f8fae renamed folder 2025-09-17 18:07:28 +03:00
Orange
d71795006d added performance folder 2025-09-17 17:47:55 +03:00
Orange++
561438d45c Merge pull request #72 from orange-cpp/feature/mat_refactor 
Feature/mat refactor
 2025-09-17 17:41:15 +03:00
Orange
874b028e86 removed unused var 2025-09-17 17:38:17 +03:00
Orange
68ec42d9ed added space 2025-09-17 17:33:05 +03:00
Orange
8aeb4667d7 decomposed mutiplication 2025-09-17 17:30:57 +03:00
Orange
565464f0cd forgot std 2025-09-17 17:23:02 +03:00
Orange++
04b50d4545 Merge pull request #71 from orange-cpp/feature/mat_perf_boost 
Improves matrix multiplication performance
 2025-09-17 17:18:12 +03:00
Orange
e01d32fb22 Improves matrix multiplication performance 
Optimizes matrix multiplication by specializing the algorithm
based on the matrix storage type (row-major or column-major).

This change significantly improves performance by leveraging
memory access patterns specific to each storage order.
 2025-09-17 17:12:41 +03:00
Orange++
a3a023a664 Add acknowledgment for AmbushedRaccoon's contribution 2025-09-16 16:58:00 +03:00
Orange++
1b5a7ed4fd Merge pull request #69 from luadebug/patch-1 
Repair omath.hpp by removing unexisting header include
 2025-09-15 15:01:04 +03:00
Saikari
362b818a71 Update omath.hpp 2025-09-15 13:13:55 +03:00
Orange
29a96d64bb Adds 2D screen to world conversion 
Adds an overload for screen_to_world that accepts a 2D screen position.

Renames screen_to_dnc to screen_to_ndc for clarity.
 2025-09-14 04:48:56 +03:00
Orange
256365e52e patch 2025-09-14 04:43:25 +03:00
Orange
e333d81b81 Enables formatting support for Angle objects 
Adds a partial specialization of `std::formatter` for `omath::Angle`
to provide formatting support using `std::format`.

This allows `Angle` objects to be easily formatted as strings,
including degree symbol representation, using standard formatting
techniques.
 2025-09-14 04:43:01 +03:00
Orange
d66f60d419 Removes unnecessary div tag 
Removes an empty div tag, which streamlines the HTML structure and contributes to cleaner code.
 2025-09-13 20:13:35 +03:00
Orange
4a4939b604 Repositions YouTube preview link 
Moves the YouTube preview link to improve the README's visual flow.
 2025-09-13 20:08:48 +03:00
Orange
ebe8d1a90e Improves README readability 
Adds a newline to the README file for better visual separation
between the contribute button and the horizontal rule.
 2025-09-13 19:55:23 +03:00
Orange
1a3376fe6c Improves button aesthetics on README 
Adds whitespace to the buttons displayed on the README to improve their appearance.
 2025-09-13 19:53:09 +03:00
Orange
20188d7043 Updates README with gallery, install and usage 
Enhances the README by adding a gallery showcasing OMath's capabilities,
providing a clearer installation guide, and improving usage examples
to facilitate easier adoption.
Also restructures the navigation for better user experience.
 2025-09-13 19:50:58 +03:00
Orange++
f59e0d255f Update README.md 2025-09-13 19:20:37 +03:00
Orange++
071cb15492 Update README.md 2025-09-13 19:16:19 +03:00
Orange++
f8812ed9e7 Update README.md 2025-09-09 22:15:00 +03:00
Orange++
19d310d35f Update README.md 2025-09-09 21:48:54 +03:00
Orange++
c364879b5f Merge pull request #68 from orange-cpp/feature/screen_to_world 
Feature/screen to world
 2025-09-09 02:58:32 +03:00
Orange
418b7c0e7e Fixes float type conversion in world_to_screen 
Fixes a potential type conversion issue by explicitly casting the x-coordinate to float in the world_to_screen test. This prevents possible compiler warnings and ensures the intended behavior.
 2025-09-09 02:13:45 +03:00
Orange
69f46abce1 Adds projection test for world-to-screen consistency 
Adds a test to verify the consistency of world-to-screen and
screen-to-world projections. This ensures that projecting a point
from world to screen and back results in the same point, thereby
validating the correctness of the camera projection transformations.
 2025-09-09 01:37:38 +03:00
Orange
de61f7a5d8 Adds screen to world space conversion 
Adds functionality to convert screen coordinates to world space, including handling for cases where the inverse view projection matrix is singular or when the world position is out of screen bounds.

Also exposes Camera class to unit tests.
 2025-09-09 01:31:23 +03:00
Orange
07a449b633 Simplifies raycast early exit condition 
Combines the infinite length raycast hit check into a single condition.

This clarifies the logic and avoids redundant checks for early exit
in the ray-triangle intersection test, improving performance.
 2025-09-08 23:52:35 +03:00
Orange++
6bb549ef4c Merge pull request #67 from orange-cpp/feature/angle-improvement 
Implements angle class with normalization
 2025-09-08 20:18:11 +03:00
Orange
14fa810ecb Implements angle class with normalization 
Adds an angle class with support for different normalization
and clamping strategies. Includes trigonometric functions and
arithmetic operators. Introduces unit tests to verify correct
functionality.

Disables unity builds to address a compilation issue.
 2025-09-08 20:15:59 +03:00
Orange++
b964661030 Merge pull request #66 from orange-cpp/feature/remove-legacy 
Removes deprecated Matrix class
 2025-09-08 19:59:34 +03:00
Orange
9c11551c9a Removes deprecated Matrix class 
Removes the deprecated `Matrix` class and its associated source files and unit tests.

This change is to ensure code cleanliness and prevent accidental usage of the slow and outdated `Matrix` class.
The `Mat` class should be used instead.
 2025-09-08 19:56:04 +03:00
Orange++
21fece7c84 Update LICENSE 2025-09-08 15:52:01 +03:00
Orange
996618994d updated logo psd 2025-09-06 23:14:14 +03:00
Orange++
ce8be6dd52 Update README.md 2025-09-04 23:49:07 +03:00
Orange++
17aac2f80e Update CREDITS.md 2025-09-04 20:36:12 +03:00
Orange++
ba927734d2 Update LICENSE 2025-09-04 20:35:25 +03:00
Orange++
c0d5fd18f5 Update SECURITY.md 2025-09-04 20:35:04 +03:00
Orange++
996a9cf15a Update LICENSE 2025-09-04 19:35:05 +03:00
Orange++
91078f5701 Update LICENSE 2025-09-04 19:33:59 +03:00
Orange
036d3a8992 updated logo 2025-09-03 22:18:54 +03:00
Orange
7534fe8969 removed unused defines 2025-09-03 12:52:00 +03:00
Orange
8e4f1812cc fix 2025-09-03 12:50:31 +03:00
Orange++
e8f40218dd Merge pull request #62 from orange-cpp/feaure/added_logo 
Feaure/added logo
 2025-09-01 17:04:50 +03:00
Orange
50054ca937 Acknowledges logo design contribution 
Updates the credits to acknowledge the new initial logo design.
 2025-09-01 17:04:29 +03:00
Orange
63220c0be7 Adds an omath.psd file. 
Adds a binary file named omath.psd.
 2025-09-01 17:03:31 +03:00
Orange
3b6d19782c Updates README with local image links 
Updates the README to use local image links instead of Imgur links for the showcase section.

This improves the project's resilience against external link rot and
ensures the images remain accessible even if Imgur experiences issues.
 2025-09-01 17:02:23 +03:00
Orange
2d58330508 Replaces banner with logo 
Replaces the project banner in the README with a dedicated logo.

This change simplifies the banner implementation and improves maintainability
by using a local image file instead of referencing an external URL.
 2025-09-01 16:56:43 +03:00
Orange
abf57a55ea Updates include paths and removes dependency 
Updates the include paths in omath.hpp to be more explicit,
ensuring correct referencing of header files.

Removes unnecessary include of vector3.hpp from vector2.hpp.
 2025-09-01 01:28:04 +03:00
Orange++
463532ba81 Merge pull request #60 from orange-cpp/feature/moved_to_dear 
Refactors: Moves linear algebra to new directory
 2025-09-01 00:02:00 +03:00
Orange
d74c66990a Refactors: Moves linear algebra to new directory 
Moves linear algebra headers to a new subdirectory to improve project structure.

Updates includes to reflect the directory change.
Adds vcpkg to the tracked repositories.
 2025-08-31 23:36:05 +03:00
Orange
7f1bc51905 Updates project version to 3.5.0 
Increments the project version number in CMakeLists.txt
from 3.4.0 to 3.5.0.
 2025-08-29 22:04:12 +03:00
Orange
71127f1f12 Updates project version to 3.4.0 
Bumps the project's version number from 3.3.0 to 3.4.0.

Adds a compile definition to expose the project version via the
`OMATH_VERSION` macro.
 2025-08-29 22:03:35 +03:00
Orange++
89041e20ae Merge pull request #59 from orange-cpp/feature/new_primitives 
Adds plane primitive generation
 2025-08-29 14:41:36 +03:00
Orange
a54dd4b52a Fixes plane triangle generation 
Corrects the order of vertices when constructing triangles
for the plane primitive, addressing a potential winding order
issue that could lead to incorrect surface normals and rendering.
 2025-08-29 00:11:31 +03:00
Orange
d7e497b617 Simplifies plane creation logic 
Refactors the plane creation function to directly compute the triangle vertices, removing unnecessary intermediate variables. This results in more concise and readable code.
 2025-08-28 23:57:22 +03:00
Orange
80938cd913 Adds plane primitive generation 
Implements a function to generate a plane primitive from two vertices, a direction vector, and a size, returning an array of two triangles.
 2025-08-28 23:18:36 +03:00
Orange++
830505dbe5 Merge pull request #58 from orange-cpp/feature/ortho-proj 
Adds left- and right-handed ortho matrices
 2025-08-27 23:23:40 +03:00
Orange
75565ecf2d Adds left- and right-handed ortho matrices. 
Adds functions to generate left- and right-handed orthographic projection matrices.
This provides more flexibility when defining a projection for rendering.
 2025-08-27 23:17:56 +03:00
Orange
9a7a4c7fff Removed submodule extlibs/glm 2025-08-27 20:22:33 +03:00
Orange
c0f0bb3c2e com 2025-08-27 20:07:47 +03:00
Orange++
a097c0a2f4 Merge pull request #57 from orange-cpp/feature/added_formatters 
Adds std::format support for math types
 2025-08-26 12:37:13 +03:00
Orange
20ae2b4dd1 Adds formatters for Angle and Color 
Adds formatters for `omath::Angle` and `omath::Color` to allow for easy formatting using `std::format`.

This allows users to easily output Angle and Color values in a human-readable format.
 2025-08-26 12:35:40 +03:00
Orange
115b5a3471 Adds std::format support for math types 
Adds `std::formatter` specializations for `Mat`, `Vector2`, `Vector3`, and `Vector4` types, enabling the use of `std::format` for these types.

This simplifies formatting and printing of these mathematical objects, improving code readability and consistency.

Also adds a hash function specialization for Vector3.
 2025-08-26 12:22:33 +03:00
Orange
77893629f9 Adds omath library header 
Creates the main omath header file that includes all
omath library components. This provides a single point
of inclusion for the entire library, simplifying usage
and dependency management.

Also, adjusts the return types for projectile prediction
functions within the legacy engine to explicitly use
the `Vector3` type for consistency and clarity.
 2025-08-25 22:33:00 +03:00
Orange
afb27b1aa9 Adds build test status message 
Adds a status message to the build process that displays whether unit tests are enabled.

This provides better visibility into the build configuration.
 2025-08-25 22:11:39 +03:00
Orange
61006122ae Displays build configuration options 
Prints the values of various CMake configuration options to the console during the build process.

This provides better visibility into the build configuration and helps with debugging build-related issues.
 2025-08-25 22:10:10 +03:00
Orange
4eb0f59fc0 Updates build status message 
Updates the build status message in CMake to include the project name, providing more context during the build process.
 2025-08-25 21:59:25 +03:00
Orange
3b4bf24a16 Updates project version to 3.3.0 
Increments the project version number in CMakeLists.txt
from 3.2.1 to 3.3.0.
 2025-08-25 21:57:07 +03:00
Orange
51d93c4464 Removes outdated header comments 
Removes redundant and outdated header comments. These comments are no longer necessary for maintaining the codebase.
 2025-08-25 21:54:59 +03:00
Orange++
d83a8121db Merge pull request #55 from orange-cpp/feature/unreal-support 
Adds Unreal Engine math library
 2025-08-25 21:49:11 +03:00
Orange
2584cda5c3 Fixes namespace and angle calculations 
Corrects namespace naming from unity_engine to unreal_engine.

Adjusts projectile prediction and angle calculations for accuracy
in Unreal Engine environments.
 2025-08-25 21:46:50 +03:00
Orange
c90497f77b Fixes Unreal Engine view angle matrix order 
The view angle rotation matrix order in Unreal Engine was incorrect, leading to incorrect camera orientation.

This commit fixes the order of rotation matrices to roll, pitch, yaw
to correctly implement Unreal Engine camera rotations.

Adds comprehensive unit tests for Unreal Engine formulas, camera and constants.

Marks Unreal Engine as supported in README.md.
 2025-08-25 21:42:58 +03:00
Orange
0de6b4589f Adds .idea/ to .gitignore 
Adds the standard .idea/ folder contents to the .gitignore file.

This prevents project-specific IDE settings and workspace files from being tracked by Git, keeping the repository cleaner and avoiding potential conflicts between developers using different IDE configurations.
 2025-08-25 21:31:07 +03:00
Orange
8004c8c181 Adds Unreal Engine math implementations 
Adds Unreal Engine-specific implementations for camera and projectile prediction calculations.

This includes:
- Defining constants and data types tailored for Unreal Engine's coordinate system and conventions.
- Implementing functions for calculating forward, right, and up vectors, view matrices, and perspective projection matrices.
- Providing camera trait for look-at angle calculations and projection matrix generation.
- Implements projectile prediction traits and utilities.
 2025-08-25 21:30:35 +03:00
Orange++
1246c4ed07 Update README.md 2025-08-25 17:26:56 +03:00
Orange++
ab463e1caa Update README.md 2025-08-25 16:00:36 +03:00
Orange
4f13010e7d Removes workspace configuration file 
Deletes the `.idea/workspace.xml` file.
This file tracks workspace-specific settings,
and is not meant to be shared across different
development environments.
 2025-08-21 00:33:02 +03:00
Orange
83d3cc099f Improves test accuracy and adds .gitignore entry 
Updates unit tests to include more accurate assertions for camera projections.

Adds .idea/workspace.xml to .gitignore to prevent tracking local IDE settings.

Refactors some test fixture class names for consistency.
 2025-08-21 00:30:05 +03:00
Orange
625c676010 Fixes MSVC redefinition of min/max 
Adds a compiler definition for MSVC to prevent redefinition of min/max macros by the Windows SDK.

Removes unnecessary undef directives in color.hpp as the NOMINMAX definition now handles the issue.
 2025-08-21 00:17:59 +03:00
Orange
2d9ed4cfc8 Configures project IDE settings and improves gitignore 
Adds project-specific IDE settings to improve code style consistency and development environment.

Removes the .idea directory from the .gitignore file, as these files are now intended to be part of the project for consistent IDE configuration across contributors.
 2025-08-21 00:11:37 +03:00
Orange
29795e9906 Includes missing formula headers 
Includes the necessary formula headers in the camera trait files for different rendering engines.
This ensures that the required mathematical functions and definitions are available when using camera traits.
 2025-08-12 19:08:30 +03:00
Orange
0328fef4f7 Fixes Vector3 conversion from ImVec2 
Corrects the static function signature for creating a Vector3 from an ImVec2.

It was mistakenly returning a Vector3 instead of Vector3.

patch
 2025-08-12 09:38:43 +03:00
Orange
687772f073 feat(omath): Add NDC to screen position coordinate diagram 2025-08-12 09:29:14 +03:00
Orange
c66df11754 Updates project version to 3.2.1 
Increments the project version number in CMakeLists.txt
from 3.0.4.1 to 3.2.1, indicating a release or significant
changes in the project.
 2025-08-12 09:25:40 +03:00
Orange
0450dc3547 Adds concept for prediction engine traits 
Introduces a concept `PredEngineConcept` to ensure that classes used as projectile prediction engine traits conform to a specific interface.
This enforces the presence and return types of required methods and ensures that these methods are `noexcept`, improving type safety and predictability.
 2025-08-12 09:21:34 +03:00
Orange
0bd9eda48f Introduces CameraEngine concept 
Adds a concept `CameraEngineConcept` to ensure that camera
engine implementations provide the necessary functions
with the correct signatures and `noexcept` specifications.

This enables compile-time checks for valid camera engine
implementations, improving code reliability and preventing
runtime errors.
 2025-08-12 09:13:02 +03:00
Orange++
858314fa0a Merge pull request #54 from orange-cpp/feature/vec_fix_improvement 
Adds comparison operators to Vector types
 2025-08-12 08:57:31 +03:00
Orange
f277b1038c Adds comparison operators to Vector types 
Adds less than, greater than, less than or equal, and greater than or equal operators to the Vector2, Vector3 and Vector4 classes.
The comparison is based on the lengths of the vectors.

Adds corresponding unit tests.
 2025-08-12 08:54:33 +03:00
Orange
15c055beb7 Removes virtual destructor from Camera 
Removes the virtual destructor from the Camera class as it is not required,
as the class does not act as a base class. This simplifies the class
definition and avoids potential vtable overhead.
 2025-08-11 01:43:22 +03:00
Orange++
4d24815f3e Update issue templates 2025-08-11 01:30:26 +03:00
Orange
d96b0cd2f7 Marks Camera class as final 
Prevents inheritance from the Camera class.
 2025-08-11 01:18:39 +03:00
Orange++
d238bd137f Merge pull request #53 from orange-cpp/u/camera_type_traits 
Refactors camera and prediction using traits
 2025-08-11 00:47:25 +03:00
Orange
17b150499d Refactors camera and prediction engine traits. 
Moves camera and prediction engine implementations into traits for each engine,
decoupling the engine-specific logic from the core classes, promoting code reuse
and maintainability. This change allows for easier addition of new engines and
customization of existing ones.
 2025-08-11 00:32:09 +03:00
Orange
c7228c9674 Updates googletest submodule 
Updates the googletest submodule to the latest commit.

This brings in the latest fixes and improvements from the
googletest project.
 2025-08-07 23:33:30 +03:00
Orange
7a9f5d4966 Removes projectile.cpp 
Removes the projectile.cpp file. The removal indicates that the associated projectile prediction functionality is no longer needed or has been moved elsewhere.
 2025-08-06 18:37:28 +03:00
Orange
a16050242a Adds community badges to README 
Enhances the README by adding Discord and Telegram badges, providing users with direct access to community channels for support and discussions.
 2025-08-06 06:39:57 +03:00
Orange
ea8f3d8d51 Adds contributing guidelines 
Introduces a CONTRIBUTING.MD file to provide guidelines for
contributing to the project, including prerequisites, setup
instructions, pull request workflow, code style, and building
instructions.

xd

returned back

patch
 2025-08-06 06:23:06 +03:00
Orange
08d2ccc03a Refactors Vector operations for type safety 
Ensures type safety in Vector2, Vector3, and Vector4 operations by using static_cast(0) instead of relying on implicit conversions.
This prevents potential issues with different numeric types.

Adds from_im_vec2 and from_im_vec4 methods for creating vectors from ImVec2/ImVec4 types.
 2025-08-06 06:06:42 +03:00
Orange
21ec23d77b patch 2025-08-06 05:56:09 +03:00
Orange++
2c4ff37062 Merge pull request #52 from orange-cpp/feature/more_traits 
Adds engine traits for projectile prediction
 2025-08-06 05:49:25 +03:00
Orange
695a8035b5 Adds engine traits for projectile prediction 
Implements engine-specific traits for projectile and target position prediction.
Each trait encapsulates logic tailored to a specific game engine (IW, OpenGL, Unity),
accounting for engine-specific coordinate systems and calculations.
This allows for accurate projectile prediction across different game environments.
 2025-08-06 05:45:37 +03:00
Orange
d12b236e56 Refactors target position prediction 
Moves target prediction logic into engine traits, improving modularity.

This change consolidates target position prediction within the engine traits,
allowing for a more flexible and maintainable design.

This eliminates redundant code and simplifies the core prediction engine by
delegating target movement calculations to the appropriate trait.
 2025-08-04 03:16:04 +03:00
Orange
7a5090d9f6 Marks legacy engine class as final 
Prevents further inheritance from the legacy projectile prediction engine class.
 2025-08-04 01:12:22 +03:00
Orange
ec76a7239c Adds direct pitch angle calculation 
Implements a direct pitch angle calculation for scenarios with zero gravity, ensuring accurate projectile trajectory predictions in such conditions.

Also marks several methods as noexcept for better performance and exception safety.
 2025-08-04 01:11:11 +03:00
Orange
2758f549a3 Updates project version and removes legacy code 
Updates the project version to prepare for a new release.

Removes the legacy projectile prediction engine, which is no longer needed.
 2025-08-03 18:35:52 +03:00
Orange
493931ef0f Ignores vcpkg directory 
Excludes the vcpkg directory from being tracked by Git.

This prevents accidental commits of external library files
managed by vcpkg, keeping the repository cleaner.
 2025-08-03 18:31:02 +03:00
Orange
9e1990942b Refactors projectile prediction engine 
Migrates projectile prediction logic to leverage engine traits for improved flexibility and testability.

This change decouples core prediction algorithms from specific engine implementations, allowing for easier adaptation to different game engines or simulation environments.
 2025-08-03 18:28:47 +03:00
Orange++
f1984fbe46 Merge pull request #51 from orange-cpp/feature/projectile_pred_custom 
Refactors projectile prediction engine
 2025-08-03 17:38:08 +03:00
Orange
f1fbea21a7 Refactors projectile prediction engine 
Refactors the projectile prediction engine by introducing an interface
and making the legacy implementation more flexible.

The legacy engine is updated to allow for coordinate system customization
through virtual methods, enabling usage in different game environments.

Also introduces vcpkg support for easier dependency management and adds boost-asio as a dependency.
 2025-08-03 17:33:22 +03:00
Orange
4b44ce0667 Documents projectile launch angle formula 
Adds a comment documenting the formula used for calculating the projectile launch pitch angle.

The comment includes a link to the Stack Overflow discussion where the formula was found and the LaTeX representation of the formula for clarity.
 2025-07-31 21:52:16 +03:00
Orange++
231ef35a0a Merge pull request #49 from orange-cpp/feature/legacy_option 
Adds option to enable legacy classes
 2025-07-15 11:52:36 +03:00
Orange
1aa62cb396 Enables legacy code compilation 
The changes encapsulate the matrix tests within an `#ifdef` block, allowing conditional compilation based on whether `OMATH_ENABLE_LEGACY` is defined. This enables the legacy code to be compiled only when needed.
 2025-07-15 11:51:14 +03:00
Orange
8e411771c2 Adds option to enable legacy classes 
Introduces a CMake option to enable legacy classes,
allowing for backward compatibility with older code.
This ensures that older codebases can still function
while new development can utilize updated classes.
 2025-07-15 11:48:33 +03:00
Orange++
d65852d1a4 Update README.md 2025-07-14 23:11:46 +03:00
Orange++
21f5e82a20 Merge pull request #48 from luadebug/patch-1 
Update INSTALL.md
 2025-07-14 23:10:39 +03:00
Saikari
851ec37350 Update INSTALL.md 2025-07-14 18:53:41 +03:00
Orange++
f1cd9dbeb3 Update README.md 
fixed ordering
 2025-07-14 17:39:16 +03:00
Orange++
7a1c7d6cc4 Update README.md 
made badge in read me smaller
 2025-07-14 17:38:50 +03:00
Orange++
cb704b3621 Merge pull request #47 from luadebug/patch-1 
Update README.md

Thx for vcpkg port update <3 u r already in CREDITS.md
 2025-07-14 17:37:12 +03:00
Saikari
646d295876 Update README.md 2025-07-14 16:25:16 +03:00
Orange++
8e09556c25 Update README.md 2025-07-08 17:14:52 +03:00
Orange++
7dbebc996d Update README.md 2025-07-08 17:13:24 +03:00
Orange++
278ffba0ff Update README.md 2025-07-08 17:01:56 +03:00
Orange
647cf02a38 Renames test fixture for clarity. 
Updates the name of the test fixture from "lline_tracer_fixture" to "line_tracer_fixture" for improved readability and consistency in the test code.
 2025-07-07 08:28:29 +03:00
Orange
4be2986681 Fixes potential compile error 
Corrects the usage of `At` method within the unit tests to `at` to resolve a potential compile error due to incorrect case sensitivity.
 2025-07-07 08:18:00 +03:00
Orange
06d9b4c910 fixed naming in tests 2025-07-07 08:02:35 +03:00
Orange++
a074fdcb92 Merge pull request #45 from luadebug/patch-1 
Check for ImGUI dependency in omathConfig.cmake.in
 2025-07-07 05:30:19 +03:00
Saikari
8241d9c355 Update omathConfig.cmake.in 2025-07-07 04:53:56 +03:00
Orange
66258f0f6d Updates CMake export target and namespace. 
Updates the CMake export target and namespace to use the project name,
improving consistency and avoiding naming conflicts.

Adds a simple diagram to the triangle header file.
 2025-07-06 11:14:46 +03:00
Orange
65541fa2c7 Renames library target to project name 
Updates the CMakeLists.txt to use the project name as the library target name instead of hardcoding "omath".

This change ensures consistency and avoids potential conflicts when integrating the library into other projects.
It also aligns the target naming with CMake best practices.
 2025-07-06 11:07:15 +03:00
Orange
7e4a6134bf added new method 2025-06-23 06:14:17 +03:00
Orange
a54a537239 fix 2025-06-17 21:34:25 +03:00
Orange
f01bbde537 added banner to repo 2025-06-17 21:33:39 +03:00
Orange
2c710555d6 fixed example 2025-06-16 01:40:14 +03:00
Orange++
9c2be6306c Merge pull request #39 from orange-cpp/u/orange-cpp/writerside 
U/orange cpp/writerside
 2025-05-21 16:58:19 +03:00
Orange
d37840d4ef fixed stuff 2025-05-21 16:57:17 +03:00
Orange
b4a3b5d529 added text 2025-05-21 16:47:15 +03:00
Orange
c2a772142c fix 2025-05-21 16:47:15 +03:00
Orange
76fca7f527 fix 2025-05-21 16:47:15 +03:00
Orange
73ccd24e3e improved intro 2025-05-21 16:47:15 +03:00
Orange
a642feafb5 added new topic 2025-05-21 16:47:15 +03:00
Orange
faf9f34af8 stipped away text 2025-05-21 16:47:15 +03:00
Orange
b56801ac91 added files 2025-05-21 16:47:15 +03:00
Orange
a81d12d480 fixed version 2025-05-13 09:48:46 +03:00
Orange
17eb0cd0dc improved naming 2025-05-13 09:47:08 +03:00
Orange
52024285d2 added noexcept 2025-05-13 09:34:39 +03:00
Orange
f179aea4d7 removed even float type from vector classes 2025-05-13 09:22:23 +03:00
Orange++
1196bb86b4 Merge pull request #44 from orange-cpp/feature/noexcept 
Feature/noexcept
 2025-05-05 02:34:43 +03:00
Orange
5489c296e9 added more noexcept 2025-05-05 02:24:23 +03:00
Orange
50ddf2d31e added more noexcept 2025-05-05 01:46:50 +03:00
Orange
a6e4c0461d added noexcept 2025-05-05 01:16:12 +03:00
Orange
6749f9f759 added noexcept for color and angles 2025-05-04 19:16:49 +03:00
Orange
9a38d47b0d added noexcept for vector types 2025-05-04 19:13:26 +03:00
Orange
f6f8bba032 changed license to zlib 2025-05-04 19:05:10 +03:00
Orange
ce08fcdd29 removed useless source files 2025-05-04 19:03:18 +03:00
Orange
49ea113348 fixed style 2025-05-04 18:54:33 +03:00
Orange
af21f9a946 removed pow 2025-05-04 18:07:35 +03:00
Orange
f096f7179f fixed clang format 2025-05-04 17:42:32 +03:00
Orange++
e025e99d18 Update README.md 2025-05-04 00:55:35 +03:00
Orange++
30eef59360 Update cmake-multi-platform.yml 
switched to clang

Update cmake-multi-platform.yml
Update cmake-multi-platform.yml
Update cmake-multi-platform.yml
Update cmake-multi-platform.yml
Update cmake-multi-platform.yml
Update cmake-multi-platform.yml
Update cmake-multi-platform.yml
Update cmake-multi-platform.yml
added runtime dir

fix
 2025-05-03 22:51:46 +03:00
Orange++
c2a6cf5c47 Merge pull request #43 from orange-cpp/orange-cpp-ci 
Create cmake-multi-platform.yml
 2025-05-03 22:04:37 +03:00
Orange++
7f55383bc1 Create cmake-multi-platform.yml 2025-05-03 22:04:10 +03:00
Orange
449c60133c bugfix 2025-05-03 21:36:16 +03:00
Orange++
31d3359507 Merge pull request #42 from orange-cpp/feature/new-codestyle 
Feature/new codestyle
 2025-05-03 20:59:06 +03:00
Orange
dd738f365d fix 2025-05-03 20:51:50 +03:00
Orange
b5e788385d fixed style 2025-05-03 20:38:58 +03:00
Orange
df6d75e554 changed code style 2025-05-03 20:31:59 +03:00
Orange
be3fae63b8 patched clang format 2025-05-03 16:50:29 +03:00
Orange
dd731b60c3 updated clang format 2025-05-03 16:39:38 +03:00
Orange++
b06fd00673 Merge pull request #41 from orange-cpp/u/improved-cmake 
improved cmake, removed useless cmake files
 2025-04-30 21:31:34 +03:00
Orange
998c8f3a43 improved cmake, removed useless cmake files 2025-04-30 21:26:25 +03:00
Orange
faeef594b9 moved installation stuff to INSTALL.md 2025-04-30 18:15:46 +03:00
Orange++
40a301186e Merge pull request #40 from orange-cpp/u/orange/inverted-matrix 
U/orange/inverted matrix
 2025-04-29 20:53:02 +03:00
Orange
a41526c494 style fix 2025-04-29 20:52:41 +03:00
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a0d1dc4313 added test case 2025-04-29 20:49:59 +03:00
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1c5c9360c8 added inverse method 2025-04-29 20:33:39 +03:00
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4615769682 added additional methods 2025-04-29 20:10:17 +03:00
Orange
4ef674f7b4 fixed infinite recursion in compile time 2025-04-29 20:08:27 +03:00
Orange
69b9049fb0 fixed gimba lock for unity 2025-04-26 00:52:46 +03:00
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2734b58bdd fixed gimba lock for opengl camera 2025-04-26 00:32:53 +03:00
Orange
d7f1f49165 resetting state 2025-04-25 23:52:10 +03:00
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94b1453cae removed .idea folder 2025-04-23 02:48:45 +03:00
Orange
3e67d8a99c added credits 2025-04-23 02:46:08 +03:00
Orange++
8c00ab3d9d Merge pull request #38 from orange-cpp/u/orange-cpp/3d-primitives 
U/orange cpp/3d primitives
 2025-04-18 17:00:38 +03:00
Orange
d14cb1e93e reset to default 2025-04-18 16:55:07 +03:00
Orange
c692cf39e1 updated readme 2025-04-18 16:53:53 +03:00
Orange
9c934c5d9c improved tests 2025-04-18 16:36:22 +03:00
Vladislav Alpatov
f8202b116d improved line tracer 2025-04-18 16:00:23 +03:00
Orange
8bf0bb8e0d improved line trace and box primitive 2025-04-18 13:56:08 +03:00
Orange
a340766348 switched to polygons 2025-04-18 12:34:24 +03:00
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254674a62e fixed code style 2025-04-18 12:11:43 +03:00
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97c2da893b added ratio param 2025-04-18 01:33:47 +03:00
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0ce30a7038 added new build option 2025-04-18 00:51:07 +03:00
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492ddfd566 added box 2025-04-18 00:43:46 +03:00
Orange
baf7ee8f88 fixed include 2025-04-16 20:35:17 +03:00
Orange++
9fde11733f Merge pull request #37 from orange-cpp/u/engine_rotation_mats 
U/engine rotation mats
 2025-04-16 23:21:58 +03:00
Orange
0069b8bd96 improved openg gl rotation matrix, added tests 2025-04-16 19:11:02 +03:00
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127bae0b78 added tests for source 2025-04-16 18:53:31 +03:00
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bed204a663 added unit tests 2025-04-16 18:35:50 +03:00
Orange
3f6ea010dc fixed formating 2025-04-16 17:52:57 +03:00
Orange
592a98f38c removed method from Mat added method for unity 2025-04-16 17:52:19 +03:00
Orange
7873047550 added func 
added rotation matrix for opengl

updated unit tests
 2025-04-16 17:40:00 +03:00
Orange
1601f3cbc8 added func 
added rotation matrix for opengl
 2025-04-16 17:40:00 +03:00
Orange
2180f8ab97 removed whitespaces 2025-04-16 12:21:10 +03:00
Orange
b613ff9ef1 added missing header 2025-04-13 23:15:27 +03:00
Orange++
145eadfffa Merge pull request #36 from orange-cpp/u/orange-cpp/small-refactoring 
U/orange cpp/small refactoring
 2025-04-12 13:34:28 +03:00
Orange
14acebad5f fixed tests 2025-04-12 00:04:07 +03:00
Orange
4a7a631932 added const method to mat 2025-04-11 23:57:56 +03:00
Orange
e08c22f604 added new build option 2025-04-11 23:54:56 +03:00
Orange
1b47f45af9 improved naming 2025-04-11 23:30:07 +03:00
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466d8f7bec improvement 2025-04-11 23:20:16 +03:00
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3631c5d698 replaced with STL relization 2025-04-11 23:10:02 +03:00
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b58956efe3 added missing header 2025-04-11 22:59:56 +03:00
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fc1e0c62b8 disabled tests 2025-04-05 20:03:39 +03:00
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8e861b8a85 updated read me 2025-04-05 13:28:28 +03:00
Orange
55085604fd added include 2025-04-05 13:20:18 +03:00
Orange
7b712ed960 fixed for clang 2025-04-05 13:00:00 +03:00
Orange
138c996393 oops 2025-03-29 22:03:30 +03:00
Orange
0f2a858306 fixed in some cases confilcting with win api 2025-03-29 21:57:35 +03:00
Orange
ea6c1cc929 fix 2025-03-29 18:20:17 +03:00
Orange++
eeb6e40909 Merge pull request #35 from orange-cpp/u/orange-cpp/imrpoved-color 
U/orange cpp/imrpoved color
 2025-03-29 17:43:36 +03:00
Orange
d72ad663cd added new methods 2025-03-29 05:41:55 +03:00
Orange
3e75d32f59 fixed style 2025-03-29 04:00:35 +03:00
Orange
a8ce5cbaa0 added vcpkg imgui package auto link 2025-03-29 01:56:09 +03:00
Orange
79f76a0755 added new option 2025-03-29 01:53:04 +03:00
Orange
5773cc7798 improved imgui handling 2025-03-24 21:48:51 +03:00
Orange
b6b0184523 fixed for clang 2025-03-24 06:48:51 +03:00
Orange++
a797dd134a Update README.md 2025-03-24 06:46:02 +03:00
Orange
dc43411bd2 fixed unity view matrix building 2025-03-24 06:30:09 +03:00
Orange++
8959161904 Merge pull request #34 from orange-cpp/u/orange-cpp/add-unity 
U/orange cpp/add unity
 2025-03-23 01:20:16 +03:00
Orange
5d5bd215b2 fix 2025-03-23 01:17:05 +03:00
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a48a257648 removed comment 2025-03-23 01:12:46 +03:00
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ffba4e256a name fix 2025-03-23 01:06:36 +03:00
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d9219cdddb naming fixed 2025-03-23 01:02:11 +03:00
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5a1014a239 fix 2025-03-23 00:57:58 +03:00
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74f2241bcf uncommented test 2025-03-23 00:52:12 +03:00
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8977557a61 fix 2025-03-22 17:41:01 +03:00
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481d7b85df improved camera 2025-03-22 17:39:40 +03:00
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2b59fb6aa2 updated formulas 2025-03-22 08:36:06 +03:00
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4f037a1952 added unity engine tests 2025-03-22 08:12:16 +03:00
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ef11183c3f added camera files 2025-03-22 04:26:54 +03:00
Orange++
326d8baaae Update README.md 2025-03-21 05:31:44 +03:00
Orange
e46067b0b9 fixed tests includes 2025-03-21 04:58:28 +03:00
257 changed files with 19888 additions and 3490 deletions
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84
.clang-format
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@@ -1,62 +1,64 @@
# Generated from CLion C/C++ Code Style settings
---
Language: Cpp
# Generated by CLion for Stroustrup
# The Stroustrup style, named after Bjarne Stroustrup, the creator of C++, is similar to the K&R style but differs
# in its treatment of the class definitions and the placement of braces in certain contexts. The opening brace is
# placed on the same line as the control statement, and the closing brace is on its own line.
BasedOnStyle: LLVM
AccessModifierOffset: -4
AlignConsecutiveAssignments: false
AlignConsecutiveDeclarations: false
AlignOperands: true
AlignConsecutiveAssignments: None
AlignConsecutiveBitFields: None
AlignConsecutiveDeclarations: None
AlignConsecutiveMacros: AcrossEmptyLinesAndComments
AlignTrailingComments: false
AllowShortBlocksOnASingleLine: false
AllowShortBlocksOnASingleLine: Never
AllowShortFunctionsOnASingleLine: None
AlwaysBreakTemplateDeclarations: Yes
BraceWrapping:
AllowShortIfStatementsOnASingleLine: false
AllowShortLoopsOnASingleLine: false
BreakTemplateDeclarations: Leave
BreakBeforeBraces: Custom
BraceWrapping:
AfterCaseLabel: true
AfterClass: true
AfterControlStatement: true
AfterEnum: true
AfterFunction: true
AfterControlStatement: true
SplitEmptyFunction: true
AfterEnum: true
AfterNamespace: true
AfterStruct: true
AfterUnion: true
AfterExternBlock: true
BeforeCatch: false
BeforeElse: false
BeforeCatch: true
BeforeElse: true
BeforeLambdaBody: true
BeforeWhile: false
IndentBraces: false
SplitEmptyFunction: true
BeforeWhile: true
SplitEmptyRecord: true
SplitEmptyNamespace: true
BreakBeforeBraces: Custom
BreakConstructorInitializers: AfterColon
BreakConstructorInitializersBeforeComma: false
BreakBeforeBinaryOperators: NonAssignment
BreakBeforeConceptDeclarations: false
ColumnLimit: 120
ConstructorInitializerAllOnOneLineOrOnePerLine: false
ContinuationIndentWidth: 8
IncludeCategories:
- Regex: '^<.*'
Priority: 1
- Regex: '^".*'
Priority: 2
- Regex: '.*'
Priority: 3
IncludeIsMainRegex: '([-_](test|unittest))?$'
IndentCaseLabels: true
IncludeBlocks: Merge
IndentExternBlock: Indent
IndentRequiresClause: false
IndentWidth: 4
InsertNewlineAtEOF: true
MacroBlockBegin: ''
MacroBlockEnd: ''
MaxEmptyLinesToKeep: 2
ContinuationIndentWidth: 8
KeepEmptyLinesAtTheStartOfBlocks: false
NamespaceIndentation: All
PointerAlignment: Left
SpaceAfterCStyleCast: true
SortUsingDeclarations: true
SpaceAfterTemplateKeyword: false
SpaceBeforeRangeBasedForLoopColon: false
SpaceBeforeCtorInitializerColon: false
SpaceBeforeParens: Custom
SpaceBeforeParensOptions:
AfterControlStatements: true
AfterFunctionDeclarationName: false
AfterFunctionDefinitionName: false
AfterForeachMacros: true
AfterIfMacros: true
AfterOverloadedOperator: false
BeforeNonEmptyParentheses: false
SpaceBeforeRangeBasedForLoopColon: true
SpaceInEmptyParentheses: false
SpacesInAngles: false
SpacesInConditionalStatement: false
SpacesInCStyleCastParentheses: false
SpacesInParentheses: false
TabWidth: 4
...
SpacesInConditionalStatement: false
SpacesInContainerLiterals: false
SpacesInParentheses: false

38
.github/ISSUE_TEMPLATE/bug_report.md vendored Normal file
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---
name: Bug report
about: Create a report to help us improve
title: ''
labels: ''
assignees: ''
---
**Describe the bug**
A clear and concise description of what the bug is.
**To Reproduce**
Steps to reproduce the behavior:
1. Go to '...'
2. Click on '....'
3. Scroll down to '....'
4. See error
**Expected behavior**
A clear and concise description of what you expected to happen.
**Screenshots**
If applicable, add screenshots to help explain your problem.
**Desktop (please complete the following information):**
- OS: [e.g. iOS]
- Browser [e.g. chrome, safari]
- Version [e.g. 22]
**Smartphone (please complete the following information):**
- Device: [e.g. iPhone6]
- OS: [e.g. iOS8.1]
- Browser [e.g. stock browser, safari]
- Version [e.g. 22]
**Additional context**
Add any other context about the problem here.

10
.github/ISSUE_TEMPLATE/custom.md vendored Normal file
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@@ -0,0 +1,10 @@
---
name: Custom issue template
about: Describe this issue template's purpose here.
title: ''
labels: ''
assignees: ''
---

20
.github/ISSUE_TEMPLATE/feature_request.md vendored Normal file
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@@ -0,0 +1,20 @@
---
name: Feature request
about: Suggest an idea for this project
title: ''
labels: ''
assignees: ''
---
**Is your feature request related to a problem? Please describe.**
A clear and concise description of what the problem is. Ex. I'm always frustrated when [...]
**Describe the solution you'd like**
A clear and concise description of what you want to happen.
**Describe alternatives you've considered**
A clear and concise description of any alternative solutions or features you've considered.
**Additional context**
Add any other context or screenshots about the feature request here.

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122
.github/workflows/cmake-multi-platform.yml vendored Normal file
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name: Omath CI (Arch Linux / Windows)
on:
push:
branches: [ main ]
pull_request:
branches: [ main ]
concurrency:
group: ci-${{ github.ref }}
cancel-in-progress: true
##############################################################################
# 1) ARCH LINUX – Clang / Ninja
##############################################################################
jobs:
arch-build-and-test:
name: Arch Linux (Clang)
runs-on: ubuntu-latest
container: archlinux:latest
env:
VCPKG_ROOT: ${{ github.workspace }}/vcpkg
steps:
- name: Install basic tool-chain with pacman
shell: bash
run: |
pacman -Sy --noconfirm archlinux-keyring
pacman -Syu --noconfirm --needed \
git base-devel clang cmake ninja zip unzip fmt
- name: Checkout repository (with sub-modules)
uses: actions/checkout@v4
with:
submodules: recursive
- name: Set up vcpkg
shell: bash
run: |
git clone https://github.com/microsoft/vcpkg "$VCPKG_ROOT"
- name: Configure (cmake --preset)
shell: bash
run: cmake --preset linux-release-vcpkg -DOMATH_BUILD_TESTS=ON -DOMATH_BUILD_BENCHMARK=OFF -DVCPKG_MANIFEST_FEATURES="imgui;avx2;tests"
- name: Build
shell: bash
run: cmake --build cmake-build/build/linux-release-vcpkg --target unit_tests omath
- name: Run unit_tests
shell: bash
run: ./out/Release/unit_tests
##############################################################################
# 2) Windows – MSVC / Ninja
##############################################################################
windows-build-and-test:
name: Windows (MSVC)
runs-on: windows-latest
env:
OMATH_BUILD_VIA_VCPKG: ON
steps:
- name: Checkout repository (with sub-modules)
uses: actions/checkout@v4
with:
submodules: recursive
- name: Install Ninja
uses: seanmiddleditch/gha-setup-ninja@v4
- name: Set up MSVC developer command-prompt
uses: ilammy/msvc-dev-cmd@v1
- name: Configure (cmake --preset)
shell: bash
run: cmake --preset windows-release-vcpkg -DOMATH_BUILD_TESTS=ON -DOMATH_BUILD_BENCHMARK=OFF -DVCPKG_MANIFEST_FEATURES="imgui;avx2;tests"
- name: Build
shell: bash
run: cmake --build cmake-build/build/windows-release-vcpkg --target unit_tests omath
- name: Run unit_tests.exe
shell: bash
run: ./out/Release/unit_tests.exe
##############################################################################
# 3) macOS – AppleClang / Ninja
##############################################################################
macosx-build-and-test:
name: macOS (AppleClang)
runs-on: macOS-latest
env:
VCPKG_ROOT: ${{ github.workspace }}/vcpkg
steps:
- name: Install basic tool-chain with Homebrew
shell: bash
run: |
brew install cmake ninja
- name: Checkout repository (with sub-modules)
uses: actions/checkout@v4
with:
submodules: recursive
- name: Set up vcpkg
shell: bash
run: |
git clone https://github.com/microsoft/vcpkg "$VCPKG_ROOT"
- name: Configure (cmake --preset)
shell: bash
run: cmake --preset darwin-release-vcpkg -DOMATH_BUILD_TESTS=ON -DOMATH_BUILD_BENCHMARK=OFF -DVCPKG_MANIFEST_FEATURES="imgui;avx2;tests"
- name: Build
shell: bash
run: cmake --build cmake-build/build/darwin-release-vcpkg --target unit_tests omath
- name: Run unit_tests
shell: bash
run: ./out/Release/unit_tests

4
.gitignore vendored
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@@ -1,3 +1,5 @@
/cmake-build/
/.idea
/out
*.DS_Store
/extlibs/vcpkg
.idea/workspace.xml

3
.gitmodules vendored
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@@ -1,3 +0,0 @@
[submodule "extlibs/googletest"]
path = extlibs/googletest
url = https://github.com/google/googletest.git

8
.idea/.gitignore generated vendored Normal file
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@@ -0,0 +1,8 @@
# Default ignored files
/shelf/
/workspace.xml
# Editor-based HTTP Client requests
/httpRequests/
# Datasource local storage ignored files
/dataSources/
/dataSources.local.xml

209
.idea/codeStyles/Project.xml generated Normal file
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@@ -0,0 +1,209 @@
<component name="ProjectCodeStyleConfiguration">
<code_scheme name="Project" version="173">
<RiderCodeStyleSettings>
<option name="/Default/CodeStyle/CodeFormatting/CppClangFormat/EnableClangFormatSupport/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/EditorConfig/EnableClangFormatSupport/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/ALIGN_MULTILINE_BINARY_EXPRESSIONS_CHAIN/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/ALIGN_MULTILINE_CALLS_CHAIN/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/ALIGN_MULTILINE_EXPRESSION/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/ALIGN_MULTILINE_FOR_STMT/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/ALIGN_MULTIPLE_DECLARATION/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/ALIGN_TERNARY/@EntryValue" value="ALIGN_ALL" type="string" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/BLANK_LINES_AROUND_CLASS_DEFINITION/@EntryValue" value="1" type="int" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/KEEP_BLANK_LINES_IN_DECLARATIONS/@EntryValue" value="2" type="int" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/KEEP_BLANK_LINES_IN_CODE/@EntryValue" value="2" type="int" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/KEEP_USER_LINEBREAKS/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/INDENT_CASE_FROM_SWITCH/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/INDENT_COMMENT/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/INT_ALIGN_EQ/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/SIMPLE_BLOCK_STYLE/@EntryValue" value="LINE_BREAK" type="string" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/SPACE_AFTER_COMMA_IN_TEMPLATE_ARGS/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/SPACE_AFTER_COMMA_IN_TEMPLATE_PARAMS/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/SPACE_AFTER_FOR_SEMICOLON/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/SPACE_BEFORE_FOR_SEMICOLON/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/SPACE_AFTER_UNARY_OPERATOR/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/SPACE_WITHIN_ARRAY_ACCESS_BRACKETS/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/SPACE_WITHIN_CAST_EXPRESSION_PARENTHESES/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/SPACE_WITHIN_EMPTY_INITIALIZER_BRACES/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/SPACE_WITHIN_EMPTY_METHOD_PARENTHESES/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/SPACE_WITHIN_INITIALIZER_BRACES/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/SPECIAL_ELSE_IF_TREATMENT/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/SPACE_AFTER_CAST_EXPRESSION_PARENTHESES/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/WRAP_AFTER_BINARY_OPSIGN/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/WRAP_BEFORE_TERNARY_OPSIGNS/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/CASE_BLOCK_BRACES/@EntryValue" value="NEXT_LINE" type="string" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/BLANK_LINES_AROUND_FUNCTION_DECLARATION/@EntryValue" value="1" type="int" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/BLANK_LINES_AROUND_FUNCTION_DEFINITION/@EntryValue" value="1" type="int" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/PLACE_WHILE_ON_NEW_LINE/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/PLACE_ELSE_ON_NEW_LINE/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/PLACE_CATCH_ON_NEW_LINE/@EntryValue" value="false" type="bool" />
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<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/ALIGN_MULTILINE_EXTENDS_LIST/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/ALIGN_MULTILINE_PARAMETER/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/ALIGN_MULTILINE_TYPE_ARGUMENT/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/ALIGN_MULTILINE_TYPE_PARAMETER/@EntryValue" value="false" type="bool" />
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<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/INDENT_ACCESS_SPECIFIERS_FROM_CLASS/@EntryValue" value="false" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/INDENT_CLASS_MEMBERS_FROM_ACCESS_SPECIFIERS/@EntryValue" value="true" type="bool" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/LINE_BREAK_AFTER_COLON_IN_MEMBER_INITIALIZER_LISTS/@EntryValue" value="ON_SINGLE_LINE" type="string" />
<option name="/Default/CodeStyle/CodeFormatting/CppFormatting/MEMBER_INITIALIZER_LIST_STYLE/@EntryValue" value="DO_NOT_CHANGE" type="string" />
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6
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435
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<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=A4FAA2257682A94F8C2C93E123FAFC7A/@EntryIndexRemoved" value="true" type="bool" />
<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=A4FAA2257682A94F8C2C93E123FAFC7A/@EntryIndexedValue" value="" type="string" />
<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=A7EBF16DA3BDCB42A0B710704BC8A053/@EntryIndexRemoved" value="true" type="bool" />
<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=A7EBF16DA3BDCB42A0B710704BC8A053/@EntryIndexedValue" value="" type="string" />
<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=AA17EF9DE2E5364DAEBE52F9EBBEA658/@EntryIndexedValue" value="&lt;NamingElement Priority=&quot;6&quot; Title=&quot;Parameters&quot;&gt;&lt;Descriptor Static=&quot;Indeterminate&quot; Constexpr=&quot;Indeterminate&quot; Const=&quot;Indeterminate&quot; Volatile=&quot;Indeterminate&quot; Accessibility=&quot;NOT_APPLICABLE&quot;&gt;&lt;type Name=&quot;function parameter&quot; /&gt;&lt;type Name=&quot;lambda parameter&quot; /&gt;&lt;/Descriptor&gt;&lt;Policy Inspect=&quot;True&quot; WarnAboutPrefixesAndSuffixes=&quot;False&quot; Prefix=&quot;&quot; Suffix=&quot;&quot; Style=&quot;aa_bb&quot; /&gt;&lt;/NamingElement&gt;" type="string" />
<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=B6E900853D6D05429D8C57765B2E546A/@EntryIndexRemoved" value="true" type="bool" />
<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=B6E900853D6D05429D8C57765B2E546A/@EntryIndexedValue" value="" type="string" />
<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=B82A063F0DDD98498A70D8D7EBB97F8D/@EntryIndexRemoved" value="true" type="bool" />
<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=B82A063F0DDD98498A70D8D7EBB97F8D/@EntryIndexedValue" value="" type="string" />
<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=BBE8AA08E662BF409B2CB08EC597C493/@EntryIndexRemoved" value="true" type="bool" />
<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=BBE8AA08E662BF409B2CB08EC597C493/@EntryIndexedValue" value="" type="string" />
<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=BF0D1AE66D64FE4FAF613448A12051A0/@EntryIndexRemoved" value="true" type="bool" />
<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=BF0D1AE66D64FE4FAF613448A12051A0/@EntryIndexedValue" value="" type="string" />
<option name="/Default/CodeStyle/Naming/CppNamingOptions/Rules/=DC1F6BB6E0EFFC49A38E940DB8A84CF6/@EntryIndexedValue" value="&lt;NamingElement Priority=&quot;5&quot; Title=&quot;Variables&quot;&gt;&lt;Descriptor Static=&quot;Indeterminate&quot; Constexpr=&quot;Indeterminate&quot; Const=&quot;Indeterminate&quot; Volatile=&quot;Indeterminate&quot; Accessibility=&quot;NOT_APPLICABLE&quot;&gt;&lt;type Name=&quot;global variable&quot; /&gt;&lt;type Name=&quot;lambda&quot; /&gt;&lt;type Name=&quot;local variable&quot; /&gt;&lt;/Descriptor&gt;&lt;Policy Inspect=&quot;True&quot; WarnAboutPrefixesAndSuffixes=&quot;False&quot; Prefix=&quot;&quot; Suffix=&quot;&quot; Style=&quot;aa_bb&quot; /&gt;&lt;/NamingElement&gt;" type="string" />
</component>
</project>

8
.idea/inspectionProfiles/Project_Default.xml generated Normal file
View File

@@ -0,0 +1,8 @@
<component name="InspectionProjectProfileManager">
<profile version="1.0">
<option name="myName" value="Project Default" />
<inspection_tool class="CppInconsistentNaming" enabled="true" level="HINT" enabled_by_default="true" />
<inspection_tool class="CppTabsAreDisallowed" enabled="true" level="WARNING" enabled_by_default="true" />
<inspection_tool class="CppUnnecessaryWhitespace" enabled="true" level="WARNING" enabled_by_default="true" />
</profile>
</component>

7
.idea/inspectionProfiles/profiles_settings.xml generated Normal file
View File

@@ -0,0 +1,7 @@
<component name="InspectionProjectProfileManager">
<settings>
<option name="PROJECT_PROFILE" value="Default" />
<option name="USE_PROJECT_PROFILE" value="false" />
<version value="1.0" />
</settings>
</component>

12
.idea/misc.xml generated Normal file
View File

@@ -0,0 +1,12 @@
<?xml version="1.0" encoding="UTF-8"?>
<project version="4">
<component name="CMakePythonSetting">
<option name="pythonIntegrationState" value="YES" />
</component>
<component name="CMakeWorkspace" PROJECT_DIR="$PROJECT_DIR$" />
<component name="CidrRootsConfiguration">
<excludeRoots>
<file path="$PROJECT_DIR$/cmake-build" />
</excludeRoots>
</component>
</project>

2
.idea/modules.xml generated
View File

@@ -2,7 +2,7 @@
<project version="4">
<component name="ProjectModuleManager">
<modules>
<module fileurl="file://$PROJECT_DIR$/.idea/uml.iml" filepath="$PROJECT_DIR$/.idea/uml.iml" />
<module fileurl="file://$PROJECT_DIR$/.idea/omath.iml" filepath="$PROJECT_DIR$/.idea/omath.iml" />
</modules>
</component>
</project>

0
.idea/uml.iml → .idea/omath.iml generated
View File

1
.idea/vcs.xml generated
View File

@@ -2,6 +2,5 @@
<project version="4">
<component name="VcsDirectoryMappings">
<mapping directory="" vcs="Git" />
<mapping directory="$PROJECT_DIR$/extlibs/googletest" vcs="Git" />
</component>
</project>

179
CMakeLists.txt
View File

@@ -1,66 +1,165 @@
cmake_minimum_required(VERSION 3.26)
project(omath VERSION 1.0.1 LANGUAGES CXX)
file(READ VERSION OMATH_VERSION)
project(omath VERSION ${OMATH_VERSION} LANGUAGES CXX)
include(CMakePackageConfigHelpers)
include(CheckCXXCompilerFlag)
if (MSVC)
check_cxx_compiler_flag("/arch:AVX2" COMPILER_SUPPORTS_AVX2)
else ()
check_cxx_compiler_flag("-mavx2" COMPILER_SUPPORTS_AVX2)
endif ()
option(OMATH_BUILD_TESTS "Build unit tests" OFF)
option(OMATH_BUILD_BENCHMARK "Build benchmarks" OFF)
option(OMATH_THREAT_WARNING_AS_ERROR "Set highest level of warnings and force compiler to treat them as errors" ON)
option(OMATH_BUILD_AS_SHARED_LIBRARY "Build Omath as .so or .dll" OFF)
option(OMATH_USE_AVX2 "Omath will use AVX2 to boost performance" ON)
option(OMATH_USE_AVX2 "Omath will use AVX2 to boost performance" ${COMPILER_SUPPORTS_AVX2})
option(OMATH_IMGUI_INTEGRATION "Omath will define method to convert omath types to imgui types" OFF)
option(OMATH_BUILD_EXAMPLES "Build example projects with you can learn & play" OFF)
option(OMATH_STATIC_MSVC_RUNTIME_LIBRARY "Force Omath to link static runtime" OFF)
option(OMATH_SUPRESS_SAFETY_CHECKS "Supress some safety checks in release build to improve general performance" ON)
option(OMATH_USE_UNITY_BUILD "Will enable unity build to speed up compilation" OFF)
option(OMATH_ENABLE_LEGACY "Will enable legacy classes that MUST be used ONLY for backward compatibility" ON)
if (VCPKG_MANIFEST_FEATURES)
foreach (omath_feature IN LISTS VCPKG_MANIFEST_FEATURES)
if (omath_feature STREQUAL "imgui")
set(OMATH_IMGUI_INTEGRATION ON)
elseif (omath_feature STREQUAL "avx2")
set(OMATH_USE_AVX2 ${COMPILER_SUPPORTS_AVX2})
elseif (omath_feature STREQUAL "tests")
set(OMATH_BUILD_TESTS ON)
elseif (omath_feature STREQUAL "benchmark")
set(OMATH_BUILD_BENCHMARK ON)
endif ()
endforeach ()
endif ()
if (OMATH_USE_AVX2 AND NOT COMPILER_SUPPORTS_AVX2)
message(WARNING "OMATH_USE_AVX2 requested, but compiler/target does not support AVX2. Disabling.")
set(OMATH_USE_AVX2 OFF CACHE BOOL "Omath will use AVX2 to boost performance" FORCE)
endif ()
if (${PROJECT_IS_TOP_LEVEL})
message(STATUS "[${PROJECT_NAME}]: Building on ${CMAKE_HOST_SYSTEM_NAME}, compiler ${CMAKE_CXX_COMPILER_ID}")
message(STATUS "[${PROJECT_NAME}]: Warnings as errors ${OMATH_THREAT_WARNING_AS_ERROR}")
message(STATUS "[${PROJECT_NAME}]: Build unit tests ${OMATH_BUILD_TESTS}")
message(STATUS "[${PROJECT_NAME}]: Build benchmark ${OMATH_BUILD_BENCHMARK}")
message(STATUS "[${PROJECT_NAME}]: As dynamic library ${OMATH_BUILD_AS_SHARED_LIBRARY}")
message(STATUS "[${PROJECT_NAME}]: Static C++ runtime ${OMATH_STATIC_MSVC_RUNTIME_LIBRARY}")
message(STATUS "[${PROJECT_NAME}]: CMake unity build ${OMATH_USE_UNITY_BUILD}")
message(STATUS "[${PROJECT_NAME}]: Example projects ${OMATH_BUILD_EXAMPLES}")
message(STATUS "[${PROJECT_NAME}]: AVX2 feature status ${OMATH_USE_AVX2}")
message(STATUS "[${PROJECT_NAME}]: ImGUI integration feature status ${OMATH_IMGUI_INTEGRATION}")
message(STATUS "[${PROJECT_NAME}]: Legacy features support ${OMATH_ENABLE_LEGACY}")
message(STATUS "[${PROJECT_NAME}]: Building using vcpkg ${OMATH_BUILD_VIA_VCPKG}")
endif ()
file(GLOB_RECURSE OMATH_SOURCES CONFIGURE_DEPENDS "${CMAKE_CURRENT_SOURCE_DIR}/source/*.cpp")
file(GLOB_RECURSE OMATH_HEADERS CONFIGURE_DEPENDS "${CMAKE_CURRENT_SOURCE_DIR}/include/*.hpp")
if (OMATH_BUILD_AS_SHARED_LIBRARY)
add_library(omath SHARED source/Matrix.cpp)
else()
add_library(omath STATIC source/Matrix.cpp)
endif()
add_library(${PROJECT_NAME} SHARED ${OMATH_SOURCES} ${OMATH_HEADERS})
else ()
add_library(${PROJECT_NAME} STATIC ${OMATH_SOURCES} ${OMATH_HEADERS})
endif ()
add_library(omath::omath ALIAS omath)
add_library(${PROJECT_NAME}::${PROJECT_NAME} ALIAS ${PROJECT_NAME})
target_compile_definitions(${PROJECT_NAME} PUBLIC OMATH_VERSION="${PROJECT_VERSION}")
if (OMATH_IMGUI_INTEGRATION)
target_compile_definitions(omath PUBLIC OMATH_IMGUI_INTEGRATION)
endif()
target_compile_definitions(${PROJECT_NAME} PUBLIC OMATH_IMGUI_INTEGRATION)
# IMGUI is being linked as submodule
if (TARGET imgui)
target_link_libraries(${PROJECT_NAME} PUBLIC imgui)
install(TARGETS imgui
EXPORT omathTargets
ARCHIVE DESTINATION lib
LIBRARY DESTINATION lib
RUNTIME DESTINATION bin)
else ()
# Assume that IMGUI linked via VCPKG.
find_package(imgui CONFIG REQUIRED)
target_link_libraries(${PROJECT_NAME} PUBLIC imgui::imgui)
endif ()
endif ()
if (OMATH_USE_AVX2)
target_compile_definitions(omath PUBLIC OMATH_USE_AVX2)
endif()
target_compile_definitions(${PROJECT_NAME} PUBLIC OMATH_USE_AVX2)
endif ()
set_target_properties(omath PROPERTIES
if (OMATH_SUPRESS_SAFETY_CHECKS)
target_compile_definitions(${PROJECT_NAME} PUBLIC OMATH_SUPRESS_SAFETY_CHECKS)
endif ()
if (OMATH_ENABLE_LEGACY)
target_compile_definitions(${PROJECT_NAME} PUBLIC OMATH_ENABLE_LEGACY)
endif ()
set_target_properties(${PROJECT_NAME} PROPERTIES
ARCHIVE_OUTPUT_DIRECTORY "${CMAKE_SOURCE_DIR}/out/${CMAKE_BUILD_TYPE}"
LIBRARY_OUTPUT_DIRECTORY "${CMAKE_SOURCE_DIR}/out/${CMAKE_BUILD_TYPE}"
UNITY_BUILD ON
UNITY_BUILD_BATCH_SIZE 20
CXX_STANDARD 23
CXX_STANDARD_REQUIRED ON)
if (CMAKE_CXX_COMPILER_ID STREQUAL "Clang")
target_compile_options(omath PRIVATE -mavx2 -mfma)
endif()
if (OMATH_USE_UNITY_BUILD)
set_target_properties(${PROJECT_NAME} PROPERTIES
UNITY_BUILD ON
UNITY_BUILD_BATCH_SIZE 20)
endif ()
target_compile_features(omath PUBLIC cxx_std_23)
if (OMATH_STATIC_MSVC_RUNTIME_LIBRARY)
set_target_properties(${PROJECT_NAME} PROPERTIES
MSVC_RUNTIME_LIBRARY "MultiThreaded$<$<CONFIG:Debug>:Debug>"
)
endif ()
if (OMATH_USE_AVX2)
if (MSVC)
target_compile_options(${PROJECT_NAME} PUBLIC /arch:AVX2)
elseif (EMSCRIPTEN)
target_compile_options(${PROJECT_NAME} PUBLIC -msimd128 -mavx2)
elseif (CMAKE_CXX_COMPILER_ID MATCHES "GNU|Clang|AppleClang")
target_compile_options(${PROJECT_NAME} PUBLIC -mfma -mavx2)
endif ()
endif ()
add_subdirectory(source)
target_compile_features(${PROJECT_NAME} PUBLIC cxx_std_23)
if(OMATH_BUILD_TESTS)
add_subdirectory(extlibs)
if (OMATH_BUILD_TESTS)
add_subdirectory(tests)
endif()
target_compile_definitions(${PROJECT_NAME} PUBLIC OMATH_BUILD_TESTS)
endif ()
if (OMATH_BUILD_BENCHMARK)
add_subdirectory(benchmark)
endif ()
if (OMATH_BUILD_EXAMPLES)
add_subdirectory(examples)
endif()
endif ()
if (CMAKE_CXX_COMPILER_ID STREQUAL "MSVC" AND OMATH_THREAT_WARNING_AS_ERROR)
target_compile_options(omath PRIVATE /W4 /WX)
elseif(OMATH_THREAT_WARNING_AS_ERROR)
target_compile_options(omath PRIVATE -Wall -Wextra -Wpedantic -Werror)
endif()
target_compile_options(${PROJECT_NAME} PRIVATE /W4 /WX)
elseif (OMATH_THREAT_WARNING_AS_ERROR)
target_compile_options(${PROJECT_NAME} PRIVATE -Wall -Wextra -Wpedantic -Werror)
endif ()
target_include_directories(omath
# Windows SDK redefine min/max via preprocessor and break std::min and std::max
if (CMAKE_CXX_COMPILER_ID STREQUAL "MSVC")
target_compile_definitions(${PROJECT_NAME} INTERFACE NOMINMAX)
endif ()
target_include_directories(${PROJECT_NAME}
PUBLIC
$<BUILD_INTERFACE:${CMAKE_CURRENT_SOURCE_DIR}/include> # Use this path when building the project
$<INSTALL_INTERFACE:include> # Use this path when the project is installed
@@ -70,21 +169,21 @@ target_include_directories(omath
# Installation rules
# Install the library
install(TARGETS omath
EXPORT omathTargets
ARCHIVE DESTINATION lib COMPONENT omath # For static libraries
LIBRARY DESTINATION lib COMPONENT omath # For shared libraries
RUNTIME DESTINATION bin COMPONENT omath # For executables (on Windows)
install(TARGETS ${PROJECT_NAME}
EXPORT ${PROJECT_NAME}Targets
ARCHIVE DESTINATION lib COMPONENT ${PROJECT_NAME} # For static libraries
LIBRARY DESTINATION lib COMPONENT ${PROJECT_NAME} # For shared libraries
RUNTIME DESTINATION bin COMPONENT ${PROJECT_NAME} # For executables (on Windows)
)
# Install headers as part of omath_component
install(DIRECTORY include/ DESTINATION include COMPONENT omath)
install(DIRECTORY include/ DESTINATION include COMPONENT ${PROJECT_NAME})
# Export omath target for CMake find_package support, also under omath_component
install(EXPORT omathTargets
FILE omathTargets.cmake
NAMESPACE omath::
DESTINATION lib/cmake/omath COMPONENT omath
install(EXPORT ${PROJECT_NAME}Targets
FILE ${PROJECT_NAME}Targets.cmake
NAMESPACE ${PROJECT_NAME}::
DESTINATION lib/cmake/${PROJECT_NAME} COMPONENT ${PROJECT_NAME}
)
@@ -99,12 +198,12 @@ write_basic_package_version_file(
configure_package_config_file(
"${CMAKE_CURRENT_SOURCE_DIR}/cmake/omathConfig.cmake.in" # Path to the .in file
"${CMAKE_CURRENT_BINARY_DIR}/omathConfig.cmake" # Output path for the generated file
INSTALL_DESTINATION lib/cmake/omath
INSTALL_DESTINATION lib/cmake/${PROJECT_NAME}
)
# Install the generated config files
install(FILES
"${CMAKE_CURRENT_BINARY_DIR}/omathConfig.cmake"
"${CMAKE_CURRENT_BINARY_DIR}/omathConfigVersion.cmake"
DESTINATION lib/cmake/omath
DESTINATION lib/cmake/${PROJECT_NAME}
)

122
CMakePresets.json
View File

@@ -8,8 +8,8 @@
"binaryDir": "${sourceDir}/cmake-build/build/${presetName}",
"installDir": "${sourceDir}/cmake-build/install/${presetName}",
"cacheVariables": {
"CMAKE_C_COMPILER": "cl.exe",
"CMAKE_CXX_COMPILER": "cl.exe"
"CMAKE_CXX_COMPILER": "cl.exe",
"CMAKE_MAKE_PROGRAM": "Ninja"
},
"condition": {
"type": "equals",
@@ -17,6 +17,17 @@
"rhs": "Windows"
}
},
{
"name": "windows-base-vcpkg",
"hidden": true,
"inherits": "windows-base",
"cacheVariables": {
"OMATH_BUILD_VIA_VCPKG": "ON",
"CMAKE_TOOLCHAIN_FILE": "$env{VCPKG_ROOT}/scripts/buildsystems/vcpkg.cmake",
"VCPKG_INSTALLED_DIR": "${sourceDir}/cmake-build/vcpkg_installed",
"VCPKG_MANIFEST_FEATURES": "tests;imgui;avx2"
}
},
{
"name": "windows-debug",
"displayName": "Debug",
@@ -25,6 +36,23 @@
"CMAKE_BUILD_TYPE": "Debug"
}
},
{
"name": "windows-debug-vcpkg",
"displayName": "Debug",
"inherits": "windows-base-vcpkg",
"cacheVariables": {
"CMAKE_BUILD_TYPE": "Debug"
}
},
{
"name": "windows-release-vcpkg",
"displayName": "Release",
"inherits": "windows-base-vcpkg",
"cacheVariables": {
"CMAKE_BUILD_TYPE": "Release",
"OMATH_BUILD_VIA_VCPKG": "ON"
}
},
{
"name": "windows-release",
"displayName": "Release",
@@ -40,8 +68,8 @@
"binaryDir": "${sourceDir}/cmake-build/build/${presetName}",
"installDir": "${sourceDir}/cmake-build/install/${presetName}",
"cacheVariables": {
"CMAKE_C_COMPILER": "gcc",
"CMAKE_CXX_COMPILER": "g++"
"CMAKE_CXX_COMPILER": "clang++",
"CMAKE_MAKE_PROGRAM": "ninja"
},
"condition": {
"type": "equals",
@@ -49,6 +77,17 @@
"rhs": "Linux"
}
},
{
"name": "linux-base-vcpkg",
"hidden": true,
"inherits": "linux-base",
"cacheVariables": {
"OMATH_BUILD_VIA_VCPKG": "ON",
"CMAKE_TOOLCHAIN_FILE": "$env{VCPKG_ROOT}/scripts/buildsystems/vcpkg.cmake",
"VCPKG_INSTALLED_DIR": "${sourceDir}/cmake-build/vcpkg_installed",
"VCPKG_MANIFEST_FEATURES": "tests;imgui;avx2"
}
},
{
"name": "linux-debug",
"displayName": "Linux Debug",
@@ -57,6 +96,14 @@
"CMAKE_BUILD_TYPE": "Debug"
}
},
{
"name": "linux-debug-vcpkg",
"displayName": "Linux Debug",
"inherits": "linux-base-vcpkg",
"cacheVariables": {
"CMAKE_BUILD_TYPE": "Debug"
}
},
{
"name": "linux-release",
"displayName": "Linux Release",
@@ -64,6 +111,73 @@
"cacheVariables": {
"CMAKE_BUILD_TYPE": "Release"
}
},
{
"name": "linux-release-vcpkg",
"displayName": "Linux Release",
"inherits": "linux-base-vcpkg",
"cacheVariables": {
"CMAKE_BUILD_TYPE": "Release"
}
},
{
"name": "darwin-base",
"hidden": true,
"generator": "Ninja",
"binaryDir": "${sourceDir}/cmake-build/build/${presetName}",
"installDir": "${sourceDir}/cmake-build/install/${presetName}",
"cacheVariables": {
"CMAKE_CXX_COMPILER": "clang++",
"CMAKE_MAKE_PROGRAM": "ninja"
},
"condition": {
"type": "equals",
"lhs": "${hostSystemName}",
"rhs": "Darwin"
}
},
{
"name": "darwin-base-vcpkg",
"hidden": true,
"inherits": "darwin-base",
"cacheVariables": {
"OMATH_BUILD_VIA_VCPKG": "ON",
"CMAKE_TOOLCHAIN_FILE": "$env{VCPKG_ROOT}/scripts/buildsystems/vcpkg.cmake",
"VCPKG_INSTALLED_DIR": "${sourceDir}/cmake-build/vcpkg_installed",
"VCPKG_MANIFEST_FEATURES": "tests;imgui;avx2"
}
},
{
"name": "darwin-debug",
"displayName": "Darwin Debug",
"inherits": "darwin-base",
"cacheVariables": {
"CMAKE_BUILD_TYPE": "Debug"
}
},
{
"name": "darwin-debug-vcpkg",
"displayName": "Darwin Debug",
"inherits": "darwin-base-vcpkg",
"cacheVariables": {
"CMAKE_BUILD_TYPE": "Debug"
}
},
{
"name": "darwin-release",
"displayName": "Darwin Release",
"inherits": "darwin-base",
"cacheVariables": {
"CMAKE_BUILD_TYPE": "Release"
}
},
{
"name": "darwin-release-vcpkg",
"displayName": "Darwin Release",
"inherits": "darwin-base-vcpkg",
"cacheVariables": {
"CMAKE_BUILD_TYPE": "Release"
}
}
]
}

32
CONTRIBUTING.md Normal file
View File

@@ -0,0 +1,32 @@
## 🤝 Contributing to OMath or other Orange's Projects
### ❕ Prerequisites
- A working up-to-date OMath installation
- C++ knowledge
- Git knowledge
- Ability to ask for help (Feel free to create empty pull-request or PM a maintainer
in [Telegram](https://t.me/orange_cpp))
### ⏬ Setting up OMath
Please read INSTALL.md file in repository
### 🔀 Pull requests and Branches
In order to send code back to the official OMath repository, you must first create a copy of OMath on your github
account ([fork](https://help.github.com/articles/creating-a-pull-request-from-a-fork/)) and
then [create a pull request](https://help.github.com/articles/creating-a-pull-request-from-a-fork/) back to OMath.
OMath development is performed on multiple branches. Changes are then pull requested into master. By default, changes
merged into master will not roll out to stable build users unless the `stable` tag is updated.
### 📜 Code-Style
The orange code-style can be found in `.clang-format`.
### 📦 Building
OMath has already created the `cmake-build` and `out` directories where cmake/bin files are located. By default, you
can build OMath by running `cmake --build cmake-build/build/windows-release --target omath -j 6` in the source
directory.

13
CREDITS.md Normal file
View File

@@ -0,0 +1,13 @@
# OMATH CREDITS
Thanks to everyone who made this possible, including:
- Saikari aka luadebug for VCPKG port and awesome new initial logo design.
- AmbushedRaccoon for telegram post about omath to boost repository activity.
- Billy O'Neal aka BillyONeal for fixing compilation issues due to C math library compatibility.
And a big hand to everyone else who has contributed over the past!
THANKS! <3
-- Orange++ <orange_github@proton.me>

68
INSTALL.md Normal file
View File

@@ -0,0 +1,68 @@
# 📥Installation Guide
## <img width="28px" src="https://vcpkg.io/assets/mark/mark.svg" /> Using vcpkg
**Note**: Support vcpkg for package management
1. Install [vcpkg](https://github.com/microsoft/vcpkg)
2. Run the following command to install the orange-math package:
```
vcpkg install orange-math
```
CMakeLists.txt
```cmake
find_package(omath CONFIG REQUIRED)
target_link_libraries(main PRIVATE omath::omath)
```
For detailed commands on installing different versions and more information, please refer to Microsoft's [official instructions](https://learn.microsoft.com/en-us/vcpkg/get_started/overview).
## <img width="28px" src="https://xmake.io/assets/img/logo.svg" /> Using xrepo
**Note**: Support xrepo for package management
1. Install [xmake](https://xmake.io/)
2. Run the following command to install the omath package:
```
xrepo install omath
```
xmake.lua
```xmake
add_requires("omath")
target("...")
add_packages("omath")
```
## <img width="28px" src="https://upload.wikimedia.org/wikipedia/commons/e/ef/CMake_logo.svg?" /> Build from source using CMake
1. **Preparation**
Install needed tools: cmake, clang, git, msvc (windows only).
1. **Linux:**
```bash
sudo pacman -Sy cmake ninja clang git
```
2. **MacOS:**
```bash
brew install llvm git cmake ninja
```
3. **Windows:**
Install Visual Studio from [here](https://visualstudio.microsoft.com/downloads/) and Git from [here](https://git-scm.com/downloads).
Use x64 Native Tools shell to execute needed commands down below.
2. **Clone the repository:**
```bash
git clone https://github.com/orange-cpp/omath.git
```
3. **Navigate to the project directory:**
```bash
cd omath
```
4. **Build the project using CMake:**
```bash
cmake --preset windows-release -S .
cmake --build cmake-build/build/windows-release --target omath -j 6
```
Use **\<platform\>-\<build configuration\>** preset to build suitable version for yourself. Like **windows-release** or **linux-release**.
| Platform Name | Build Config |
|---------------|---------------|
| windows | release/debug |
| linux | release/debug |
| darwin | release/debug |

62
LICENSE
View File

@@ -1,9 +1,59 @@
The MIT License (MIT)
Copyright (C) 2024-2025 Orange++ <orange_github@proton.me>
Copyright (c) 2024 Orange++
This software is provided 'as-is', without any express or implied
warranty. In no event will the authors be held liable for any damages
arising from the use of this software.
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
Permission is granted to anyone to use this software for any purpose,
including commercial applications, and to alter it and redistribute it
freely, subject to the following restrictions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
1. The origin of this software must not be misrepresented; you must not
claim that you wrote the original software. If you use this software
in a product, an acknowledgment in the product documentation would be
appreciated but is not required.
2. Altered source versions must be plainly marked as such, and must not be
misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.
4. If you are an employee, contractor, volunteer, representative,
or have any other affiliation (past or present)
with any of the following entities:
* "Advertising Placement Services" LLC
* "NEW SOLUTIONS VERTICALS" LLC
* "Autoexpert" LLC
* "Creditit" LLC
* "Yandex.Taxi" LLC
* "Yandex.Eda" LLC
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* "Yandex.Telecom" LLC
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* "EDADIL PROMO" LLC
* "Kinopoisk" LLC
* "Yandex.Music" LLC
* "Refueling (Yandex.Zapravki)" LLC
* "Yandex.Pay" LLC
* "Financial and Payment Technologies" LLC
* "Yandex.Delivery" LLC
* "Delivery Club" LLC
* "Yandex.Check" LLC
* "SMB-Service" LLC
* "ADV-TECH" LLC
* "Yandex Fantech" LLC
* "Yandex Smena" LLC
* "Market.Operations" LLC
* "Yandex.Market" LLC
* "ID Tech" LLC
* "Yandex.Crowd" LLC
* "Yandex" LLC
* "Rutube" LLC
* "Kaspersky" LLC
Or if you represent or are associated with any legal, organizational, or
professional entity providing services to or on behalf of the aforementioned entities:
You are expressly forbidden from accessing, using, modifying, distributing, or
interacting with the Software and its source code in any form. You must immediately
delete or destroy any physical or digital copies of the Software and/or
its source code, including any derivative works, tools, or information obtained from the Software.

190
README.md
View File

@@ -1,89 +1,145 @@
<div align = center>
![banner](https://i.imgur.com/sjtpKi8.png)
![banner](docs/images/logos/omath_logo_macro.png)
![GitHub License](https://img.shields.io/github/license/orange-cpp/omath)
![Static Badge](https://img.shields.io/badge/license-libomath-orange)
![GitHub contributors](https://img.shields.io/github/contributors/orange-cpp/omath)
![GitHub top language](https://img.shields.io/github/languages/top/orange-cpp/omath)
[![CodeFactor](https://www.codefactor.io/repository/github/orange-cpp/omath/badge)](https://www.codefactor.io/repository/github/orange-cpp/omath)
![GitHub Actions Workflow Status](https://img.shields.io/github/actions/workflow/status/orange-cpp/omath/cmake-multi-platform.yml)
[![Vcpkg package](https://repology.org/badge/version-for-repo/vcpkg/orange-math.svg)](https://repology.org/project/orange-math/versions)
![GitHub forks](https://img.shields.io/github/forks/orange-cpp/omath)
[![discord badge](https://dcbadge.limes.pink/api/server/https://discord.gg/eDgdaWbqwZ?style=flat)](https://discord.gg/eDgdaWbqwZ)
[![telegram badge](https://img.shields.io/badge/Telegram-2CA5E0?style=flat-squeare&logo=telegram&logoColor=white)](https://t.me/orangennotes)
OMath is a 100% independent, constexpr template blazingly fast math library that doesn't have legacy C++ code.
It provides the latest features, is highly customizable, has all for cheat development, DirectX/OpenGL/Vulkan support, premade support for different game engines, much more constexpr stuff than in other libraries and more...
<br>
<br>
---
**[<kbd> <br> Install <br> </kbd>][INSTALL]** 
**[<kbd> <br> Examples <br> </kbd>][EXAMPLES]** 
**[<kbd> <br> Documentation <br> </kbd>][DOCUMENTATION]** 
**[<kbd> <br> Contribute <br> </kbd>][CONTRIBUTING]** 
**[<kbd> <br> Donate <br> </kbd>][SPONSOR]** 
---
<br>
</div>
Oranges's Math Library (omath) is a comprehensive, open-source library aimed at providing efficient, reliable, and versatile mathematical functions and algorithms. Developed primarily in C++, this library is designed to cater to a wide range of mathematical operations essential in scientific computing, engineering, and academic research.
## 👁‍🗨 Features
- **Efficiency**: Optimized for performance, ensuring quick computations using AVX2.
- **Versatility**: Includes a wide array of mathematical functions and algorithms.
- **Ease of Use**: Simplified interface for convenient integration into various projects.
- **Projectile Prediction**: Projectile prediction engine with O(N) algo complexity, that can power you projectile aim-bot.
- **3D Projection**: No need to find view-projection matrix anymore you can make your own projection pipeline.
- **Collision Detection**: Production ready code to handle collision detection by using simple interfaces.
- **No Additional Dependencies**: No additional dependencies need to use OMath except unit test execution
- **Ready for meta-programming**: Omath use templates for common types like Vectors, Matrixes etc, to handle all types!
## ⏬ Getting Started
### Prerequisites
- C++ Compiler
- CMake (for building the project)
<div align = center>
<a href="https://www.star-history.com/#orange-cpp/omath&Date">
<picture>
<source media="(prefers-color-scheme: dark)" srcset="https://api.star-history.com/svg?repos=orange-cpp/omath&type=Date&theme=dark" />
<source media="(prefers-color-scheme: light)" srcset="https://api.star-history.com/svg?repos=orange-cpp/omath&type=Date" />
<img alt="Star History Chart" src="https://api.star-history.com/svg?repos=orange-cpp/omath&type=Date" />
</picture>
</a>
</div>
### Installation
### vcpkg
**Note**: Support vcpkg for package management
1. Install vcpkg (https://github.com/microsoft/vcpkg)
2. Run the following command to install the orange-math package:
```
vcpkg install orange-math
```
CMakeLists.txt
```cmake
find_package(omath CONFIG REQUIRED)
target_link_libraries(main PRIVATE omath::omath)
```
For detailed commands on installing different versions and more information, please refer to Microsoft's official instructions (https://learn.microsoft.com/en-us/vcpkg/get_started/overview)
### Build from source
1. Clone the repository:
```
git clone https://github.com/orange-cpp/omath.git
```
2. Navigate to the project directory:
```
cd omath
```
3. Build the project using CMake:
```
cmake --preset windows-release -S .
cmake --build cmake-build/build/windows-release --target omath -j 6
```
Use **\<platform\>-\<build configuration\>** preset to build siutable version for yourself. Like **windows-release** or **linux-release**.
## ❔ Usage
Simple world to screen function
```c++
TEST(UnitTestProjection, IsPointOnScreen)
{
const omath::projection::Camera camera({0.f, 0.f, 0.f}, {0, 0.f, 0.f} , {1920.f, 1080.f}, 110.f, 0.1f, 500.f);
## 🚀 Quick Example
const auto proj = camera.WorldToScreen({100, 0, 15});
EXPECT_TRUE(proj.has_value());
```cpp
#include <omath/omath.hpp>
using namespace omath;
// 3D vector operations
Vector3<float> a{1, 2, 3};
Vector3<float> b{4, 5, 6};
auto dot = a.dot(b); // 32.0
auto cross = a.cross(b); // (-3, 6, -3)
auto distance = a.distance_to(b); // ~5.196
auto normalized = a.normalized(); // Unit vector
// World-to-screen projection (Source Engine example)
using namespace omath::source_engine;
Camera camera(position, angles, viewport, fov, near_plane, far_plane);
if (auto screen = camera.world_to_screen(world_position)) {
// Draw at screen->x, screen->y
}
```
<details>
<summary>OMATH for making cheats</summary>
**[➡️ See more examples and tutorials][TUTORIALS]**
With `omath/projection` module you can achieve simple ESP hack for powered by Source/Unreal/Unity engine games, like [Apex Legends](https://store.steampowered.com/app/1172470/Apex_Legends/).
# ✨ Features
- **🚀 Efficiency**: Optimized for performance, ensuring quick computations using AVX2.
- **🎯 Versatility**: Includes a wide array of mathematical functions and algorithms.
- **✅ Ease of Use**: Simplified interface for convenient integration into various projects.
- **🎮 Projectile Prediction**: Projectile prediction engine with O(N) algo complexity, that can power you projectile aim-bot.
- **📐 3D Projection**: No need to find view-projection matrix anymore you can make your own projection pipeline.
- **💥 Collision Detection**: Production ready code to handle collision detection by using simple interfaces.
- **📦 No Additional Dependencies**: No additional dependencies need to use OMath except unit test execution
- **🔧 Ready for meta-programming**: Omath use templates for common types like Vectors, Matrixes etc, to handle all types!
- **🎯 Engine support**: Supports coordinate systems of **Source, Unity, Unreal, Frostbite, IWEngine and canonical OpenGL**.
- **🌍 Cross platform**: Supports Windows, MacOS and Linux.
- **🔍 Algorithms**: Has ability to scan for byte pattern with wildcards in PE files/modules, binary slices, works even with Wine apps.
<div align = center>
# Gallery
![banner](https://i.imgur.com/lcJrfcZ.png)
Or for InfinityWard Engine based games. Like Call of Duty Black Ops 2!
![banner](https://i.imgur.com/F8dmdoo.png)
<br>
Or even advanced projectile aimbot
[Watch Video](https://youtu.be/lM_NJ1yCunw?si=5E87OrQMeypxSJ3E)
</details>
[![Youtube Video](docs/images/yt_previews/img.png)](https://youtu.be/lM_NJ1yCunw?si=-Qf5yzDcWbaxAXGQ)
## 🫵🏻 Contributing
Contributions to `omath` are welcome! Please read `CONTRIBUTING.md` for details on our code of conduct and the process for submitting pull requests.
<br>
## 📜 License
This project is licensed under the MIT - see the `LICENSE` file for details.
![APEX Preview]
## 💘 Acknowledgments
<br>
![BO2 Preview]
<br>
![CS2 Preview]
<br>
![TF2 Preview]
<br>
<br>
</div>
## 📚 Documentation
- **[Getting Started Guide](http://libomath.org/getting_started/)** - Installation and first steps
- **[API Overview](http://libomath.org/api_overview/)** - Complete API reference
- **[Tutorials](http://libomath.org/tutorials/)** - Step-by-step guides
- **[FAQ](http://libomath.org/faq/)** - Common questions and answers
- **[Troubleshooting](http://libomath.org/troubleshooting/)** - Solutions to common issues
- **[Best Practices](http://libomath.org/best_practices/)** - Guidelines for effective usage
## 🤝 Community & Support
- **Discord**: [Join our community](https://discord.gg/eDgdaWbqwZ)
- **Telegram**: [@orangennotes](https://t.me/orangennotes)
- **Issues**: [Report bugs or request features](https://github.com/orange-cpp/omath/issues)
- **Contributing**: See [CONTRIBUTING.md](CONTRIBUTING.md) for guidelines
# 💘 Acknowledgments
- [All contributors](https://github.com/orange-cpp/omath/graphs/contributors)
<!----------------------------------{ Images }--------------------------------->
[APEX Preview]: docs/images/showcase/apex.png
[BO2 Preview]: docs/images/showcase/cod_bo2.png
[CS2 Preview]: docs/images/showcase/cs2.jpeg
[TF2 Preview]: docs/images/showcase/tf2.jpg
<!----------------------------------{ Buttons }--------------------------------->
[QUICKSTART]: docs/getting_started.md
[INSTALL]: INSTALL.md
[DOCUMENTATION]: http://libomath.org
[TUTORIALS]: docs/tutorials.md
[CONTRIBUTING]: CONTRIBUTING.md
[EXAMPLES]: examples
[SPONSOR]: https://boosty.to/orangecpp/purchase/3568644?ssource=DIRECT&share=subscription_link

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@@ -2,4 +2,4 @@
## Reporting a Vulnerability
Please report security issues to `orange-cpp@yandex.ru`
Please report security issues to `orange_github@proton.me`

1
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4.2.0

19
benchmark/CMakeLists.txt Normal file
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project(omath_benchmark)
file(GLOB_RECURSE OMATH_BENCHMARK_SOURCES CONFIGURE_DEPENDS "${CMAKE_CURRENT_SOURCE_DIR}/*.cpp")
add_executable(${PROJECT_NAME} ${OMATH_BENCHMARK_SOURCES})
set_target_properties(${PROJECT_NAME} PROPERTIES
ARCHIVE_OUTPUT_DIRECTORY "${CMAKE_SOURCE_DIR}/out/${CMAKE_BUILD_TYPE}"
LIBRARY_OUTPUT_DIRECTORY "${CMAKE_SOURCE_DIR}/out/${CMAKE_BUILD_TYPE}"
RUNTIME_OUTPUT_DIRECTORY "${CMAKE_SOURCE_DIR}/out/${CMAKE_BUILD_TYPE}"
CXX_STANDARD 23
CXX_STANDARD_REQUIRED ON)
if (TARGET benchmark::benchmark) # Benchmark is being linked as submodule
target_link_libraries(${PROJECT_NAME} PRIVATE benchmark::benchmark omath)
else()
find_package(benchmark CONFIG REQUIRED) # Benchmark is being linked as vcpkg package
target_link_libraries(${PROJECT_NAME} PRIVATE benchmark::benchmark omath)
endif ()

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//
// Created by Vlad on 9/17/2025.
//
#include <benchmark/benchmark.h>
#include <omath/omath.hpp>
using namespace omath;
void mat_float_multiplication_col_major(benchmark::State& state)
{
using MatType = Mat<128, 128, float, MatStoreType::COLUMN_MAJOR>;
MatType a;
MatType b;
a.set(3.f);
b.set(7.f);
for ([[maybe_unused]] const auto _ : state)
std::ignore = a * b;
}
void mat_float_multiplication_row_major(benchmark::State& state)
{
using MatType = Mat<128, 128, float, MatStoreType::ROW_MAJOR>;
MatType a;
MatType b;
a.set(3.f);
b.set(7.f);
for ([[maybe_unused]] const auto _ : state)
std::ignore = a * b;
}
void mat_double_multiplication_row_major(benchmark::State& state)
{
using MatType = Mat<128, 128, double, MatStoreType::ROW_MAJOR>;
MatType a;
MatType b;
a.set(3.f);
b.set(7.f);
for ([[maybe_unused]] const auto _ : state)
std::ignore = a * b;
}
void mat_double_multiplication_col_major(benchmark::State& state)
{
using MatType = Mat<128, 128, double, MatStoreType::COLUMN_MAJOR>;
MatType a;
MatType b;
a.set(3.f);
b.set(7.f);
for ([[maybe_unused]] const auto _ : state)
std::ignore = a * b;
}
BENCHMARK(mat_float_multiplication_col_major)->Iterations(5000);
BENCHMARK(mat_float_multiplication_row_major)->Iterations(5000);
BENCHMARK(mat_double_multiplication_col_major)->Iterations(5000);
BENCHMARK(mat_double_multiplication_row_major)->Iterations(5000);

23
benchmark/benchmark_projectile_pred.cpp Normal file
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//
// Created by Vlad on 9/18/2025.
//
#include <benchmark/benchmark.h>
#include <omath/omath.hpp>
using namespace omath;
using namespace omath::projectile_prediction;
constexpr float simulation_time_step = 1.f / 1000.f;
constexpr float hit_distance_tolerance = 5.f;
void source_engine_projectile_prediction(benchmark::State& state)
{
constexpr Target target{.m_origin = {100, 0, 90}, .m_velocity = {0, 0, 0}, .m_is_airborne = false};
constexpr Projectile projectile = {.m_origin = {3, 2, 1}, .m_launch_speed = 5000, .m_gravity_scale = 0.4};
for ([[maybe_unused]] const auto _: state)
std::ignore = ProjPredEngineLegacy(400, simulation_time_step, 50, hit_distance_tolerance)
.maybe_calculate_aim_point(projectile, target);
}
BENCHMARK(source_engine_projectile_prediction)->Iterations(10'000);

5
benchmark/main.cpp Normal file
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@@ -0,0 +1,5 @@
//
// Created by Vlad on 9/17/2025.
//
#include <benchmark/benchmark.h>
BENCHMARK_MAIN();

4
cmake/omathConfig.cmake.in
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@@ -2,6 +2,10 @@
include(CMakeFindDependencyMacro)
if (@OMATH_IMGUI_INTEGRATION@)
find_dependency(imgui CONFIG)
endif()
# Load the targets for the omath library
include("${CMAKE_CURRENT_LIST_DIR}/omathTargets.cmake")
check_required_components(omath)

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# `omath::primitives::create_box` — Build an oriented box as 12 triangles
> Header: your project’s `primitives/box.hpp` (declares `create_box`)
> Namespace: `omath::primitives`
> Depends on: `omath::Triangle<omath::Vector3<float>>`, `omath::Vector3<float>`
```cpp
[[nodiscard]]
std::array<Triangle<Vector3<float>>, 12>
create_box(const Vector3<float>& top,
const Vector3<float>& bottom,
const Vector3<float>& dir_forward,
const Vector3<float>& dir_right,
float ratio = 4.f) noexcept;
```
---
## What it does
Constructs a **rectangular cuboid (“box”)** oriented in 3D space and returns its surface as **12 triangles** (2 per face × 6 faces). The box’s central axis runs from `bottom` → `top`. The **up** direction is inferred from that segment; the **forward** and **right** directions define the box’s orientation around that axis.
The lateral half-extents are derived from the axis length and `ratio`:
> Let `H = |top - bottom|`. Lateral half-size ≈ `H / ratio` along both `dir_forward` and `dir_right`
> (i.e., the cross-section is a square of side `2H/ratio`).
> **Note:** This describes the intended behavior from the interface. If you rely on a different sizing rule, document it next to your implementation.
---
## Parameters
* `top`
Center of the **top face**.
* `bottom`
Center of the **bottom face**.
* `dir_forward`
A direction that orients the box around its up axis. Should be **non-zero** and **not collinear** with `top - bottom`.
* `dir_right`
A direction roughly orthogonal to both `dir_forward` and `top - bottom`. Used to fully fix orientation.
* `ratio` (default `4.0f`)
Controls thickness relative to height. Larger values → thinner box.
With the default rule above, half-extent = `|top-bottom|/ratio`.
---
## Return value
`std::array<Triangle<Vector3<float>>, 12>` — the six faces of the box, triangulated.
Winding is intended to be **outward-facing** (right-handed coordinates). Do not rely on a specific **face ordering**; treat the array as opaque unless your implementation guarantees an order.
---
## Expected math & robustness
* Define `u = normalize(top - bottom)`.
* Re-orthonormalize the basis to avoid skew:
```cpp
f = normalize(dir_forward - u * u.dot(dir_forward)); // drop any up component
r = normalize(u.cross(f)); // right-handed basis
// (Optionally recompute f = r.cross(u) for orthogonality)
```
* Half-extents: `h = length(top - bottom) / ratio; hf = h * f; hr = h * r`.
* Corners (top): `t±r±f = top ± hr ± hf`; (bottom): `b±r±f = bottom ± hr ± hf`.
* Triangulate each face with consistent CCW winding when viewed from outside.
---
## Example
```cpp
using omath::Vector3;
using omath::Triangle;
using omath::primitives::create_box;
// Axis from bottom to top (height 2)
Vector3<float> bottom{0, 0, 0};
Vector3<float> top {0, 2, 0};
// Orientation around the axis
Vector3<float> forward{0, 0, 1};
Vector3<float> right {1, 0, 0};
// Ratio 4 → lateral half-size = height/4 = 0.5
auto tris = create_box(top, bottom, forward, right, 4.0f);
// Use the triangles (normals, rendering, collision, etc.)
for (const auto& tri : tris) {
auto n = tri.calculate_normal();
(void)n;
}
```
---
## Usage notes & pitfalls
* **Degenerate axis**: If `top == bottom`, the box is undefined (zero height). Guard against this.
* **Directions**: Provide **non-zero**, **reasonably orthogonal** `dir_forward`/`dir_right`. A robust implementation should project/normalize internally, but callers should still pass sensible inputs.
* **Winding**: If your renderer or collision expects a specific winding, verify with a unit test and flip vertex order per face if necessary.
* **Thickness policy**: This doc assumes both lateral half-extents equal `|top-bottom|/ratio`. If your implementation diverges (e.g., separate forward/right ratios), document it.
---
## See also
* `omath::Triangle` (vertex utilities: normals, centroid, etc.)
* `omath::Vector3` (geometry operations used by the construction)
---
*Last updated: 31 Oct 2025*

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# `omath::primitives::create_plane` — Build an oriented quad (2 triangles)
> Header: your project’s `primitives/plane.hpp`
> Namespace: `omath::primitives`
> Depends on: `omath::Triangle<omath::Vector3<float>>`, `omath::Vector3<float>`
```cpp
[[nodiscard]]
std::array<Triangle<Vector3<float>>, 2>
create_plane(const Vector3<float>& vertex_a,
const Vector3<float>& vertex_b,
const Vector3<float>& direction,
float size) noexcept;
```
---
## What it does
Creates a **rectangle (quad)** in 3D oriented by the edge **A→B** and a second in-plane **direction**. The quad is returned as **two triangles** suitable for rendering or collision.
* Edge axis: `e = vertex_b - vertex_a`
* Width axis: “direction”, **projected to be perpendicular to `e`** so the quad is planar and well-formed.
* Normal (by right-hand rule): `n ∝ e × width`.
> **Sizing convention**
> Typical construction uses **half-width = `size`** along the (normalized, orthogonalized) *direction*, i.e. the total width is `2*size`.
> If your implementation interprets `size` as full width, adjust your expectations accordingly.
---
## Parameters
* `vertex_a`, `vertex_b` — two adjacent quad vertices defining the **long edge** of the plane.
* `direction` — a vector indicating the **cross-edge direction** within the plane (does not need to be orthogonal or normalized).
* `size` — **half-width** of the quad along the (processed) `direction`.
---
## Return
`std::array<Triangle<Vector3<float>>, 2>` — the quad triangulated (consistent CCW winding, outward normal per `e × width`).
---
## Robust construction (expected math)
1. `e = vertex_b - vertex_a`
2. Make `d` perpendicular to `e`:
```
d = direction - e * (e.dot(direction) / e.length_sqr());
if (d.length_sqr() == 0) pick an arbitrary perpendicular to e
d = d.normalized();
```
3. Offsets: `w = d * size`
4. Four corners:
```
A0 = vertex_a - w; A1 = vertex_a + w;
B0 = vertex_b - w; B1 = vertex_b + w;
```
5. Triangles (CCW when viewed from +normal):
```
T0 = Triangle{ A0, A1, B1 }
T1 = Triangle{ A0, B1, B0 }
```
---
## Example
```cpp
using omath::Vector3;
using omath::Triangle;
using omath::primitives::create_plane;
Vector3<float> a{ -1, 0, -1 }; // edge start
Vector3<float> b{ 1, 0, -1 }; // edge end
Vector3<float> dir{ 0, 0, 1 }; // cross-edge direction within the plane (roughly +Z)
float half_width = 2.0f;
auto quad = create_plane(a, b, dir, half_width);
// e.g., compute normals
for (const auto& tri : quad) {
auto n = tri.calculate_normal(); (void)n;
}
```
---
## Notes & edge cases
* **Degenerate edge**: if `vertex_a == vertex_b`, the plane is undefined.
* **Collinearity**: if `direction` is parallel to `vertex_b - vertex_a`, the function must choose an alternate perpendicular; expect a fallback.
* **Winding**: If your renderer expects a specific face order, verify and swap the two vertices in each triangle as needed.

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# API Overview
This document provides a high-level overview of OMath's API, organized by functionality area.
---
## Module Organization
OMath is organized into several logical modules:
### Core Mathematics
- **Linear Algebra** - Vectors, matrices, triangles
- **Trigonometry** - Angles, view angles, trigonometric functions
- **3D Primitives** - Boxes, planes, geometric shapes
### Game Development
- **Collision Detection** - Ray tracing, intersection tests
- **Projectile Prediction** - Ballistics and aim-assist calculations
- **Projection** - Camera systems and world-to-screen transformations
- **Pathfinding** - A* algorithm, navigation meshes
### Engine Support
- **Source Engine** - Valve's Source Engine (CS:GO, TF2, etc.)
- **Unity Engine** - Unity game engine
- **Unreal Engine** - Epic's Unreal Engine
- **Frostbite Engine** - EA's Frostbite Engine
- **IW Engine** - Infinity Ward's engine (Call of Duty)
- **OpenGL Engine** - Canonical OpenGL coordinate system
### Utilities
- **Color** - RGBA color representation
- **Pattern Scanning** - Memory pattern search (wildcards, PE files)
- **Reverse Engineering** - Internal/external memory manipulation
---
## Core Types
### Vectors
All vector types are template-based and support arithmetic types.
| Type | Description | Key Methods |
|------|-------------|-------------|
| `Vector2<T>` | 2D vector | `length()`, `normalized()`, `dot()`, `distance_to()` |
| `Vector3<T>` | 3D vector | `length()`, `normalized()`, `dot()`, `cross()`, `angle_between()` |
| `Vector4<T>` | 4D vector | Extends Vector3 with `w` component |
**Common aliases:**
```cpp
using Vec2f = Vector2<float>;
using Vec3f = Vector3<float>;
using Vec4f = Vector4<float>;
```
**Key features:**
- Component-wise arithmetic (+, -, *, /)
- Scalar multiplication/division
- Dot and cross products
- Safe normalization (returns original if length is zero)
- Distance calculations
- Angle calculations with error handling
- Hash support for `float` variants
- `std::formatter` support
### Matrices
| Type | Description | Key Methods |
|------|-------------|-------------|
| `Mat4X4` | 4×4 matrix | `identity()`, `transpose()`, `determinant()`, `inverse()` |
**Use cases:**
- Transformation matrices
- View matrices
- Projection matrices
- Model-view-projection pipelines
### Angles
Strong-typed angle system with compile-time range enforcement:
| Type | Range | Description |
|------|-------|-------------|
| `Angle<T, Min, Max, Flags>` | Custom | Generic angle type with bounds |
| `PitchAngle` | [-89°, 89°] | Vertical camera rotation |
| `YawAngle` | [-180°, 180°] | Horizontal camera rotation |
| `RollAngle` | [-180°, 180°] | Camera roll |
| `ViewAngles` | - | Composite pitch/yaw/roll |
**Features:**
- Automatic normalization/clamping based on flags
- Conversions between degrees and radians
- Type-safe arithmetic
- Prevents common angle bugs
---
## Projection System
### Camera
Generic camera template that works with any engine trait:
```cpp
template<class MatrixType, class AnglesType, class EngineTrait>
class Camera;
```
**Engine-specific cameras:**
```cpp
omath::source_engine::Camera // Source Engine
omath::unity_engine::Camera // Unity
omath::unreal_engine::Camera // Unreal
omath::frostbite_engine::Camera // Frostbite
omath::iw_engine::Camera // IW Engine
omath::opengl_engine::Camera // OpenGL
```
**Core methods:**
- `world_to_screen(Vector3<float>)` - Project 3D point to 2D screen
- `get_view_matrix()` - Get current view matrix
- `get_projection_matrix()` - Get current projection matrix
- `update(position, angles)` - Update camera state
**Supporting types:**
- `ViewPort` - Screen dimensions and aspect ratio
- `FieldOfView` - FOV in degrees with validation
- `ProjectionError` - Error codes for projection failures
---
## Collision Detection
### LineTracer
Ray-casting and line tracing utilities:
```cpp
namespace omath::collision {
class LineTracer;
}
```
**Features:**
- Ray-triangle intersection
- Ray-plane intersection
- Ray-box intersection
- Distance calculations
- Normal calculations at hit points
### 3D Primitives
| Type | Description | Key Methods |
|------|-------------|-------------|
| `Plane` | Infinite plane | `intersects_ray()`, `distance_to_point()` |
| `Box` | Axis-aligned bounding box | `contains()`, `intersects()` |
---
## Projectile Prediction
### Interfaces
**`ProjPredEngineInterface`** - Base interface for all prediction engines
```cpp
virtual std::optional<Vector3<float>>
maybe_calculate_aim_point(const Projectile&, const Target&) const = 0;
```
### Implementations
| Engine | Description | Optimizations |
|--------|-------------|---------------|
| `ProjPredEngineLegacy` | Standard implementation | Portable, works everywhere |
| `ProjPredEngineAVX2` | AVX2 optimized | 2-4x faster on modern CPUs |
### Supporting Types
**`Projectile`** - Defines projectile properties:
```cpp
struct Projectile {
Vector3<float> origin;
float speed;
Vector3<float> gravity;
// ... additional properties
};
```
**`Target`** - Defines target state:
```cpp
struct Target {
Vector3<float> position;
Vector3<float> velocity;
// ... additional properties
};
```
---
## Pathfinding
### A* Algorithm
```cpp
namespace omath::pathfinding {
template<typename NodeType>
class AStar;
}
```
**Features:**
- Generic node type support
- Customizable heuristics
- Efficient priority queue implementation
- Path reconstruction
### Navigation Mesh
```cpp
namespace omath::pathfinding {
class NavigationMesh;
}
```
**Features:**
- Triangle-based navigation
- Neighbor connectivity
- Walkable area definitions
---
## Engine Traits
Each game engine has a trait system providing engine-specific math:
### CameraTrait
Implements camera math for an engine:
- `calc_look_at_angle()` - Calculate angles to look at a point
- `calc_view_matrix()` - Build view matrix from angles and position
- `calc_projection_matrix()` - Build projection matrix from FOV and viewport
### PredEngineTrait
Provides physics/ballistics specific to an engine:
- Gravity vectors
- Coordinate system conventions
- Unit conversions
- Physics parameters
### Available Traits
| Engine | Camera Trait | Pred Engine Trait | Constants | Formulas |
|--------|--------------|-------------------|-----------|----------|
| Source Engine | ✓ | ✓ | ✓ | ✓ |
| Unity Engine | ✓ | ✓ | ✓ | ✓ |
| Unreal Engine | ✓ | ✓ | ✓ | ✓ |
| Frostbite | ✓ | ✓ | ✓ | ✓ |
| IW Engine | ✓ | ✓ | ✓ | ✓ |
| OpenGL | ✓ | ✓ | ✓ | ✓ |
**Documentation:**
- See `docs/engines/<engine_name>/` for detailed per-engine docs
- Each engine has separate docs for camera_trait, pred_engine_trait, constants, and formulas
---
## Utility Functions
### Color
```cpp
struct Color {
uint8_t r, g, b, a;
// Conversions
static Color from_hsv(float h, float s, float v);
static Color from_hex(uint32_t hex);
uint32_t to_hex() const;
// Blending
Color blend(const Color& other, float t) const;
};
```
### Pattern Scanning
**Binary pattern search with wildcards:**
```cpp
// Pattern with wildcards (?? = any byte)
PatternView pattern{"48 8B 05 ?? ?? ?? ?? 48 85 C0"};
// Scan memory
auto result = pattern_scan(memory_buffer, pattern);
if (result) {
std::cout << "Found at offset: " << result->offset << "\n";
}
```
**PE file scanning:**
```cpp
PEPatternScanner scanner("target.exe");
if (auto addr = scanner.scan_pattern(pattern)) {
std::cout << "Found at RVA: " << *addr << "\n";
}
```
### Reverse Engineering
**External memory access:**
```cpp
ExternalRevObject process("game.exe");
Vector3<float> position = process.read<Vector3<float>>(address);
process.write(address, new_position);
```
**Internal memory access:**
```cpp
InternalRevObject memory;
auto value = memory.read<float>(address);
memory.write(address, new_value);
```
---
## Concepts and Constraints
OMath uses C++20 concepts for type safety:
```cpp
template<class T>
concept Arithmetic = std::is_arithmetic_v<T>;
template<class EngineTrait>
concept CameraEngineConcept = requires(EngineTrait t) {
{ t.calc_look_at_angle(...) } -> /* returns angles */;
{ t.calc_view_matrix(...) } -> /* returns matrix */;
{ t.calc_projection_matrix(...) } -> /* returns matrix */;
};
```
---
## Error Handling
OMath uses modern C++ error handling:
### std::expected (C++23)
```cpp
std::expected<Angle<...>, Vector3Error>
angle_between(const Vector3& other) const;
if (auto angle = v1.angle_between(v2)) {
// Success: use *angle
} else {
// Error: angle.error() gives Vector3Error
}
```
### std::optional
```cpp
std::optional<Vector2<float>>
world_to_screen(const Vector3<float>& world);
if (auto screen = camera.world_to_screen(pos)) {
// Success: use screen->x, screen->y
} else {
// Point not visible
}
```
### Error Codes
```cpp
enum class ProjectionError {
SUCCESS = 0,
POINT_BEHIND_CAMERA,
INVALID_VIEWPORT,
// ...
};
```
---
## Performance Considerations
### constexpr Support
Most operations are `constexpr` where possible:
```cpp
constexpr Vector3<float> v{1, 2, 3};
constexpr auto len_sq = v.length_sqr(); // Computed at compile time
```
### AVX2 Optimizations
Use AVX2 variants when available:
```cpp
// Standard: portable but slower
ProjPredEngineLegacy legacy_engine;
// AVX2: 2-4x faster on modern CPUs
ProjPredEngineAVX2 fast_engine;
```
**When to use AVX2:**
- Modern Intel/AMD processors (2013+)
- Performance-critical paths
- Batch operations
**When to use Legacy:**
- Older processors
- ARM platforms
- Guaranteed compatibility
### Cache Efficiency
```cpp
// Good: contiguous storage
std::vector<Vector3<float>> positions;
// Good: structure of arrays for SIMD
struct Particles {
std::vector<float> x, y, z;
};
```
---
## Platform Support
| Platform | Support | Notes |
|----------|---------|-------|
| Windows | ✓ | MSVC, Clang, GCC |
| Linux | ✓ | GCC, Clang |
| macOS | ✓ | Clang |
**Minimum requirements:**
- C++20 compiler
- C++23 recommended for `std::expected`
---
## Thread Safety
- **Vector/Matrix types**: Thread-safe (immutable operations)
- **Camera**: Not thread-safe (mutable state)
- **Pattern scanning**: Thread-safe (read-only operations)
- **Memory access**: Depends on OS/process synchronization
**Thread-safe example:**
```cpp
// Safe: each thread gets its own camera
std::vector<std::thread> threads;
for (int i = 0; i < num_threads; ++i) {
threads.emplace_back([i]() {
Camera camera = /* create camera */;
// Use camera in this thread
});
}
```
---
## Best Practices
### 1. Use Type Aliases
```cpp
using Vec3f = omath::Vector3<float>;
using Mat4 = omath::Mat4X4;
```
### 2. Prefer constexpr When Possible
```cpp
constexpr auto compute_at_compile_time() {
Vector3<float> v{1, 2, 3};
return v.length_sqr();
}
```
### 3. Check Optional/Expected Results
```cpp
// Good
if (auto result = camera.world_to_screen(pos)) {
use(*result);
}
// Bad - may crash
auto result = camera.world_to_screen(pos);
use(result->x); // Undefined behavior if nullopt
```
### 4. Use Engine-Specific Types
```cpp
// Good: uses correct coordinate system
using namespace omath::source_engine;
Camera camera = /* ... */;
// Bad: mixing engine types
using UnityCamera = omath::unity_engine::Camera;
using SourceAngles = omath::source_engine::ViewAngles;
UnityCamera camera{pos, SourceAngles{}}; // Wrong!
```
---
## See Also
- [Getting Started Guide](getting_started.md)
- [Installation Instructions](install.md)
- [Examples Directory](../examples/)
- Individual module documentation in respective folders
---
*Last updated: 1 Nov 2025*

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# Best Practices
Guidelines for using OMath effectively and avoiding common pitfalls.
---
## Code Organization
### Use Type Aliases
Define clear type aliases for commonly used types:
```cpp
// Good: Clear and concise
using Vec3f = omath::Vector3<float>;
using Vec2f = omath::Vector2<float>;
using Mat4 = omath::Mat4X4;
Vec3f position{1.0f, 2.0f, 3.0f};
```
```cpp
// Avoid: Verbose and repetitive
omath::Vector3<float> position{1.0f, 2.0f, 3.0f};
omath::Vector3<float> velocity{0.0f, 0.0f, 0.0f};
```
### Namespace Usage
Be selective with `using namespace`:
```cpp
// Good: Specific namespace for your engine
using namespace omath::source_engine;
// Good: Import specific types
using omath::Vector3;
using omath::Vector2;
// Avoid: Too broad
using namespace omath; // Imports everything
```
### Include What You Use
```cpp
// Good: Include specific headers
#include <omath/linear_algebra/vector3.hpp>
#include <omath/projection/camera.hpp>
// Okay for development
#include <omath/omath.hpp>
// Production: Include only what you need
// to reduce compile times
```
---
## Error Handling
### Always Check Optional Results
```cpp
// Good: Check before using
if (auto screen = camera.world_to_screen(world_pos)) {
draw_at(screen->x, screen->y);
} else {
// Handle point not visible
}
// Bad: Unchecked access can crash
auto screen = camera.world_to_screen(world_pos);
draw_at(screen->x, screen->y); // Undefined behavior if nullopt!
```
### Handle Expected Errors
```cpp
// Good: Handle error case
if (auto angle = v1.angle_between(v2)) {
use_angle(*angle);
} else {
switch (angle.error()) {
case Vector3Error::IMPOSSIBLE_BETWEEN_ANGLE:
// Handle zero-length vector
break;
}
}
// Bad: Assume success
auto angle = v1.angle_between(v2);
use_angle(*angle); // Throws if error!
```
### Validate Inputs
```cpp
// Good: Validate before expensive operations
bool is_valid_projectile(const Projectile& proj) {
return proj.speed > 0.0f &&
std::isfinite(proj.speed) &&
std::isfinite(proj.origin.length());
}
if (is_valid_projectile(proj) && is_valid_target(target)) {
auto aim = engine.maybe_calculate_aim_point(proj, target);
}
```
---
## Performance
### Use constexpr When Possible
```cpp
// Good: Computed at compile time
constexpr Vector3<float> gravity{0.0f, 0.0f, -9.81f};
constexpr float max_range = 1000.0f;
constexpr float max_range_sq = max_range * max_range;
// Use in runtime calculations
if (position.length_sqr() < max_range_sq) {
// ...
}
```
### Prefer Squared Distance
```cpp
// Good: Avoids expensive sqrt
constexpr float max_dist_sq = 100.0f * 100.0f;
for (const auto& entity : entities) {
if (entity.pos.distance_to_sqr(player_pos) < max_dist_sq) {
// Process nearby entity
}
}
// Avoid: Unnecessary sqrt calls
constexpr float max_dist = 100.0f;
for (const auto& entity : entities) {
if (entity.pos.distance_to(player_pos) < max_dist) {
// More expensive
}
}
```
### Cache Expensive Calculations
```cpp
// Good: Update camera once per frame
void update_frame() {
camera.update(current_position, current_angles);
// All projections use cached matrices
for (const auto& entity : entities) {
if (auto screen = camera.world_to_screen(entity.pos)) {
draw_entity(screen->x, screen->y);
}
}
}
// Bad: Camera recreated each call
for (const auto& entity : entities) {
Camera cam(pos, angles, viewport, fov, near, far); // Expensive!
auto screen = cam.world_to_screen(entity.pos);
}
```
### Choose the Right Engine
```cpp
// Good: Use AVX2 when available
#ifdef __AVX2__
using Engine = ProjPredEngineAVX2;
#else
using Engine = ProjPredEngineLegacy;
#endif
Engine prediction_engine;
// Or runtime detection
Engine* create_best_engine() {
if (cpu_supports_avx2()) {
return new ProjPredEngineAVX2();
}
return new ProjPredEngineLegacy();
}
```
### Minimize Allocations
```cpp
// Good: Reuse vectors
std::vector<Vector3<float>> positions;
positions.reserve(expected_count);
// In loop
positions.clear(); // Doesn't deallocate
for (...) {
positions.push_back(compute_position());
}
// Bad: Allocate every time
for (...) {
std::vector<Vector3<float>> positions; // Allocates each iteration
// ...
}
```
---
## Type Safety
### Use Strong Angle Types
```cpp
// Good: Type-safe angles
PitchAngle pitch = PitchAngle::from_degrees(45.0f);
YawAngle yaw = YawAngle::from_degrees(90.0f);
ViewAngles angles{pitch, yaw, RollAngle::from_degrees(0.0f)};
// Bad: Raw floats lose safety
float pitch = 45.0f; // No range checking
float yaw = 90.0f; // Can go out of bounds
```
### Match Engine Types
```cpp
// Good: Use matching types from same engine
using namespace omath::source_engine;
Camera camera = /* ... */;
ViewAngles angles = /* ... */;
// Bad: Mixing engine types
using UnityCamera = omath::unity_engine::Camera;
using SourceAngles = omath::source_engine::ViewAngles;
UnityCamera camera{pos, SourceAngles{}, ...}; // May cause issues!
```
### Template Type Parameters
```cpp
// Good: Explicit and clear
Vector3<float> position;
Vector3<double> high_precision_pos;
// Okay: Use default float
Vector3<> position; // Defaults to float
// Avoid: Mixing types unintentionally
Vector3<float> a;
Vector3<double> b;
auto result = a + b; // Type mismatch!
```
---
## Testing & Validation
### Test Edge Cases
```cpp
void test_projection() {
Camera camera = setup_camera();
// Test normal case
assert(camera.world_to_screen({100, 100, 100}).has_value());
// Test edge cases
assert(!camera.world_to_screen({0, 0, -100}).has_value()); // Behind
assert(!camera.world_to_screen({1e10, 0, 0}).has_value()); // Too far
// Test boundaries
Vector3<float> at_near{0, 0, camera.near_plane() + 0.1f};
assert(camera.world_to_screen(at_near).has_value());
}
```
### Validate Assumptions
```cpp
void validate_game_data() {
// Validate FOV
float fov = read_game_fov();
assert(fov > 1.0f && fov < 179.0f);
// Validate positions
Vector3<float> pos = read_player_position();
assert(std::isfinite(pos.x));
assert(std::isfinite(pos.y));
assert(std::isfinite(pos.z));
// Validate viewport
ViewPort vp = read_viewport();
assert(vp.width > 0 && vp.height > 0);
}
```
### Use Assertions
```cpp
// Good: Catch errors early in development
void shoot_projectile(const Projectile& proj) {
assert(proj.speed > 0.0f && "Projectile speed must be positive");
assert(std::isfinite(proj.origin.length()) && "Invalid projectile origin");
// Continue with logic
}
// Add debug-only checks
#ifndef NDEBUG
if (!is_valid_input(data)) {
std::cerr << "Warning: Invalid input detected\n";
}
#endif
```
---
## Memory & Resources
### RAII for Resources
```cpp
// Good: Automatic cleanup
class GameOverlay {
Camera camera_;
std::vector<Entity> entities_;
public:
GameOverlay(/* ... */) : camera_(/* ... */) {
entities_.reserve(1000);
}
// Resources cleaned up automatically
~GameOverlay() = default;
};
```
### Avoid Unnecessary Copies
```cpp
// Good: Pass by const reference
void draw_entities(const std::vector<Vector3<float>>& positions) {
for (const auto& pos : positions) {
// Process position
}
}
// Bad: Copies entire vector
void draw_entities(std::vector<Vector3<float>> positions) {
// Expensive copy!
}
// Good: Move when transferring ownership
std::vector<Vector3<float>> compute_positions();
auto positions = compute_positions(); // Move, not copy
```
### Use Structured Bindings
```cpp
// Good: Clear and concise
if (auto [success, screen_pos] = try_project(world_pos); success) {
draw_at(screen_pos.x, screen_pos.y);
}
// Good: Decompose results
auto [x, y, z] = position.as_tuple();
```
---
## Documentation
### Document Assumptions
```cpp
// Good: Clear documentation
/**
* Projects world position to screen space.
*
* @param world_pos Position in world coordinates (meters)
* @return Screen position if visible, nullopt if behind camera or out of view
*
* @note Assumes camera.update() was called this frame
* @note Screen coordinates are in viewport space [0, width] x [0, height]
*/
std::optional<Vector2<float>> project(const Vector3<float>& world_pos);
```
### Explain Non-Obvious Code
```cpp
// Good: Explain the math
// Use squared distance to avoid expensive sqrt
// max_range = 100.0 → max_range_sq = 10000.0
constexpr float max_range_sq = 100.0f * 100.0f;
if (dist_sq < max_range_sq) {
// Entity is in range
}
// Explain engine-specific quirks
// Source Engine uses Z-up coordinates, but angles are in degrees
// Pitch: [-89, 89], Yaw: [-180, 180], Roll: [-180, 180]
ViewAngles angles{pitch, yaw, roll};
```
---
## Debugging
### Add Debug Visualization
```cpp
#ifndef NDEBUG
void debug_draw_projection() {
// Draw camera frustum
draw_frustum(camera);
// Draw world axes
draw_line({0,0,0}, {100,0,0}, Color::Red); // X
draw_line({0,0,0}, {0,100,0}, Color::Green); // Y
draw_line({0,0,0}, {0,0,100}, Color::Blue); // Z
// Draw projected points
for (const auto& entity : entities) {
if (auto screen = camera.world_to_screen(entity.pos)) {
draw_cross(screen->x, screen->y);
}
}
}
#endif
```
### Log Important Values
```cpp
void debug_projection_failure(const Vector3<float>& pos) {
std::cerr << "Projection failed for position: "
<< pos.x << ", " << pos.y << ", " << pos.z << "\n";
auto view_matrix = camera.get_view_matrix();
std::cerr << "View matrix:\n";
// Print matrix...
std::cerr << "Camera position: "
<< camera.position().x << ", "
<< camera.position().y << ", "
<< camera.position().z << "\n";
}
```
### Use Debug Builds
```cmake
# CMakeLists.txt
if(CMAKE_BUILD_TYPE STREQUAL "Debug")
target_compile_definitions(your_target PRIVATE
DEBUG_PROJECTION=1
VALIDATE_INPUTS=1
)
endif()
```
```cpp
#ifdef DEBUG_PROJECTION
std::cout << "Projecting: " << world_pos << "\n";
#endif
#ifdef VALIDATE_INPUTS
assert(std::isfinite(world_pos.length()));
#endif
```
---
## Platform Considerations
### Cross-Platform Code
```cpp
// Good: Platform-agnostic
constexpr float PI = 3.14159265359f;
// Avoid: Platform-specific
#ifdef _WIN32
// Windows-only code
#endif
```
### Handle Different Compilers
```cpp
// Good: Compiler-agnostic
#if defined(_MSC_VER)
// MSVC-specific
#elif defined(__GNUC__)
// GCC/Clang-specific
#endif
// Use OMath's built-in compatibility
// It handles compiler differences automatically
```
---
## Summary
**Key principles:**
1. **Safety first**: Always check optional/expected results
2. **Performance matters**: Use constexpr, avoid allocations, cache results
3. **Type safety**: Use strong types, match engine types
4. **Clear code**: Use aliases, document assumptions, explain non-obvious logic
5. **Test thoroughly**: Validate inputs, test edge cases, add assertions
6. **Debug effectively**: Add visualization, log values, use debug builds
---
## See Also
- [Troubleshooting Guide](troubleshooting.md)
- [FAQ](faq.md)
- [API Overview](api_overview.md)
- [Tutorials](tutorials.md)
---
*Last updated: 1 Nov 2025*

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# `omath::collision::Ray` & `LineTracer` — Ray–Triangle intersection (Möller–Trumbore)
> Headers: your project’s `ray.hpp` (includes `omath/linear_algebra/triangle.hpp`, `omath/linear_algebra/vector3.hpp`)
> Namespace: `omath::collision`
> Depends on: `omath::Vector3<float>`, `omath::Triangle<Vector3<float>>`
> Algorithm: **Möller–Trumbore** ray–triangle intersection (no allocation)
---
## Overview
These types provide a minimal, fast path to test and compute intersections between a **ray or line segment** and a **single triangle**:
* `Ray` — start/end points plus a flag to treat the ray as **infinite** (half-line) or a **finite segment**.
* `LineTracer` — static helpers:
* `can_trace_line(ray, triangle)` → `true` if they intersect.
* `get_ray_hit_point(ray, triangle)` → the hit point (precondition: intersection exists).
---
## `Ray`
```cpp
class Ray {
public:
omath::Vector3<float> start; // ray origin
omath::Vector3<float> end; // end point (for finite segment) or a point along the direction
bool infinite_length = false;
[[nodiscard]] omath::Vector3<float> direction_vector() const noexcept;
[[nodiscard]] omath::Vector3<float> direction_vector_normalized() const noexcept;
};
```
### Semantics
* **Direction**: `direction_vector() == end - start`.
The normalized variant returns a unit vector (or `{0,0,0}` if the direction length is zero).
* **Extent**:
* `infinite_length == true` → treat as a **semi-infinite ray** from `start` along `direction`.
* `infinite_length == false` → treat as a **closed segment** from `start` to `end`.
> Tip: For an infinite ray that points along some vector `d`, set `end = start + d`.
---
## `LineTracer`
```cpp
class LineTracer {
public:
LineTracer() = delete;
[[nodiscard]]
static bool can_trace_line(
const Ray& ray,
const omath::Triangle<omath::Vector3<float>>& triangle
) noexcept;
// Möller–Trumbore intersection
[[nodiscard]]
static omath::Vector3<float> get_ray_hit_point(
const Ray& ray,
const omath::Triangle<omath::Vector3<float>>& triangle
) noexcept;
};
```
### Behavior & contract
* **Intersection test**: `can_trace_line` returns `true` iff the ray/segment intersects the triangle (within the ray’s extent).
* **Hit point**: `get_ray_hit_point` **assumes** there is an intersection.
Call **only after** `can_trace_line(...) == true`. Otherwise the result is unspecified.
* **Triangle winding**: Standard Möller–Trumbore works with either winding; no backface culling is implied here.
* **Degenerate inputs**: A zero-length ray or degenerate triangle yields **no hit** under typical Möller–Trumbore tolerances.
---
## Quick examples
### 1) Segment vs triangle
```cpp
using omath::Vector3;
using omath::Triangle;
using omath::collision::Ray;
using omath::collision::LineTracer;
Triangle<Vector3<float>> tri(
Vector3<float>{0, 0, 0},
Vector3<float>{1, 0, 0},
Vector3<float>{0, 1, 0}
);
Ray seg;
seg.start = {0.25f, 0.25f, 1.0f};
seg.end = {0.25f, 0.25f,-1.0f};
seg.infinite_length = false; // finite segment
if (LineTracer::can_trace_line(seg, tri)) {
Vector3<float> hit = LineTracer::get_ray_hit_point(seg, tri);
// use hit
}
```
### 2) Infinite ray
```cpp
Ray ray;
ray.start = {0.5f, 0.5f, 1.0f};
ray.end = ray.start + Vector3<float>{0, 0, -1}; // direction only
ray.infinite_length = true;
bool hit = LineTracer::can_trace_line(ray, tri);
```
---
## Notes & edge cases
* **Normalization**: `direction_vector_normalized()` returns `{0,0,0}` for a zero-length direction (safe, but unusable for tracing).
* **Precision**: The underlying algorithm uses EPS thresholds to reject nearly parallel cases; results near edges can be sensitive to floating-point error. If you need robust edge inclusion/exclusion, document and enforce a policy (e.g., inclusive barycentric range with small epsilon).
* **Hit location**: The point returned by `get_ray_hit_point` lies **on the triangle plane** and within its area by construction (when `can_trace_line` is `true`).
---
## API summary
```cpp
namespace omath::collision {
class Ray {
public:
Vector3<float> start, end;
bool infinite_length = false;
[[nodiscard]] Vector3<float> direction_vector() const noexcept;
[[nodiscard]] Vector3<float> direction_vector_normalized() const noexcept;
};
class LineTracer {
public:
LineTracer() = delete;
[[nodiscard]] static bool can_trace_line(
const Ray&,
const omath::Triangle<omath::Vector3<float>>&
) noexcept;
[[nodiscard]] static Vector3<float> get_ray_hit_point(
const Ray&,
const omath::Triangle<omath::Vector3<float>>&
) noexcept; // precondition: can_trace_line(...) == true
};
} // namespace omath::collision
```
---
## Implementation hints (if you extend it)
* Expose a variant that returns **barycentric coordinates** `(u, v, w)` alongside the hit point to support texture lookup or edge tests.
* Provide an overload returning `std::optional<Vector3<float>>` (or `expected`) for safer one-shot queries without a separate test call.
* If you need backface culling, add a flag or dedicated function (reject hits where the signed distance is negative with respect to triangle normal).
---
## See Also
- [Plane Documentation](../3d_primitives/plane.md) - Ray-plane intersection
- [Box Documentation](../3d_primitives/box.md) - AABB collision detection
- [Triangle Documentation](../linear_algebra/triangle.md) - Triangle primitives
- [Tutorials - Collision Detection](../tutorials.md#tutorial-4-collision-detection) - Complete collision tutorial
- [Getting Started Guide](../getting_started.md) - Quick start with OMath
---
*Last updated: 1 Nov 2025*

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# `omath::frostbite_engine::CameraTrait` — plug-in trait for `projection::Camera`
> Header: `omath/engines/frostbite_engine/traits/camera_trait.hpp` • Impl: `omath/engines/frostbite_engine/traits/camera_trait.cpp`
> Namespace: `omath::frostbite_engine`
> Purpose: provide Frostbite-style **look-at**, **view**, and **projection** math to the generic `omath::projection::Camera` (satisfies `CameraEngineConcept`).
---
## Summary
`CameraTrait` exposes three `static` functions:
* `calc_look_at_angle(origin, look_at)` – computes Euler angles so the camera at `origin` looks at `look_at`. Implementation normalizes the direction, computes **pitch** as `-asin(dir.y)` and **yaw** as `atan2(dir.x, dir.z)`; **roll** is `0`. Pitch/yaw are returned using the project’s strong angle types (`PitchAngle`, `YawAngle`, `RollAngle`).
* `calc_view_matrix(angles, origin)` – delegates to Frostbite formulas `frostbite_engine::calc_view_matrix`, producing a `Mat4X4` view matrix for the given angles and origin.
* `calc_projection_matrix(fov, viewport, near, far)` – builds a perspective projection by calling `calc_perspective_projection_matrix(fov_degrees, aspect, near, far)`, where `aspect = viewport.aspect_ratio()`. Accepts `FieldOfView` (degrees).
The trait’s types (`ViewAngles`, `Mat4X4`, angle aliases) and helpers live in the Frostbite engine math headers included by the trait (`formulas.hpp`) and the shared projection header (`projection/camera.hpp`).
---
## API
```cpp
namespace omath::frostbite_engine {
class CameraTrait final {
public:
// Compute Euler angles (pitch/yaw/roll) to look from cam_origin to look_at.
static ViewAngles
calc_look_at_angle(const Vector3<float>& cam_origin,
const Vector3<float>& look_at) noexcept;
// Build view matrix for given angles and origin.
static Mat4X4
calc_view_matrix(const ViewAngles& angles,
const Vector3<float>& cam_origin) noexcept;
// Build perspective projection from FOV (deg), viewport, near/far.
static Mat4X4
calc_projection_matrix(const projection::FieldOfView& fov,
const projection::ViewPort& view_port,
float near, float far) noexcept;
};
} // namespace omath::frostbite_engine
```
Uses: `Vector3<float>`, `ViewAngles` (pitch/yaw/roll), `Mat4X4`, `projection::FieldOfView`, `projection::ViewPort`.
---
## Behavior & conventions
* **Angles from look-at**:
```
dir = normalize(look_at - origin)
pitch = -asin(dir.y) // +Y is up
yaw = atan2(dir.x, dir.z)
roll = 0
```
Returned as `PitchAngle::from_radians(...)`, `YawAngle::from_radians(...)`, etc.
* **View matrix**: built by the Frostbite engine helper `frostbite_engine::calc_view_matrix(angles, origin)` to match the engine’s handedness and axis conventions.
* **Projection**: uses `calc_perspective_projection_matrix(fov.as_degrees(), viewport.aspect_ratio(), near, far)`. Pass your **vertical FOV** in degrees via `FieldOfView`; the helper computes a standard perspective matrix.
---
## Using with `projection::Camera`
Create a camera whose math is driven by this trait:
```cpp
using Mat4 = Mat4X4; // from Frostbite math headers
using Angs = ViewAngles; // pitch/yaw/roll type
using FBcam = omath::projection::Camera<Mat4, Angs, omath::frostbite_engine::CameraTrait>;
omath::projection::ViewPort vp{1920.f, 1080.f};
auto fov = omath::projection::FieldOfView::from_degrees(70.f);
FBcam cam(
/*position*/ {0.f, 1.7f, -3.f},
/*angles*/ omath::frostbite_engine::CameraTrait::calc_look_at_angle({0,1.7f,-3},{0,1.7f,0}),
/*viewport*/ vp,
/*fov*/ fov,
/*near*/ 0.1f,
/*far*/ 1000.f
);
```
This satisfies `CameraEngineConcept` expected by `projection::Camera` (look-at, view, projection) as declared in the trait header.
---
## Notes & tips
* Ensure your `ViewAngles` aliases (`PitchAngle`, `YawAngle`, `RollAngle`) match the project’s angle policy (ranges/normalization). The implementation constructs them **from radians**.
* `aspect_ratio()` is taken directly from `ViewPort` (`width / height`), so keep both positive and non-zero.
* `near` must be > 0 and `< far` for a valid projection matrix (enforced by your math helpers).
---
## See also
* Frostbite math helpers in `omath/engines/frostbite_engine/formulas.hpp` (view/projection builders used above).
* Generic camera wrapper `omath::projection::Camera` and its `CameraEngineConcept` (this trait is designed to plug straight into it).

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Nice! A clean little “types + constants” header. A few quick fixes and polish:
## Issues / suggestions
1. **Mat3X3 alias is wrong**
* You wrote `using Mat3X3 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;`
* That should be `Mat<3, 3, ...>`.
2. **`constexpr` globals in a header → make them `inline constexpr`**
* Since this is in a header included by multiple TUs, use `inline constexpr` to avoid ODR/link issues (C++17+).
3. **Consider column-major vs row-major**
* Most game/graphics stacks (GLSL/HLSL, many engines) lean column-major and column vectors. If the rest of your math lib or shaders assume column-major, align these typedefs now to avoid silent transposes later. If row-major is intentional, all good—just be consistent.
4. **Naming consistency**
* If you prefer `k_` prefix, keep it; otherwise consider `kAbsUp`/`ABS_UP` to match your codebase’s conventions.
5. **`Mat1X3` as a “row vector”**
* If you actually use it as a 3-component vector, consider just `Vector3<float>` (clearer) and reserve `Mat1X3` for real row-vector math.
---
## Tidied version
```cpp
// Created by Vlad on 10/21/2025.
#pragma once
#include "omath/linear_algebra/mat.hpp"
#include "omath/linear_algebra/vector3.hpp"
#include <omath/trigonometry/angle.hpp>
#include <omath/trigonometry/view_angles.hpp>
namespace omath::frostbite_engine
{
// Inline to avoid ODR across translation units
inline constexpr Vector3<float> k_abs_up = {0.0f, 1.0f, 0.0f};
inline constexpr Vector3<float> k_abs_right = {1.0f, 0.0f, 0.0f};
inline constexpr Vector3<float> k_abs_forward = {0.0f, 0.0f, 1.0f};
// NOTE: verify row/column major matches the rest of your engine
using Mat4X4 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;
using Mat3X3 = Mat<3, 3, float, MatStoreType::ROW_MAJOR>;
using Mat1X3 = Mat<1, 3, float, MatStoreType::ROW_MAJOR>;
using PitchAngle = Angle<float, -90.0f, 90.0f, AngleFlags::Clamped >;
using YawAngle = Angle<float,-180.0f, 180.0f, AngleFlags::Normalized>;
using RollAngle = Angle<float,-180.0f, 180.0f, AngleFlags::Normalized>;
using ViewAngles = omath::ViewAngles<PitchAngle, YawAngle, RollAngle>;
} // namespace omath::frostbite_engine
```
If you share how your matrices multiply vectors (row vs column) and your world handedness, I can double-check the axis constants and angle normalization to make sure yaw/pitch signs line up with your camera and `atan2` usage.

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// Created by Vlad on 8/6/2025.
#pragma once
#include <cmath> // sqrt, hypot, tan, asin, atan2
#include <optional>
#include "omath/engines/frostbite_engine/formulas.hpp"
#include "omath/projectile_prediction/projectile.hpp"
#include "omath/projectile_prediction/target.hpp"
namespace omath::frostbite_engine
{
class PredEngineTrait final
{
public:
// Predict projectile position given launch angles (degrees), time (s), and world gravity (m/s^2).
// Note: kept runtime function; remove constexpr to avoid CTAD surprises across toolchains.
static Vector3<float> predict_projectile_position(
const projectile_prediction::Projectile& projectile,
float pitch_deg, float yaw_deg,
float time, float gravity) noexcept
{
// Engine convention: negative pitch looks up (your original used -pitch).
const auto fwd = forward_vector({
PitchAngle::from_degrees(-pitch_deg),
YawAngle::from_degrees(yaw_deg),
RollAngle::from_degrees(0.0f)
});
Vector3<float> pos =
projectile.m_origin +
fwd * (projectile.m_launch_speed * time);
// s = 1/2 a t^2 downward
pos.y -= (gravity * projectile.m_gravity_scale) * (time * time) * 0.5f;
return pos;
}
[[nodiscard]]
static Vector3<float> predict_target_position(
const projectile_prediction::Target& target,
float time, float gravity) noexcept
{
Vector3<float> predicted = target.m_origin + target.m_velocity * time;
if (target.m_is_airborne) {
// If targets also have a gravity scale in your model, multiply here.
predicted.y -= gravity * (time * time) * 0.5f;
}
return predicted;
}
[[nodiscard]]
static float calc_vector_2d_distance(const Vector3<float>& delta) noexcept
{
// More stable than sqrt(x*x + z*z)
return std::hypot(delta.x, delta.z);
}
[[nodiscard]]
static float get_vector_height_coordinate(const Vector3<float>& vec) noexcept
{
return vec.y;
}
// Computes a viewpoint above the predicted target, using an optional projectile pitch.
// If pitch is absent, we leave Y unchanged (or you can choose a sensible default).
[[nodiscard]]
static Vector3<float> calc_viewpoint_from_angles(
const projectile_prediction::Projectile& projectile,
const Vector3<float>& predicted_target_position,
const std::optional<float> projectile_pitch_deg) noexcept
{
// Lateral separation from projectile to target (X/Z plane).
const auto delta2d = calc_vector_2d_distance(predicted_target_position - projectile.m_origin);
float y = predicted_target_position.y;
if (projectile_pitch_deg.has_value()) {
const float pitch_rad = angles::degrees_to_radians(*projectile_pitch_deg);
const float height = delta2d * std::tan(pitch_rad);
y += height;
}
// Use the target's Z, not the projectile's Z (likely bugfix).
return { predicted_target_position.x, y, predicted_target_position.z };
}
// Due to maybe_calculate_projectile_launch_pitch_angle spec: +89° up, -89° down.
[[nodiscard]]
static float calc_direct_pitch_angle(const Vector3<float>& origin,
const Vector3<float>& view_to) noexcept
{
const auto direction = (view_to - origin).normalized();
return angles::radians_to_degrees(std::asin(direction.y));
}
[[nodiscard]]
static float calc_direct_yaw_angle(const Vector3<float>& origin,
const Vector3<float>& view_to) noexcept
{
const auto direction = (view_to - origin).normalized();
return angles::radians_to_degrees(std::atan2(direction.x, direction.z));
}
};
} // namespace omath::frostbite_engine

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# `omath::iw_engine::CameraTrait` — plug-in trait for `projection::Camera`
> Header: `omath/engines/iw_engine/traits/camera_trait.hpp` • Impl: `omath/engines/iw_engine/traits/camera_trait.cpp`
> Namespace: `omath::iw_engine`
> Purpose: provide IW Engine (Call of Duty)-style **look-at**, **view**, and **projection** math to the generic `omath::projection::Camera` (satisfies `CameraEngineConcept`).
---
## Summary
`CameraTrait` exposes three `static` functions:
* `calc_look_at_angle(origin, look_at)` – computes Euler angles so the camera at `origin` looks at `look_at`. Implementation normalizes the direction, computes **pitch** as `asin(dir.z)` and **yaw** as `atan2(dir.y, dir.x)`; **roll** is `0`. Pitch/yaw are returned using the project's strong angle types (`PitchAngle`, `YawAngle`, `RollAngle`).
* `calc_view_matrix(angles, origin)` – delegates to IW Engine formulas `iw_engine::calc_view_matrix`, producing a `Mat4X4` view matrix for the given angles and origin.
* `calc_projection_matrix(fov, viewport, near, far)` – builds a perspective projection by calling `calc_perspective_projection_matrix(fov_degrees, aspect, near, far)`, where `aspect = viewport.aspect_ratio()`. Accepts `FieldOfView` (degrees).
The trait's types (`ViewAngles`, `Mat4X4`, angle aliases) and helpers live in the IW Engine math headers included by the trait (`formulas.hpp`) and the shared projection header (`projection/camera.hpp`).
---
## API
```cpp
namespace omath::iw_engine {
class CameraTrait final {
public:
// Compute Euler angles (pitch/yaw/roll) to look from cam_origin to look_at.
static ViewAngles
calc_look_at_angle(const Vector3<float>& cam_origin,
const Vector3<float>& look_at) noexcept;
// Build view matrix for given angles and origin.
static Mat4X4
calc_view_matrix(const ViewAngles& angles,
const Vector3<float>& cam_origin) noexcept;
// Build perspective projection from FOV (deg), viewport, near/far.
static Mat4X4
calc_projection_matrix(const projection::FieldOfView& fov,
const projection::ViewPort& view_port,
float near, float far) noexcept;
};
} // namespace omath::iw_engine
```
Uses: `Vector3<float>`, `ViewAngles` (pitch/yaw/roll), `Mat4X4`, `projection::FieldOfView`, `projection::ViewPort`.
---
## Behavior & conventions
* **Angles from look-at** (Z-up coordinate system):
```
dir = normalize(look_at - origin)
pitch = asin(dir.z) // +Z is up
yaw = atan2(dir.y, dir.x) // horizontal rotation
roll = 0
```
Returned as `PitchAngle::from_radians(...)`, `YawAngle::from_radians(...)`, etc.
* **View matrix**: built by the IW Engine helper `iw_engine::calc_view_matrix(angles, origin)` to match the engine's handedness and axis conventions.
* **Projection**: uses `calc_perspective_projection_matrix(fov.as_degrees(), viewport.aspect_ratio(), near, far)`. Pass your **vertical FOV** in degrees via `FieldOfView`; the helper computes a standard perspective matrix.
---
## Using with `projection::Camera`
Create a camera whose math is driven by this trait:
```cpp
using Mat4 = Mat4X4; // from IW Engine math headers
using Angs = ViewAngles; // pitch/yaw/roll type
using IWcam = omath::projection::Camera<Mat4, Angs, omath::iw_engine::CameraTrait>;
omath::projection::ViewPort vp{1920.f, 1080.f};
auto fov = omath::projection::FieldOfView::from_degrees(65.f);
IWcam cam(
/*position*/ {500.f, 200.f, 100.f},
/*angles*/ omath::iw_engine::CameraTrait::calc_look_at_angle({500,200,100},{0,0,100}),
/*viewport*/ vp,
/*fov*/ fov,
/*near*/ 0.1f,
/*far*/ 5000.f
);
```
This satisfies `CameraEngineConcept` expected by `projection::Camera` (look-at, view, projection) as declared in the trait header.
---
## Notes & tips
* Ensure your `ViewAngles` aliases (`PitchAngle`, `YawAngle`, `RollAngle`) match the project's angle policy (ranges/normalization). The implementation constructs them **from radians**.
* `aspect_ratio()` is taken directly from `ViewPort` (`width / height`), so keep both positive and non-zero.
* `near` must be > 0 and `< far` for a valid projection matrix (enforced by your math helpers).
* IW Engine uses **Z-up**: pitch angles control vertical look, positive = up.
---
## See also
* IW Engine math helpers in `omath/engines/iw_engine/formulas.hpp` (view/projection builders used above).
* Generic camera wrapper `omath::projection::Camera` and its `CameraEngineConcept` (this trait is designed to plug straight into it).

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# `omath::iw_engine` — types & constants
> Header: `omath/engines/iw_engine/constants.hpp`
> Namespace: `omath::iw_engine`
> Purpose: define IW Engine (Call of Duty) coordinate system, matrix types, and angle ranges
---
## Summary
The **IW Engine** (Infinity Ward Engine, used in Call of Duty series) uses a **Z-up, right-handed** coordinate system:
* **Up** = `{0, 0, 1}` (Z-axis)
* **Right** = `{0, -1, 0}` (negative Y-axis)
* **Forward** = `{1, 0, 0}` (X-axis)
Matrices are **row-major**. Angles are **clamped pitch** (±89°) and **normalized yaw/roll** (±180°).
---
## Constants
```cpp
namespace omath::iw_engine {
constexpr Vector3<float> k_abs_up = {0, 0, 1};
constexpr Vector3<float> k_abs_right = {0, -1, 0};
constexpr Vector3<float> k_abs_forward = {1, 0, 0};
}
```
These basis vectors define the engine's **world coordinate frame**.
---
## Matrix types
```cpp
using Mat4X4 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;
using Mat3X3 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;
using Mat1X3 = Mat<1, 3, float, MatStoreType::ROW_MAJOR>;
```
**Row-major** storage means rows are contiguous in memory. Suitable for CPU-side transforms and typical C++ math libraries.
---
## Angle types
```cpp
using PitchAngle = Angle<float, -89.f, 89.f, AngleFlags::Clamped>;
using YawAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
using RollAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
using ViewAngles = omath::ViewAngles<PitchAngle, YawAngle, RollAngle>;
```
* **PitchAngle**: clamped to **[-89°, +89°]** (looking down vs. up)
* **YawAngle**: normalized to **[-180°, +180°]** (horizontal rotation)
* **RollAngle**: normalized to **[-180°, +180°]** (camera roll)
`ViewAngles` bundles all three into a single type for camera/view transforms.
---
## Coordinate system notes
* **Z-up**: gravity points along `-Z`, height increases with `+Z`
* **Right-handed**: cross product `forward × right = up` holds
* This matches **IW Engine** (Call of Duty series: Modern Warfare, Black Ops, etc.) conventions
---
## See also
* `omath/engines/iw_engine/formulas.hpp` — view/projection matrix builders
* `omath/trigonometry/angle.hpp` — angle normalization & clamping helpers
* `omath/trigonometry/view_angles.hpp` — generic pitch/yaw/roll wrapper

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# `omath::iw_engine` — formulas & matrix helpers
> Header: `omath/engines/iw_engine/formulas.hpp`
> Namespace: `omath::iw_engine`
> Purpose: compute direction vectors, rotation matrices, view matrices, and perspective projections for IW Engine (Call of Duty)
---
## Summary
This header provides **IW Engine**-specific math for:
* **Direction vectors** (`forward`, `right`, `up`) from `ViewAngles`
* **Rotation matrices** from Euler angles
* **View matrices** (camera transforms)
* **Perspective projection** matrices
All functions respect IW Engine's **Z-up, right-handed** coordinate system.
---
## API
```cpp
namespace omath::iw_engine {
// Compute forward direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> forward_vector(const ViewAngles& angles) noexcept;
// Compute right direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> right_vector(const ViewAngles& angles) noexcept;
// Compute up direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> up_vector(const ViewAngles& angles) noexcept;
// Build 3x3 rotation matrix from angles
[[nodiscard]]
Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept;
// Build view matrix (camera space transform)
[[nodiscard]]
Mat4X4 calc_view_matrix(const ViewAngles& angles,
const Vector3<float>& cam_origin) noexcept;
// Build perspective projection matrix
[[nodiscard]]
Mat4X4 calc_perspective_projection_matrix(float field_of_view,
float aspect_ratio,
float near, float far) noexcept;
} // namespace omath::iw_engine
```
---
## Direction vectors
Given camera angles (pitch/yaw/roll):
* `forward_vector(angles)` → unit vector pointing where the camera looks
* `right_vector(angles)` → unit vector pointing to the camera's right
* `up_vector(angles)` → unit vector pointing upward relative to the camera
These are used for movement, aim direction, and building coordinate frames.
---
## Rotation & view matrices
* `rotation_matrix(angles)` → 3×3 (or 4×4) rotation matrix from Euler angles
* `calc_view_matrix(angles, origin)` → camera view matrix
The view matrix transforms world coordinates into camera space (origin at camera, axes aligned with camera orientation).
---
## Perspective projection
```cpp
Mat4X4 proj = calc_perspective_projection_matrix(
fov_degrees, // vertical field of view (e.g., 65)
aspect_ratio, // width / height (e.g., 16/9)
near_plane, // e.g., 0.1
far_plane // e.g., 5000.0
);
```
Produces a **perspective projection matrix** suitable for 3D rendering pipelines. Combined with the view matrix, this implements the standard camera transform chain.
---
## Usage example
```cpp
using namespace omath::iw_engine;
// Camera setup
ViewAngles angles = {
PitchAngle::from_degrees(-10.0f),
YawAngle::from_degrees(90.0f),
RollAngle::from_degrees(0.0f)
};
Vector3<float> cam_pos{500.0f, 200.0f, 100.0f};
// Compute direction
auto forward = forward_vector(angles);
auto right = right_vector(angles);
auto up = up_vector(angles);
// Build matrices
auto view_mat = calc_view_matrix(angles, cam_pos);
auto proj_mat = calc_perspective_projection_matrix(65.0f, 16.0f/9.0f, 0.1f, 5000.0f);
// Use view_mat and proj_mat for rendering...
```
---
## Conventions
* **Angles**: pitch (up/down), yaw (left/right), roll (tilt)
* **Pitch**: positive = looking up, negative = looking down
* **Yaw**: increases counter-clockwise from the +X axis
* **Coordinate system**: Z-up, X-forward, Y-right (negative in code convention)
---
## See also
* `omath/engines/iw_engine/constants.hpp` — coordinate frame & angle types
* `omath/engines/iw_engine/traits/camera_trait.hpp` — plug-in for generic `Camera`
* `omath/projection/camera.hpp` — generic camera wrapper using these formulas

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# `omath::iw_engine::PredEngineTrait` — projectile prediction trait
> Header: `omath/engines/iw_engine/traits/pred_engine_trait.hpp`
> Namespace: `omath::iw_engine`
> Purpose: provide IW Engine (Call of Duty)-specific projectile and target prediction for ballistic calculations
---
## Summary
`PredEngineTrait` implements engine-specific helpers for **projectile prediction**:
* `predict_projectile_position` – computes where a projectile will be after `time` seconds
* `predict_target_position` – computes where a moving target will be after `time` seconds
* `calc_vector_2d_distance` – horizontal distance (X/Y plane, ignoring Z)
* `get_vector_height_coordinate` – extracts vertical coordinate (Z in IW Engine)
* `calc_viewpoint_from_angles` – computes aim point given pitch angle
* `calc_direct_pitch_angle` – pitch angle to look from origin to target
* `calc_direct_yaw_angle` – yaw angle to look from origin to target
These methods satisfy the `PredEngineTraitConcept` required by generic projectile prediction algorithms.
---
## API
```cpp
namespace omath::iw_engine {
class PredEngineTrait final {
public:
// Predict projectile position after `time` seconds
static constexpr Vector3<float>
predict_projectile_position(const projectile_prediction::Projectile& projectile,
float pitch, float yaw, float time,
float gravity) noexcept;
// Predict target position after `time` seconds
static constexpr Vector3<float>
predict_target_position(const projectile_prediction::Target& target,
float time, float gravity) noexcept;
// Compute horizontal (2D) distance
static float
calc_vector_2d_distance(const Vector3<float>& delta) noexcept;
// Get vertical coordinate (Z in IW Engine)
static constexpr float
get_vector_height_coordinate(const Vector3<float>& vec) noexcept;
// Compute aim point from angles
static Vector3<float>
calc_viewpoint_from_angles(const projectile_prediction::Projectile& projectile,
Vector3<float> predicted_target_position,
std::optional<float> projectile_pitch) noexcept;
// Compute pitch angle to look at target
static float
calc_direct_pitch_angle(const Vector3<float>& origin,
const Vector3<float>& view_to) noexcept;
// Compute yaw angle to look at target
static float
calc_direct_yaw_angle(const Vector3<float>& origin,
const Vector3<float>& view_to) noexcept;
};
} // namespace omath::iw_engine
```
---
## Projectile prediction
```cpp
auto pos = PredEngineTrait::predict_projectile_position(
projectile, // initial position, speed, gravity scale
pitch_deg, // launch pitch (positive = up)
yaw_deg, // launch yaw
time, // time in seconds
gravity // gravity constant (e.g., 800 units/s²)
);
```
Computes:
1. Forward vector from pitch/yaw (using `forward_vector`)
2. Initial velocity: `forward * launch_speed`
3. Position after `time`: `origin + velocity*time - 0.5*gravity*gravityScale*time²` (Z component only)
**Note**: Negative pitch in `forward_vector` convention → positive pitch looks up.
---
## Target prediction
```cpp
auto pos = PredEngineTrait::predict_target_position(
target, // position, velocity, airborne flag
time, // time in seconds
gravity // gravity constant
);
```
Simple linear extrapolation plus gravity if target is airborne:
```
predicted = origin + velocity * time
if (airborne)
predicted.z -= 0.5 * gravity * time²
```
---
## Distance & height helpers
* `calc_vector_2d_distance(delta)` → `sqrt(delta.x² + delta.y²)` (horizontal distance)
* `get_vector_height_coordinate(vec)` → `vec.z` (vertical coordinate in IW Engine)
Used to compute ballistic arc parameters.
---
## Aim angle calculation
* `calc_direct_pitch_angle(origin, target)` → pitch in degrees to look from `origin` to `target`
- Formula: `asin(Δz / distance)` converted to degrees
- Positive = looking up, negative = looking down
* `calc_direct_yaw_angle(origin, target)` → yaw in degrees to look from `origin` to `target`
- Formula: `atan2(Δy, Δx)` converted to degrees
- Horizontal rotation around Z-axis
---
## Viewpoint from angles
```cpp
auto aim_point = PredEngineTrait::calc_viewpoint_from_angles(
projectile,
predicted_target_pos,
optional_pitch_deg
);
```
Computes where to aim in 3D space given a desired pitch angle. Uses horizontal distance and `tan(pitch)` to compute height offset.
---
## Conventions
* **Coordinate system**: Z-up (height increases with Z)
* **Angles**: pitch in [-89°, +89°], yaw in [-180°, +180°]
* **Gravity**: applied downward along -Z axis
* **Pitch convention**: +89° = straight up, -89° = straight down
---
## Usage example
```cpp
using namespace omath::iw_engine;
using namespace omath::projectile_prediction;
Projectile proj{
.m_origin = {0, 0, 100},
.m_launch_speed = 1200.0f,
.m_gravity_scale = 1.0f
};
Target tgt{
.m_origin = {800, 300, 100},
.m_velocity = {15, 8, 0},
.m_is_airborne = false
};
float gravity = 800.0f;
float time = 0.5f;
// Predict where target will be
auto target_pos = PredEngineTrait::predict_target_position(tgt, time, gravity);
// Compute aim angles
float pitch = PredEngineTrait::calc_direct_pitch_angle(proj.m_origin, target_pos);
float yaw = PredEngineTrait::calc_direct_yaw_angle(proj.m_origin, target_pos);
// Predict projectile position with those angles
auto proj_pos = PredEngineTrait::predict_projectile_position(proj, pitch, yaw, time, gravity);
```
---
## See also
* `omath/engines/iw_engine/formulas.hpp` — direction vectors and matrix builders
* `omath/projectile_prediction/projectile.hpp` — `Projectile` struct
* `omath/projectile_prediction/target.hpp` — `Target` struct
* Generic projectile prediction algorithms that use `PredEngineTraitConcept`

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# `omath::opengl_engine::CameraTrait` — plug-in trait for `projection::Camera`
> Header: `omath/engines/opengl_engine/traits/camera_trait.hpp` • Impl: `omath/engines/opengl_engine/traits/camera_trait.cpp`
> Namespace: `omath::opengl_engine`
> Purpose: provide OpenGL-style **look-at**, **view**, and **projection** math to the generic `omath::projection::Camera` (satisfies `CameraEngineConcept`).
---
## Summary
`CameraTrait` exposes three `static` functions:
* `calc_look_at_angle(origin, look_at)` – computes Euler angles so the camera at `origin` looks at `look_at`. Implementation normalizes the direction, computes **pitch** as `asin(dir.y)` and **yaw** as `-atan2(dir.x, -dir.z)`; **roll** is `0`. Pitch/yaw are returned using the project's strong angle types (`PitchAngle`, `YawAngle`, `RollAngle`).
* `calc_view_matrix(angles, origin)` – delegates to OpenGL formulas `opengl_engine::calc_view_matrix`, producing a `Mat4X4` view matrix (column-major) for the given angles and origin.
* `calc_projection_matrix(fov, viewport, near, far)` – builds a perspective projection by calling `calc_perspective_projection_matrix(fov_degrees, aspect, near, far)`, where `aspect = viewport.aspect_ratio()`. Accepts `FieldOfView` (degrees).
The trait's types (`ViewAngles`, `Mat4X4`, angle aliases) and helpers live in the OpenGL math headers included by the trait (`formulas.hpp`) and the shared projection header (`projection/camera.hpp`).
---
## API
```cpp
namespace omath::opengl_engine {
class CameraTrait final {
public:
// Compute Euler angles (pitch/yaw/roll) to look from cam_origin to look_at.
static ViewAngles
calc_look_at_angle(const Vector3<float>& cam_origin,
const Vector3<float>& look_at) noexcept;
// Build view matrix for given angles and origin (column-major).
static Mat4X4
calc_view_matrix(const ViewAngles& angles,
const Vector3<float>& cam_origin) noexcept;
// Build perspective projection from FOV (deg), viewport, near/far (column-major).
static Mat4X4
calc_projection_matrix(const projection::FieldOfView& fov,
const projection::ViewPort& view_port,
float near, float far) noexcept;
};
} // namespace omath::opengl_engine
```
Uses: `Vector3<float>`, `ViewAngles` (pitch/yaw/roll), `Mat4X4`, `projection::FieldOfView`, `projection::ViewPort`.
---
## Behavior & conventions
* **Angles from look-at** (Y-up, -Z forward coordinate system):
```
dir = normalize(look_at - origin)
pitch = asin(dir.y) // +Y is up
yaw = -atan2(dir.x, -dir.z) // horizontal rotation
roll = 0
```
Returned as `PitchAngle::from_radians(...)`, `YawAngle::from_radians(...)`, etc.
* **View matrix**: built by the OpenGL helper `opengl_engine::calc_view_matrix(angles, origin)` to match OpenGL's right-handed, Y-up, -Z forward conventions. Matrix is **column-major**.
* **Projection**: uses `calc_perspective_projection_matrix(fov.as_degrees(), viewport.aspect_ratio(), near, far)`. Pass your **vertical FOV** in degrees via `FieldOfView`; the helper computes a standard perspective matrix (column-major).
---
## Using with `projection::Camera`
Create a camera whose math is driven by this trait:
```cpp
using Mat4 = Mat4X4; // from OpenGL math headers (column-major)
using Angs = ViewAngles; // pitch/yaw/roll type
using GLcam = omath::projection::Camera<Mat4, Angs, omath::opengl_engine::CameraTrait>;
omath::projection::ViewPort vp{1920.f, 1080.f};
auto fov = omath::projection::FieldOfView::from_degrees(45.f);
GLcam cam(
/*position*/ {5.f, 3.f, 5.f},
/*angles*/ omath::opengl_engine::CameraTrait::calc_look_at_angle({5,3,5},{0,0,0}),
/*viewport*/ vp,
/*fov*/ fov,
/*near*/ 0.1f,
/*far*/ 100.f
);
```
This satisfies `CameraEngineConcept` expected by `projection::Camera` (look-at, view, projection) as declared in the trait header.
---
## Notes & tips
* Ensure your `ViewAngles` aliases (`PitchAngle`, `YawAngle`, `RollAngle`) match the project's angle policy (ranges/normalization). The implementation constructs them **from radians**.
* `aspect_ratio()` is taken directly from `ViewPort` (`width / height`), so keep both positive and non-zero.
* `near` must be > 0 and `< far` for a valid projection matrix (enforced by your math helpers).
* OpenGL uses **Y-up, -Z forward**: pitch angles control vertical look (positive = up), yaw controls horizontal rotation.
* Matrices are **column-major** (no transpose needed for OpenGL shaders).
---
## See also
* OpenGL math helpers in `omath/engines/opengl_engine/formulas.hpp` (view/projection builders used above).
* Generic camera wrapper `omath::projection::Camera` and its `CameraEngineConcept` (this trait is designed to plug straight into it).

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# `omath::opengl_engine` — types & constants
> Header: `omath/engines/opengl_engine/constants.hpp`
> Namespace: `omath::opengl_engine`
> Purpose: define OpenGL coordinate system, matrix types, and angle ranges
---
## Summary
The **OpenGL Engine** uses a **Y-up, right-handed** coordinate system:
* **Up** = `{0, 1, 0}` (Y-axis)
* **Right** = `{1, 0, 0}` (X-axis)
* **Forward** = `{0, 0, -1}` (negative Z-axis)
Matrices are **column-major**. Angles are **clamped pitch** (±90°) and **normalized yaw/roll** (±180°).
---
## Constants
```cpp
namespace omath::opengl_engine {
constexpr Vector3<float> k_abs_up = {0, 1, 0};
constexpr Vector3<float> k_abs_right = {1, 0, 0};
constexpr Vector3<float> k_abs_forward = {0, 0, -1};
}
```
These basis vectors define the engine's **world coordinate frame**.
---
## Matrix types
```cpp
using Mat4X4 = Mat<4, 4, float, MatStoreType::COLUMN_MAJOR>;
using Mat3X3 = Mat<4, 4, float, MatStoreType::COLUMN_MAJOR>;
using Mat1X3 = Mat<1, 3, float, MatStoreType::COLUMN_MAJOR>;
```
**Column-major** storage means columns are contiguous in memory. This matches OpenGL's native matrix layout and shader expectations (GLSL).
---
## Angle types
```cpp
using PitchAngle = Angle<float, -90.f, 90.f, AngleFlags::Clamped>;
using YawAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
using RollAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
using ViewAngles = omath::ViewAngles<PitchAngle, YawAngle, RollAngle>;
```
* **PitchAngle**: clamped to **[-90°, +90°]** (looking down vs. up)
* **YawAngle**: normalized to **[-180°, +180°]** (horizontal rotation)
* **RollAngle**: normalized to **[-180°, +180°]** (camera roll)
`ViewAngles` bundles all three into a single type for camera/view transforms.
---
## Coordinate system notes
* **Y-up**: gravity points along `-Y`, height increases with `+Y`
* **Right-handed**: cross product `right × up = forward` (forward is `-Z`)
* **Forward = -Z**: the camera looks down the negative Z-axis (OpenGL convention)
* This matches **OpenGL** conventions for 3D graphics pipelines
---
## See also
* `omath/engines/opengl_engine/formulas.hpp` — view/projection matrix builders
* `omath/trigonometry/angle.hpp` — angle normalization & clamping helpers
* `omath/trigonometry/view_angles.hpp` — generic pitch/yaw/roll wrapper

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# `omath::opengl_engine` — formulas & matrix helpers
> Header: `omath/engines/opengl_engine/formulas.hpp`
> Namespace: `omath::opengl_engine`
> Purpose: compute direction vectors, rotation matrices, view matrices, and perspective projections for OpenGL
---
## Summary
This header provides **OpenGL**-specific math for:
* **Direction vectors** (`forward`, `right`, `up`) from `ViewAngles`
* **Rotation matrices** from Euler angles
* **View matrices** (camera transforms)
* **Perspective projection** matrices
All functions respect OpenGL's **Y-up, right-handed** coordinate system with **forward = -Z**.
---
## API
```cpp
namespace omath::opengl_engine {
// Compute forward direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> forward_vector(const ViewAngles& angles) noexcept;
// Compute right direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> right_vector(const ViewAngles& angles) noexcept;
// Compute up direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> up_vector(const ViewAngles& angles) noexcept;
// Build 3x3 rotation matrix from angles
[[nodiscard]]
Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept;
// Build view matrix (camera space transform)
[[nodiscard]]
Mat4X4 calc_view_matrix(const ViewAngles& angles,
const Vector3<float>& cam_origin) noexcept;
// Build perspective projection matrix
[[nodiscard]]
Mat4X4 calc_perspective_projection_matrix(float field_of_view,
float aspect_ratio,
float near, float far) noexcept;
} // namespace omath::opengl_engine
```
---
## Direction vectors
Given camera angles (pitch/yaw/roll):
* `forward_vector(angles)` → unit vector pointing where the camera looks (typically `-Z` direction)
* `right_vector(angles)` → unit vector pointing to the camera's right (`+X` direction)
* `up_vector(angles)` → unit vector pointing upward relative to the camera (`+Y` direction)
These are used for movement, aim direction, and building coordinate frames.
---
## Rotation & view matrices
* `rotation_matrix(angles)` → 3×3 (or 4×4) rotation matrix from Euler angles (column-major)
* `calc_view_matrix(angles, origin)` → camera view matrix (column-major)
The view matrix transforms world coordinates into camera space (origin at camera, axes aligned with camera orientation).
**Note**: Matrices are **column-major** to match OpenGL/GLSL conventions. No transpose needed when uploading to shaders.
---
## Perspective projection
```cpp
Mat4X4 proj = calc_perspective_projection_matrix(
fov_degrees, // vertical field of view (e.g., 45)
aspect_ratio, // width / height (e.g., 16/9)
near_plane, // e.g., 0.1
far_plane // e.g., 100.0
);
```
Produces a **perspective projection matrix** suitable for OpenGL rendering. Combined with the view matrix, this implements the standard camera transform chain.
---
## Usage example
```cpp
using namespace omath::opengl_engine;
// Camera setup
ViewAngles angles = {
PitchAngle::from_degrees(-20.0f),
YawAngle::from_degrees(135.0f),
RollAngle::from_degrees(0.0f)
};
Vector3<float> cam_pos{5.0f, 3.0f, 5.0f};
// Compute direction
auto forward = forward_vector(angles);
auto right = right_vector(angles);
auto up = up_vector(angles);
// Build matrices (column-major for OpenGL)
auto view_mat = calc_view_matrix(angles, cam_pos);
auto proj_mat = calc_perspective_projection_matrix(45.0f, 16.0f/9.0f, 0.1f, 100.0f);
// Upload to OpenGL shaders (no transpose needed)
glUniformMatrix4fv(view_loc, 1, GL_FALSE, view_mat.data());
glUniformMatrix4fv(proj_loc, 1, GL_FALSE, proj_mat.data());
```
---
## Conventions
* **Angles**: pitch (up/down), yaw (left/right), roll (tilt)
* **Pitch**: positive = looking up, negative = looking down
* **Yaw**: increases counter-clockwise from the -Z axis
* **Coordinate system**: Y-up, -Z-forward, X-right (right-handed)
* **Matrix storage**: column-major (matches OpenGL/GLSL)
---
## See also
* `omath/engines/opengl_engine/constants.hpp` — coordinate frame & angle types
* `omath/engines/opengl_engine/traits/camera_trait.hpp` — plug-in for generic `Camera`
* `omath/projection/camera.hpp` — generic camera wrapper using these formulas

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# `omath::opengl_engine::PredEngineTrait` — projectile prediction trait
> Header: `omath/engines/opengl_engine/traits/pred_engine_trait.hpp`
> Namespace: `omath::opengl_engine`
> Purpose: provide OpenGL-specific projectile and target prediction for ballistic calculations
---
## Summary
`PredEngineTrait` implements engine-specific helpers for **projectile prediction**:
* `predict_projectile_position` – computes where a projectile will be after `time` seconds
* `predict_target_position` – computes where a moving target will be after `time` seconds
* `calc_vector_2d_distance` – horizontal distance (X/Z plane, ignoring Y)
* `get_vector_height_coordinate` – extracts vertical coordinate (Y in OpenGL)
* `calc_viewpoint_from_angles` – computes aim point given pitch angle
* `calc_direct_pitch_angle` – pitch angle to look from origin to target
* `calc_direct_yaw_angle` – yaw angle to look from origin to target
These methods satisfy the `PredEngineTraitConcept` required by generic projectile prediction algorithms.
---
## API
```cpp
namespace omath::opengl_engine {
class PredEngineTrait final {
public:
// Predict projectile position after `time` seconds
static constexpr Vector3<float>
predict_projectile_position(const projectile_prediction::Projectile& projectile,
float pitch, float yaw, float time,
float gravity) noexcept;
// Predict target position after `time` seconds
static constexpr Vector3<float>
predict_target_position(const projectile_prediction::Target& target,
float time, float gravity) noexcept;
// Compute horizontal (2D) distance
static float
calc_vector_2d_distance(const Vector3<float>& delta) noexcept;
// Get vertical coordinate (Y in OpenGL)
static constexpr float
get_vector_height_coordinate(const Vector3<float>& vec) noexcept;
// Compute aim point from angles
static Vector3<float>
calc_viewpoint_from_angles(const projectile_prediction::Projectile& projectile,
Vector3<float> predicted_target_position,
std::optional<float> projectile_pitch) noexcept;
// Compute pitch angle to look at target
static float
calc_direct_pitch_angle(const Vector3<float>& origin,
const Vector3<float>& view_to) noexcept;
// Compute yaw angle to look at target
static float
calc_direct_yaw_angle(const Vector3<float>& origin,
const Vector3<float>& view_to) noexcept;
};
} // namespace omath::opengl_engine
```
---
## Projectile prediction
```cpp
auto pos = PredEngineTrait::predict_projectile_position(
projectile, // initial position, speed, gravity scale
pitch_deg, // launch pitch (positive = up)
yaw_deg, // launch yaw
time, // time in seconds
gravity // gravity constant (e.g., 9.81 m/s²)
);
```
Computes:
1. Forward vector from pitch/yaw (using `forward_vector`)
2. Initial velocity: `forward * launch_speed`
3. Position after `time`: `origin + velocity*time - 0.5*gravity*gravityScale*time²` (Y component only)
**Note**: Negative pitch in `forward_vector` convention → positive pitch looks up.
---
## Target prediction
```cpp
auto pos = PredEngineTrait::predict_target_position(
target, // position, velocity, airborne flag
time, // time in seconds
gravity // gravity constant
);
```
Simple linear extrapolation plus gravity if target is airborne:
```
predicted = origin + velocity * time
if (airborne)
predicted.y -= 0.5 * gravity * time²
```
---
## Distance & height helpers
* `calc_vector_2d_distance(delta)` → `sqrt(delta.x² + delta.z²)` (horizontal distance)
* `get_vector_height_coordinate(vec)` → `vec.y` (vertical coordinate in OpenGL)
Used to compute ballistic arc parameters.
---
## Aim angle calculation
* `calc_direct_pitch_angle(origin, target)` → pitch in degrees to look from `origin` to `target`
- Formula: `asin(Δy / distance)` converted to degrees (direction normalized first)
- Positive = looking up, negative = looking down
* `calc_direct_yaw_angle(origin, target)` → yaw in degrees to look from `origin` to `target`
- Formula: `-atan2(Δx, -Δz)` converted to degrees (direction normalized first)
- Horizontal rotation around Y-axis (accounts for -Z forward convention)
---
## Viewpoint from angles
```cpp
auto aim_point = PredEngineTrait::calc_viewpoint_from_angles(
projectile,
predicted_target_pos,
optional_pitch_deg
);
```
Computes where to aim in 3D space given a desired pitch angle. Uses horizontal distance and `tan(pitch)` to compute height offset. Result has adjusted Y coordinate.
---
## Conventions
* **Coordinate system**: Y-up, -Z forward (height increases with Y)
* **Angles**: pitch in [-90°, +90°], yaw in [-180°, +180°]
* **Gravity**: applied downward along -Y axis
* **Pitch convention**: +90° = straight up, -90° = straight down
* **Forward direction**: negative Z-axis
---
## Usage example
```cpp
using namespace omath::opengl_engine;
using namespace omath::projectile_prediction;
Projectile proj{
.m_origin = {0, 2, 0},
.m_launch_speed = 30.0f,
.m_gravity_scale = 1.0f
};
Target tgt{
.m_origin = {10, 2, -15},
.m_velocity = {0.5f, 0, -1.0f},
.m_is_airborne = false
};
float gravity = 9.81f;
float time = 0.5f;
// Predict where target will be
auto target_pos = PredEngineTrait::predict_target_position(tgt, time, gravity);
// Compute aim angles
float pitch = PredEngineTrait::calc_direct_pitch_angle(proj.m_origin, target_pos);
float yaw = PredEngineTrait::calc_direct_yaw_angle(proj.m_origin, target_pos);
// Predict projectile position with those angles
auto proj_pos = PredEngineTrait::predict_projectile_position(proj, pitch, yaw, time, gravity);
```
---
## See also
* `omath/engines/opengl_engine/formulas.hpp` — direction vectors and matrix builders
* `omath/projectile_prediction/projectile.hpp` — `Projectile` struct
* `omath/projectile_prediction/target.hpp` — `Target` struct
* Generic projectile prediction algorithms that use `PredEngineTraitConcept`

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# `omath::source_engine::CameraTrait` — plug-in trait for `projection::Camera`
> Header: `omath/engines/source_engine/traits/camera_trait.hpp` • Impl: `omath/engines/source_engine/traits/camera_trait.cpp`
> Namespace: `omath::source_engine`
> Purpose: provide Source Engine-style **look-at**, **view**, and **projection** math to the generic `omath::projection::Camera` (satisfies `CameraEngineConcept`).
---
## Summary
`CameraTrait` exposes three `static` functions:
* `calc_look_at_angle(origin, look_at)` – computes Euler angles so the camera at `origin` looks at `look_at`. Implementation normalizes the direction, computes **pitch** as `asin(dir.z)` and **yaw** as `atan2(dir.y, dir.x)`; **roll** is `0`. Pitch/yaw are returned using the project's strong angle types (`PitchAngle`, `YawAngle`, `RollAngle`).
* `calc_view_matrix(angles, origin)` – delegates to Source Engine formulas `source_engine::calc_view_matrix`, producing a `Mat4X4` view matrix for the given angles and origin.
* `calc_projection_matrix(fov, viewport, near, far)` – builds a perspective projection by calling `calc_perspective_projection_matrix(fov_degrees, aspect, near, far)`, where `aspect = viewport.aspect_ratio()`. Accepts `FieldOfView` (degrees).
The trait's types (`ViewAngles`, `Mat4X4`, angle aliases) and helpers live in the Source Engine math headers included by the trait (`formulas.hpp`) and the shared projection header (`projection/camera.hpp`).
---
## API
```cpp
namespace omath::source_engine {
class CameraTrait final {
public:
// Compute Euler angles (pitch/yaw/roll) to look from cam_origin to look_at.
static ViewAngles
calc_look_at_angle(const Vector3<float>& cam_origin,
const Vector3<float>& look_at) noexcept;
// Build view matrix for given angles and origin.
static Mat4X4
calc_view_matrix(const ViewAngles& angles,
const Vector3<float>& cam_origin) noexcept;
// Build perspective projection from FOV (deg), viewport, near/far.
static Mat4X4
calc_projection_matrix(const projection::FieldOfView& fov,
const projection::ViewPort& view_port,
float near, float far) noexcept;
};
} // namespace omath::source_engine
```
Uses: `Vector3<float>`, `ViewAngles` (pitch/yaw/roll), `Mat4X4`, `projection::FieldOfView`, `projection::ViewPort`.
---
## Behavior & conventions
* **Angles from look-at** (Z-up coordinate system):
```
dir = normalize(look_at - origin)
pitch = asin(dir.z) // +Z is up
yaw = atan2(dir.y, dir.x) // horizontal rotation
roll = 0
```
Returned as `PitchAngle::from_radians(...)`, `YawAngle::from_radians(...)`, etc.
* **View matrix**: built by the Source Engine helper `source_engine::calc_view_matrix(angles, origin)` to match the engine's handedness and axis conventions.
* **Projection**: uses `calc_perspective_projection_matrix(fov.as_degrees(), viewport.aspect_ratio(), near, far)`. Pass your **vertical FOV** in degrees via `FieldOfView`; the helper computes a standard perspective matrix.
---
## Using with `projection::Camera`
Create a camera whose math is driven by this trait:
```cpp
using Mat4 = Mat4X4; // from Source Engine math headers
using Angs = ViewAngles; // pitch/yaw/roll type
using SEcam = omath::projection::Camera<Mat4, Angs, omath::source_engine::CameraTrait>;
omath::projection::ViewPort vp{1920.f, 1080.f};
auto fov = omath::projection::FieldOfView::from_degrees(90.f);
SEcam cam(
/*position*/ {100.f, 50.f, 80.f},
/*angles*/ omath::source_engine::CameraTrait::calc_look_at_angle({100,50,80},{0,0,80}),
/*viewport*/ vp,
/*fov*/ fov,
/*near*/ 0.1f,
/*far*/ 1000.f
);
```
This satisfies `CameraEngineConcept` expected by `projection::Camera` (look-at, view, projection) as declared in the trait header.
---
## Notes & tips
* Ensure your `ViewAngles` aliases (`PitchAngle`, `YawAngle`, `RollAngle`) match the project's angle policy (ranges/normalization). The implementation constructs them **from radians**.
* `aspect_ratio()` is taken directly from `ViewPort` (`width / height`), so keep both positive and non-zero.
* `near` must be > 0 and `< far` for a valid projection matrix (enforced by your math helpers).
* Source Engine uses **Z-up**: pitch angles control vertical look, positive = up.
---
## See also
* [Source Engine Formulas](formulas.md) - View/projection matrix builders
* [Source Engine Constants](constants.md) - Engine-specific constants
* [Source Engine Pred Engine Trait](pred_engine_trait.md) - Projectile prediction for Source Engine
* [Generic Camera Documentation](../../projection/camera.md) - Camera base class
* [Getting Started Guide](../../getting_started.md) - Quick start with OMath
* [Tutorials - World-to-Screen](../../tutorials.md#tutorial-2-world-to-screen-projection) - Projection tutorial

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# `omath::source_engine` — types & constants
> Header: `omath/engines/source_engine/constants.hpp`
> Namespace: `omath::source_engine`
> Purpose: define Source Engine coordinate system, matrix types, and angle ranges
---
## Summary
The **Source Engine** uses a **Z-up, right-handed** coordinate system:
* **Up** = `{0, 0, 1}` (Z-axis)
* **Right** = `{0, -1, 0}` (negative Y-axis)
* **Forward** = `{1, 0, 0}` (X-axis)
Matrices are **row-major**. Angles are **clamped pitch** (±89°) and **normalized yaw/roll** (±180°).
---
## Constants
```cpp
namespace omath::source_engine {
constexpr Vector3<float> k_abs_up = {0, 0, 1};
constexpr Vector3<float> k_abs_right = {0, -1, 0};
constexpr Vector3<float> k_abs_forward = {1, 0, 0};
}
```
These basis vectors define the engine's **world coordinate frame**.
---
## Matrix types
```cpp
using Mat4X4 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;
using Mat3X3 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;
using Mat1X3 = Mat<1, 3, float, MatStoreType::ROW_MAJOR>;
```
**Row-major** storage means rows are contiguous in memory. Suitable for CPU-side transforms and typical C++ math libraries.
---
## Angle types
```cpp
using PitchAngle = Angle<float, -89.f, 89.f, AngleFlags::Clamped>;
using YawAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
using RollAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
using ViewAngles = omath::ViewAngles<PitchAngle, YawAngle, RollAngle>;
```
* **PitchAngle**: clamped to **[-89°, +89°]** (looking down vs. up)
* **YawAngle**: normalized to **[-180°, +180°]** (horizontal rotation)
* **RollAngle**: normalized to **[-180°, +180°]** (camera roll)
`ViewAngles` bundles all three into a single type for camera/view transforms.
---
## Coordinate system notes
* **Z-up**: gravity points along `-Z`, height increases with `+Z`
* **Right-handed**: cross product `forward × right = up` holds
* This matches **Source Engine** (Half-Life 2, TF2, CS:GO, etc.) conventions
---
## See also
* `omath/engines/source_engine/formulas.hpp` — view/projection matrix builders
* `omath/trigonometry/angle.hpp` — angle normalization & clamping helpers
* `omath/trigonometry/view_angles.hpp` — generic pitch/yaw/roll wrapper

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# `omath::source_engine` — formulas & matrix helpers
> Header: `omath/engines/source_engine/formulas.hpp`
> Namespace: `omath::source_engine`
> Purpose: compute direction vectors, rotation matrices, view matrices, and perspective projections for Source Engine
---
## Summary
This header provides **Source Engine**-specific math for:
* **Direction vectors** (`forward`, `right`, `up`) from `ViewAngles`
* **Rotation matrices** from Euler angles
* **View matrices** (camera transforms)
* **Perspective projection** matrices
All functions respect Source Engine's **Z-up, right-handed** coordinate system.
---
## API
```cpp
namespace omath::source_engine {
// Compute forward direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> forward_vector(const ViewAngles& angles) noexcept;
// Compute right direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> right_vector(const ViewAngles& angles) noexcept;
// Compute up direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> up_vector(const ViewAngles& angles) noexcept;
// Build 3x3 rotation matrix from angles
[[nodiscard]]
Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept;
// Build view matrix (camera space transform)
[[nodiscard]]
Mat4X4 calc_view_matrix(const ViewAngles& angles,
const Vector3<float>& cam_origin) noexcept;
// Build perspective projection matrix
[[nodiscard]]
Mat4X4 calc_perspective_projection_matrix(float field_of_view,
float aspect_ratio,
float near, float far) noexcept;
} // namespace omath::source_engine
```
---
## Direction vectors
Given camera angles (pitch/yaw/roll):
* `forward_vector(angles)` → unit vector pointing where the camera looks
* `right_vector(angles)` → unit vector pointing to the camera's right
* `up_vector(angles)` → unit vector pointing upward relative to the camera
These are used for movement, aim direction, and building coordinate frames.
---
## Rotation & view matrices
* `rotation_matrix(angles)` → 3×3 (or 4×4) rotation matrix from Euler angles
* `calc_view_matrix(angles, origin)` → camera view matrix
The view matrix transforms world coordinates into camera space (origin at camera, axes aligned with camera orientation).
---
## Perspective projection
```cpp
Mat4X4 proj = calc_perspective_projection_matrix(
fov_degrees, // vertical field of view (e.g., 90)
aspect_ratio, // width / height (e.g., 16/9)
near_plane, // e.g., 0.1
far_plane // e.g., 1000.0
);
```
Produces a **perspective projection matrix** suitable for 3D rendering pipelines. Combined with the view matrix, this implements the standard camera transform chain.
---
## Usage example
```cpp
using namespace omath::source_engine;
// Camera setup
ViewAngles angles = {
PitchAngle::from_degrees(-15.0f),
YawAngle::from_degrees(45.0f),
RollAngle::from_degrees(0.0f)
};
Vector3<float> cam_pos{100.0f, 50.0f, 80.0f};
// Compute direction
auto forward = forward_vector(angles);
auto right = right_vector(angles);
auto up = up_vector(angles);
// Build matrices
auto view_mat = calc_view_matrix(angles, cam_pos);
auto proj_mat = calc_perspective_projection_matrix(90.0f, 16.0f/9.0f, 0.1f, 1000.0f);
// Use view_mat and proj_mat for rendering...
```
---
## Conventions
* **Angles**: pitch (up/down), yaw (left/right), roll (tilt)
* **Pitch**: positive = looking up, negative = looking down
* **Yaw**: increases counter-clockwise from the +X axis
* **Coordinate system**: Z-up, X-forward, Y-right (negative in code convention)
---
## See also
* `omath/engines/source_engine/constants.hpp` — coordinate frame & angle types
* `omath/engines/source_engine/traits/camera_trait.hpp` — plug-in for generic `Camera`
* `omath/projection/camera.hpp` — generic camera wrapper using these formulas

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# `omath::source_engine::PredEngineTrait` — projectile prediction trait
> Header: `omath/engines/source_engine/traits/pred_engine_trait.hpp`
> Namespace: `omath::source_engine`
> Purpose: provide Source Engine-specific projectile and target prediction for ballistic calculations
---
## Summary
`PredEngineTrait` implements engine-specific helpers for **projectile prediction**:
* `predict_projectile_position` – computes where a projectile will be after `time` seconds
* `predict_target_position` – computes where a moving target will be after `time` seconds
* `calc_vector_2d_distance` – horizontal distance (X/Y plane, ignoring Z)
* `get_vector_height_coordinate` – extracts vertical coordinate (Z in Source Engine)
* `calc_viewpoint_from_angles` – computes aim point given pitch angle
* `calc_direct_pitch_angle` – pitch angle to look from origin to target
* `calc_direct_yaw_angle` – yaw angle to look from origin to target
These methods satisfy the `PredEngineTraitConcept` required by generic projectile prediction algorithms.
---
## API
```cpp
namespace omath::source_engine {
class PredEngineTrait final {
public:
// Predict projectile position after `time` seconds
static constexpr Vector3<float>
predict_projectile_position(const projectile_prediction::Projectile& projectile,
float pitch, float yaw, float time,
float gravity) noexcept;
// Predict target position after `time` seconds
static constexpr Vector3<float>
predict_target_position(const projectile_prediction::Target& target,
float time, float gravity) noexcept;
// Compute horizontal (2D) distance
static float
calc_vector_2d_distance(const Vector3<float>& delta) noexcept;
// Get vertical coordinate (Z in Source Engine)
static constexpr float
get_vector_height_coordinate(const Vector3<float>& vec) noexcept;
// Compute aim point from angles
static Vector3<float>
calc_viewpoint_from_angles(const projectile_prediction::Projectile& projectile,
Vector3<float> predicted_target_position,
std::optional<float> projectile_pitch) noexcept;
// Compute pitch angle to look at target
static float
calc_direct_pitch_angle(const Vector3<float>& origin,
const Vector3<float>& view_to) noexcept;
// Compute yaw angle to look at target
static float
calc_direct_yaw_angle(const Vector3<float>& origin,
const Vector3<float>& view_to) noexcept;
};
} // namespace omath::source_engine
```
---
## Projectile prediction
```cpp
auto pos = PredEngineTrait::predict_projectile_position(
projectile, // initial position, speed, gravity scale
pitch_deg, // launch pitch (positive = up)
yaw_deg, // launch yaw
time, // time in seconds
gravity // gravity constant (e.g., 800 units/s²)
);
```
Computes:
1. Forward vector from pitch/yaw (using `forward_vector`)
2. Initial velocity: `forward * launch_speed`
3. Position after `time`: `origin + velocity*time - 0.5*gravity*gravityScale*time²` (Z component only)
**Note**: Negative pitch in `forward_vector` convention → positive pitch looks up.
---
## Target prediction
```cpp
auto pos = PredEngineTrait::predict_target_position(
target, // position, velocity, airborne flag
time, // time in seconds
gravity // gravity constant
);
```
Simple linear extrapolation plus gravity if target is airborne:
```
predicted = origin + velocity * time
if (airborne)
predicted.z -= 0.5 * gravity * time²
```
---
## Distance & height helpers
* `calc_vector_2d_distance(delta)` → `sqrt(delta.x² + delta.y²)` (horizontal distance)
* `get_vector_height_coordinate(vec)` → `vec.z` (vertical coordinate in Source Engine)
Used to compute ballistic arc parameters.
---
## Aim angle calculation
* `calc_direct_pitch_angle(origin, target)` → pitch in degrees to look from `origin` to `target`
- Formula: `asin(Δz / distance)` converted to degrees
- Positive = looking up, negative = looking down
* `calc_direct_yaw_angle(origin, target)` → yaw in degrees to look from `origin` to `target`
- Formula: `atan2(Δy, Δx)` converted to degrees
- Horizontal rotation around Z-axis
---
## Viewpoint from angles
```cpp
auto aim_point = PredEngineTrait::calc_viewpoint_from_angles(
projectile,
predicted_target_pos,
optional_pitch_deg
);
```
Computes where to aim in 3D space given a desired pitch angle. Uses horizontal distance and `tan(pitch)` to compute height offset.
---
## Conventions
* **Coordinate system**: Z-up (height increases with Z)
* **Angles**: pitch in [-89°, +89°], yaw in [-180°, +180°]
* **Gravity**: applied downward along -Z axis
* **Pitch convention**: +89° = straight up, -89° = straight down
---
## Usage example
```cpp
using namespace omath::source_engine;
using namespace omath::projectile_prediction;
Projectile proj{
.m_origin = {0, 0, 100},
.m_launch_speed = 1000.0f,
.m_gravity_scale = 1.0f
};
Target tgt{
.m_origin = {500, 200, 100},
.m_velocity = {10, 5, 0},
.m_is_airborne = false
};
float gravity = 800.0f;
float time = 0.5f;
// Predict where target will be
auto target_pos = PredEngineTrait::predict_target_position(tgt, time, gravity);
// Compute aim angles
float pitch = PredEngineTrait::calc_direct_pitch_angle(proj.m_origin, target_pos);
float yaw = PredEngineTrait::calc_direct_yaw_angle(proj.m_origin, target_pos);
// Predict projectile position with those angles
auto proj_pos = PredEngineTrait::predict_projectile_position(proj, pitch, yaw, time, gravity);
```
---
## See also
* `omath/engines/source_engine/formulas.hpp` — direction vectors and matrix builders
* `omath/projectile_prediction/projectile.hpp` — `Projectile` struct
* `omath/projectile_prediction/target.hpp` — `Target` struct
* Generic projectile prediction algorithms that use `PredEngineTraitConcept`

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# `omath::unity_engine::CameraTrait` — plug-in trait for `projection::Camera`
> Header: `omath/engines/unity_engine/traits/camera_trait.hpp` • Impl: `omath/engines/unity_engine/traits/camera_trait.cpp`
> Namespace: `omath::unity_engine`
> Purpose: provide Unity Engine-style **look-at**, **view**, and **projection** math to the generic `omath::projection::Camera` (satisfies `CameraEngineConcept`).
---
## Summary
`CameraTrait` exposes three `static` functions:
* `calc_look_at_angle(origin, look_at)` – computes Euler angles so the camera at `origin` looks at `look_at`. Implementation normalizes the direction, computes **pitch** as `asin(dir.y)` and **yaw** as `atan2(dir.x, dir.z)`; **roll** is `0`. Pitch/yaw are returned using the project's strong angle types (`PitchAngle`, `YawAngle`, `RollAngle`).
* `calc_view_matrix(angles, origin)` – delegates to Unity Engine formulas `unity_engine::calc_view_matrix`, producing a `Mat4X4` view matrix for the given angles and origin.
* `calc_projection_matrix(fov, viewport, near, far)` – builds a perspective projection by calling `calc_perspective_projection_matrix(fov_degrees, aspect, near, far)`, where `aspect = viewport.aspect_ratio()`. Accepts `FieldOfView` (degrees).
The trait's types (`ViewAngles`, `Mat4X4`, angle aliases) and helpers live in the Unity Engine math headers included by the trait (`formulas.hpp`) and the shared projection header (`projection/camera.hpp`).
---
## API
```cpp
namespace omath::unity_engine {
class CameraTrait final {
public:
// Compute Euler angles (pitch/yaw/roll) to look from cam_origin to look_at.
static ViewAngles
calc_look_at_angle(const Vector3<float>& cam_origin,
const Vector3<float>& look_at) noexcept;
// Build view matrix for given angles and origin.
static Mat4X4
calc_view_matrix(const ViewAngles& angles,
const Vector3<float>& cam_origin) noexcept;
// Build perspective projection from FOV (deg), viewport, near/far.
static Mat4X4
calc_projection_matrix(const projection::FieldOfView& fov,
const projection::ViewPort& view_port,
float near, float far) noexcept;
};
} // namespace omath::unity_engine
```
Uses: `Vector3<float>`, `ViewAngles` (pitch/yaw/roll), `Mat4X4`, `projection::FieldOfView`, `projection::ViewPort`.
---
## Behavior & conventions
* **Angles from look-at** (Y-up coordinate system):
```
dir = normalize(look_at - origin)
pitch = asin(dir.y) // +Y is up
yaw = atan2(dir.x, dir.z) // horizontal rotation
roll = 0
```
Returned as `PitchAngle::from_radians(...)`, `YawAngle::from_radians(...)`, etc.
* **View matrix**: built by the Unity Engine helper `unity_engine::calc_view_matrix(angles, origin)` to match the engine's handedness and axis conventions.
* **Projection**: uses `calc_perspective_projection_matrix(fov.as_degrees(), viewport.aspect_ratio(), near, far)`. Pass your **vertical FOV** in degrees via `FieldOfView`; the helper computes a standard perspective matrix.
---
## Using with `projection::Camera`
Create a camera whose math is driven by this trait:
```cpp
using Mat4 = Mat4X4; // from Unity Engine math headers
using Angs = ViewAngles; // pitch/yaw/roll type
using UEcam = omath::projection::Camera<Mat4, Angs, omath::unity_engine::CameraTrait>;
omath::projection::ViewPort vp{1920.f, 1080.f};
auto fov = omath::projection::FieldOfView::from_degrees(60.f);
UEcam cam(
/*position*/ {10.f, 5.f, -10.f},
/*angles*/ omath::unity_engine::CameraTrait::calc_look_at_angle({10,5,-10},{0,5,0}),
/*viewport*/ vp,
/*fov*/ fov,
/*near*/ 0.3f,
/*far*/ 1000.f
);
```
This satisfies `CameraEngineConcept` expected by `projection::Camera` (look-at, view, projection) as declared in the trait header.
---
## Notes & tips
* Ensure your `ViewAngles` aliases (`PitchAngle`, `YawAngle`, `RollAngle`) match the project's angle policy (ranges/normalization). The implementation constructs them **from radians**.
* `aspect_ratio()` is taken directly from `ViewPort` (`width / height`), so keep both positive and non-zero.
* `near` must be > 0 and `< far` for a valid projection matrix (enforced by your math helpers).
* Unity Engine uses **Y-up**: pitch angles control vertical look, positive = up.
---
## See also
* Unity Engine math helpers in `omath/engines/unity_engine/formulas.hpp` (view/projection builders used above).
* Generic camera wrapper `omath::projection::Camera` and its `CameraEngineConcept` (this trait is designed to plug straight into it).

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# `omath::unity_engine` — types & constants
> Header: `omath/engines/unity_engine/constants.hpp`
> Namespace: `omath::unity_engine`
> Purpose: define Unity Engine coordinate system, matrix types, and angle ranges
---
## Summary
The **Unity Engine** uses a **Y-up, left-handed** coordinate system:
* **Up** = `{0, 1, 0}` (Y-axis)
* **Right** = `{1, 0, 0}` (X-axis)
* **Forward** = `{0, 0, 1}` (Z-axis)
Matrices are **row-major**. Angles are **clamped pitch** (±90°) and **normalized yaw/roll** (±180°).
---
## Constants
```cpp
namespace omath::unity_engine {
constexpr Vector3<float> k_abs_up = {0, 1, 0};
constexpr Vector3<float> k_abs_right = {1, 0, 0};
constexpr Vector3<float> k_abs_forward = {0, 0, 1};
}
```
These basis vectors define the engine's **world coordinate frame**.
---
## Matrix types
```cpp
using Mat4X4 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;
using Mat3X3 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;
using Mat1X3 = Mat<1, 3, float, MatStoreType::ROW_MAJOR>;
```
**Row-major** storage means rows are contiguous in memory. Suitable for CPU-side transforms and typical C++ math libraries.
---
## Angle types
```cpp
using PitchAngle = Angle<float, -90.f, 90.f, AngleFlags::Clamped>;
using YawAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
using RollAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
using ViewAngles = omath::ViewAngles<PitchAngle, YawAngle, RollAngle>;
```
* **PitchAngle**: clamped to **[-90°, +90°]** (looking down vs. up)
* **YawAngle**: normalized to **[-180°, +180°]** (horizontal rotation)
* **RollAngle**: normalized to **[-180°, +180°]** (camera roll)
`ViewAngles` bundles all three into a single type for camera/view transforms.
---
## Coordinate system notes
* **Y-up**: gravity points along `-Y`, height increases with `+Y`
* **Left-handed**: cross product `forward × right = up` with left-hand rule
* This matches **Unity Engine** conventions for 3D games and simulations
---
## See also
* `omath/engines/unity_engine/formulas.hpp` — view/projection matrix builders
* `omath/trigonometry/angle.hpp` — angle normalization & clamping helpers
* `omath/trigonometry/view_angles.hpp` — generic pitch/yaw/roll wrapper

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# `omath::unity_engine` — formulas & matrix helpers
> Header: `omath/engines/unity_engine/formulas.hpp`
> Namespace: `omath::unity_engine`
> Purpose: compute direction vectors, rotation matrices, view matrices, and perspective projections for Unity Engine
---
## Summary
This header provides **Unity Engine**-specific math for:
* **Direction vectors** (`forward`, `right`, `up`) from `ViewAngles`
* **Rotation matrices** from Euler angles
* **View matrices** (camera transforms)
* **Perspective projection** matrices
All functions respect Unity Engine's **Y-up, left-handed** coordinate system.
---
## API
```cpp
namespace omath::unity_engine {
// Compute forward direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> forward_vector(const ViewAngles& angles) noexcept;
// Compute right direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> right_vector(const ViewAngles& angles) noexcept;
// Compute up direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> up_vector(const ViewAngles& angles) noexcept;
// Build 3x3 rotation matrix from angles
[[nodiscard]]
Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept;
// Build view matrix (camera space transform)
[[nodiscard]]
Mat4X4 calc_view_matrix(const ViewAngles& angles,
const Vector3<float>& cam_origin) noexcept;
// Build perspective projection matrix
[[nodiscard]]
Mat4X4 calc_perspective_projection_matrix(float field_of_view,
float aspect_ratio,
float near, float far) noexcept;
} // namespace omath::unity_engine
```
---
## Direction vectors
Given camera angles (pitch/yaw/roll):
* `forward_vector(angles)` → unit vector pointing where the camera looks
* `right_vector(angles)` → unit vector pointing to the camera's right
* `up_vector(angles)` → unit vector pointing upward relative to the camera
These are used for movement, aim direction, and building coordinate frames.
---
## Rotation & view matrices
* `rotation_matrix(angles)` → 3×3 (or 4×4) rotation matrix from Euler angles
* `calc_view_matrix(angles, origin)` → camera view matrix
The view matrix transforms world coordinates into camera space (origin at camera, axes aligned with camera orientation).
---
## Perspective projection
```cpp
Mat4X4 proj = calc_perspective_projection_matrix(
fov_degrees, // vertical field of view (e.g., 60)
aspect_ratio, // width / height (e.g., 16/9)
near_plane, // e.g., 0.3
far_plane // e.g., 1000.0
);
```
Produces a **perspective projection matrix** suitable for 3D rendering pipelines. Combined with the view matrix, this implements the standard camera transform chain.
---
## Usage example
```cpp
using namespace omath::unity_engine;
// Camera setup
ViewAngles angles = {
PitchAngle::from_degrees(-15.0f),
YawAngle::from_degrees(45.0f),
RollAngle::from_degrees(0.0f)
};
Vector3<float> cam_pos{10.0f, 5.0f, -10.0f};
// Compute direction
auto forward = forward_vector(angles);
auto right = right_vector(angles);
auto up = up_vector(angles);
// Build matrices
auto view_mat = calc_view_matrix(angles, cam_pos);
auto proj_mat = calc_perspective_projection_matrix(60.0f, 16.0f/9.0f, 0.3f, 1000.0f);
// Use view_mat and proj_mat for rendering...
```
---
## Conventions
* **Angles**: pitch (up/down), yaw (left/right), roll (tilt)
* **Pitch**: positive = looking up, negative = looking down
* **Yaw**: increases counter-clockwise from the +Z axis
* **Coordinate system**: Y-up, Z-forward, X-right (left-handed)
---
## See also
* `omath/engines/unity_engine/constants.hpp` — coordinate frame & angle types
* `omath/engines/unity_engine/traits/camera_trait.hpp` — plug-in for generic `Camera`
* `omath/projection/camera.hpp` — generic camera wrapper using these formulas

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# `omath::unity_engine::PredEngineTrait` — projectile prediction trait
> Header: `omath/engines/unity_engine/traits/pred_engine_trait.hpp`
> Namespace: `omath::unity_engine`
> Purpose: provide Unity Engine-specific projectile and target prediction for ballistic calculations
---
## Summary
`PredEngineTrait` implements engine-specific helpers for **projectile prediction**:
* `predict_projectile_position` – computes where a projectile will be after `time` seconds
* `predict_target_position` – computes where a moving target will be after `time` seconds
* `calc_vector_2d_distance` – horizontal distance (X/Z plane, ignoring Y)
* `get_vector_height_coordinate` – extracts vertical coordinate (Y in Unity Engine)
* `calc_viewpoint_from_angles` – computes aim point given pitch angle
* `calc_direct_pitch_angle` – pitch angle to look from origin to target
* `calc_direct_yaw_angle` – yaw angle to look from origin to target
These methods satisfy the `PredEngineTraitConcept` required by generic projectile prediction algorithms.
---
## API
```cpp
namespace omath::unity_engine {
class PredEngineTrait final {
public:
// Predict projectile position after `time` seconds
static constexpr Vector3<float>
predict_projectile_position(const projectile_prediction::Projectile& projectile,
float pitch, float yaw, float time,
float gravity) noexcept;
// Predict target position after `time` seconds
static constexpr Vector3<float>
predict_target_position(const projectile_prediction::Target& target,
float time, float gravity) noexcept;
// Compute horizontal (2D) distance
static float
calc_vector_2d_distance(const Vector3<float>& delta) noexcept;
// Get vertical coordinate (Y in Unity Engine)
static constexpr float
get_vector_height_coordinate(const Vector3<float>& vec) noexcept;
// Compute aim point from angles
static Vector3<float>
calc_viewpoint_from_angles(const projectile_prediction::Projectile& projectile,
Vector3<float> predicted_target_position,
std::optional<float> projectile_pitch) noexcept;
// Compute pitch angle to look at target
static float
calc_direct_pitch_angle(const Vector3<float>& origin,
const Vector3<float>& view_to) noexcept;
// Compute yaw angle to look at target
static float
calc_direct_yaw_angle(const Vector3<float>& origin,
const Vector3<float>& view_to) noexcept;
};
} // namespace omath::unity_engine
```
---
## Projectile prediction
```cpp
auto pos = PredEngineTrait::predict_projectile_position(
projectile, // initial position, speed, gravity scale
pitch_deg, // launch pitch (positive = up)
yaw_deg, // launch yaw
time, // time in seconds
gravity // gravity constant (e.g., 9.81 m/s²)
);
```
Computes:
1. Forward vector from pitch/yaw (using `forward_vector`)
2. Initial velocity: `forward * launch_speed`
3. Position after `time`: `origin + velocity*time - 0.5*gravity*gravityScale*time²` (Y component only)
**Note**: Negative pitch in `forward_vector` convention → positive pitch looks up.
---
## Target prediction
```cpp
auto pos = PredEngineTrait::predict_target_position(
target, // position, velocity, airborne flag
time, // time in seconds
gravity // gravity constant
);
```
Simple linear extrapolation plus gravity if target is airborne:
```
predicted = origin + velocity * time
if (airborne)
predicted.y -= 0.5 * gravity * time²
```
---
## Distance & height helpers
* `calc_vector_2d_distance(delta)` → `sqrt(delta.x² + delta.z²)` (horizontal distance)
* `get_vector_height_coordinate(vec)` → `vec.y` (vertical coordinate in Unity Engine)
Used to compute ballistic arc parameters.
---
## Aim angle calculation
* `calc_direct_pitch_angle(origin, target)` → pitch in degrees to look from `origin` to `target`
- Formula: `asin(Δy / distance)` converted to degrees (direction normalized first)
- Positive = looking up, negative = looking down
* `calc_direct_yaw_angle(origin, target)` → yaw in degrees to look from `origin` to `target`
- Formula: `atan2(Δx, Δz)` converted to degrees (direction normalized first)
- Horizontal rotation around Y-axis
---
## Viewpoint from angles
```cpp
auto aim_point = PredEngineTrait::calc_viewpoint_from_angles(
projectile,
predicted_target_pos,
optional_pitch_deg
);
```
Computes where to aim in 3D space given a desired pitch angle. Uses horizontal distance and `tan(pitch)` to compute height offset. Result has adjusted Y coordinate.
---
## Conventions
* **Coordinate system**: Y-up (height increases with Y)
* **Angles**: pitch in [-90°, +90°], yaw in [-180°, +180°]
* **Gravity**: applied downward along -Y axis
* **Pitch convention**: +90° = straight up, -90° = straight down
---
## Usage example
```cpp
using namespace omath::unity_engine;
using namespace omath::projectile_prediction;
Projectile proj{
.m_origin = {0, 2, 0},
.m_launch_speed = 50.0f,
.m_gravity_scale = 1.0f
};
Target tgt{
.m_origin = {20, 2, 15},
.m_velocity = {1, 0, 0.5f},
.m_is_airborne = false
};
float gravity = 9.81f;
float time = 0.5f;
// Predict where target will be
auto target_pos = PredEngineTrait::predict_target_position(tgt, time, gravity);
// Compute aim angles
float pitch = PredEngineTrait::calc_direct_pitch_angle(proj.m_origin, target_pos);
float yaw = PredEngineTrait::calc_direct_yaw_angle(proj.m_origin, target_pos);
// Predict projectile position with those angles
auto proj_pos = PredEngineTrait::predict_projectile_position(proj, pitch, yaw, time, gravity);
```
---
## See also
* `omath/engines/unity_engine/formulas.hpp` — direction vectors and matrix builders
* `omath/projectile_prediction/projectile.hpp` — `Projectile` struct
* `omath/projectile_prediction/target.hpp` — `Target` struct
* Generic projectile prediction algorithms that use `PredEngineTraitConcept`

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# `omath::unreal_engine::CameraTrait` — plug-in trait for `projection::Camera`
> Header: `omath/engines/unreal_engine/traits/camera_trait.hpp` • Impl: `omath/engines/unreal_engine/traits/camera_trait.cpp`
> Namespace: `omath::unreal_engine`
> Purpose: provide Unreal Engine-style **look-at**, **view**, and **projection** math to the generic `omath::projection::Camera` (satisfies `CameraEngineConcept`).
---
## Summary
`CameraTrait` exposes three `static` functions:
* `calc_look_at_angle(origin, look_at)` – computes Euler angles so the camera at `origin` looks at `look_at`. Implementation normalizes the direction, computes **pitch** as `asin(dir.z)` and **yaw** as `atan2(dir.y, dir.x)`; **roll** is `0`. Pitch/yaw are returned using the project's strong angle types (`PitchAngle`, `YawAngle`, `RollAngle`).
* `calc_view_matrix(angles, origin)` – delegates to Unreal Engine formulas `unreal_engine::calc_view_matrix`, producing a `Mat4X4` view matrix for the given angles and origin.
* `calc_projection_matrix(fov, viewport, near, far)` – builds a perspective projection by calling `calc_perspective_projection_matrix(fov_degrees, aspect, near, far)`, where `aspect = viewport.aspect_ratio()`. Accepts `FieldOfView` (degrees).
The trait's types (`ViewAngles`, `Mat4X4`, angle aliases) and helpers live in the Unreal Engine math headers included by the trait (`formulas.hpp`) and the shared projection header (`projection/camera.hpp`).
---
## API
```cpp
namespace omath::unreal_engine {
class CameraTrait final {
public:
// Compute Euler angles (pitch/yaw/roll) to look from cam_origin to look_at.
static ViewAngles
calc_look_at_angle(const Vector3<float>& cam_origin,
const Vector3<float>& look_at) noexcept;
// Build view matrix for given angles and origin.
static Mat4X4
calc_view_matrix(const ViewAngles& angles,
const Vector3<float>& cam_origin) noexcept;
// Build perspective projection from FOV (deg), viewport, near/far.
static Mat4X4
calc_projection_matrix(const projection::FieldOfView& fov,
const projection::ViewPort& view_port,
float near, float far) noexcept;
};
} // namespace omath::unreal_engine
```
Uses: `Vector3<float>`, `ViewAngles` (pitch/yaw/roll), `Mat4X4`, `projection::FieldOfView`, `projection::ViewPort`.
---
## Behavior & conventions
* **Angles from look-at** (Z-up coordinate system):
```
dir = normalize(look_at - origin)
pitch = asin(dir.z) // +Z is up
yaw = atan2(dir.y, dir.x) // horizontal rotation
roll = 0
```
Returned as `PitchAngle::from_radians(...)`, `YawAngle::from_radians(...)`, etc.
* **View matrix**: built by the Unreal Engine helper `unreal_engine::calc_view_matrix(angles, origin)` to match the engine's handedness and axis conventions.
* **Projection**: uses `calc_perspective_projection_matrix(fov.as_degrees(), viewport.aspect_ratio(), near, far)`. Pass your **vertical FOV** in degrees via `FieldOfView`; the helper computes a standard perspective matrix.
---
## Using with `projection::Camera`
Create a camera whose math is driven by this trait:
```cpp
using Mat4 = Mat4X4; // from Unreal Engine math headers
using Angs = ViewAngles; // pitch/yaw/roll type
using UEcam = omath::projection::Camera<Mat4, Angs, omath::unreal_engine::CameraTrait>;
omath::projection::ViewPort vp{1920.f, 1080.f};
auto fov = omath::projection::FieldOfView::from_degrees(90.f);
UEcam cam(
/*position*/ {1000.f, 500.f, 200.f},
/*angles*/ omath::unreal_engine::CameraTrait::calc_look_at_angle({1000,500,200},{0,0,200}),
/*viewport*/ vp,
/*fov*/ fov,
/*near*/ 10.f,
/*far*/ 100000.f
);
```
This satisfies `CameraEngineConcept` expected by `projection::Camera` (look-at, view, projection) as declared in the trait header.
---
## Notes & tips
* Ensure your `ViewAngles` aliases (`PitchAngle`, `YawAngle`, `RollAngle`) match the project's angle policy (ranges/normalization). The implementation constructs them **from radians**.
* `aspect_ratio()` is taken directly from `ViewPort` (`width / height`), so keep both positive and non-zero.
* `near` must be > 0 and `< far` for a valid projection matrix (enforced by your math helpers).
* Unreal Engine uses **Z-up**: pitch angles control vertical look, positive = up.
---
## See also
* Unreal Engine math helpers in `omath/engines/unreal_engine/formulas.hpp` (view/projection builders used above).
* Generic camera wrapper `omath::projection::Camera` and its `CameraEngineConcept` (this trait is designed to plug straight into it).

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# `omath::unreal_engine` — types & constants
> Header: `omath/engines/unreal_engine/constants.hpp`
> Namespace: `omath::unreal_engine`
> Purpose: define Unreal Engine coordinate system, matrix types, and angle ranges
---
## Summary
The **Unreal Engine** uses a **Z-up, left-handed** coordinate system:
* **Up** = `{0, 0, 1}` (Z-axis)
* **Right** = `{0, 1, 0}` (Y-axis)
* **Forward** = `{1, 0, 0}` (X-axis)
Matrices are **row-major**. Angles are **clamped pitch** (±90°) and **normalized yaw/roll** (±180°).
---
## Constants
```cpp
namespace omath::unreal_engine {
constexpr Vector3<float> k_abs_up = {0, 0, 1};
constexpr Vector3<float> k_abs_right = {0, 1, 0};
constexpr Vector3<float> k_abs_forward = {1, 0, 0};
}
```
These basis vectors define the engine's **world coordinate frame**.
---
## Matrix types
```cpp
using Mat4X4 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;
using Mat3X3 = Mat<4, 4, float, MatStoreType::ROW_MAJOR>;
using Mat1X3 = Mat<1, 3, float, MatStoreType::ROW_MAJOR>;
```
**Row-major** storage means rows are contiguous in memory. Suitable for CPU-side transforms and typical C++ math libraries.
---
## Angle types
```cpp
using PitchAngle = Angle<float, -90.f, 90.f, AngleFlags::Clamped>;
using YawAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
using RollAngle = Angle<float, -180.f, 180.f, AngleFlags::Normalized>;
using ViewAngles = omath::ViewAngles<PitchAngle, YawAngle, RollAngle>;
```
* **PitchAngle**: clamped to **[-90°, +90°]** (looking down vs. up)
* **YawAngle**: normalized to **[-180°, +180°]** (horizontal rotation)
* **RollAngle**: normalized to **[-180°, +180°]** (camera roll)
`ViewAngles` bundles all three into a single type for camera/view transforms.
---
## Coordinate system notes
* **Z-up**: gravity points along `-Z`, height increases with `+Z`
* **Left-handed**: cross product `forward × right = up` with left-hand rule
* This matches **Unreal Engine** conventions for 3D games and simulations
---
## See also
* `omath/engines/unreal_engine/formulas.hpp` — view/projection matrix builders
* `omath/trigonometry/angle.hpp` — angle normalization & clamping helpers
* `omath/trigonometry/view_angles.hpp` — generic pitch/yaw/roll wrapper

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# `omath::unreal_engine` — formulas & matrix helpers
> Header: `omath/engines/unreal_engine/formulas.hpp`
> Namespace: `omath::unreal_engine`
> Purpose: compute direction vectors, rotation matrices, view matrices, and perspective projections for Unreal Engine
---
## Summary
This header provides **Unreal Engine**-specific math for:
* **Direction vectors** (`forward`, `right`, `up`) from `ViewAngles`
* **Rotation matrices** from Euler angles
* **View matrices** (camera transforms)
* **Perspective projection** matrices
All functions respect Unreal Engine's **Z-up, left-handed** coordinate system.
---
## API
```cpp
namespace omath::unreal_engine {
// Compute forward direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> forward_vector(const ViewAngles& angles) noexcept;
// Compute right direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> right_vector(const ViewAngles& angles) noexcept;
// Compute up direction from pitch/yaw/roll
[[nodiscard]]
Vector3<float> up_vector(const ViewAngles& angles) noexcept;
// Build 3x3 rotation matrix from angles
[[nodiscard]]
Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept;
// Build view matrix (camera space transform)
[[nodiscard]]
Mat4X4 calc_view_matrix(const ViewAngles& angles,
const Vector3<float>& cam_origin) noexcept;
// Build perspective projection matrix
[[nodiscard]]
Mat4X4 calc_perspective_projection_matrix(float field_of_view,
float aspect_ratio,
float near, float far) noexcept;
} // namespace omath::unreal_engine
```
---
## Direction vectors
Given camera angles (pitch/yaw/roll):
* `forward_vector(angles)` → unit vector pointing where the camera looks
* `right_vector(angles)` → unit vector pointing to the camera's right
* `up_vector(angles)` → unit vector pointing upward relative to the camera
These are used for movement, aim direction, and building coordinate frames.
---
## Rotation & view matrices
* `rotation_matrix(angles)` → 3×3 (or 4×4) rotation matrix from Euler angles
* `calc_view_matrix(angles, origin)` → camera view matrix
The view matrix transforms world coordinates into camera space (origin at camera, axes aligned with camera orientation).
---
## Perspective projection
```cpp
Mat4X4 proj = calc_perspective_projection_matrix(
fov_degrees, // vertical field of view (e.g., 90)
aspect_ratio, // width / height (e.g., 16/9)
near_plane, // e.g., 10.0
far_plane // e.g., 100000.0
);
```
Produces a **perspective projection matrix** suitable for 3D rendering pipelines. Combined with the view matrix, this implements the standard camera transform chain.
---
## Usage example
```cpp
using namespace omath::unreal_engine;
// Camera setup
ViewAngles angles = {
PitchAngle::from_degrees(-20.0f),
YawAngle::from_degrees(45.0f),
RollAngle::from_degrees(0.0f)
};
Vector3<float> cam_pos{1000.0f, 500.0f, 200.0f};
// Compute direction
auto forward = forward_vector(angles);
auto right = right_vector(angles);
auto up = up_vector(angles);
// Build matrices
auto view_mat = calc_view_matrix(angles, cam_pos);
auto proj_mat = calc_perspective_projection_matrix(90.0f, 16.0f/9.0f, 10.0f, 100000.0f);
// Use view_mat and proj_mat for rendering...
```
---
## Conventions
* **Angles**: pitch (up/down), yaw (left/right), roll (tilt)
* **Pitch**: positive = looking up, negative = looking down
* **Yaw**: increases counter-clockwise from the +X axis
* **Coordinate system**: Z-up, X-forward, Y-right (left-handed)
---
## See also
* `omath/engines/unreal_engine/constants.hpp` — coordinate frame & angle types
* `omath/engines/unreal_engine/traits/camera_trait.hpp` — plug-in for generic `Camera`
* `omath/projection/camera.hpp` — generic camera wrapper using these formulas

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# `omath::unreal_engine::PredEngineTrait` — projectile prediction trait
> Header: `omath/engines/unreal_engine/traits/pred_engine_trait.hpp`
> Namespace: `omath::unreal_engine`
> Purpose: provide Unreal Engine-specific projectile and target prediction for ballistic calculations
---
## Summary
`PredEngineTrait` implements engine-specific helpers for **projectile prediction**:
* `predict_projectile_position` – computes where a projectile will be after `time` seconds
* `predict_target_position` – computes where a moving target will be after `time` seconds
* `calc_vector_2d_distance` – horizontal distance (X/Y plane, ignoring Z)
* `get_vector_height_coordinate` – extracts vertical coordinate (Y in Unreal Engine, note: code uses Z)
* `calc_viewpoint_from_angles` – computes aim point given pitch angle
* `calc_direct_pitch_angle` – pitch angle to look from origin to target
* `calc_direct_yaw_angle` – yaw angle to look from origin to target
These methods satisfy the `PredEngineTraitConcept` required by generic projectile prediction algorithms.
---
## API
```cpp
namespace omath::unreal_engine {
class PredEngineTrait final {
public:
// Predict projectile position after `time` seconds
static constexpr Vector3<float>
predict_projectile_position(const projectile_prediction::Projectile& projectile,
float pitch, float yaw, float time,
float gravity) noexcept;
// Predict target position after `time` seconds
static constexpr Vector3<float>
predict_target_position(const projectile_prediction::Target& target,
float time, float gravity) noexcept;
// Compute horizontal (2D) distance
static float
calc_vector_2d_distance(const Vector3<float>& delta) noexcept;
// Get vertical coordinate (implementation returns Y, but UE is Z-up)
static constexpr float
get_vector_height_coordinate(const Vector3<float>& vec) noexcept;
// Compute aim point from angles
static Vector3<float>
calc_viewpoint_from_angles(const projectile_prediction::Projectile& projectile,
Vector3<float> predicted_target_position,
std::optional<float> projectile_pitch) noexcept;
// Compute pitch angle to look at target
static float
calc_direct_pitch_angle(const Vector3<float>& origin,
const Vector3<float>& view_to) noexcept;
// Compute yaw angle to look at target
static float
calc_direct_yaw_angle(const Vector3<float>& origin,
const Vector3<float>& view_to) noexcept;
};
} // namespace omath::unreal_engine
```
---
## Projectile prediction
```cpp
auto pos = PredEngineTrait::predict_projectile_position(
projectile, // initial position, speed, gravity scale
pitch_deg, // launch pitch (positive = up)
yaw_deg, // launch yaw
time, // time in seconds
gravity // gravity constant (e.g., 980 cm/s²)
);
```
Computes:
1. Forward vector from pitch/yaw (using `forward_vector`)
2. Initial velocity: `forward * launch_speed`
3. Position after `time`: `origin + velocity*time - 0.5*gravity*gravityScale*time²` (Y component per implementation, though UE is Z-up)
**Note**: Negative pitch in `forward_vector` convention → positive pitch looks up.
---
## Target prediction
```cpp
auto pos = PredEngineTrait::predict_target_position(
target, // position, velocity, airborne flag
time, // time in seconds
gravity // gravity constant
);
```
Simple linear extrapolation plus gravity if target is airborne:
```
predicted = origin + velocity * time
if (airborne)
predicted.y -= 0.5 * gravity * time² // Note: implementation uses Y
```
---
## Distance & height helpers
* `calc_vector_2d_distance(delta)` → `sqrt(delta.x² + delta.z²)` (horizontal distance in X/Z plane)
* `get_vector_height_coordinate(vec)` → `vec.y` (implementation returns Y; UE convention is Z-up)
Used to compute ballistic arc parameters.
---
## Aim angle calculation
* `calc_direct_pitch_angle(origin, target)` → pitch in degrees to look from `origin` to `target`
- Formula: `asin(Δz / distance)` converted to degrees (direction normalized first)
- Positive = looking up, negative = looking down
* `calc_direct_yaw_angle(origin, target)` → yaw in degrees to look from `origin` to `target`
- Formula: `atan2(Δy, Δx)` converted to degrees (direction normalized first)
- Horizontal rotation around Z-axis
---
## Viewpoint from angles
```cpp
auto aim_point = PredEngineTrait::calc_viewpoint_from_angles(
projectile,
predicted_target_pos,
optional_pitch_deg
);
```
Computes where to aim in 3D space given a desired pitch angle. Uses horizontal distance and `tan(pitch)` to compute height offset.
---
## Conventions
* **Coordinate system**: Z-up (height increases with Z)
* **Angles**: pitch in [-90°, +90°], yaw in [-180°, +180°]
* **Gravity**: applied downward (implementation uses Y component, but UE is Z-up)
* **Pitch convention**: +90° = straight up, -90° = straight down
**Note**: Some implementation details (gravity application to Y coordinate) may need adjustment for full Unreal Engine Z-up consistency.
---
## Usage example
```cpp
using namespace omath::unreal_engine;
using namespace omath::projectile_prediction;
Projectile proj{
.m_origin = {0, 0, 200},
.m_launch_speed = 5000.0f,
.m_gravity_scale = 1.0f
};
Target tgt{
.m_origin = {2000, 1000, 200},
.m_velocity = {50, 20, 0},
.m_is_airborne = false
};
float gravity = 980.0f; // cm/s² in Unreal units
float time = 0.5f;
// Predict where target will be
auto target_pos = PredEngineTrait::predict_target_position(tgt, time, gravity);
// Compute aim angles
float pitch = PredEngineTrait::calc_direct_pitch_angle(proj.m_origin, target_pos);
float yaw = PredEngineTrait::calc_direct_yaw_angle(proj.m_origin, target_pos);
// Predict projectile position with those angles
auto proj_pos = PredEngineTrait::predict_projectile_position(proj, pitch, yaw, time, gravity);
```
---
## See also
* `omath/engines/unreal_engine/formulas.hpp` — direction vectors and matrix builders
* `omath/projectile_prediction/projectile.hpp` — `Projectile` struct
* `omath/projectile_prediction/target.hpp` — `Target` struct
* Generic projectile prediction algorithms that use `PredEngineTraitConcept`

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# FAQ
Common questions and answers about OMath.
---
## General Questions
### What is OMath?
OMath is a modern C++ math library designed for game development, graphics programming, and high-performance computing. It provides:
- Vector and matrix operations
- 3D projection and camera systems
- Projectile prediction
- Collision detection
- Support for multiple game engines (Source, Unity, Unreal, etc.)
- Pattern scanning utilities
### Why choose OMath over other math libraries?
- **Modern C++**: Uses C++20/23 features (concepts, `constexpr`, `std::expected`)
- **No legacy code**: Built from scratch without legacy baggage
- **Game engine support**: Pre-configured for Source, Unity, Unreal, Frostbite, etc.
- **Zero dependencies**: No external dependencies needed (except for testing)
- **Performance**: AVX2 optimizations available
- **Type safety**: Strong typing prevents common errors
- **Cross-platform**: Works on Windows, Linux, and macOS
### Is OMath suitable for production use?
Yes! OMath is production-ready and used in various projects. It has:
- Comprehensive test coverage
- Clear error handling
- Well-documented API
- Active maintenance and community support
---
## Installation & Setup
### How do I install OMath?
Three main methods:
**vcpkg (recommended):**
```bash
vcpkg install orange-math
```
**xrepo:**
```bash
xrepo install omath
```
**From source:**
See [Installation Guide](install.md)
### What are the minimum requirements?
- **Compiler**: C++20 support required
- GCC 10+
- Clang 11+
- MSVC 2019 16.10+
- **CMake**: 3.15+ (if building from source)
- **Platform**: Windows, Linux, or macOS
### Do I need C++23?
C++23 is **recommended** but not required. Some features like `std::expected` work better with C++23, but fallbacks are available for C++20.
### Can I use OMath in a C++17 project?
No, OMath requires C++20 minimum due to use of concepts, `constexpr` enhancements, and other C++20 features.
---
## Usage Questions
### How do I include OMath in my project?
**Full library:**
```cpp
#include <omath/omath.hpp>
```
**Specific components:**
```cpp
#include <omath/linear_algebra/vector3.hpp>
#include <omath/engines/source_engine/camera.hpp>
```
### Which game engine should I use?
Choose based on your target game or application:
| Engine | Use For |
|--------|---------|
| **Source Engine** | CS:GO, TF2, CS2, Half-Life, Portal, L4D |
| **Unity Engine** | Unity games (many indie and mobile games) |
| **Unreal Engine** | Fortnite, Unreal games |
| **Frostbite** | Battlefield, Star Wars games (EA titles) |
| **IW Engine** | Call of Duty series |
| **OpenGL** | Custom OpenGL applications, generic 3D |
### How do I switch between engines?
Just change the namespace:
```cpp
// Source Engine
using namespace omath::source_engine;
Camera cam = /* ... */;
// Unity Engine
using namespace omath::unity_engine;
Camera cam = /* ... */;
```
Each engine has the same API but different coordinate system handling.
### What if my game isn't listed?
Use the **OpenGL engine** as a starting point - it uses canonical OpenGL conventions. You may need to adjust coordinate transformations based on your specific game.
---
## Performance Questions
### Should I use the AVX2 or Legacy engine?
**Use AVX2 if:**
- Target modern CPUs (2013+)
- Need maximum performance
- Can accept reduced compatibility
**Use Legacy if:**
- Need broad compatibility
- Target older CPUs or ARM
- Unsure about target hardware
The API is identical - just change the class:
```cpp
// Legacy (compatible)
ProjPredEngineLegacy engine;
// AVX2 (faster)
ProjPredEngineAVX2 engine;
```
### How much faster is AVX2?
Typically 2-4x faster for projectile prediction calculations, depending on the CPU and specific use case.
### Are vector operations constexpr?
Yes! Most operations are `constexpr` and can be evaluated at compile-time:
```cpp
constexpr Vector3<float> v{1, 2, 3};
constexpr auto len_sq = v.length_sqr(); // Computed at compile time
```
### Is OMath thread-safe?
- **Immutable operations** (vector math, etc.) are thread-safe
- **Mutable state** (Camera updates) is NOT thread-safe
- Use separate instances per thread or synchronize access
---
## Troubleshooting
### `world_to_screen()` always returns `nullopt`
Check:
1. **Is the point behind the camera?** Points behind the camera cannot be projected.
2. **Are near/far planes correct?** Ensure `near < far` and both are positive.
3. **Is FOV valid?** FOV should be between 1° and 179°.
4. **Are camera angles normalized?** Use engine-provided angle types.
### Angles are wrapping incorrectly
Use the correct angle type:
```cpp
// Good: uses proper angle type
PitchAngle pitch = PitchAngle::from_degrees(45.0f);
// Bad: raw float loses normalization
float pitch = 45.0f;
```
### Projection seems mirrored or inverted
You may be using the wrong engine trait. Each engine has different coordinate conventions:
- **Source/Unity**: Z-up
- **Unreal**: Z-up, different handedness
- **OpenGL**: Y-up
Ensure you're using the trait matching your game.
### Pattern scanning finds multiple matches
This is normal! Patterns may appear multiple times. Solutions:
1. Make the pattern more specific (more bytes, fewer wildcards)
2. Use additional context (nearby code patterns)
3. Verify each match programmatically
### Projectile prediction returns `nullopt`
Common reasons:
1. **Target too fast**: Target velocity exceeds projectile speed
2. **Out of range**: Distance exceeds max flight time
3. **Invalid input**: Check projectile speed > 0
4. **Gravity too strong**: Projectile can't reach target height
### Compilation errors about `std::expected`
If using C++20 (not C++23), you may need a backport library like `tl::expected`:
```cmake
# CMakeLists.txt
find_package(tl-expected CONFIG REQUIRED)
target_link_libraries(your_target PRIVATE tl::expected)
```
Or upgrade to C++23 if possible.
---
## Feature Questions
### Can I use OMath with DirectX/OpenGL/Vulkan?
Yes! OMath matrices and vectors work with all graphics APIs. Use:
- **OpenGL**: `opengl_engine` traits
- **DirectX**: Use appropriate engine trait or OpenGL as base
- **Vulkan**: Use OpenGL traits as starting point
### Does OMath support quaternions?
Not currently. Quaternion support may be added in future versions. For now, use euler angles (ViewAngles) or convert manually.
### Can I extend OMath with custom engine traits?
Yes! Implement the `CameraEngineConcept`:
```cpp
class MyEngineTrait {
public:
static ViewAngles calc_look_at_angle(
const Vector3<float>& origin,
const Vector3<float>& target
);
static Mat4X4 calc_view_matrix(
const ViewAngles& angles,
const Vector3<float>& origin
);
static Mat4X4 calc_projection_matrix(
const FieldOfView& fov,
const ViewPort& viewport,
float near, float far
);
};
// Use with Camera
using MyCamera = Camera<Mat4X4, ViewAngles, MyEngineTrait>;
```
### Does OMath support SIMD for vector operations?
AVX2 support is available for projectile prediction. General vector SIMD may be added in future versions. The library already compiles to efficient code with compiler optimizations enabled.
### Can I use OMath for machine learning?
OMath is optimized for game development and graphics, not ML. For machine learning, consider libraries like Eigen or xtensor which are designed for that domain.
---
## Debugging Questions
### How do I print vectors?
OMath provides `std::formatter` support:
```cpp
#include <format>
#include <iostream>
Vector3<float> v{1, 2, 3};
std::cout << std::format("{}", v) << "\n"; // Prints: [1, 2, 3]
```
### How do I visualize projection problems?
1. Check if `world_to_screen()` succeeds
2. Print camera matrices:
```cpp
auto view = camera.get_view_matrix();
auto proj = camera.get_projection_matrix();
// Print matrix values
```
3. Test with known good points (e.g., origin, simple positions)
4. Verify viewport and FOV values
### How can I debug pattern scanning?
```cpp
PatternView pattern{"48 8B 05 ?? ?? ?? ??"};
// Print pattern details
std::cout << "Pattern length: " << pattern.size() << "\n";
std::cout << "Pattern bytes: ";
for (auto byte : pattern) {
if (byte.has_value()) {
std::cout << std::hex << (int)*byte << " ";
} else {
std::cout << "?? ";
}
}
std::cout << "\n";
```
---
## Contributing
### How can I contribute to OMath?
See [CONTRIBUTING.md](https://github.com/orange-cpp/omath/blob/master/CONTRIBUTING.md) for guidelines. Contributions welcome:
- Bug fixes
- New features
- Documentation improvements
- Test coverage
- Examples
### Where do I report bugs?
[GitHub Issues](https://github.com/orange-cpp/omath/issues)
Please include:
- OMath version
- Compiler and version
- Minimal reproducible example
- Expected vs actual behavior
### How do I request a feature?
Open a GitHub issue with:
- Use case description
- Proposed API (if applicable)
- Why existing features don't meet your needs
---
## License & Legal
### What license does OMath use?
OMath uses a custom "libomath" license. See [LICENSE](https://github.com/orange-cpp/omath/blob/master/LICENSE) for full details.
### Can I use OMath in commercial projects?
Check the LICENSE file for commercial use terms.
### Can I use OMath for game cheating/hacking?
OMath is a math library and can be used for various purposes. However:
- Using it to cheat in online games may violate game ToS
- Creating cheats may be illegal in your jurisdiction
- The developers do not condone cheating in online games
Use responsibly and ethically.
---
## Getting Help
### Where can I get help?
- **Documentation**: [http://libomath.org](http://libomath.org)
- **Discord**: [Join community](https://discord.gg/eDgdaWbqwZ)
- **Telegram**: [@orangennotes](https://t.me/orangennotes)
- **GitHub Issues**: [Report bugs/ask questions](https://github.com/orange-cpp/omath/issues)
### Is there a Discord/community?
Yes! Join our Discord: [https://discord.gg/eDgdaWbqwZ](https://discord.gg/eDgdaWbqwZ)
### Are there video tutorials?
Check our [YouTube channel](https://youtu.be/lM_NJ1yCunw?si=-Qf5yzDcWbaxAXGQ) for demonstrations and tutorials.
---
## Didn't find your answer?
- Search the [documentation](index.md)
- Check [tutorials](tutorials.md)
- Ask on [Discord](https://discord.gg/eDgdaWbqwZ)
- Open a [GitHub issue](https://github.com/orange-cpp/omath/issues)
---
*Last updated: 1 Nov 2025*

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# Getting Started
Welcome to OMath! This guide will help you get up and running with the library quickly.
## What is OMath?
OMath is a modern, blazingly fast C++ math library designed for:
- **Game development** and cheat development
- **Graphics programming** (DirectX/OpenGL/Vulkan)
- **3D applications** with support for multiple game engines
- **High-performance computing** with AVX2 optimizations
Key features:
- 100% independent, no legacy C++ code
- Fully `constexpr` template-based design
- Zero additional dependencies (except for unit tests)
- Cross-platform (Windows, macOS, Linux)
- Built-in support for Source, Unity, Unreal, Frostbite, IWEngine, and OpenGL coordinate systems
---
## Installation
Choose one of the following methods to install OMath:
### Using vcpkg (Recommended)
```bash
vcpkg install orange-math
```
Then in your CMakeLists.txt:
```cmake
find_package(omath CONFIG REQUIRED)
target_link_libraries(your_target PRIVATE omath::omath)
```
### Using xrepo
```bash
xrepo install omath
```
Then in your xmake.lua:
```lua
add_requires("omath")
target("your_target")
add_packages("omath")
```
### Building from Source
See the detailed [Installation Guide](install.md) for complete instructions.
---
## Quick Example
Here's a simple example to get you started:
```cpp
#include <omath/omath.hpp>
#include <iostream>
int main() {
using namespace omath;
// Create 3D vectors
Vector3<float> a{1.0f, 2.0f, 3.0f};
Vector3<float> b{4.0f, 5.0f, 6.0f};
// Vector operations
auto sum = a + b; // Vector addition
auto dot_product = a.dot(b); // Dot product: 32.0
auto cross_product = a.cross(b); // Cross product: (-3, 6, -3)
auto length = a.length(); // Length: ~3.74
auto normalized = a.normalized(); // Unit vector
std::cout << "Sum: [" << sum.x << ", " << sum.y << ", " << sum.z << "]\n";
std::cout << "Dot product: " << dot_product << "\n";
std::cout << "Length: " << length << "\n";
return 0;
}
```
---
## Core Concepts
### 1. Vectors
OMath provides 2D, 3D, and 4D vector types:
```cpp
using namespace omath;
Vector2<float> vec2{1.0f, 2.0f};
Vector3<float> vec3{1.0f, 2.0f, 3.0f};
Vector4<float> vec4{1.0f, 2.0f, 3.0f, 4.0f};
```
All vector types support:
- Arithmetic operations (+, -, *, /)
- Dot and cross products (where applicable)
- Length and distance calculations
- Normalization
- Component-wise operations
See: [Vector2](linear_algebra/vector2.md), [Vector3](linear_algebra/vector3.md), [Vector4](linear_algebra/vector4.md)
### 2. Matrices
4x4 matrices for transformations:
```cpp
using namespace omath;
Mat4X4 matrix = Mat4X4::identity();
// Use for transformations, projections, etc.
```
See: [Matrix Documentation](linear_algebra/mat.md)
### 3. Angles
Strong-typed angle system with automatic range management:
```cpp
using namespace omath;
auto angle = Angle<float, 0.0f, 360.0f>::from_degrees(45.0f);
auto radians = angle.as_radians();
// View angles for camera systems
ViewAngles view{
PitchAngle::from_degrees(-10.0f),
YawAngle::from_degrees(90.0f),
RollAngle::from_degrees(0.0f)
};
```
See: [Angle](trigonometry/angle.md), [View Angles](trigonometry/view_angles.md)
### 4. 3D Projection
Built-in camera and projection systems:
```cpp
using namespace omath;
using namespace omath::projection;
ViewPort viewport{1920.0f, 1080.0f};
auto fov = FieldOfView::from_degrees(90.0f);
// Example using Source Engine
using namespace omath::source_engine;
Camera cam(
Vector3<float>{0, 0, 100}, // Position
ViewAngles{}, // Angles
viewport,
fov,
0.1f, // near plane
1000.0f // far plane
);
// Project 3D point to 2D screen
Vector3<float> world_pos{100, 50, 75};
if (auto screen_pos = cam.world_to_screen(world_pos)) {
std::cout << "Screen: " << screen_pos->x << ", " << screen_pos->y << "\n";
}
```
See: [Camera](projection/camera.md)
### 5. Game Engine Support
OMath provides pre-configured traits for major game engines:
```cpp
// Source Engine
#include <omath/engines/source_engine/camera.hpp>
using SourceCamera = omath::source_engine::Camera;
// Unity Engine
#include <omath/engines/unity_engine/camera.hpp>
using UnityCamera = omath::unity_engine::Camera;
// Unreal Engine
#include <omath/engines/unreal_engine/camera.hpp>
using UnrealCamera = omath::unreal_engine::Camera;
// And more: OpenGL, Frostbite, IWEngine
```
Each engine has its own coordinate system conventions automatically handled.
See: Engine-specific docs in [engines/](engines/) folder
---
## Common Use Cases
### World-to-Screen Projection
```cpp
using namespace omath;
using namespace omath::source_engine;
Camera cam = /* initialize camera */;
Vector3<float> enemy_position{100, 200, 50};
if (auto screen = cam.world_to_screen(enemy_position)) {
// Draw ESP box at screen->x, screen->y
std::cout << "Enemy on screen at: " << screen->x << ", " << screen->y << "\n";
} else {
// Enemy not visible (behind camera or outside frustum)
}
```
### Projectile Prediction
```cpp
using namespace omath::projectile_prediction;
Projectile bullet{
Vector3<float>{0, 0, 0}, // shooter position
1000.0f, // muzzle velocity (m/s)
Vector3<float>{0, 0, -9.81f} // gravity
};
Target enemy{
Vector3<float>{100, 200, 50}, // position
Vector3<float>{10, 0, 0} // velocity
};
// Calculate where to aim
ProjPredEngineLegacy engine;
if (auto aim_point = engine.maybe_calculate_aim_point(bullet, enemy)) {
// Aim at *aim_point to hit moving target
}
```
See: [Projectile Prediction](projectile_prediction/projectile_engine.md)
### Collision Detection
```cpp
using namespace omath;
// Ray-plane intersection
Plane ground{
Vector3<float>{0, 0, 0}, // point on plane
Vector3<float>{0, 0, 1} // normal (pointing up)
};
Vector3<float> ray_origin{0, 0, 100};
Vector3<float> ray_direction{0, 0, -1};
if (auto hit = ground.intersects_ray(ray_origin, ray_direction)) {
std::cout << "Hit ground at: " << hit->x << ", " << hit->y << ", " << hit->z << "\n";
}
```
See: [Collision Detection](collision/line_tracer.md)
### Pattern Scanning
```cpp
#include <omath/utility/pattern_scan.hpp>
using namespace omath;
std::vector<uint8_t> memory = /* ... */;
PatternView pattern{"48 8B 05 ?? ?? ?? ?? 48 85 C0"};
if (auto result = pattern_scan(memory, pattern)) {
std::cout << "Pattern found at offset: " << result->offset << "\n";
}
```
See: [Pattern Scanning](utility/pattern_scan.md)
---
## Next Steps
Now that you have the basics, explore these topics:
1. **[API Reference](index.md)** - Complete API documentation
2. **[Examples](../examples/)** - Working code examples
3. **[Engine-Specific Features](engines/)** - Deep dive into game engine support
4. **[Advanced Topics](#)** - Performance optimization, custom traits, etc.
---
## Getting Help
- **Documentation**: [http://libomath.org](http://libomath.org)
- **Discord**: [Join our community](https://discord.gg/eDgdaWbqwZ)
- **Telegram**: [@orangennotes](https://t.me/orangennotes)
- **Issues**: [GitHub Issues](https://github.com/orange-cpp/omath/issues)
---
*Last updated: 1 Nov 2025*

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<div class="center-text">
<!-- Banner -->
<p>
<img src="images/logos/omath_logo_macro.png" alt="omath banner">
</p>
<!-- Badges -->
<p>
<img src="https://img.shields.io/badge/license-libomath-orange" alt="license: libomath">
<img src="https://img.shields.io/github/contributors/orange-cpp/omath" alt="GitHub contributors">
<img src="https://img.shields.io/github/languages/top/orange-cpp/omath" alt="Top language">
<a href="https://www.codefactor.io/repository/github/orange-cpp/omath">
<img src="https://www.codefactor.io/repository/github/orange-cpp/omath/badge" alt="CodeFactor">
</a>
<img src="https://img.shields.io/github/actions/workflow/status/orange-cpp/omath/cmake-multi-platform.yml" alt="GitHub Actions Workflow Status">
<a href="https://repology.org/project/orange-math/versions">
<img src="https://repology.org/badge/version-for-repo/vcpkg/orange-math.svg" alt="Vcpkg package">
</a>
<img src="https://img.shields.io/github/forks/orange-cpp/omath" alt="GitHub forks">
<a href="https://discord.gg/eDgdaWbqwZ">
<img src="https://dcbadge.limes.pink/api/server/https://discord.gg/eDgdaWbqwZ?style=flat" alt="Join us on Discord">
</a>
<a href="https://t.me/orangennotes">
<img src="https://img.shields.io/badge/Telegram-2CA5E0?style=flat-squeare&logo=telegram&logoColor=white" alt="Telegram">
</a>
</p>
</div>
OMath is a 100% independent, constexpr template blazingly fast math library that doesn't have legacy C++ code.
It provides the latest features, is highly customizable, has all for cheat development, DirectX/OpenGL/Vulkan support, premade support for different game engines, much more constexpr stuff than in other libraries and more...
---
## 🚀 Quick Start
**New to OMath?** Start here:
- **[Getting Started Guide](getting_started.md)** - Installation and first steps
- **[API Overview](api_overview.md)** - High-level API reference
- **[Installation Instructions](install.md)** - Detailed setup guide
**Quick example:**
```cpp
#include <omath/omath.hpp>
using namespace omath;
Vector3<float> a{1, 2, 3};
Vector3<float> b{4, 5, 6};
auto dot = a.dot(b); // 32.0
auto cross = a.cross(b); // (-3, 6, -3)
auto distance = a.distance_to(b); // ~5.196
```
---
## 📚 Documentation Structure
### Core Mathematics
**Linear Algebra**
- [Vector2](linear_algebra/vector2.md) - 2D vectors with full operator support
- [Vector3](linear_algebra/vector3.md) - 3D vectors, dot/cross products, angles
- [Vector4](linear_algebra/vector4.md) - 4D vectors (homogeneous coordinates)
- [Mat4X4](linear_algebra/mat.md) - 4×4 matrices for transformations
- [Triangle](linear_algebra/triangle.md) - Triangle primitive and utilities
**Trigonometry**
- [Angle](trigonometry/angle.md) - Strong-typed angle system with range enforcement
- [Angles](trigonometry/angles.md) - Angle utilities and conversions
- [View Angles](trigonometry/view_angles.md) - Pitch/Yaw/Roll for camera systems
**3D Primitives**
- [Box](3d_primitives/box.md) - Axis-aligned bounding boxes
- [Plane](3d_primitives/plane.md) - Infinite planes and intersections
### Game Development Features
**Projection & Camera**
- [Camera](projection/camera.md) - Generic camera system with engine traits
- [Error Codes](projection/error_codes.md) - Projection error handling
**Collision Detection**
- [Line Tracer](collision/line_tracer.md) - Ray-triangle, ray-plane intersections
**Projectile Prediction**
- [Projectile Engine Interface](projectile_prediction/projectile_engine.md) - Base interface
- [Projectile](projectile_prediction/projectile.md) - Projectile properties
- [Target](projectile_prediction/target.md) - Target state representation
- [Legacy Engine](projectile_prediction/proj_pred_engine_legacy.md) - Standard implementation
- [AVX2 Engine](projectile_prediction/proj_pred_engine_avx2.md) - Optimized implementation
**Pathfinding**
- [A* Algorithm](pathfinding/a_star.md) - A* pathfinding implementation
- [Navigation Mesh](pathfinding/navigation_mesh.md) - Triangle-based navigation
### Game Engine Support
OMath provides built-in support for multiple game engines with proper coordinate system handling:
**Source Engine** (Valve - CS:GO, TF2, etc.)
- [Camera Trait](engines/source_engine/camera_trait.md)
- [Pred Engine Trait](engines/source_engine/pred_engine_trait.md)
- [Constants](engines/source_engine/constants.md)
- [Formulas](engines/source_engine/formulas.md)
**Unity Engine**
- [Camera Trait](engines/unity_engine/camera_trait.md)
- [Pred Engine Trait](engines/unity_engine/pred_engine_trait.md)
- [Constants](engines/unity_engine/constants.md)
- [Formulas](engines/unity_engine/formulas.md)
**Unreal Engine** (Epic Games)
- [Camera Trait](engines/unreal_engine/camera_trait.md)
- [Pred Engine Trait](engines/unreal_engine/pred_engine_trait.md)
- [Constants](engines/unreal_engine/constants.md)
- [Formulas](engines/unreal_engine/formulas.md)
**Frostbite Engine** (EA - Battlefield, etc.)
- [Camera Trait](engines/frostbite/camera_trait.md)
- [Pred Engine Trait](engines/frostbite/pred_engine_trait.md)
- [Constants](engines/frostbite/constants.md)
- [Formulas](engines/frostbite/formulas.md)
**IW Engine** (Infinity Ward - Call of Duty)
- [Camera Trait](engines/iw_engine/camera_trait.md)
- [Pred Engine Trait](engines/iw_engine/pred_engine_trait.md)
- [Constants](engines/iw_engine/constants.md)
- [Formulas](engines/iw_engine/formulas.md)
**OpenGL Engine** (Canonical OpenGL)
- [Camera Trait](engines/opengl_engine/camera_trait.md)
- [Pred Engine Trait](engines/opengl_engine/pred_engine_trait.md)
- [Constants](engines/opengl_engine/constants.md)
- [Formulas](engines/opengl_engine/formulas.md)
### Utilities
**Color**
- [Color](utility/color.md) - RGBA color with conversions
**Pattern Scanning & Memory**
- [Pattern Scan](utility/pattern_scan.md) - Binary pattern search with wildcards
- [PE Pattern Scan](utility/pe_pattern_scan.md) - PE file pattern scanning
**Reverse Engineering**
- [External Rev Object](rev_eng/external_rev_object.md) - External process memory access
- [Internal Rev Object](rev_eng/internal_rev_object.md) - Internal memory access
---
## ✨ Key Features
- **Efficiency**: Optimized for performance, ensuring quick computations using AVX2.
- **Versatility**: Includes a wide array of mathematical functions and algorithms.
- **Ease of Use**: Simplified interface for convenient integration into various projects.
- **Projectile Prediction**: Projectile prediction engine with O(N) algo complexity, that can power you projectile aim-bot.
- **3D Projection**: No need to find view-projection matrix anymore you can make your own projection pipeline.
- **Collision Detection**: Production ready code to handle collision detection by using simple interfaces.
- **No Additional Dependencies**: No additional dependencies need to use OMath except unit test execution
- **Ready for meta-programming**: Omath use templates for common types like Vectors, Matrixes etc, to handle all types!
- **Engine support**: Supports coordinate systems of **Source, Unity, Unreal, Frostbite, IWEngine and canonical OpenGL**.
- **Cross platform**: Supports Windows, MacOS and Linux.
- **Algorithms**: Has ability to scan for byte pattern with wildcards in PE files/modules, binary slices, works even with Wine apps.
---
## 📖 Common Use Cases
### World-to-Screen Projection
Project 3D world coordinates to 2D screen space for ESP overlays, UI elements, or visualization.
### Projectile Prediction
Calculate aim points for moving targets considering projectile speed, gravity, and target velocity.
### Collision Detection
Perform ray-casting, line tracing, and intersection tests for hit detection and physics.
### Pattern Scanning
Search for byte patterns in memory for reverse engineering, modding, or tool development.
### Pathfinding
Find optimal paths through 3D spaces using A* algorithm and navigation meshes.
---
## 🎮 Gallery
<br>
[![Youtube Video](images/yt_previews/img.png)](https://youtu.be/lM_NJ1yCunw?si=-Qf5yzDcWbaxAXGQ)
<br>
![APEX Preview]
<br>
![BO2 Preview]
<br>
![CS2 Preview]
<br>
![TF2 Preview]
<br>
<br>
---
## 🤝 Community & Support
- **Documentation**: [http://libomath.org](http://libomath.org)
- **GitHub**: [orange-cpp/omath](https://github.com/orange-cpp/omath)
- **Discord**: [Join our community](https://discord.gg/eDgdaWbqwZ)
- **Telegram**: [@orangennotes](https://t.me/orangennotes)
- **Issues**: [Report bugs or request features](https://github.com/orange-cpp/omath/issues)
---
## 💡 Contributing
OMath is open source and welcomes contributions! See [CONTRIBUTING.md](https://github.com/orange-cpp/omath/blob/master/CONTRIBUTING.md) for guidelines.
---
*Last updated: 1 Nov 2025*
<!----------------------------------{ Images }--------------------------------->
[APEX Preview]: images/showcase/apex.png
[BO2 Preview]: images/showcase/cod_bo2.png
[CS2 Preview]: images/showcase/cs2.jpeg
[TF2 Preview]: images/showcase/tf2.jpg

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# Installation
## <img width="28px" src="https://vcpkg.io/assets/mark/mark.svg" /> Using vcpkg
**Note**: Support vcpkg for package management
1. Install [vcpkg](https://github.com/microsoft/vcpkg)
2. Run the following command to install the orange-math package:
```
vcpkg install orange-math
```
CMakeLists.txt
```cmake
find_package(omath CONFIG REQUIRED)
target_link_libraries(main PRIVATE omath::omath)
```
For detailed commands on installing different versions and more information, please refer to Microsoft's [official instructions](https://learn.microsoft.com/en-us/vcpkg/get_started/overview).
## <img width="28px" src="https://xmake.io/assets/img/logo.svg" /> Using xrepo
**Note**: Support xrepo for package management
1. Install [xmake](https://xmake.io/)
2. Run the following command to install the omath package:
```
xrepo install omath
```
xmake.lua
```xmake
add_requires("omath")
target("...")
add_packages("omath")
```
## <img width="28px" src="https://upload.wikimedia.org/wikipedia/commons/e/ef/CMake_logo.svg?" /> Build from source using CMake
1. **Preparation**
Install needed tools: cmake, clang, git, msvc (windows only).
1. **Linux:**
```bash
sudo pacman -Sy cmake ninja clang git
```
2. **MacOS:**
```bash
brew install llvm git cmake ninja
```
3. **Windows:**
Install Visual Studio from [here](https://visualstudio.microsoft.com/downloads/) and Git from [here](https://git-scm.com/downloads).
Use x64 Native Tools shell to execute needed commands down below.
2. **Clone the repository:**
```bash
git clone https://github.com/orange-cpp/omath.git
```
3. **Navigate to the project directory:**
```bash
cd omath
```
4. **Build the project using CMake:**
```bash
cmake --preset windows-release -S .
cmake --build cmake-build/build/windows-release --target omath -j 6
```
Use **\<platform\>-\<build configuration\>** preset to build suitable version for yourself. Like **windows-release** or **linux-release**.
| Platform Name | Build Config |
|---------------|---------------|
| windows | release/debug |
| linux | release/debug |
| darwin | release/debug |

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# `omath::Mat` — Matrix class (C++20/23)
> Header: your project’s `mat.hpp` (requires `vector3.hpp`)
> Namespace: `omath`
> Requires: **C++23** (uses multi-parameter `operator[]`)
> SIMD (optional): define **`OMATH_USE_AVX2`** to enable AVX2-accelerated multiplication for `float`/`double`.
---
## Overview
`omath::Mat<Rows, Columns, Type, StoreType>` is a compile-time, fixed-size matrix with:
* **Row/column counts** as template parameters (no heap allocations).
* **Row-major** or **column-major** storage (compile-time via `MatStoreType`).
* **Arithmetic** and **linear algebra**: matrix × matrix, scalar ops, transpose, determinant, inverse (optional), etc.
* **Transform helpers**: translation, axis rotations, look-at, perspective & orthographic projections.
* **I/O helpers**: `to_string`/`to_wstring`/`to_u8string` and `std::formatter` specializations.
---
## Template parameters
| Parameter | Description | Default |
| ----------- | ------------------------------------------------------------------------ | ----------- |
| `Rows` | Number of rows (size_t, compile-time) | — |
| `Columns` | Number of columns (size_t, compile-time) | — |
| `Type` | Element type (arithmetic) | `float` |
| `StoreType` | Storage order: `MatStoreType::ROW_MAJOR` or `MatStoreType::COLUMN_MAJOR` | `ROW_MAJOR` |
```cpp
enum class MatStoreType : uint8_t { ROW_MAJOR = 0, COLUMN_MAJOR };
```
---
## Quick start
```cpp
#include "mat.hpp"
using omath::Mat;
// 4x4 float, row-major
Mat<4,4> I = {
{1,0,0,0},
{0,1,0,0},
{0,0,1,0},
{0,0,0,1},
};
// Multiply 4x4 transforms
Mat<4,4> A = { {1,2,3,0},{0,1,4,0},{5,6,0,0},{0,0,0,1} };
Mat<4,4> B = { {2,0,0,0},{0,2,0,0},{0,0,2,0},{0,0,0,1} };
Mat<4,4> C = A * B; // matrix × matrix
// Scalar ops
auto D = C * 0.5f; // scale all entries
// Indexing (C++23 multi-parameter operator[])
float a03 = A[0,3]; // same as A.at(0,3)
A[1,2] = 42.0f;
// Transpose, determinant, inverse
auto AT = A.transposed();
float det = A.determinant(); // only for square matrices
auto inv = A.inverted(); // std::optional<Mat>; std::nullopt if non-invertible
```
> **Note**
> Multiplication requires the **same** `StoreType` and `Type` on both operands, and dimensions must match at compile time.
---
## Construction
```cpp
Mat(); // zero-initialized
Mat(std::initializer_list<std::initializer_list<Type>> rows);
explicit Mat(const Type* raw_data); // copies Rows*Columns elements
Mat(const Mat&); Mat(Mat&&);
```
* **Zeroing/setting**
```cpp
m.clear(); // set all entries to 0
m.set(3.14f); // set all entries to a value
```
* **Shape & metadata**
```cpp
Mat<>::row_count(); // constexpr size_t
Mat<>::columns_count(); // constexpr size_t
Mat<>::size(); // constexpr MatSize {rows, columns}
Mat<>::get_store_ordering(); // constexpr MatStoreType
using ContainedType = Type; // alias
```
---
## Element access
```cpp
T& at(size_t r, size_t c);
T const& at(size_t r, size_t c) const;
T& operator[](size_t r, size_t c); // C++23
T const& operator[](size_t r, size_t c) const; // C++23
```
> **Bounds checking**
> In debug builds you may enable/disable range checks via your compile-time macros (see the source guard around `at()`).
---
## Arithmetic
* **Matrix × matrix**
```cpp
// (Rows x Columns) * (Columns x OtherColumns) -> (Rows x OtherColumns)
template<size_t OtherColumns>
Mat<Rows, OtherColumns, Type, StoreType>
operator*(const Mat<Columns, OtherColumns, Type, StoreType>&) const;
```
* Complexity: `O(Rows * Columns * OtherColumns)`.
* AVX2-accelerated when `OMATH_USE_AVX2` is defined and `Type` is `float` or `double`.
* **Scalars**
```cpp
Mat operator*(const Type& s) const; Mat& operator*=(const Type& s);
Mat operator/(const Type& s) const; Mat& operator/=(const Type& s);
```
* **Transpose**
```cpp
Mat<Columns, Rows, Type, StoreType> transposed() const noexcept;
```
* **Determinant (square only)**
```cpp
Type determinant() const; // 1x1, 2x2 fast path; larger uses Laplace expansion
```
* **Inverse (square only)**
```cpp
std::optional<Mat> inverted() const; // nullopt if det == 0
```
* **Minors & cofactors (square only)**
```cpp
Mat<Rows-1, Columns-1, Type, StoreType> strip(size_t r, size_t c) const;
Type minor(size_t r, size_t c) const;
Type alg_complement(size_t r, size_t c) const; // cofactor
```
* **Utilities**
```cpp
Type sum() const noexcept;
auto& raw_array(); // std::array<Type, Rows*Columns>&
auto const& raw_array() const;
```
* **Comparison / formatting**
```cpp
bool operator==(const Mat&) const;
bool operator!=(const Mat&) const;
std::string to_string() const noexcept;
std::wstring to_wstring() const noexcept;
std::u8string to_u8string() const noexcept;
```
// std::formatter specialization provided for char, wchar_t, char8_t
````
---
## Storage order notes
- **Row-major**: `index = row * Columns + column`
- **Column-major**: `index = row + column * Rows`
Choose one **consistently** across your math types and shader conventions. Mixed orders are supported by the type system but not for cross-multiplying (store types must match).
---
## Transform helpers
### From vectors
```cpp
template<class T=float, MatStoreType St=ROW_MAJOR>
Mat<1,4,T,St> mat_row_from_vector(const Vector3<T>& v);
template<class T=float, MatStoreType St=ROW_MAJOR>
Mat<4,1,T,St> mat_column_from_vector(const Vector3<T>& v);
````
### Translation
```cpp
template<class T=float, MatStoreType St=ROW_MAJOR>
Mat<4,4,T,St> mat_translation(const Vector3<T>& d) noexcept;
```
### Axis rotations
```cpp
// Angle type must provide angle.cos() and angle.sin()
template<class T=float, MatStoreType St=ROW_MAJOR, class Angle>
Mat<4,4,T,St> mat_rotation_axis_x(const Angle& a) noexcept;
template<class T=float, MatStoreType St=ROW_MAJOR, class Angle>
Mat<4,4,T,St> mat_rotation_axis_y(const Angle& a) noexcept;
template<class T=float, MatStoreType St=ROW_MAJOR, class Angle>
Mat<4,4,T,St> mat_rotation_axis_z(const Angle& a) noexcept;
```
### Camera/view
```cpp
template<class T=float, MatStoreType St=ROW_MAJOR>
Mat<4,4,T,St> mat_camera_view(const Vector3<T>& forward,
const Vector3<T>& right,
const Vector3<T>& up,
const Vector3<T>& camera_origin) noexcept;
```
### Perspective projections
```cpp
template<class T=float, MatStoreType St=ROW_MAJOR>
Mat<4,4,T,St> mat_perspective_left_handed (float fov_deg, float aspect, float near, float far) noexcept;
template<class T=float, MatStoreType St=ROW_MAJOR>
Mat<4,4,T,St> mat_perspective_right_handed(float fov_deg, float aspect, float near, float far) noexcept;
```
### Orthographic projections
```cpp
template<class T=float, MatStoreType St=ROW_MAJOR>
Mat<4,4,T,St> mat_ortho_left_handed (T left, T right, T bottom, T top, T near, T far) noexcept;
template<class T=float, MatStoreType St=ROW_MAJOR>
Mat<4,4,T,St> mat_ortho_right_handed(T left, T right, T bottom, T top, T near, T far) noexcept;
```
### Look-at matrices
```cpp
template<class T=float, MatStoreType St=COLUMN_MAJOR>
Mat<4,4,T,St> mat_look_at_left_handed (const Vector3<T>& eye,
const Vector3<T>& center,
const Vector3<T>& up);
template<class T=float, MatStoreType St=COLUMN_MAJOR>
Mat<4,4,T,St> mat_look_at_right_handed(const Vector3<T>& eye,
const Vector3<T>& center,
const Vector3<T>& up);
```
---
## Screen-space helper
```cpp
template<class Type=float>
static constexpr Mat<4,4> to_screen_mat(const Type& screen_w, const Type& screen_h) noexcept;
// Maps NDC to screen space (origin top-left, y down)
```
---
## Examples
### 1) Building a left-handed camera and perspective
```cpp
using V3 = omath::Vector3<float>;
using M4 = omath::Mat<4,4,float, omath::MatStoreType::COLUMN_MAJOR>;
V3 eye{0, 1, -5}, center{0, 0, 0}, up{0, 1, 0};
M4 view = omath::mat_look_at_left_handed<float, omath::MatStoreType::COLUMN_MAJOR>(eye, center, up);
float fov = 60.f, aspect = 16.f/9.f, n = 0.1f, f = 100.f;
M4 proj = omath::mat_perspective_left_handed<float, omath::MatStoreType::COLUMN_MAJOR>(fov, aspect, n, f);
// final VP
M4 vp = proj * view;
```
### 2) Inverting a transform safely
```cpp
omath::Mat<4,4> T = omath::mat_translation(omath::Vector3<float>{2,3,4});
if (auto inv = T.inverted()) {
// use *inv
} else {
// handle non-invertible
}
```
### 3) Formatting for logs
```cpp
omath::Mat<2,2> A = { {1,2},{3,4} };
std::string s = A.to_string(); // "[[ 1.000, 2.000]\n [ 3.000, 4.000]]"
std::string f = std::format("A = {}", A); // uses std::formatter
```
---
## Performance
* **Cache-friendly kernels** per storage order when AVX2 is not enabled.
* **AVX2 path** (`OMATH_USE_AVX2`) for `float`/`double` implements FMAs with 256-bit vectors for both row-major and column-major multiplication.
* Complexity for `A(R×K) * B(K×C)`: **O(RKC)** regardless of storage order.
---
## Constraints & concepts
```cpp
template<typename M1, typename M2>
concept MatTemplateEqual =
(M1::rows == M2::rows) &&
(M1::columns == M2::columns) &&
std::is_same_v<typename M1::value_type, typename M2::value_type> &&
(M1::store_type == M2::store_type);
```
> Use this concept to constrain generic functions that operate on like-shaped matrices.
---
## Exceptions
* `std::invalid_argument` — initializer list dimensions mismatch.
* `std::out_of_range` — out-of-bounds in `at()` when bounds checking is active (see source guard).
* `inverted()` does **not** throw; returns `std::nullopt` if `determinant() == 0`.
---
## Build switches
* **`OMATH_USE_AVX2`** — enable AVX2 vectorized multiplication paths (`<immintrin.h>` required).
* **Debug checks** — the `at()` method contains a conditional range check; refer to the preprocessor guard in the code to enable/disable in your configuration.
---
## Known requirements & interoperability
* **C++23** is required for multi-parameter `operator[]`. If you target pre-C++23, use `at(r,c)` instead.
* All binary operations require matching `Type` and `StoreType`. Convert explicitly if needed.
---
## See also
* `omath::Vector3<T>`
* Projection helpers: `mat_perspective_*`, `mat_ortho_*`
* View helpers: `mat_look_at_*`, `mat_camera_view`
* Construction helpers: `mat_row_from_vector`, `mat_column_from_vector`, `mat_translation`, `mat_rotation_axis_*`
---
## Appendix: API summary (signatures)
```cpp
// Core
Mat(); Mat(const Mat&); Mat(Mat&&);
Mat(std::initializer_list<std::initializer_list<Type>>);
explicit Mat(const Type* raw);
Mat& operator=(const Mat&); Mat& operator=(Mat&&);
static constexpr size_t row_count();
static constexpr size_t columns_count();
static consteval MatSize size();
static constexpr MatStoreType get_store_ordering();
T& at(size_t r, size_t c);
T const& at(size_t r, size_t c) const;
T& operator[](size_t r, size_t c);
T const& operator[](size_t r, size_t c) const;
void clear();
void set(const Type& v);
Type sum() const noexcept;
template<size_t OC> Mat<Rows,OC,Type,StoreType> operator*(const Mat<Columns,OC,Type,StoreType>&) const;
Mat& operator*=(const Type&); Mat operator*(const Type&) const;
Mat& operator/=(const Type&); Mat operator/(const Type&) const;
Mat<Columns,Rows,Type,StoreType> transposed() const noexcept;
Type determinant() const; // square only
std::optional<Mat> inverted() const; // square only
Mat<Rows-1,Columns-1,Type,StoreType> strip(size_t r, size_t c) const;
Type minor(size_t r, size_t c) const;
Type alg_complement(size_t r, size_t c) const;
auto& raw_array(); auto const& raw_array() const;
std::string to_string() const noexcept;
std::wstring to_wstring() const noexcept;
std::u8string to_u8string() const noexcept;
bool operator==(const Mat&) const;
bool operator!=(const Mat&) const;
// Helpers (see sections above)
```
---
*Last updated: 31 Oct 2025*

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# `omath::Triangle` — Simple 3D triangle utility
> Header: your project’s `triangle.hpp`
> Namespace: `omath`
> Depends on: `omath::Vector3<float>` (from `vector3.hpp`)
A tiny helper around three `Vector3<float>` vertices with convenience methods for normals, edge vectors/lengths, a right-angle test (at **`v2`**), and the triangle centroid.
> **Note on the template parameter**
>
> The class is declared as `template<class Vector> class Triangle`, but the stored vertices are concretely `Vector3<float>`. In practice this type is currently **fixed to `Vector3<float>`**. You can ignore the template parameter or refactor to store `Vector` if you intend true genericity.
---
## Vertex layout & naming
```
v1
|\
| \
a | \ hypot = |v1 - v3|
| \
v2 -- v3
b
a = |v1 - v2| (side_a_length)
b = |v3 - v2| (side_b_length)
```
* **`side_a_vector()`** = `v1 - v2` (points from v2 → v1)
* **`side_b_vector()`** = `v3 - v2` (points from v2 → v3)
* **Right-angle check** uses `a² + b² ≈ hypot²` with an epsilon of `1e-4`.
---
## Quick start
```cpp
#include "triangle.hpp"
using omath::Vector3;
using omath::Triangle;
Triangle<void> tri( // template arg unused; any placeholder ok
Vector3<float>{0,0,0}, // v1
Vector3<float>{0,0,1}, // v2 (right angle is tested at v2)
Vector3<float>{1,0,1} // v3
);
auto n = tri.calculate_normal(); // unit normal (right-handed: (v3-v2) × (v1-v2))
float a = tri.side_a_length(); // |v1 - v2|
float b = tri.side_b_length(); // |v3 - v2|
float hyp = tri.hypot(); // |v1 - v3|
bool rect = tri.is_rectangular(); // true if ~right triangle at v2
auto C = tri.mid_point(); // centroid (average of v1,v2,v3)
```
---
## Data members
```cpp
Vector3<float> m_vertex1; // v1
Vector3<float> m_vertex2; // v2 (the corner tested by is_rectangular)
Vector3<float> m_vertex3; // v3
```
---
## Constructors
```cpp
constexpr Triangle() = default;
constexpr Triangle(const Vector3<float>& v1,
const Vector3<float>& v2,
const Vector3<float>& v3);
```
---
## Methods
```cpp
// Normal (unit) using right-handed cross product:
// n = (v3 - v2) × (v1 - v2), then normalized()
[[nodiscard]] constexpr Vector3<float> calculate_normal() const;
// Edge lengths with the naming from the diagram
[[nodiscard]] float side_a_length() const; // |v1 - v2|
[[nodiscard]] float side_b_length() const; // |v3 - v2|
// Edge vectors (from v2 to the other vertex)
[[nodiscard]] constexpr Vector3<float> side_a_vector() const; // v1 - v2
[[nodiscard]] constexpr Vector3<float> side_b_vector() const; // v3 - v2
// Hypotenuse length between v1 and v3
[[nodiscard]] constexpr float hypot() const; // |v1 - v3|
// Right-triangle check at vertex v2 (Pythagoras with epsilon 1e-4)
[[nodiscard]] constexpr bool is_rectangular() const;
// Centroid of the triangle (average of the 3 vertices)
[[nodiscard]] constexpr Vector3<float> mid_point() const; // actually the centroid
```
### Notes & edge cases
* **Normal direction** follows the right-hand rule for the ordered vertices `{v2 → v3} × {v2 → v1}`.
Swap vertex order to flip the normal.
* **Degenerate triangles** (collinear or overlapping vertices) yield a **zero vector** normal (since `normalized()` of the zero vector returns the zero vector in your math types).
* **`mid_point()` is the centroid**, not the midpoint of any single edge. If you need the midpoint of edge `v1–v2`, use `(m_vertex1 + m_vertex2) * 0.5f`.
---
## Examples
### Area and plane from existing API
```cpp
const auto a = tri.side_a_vector();
const auto b = tri.side_b_vector();
const auto n = b.cross(a); // unnormalized normal
float area = 0.5f * n.length(); // triangle area
// Plane equation n̂·(x - v2) = 0
auto nhat = n.length() > 0 ? n / n.length() : n;
float d = -nhat.dot(tri.m_vertex2);
```
### Project a point onto the triangle’s plane
```cpp
Vector3<float> p{0.3f, 1.0f, 0.7f};
auto n = tri.calculate_normal();
float t = n.dot(tri.m_vertex2 - p); // signed distance along normal
auto projected = p + n * t; // on-plane projection
```
---
## API summary (signatures)
```cpp
class Triangle final {
public:
constexpr Triangle();
constexpr Triangle(const Vector3<float>& v1,
const Vector3<float>& v2,
const Vector3<float>& v3);
Vector3<float> m_vertex1, m_vertex2, m_vertex3;
[[nodiscard]] constexpr Vector3<float> calculate_normal() const;
[[nodiscard]] float side_a_length() const;
[[nodiscard]] float side_b_length() const;
[[nodiscard]] constexpr Vector3<float> side_a_vector() const;
[[nodiscard]] constexpr Vector3<float> side_b_vector() const;
[[nodiscard]] constexpr float hypot() const;
[[nodiscard]] constexpr bool is_rectangular() const;
[[nodiscard]] constexpr Vector3<float> mid_point() const;
};
```
---
## Suggestions (optional improvements)
* If generic vectors are intended, store `Vector m_vertex*;` and constrain `Vector` to the required ops (`-`, `cross`, `normalized`, `distance_to`, `+`, `/`).
* Consider renaming `mid_point()` → `centroid()` to avoid ambiguity.
* Expose an `area()` helper and (optionally) a barycentric coordinate routine if you plan to use this in rasterization or intersection tests.
---
*Last updated: 31 Oct 2025*

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# `omath::Vector2` — 2D vector (C++20/23)
> Header: your project’s `vector2.hpp`
> Namespace: `omath`
> Template: `template<class Type> requires std::is_arithmetic_v<Type>`
`Vector2<Type>` is a lightweight, POD-like 2D math type with arithmetic, geometry helpers, comparisons, hashing (for `float`), optional ImGui interop, and `std::formatter` support.
---
## Quick start
```cpp
#include "vector2.hpp"
using omath::Vector2;
using Vec2f = Vector2<float>;
Vec2f a{3.f, 4.f};
Vec2f b{1.f, 2.f};
auto d = a.distance_to(b); // ≈ 3.1623
auto dot = a.dot(b); // 11
auto len = a.length(); // 5
auto unit_a = a.normalized(); // (0.6, 0.8)
// Component-wise mutate
Vec2f c{2, 3};
c *= b; // c -> (2*1, 3*2) = (2, 6)
// Scalar ops (non-mutating + mutating)
auto scaled = a * 0.5f; // (1.5, 2)
a *= 2.f; // (6, 8)
// Ordering by length()
bool shorter = (b < a);
// Formatted printing
std::string s = std::format("a = {}", a); // "a = [6, 8]"
```
---
## Members
```cpp
Type x{0};
Type y{0};
```
---
## Constructors
```cpp
constexpr Vector2(); // (0,0)
constexpr Vector2(const Type& x, const Type& y) noexcept;
```
---
## Equality & ordering
```cpp
constexpr bool operator==(const Vector2&) const noexcept; // component-wise equality
constexpr bool operator!=(const Vector2&) const noexcept;
bool operator< (const Vector2&) const noexcept; // compares by length()
bool operator> (const Vector2&) const noexcept;
bool operator<=(const Vector2&) const noexcept;
bool operator>=(const Vector2&) const noexcept;
```
> **Note:** `<`, `>`, `<=`, `>=` order vectors by **magnitude** (not lexicographically).
---
## Arithmetic
### With another vector (component-wise, **mutating**)
```cpp
Vector2& operator+=(const Vector2&) noexcept;
Vector2& operator-=(const Vector2&) noexcept;
Vector2& operator*=(const Vector2&) noexcept; // Hadamard product (x*=x, y*=y)
Vector2& operator/=(const Vector2&) noexcept;
```
> Non-mutating `v * u` / `v / u` (vector × vector) are **not** provided.
> Use `v *= u` (mutating) or build a new vector explicitly.
### With a scalar
```cpp
Vector2& operator*=(const Type& v) noexcept;
Vector2& operator/=(const Type& v) noexcept;
Vector2& operator+=(const Type& v) noexcept;
Vector2& operator-=(const Type& v) noexcept;
constexpr Vector2 operator*(const Type& v) const noexcept;
constexpr Vector2 operator/(const Type& v) const noexcept;
```
### Binary (+/−) with another vector (non-mutating)
```cpp
constexpr Vector2 operator+(const Vector2&) const noexcept;
constexpr Vector2 operator-(const Vector2&) const noexcept;
```
### Unary
```cpp
constexpr Vector2 operator-() const noexcept; // negation
```
---
## Geometry & helpers
```cpp
Type distance_to (const Vector2&) const noexcept; // sqrt of squared distance
constexpr Type distance_to_sqr(const Vector2&) const noexcept;
constexpr Type dot(const Vector2&) const noexcept;
#ifndef _MSC_VER
constexpr Type length() const noexcept; // uses std::hypot; constexpr on non-MSVC
constexpr Vector2 normalized() const noexcept; // returns *this if length==0
#else
Type length() const noexcept;
Vector2 normalized() const noexcept;
#endif
constexpr Type length_sqr() const noexcept; // x*x + y*y
Vector2& abs() noexcept; // component-wise absolute (constexpr-friendly impl)
constexpr Type sum() const noexcept; // x + y
constexpr std::tuple<Type, Type> as_tuple() const noexcept;
```
---
## ImGui integration (optional)
Define `OMATH_IMGUI_INTEGRATION` **before** including the header.
```cpp
#ifdef OMATH_IMGUI_INTEGRATION
constexpr ImVec2 to_im_vec2() const noexcept; // {float(x), float(y)}
static Vector2 from_im_vec2(const ImVec2&) noexcept;
#endif
```
---
## Hashing & formatting
* **Hash (for `Vector2<float>`)**
```cpp
template<> struct std::hash<omath::Vector2<float>> {
std::size_t operator()(const omath::Vector2<float>&) const noexcept;
};
```
Example:
```cpp
std::unordered_set<omath::Vector2<float>> set;
set.insert({1.f, 2.f});
```
* **`std::formatter`** (for any `Type`)
```cpp
// prints "[x, y]" for char / wchar_t / char8_t
template<class Type>
struct std::formatter<omath::Vector2<Type>>;
```
---
## Notes & invariants
* `Type` must be arithmetic (e.g., `float`, `double`, `int`, …).
* `normalized()` returns the input unchanged if `length() == 0`.
* `abs()` uses a constexpr-friendly implementation (not `std::abs`) to allow compile-time evaluation.
* On MSVC, `length()`/`normalized()` are not `constexpr` due to library constraints; they’re still `noexcept`.
---
## Examples
### Component-wise operations and scalar scaling
```cpp
omath::Vector2<float> u{2, 3}, v{4, 5};
u += v; // (6, 8)
u -= v; // (2, 3)
u *= v; // (8, 15) Hadamard product (mutates u)
auto w = v * 2.0f; // (8, 10) non-mutating scalar multiply
```
### Geometry helpers
```cpp
omath::Vector2<double> p{0.0, 0.0}, q{3.0, 4.0};
auto dsq = p.distance_to_sqr(q); // 25
auto d = p.distance_to(q); // 5
auto dot = p.dot(q); // 0
auto uq = q.normalized(); // (0.6, 0.8)
```
### Using as a key in unordered containers (`float`)
```cpp
std::unordered_map<omath::Vector2<float>, int> counts;
counts[{1.f, 2.f}] = 42;
```
### ImGui interop
```cpp
#define OMATH_IMGUI_INTEGRATION
#include "vector2.hpp"
omath::Vector2<float> v{10, 20};
ImVec2 iv = v.to_im_vec2();
v = omath::Vector2<float>::from_im_vec2(iv);
```
---
## API summary (signatures)
```cpp
// Constructors
constexpr Vector2();
constexpr Vector2(const Type& x, const Type& y) noexcept;
// Equality & ordering
constexpr bool operator==(const Vector2&) const noexcept;
constexpr bool operator!=(const Vector2&) const noexcept;
bool operator< (const Vector2&) const noexcept;
bool operator> (const Vector2&) const noexcept;
bool operator<=(const Vector2&) const noexcept;
bool operator>=(const Vector2&) const noexcept;
// Compound (vector/vector and scalar)
Vector2& operator+=(const Vector2&) noexcept;
Vector2& operator-=(const Vector2&) noexcept;
Vector2& operator*=(const Vector2&) noexcept;
Vector2& operator/=(const Vector2&) noexcept;
Vector2& operator*=(const Type&) noexcept;
Vector2& operator/=(const Type&) noexcept;
Vector2& operator+=(const Type&) noexcept;
Vector2& operator-=(const Type&) noexcept;
// Non-mutating arithmetic
constexpr Vector2 operator+(const Vector2&) const noexcept;
constexpr Vector2 operator-(const Vector2&) const noexcept;
constexpr Vector2 operator*(const Type&) const noexcept;
constexpr Vector2 operator/(const Type&) const noexcept;
constexpr Vector2 operator-() const noexcept;
// Geometry
Type distance_to(const Vector2&) const noexcept;
constexpr Type distance_to_sqr(const Vector2&) const noexcept;
constexpr Type dot(const Vector2&) const noexcept;
Type length() const noexcept; // constexpr on non-MSVC
Vector2 normalized() const noexcept; // constexpr on non-MSVC
constexpr Type length_sqr() const noexcept;
Vector2& abs() noexcept;
constexpr Type sum() const noexcept;
constexpr std::tuple<Type,Type> as_tuple() const noexcept;
// ImGui (optional)
#ifdef OMATH_IMGUI_INTEGRATION
constexpr ImVec2 to_im_vec2() const noexcept;
static Vector2 from_im_vec2(const ImVec2&) noexcept;
#endif
// Hash (float) and formatter are specialized in the header
```
---
## See Also
- [Vector3 Documentation](vector3.md) - 3D vector operations
- [Vector4 Documentation](vector4.md) - 4D vector operations
- [Getting Started Guide](../getting_started.md) - Quick start with OMath
- [Tutorials](../tutorials.md) - Step-by-step examples
---
*Last updated: 1 Nov 2025*

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# `omath::Vector3` — 3D vector (C++20/23)
> Header: your project’s `vector3.hpp`
> Namespace: `omath`
> Template: `template<class Type> requires std::is_arithmetic_v<Type>`
> Depends on: `omath::Vector2<Type>` (base class), `omath::Angle` (for `angle_between`)
> C++: uses `std::expected` ⇒ **C++23** recommended (or a backport)
`Vector3<Type>` extends `Vector2<Type>` with a `z` component and 3D operations: arithmetic, geometry (dot, cross, distance), normalization, angle-between with robust error signaling, hashing (for `float`) and `std::formatter` support.
---
## Quick start
```cpp
#include "vector3.hpp"
using omath::Vector3;
using Vec3f = Vector3<float>;
Vec3f a{3, 4, 0};
Vec3f b{1, 2, 2};
auto d = a.distance_to(b); // Euclidean distance
auto dot = a.dot(b); // 3*1 + 4*2 + 0*2 = 11
auto cr = a.cross(b); // (8, -6, 2)
auto len = a.length(); // hypot(x,y,z)
auto unit = a.normalized(); // safe normalize (returns a if length==0)
if (auto ang = a.angle_between(b)) {
float deg = ang->as_degrees(); // [0, 180], clamped
} else {
// vectors have zero length -> no defined angle
}
```
---
## Data members
```cpp
Type x{0}; // inherited from Vector2<Type>
Type y{0}; // inherited from Vector2<Type>
Type z{0};
```
---
## Constructors
```cpp
constexpr Vector3() noexcept;
constexpr Vector3(const Type& x, const Type& y, const Type& z) noexcept;
```
---
## Equality & ordering
```cpp
constexpr bool operator==(const Vector3&) const noexcept; // component-wise
constexpr bool operator!=(const Vector3&) const noexcept;
bool operator< (const Vector3&) const noexcept; // compare by length()
bool operator> (const Vector3&) const noexcept;
bool operator<=(const Vector3&) const noexcept;
bool operator>=(const Vector3&) const noexcept;
```
> **Note:** Ordering uses **magnitude**, not lexicographic order.
---
## Arithmetic (mutating)
Component-wise with another vector:
```cpp
Vector3& operator+=(const Vector3&) noexcept;
Vector3& operator-=(const Vector3&) noexcept;
Vector3& operator*=(const Vector3&) noexcept; // Hadamard product
Vector3& operator/=(const Vector3&) noexcept;
```
With a scalar:
```cpp
Vector3& operator*=(const Type& v) noexcept;
Vector3& operator/=(const Type& v) noexcept;
Vector3& operator+=(const Type& v) noexcept;
Vector3& operator-=(const Type& v) noexcept;
```
---
## Arithmetic (non-mutating)
```cpp
constexpr Vector3 operator-() const noexcept;
constexpr Vector3 operator+(const Vector3&) const noexcept;
constexpr Vector3 operator-(const Vector3&) const noexcept;
constexpr Vector3 operator*(const Vector3&) const noexcept; // Hadamard
constexpr Vector3 operator/(const Vector3&) const noexcept; // Hadamard
constexpr Vector3 operator*(const Type& scalar) const noexcept;
constexpr Vector3 operator/(const Type& scalar) const noexcept;
```
---
## Geometry & helpers
```cpp
// Distances & lengths
Type distance_to(const Vector3&) const; // sqrt of squared distance
constexpr Type distance_to_sqr(const Vector3&) const noexcept;
#ifndef _MSC_VER
constexpr Type length() const; // hypot(x,y,z)
constexpr Type length_2d() const; // 2D length from base
constexpr Vector3 normalized() const; // returns *this if length==0
#else
Type length() const noexcept;
Type length_2d() const noexcept;
Vector3 normalized() const noexcept;
#endif
constexpr Type length_sqr() const noexcept;
// Products
constexpr Type dot(const Vector3&) const noexcept;
constexpr Vector3 cross(const Vector3&) const noexcept; // right-handed
// Sums & tuples
constexpr Type sum() const noexcept; // x + y + z
constexpr Type sum_2d() const noexcept; // x + y
constexpr auto as_tuple() const noexcept -> std::tuple<Type,Type,Type>;
// Utilities
Vector3& abs() noexcept; // component-wise absolute
```
---
## Angles & orthogonality
```cpp
enum class Vector3Error { IMPOSSIBLE_BETWEEN_ANGLE };
// Angle in degrees, clamped to [0,180]. Error if any vector has zero length.
std::expected<
omath::Angle<float, 0.f, 180.f, AngleFlags::Clamped>,
Vector3Error
> angle_between(const Vector3& other) const noexcept;
bool is_perpendicular(const Vector3& other) const noexcept; // true if angle == 90°
```
---
## Hashing & formatting
* **Hash (for `Vector3<float>`)**
```cpp
template<> struct std::hash<omath::Vector3<float>> {
std::size_t operator()(const omath::Vector3<float>&) const noexcept;
};
```
Example:
```cpp
std::unordered_map<omath::Vector3<float>, int> counts;
counts[{1.f, 2.f, 3.f}] = 7;
```
* **`std::formatter`** (all character types)
```cpp
template<class Type>
struct std::formatter<omath::Vector3<Type>>; // prints "[x, y, z]"
```
---
## Error handling
* `angle_between()` returns `std::unexpected(Vector3Error::IMPOSSIBLE_BETWEEN_ANGLE)` if either vector length is zero.
* Other operations are total for arithmetic `Type` (no throwing behavior in this class).
---
## Examples
### Cross product & perpendicular check
```cpp
omath::Vector3<float> x{1,0,0}, y{0,1,0};
auto z = x.cross(y); // (0,0,1)
bool perp = x.is_perpendicular(y); // true
```
### Safe normalization and angle
```cpp
omath::Vector3<float> u{0,0,0}, v{1,1,0};
auto nu = u.normalized(); // returns {0,0,0}
if (auto ang = u.angle_between(v)) {
// won't happen: u has zero length → error
} else {
// handle degenerate case
}
```
### Hadamard vs scalar multiply
```cpp
omath::Vector3<float> a{2,3,4}, b{5,6,7};
auto h = a * b; // (10, 18, 28) component-wise
auto s = a * 2.f; // (4, 6, 8) scalar
```
---
## API summary (signatures)
```cpp
// Ctors
constexpr Vector3() noexcept;
constexpr Vector3(const Type& x, const Type& y, const Type& z) noexcept;
// Equality & ordering
constexpr bool operator==(const Vector3&) const noexcept;
constexpr bool operator!=(const Vector3&) const noexcept;
bool operator< (const Vector3&) const noexcept;
bool operator> (const Vector3&) const noexcept;
bool operator<=(const Vector3&) const noexcept;
bool operator>=(const Vector3&) const noexcept;
// Mutating arithmetic
Vector3& operator+=(const Vector3&) noexcept;
Vector3& operator-=(const Vector3&) noexcept;
Vector3& operator*=(const Vector3&) noexcept;
Vector3& operator/=(const Vector3&) noexcept;
Vector3& operator*=(const Type&) noexcept;
Vector3& operator/=(const Type&) noexcept;
Vector3& operator+=(const Type&) noexcept;
Vector3& operator-=(const Type&) noexcept;
// Non-mutating arithmetic
constexpr Vector3 operator-() const noexcept;
constexpr Vector3 operator+(const Vector3&) const noexcept;
constexpr Vector3 operator-(const Vector3&) const noexcept;
constexpr Vector3 operator*(const Vector3&) const noexcept;
constexpr Vector3 operator/(const Vector3&) const noexcept;
constexpr Vector3 operator*(const Type&) const noexcept;
constexpr Vector3 operator/(const Type&) const noexcept;
// Geometry
Type distance_to(const Vector3&) const;
constexpr Type distance_to_sqr(const Vector3&) const noexcept;
#ifndef _MSC_VER
constexpr Type length() const;
constexpr Type length_2d() const;
constexpr Vector3 normalized() const;
#else
Type length() const noexcept;
Type length_2d() const noexcept;
Vector3 normalized() const noexcept;
#endif
constexpr Type length_sqr() const noexcept;
constexpr Type dot(const Vector3&) const noexcept;
constexpr Vector3 cross(const Vector3&) const noexcept;
Vector3& abs() noexcept;
constexpr Type sum() const noexcept;
constexpr Type sum_2d() const noexcept;
constexpr auto as_tuple() const noexcept -> std::tuple<Type,Type,Type>;
// Angles
std::expected<omath::Angle<float,0.f,180.f,AngleFlags::Clamped>, omath::Vector3Error>
angle_between(const Vector3&) const noexcept;
bool is_perpendicular(const Vector3&) const noexcept;
// Hash (float) and formatter specializations provided below the class
```
---
## Notes
* Inherits all public API of `Vector2<Type>` (including `x`, `y`, many operators, and helpers used internally).
* `normalized()` returns the original vector if its length is zero (no NaNs).
* `cross()` uses the standard right-handed definition.
* `length()`/`normalized()` are `constexpr` on non-MSVC; MSVC builds provide `noexcept` runtime versions.
---
## See Also
- [Vector2 Documentation](vector2.md) - 2D vector operations
- [Vector4 Documentation](vector4.md) - 4D vector operations
- [Angle Documentation](../trigonometry/angle.md) - Working with angles
- [Getting Started Guide](../getting_started.md) - Quick start with OMath
- [Tutorials](../tutorials.md) - Practical examples including vector math
---
*Last updated: 1 Nov 2025*

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# `omath::Vector4` — 4D vector (C++20/23)
> Header: your project’s `vector4.hpp`
> Namespace: `omath`
> Template: `template<class Type> requires std::is_arithmetic_v<Type>`
> Inherits: `omath::Vector3<Type>` (brings `x`, `y`, `z` and most scalar ops)
`Vector4<Type>` extends `Vector3<Type>` with a `w` component and 4D operations: component-wise arithmetic, scalar ops, dot/length helpers, clamping, hashing (for `float`) and `std::formatter` support. Optional ImGui interop is available behind a macro.
---
## Quick start
```cpp
#include "vector4.hpp"
using omath::Vector4;
using Vec4f = Vector4<float>;
Vec4f a{1, 2, 3, 1};
Vec4f b{4, 5, 6, 2};
// Component-wise & scalar ops
auto c = a + b; // (5, 7, 9, 3)
c *= 0.5f; // (2.5, 3.5, 4.5, 1.5)
auto h = a * b; // Hadamard: (4, 10, 18, 2)
// Dot / length
float d = a.dot(b); // 1*4 + 2*5 + 3*6 + 1*2 = 32
float L = a.length(); // sqrt(x²+y²+z²+w²)
// Clamp (x,y,z only; see notes)
Vec4f col{1.4f, -0.2f, 0.7f, 42.f};
col.clamp(0.f, 1.f); // -> (1, 0, 0.7, w unchanged)
```
---
## Data members
```cpp
// Inherited from Vector3<Type>:
Type x{0};
Type y{0};
Type z{0};
// Added in Vector4:
Type w{0};
```
---
## Constructors
```cpp
constexpr Vector4() noexcept; // (0,0,0,0)
constexpr Vector4(const Type& x, const Type& y,
const Type& z, const Type& w); // value-init
```
---
## Equality & ordering
```cpp
constexpr bool operator==(const Vector4&) const noexcept; // component-wise
constexpr bool operator!=(const Vector4&) const noexcept;
bool operator< (const Vector4&) const noexcept; // compare by length()
bool operator> (const Vector4&) const noexcept;
bool operator<=(const Vector4&) const noexcept;
bool operator>=(const Vector4&) const noexcept;
```
> **Note:** Ordering uses **magnitude** (Euclidean norm), not lexicographic order.
---
## Arithmetic (mutating)
With another vector (component-wise):
```cpp
Vector4& operator+=(const Vector4&) noexcept;
Vector4& operator-=(const Vector4&) noexcept;
Vector4& operator*=(const Vector4&) noexcept; // Hadamard
Vector4& operator/=(const Vector4&) noexcept;
```
With a scalar:
```cpp
Vector4& operator*=(const Type& v) noexcept;
Vector4& operator/=(const Type& v) noexcept;
// From base class (inherited):
Vector4& operator+=(const Type& v) noexcept; // adds v to x,y,z (and w via base? see notes)
Vector4& operator-=(const Type& v) noexcept;
```
---
## Arithmetic (non-mutating)
```cpp
constexpr Vector4 operator-() const noexcept;
constexpr Vector4 operator+(const Vector4&) const noexcept;
constexpr Vector4 operator-(const Vector4&) const noexcept;
constexpr Vector4 operator*(const Vector4&) const noexcept; // Hadamard
constexpr Vector4 operator/(const Vector4&) const noexcept; // Hadamard
constexpr Vector4 operator*(const Type& scalar) const noexcept;
constexpr Vector4 operator/(const Type& scalar) const noexcept;
```
---
## Geometry & helpers
```cpp
constexpr Type length_sqr() const noexcept; // x² + y² + z² + w²
Type length() const noexcept; // std::sqrt(length_sqr())
constexpr Type dot(const Vector4& rhs) const noexcept;
Vector4& abs() noexcept; // component-wise absolute
Vector4& clamp(const Type& min, const Type& max) noexcept;
// clamps x,y,z; leaves w unchanged (see notes)
constexpr Type sum() const noexcept; // x + y + z + w
```
---
## ImGui integration (optional)
Guarded by `OMATH_IMGUI_INTEGRATION`:
```cpp
#ifdef OMATH_IMGUI_INTEGRATION
constexpr ImVec4 to_im_vec4() const noexcept;
// NOTE: Provided signature returns Vector4<float> and (in current code) sets only x,y,z.
// See "Notes & caveats" for a corrected version you may prefer.
static Vector4<float> from_im_vec4(const ImVec4& other) noexcept;
#endif
```
---
## Hashing & formatting
* **Hash specialization** (only for `Vector4<float>`):
```cpp
template<> struct std::hash<omath::Vector4<float>> {
std::size_t operator()(const omath::Vector4<float>&) const noexcept;
};
```
Example:
```cpp
std::unordered_map<omath::Vector4<float>, int> counts;
counts[{1.f, 2.f, 3.f, 1.f}] = 7;
```
* **`std::formatter`** (for any `Type`, all character kinds):
```cpp
template<class Type>
struct std::formatter<omath::Vector4<Type>>; // -> "[x, y, z, w]"
```
---
## Notes & caveats (as implemented)
* `clamp(min,max)` **clamps only `x`, `y`, `z`** and **does not clamp `w`**. This may be intentional (e.g., when `w` is a homogeneous coordinate) — document your intent in your codebase.
If you want to clamp `w` too:
```cpp
w = std::clamp(w, min, max);
```
* **ImGui interop**:
* The header references `ImVec4` but does not include `<imgui.h>` itself. Ensure it’s included **before** this header whenever `OMATH_IMGUI_INTEGRATION` is defined.
* `from_im_vec4` currently returns `Vector4<float>` and (in the snippet shown) initializes **only x,y,z**. A more consistent version would be:
```cpp
#ifdef OMATH_IMGUI_INTEGRATION
static Vector4<Type> from_im_vec4(const ImVec4& v) noexcept {
return {static_cast<Type>(v.x), static_cast<Type>(v.y),
static_cast<Type>(v.z), static_cast<Type>(v.w)};
}
#endif
```
* Many scalar compound operators (`+= Type`, `-= Type`) are inherited from `Vector3<Type>`.
---
## API summary (signatures)
```cpp
// Ctors
constexpr Vector4() noexcept;
constexpr Vector4(const Type& x, const Type& y, const Type& z, const Type& w);
// Equality & ordering
constexpr bool operator==(const Vector4&) const noexcept;
constexpr bool operator!=(const Vector4&) const noexcept;
bool operator< (const Vector4&) const noexcept;
bool operator> (const Vector4&) const noexcept;
bool operator<=(const Vector4&) const noexcept;
bool operator>=(const Vector4&) const noexcept;
// Mutating arithmetic
Vector4& operator+=(const Vector4&) noexcept;
Vector4& operator-=(const Vector4&) noexcept;
Vector4& operator*=(const Vector4&) noexcept;
Vector4& operator/=(const Vector4&) noexcept;
Vector4& operator*=(const Type&) noexcept;
Vector4& operator/=(const Type&) noexcept;
// (inherited) Vector4& operator+=(const Type&) noexcept;
// (inherited) Vector4& operator-=(const Type&) noexcept;
// Non-mutating arithmetic
constexpr Vector4 operator-() const noexcept;
constexpr Vector4 operator+(const Vector4&) const noexcept;
constexpr Vector4 operator-(const Vector4&) const noexcept;
constexpr Vector4 operator*(const Vector4&) const noexcept;
constexpr Vector4 operator/(const Vector4&) const noexcept;
constexpr Vector4 operator*(const Type&) const noexcept;
constexpr Vector4 operator/(const Type&) const noexcept;
// Geometry & helpers
constexpr Type length_sqr() const noexcept;
Type length() const noexcept;
constexpr Type dot(const Vector4&) const noexcept;
Vector4& abs() noexcept;
Vector4& clamp(const Type& min, const Type& max) noexcept;
constexpr Type sum() const noexcept;
// ImGui (optional)
#ifdef OMATH_IMGUI_INTEGRATION
constexpr ImVec4 to_im_vec4() const noexcept;
static Vector4<float> from_im_vec4(const ImVec4&) noexcept; // see note for preferred template version
#endif
// Hash (float) and formatter specializations provided below the class
```
---
*Last updated: 31 Oct 2025*

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# `omath::pathfinding::Astar` — Pathfinding over a navigation mesh
> Header: your project’s `pathfinding/astar.hpp`
> Namespace: `omath::pathfinding`
> Inputs: start/end as `Vector3<float>`, a `NavigationMesh`
> Output: ordered list of waypoints `std::vector<Vector3<float>>`
`Astar` exposes a single public function, `find_path`, that computes a path of 3D waypoints on a navigation mesh. Internally it reconstructs the result with `reconstruct_final_path` from a closed set keyed by `Vector3<float>`.
---
## API
```cpp
namespace omath::pathfinding {
struct PathNode; // holds per-node search data (see "Expected PathNode fields")
class Astar final {
public:
[[nodiscard]]
static std::vector<Vector3<float>>
find_path(const Vector3<float>& start,
const Vector3<float>& end,
const NavigationMesh& nav_mesh) noexcept;
private:
[[nodiscard]]
static std::vector<Vector3<float>>
reconstruct_final_path(
const std::unordered_map<Vector3<float>, PathNode>& closed_list,
const Vector3<float>& current) noexcept;
};
} // namespace omath::pathfinding
```
### Semantics
* Returns a **polyline** of 3D points from `start` to `end`.
* If no path exists, the function typically returns an **empty vector** (behavior depends on implementation details; keep this contract in unit tests).
---
## What `NavigationMesh` is expected to provide
The header doesn’t constrain `NavigationMesh`, but for A* it commonly needs:
* **Neighborhood queries**: given a position or node key → iterable neighbors.
* **Traversal cost**: `g(u,v)` (often Euclidean distance or edge weight).
* **Heuristic**: `h(x,end)` (commonly straight-line distance on the mesh).
* **Projection / snap**: the ability to map `start`/`end` to valid nodes/points on the mesh (if they are off-mesh).
> If your `NavigationMesh` doesn’t directly expose these, `Astar::find_path` likely does the adapter work (snapping to the nearest convex polygon/portal nodes and expanding across adjacency).
---
## Expected `PathNode` fields
Although not visible here, `PathNode` typically carries:
* `Vector3<float> parent;` — predecessor position or key for backtracking
* `float g;` — cost from `start`
* `float h;` — heuristic to `end`
* `float f;` — `g + h`
`reconstruct_final_path(closed_list, current)` walks `parent` links from `current` back to the start, **reverses** the chain, and returns the path.
---
## Heuristic & optimality
* Use an **admissible** heuristic (never overestimates true cost) to keep A* optimal.
The usual choice is **Euclidean distance** in 3D:
```cpp
h(x, goal) = (goal - x).length();
```
* For best performance, make it **consistent** (triangle inequality holds). Euclidean distance is consistent on standard navmeshes.
---
## Complexity
Let `V` be explored vertices (or portal nodes) and `E` the traversed edges.
* With a binary heap open list: **O(E log V)** time, **O(V)** memory.
* With a d-ary heap or pairing heap you may reduce practical constants.
---
## Typical usage
```cpp
#include "omath/pathfinding/astar.hpp"
#include "omath/pathfinding/navigation_mesh.hpp"
using omath::Vector3;
using omath::pathfinding::Astar;
NavigationMesh nav = /* ... load/build mesh ... */;
Vector3<float> start{2.5f, 0.0f, -1.0f};
Vector3<float> goal {40.0f, 0.0f, 12.0f};
auto path = Astar::find_path(start, goal, nav);
if (!path.empty()) {
// feed to your agent/renderer
for (const auto& p : path) {
// draw waypoint p or push to steering
}
} else {
// handle "no path" (e.g., unreachable or disconnected mesh)
}
```
---
## Notes & recommendations
* **Start/end snapping**: If `start` or `end` are outside the mesh, decide whether to snap to the nearest polygon/portal or fail early. Keep this behavior consistent and document it where `NavigationMesh` is defined.
* **Numerical stability**: Prefer squared distances when only comparing (`dist2`) to avoid unnecessary `sqrt`.
* **Tie-breaking**: When `f` ties are common (grid-like graphs), bias toward larger `g` or smaller `h` to reduce zig-zagging.
* **Smoothing**: A* returns a polyline that may hug polygon edges. Consider:
* **String pulling / Funnel algorithm** over the corridor of polygons to get a straightened path.
* **Raycast smoothing** (visibility checks) to remove redundant interior points.
* **Hashing `Vector3<float>`**: Your repo defines `std::hash<omath::Vector3<float>>`. Ensure equality/precision rules for using float keys are acceptable (or use discrete node IDs instead).
---
## Testing checklist
* Start/end on the **same polygon** → direct path of 2 points.
* **Disconnected components** → empty result.
* **Narrow corridors** → path stays inside.
* **Obstacles blocking** → no path.
* **Floating-point noise** → still reconstructs a valid chain from parents.
---
## Minimal pseudo-implementation outline (for reference)
```cpp
// Pseudocode only — matches the header’s intent
std::vector<Vec3> find_path(start, goal, mesh) {
auto [snode, gnode] = mesh.snap_to_nodes(start, goal);
OpenSet open; // min-heap by f
std::unordered_map<Vec3, PathNode> closed;
open.push({snode, g=0, h=heuristic(snode, gnode)});
parents.clear();
while (!open.empty()) {
auto current = open.pop_min(); // node with lowest f
if (current.pos == gnode.pos)
return reconstruct_final_path(closed, current.pos);
for (auto [nbr, cost] : mesh.neighbors(current.pos)) {
float tentative_g = current.g + cost;
if (auto it = closed.find(nbr); it == closed.end() || tentative_g < it->second.g) {
closed[nbr] = { .parent = current.pos,
.g = tentative_g,
.h = heuristic(nbr, gnode.pos),
.f = tentative_g + heuristic(nbr, gnode.pos) };
open.push(closed[nbr]);
}
}
}
return {}; // no path
}
```
---
## FAQ
* **Why return `std::vector<Vector3<float>>` and not polygon IDs?**
Waypoints are directly usable by agents/steering and for rendering. If you also need the corridor (polygon chain), extend the API or `PathNode` to store it.
* **Does `find_path` modify the mesh?**
No; it should be a read-only search over `NavigationMesh`.
---
*Last updated: 31 Oct 2025*

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# `omath::pathfinding::NavigationMesh` — Lightweight vertex graph for A*
> Header: your project’s `pathfinding/navigation_mesh.hpp`
> Namespace: `omath::pathfinding`
> Nodes: `Vector3<float>` (3D points)
> Storage: adjacency map `unordered_map<Vector3<float>, std::vector<Vector3<float>>>`
A minimal navigation mesh represented as a **vertex/edge graph**. Each vertex is a `Vector3<float>` and neighbors are stored in an adjacency list. Designed to pair with `Astar::find_path`.
---
## API
```cpp
class NavigationMesh final {
public:
// Nearest graph vertex to an arbitrary 3D point.
// On success -> closest vertex; on failure -> std::string error (e.g., empty mesh).
[[nodiscard]]
std::expected<Vector3<float>, std::string>
get_closest_vertex(const Vector3<float>& point) const noexcept;
// Read-only neighbor list for a vertex key.
// If vertex is absent, implementation should return an empty list (see notes).
[[nodiscard]]
const std::vector<Vector3<float>>&
get_neighbors(const Vector3<float>& vertex) const noexcept;
// True if the graph has no vertices/edges.
[[nodiscard]]
bool empty() const;
// Serialize/deserialize the graph (opaque binary).
[[nodiscard]] std::vector<uint8_t> serialize() const noexcept;
void deserialize(const std::vector<uint8_t>& raw) noexcept;
// Public adjacency (vertex -> neighbors)
std::unordered_map<Vector3<float>, std::vector<Vector3<float>>> m_vertex_map;
};
```
---
## Quick start
```cpp
using omath::Vector3;
using omath::pathfinding::NavigationMesh;
// Build a tiny mesh (triangle)
NavigationMesh nav;
nav.m_vertex_map[ {0,0,0} ] = { {1,0,0}, {0,0,1} };
nav.m_vertex_map[ {1,0,0} ] = { {0,0,0}, {0,0,1} };
nav.m_vertex_map[ {0,0,1} ] = { {0,0,0}, {1,0,0} };
// Query the closest node to an arbitrary point
auto q = nav.get_closest_vertex({0.3f, 0.0f, 0.2f});
if (q) {
const auto& v = *q;
const auto& nbrs = nav.get_neighbors(v);
(void)nbrs;
}
```
---
## Semantics & expectations
* **Nearest vertex**
`get_closest_vertex(p)` should scan known vertices and return the one with minimal Euclidean distance to `p`. If the mesh is empty, expect an error (`unexpected` with a message).
* **Neighbors**
`get_neighbors(v)` returns the adjacency list for `v`. If `v` is not present, a conventional behavior is to return a **reference to a static empty vector** (since the API is `noexcept` and returns by reference). Verify in your implementation.
* **Graph invariants** (recommended)
* Neighbor links are **symmetric** for undirected navigation (if `u` has `v`, then `v` has `u`).
* No self-loops unless explicitly desired.
* Vertices are unique keys; hashing uses `std::hash<Vector3<float>>` (be mindful of floating-point equality).
---
## Serialization
* `serialize()` → opaque, implementation-defined binary of the current `m_vertex_map`.
* `deserialize(raw)` → restores the internal map from `raw`.
Keep versioning in mind if you evolve the format (e.g., add a header/magic/version).
---
## Performance
Let `V = m_vertex_map.size()` and `E = Σ|neighbors(v)|`.
* `get_closest_vertex`: **O(V)** (linear scan) unless you back it with a spatial index (KD-tree, grid, etc.).
* `get_neighbors`: **O(1)** average (hash lookup).
* Memory: **O(V + E)**.
---
## Usage notes
* **Floating-point keys**: Using `Vector3<float>` as an unordered_map key relies on your `std::hash<omath::Vector3<float>>` and exact `operator==`. Avoid building meshes with numerically “close but not equal” duplicates; consider canonicalizing or using integer IDs if needed.
* **Pathfinding**: Pair with `Astar::find_path(start, end, nav)`; the A* heuristic can use straight-line distance between vertex positions.
---
## Minimal test ideas
* Empty mesh → `get_closest_vertex` returns error; `empty() == true`.
* Single vertex → nearest always that vertex; neighbors empty.
* Symmetric edges → `get_neighbors(a)` contains `b` and vice versa.
* Serialization round-trip preserves vertex/edge counts and neighbor lists.

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# `omath::projectile_prediction::ProjPredEngineAvx2` — AVX2-accelerated ballistic aim solver
> Header: your project’s `projectile_prediction/proj_pred_engine_avx2.hpp`
> Namespace: `omath::projectile_prediction`
> Inherits: `ProjPredEngineInterface`
> Depends on: `Vector3<float>`, `Projectile`, `Target`
> CPU: Uses AVX2 when available; falls back to scalar elsewhere (fields are marked `[[maybe_unused]]` for non-x86/AVX2 builds).
This engine computes a **world-space aim point** (and implicitly the firing **yaw/pitch**) to intersect a moving target under a **constant gravity** model and **constant muzzle speed**. It typically scans candidate times of flight and solves for the elevation (`pitch`) that makes the vertical and horizontal kinematics meet at the same time.
---
## API
```cpp
class ProjPredEngineAvx2 final : public ProjPredEngineInterface {
public:
[[nodiscard]]
std::optional<Vector3<float>>
maybe_calculate_aim_point(const Projectile& projectile,
const Target& target) const override;
ProjPredEngineAvx2(float gravity_constant,
float simulation_time_step,
float maximum_simulation_time);
~ProjPredEngineAvx2() override = default;
private:
// Solve for pitch at a fixed time-of-flight t.
[[nodiscard]]
static std::optional<float>
calculate_pitch(const Vector3<float>& proj_origin,
const Vector3<float>& target_pos,
float bullet_gravity, float v0, float time);
// Tunables (may be unused on non-AVX2 builds)
[[maybe_unused]] const float m_gravity_constant; // |g| (e.g., 9.81)
[[maybe_unused]] const float m_simulation_time_step; // Δt (e.g., 1/240 s)
[[maybe_unused]] const float m_maximum_simulation_time; // Tmax (e.g., 3 s)
};
```
### Parameters (constructor)
* `gravity_constant` — magnitude of gravity (units consistent with your world, e.g., **m/s²**).
* `simulation_time_step` — Δt used to scan candidate intercept times.
* `maximum_simulation_time` — cap on time of flight; larger allows longer-range solutions but increases cost.
### Return (solver)
* `maybe_calculate_aim_point(...)`
* **`Vector3<float>`**: a world-space **aim point** yielding an intercept under the model.
* **`std::nullopt`**: no feasible solution (e.g., target receding too fast, out of range, or kinematics inconsistent).
---
## How it solves (expected flow)
1. **Predict target at time `t`** (constant-velocity model unless your `Target` carries more):
```
T(t) = target.position + target.velocity * t
```
2. **Horizontal/vertical kinematics at fixed `t`** with muzzle speed `v0` and gravity `g`:
* Let `Δ = T(t) - proj_origin`, `d = length(Δ.xz)`, `h = Δ.y`.
* Required initial components:
```
cosθ = d / (v0 * t)
sinθ = (h + 0.5 * g * t^2) / (v0 * t)
```
* If `cosθ` ∈ [−1,1] and `sinθ` ∈ [−1,1] and `sin²θ + cos²θ ≈ 1`, then
```
θ = atan2(sinθ, cosθ)
```
That is what `calculate_pitch(...)` returns on success.
3. **Yaw** is the azimuth toward `Δ.xz`.
4. **Pick the earliest feasible `t`** in `[Δt, Tmax]` (scanned in steps of `Δt`; AVX2 batches several `t` at once).
5. **Return the aim point.** Common choices:
* The **impact point** `T(t*)` (useful as a HUD marker), or
* A point along the **initial firing ray** at some convenient range using `(yaw, pitch)`; both are consistent—pick the convention your caller expects.
> The private `calculate_pitch(...)` matches step **2** and returns `nullopt` if the trigonometric constraints are violated for that `t`.
---
## AVX2 notes
* On x86/x64 with AVX2, candidate times `t` can be evaluated **8 at a time** using FMA (great for dense scans).
* On ARM/ARM64 (no AVX2), code falls back to scalar math; the `[[maybe_unused]]` members acknowledge compilation without SIMD.
---
## Usage example
```cpp
using namespace omath::projectile_prediction;
ProjPredEngineAvx2 solver(
/*gravity*/ 9.81f,
/*dt*/ 1.0f/240.0f,
/*Tmax*/ 3.0f
);
Projectile proj; // fill: origin, muzzle_speed, etc.
Target tgt; // fill: position, velocity
if (auto aim = solver.maybe_calculate_aim_point(proj, tgt)) {
// Aim your weapon at *aim and fire with muzzle speed proj.v0
// If you need yaw/pitch explicitly, replicate the pitch solve and azimuth.
} else {
// No solution (out of envelope) — pick a fallback
}
```
---
## Edge cases & failure modes
* **Zero or tiny `v0`** → no solution.
* **Target collinear & receding faster than `v0`** → no solution.
* **`t` constraints**: if viable solutions exist only beyond `Tmax`, you’ll get `nullopt`.
* **Geometric infeasibility** at a given `t` (e.g., `d > v0*t`) causes `calculate_pitch` to fail that sample.
* **Numerical tolerance**: check `sin²θ + cos²θ` against 1 with a small epsilon (e.g., `1e-3`).
---
## Performance & tuning
* Work is roughly `O(Nt)` where `Nt ≈ Tmax / Δt`.
* Smaller `Δt` → better accuracy, higher cost. With AVX2 you can afford smaller steps.
* If you frequently miss solutions **between** steps, consider:
* **Coarse-to-fine**: coarse scan, then local refine around the best `t`.
* **Newton on time**: root-find `‖horizontal‖ − v0 t cosθ(t) = 0` shaped from the kinematics.
---
## Testing checklist
* **Stationary target** at same height → θ ≈ 0, aim point ≈ target.
* **Higher target** → positive pitch; **lower target** → negative pitch.
* **Perpendicular moving target** → feasible at moderate speeds.
* **Very fast receding target** → `nullopt`.
* **Boundary**: `d ≈ v0*Tmax` and `h` large → verify pass/fail around thresholds.
---
## See also
* `ProjPredEngineInterface` — base interface and general contract
* `Projectile`, `Target` — data carriers for solver inputs (speed, origin, position, velocity, etc.)
---
*Last updated: 1 Nov 2025*

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# `omath::projectile_prediction::ProjPredEngineLegacy` — Legacy trait-based aim solver
> Header: `omath/projectile_prediction/proj_pred_engine_legacy.hpp`
> Namespace: `omath::projectile_prediction`
> Inherits: `ProjPredEngineInterface`
> Template param (default): `EngineTrait = source_engine::PredEngineTrait`
> Purpose: compute a world-space **aim point** to hit a (possibly moving) target using a **discrete time scan** and a **closed-form ballistic pitch** under constant gravity.
---
## Overview
`ProjPredEngineLegacy` is a portable, trait-driven projectile lead solver. At each simulation time step `t` it:
1. **Predicts target position** with `EngineTrait::predict_target_position(target, t, g)`.
2. **Computes launch pitch** via a gravity-aware closed form (or a direct angle if gravity is zero).
3. **Validates** that a projectile fired with that pitch (and direct yaw) actually reaches the predicted target within a **distance tolerance** at time `t`.
4. On success, **returns an aim point** computed by `EngineTrait::calc_viewpoint_from_angles(...)`.
If no time step yields a feasible solution up to `maximum_simulation_time`, returns `std::nullopt`.
---
## API
```cpp
template<class EngineTrait = source_engine::PredEngineTrait>
requires PredEngineConcept<EngineTrait>
class ProjPredEngineLegacy final : public ProjPredEngineInterface {
public:
ProjPredEngineLegacy(float gravity_constant,
float simulation_time_step,
float maximum_simulation_time,
float distance_tolerance);
[[nodiscard]]
std::optional<Vector3<float>>
maybe_calculate_aim_point(const Projectile& projectile,
const Target& target) const override;
private:
// Closed-form ballistic pitch solver (internal)
std::optional<float>
maybe_calculate_projectile_launch_pitch_angle(const Projectile& projectile,
const Vector3<float>& target_position) const noexcept;
bool is_projectile_reached_target(const Vector3<float>& target_position,
const Projectile& projectile,
float pitch, float time) const noexcept;
const float m_gravity_constant;
const float m_simulation_time_step;
const float m_maximum_simulation_time;
const float m_distance_tolerance;
};
```
### Constructor parameters
* `gravity_constant` — magnitude of gravity (e.g., `9.81f`), world units/s².
* `simulation_time_step` — Δt for the scan (e.g., `1/240.f`).
* `maximum_simulation_time` — search horizon in seconds.
* `distance_tolerance` — max allowed miss distance at time `t` to accept a solution.
---
## Trait requirements (`PredEngineConcept`)
Your `EngineTrait` must expose **noexcept** static methods with these signatures:
```cpp
Vector3<float> predict_projectile_position(const Projectile&, float pitch_deg, float yaw_deg,
float time, float gravity) noexcept;
Vector3<float> predict_target_position(const Target&, float time, float gravity) noexcept;
float calc_vector_2d_distance(const Vector3<float>& v) noexcept; // typically length in XZ plane
float get_vector_height_coordinate(const Vector3<float>& v) noexcept; // typically Y
Vector3<float> calc_viewpoint_from_angles(const Projectile&, Vector3<float> target,
std::optional<float> maybe_pitch_deg) noexcept;
float calc_direct_pitch_angle(const Vector3<float>& from, const Vector3<float>& to) noexcept;
float calc_direct_yaw_angle (const Vector3<float>& from, const Vector3<float>& to) noexcept;
```
> This design lets you adapt different game/physics conventions (axes, units, handedness) without changing the solver.
---
## Algorithm details
### Time scan
For `t = 0 .. maximum_simulation_time` in steps of `simulation_time_step`:
1. `T = EngineTrait::predict_target_position(target, t, g)`
2. `pitch = maybe_calculate_projectile_launch_pitch_angle(projectile, T)`
* If `std::nullopt`: continue
3. `yaw = EngineTrait::calc_direct_yaw_angle(projectile.m_origin, T)`
4. `P = EngineTrait::predict_projectile_position(projectile, pitch, yaw, t, g)`
5. Accept if `|P - T| <= distance_tolerance`
6. Return `EngineTrait::calc_viewpoint_from_angles(projectile, T, pitch)`
### Closed-form pitch (gravity on)
Implements the classic ballistic formula (low-arc branch), where:
* `v` = muzzle speed,
* `g` = `gravity_constant * projectile.m_gravity_scale`,
* `x` = horizontal (2D) distance to target,
* `y` = vertical offset to target.
[
\theta ;=; \arctan!\left(\frac{v^{2} ;-; \sqrt{v^{4}-g!\left(gx^{2}+2yv^{2}\right)}}{gx}\right)
]
* If the **discriminant** ( v^{4}-g(gx^{2}+2yv^{2}) < 0 ) ⇒ **no real solution**.
* If `g == 0`, falls back to `EngineTrait::calc_direct_pitch_angle(...)`.
* Returns **degrees** (internally converts from radians).
---
## Usage example
```cpp
using namespace omath::projectile_prediction;
ProjPredEngineLegacy solver(
/*gravity*/ 9.81f,
/*dt*/ 1.f / 240.f,
/*Tmax*/ 3.0f,
/*tol*/ 0.05f
);
Projectile proj; // fill: m_origin, m_launch_speed, m_gravity_scale, etc.
Target tgt; // fill: position/velocity as required by your trait
if (auto aim = solver.maybe_calculate_aim_point(proj, tgt)) {
// Drive your turret/reticle toward *aim
} else {
// No feasible intercept in the given horizon
}
```
---
## Behavior & edge cases
* **Zero gravity or zero distance**: uses direct pitch toward the target.
* **Negative discriminant** in the pitch formula: returns `std::nullopt` for that time step.
* **Very small `x`** (horizontal distance): the formula’s denominator `gx` approaches zero; your trait’s direct pitch helper provides a stable fallback.
* **Tolerance**: `distance_tolerance` controls acceptance; tighten for accuracy, loosen for robustness.
---
## Complexity & tuning
* Time: **O(T)** where ( T \approx \frac{\text{maximum_simulation_time}}{\text{simulation_time_step}} )
plus trait costs for prediction and angle math per step.
* Smaller `simulation_time_step` improves precision but increases runtime.
* If needed, do a **coarse-to-fine** search: coarse Δt scan, then refine around the best hit time.
---
## Testing checklist
* Stationary, level target → pitch ≈ 0 for short ranges; accepted within tolerance.
* Elevated/depressed targets → pitch positive/negative as expected.
* Receding fast target → unsolved within horizon ⇒ `nullopt`.
* Gravity scale = 0 → identical to straight-line solution.
* Near-horizon shots (large range, small arc) → discriminant near zero; verify stability.
---
## Notes
* All angles produced/consumed by the trait in this implementation are **degrees**.
* `calc_viewpoint_from_angles` defines what “aim point” means in your engine (e.g., a point along the initial ray or the predicted impact point). Keep this consistent with your HUD/reticle.
---
*Last updated: 1 Nov 2025*

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# `omath::projectile_prediction::Projectile` — Projectile parameters for aim solvers
> Header: `omath/projectile_prediction/projectile.hpp`
> Namespace: `omath::projectile_prediction`
> Used by: `ProjPredEngineInterface` implementations (e.g., `ProjPredEngineLegacy`, `ProjPredEngineAvx2`)
`Projectile` is a tiny data holder that describes how a projectile is launched: **origin** (world position), **launch speed**, and a **gravity scale** (multiplier applied to the engine’s gravity constant).
---
## API
```cpp
namespace omath::projectile_prediction {
class Projectile final {
public:
Vector3<float> m_origin; // Launch position (world space)
float m_launch_speed{}; // Initial speed magnitude (units/sec)
float m_gravity_scale{}; // Multiplier for global gravity (dimensionless)
};
} // namespace omath::projectile_prediction
```
---
## Field semantics
* **`m_origin`**
World-space position where the projectile is spawned (e.g., muzzle or emitter point).
* **`m_launch_speed`**
Initial speed **magnitude** in your world units per second. Direction is determined by the solver (from yaw/pitch).
* Must be **non-negative**. Zero disables meaningful ballistic solutions.
* **`m_gravity_scale`**
Multiplies the engine’s gravity constant provided to the solver (e.g., `g = gravity_constant * m_gravity_scale`).
* Use `1.0f` for normal gravity, `0.0f` for no-drop projectiles, other values to simulate heavier/lighter rounds.
> Units must be consistent across your project (e.g., meters & seconds). If `gravity_constant = 9.81f`, then `m_launch_speed` is in m/s and positions are in meters.
---
## Typical usage
```cpp
using namespace omath::projectile_prediction;
Projectile proj;
proj.m_origin = { 0.0f, 1.6f, 0.0f }; // player eye / muzzle height
proj.m_launch_speed = 850.0f; // e.g., 850 m/s
proj.m_gravity_scale = 1.0f; // normal gravity
// With an aim solver:
auto aim = engine->maybe_calculate_aim_point(proj, target);
if (aim) {
// rotate/aim toward *aim and fire
}
```
---
## With gravity-aware solver (outline)
Engines typically compute the firing angles to reach a predicted target position:
* Horizontal distance `x` and vertical offset `y` are derived from `target - m_origin`.
* Gravity used is `g = gravity_constant * m_gravity_scale`.
* Launch direction has speed `m_launch_speed` and angles solved by the engine.
If `m_gravity_scale == 0`, engines usually fall back to straight-line (no-drop) solutions.
---
## Validation & tips
* Keep `m_launch_speed ≥ 0`. Negative values are nonsensical.
* If your weapon can vary muzzle speed (charge-up, attachments), update `m_launch_speed` per shot.
* For different ammo types (tracers, grenades), prefer tweaking **`m_gravity_scale`** (and possibly the engine’s gravity constant) to match observed arc.
---
## See also
* `ProjPredEngineInterface` — common interface for aim solvers
* `ProjPredEngineLegacy` — trait-based, time-stepped ballistic solver
* `ProjPredEngineAvx2` — AVX2-accelerated solver with fixed-time pitch solve
* `Target` — target state consumed by the solvers
* `Vector3<float>` — math type used for positions and directions
---
*Last updated: 1 Nov 2025*

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# `omath::projectile_prediction::ProjPredEngineInterface` — Aim-point solver interface
> Header: your project’s `projectile_prediction/proj_pred_engine_interface.hpp`
> Namespace: `omath::projectile_prediction`
> Depends on: `Vector3<float>`, `Projectile`, `Target`
> Purpose: **contract** for engines that compute a lead/aim point to hit a moving target.
---
## Overview
`ProjPredEngineInterface` defines a single pure-virtual method that attempts to compute the **world-space aim point** where a projectile should be launched to intersect a target under the engine’s physical model (e.g., constant projectile speed, gravity, drag, max flight time, etc.).
If a valid solution exists, the engine returns the 3D aim point. Otherwise, it returns `std::nullopt` (no feasible intercept).
---
## API
```cpp
namespace omath::projectile_prediction {
class ProjPredEngineInterface {
public:
[[nodiscard]]
virtual std::optional<Vector3<float>>
maybe_calculate_aim_point(const Projectile& projectile,
const Target& target) const = 0;
virtual ~ProjPredEngineInterface() = default;
};
} // namespace omath::projectile_prediction
```
### Semantics
* **Input**
* `Projectile` — engine-specific projectile properties (typical: muzzle speed, gravity vector, drag flag/coeff, max range / flight time).
* `Target` — target state (typical: position, velocity, possibly acceleration).
* **Output**
* `std::optional<Vector3<float>>`
* `value()` — world-space point to aim at **now** so that the projectile intersects the target under the model.
* `std::nullopt` — no solution (e.g., target outruns projectile, blocked by constraints, numerical failure).
* **No side effects**: method is `const` and should not modify inputs.
---
## Typical usage
```cpp
using namespace omath::projectile_prediction;
std::unique_ptr<ProjPredEngineInterface> engine = /* your implementation */;
Projectile proj = /* fill from weapon config */;
Target tgt = /* read from tracking system */;
if (auto aim = engine->maybe_calculate_aim_point(proj, tgt)) {
// Rotate/steer to (*aim)
} else {
// Fall back: no-lead, predictive UI, or do not fire
}
```
---
## Implementation guidance (for engine authors)
**Common models:**
1. **No gravity, constant speed**
Closed form intersect time `t` solves `‖p_t + v_t t − p_0‖ = v_p t`.
Choose the smallest non-negative real root; aim point = `p_t + v_t t`.
2. **Gravity (constant g), constant speed**
Solve ballistics with vertical drop: either numerical (Newton–Raphson on time) or 2D elevation + azimuth decomposition. Ensure convergence caps and time bounds.
3. **Drag**
Typically requires numeric integration (e.g., RK4) wrapped in a root find on time-of-flight.
**Robustness tips:**
* **Feasibility checks:** return `nullopt` when:
* projectile speed ≤ 0; target too fast in receding direction; solution time outside `[0, t_max]`.
* **Bounds:** clamp search time to reasonable `[t_min, t_max]` (e.g., `[0, max_flight_time]` or by range).
* **Tolerances:** use epsilons for convergence (e.g., `|f(t)| < 1e-4`, `|Δt| < 1e-4 s`).
* **Determinism:** fix iteration counts or seeds if needed for replayability.
---
## Example: constant-speed, no-gravity intercept (closed form)
```cpp
// Solve ||p + v t|| = s t where p = target_pos - shooter_pos, v = target_vel, s = projectile_speed
// Quadratic: (v·v - s^2) t^2 + 2 (p·v) t + (p·p) = 0
inline std::optional<float> intercept_time_no_gravity(const Vector3<float>& p,
const Vector3<float>& v,
float s) {
const float a = v.dot(v) - s*s;
const float b = 2.f * p.dot(v);
const float c = p.dot(p);
if (std::abs(a) < 1e-6f) { // near linear
if (std::abs(b) < 1e-6f) return std::nullopt;
float t = -c / b;
return t >= 0.f ? std::optional{t} : std::nullopt;
}
const float disc = b*b - 4.f*a*c;
if (disc < 0.f) return std::nullopt;
const float sqrtD = std::sqrt(disc);
float t1 = (-b - sqrtD) / (2.f*a);
float t2 = (-b + sqrtD) / (2.f*a);
float t = (t1 >= 0.f ? t1 : t2);
return t >= 0.f ? std::optional{t} : std::nullopt;
}
```
Aim point (given shooter origin `S`, target pos `T`, vel `V`):
```
p = T - S
t* = intercept_time_no_gravity(p, V, speed)
aim = T + V * t*
```
Return `nullopt` if `t*` is absent.
---
## Testing checklist
* **Stationary target**: aim point equals target position when `s > 0`.
* **Target perpendicular motion**: lead equals lateral displacement `V⊥ * t`.
* **Receding too fast**: expect `nullopt`.
* **Gravity model**: verify arc solutions exist for short & long trajectories (if implemented).
* **Numerics**: convergence within max iterations; monotonic improvement of residuals.
---
## Notes
* This is an **interface** only; concrete engines (e.g., `SimpleNoGravityEngine`, `BallisticGravityEngine`) should document their assumptions (gravity, drag, wind, bounds) and units (meters, seconds).
* The coordinate system and handedness should be consistent with `Vector3<float>` and the rest of your math stack.
---
## See Also
- [Projectile Documentation](projectile.md) - Projectile properties
- [Target Documentation](target.md) - Target state representation
- [Legacy Implementation](proj_pred_engine_legacy.md) - Standard projectile prediction engine
- [AVX2 Implementation](proj_pred_engine_avx2.md) - Optimized AVX2 engine
- [Tutorials - Projectile Prediction](../tutorials.md#tutorial-3-projectile-prediction-aim-bot) - Complete aim-bot tutorial
---
*Last updated: 1 Nov 2025*

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# `omath::projectile_prediction::Target` — Target state for aim solvers
> Header: `omath/projectile_prediction/target.hpp`
> Namespace: `omath::projectile_prediction`
> Used by: `ProjPredEngineInterface` implementations (e.g., Legacy/AVX2 engines)
A small POD-style container describing a target’s **current pose** and **motion** for projectile lead/aim computations.
---
## API
```cpp
namespace omath::projectile_prediction {
class Target final {
public:
Vector3<float> m_origin; // Current world-space position of the target
Vector3<float> m_velocity; // World-space linear velocity (units/sec)
bool m_is_airborne{}; // Domain hint (e.g., ignore ground snapping)
};
} // namespace omath::projectile_prediction
```
---
## Field semantics
* **`m_origin`** — target position in world coordinates (same units as your `Vector3<float>` grid).
* **`m_velocity`** — instantaneous linear velocity. Solvers commonly assume **constant velocity** between “now” and impact unless your trait injects gravity/accel.
* **`m_is_airborne`** — optional hint for engine/trait logic (e.g., apply gravity to the target, skip ground friction/snap). Exact meaning is engine-dependent.
> Keep units consistent with your projectile model (e.g., meters & seconds). If projectiles use `g = 9.81 m/s²`, velocity should be in m/s and positions in meters.
---
## Typical usage
```cpp
using namespace omath::projectile_prediction;
Target tgt;
tgt.m_origin = { 42.0f, 1.8f, -7.5f };
tgt.m_velocity = { 3.0f, 0.0f, 0.0f }; // moving +X at 3 units/s
tgt.m_is_airborne = false;
// Feed into an aim solver with a Projectile
auto aim = engine->maybe_calculate_aim_point(projectile, tgt);
```
---
## Notes & tips
* If you track acceleration (e.g., gravity on ragdolls), your **EngineTrait** may derive it from `m_is_airborne` and world gravity; otherwise most solvers treat the target’s motion as linear.
* For highly agile targets, refresh `m_origin`/`m_velocity` every tick and re-solve; don’t reuse stale aim points.
* Precision: `Vector3<float>` is typically enough; if you need sub-millimeter accuracy over long ranges, consider double-precision internally in your trait.
---
## See also
* `Projectile` — shooter origin, muzzle speed, gravity scale
* `ProjPredEngineInterface` — common interface for aim solvers
* `ProjPredEngineLegacy`, `ProjPredEngineAvx2` — concrete solvers using this data
---
*Last updated: 1 Nov 2025*

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# `omath::projection::Camera` — Generic, trait-driven camera with screen/world conversion
> Header: `omath/projection/camera.hpp` (this header)
> Namespace: `omath::projection`
> Template: `Camera<Mat4X4Type, ViewAnglesType, TraitClass>`
> Requires: `CameraEngineConcept<TraitClass, Mat4X4Type, ViewAnglesType>`
> Key features: **lazy view-projection caching**, world↔screen helpers, pluggable math via a **Trait**
---
## Overview
`Camera` is a small, zero-allocation camera wrapper. It delegates the math for **view**, **projection**, and **look-at** to a **Trait** (`TraitClass`), which lets you plug in different coordinate systems or conventions without changing the camera code. The class caches the **View×Projection** matrix and invalidates it when any parameter changes.
Alongside the camera, the header defines:
* `struct ViewPort { float m_width, m_height; float aspect_ratio() const; }`
* `using FieldOfView = Angle<float, 0.f, 180.f, AngleFlags::Clamped>;`
---
## Template & trait requirements
```cpp
template<class T, class MatType, class ViewAnglesType>
concept CameraEngineConcept = requires(
const omath::Vector3<float>& cam_origin,
const omath::Vector3<float>& look_at,
const ViewAnglesType& angles,
const omath::projection::FieldOfView& fov,
const omath::projection::ViewPort& viewport,
float znear, float zfar
) {
{ T::calc_look_at_angle(cam_origin, look_at) } noexcept -> std::same_as<ViewAnglesType>;
{ T::calc_view_matrix(angles, cam_origin) } noexcept -> std::same_as<MatType>;
{ T::calc_projection_matrix(fov, viewport, znear, zfar)}noexcept -> std::same_as<MatType>;
};
```
Your `Mat4X4Type` must behave like the library’s `Mat<4,4,...>` (supports `*`, `/`, `inverted()`, `.at(r,c)`, `.raw_array()`, and `static constexpr get_store_ordering()`).
---
## Quick start
```cpp
using Mat4 = omath::Mat<4,4,float, omath::MatStoreType::COLUMN_MAJOR>;
// Example trait (sketch): assumes Y-up, column-major, left-handed
struct MyCamTrait {
static ViewAnglesType calc_look_at_angle(const Vector3<float>& eye,
const Vector3<float>& at) noexcept;
static Mat4 calc_view_matrix(const ViewAnglesType& ang,
const Vector3<float>& eye) noexcept;
static Mat4 calc_projection_matrix(const FieldOfView& fov,
const ViewPort& vp,
float znear, float zfar) noexcept;
};
using Camera = omath::projection::Camera<Mat4, MyViewAngles, MyCamTrait>;
omath::projection::ViewPort vp{1920, 1080};
omath::projection::FieldOfView fov = omath::angles::degrees(70.f);
Camera cam(/*position*/ {0,1.7f, -3},
/*angles*/ MyViewAngles{/*...*/},
/*viewport*/ vp, fov,
/*near*/ 0.1f,
/*far*/ 1000.f);
// Project world → screen (origin top-left)
auto s = cam.world_to_screen<Camera::ScreenStart::TOP_LEFT_CORNER>({1, 1, 0});
if (s) {
// s->x, s->y in pixels; s->z in NDC depth
}
```
---
## API
```cpp
enum class ScreenStart { TOP_LEFT_CORNER, BOTTOM_LEFT_CORNER };
class Camera final {
public:
~Camera() = default;
Camera(const Vector3<float>& position,
const ViewAnglesType& view_angles,
const ViewPort& view_port,
const FieldOfView& fov,
float near, float far) noexcept;
void look_at(const Vector3<float>& target); // recomputes view angles; invalidates cache
// Lazily computed and cached:
const Mat4X4Type& get_view_projection_matrix() const noexcept;
// Setters (all invalidate cached VP):
void set_field_of_view(const FieldOfView&) noexcept;
void set_near_plane(float) noexcept;
void set_far_plane(float) noexcept;
void set_view_angles(const ViewAnglesType&) noexcept;
void set_origin(const Vector3<float>&) noexcept;
void set_view_port(const ViewPort&) noexcept;
// Getters:
const FieldOfView& get_field_of_view() const noexcept;
const float& get_near_plane() const noexcept;
const float& get_far_plane() const noexcept;
const ViewAnglesType& get_view_angles() const noexcept;
const Vector3<float>& get_origin() const noexcept;
// World → Screen (pixels) via NDC; choose screen origin:
template<ScreenStart screen_start = ScreenStart::TOP_LEFT_CORNER>
std::expected<Vector3<float>, Error>
world_to_screen(const Vector3<float>& world) const noexcept;
// World → NDC (aka “viewport” in this code) ∈ [-1,1]^3
std::expected<Vector3<float>, Error>
world_to_view_port(const Vector3<float>& world) const noexcept;
// NDC → World (uses inverse VP)
std::expected<Vector3<float>, Error>
view_port_to_screen(const Vector3<float>& ndc) const noexcept;
// Screen (pixels) → World
std::expected<Vector3<float>, Error>
screen_to_world(const Vector3<float>& screen) const noexcept;
// 2D overload (z defaults to 1, i.e., far plane ray-end in NDC)
std::expected<Vector3<float>, Error>
screen_to_world(const Vector2<float>& screen) const noexcept;
protected:
ViewPort m_view_port{};
FieldOfView m_field_of_view;
mutable std::optional<Mat4X4Type> m_view_projection_matrix;
float m_far_plane_distance{};
float m_near_plane_distance{};
ViewAnglesType m_view_angles;
Vector3<float> m_origin;
private:
static constexpr bool is_ndc_out_of_bounds(const Mat4X4Type& ndc) noexcept;
Vector3<float> ndc_to_screen_position_from_top_left_corner(const Vector3<float>& ndc) const noexcept;
Vector3<float> ndc_to_screen_position_from_bottom_left_corner(const Vector3<float>& ndc) const noexcept;
Vector3<float> screen_to_ndc(const Vector3<float>& screen) const noexcept;
};
```
### Error handling
All conversions return `std::expected<..., Error>` with errors from `error_codes.hpp`, notably:
* `Error::WORLD_POSITION_IS_OUT_OF_SCREEN_BOUNDS` — clip space W=0 or NDC outside `[-1,1]`.
* `Error::INV_VIEW_PROJ_MAT_DET_EQ_ZERO` — non-invertible View×Projection matrix.
---
## Coordinate spaces & conversions
### World → NDC (`world_to_view_port`)
1. Build (or reuse cached) `VP = P * V` (projection * view).
2. Multiply by homogeneous column from the world point.
3. Reject if `w == 0`.
4. Perspective divide → NDC in `[-1,1]^3`.
5. Reject if any component is out of range.
Returns `{x_ndc, y_ndc, z_ndc}`.
### NDC → Screen (pixels)
The class offers two origins:
* **Top-left (default)**
```
x_px = (x_ndc + 1)/2 * width
y_px = ( -y_ndc/2 + 0.5) * height // flips Y
```
* **Bottom-left**
```
x_px = (x_ndc + 1)/2 * width
y_px = ( y_ndc/2 + 0.5) * height
```
### Screen (pixels) → NDC
```
x_ndc = screen_x / width * 2 - 1
y_ndc = 1 - screen_y / height * 2 // Top-left screen origin assumed here
z_ndc = screen_z // Caller-provided (e.g., 0..1 depth)
```
### NDC → World (`view_port_to_screen`)
Despite the method name, this function **unprojects** an NDC point back to world space:
1. Compute `VP^{-1}`; if not invertible → error.
2. Multiply by NDC (homogeneous 4D) and divide by `w`.
3. Return world point.
> Tip: to build a **world-space ray** from a screen pixel, unproject at `z=0` (near) and `z=1` (far).
---
## Caching & invalidation
* `get_view_projection_matrix()` computes `P*V` once and caches it.
* Any setter (`set_*`) or `look_at()` clears the cache (`m_view_projection_matrix = std::nullopt`).
---
## Notes & gotchas
* **Matrix order**: The camera multiplies `P * V`. Make sure your **Trait** matches this convention.
* **Store ordering**: The `Mat4X4Type::get_store_ordering()` is used when building homogeneous columns; ensure it’s consistent with your matrix implementation.
* **Naming quirk**: `view_port_to_screen()` returns a **world** point from **NDC** (it’s an unproject). Consider renaming to `ndc_to_world()` in your codebase for clarity.
* **FOV units**: `FieldOfView` uses the project’s `Angle` type; pass degrees via `angles::degrees(...)`.
---
## Minimal trait sketch (column-major, left-handed)
```cpp
struct LHCTrait {
static MyAngles calc_look_at_angle(const Vector3<float>& eye,
const Vector3<float>& at) noexcept { /* ... */ }
static Mat4 calc_view_matrix(const MyAngles& ang,
const Vector3<float>& eye) noexcept {
// Build from forward/right/up and translation
}
static Mat4 calc_projection_matrix(const FieldOfView& fov,
const ViewPort& vp,
float zn, float zf) noexcept {
return omath::mat_perspective_left_handed<float, omath::MatStoreType::COLUMN_MAJOR>(
fov.as_degrees(), vp.aspect_ratio(), zn, zf
);
}
};
```
---
## Testing checklist
* World point centered in view projects to **screen center**.
* Points outside frustum → `WORLD_POSITION_IS_OUT_OF_SCREEN_BOUNDS`.
* Inverting `VP` fails gracefully for singular matrices.
* `ScreenStart` switch flips Y as expected.
* Screen→World ray: unproject `(x,y,0)` and `(x,y,1)` and verify direction passes through the camera frustum.
---
## See Also
- [Engine-Specific Camera Traits](../engines/) - Camera implementations for different game engines
- [View Angles Documentation](../trigonometry/view_angles.md) - Understanding pitch/yaw/roll
- [Getting Started Guide](../getting_started.md) - Quick start with projection
- [Tutorials - World-to-Screen](../tutorials.md#tutorial-2-world-to-screen-projection) - Complete projection tutorial
---
*Last updated: 1 Nov 2025*

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# `omath::projection::Error` — Error codes for world/screen projection
> Header: `omath/projection/error_codes.hpp`
> Namespace: `omath::projection`
> Type: `enum class Error : uint16_t`
These error codes are returned by camera/projection helpers (e.g., `Camera::world_to_screen`, `Camera::screen_to_world`) wrapped in `std::expected<..., Error>`. Use them to distinguish **clipping/visibility** problems from **matrix/math** failures.
---
## Enum values
```cpp
enum class Error : uint16_t {
WORLD_POSITION_IS_OUT_OF_SCREEN_BOUNDS,
INV_VIEW_PROJ_MAT_DET_EQ_ZERO,
};
```
* **`WORLD_POSITION_IS_OUT_OF_SCREEN_BOUNDS`**
The input point cannot produce a valid on-screen coordinate:
* Clip-space `w == 0` (point at/infinite or behind camera plane), or
* After projection, any NDC component is outside `[-1, 1]`.
* **`INV_VIEW_PROJ_MAT_DET_EQ_ZERO`**
The **View × Projection** matrix is not invertible (determinant ≈ 0).
Unprojection (`screen_to_world` / `view_port_to_screen`) requires an invertible matrix.
---
## Typical usage
```cpp
using omath::projection::Error;
auto pix = cam.world_to_screen(point);
if (!pix) {
switch (pix.error()) {
case Error::WORLD_POSITION_IS_OUT_OF_SCREEN_BOUNDS:
// Cull label/marker; point is off-screen or behind camera.
break;
case Error::INV_VIEW_PROJ_MAT_DET_EQ_ZERO:
// Investigate camera/projection setup; near/far/FOV or trait bug.
break;
}
}
// Unproject a screen pixel (top-left origin) at depth 1.0
if (auto world = cam.screen_to_world({sx, sy, 1.0f})) {
// use *world
} else if (world.error() == Error::INV_VIEW_PROJ_MAT_DET_EQ_ZERO) {
// handle singular VP matrix
}
```
---
## When you might see these errors
* **Out-of-bounds**
* The world point lies outside the camera frustum.
* The point is behind the camera (clip `w <= 0`).
* Extremely large coordinates cause overflow and fail NDC bounds.
* **Non-invertible VP**
* Degenerate projection settings (e.g., `near == far`, zero FOV).
* Trait builds `P` or `V` incorrectly (wrong handedness/order).
* Numerical issues from nearly singular configurations.
---
## Recommendations
* Validate camera setup: `near > 0`, `far > near`, sensible FOV (e.g., 30°–120°).
* For UI markers: treat `WORLD_POSITION_IS_OUT_OF_SCREEN_BOUNDS` as a simple **cull** signal.
* Log `INV_VIEW_PROJ_MAT_DET_EQ_ZERO` — it usually indicates a configuration or math bug worth fixing rather than hiding.

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# `omath::rev_eng::ExternalReverseEngineeredObject` — typed offsets over external memory
> Header: `omath/rev_eng/external_reverse_engineered_object.hpp`
> Namespace: `omath::rev_eng`
> Pattern: **CRTP-style wrapper** around a user-provided *ExternalMemoryManagementTrait* that actually reads/writes another process or device’s memory.
A tiny base class for reverse-engineered objects that live **outside** your address space. You pass an absolute base address and a trait with `read_memory` / `write_memory`. Your derived types then expose strongly-typed getters/setters that delegate into the trait using **byte offsets**.
---
## Quick look
```cpp
template<class ExternalMemoryManagementTrait>
class ExternalReverseEngineeredObject {
public:
explicit ExternalReverseEngineeredObject(std::uintptr_t addr)
: m_object_address(addr) {}
protected:
template<class Type>
[[nodiscard]] Type get_by_offset(std::ptrdiff_t offset) const {
return ExternalMemoryManagementTrait::read_memory(m_object_address + offset);
}
template<class Type>
void set_by_offset(std::ptrdiff_t offset, const Type& value) const {
ExternalMemoryManagementTrait::write_memory(m_object_address + offset, value);
}
private:
std::uintptr_t m_object_address{};
};
```
---
## Trait requirements
Your `ExternalMemoryManagementTrait` must provide:
```cpp
// Reads sizeof(T) bytes starting at absolute address and returns T.
template<class T>
static T read_memory(std::uintptr_t absolute_address);
// Writes sizeof(T) bytes to absolute address.
template<class T>
static void write_memory(std::uintptr_t absolute_address, const T& value);
```
> Tip: If your implementation prefers returning `bool`/`expected<>` for writes, either:
>
> * make `write_memory` `void` and throw/log internally, or
> * adjust `set_by_offset` in your fork to surface the status.
### Common implementations
* **Windows**: wrap `ReadProcessMemory` / `WriteProcessMemory` with a stored `HANDLE` (often captured via a singleton or embedded in the trait).
* **Linux**: `/proc/<pid>/mem`, `process_vm_readv/writev`, `ptrace`.
* **Device/FPGA**: custom MMIO/driver APIs.
---
## How to use (derive and map fields)
Create a concrete type for your target structure and map known offsets:
```cpp
struct WinRPMTrait {
template<class T>
static T read_memory(std::uintptr_t addr) {
T out{};
SIZE_T n{};
if (!ReadProcessMemory(g_handle, reinterpret_cast<LPCVOID>(addr), &out, sizeof(T), &n) || n != sizeof(T))
throw std::runtime_error("RPM failed");
return out;
}
template<class T>
static void write_memory(std::uintptr_t addr, const T& val) {
SIZE_T n{};
if (!WriteProcessMemory(g_handle, reinterpret_cast<LPVOID>(addr), &val, sizeof(T), &n) || n != sizeof(T))
throw std::runtime_error("WPM failed");
}
};
class Player final : public omath::rev_eng::ExternalReverseEngineeredObject<WinRPMTrait> {
using Base = omath::rev_eng::ExternalReverseEngineeredObject<WinRPMTrait>;
public:
using Base::Base; // inherit ctor (takes base address)
// Offsets taken from your RE notes (in bytes)
Vector3<float> position() const { return get_by_offset<Vector3<float>>(0x30); }
void set_position(const Vector3<float>& p) const { set_by_offset(0x30, p); }
float health() const { return get_by_offset<float>(0x100); }
void set_health(float h) const { set_by_offset(0x100, h); }
};
```
Then:
```cpp
Player p{ /* base address you discovered */ 0x7FF6'1234'0000ull };
auto pos = p.position();
p.set_health(100.f);
```
---
## Design notes & constraints
* **Offsets are byte offsets** from the object’s **base address** passed to the constructor.
* **Type safety is on you**: `Type` must match the external layout at that offset (endian, packing, alignment).
* **No lifetime tracking**: if the target object relocates/frees, you must update/recreate the wrapper with the new base address.
* **Thread safety**: the class itself is stateless; thread safety depends on your trait implementation.
* **Endianness**: assumes the host and target endianness agree, or your trait handles conversion.
* **Error handling**: this header doesn’t prescribe it; adopt exceptions/expected/logging inside the trait.
---
## Best practices
* Centralize offsets in one place (constexprs or a small struct) and **comment source/version** (e.g., *game v1.2.3*).
* Wrap fragile multi-field writes in a trait-level **transaction** if your platform supports it.
* Validate pointers/guards (e.g., vtable signature, canary) before trusting offsets.
* Prefer **plain old data** (`struct` without virtuals) for `Type` to ensure trivial byte copies.
---
## Minimal trait sketch (POSIX, `process_vm_readv`)
```cpp
struct LinuxPvmTrait {
static pid_t pid;
template<class T> static T read_memory(std::uintptr_t addr) {
T out{};
iovec local{ &out, sizeof(out) }, remote{ reinterpret_cast<void*>(addr), sizeof(out) };
if (process_vm_readv(pid, &local, 1, &remote, 1, 0) != ssize_t(sizeof(out)))
throw std::runtime_error("pvm_readv failed");
return out;
}
template<class T> static void write_memory(std::uintptr_t addr, const T& val) {
iovec local{ const_cast<T*>(&val), sizeof(val) }, remote{ reinterpret_cast<void*>(addr), sizeof(val) };
if (process_vm_writev(pid, &local, 1, &remote, 1, 0) != ssize_t(sizeof(val)))
throw std::runtime_error("pvm_writev failed");
}
};
```
---
## Troubleshooting
* **Garbled values** → wrong offset/Type, or target’s structure changed between versions.
* **Access denied** → missing privileges (admin/root), wrong process handle, or page protections.
* **Crashes in trait** → add bounds/sanity checks; many APIs fail on unmapped pages.
* **Writes “stick” only briefly** → the target may constantly overwrite (server authority / anti-cheat / replication).
---
*Last updated: 1 Nov 2025*

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# `omath::rev_eng::InternalReverseEngineeredObject` — raw in-process offset/VTABLE access
> Header: `omath/rev_eng/internal_reverse_engineered_object.hpp`
> Namespace: `omath::rev_eng`
> Purpose: Convenience base for **internal** (same-process) RE wrappers that:
>
> * read/write fields by **byte offset** from `this`
> * call **virtual methods** by **vtable index**
---
## At a glance
```cpp
class InternalReverseEngineeredObject {
protected:
template<class Type>
[[nodiscard]] Type& get_by_offset(std::ptrdiff_t offset);
template<class Type>
[[nodiscard]] const Type& get_by_offset(std::ptrdiff_t offset) const;
template<std::size_t id, class ReturnType>
ReturnType call_virtual_method(auto... arg_list);
};
```
* `get_by_offset<T>(off)` — returns a **reference** to `T` located at `reinterpret_cast<uintptr_t>(this) + off`.
* `call_virtual_method<id, Ret>(args...)` — fetches the function pointer from `(*reinterpret_cast<void***>(this))[id]` and invokes it as a free function with implicit `this` passed explicitly.
On MSVC builds the function pointer type uses `__thiscall`; on non-MSVC it uses a plain function pointer taking `void*` as the first parameter (the typical Itanium ABI shape).
---
## Example: wrapping a reverse-engineered class
```cpp
struct Player : omath::rev_eng::InternalReverseEngineeredObject {
// Field offsets (document game/app version!)
static constexpr std::ptrdiff_t kHealth = 0x100;
static constexpr std::ptrdiff_t kPosition = 0x30;
// Accessors
float& health() { return get_by_offset<float>(kHealth); }
const float& health() const { return get_by_offset<float>(kHealth); }
Vector3<float>& position() { return get_by_offset<Vector3<float>>(kPosition); }
const Vector3<float>& position() const { return get_by_offset<Vector3<float>>(kPosition); }
// Virtuals (vtable indices discovered via RE)
int getTeam() { return call_virtual_method<27, int>(); }
void setArmor(float val) { call_virtual_method<42, void>(val); } // signature must match!
};
```
Usage:
```cpp
auto* p = /* pointer to live Player instance within the same process */;
p->health() = 100.f;
int team = p->getTeam();
```
---
## How `call_virtual_method` resolves the signature
```cpp
template<std::size_t id, class ReturnType>
ReturnType call_virtual_method(auto... arg_list) {
#ifdef _MSC_VER
using Fn = ReturnType(__thiscall*)(void*, decltype(arg_list)...);
#else
using Fn = ReturnType(*)(void*, decltype(arg_list)...);
#endif
return (*reinterpret_cast<Fn**>(this))[id](this, arg_list...);
}
```
* The **first parameter** is always `this` (`void*`).
* Remaining parameter types are deduced from the **actual arguments** (`decltype(arg_list)...`).
Ensure you pass arguments with the correct types (e.g., `int32_t` vs `int`, pointer/ref qualifiers), or define thin wrappers that cast to the exact signature you recovered.
> ⚠ On 32-bit MSVC the `__thiscall` distinction matters; on 64-bit MSVC it’s ignored (all member funcs use the common x64 calling convention).
---
## Safety notes (read before using!)
Working at this level is inherently unsafe; be deliberate:
1. **Correct offsets & alignment**
* `get_by_offset<T>` assumes `this + offset` is **properly aligned** for `T` and points to an object of type `T`.
* Wrong offsets or misalignment ⇒ **undefined behavior** (UB), crashes, silent corruption.
2. **Object layout assumptions**
* The vtable pointer is assumed to be at the **start of the most-derived subobject at `this`**.
* With **multiple/virtual inheritance**, the desired subobject’s vptr may be at a non-zero offset. If so, adjust `this` to that subobject before calling, e.g.:
```cpp
auto* sub = reinterpret_cast<void*>(reinterpret_cast<std::uintptr_t>(this) + kSubobjectOffset);
// … then reinterpret sub instead of this inside a custom helper
```
3. **ABI & calling convention**
* Indices and signatures are **compiler/ABI-specific**. Recheck after updates or different builds (MSVC vs Clang/LLVM-MSVC vs MinGW).
4. **Strict aliasing**
* Reinterpreting memory as unrelated `T` can violate aliasing rules. Prefer **trivially copyable** PODs and exact original types where possible.
5. **Const-correctness**
* The `const` overload returns `const T&` but still reinterprets memory; do not write through it. Use the non-const overload to mutate.
6. **Thread safety**
* No synchronization is provided. Ensure the underlying object isn’t concurrently mutated in incompatible ways.
---
## Tips & patterns
* **Centralize offsets** in `constexpr` with comments (`// game v1.2.3, sig XYZ`).
* **Guard reads**: if you have a canary or RTTI/vtable hash, check it before relying on offsets.
* **Prefer accessors** returning references**:** lets you both read and write with natural syntax.
* **Wrap tricky virtuals**: if a method takes complex/reference params, wrap `call_virtual_method` in a strongly typed member that casts exactly as needed.
---
## Troubleshooting
* **Crash on virtual call** → wrong index or wrong `this` (subobject), or mismatched signature (args/ret or calling conv).
* **Weird field values** → wrong offset, wrong type size/packing, stale layout after an update.
* **Only in 32-bit** → double-check `__thiscall` and parameter passing (register vs stack).
---
*Last updated: 1 Nov 2025*

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/* docs/css/custom.css */
.center-text {
text-align: center;
}

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/* Widen the navbar container */
.navbar .container {
max-width: 100%; /* adjust to your target width */
width: 95%;
}
/* Tighter spacing between navbar items */
.navbar-nav > li > a {
padding-left: 8px;
padding-right: 8px;
}

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# `omath::Angle` — templated angle with normalize/clamper + trig
> Header: `omath/trigonometry/angle.hpp`
> Namespace: `omath`
> Template: `Angle<Type = float, min = 0, max = 360, flags = AngleFlags::Normalized>`
> Requires: `std::is_arithmetic_v<Type>`
> Formatters: `std::formatter` for `char`, `wchar_t`, `char8_t` → `"{}deg"`
---
## Overview
`Angle` is a tiny value-type that stores an angle in **degrees** and automatically **normalizes** or **clamps** it into a compile-time range. It exposes conversions to/from radians, common trig (`sin/cos/tan/cot`), arithmetic with wrap/clamp semantics, and lightweight formatting.
Two behaviors via `AngleFlags`:
* `AngleFlags::Normalized` (default): values are wrapped into `[min, max]` using `angles::wrap_angle`.
* `AngleFlags::Clamped`: values are clamped to `[min, max]` using `std::clamp`.
---
## API
```cpp
namespace omath {
enum class AngleFlags { Normalized = 0, Clamped = 1 };
template<class Type = float, Type min = Type(0), Type max = Type(360),
AngleFlags flags = AngleFlags::Normalized>
requires std::is_arithmetic_v<Type>
class Angle {
public:
// Construction
static constexpr Angle from_degrees(const Type& deg) noexcept;
static constexpr Angle from_radians(const Type& rad) noexcept;
constexpr Angle() noexcept; // 0 deg, adjusted by flags/range
// Accessors / conversions (degrees stored internally)
constexpr const Type& operator*() const noexcept; // raw degrees reference
constexpr Type as_degrees() const noexcept;
constexpr Type as_radians() const noexcept;
// Trig (computed from radians)
Type sin() const noexcept;
Type cos() const noexcept;
Type tan() const noexcept;
Type atan() const noexcept; // atan(as_radians()) (rarely used)
Type cot() const noexcept; // cos()/sin() (watch sin≈0)
// Arithmetic (wraps or clamps per flags and [min,max])
constexpr Angle& operator+=(const Angle&) noexcept;
constexpr Angle& operator-=(const Angle&) noexcept;
constexpr Angle operator+(const Angle&) noexcept;
constexpr Angle operator-(const Angle&) noexcept;
constexpr Angle operator-() const noexcept;
// Comparison (partial ordering)
constexpr std::partial_ordering operator<=>(const Angle&) const noexcept = default;
};
} // namespace omath
```
### Formatting
```cpp
std::format("{}", Angle<float>::from_degrees(45)); // "45deg"
```
Formatters exist for `char`, `wchar_t`, and `char8_t`.
---
## Usage examples
### Defaults (0–360, normalized)
```cpp
using Deg = omath::Angle<>; // float, [0,360], Normalized
auto a = Deg::from_degrees(370); // -> 10deg
auto b = Deg::from_radians(omath::angles::pi); // -> 180deg
a += Deg::from_degrees(355); // 10 + 355 -> 365 -> wraps -> 5deg
float s = a.sin(); // sin(5°)
```
### Clamped range
```cpp
using Fov = omath::Angle<float, 1.f, 179.f, omath::AngleFlags::Clamped>;
auto fov = Fov::from_degrees(200.f); // -> 179deg (clamped)
```
### Signed, normalized range
```cpp
using SignedDeg = omath::Angle<float, -180.f, 180.f, omath::AngleFlags::Normalized>;
auto x = SignedDeg::from_degrees(190.f); // -> -170deg
auto y = SignedDeg::from_degrees(-200.f); // -> 160deg
auto z = x + y; // -170 + 160 = -10deg (wrapped if needed)
```
### Get/set raw degrees
```cpp
auto yaw = SignedDeg::from_degrees(-45.f);
float deg = *yaw; // same as yaw.as_degrees()
```
---
## Semantics & notes
* **Storage & units:** Internally stores **degrees** (`Type m_angle`). `as_radians()`/`from_radians()` use the project helpers in `omath::angles`.
* **Arithmetic honors policy:** `operator+=`/`-=` and the binary `+`/`-` apply **wrap** or **clamp** in `[min,max]`, mirroring construction behavior.
* **`atan()`**: returns `std::atan(as_radians())` (the arctangent of the *radian value*). This is mathematically unusual for an angle type and is rarely useful; prefer `tan()`/`atan2` in client code when solving geometry problems.
* **`cot()` / `tan()` singularities:** Near multiples where `sin() ≈ 0` or `cos() ≈ 0`, results blow up. Guard in your usage if inputs can approach these points.
* **Comparison:** `operator<=>` is defaulted. With normalization, distinct representatives can compare as expected (e.g., `-180` vs `180` in signed ranges are distinct endpoints).
* **No implicit numeric conversion:** There’s **no `operator Type()`**. Use `as_degrees()`/`as_radians()` (or `*angle`) explicitly—this intentional friction avoids unit mistakes.
---
## Customization patterns
* **Radians workflow:** Keep angles in degrees internally but wrap helper creators:
```cpp
inline Deg degf(float d) { return Deg::from_degrees(d); }
inline Deg radf(float r) { return Deg::from_radians(r); }
```
* **Compile-time policy:** Pick ranges/flags at the type level to enforce invariants (e.g., `YawDeg = Angle<float,-180,180,Normalized>`; `FovDeg = Angle<float,1,179,Clamped>`).
---
## Pitfalls & gotchas
* Ensure `min < max` at compile time for meaningful wrap/clamp behavior.
* For normalized signed ranges, decide whether your `wrap_angle(min,max)` treats endpoints half-open (e.g., `[-180,180)`) to avoid duplicate representations; the formatter will print the stored value verbatim.
* If you need **sum of many angles**, accumulating in radians then converting back can improve numeric stability at extreme values.
---
## Minimal tests
```cpp
using A = omath::Angle<>;
REQUIRE(A::from_degrees(360).as_degrees() == 0.f);
REQUIRE(A::from_degrees(-1).as_degrees() == 359.f);
using S = omath::Angle<float,-180.f,180.f, omath::AngleFlags::Normalized>;
REQUIRE(S::from_degrees( 181).as_degrees() == -179.f);
REQUIRE(S::from_degrees(-181).as_degrees() == 179.f);
using C = omath::Angle<float, 10.f, 20.f, omath::AngleFlags::Clamped>;
REQUIRE(C::from_degrees(5).as_degrees() == 10.f);
REQUIRE(C::from_degrees(25).as_degrees() == 20.f);
```
---
*Last updated: 1 Nov 2025*

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# `omath::angles` — angle conversions, FOV helpers, and wrapping
> Header: `omath/trigonometry/angles.hpp`
> Namespace: `omath::angles`
> All functions are `[[nodiscard]]` and `noexcept` where applicable.
A small set of constexpr-friendly utilities for converting between degrees/radians, converting horizontal/vertical field of view, and wrapping angles into a closed interval.
---
## API
```cpp
// Degrees ↔ Radians (Type must be floating-point)
template<class Type>
requires std::is_floating_point_v<Type>
constexpr Type radians_to_degrees(const Type& radians) noexcept;
template<class Type>
requires std::is_floating_point_v<Type>
constexpr Type degrees_to_radians(const Type& degrees) noexcept;
// FOV conversion (inputs/outputs in degrees, aspect = width/height)
template<class Type>
requires std::is_floating_point_v<Type>
Type horizontal_fov_to_vertical(const Type& horizontal_fov, const Type& aspect) noexcept;
template<class Type>
requires std::is_floating_point_v<Type>
Type vertical_fov_to_horizontal(const Type& vertical_fov, const Type& aspect) noexcept;
// Wrap angle into [min, max] (any arithmetic type)
template<class Type>
requires std::is_arithmetic_v<Type>
Type wrap_angle(const Type& angle, const Type& min, const Type& max) noexcept;
```
---
## Usage
### Degrees ↔ Radians
```cpp
float rad = omath::angles::degrees_to_radians(180.0f); // π
double deg = omath::angles::radians_to_degrees(std::numbers::pi); // 180
```
### Horizontal ↔ Vertical FOV
* `aspect` = **width / height**.
* Inputs/outputs are **degrees**.
```cpp
float hdeg = 90.0f;
float aspect = 16.0f / 9.0f;
float vdeg = omath::angles::horizontal_fov_to_vertical(hdeg, aspect); // ~58.0°
float hdeg2 = omath::angles::vertical_fov_to_horizontal(vdeg, aspect); // ≈ 90.0°
```
Formulas (in radians):
* `v = 2 * atan( tan(h/2) / aspect )`
* `h = 2 * atan( tan(v/2) * aspect )`
### Wrapping angles (or any periodic value)
Wrap any numeric `angle` into `[min, max]`:
```cpp
// Wrap degrees into [0, 360]
float a = omath::angles::wrap_angle( 370.0f, 0.0f, 360.0f); // 10
float b = omath::angles::wrap_angle( -15.0f, 0.0f, 360.0f); // 345
// Signed range [-180,180]
float c = omath::angles::wrap_angle( 200.0f, -180.0f, 180.0f); // -160
```
---
## Notes & edge cases
* **Type requirements**
* Converters & FOV helpers require **floating-point** `Type`.
* `wrap_angle` accepts any arithmetic `Type` (floats or integers).
* **Aspect ratio** must be **positive** and finite. For `aspect == 0` the FOV helpers are undefined.
* **Units**: FOV functions accept/return **degrees** but compute internally in radians.
* **Wrapping interval**: Behavior assumes `max > min`. The result lies in the **closed interval** `[min, max]` with modulo arithmetic; if you need half-open behavior (e.g., `[min,max)`), adjust your range or post-process endpoint cases.
* **constexpr**: Converters are `constexpr`; FOV helpers are runtime constexpr-compatible except for `std::atan/std::tan` constraints on some standard libraries.
---
## Quick tests
```cpp
using namespace omath::angles;
static_assert(degrees_to_radians(180.0) == std::numbers::pi);
static_assert(radians_to_degrees(std::numbers::pi_v<float>) == 180.0f);
float v = horizontal_fov_to_vertical(90.0f, 16.0f/9.0f);
float h = vertical_fov_to_horizontal(v, 16.0f/9.0f);
assert(std::abs(h - 90.0f) < 1e-5f);
assert(wrap_angle(360.0f, 0.0f, 360.0f) == 0.0f || wrap_angle(360.0f, 0.0f, 360.0f) == 360.0f);
```

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# `omath::ViewAngles` — tiny POD for pitch/yaw/roll
> Header: your project’s `view_angles.hpp`
> Namespace: `omath`
> Kind: **aggregate struct** (POD), no methods, no allocation
A minimal container for Euler angles. You choose the types for each component (e.g., raw `float` or the strong `omath::Angle<>` type), and plug it into systems like `projection::Camera`.
---
## API
```cpp
namespace omath {
template<class PitchType, class YawType, class RollType>
struct ViewAngles {
PitchType pitch;
YawType yaw;
RollType roll;
};
}
```
* Aggregate: supports brace-init, aggregate copying, and `constexpr` usage when the component types do.
* Semantics (units/handedness/ranges) are **entirely defined by your chosen types**.
---
## Common aliases
```cpp
// Simple, raw degrees as floats (be careful with wrapping!)
using ViewAnglesF = omath::ViewAngles<float, float, float>;
// Safer, policy-based angles (recommended)
using PitchDeg = omath::Angle<float, -89.f, 89.f, omath::AngleFlags::Clamped>;
using YawDeg = omath::Angle<float, -180.f, 180.f, omath::AngleFlags::Normalized>;
using RollDeg = omath::Angle<float, -180.f, 180.f, omath::AngleFlags::Normalized>;
using ViewAnglesDeg = omath::ViewAngles<PitchDeg, YawDeg, RollDeg>;
```
---
## Examples
### Basic construction
```cpp
omath::ViewAngles<float,float,float> a{ 10.f, 45.f, 0.f }; // pitch, yaw, roll in degrees
```
### With `omath::Angle<>` (automatic wrap/clamper)
```cpp
ViewAnglesDeg v{
PitchDeg::from_degrees( 95.f), // -> 89deg (clamped)
YawDeg::from_degrees (-190.f), // -> 170deg (wrapped)
RollDeg::from_degrees ( 30.f)
};
```
### Using with `projection::Camera`
```cpp
using Mat4 = omath::Mat<4,4,float, omath::MatStoreType::COLUMN_MAJOR>;
using Cam = omath::projection::Camera<Mat4, ViewAnglesDeg, MyCameraTrait>;
omath::projection::ViewPort vp{1920,1080};
auto fov = omath::angles::degrees_to_radians(70.f); // or your Angle type
Cam cam(/*position*/ {0,1.7f,-3},
/*angles*/ ViewAnglesDeg{ PitchDeg::from_degrees(0),
YawDeg::from_degrees(0),
RollDeg::from_degrees(0) },
/*viewport*/ vp,
/*fov*/ omath::Angle<float,0.f,180.f,omath::AngleFlags::Clamped>::from_degrees(70.f),
/*near*/ 0.1f,
/*far*/ 1000.f);
```
---
## Notes & tips
* **Ranges/units**: pick types that encode your policy (e.g., signed yaw in `[-180,180]`, pitch clamped to avoid gimbal flips).
* **Handedness & order**: this struct doesn’t impose rotation order. Your math/trait layer (e.g., `MyCameraTrait`) must define how `(pitch, yaw, roll)` map to a view matrix (common orders: ZYX or XYZ).
* **Zero-cost**: with plain `float`s this is as cheap as three scalars; with `Angle<>` you gain safety at the cost of tiny wrap/clamp logic on construction/arithmetic.

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# Troubleshooting
Solutions to common problems when using OMath.
---
## Build & Compilation Issues
### Error: C++20 features not available
**Problem:** Compiler doesn't support C++20.
**Solution:**
Upgrade your compiler:
- **GCC**: Version 10 or newer
- **Clang**: Version 11 or newer
- **MSVC**: Visual Studio 2019 16.10 or newer
Set C++20 in CMakeLists.txt:
```cmake
set(CMAKE_CXX_STANDARD 20)
set(CMAKE_CXX_STANDARD_REQUIRED ON)
```
### Error: `std::expected` not found
**Problem:** Using C++20 without C++23's `std::expected`.
**Solutions:**
1. **Upgrade to C++23** (recommended):
```cmake
set(CMAKE_CXX_STANDARD 23)
```
2. **Use a backport library**:
```cmake
find_package(tl-expected CONFIG REQUIRED)
target_link_libraries(your_target PRIVATE tl::expected)
```
### Error: `omath/omath.hpp` not found
**Problem:** OMath not installed or not in include path.
**Solution:**
Check installation:
```bash
# vcpkg
vcpkg list | grep omath
# Check if files exist
ls /path/to/vcpkg/installed/x64-linux/include/omath
```
In CMakeLists.txt:
```cmake
find_package(omath CONFIG REQUIRED)
target_link_libraries(your_target PRIVATE omath::omath)
```
### Linker errors with AVX2 engine
**Problem:** Undefined references to AVX2 functions.
**Solution:**
Enable AVX2 in your build:
```cmake
if(MSVC)
target_compile_options(your_target PRIVATE /arch:AVX2)
else()
target_compile_options(your_target PRIVATE -mavx2)
endif()
```
Or use the legacy engine instead:
```cpp
// Use this instead of ProjPredEngineAVX2
ProjPredEngineLegacy engine;
```
---
## Runtime Issues
### `world_to_screen()` always returns `nullopt`
**Common causes:**
1. **Point behind camera**
```cpp
// Point is behind the camera
Vector3<float> behind = camera_pos - Vector3<float>{0, 0, 100};
auto result = camera.world_to_screen(behind); // Returns nullopt
```
**Fix:** Only project points in front of camera. Check Z-coordinate in view space.
2. **Invalid near/far planes**
```cpp
// Bad: near >= far
Camera camera(pos, angles, viewport, fov, 100.0f, 1.0f);
// Good: near < far
Camera camera(pos, angles, viewport, fov, 0.1f, 1000.0f);
```
3. **Invalid FOV**
```cpp
// Bad: FOV out of range
auto fov = FieldOfView::from_degrees(0.0f); // Too small
auto fov = FieldOfView::from_degrees(180.0f); // Too large
// Good: FOV in valid range
auto fov = FieldOfView::from_degrees(90.0f);
```
4. **Uninitialized camera**
```cpp
// Make sure camera is properly initialized
camera.update(current_position, current_angles);
```
**Debugging:**
```cpp
Vector3<float> world_pos{100, 100, 100};
// Check projection step by step
std::cout << "World pos: " << world_pos.x << ", "
<< world_pos.y << ", " << world_pos.z << "\n";
auto view_matrix = camera.get_view_matrix();
// Transform to view space manually and check if Z > 0
if (auto screen = camera.world_to_screen(world_pos)) {
std::cout << "Success: " << screen->x << ", " << screen->y << "\n";
} else {
std::cout << "Failed - check if point is behind camera\n";
}
```
### Angles wrapping incorrectly
**Problem:** Angles not normalizing to expected ranges.
**Solution:**
Use proper angle types:
```cpp
// Wrong: using raw floats
float pitch = 95.0f; // Out of valid range!
// Right: using typed angles
auto pitch = PitchAngle::from_degrees(89.0f); // Clamped to valid range
```
For custom ranges:
```cpp
// Define custom angle with wrapping
auto angle = Angle<float, -180.0f, 180.0f, AngleFlags::Normalized>::from_degrees(270.0f);
// Result: -90° (wrapped)
```
### Projection appears mirrored or inverted
**Problem:** Using wrong engine trait for your game.
**Solution:**
Different engines have different coordinate systems:
| Symptom | Likely Issue | Fix |
|---------|-------------|-----|
| Upside down | Y-axis inverted | Try different engine or negate Y |
| Left-right flipped | Wrong handedness | Check engine documentation |
| Rotated 90° | Axis swap | Verify engine coordinate system |
```cpp
// Try different engine traits
using namespace omath::source_engine; // Z-up, left-handed
using namespace omath::unity_engine; // Y-up, left-handed
using namespace omath::unreal_engine; // Z-up, left-handed (different conventions)
using namespace omath::opengl_engine; // Y-up, right-handed
```
If still wrong, manually transform coordinates:
```cpp
// Example: swap Y and Z for Y-up to Z-up conversion
Vector3<float> convert_y_up_to_z_up(const Vector3<float>& pos) {
return Vector3<float>{pos.x, pos.z, pos.y};
}
```
---
## Projectile Prediction Issues
### `maybe_calculate_aim_point()` returns `nullopt`
**Common causes:**
1. **Target moving too fast**
```cpp
Target target;
target.velocity = Vector3<float>{1000, 0, 0}; // Very fast!
Projectile proj;
proj.speed = 500.0f; // Too slow to catch target
// Returns nullopt - projectile can't catch target
```
**Fix:** Check if projectile speed > target speed in the direction of motion.
2. **Zero projectile speed**
```cpp
Projectile proj;
proj.speed = 0.0f; // Invalid!
// Returns nullopt
```
**Fix:** Ensure `proj.speed > 0`.
3. **Invalid positions**
```cpp
// NaN or infinite values
target.position = Vector3<float>{NAN, 0, 0};
// Returns nullopt
```
**Fix:** Validate all input values are finite.
4. **Target out of range**
```cpp
// Target very far away
float distance = shooter_pos.distance_to(target.position);
float max_range = proj.speed * max_flight_time;
if (distance > max_range) {
// Will return nullopt
}
```
**Debugging:**
```cpp
Projectile proj{/* ... */};
Target target{/* ... */};
// Check inputs
assert(proj.speed > 0);
assert(std::isfinite(target.position.length()));
assert(std::isfinite(target.velocity.length()));
// Check if target is reachable
float distance = proj.origin.distance_to(target.position);
float target_speed = target.velocity.length();
std::cout << "Distance: " << distance << "\n";
std::cout << "Projectile speed: " << proj.speed << "\n";
std::cout << "Target speed: " << target_speed << "\n";
if (target_speed >= proj.speed) {
std::cout << "Target may be too fast!\n";
}
```
### Aim point is inaccurate
**Problem:** Calculated aim point doesn't hit target.
**Possible causes:**
1. **Unit mismatch**
```cpp
// All units must match!
proj.speed = 800.0f; // meters per second
target.velocity = Vector3<float>{2, 1, 0}; // Must also be m/s!
// If using different units (e.g., game units vs meters), convert:
float game_units_to_meters = 0.01905f; // Example for Source
target.velocity = game_velocity * game_units_to_meters;
```
2. **Wrong gravity vector**
```cpp
// Source Engine: Z-up
proj.gravity = Vector3<float>{0, 0, -9.81f};
// Unity: Y-up
proj.gravity = Vector3<float>{0, -9.81f, 0};
```
3. **Target velocity not updated**
```cpp
// Update target velocity each frame
target.velocity = current_velocity; // Not last frame's velocity!
```
---
## Pattern Scanning Issues
### Pattern not found when it should be
**Problem:** `pattern_scan()` returns `nullopt` but pattern exists.
**Solutions:**
1. **Pattern syntax error**
```cpp
// Wrong: missing spaces
PatternView pattern{"488B05????????"};
// Right: spaces between bytes
PatternView pattern{"48 8B 05 ?? ?? ?? ??"};
```
2. **Pattern too specific**
```cpp
// May fail if any byte is different
PatternView pattern{"48 8B 05 01 02 03 04 48 85 C0"};
// Better: use wildcards for variable bytes
PatternView pattern{"48 8B 05 ?? ?? ?? ?? 48 85 C0"};
```
3. **Searching wrong memory region**
```cpp
// Make sure you're scanning the right memory
std::vector<uint8_t> code_section = get_code_section();
auto result = pattern_scan(code_section, pattern);
```
4. **Pattern might have multiple matches**
```cpp
// Find all matches instead of just first
size_t offset = 0;
while (offset < memory.size()) {
auto result = pattern_scan(
std::span(memory.begin() + offset, memory.end()),
pattern
);
if (result) {
std::cout << "Match at: " << offset + result->offset << "\n";
offset += result->offset + 1;
} else {
break;
}
}
```
### Pattern found at wrong location
**Problem:** Pattern matches unintended code.
**Solutions:**
1. **Make pattern more specific**
```cpp
// Too generic
PatternView pattern{"48 8B"};
// More specific - include more context
PatternView pattern{"48 8B 05 ?? ?? ?? ?? 48 85 C0 74 ??"};
```
2. **Verify found address**
```cpp
if (auto result = pattern_scan(memory, pattern)) {
// Verify by checking nearby bytes
size_t offset = result->offset;
// Check if instruction makes sense
if (memory[offset] == 0x48 && memory[offset + 1] == 0x8B) {
// Looks good
}
}
```
3. **Use multiple patterns**
```cpp
// Find reference function first
auto ref_pattern = PatternView{"E8 ?? ?? ?? ?? 85 C0"};
auto ref_result = pattern_scan(memory, ref_pattern);
// Then search near that location
// This provides context validation
```
---
## Vector & Math Issues
### `normalized()` returns zero vector
**Problem:** Normalizing a zero-length vector.
**Behavior:**
```cpp
Vector3<float> zero{0, 0, 0};
auto result = zero.normalized(); // Returns {0, 0, 0}
```
This is **intentional** to avoid NaN. Check vector length first:
```cpp
if (v.length() > 0.001f) {
auto normalized = v.normalized();
// Use normalized vector
} else {
// Handle zero-length case
}
```
### `angle_between()` returns error
**Problem:** One or both vectors have zero length.
**Solution:**
```cpp
auto angle_result = v1.angle_between(v2);
if (angle_result) {
float degrees = angle_result->as_degrees();
} else {
// Handle error - one or both vectors have zero length
std::cerr << "Cannot compute angle between zero-length vectors\n";
}
```
### Cross product seems wrong
**Problem:** Unexpected cross product result.
**Check:**
1. **Right-handed system**
```cpp
Vector3<float> x{1, 0, 0};
Vector3<float> y{0, 1, 0};
auto z = x.cross(y); // Should be {0, 0, 1} in right-handed system
```
2. **Order matters**
```cpp
auto cross1 = a.cross(b); // {x1, y1, z1}
auto cross2 = b.cross(a); // {-x1, -y1, -z1} (opposite direction!)
```
---
## Performance Issues
### Code is slower than expected
**Solutions:**
1. **Enable optimizations**
```cmake
# CMakeLists.txt
target_compile_options(your_target PRIVATE
$<$<CONFIG:Release>:-O3>
$<$<CONFIG:Release>:-march=native>
)
```
2. **Use AVX2 engine**
```cpp
// Instead of
ProjPredEngineLegacy engine;
// Use
ProjPredEngineAVX2 engine;
```
3. **Avoid unnecessary operations**
```cpp
// Bad: recompute every frame
for (auto& entity : entities) {
float dist = entity.pos.distance_to(player_pos); // Expensive sqrt!
if (dist < 100.0f) { /* ... */ }
}
// Good: use squared distance
constexpr float max_dist_sq = 100.0f * 100.0f;
for (auto& entity : entities) {
float dist_sq = entity.pos.distance_to_sqr(player_pos); // No sqrt!
if (dist_sq < max_dist_sq) { /* ... */ }
}
```
4. **Cache matrices**
```cpp
// Bad: recompute matrix every call
for (auto& pos : positions) {
auto screen = camera.world_to_screen(pos); // Recomputes matrices!
}
// Good: matrices are cached in camera automatically
camera.update(pos, angles); // Updates matrices once
for (auto& pos : positions) {
auto screen = camera.world_to_screen(pos); // Uses cached matrices
}
```
---
## Getting More Help
If your issue isn't covered here:
1. **Check the docs**: [API Overview](api_overview.md), [Tutorials](tutorials.md)
2. **Search GitHub issues**: [Issues page](https://github.com/orange-cpp/omath/issues)
3. **Ask on Discord**: [Join community](https://discord.gg/eDgdaWbqwZ)
4. **Open a new issue**: Include:
- OMath version
- Compiler and version
- Minimal reproducible example
- What you expected vs what happened
---
*Last updated: 1 Nov 2025*

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# Tutorials
This page provides step-by-step tutorials for common OMath use cases.
---
## Tutorial 1: Basic Vector Math
Learn the fundamentals of vector operations in OMath.
### Step 1: Include OMath
```cpp
#include <omath/omath.hpp>
#include <iostream>
using namespace omath;
```
### Step 2: Create Vectors
```cpp
// 2D vectors
Vector2<float> v2a{3.0f, 4.0f};
Vector2<float> v2b{1.0f, 2.0f};
// 3D vectors
Vector3<float> v3a{1.0f, 2.0f, 3.0f};
Vector3<float> v3b{4.0f, 5.0f, 6.0f};
// 4D vectors (often used for homogeneous coordinates)
Vector4<float> v4{1.0f, 2.0f, 3.0f, 1.0f};
```
### Step 3: Perform Operations
```cpp
// Addition
auto sum = v3a + v3b; // {5, 7, 9}
// Subtraction
auto diff = v3a - v3b; // {-3, -3, -3}
// Scalar multiplication
auto scaled = v3a * 2.0f; // {2, 4, 6}
// Dot product
float dot = v3a.dot(v3b); // 32.0
// Cross product (3D only)
auto cross = v3a.cross(v3b); // {-3, 6, -3}
// Length
float len = v3a.length(); // ~3.74
// Normalization (safe - returns original if length is zero)
auto normalized = v3a.normalized();
// Distance between vectors
float dist = v3a.distance_to(v3b); // ~5.196
```
### Step 4: Angle Calculations
```cpp
if (auto angle = v3a.angle_between(v3b)) {
std::cout << "Angle in degrees: " << angle->as_degrees() << "\n";
std::cout << "Angle in radians: " << angle->as_radians() << "\n";
} else {
std::cout << "Cannot compute angle (zero-length vector)\n";
}
// Check if perpendicular
if (v3a.is_perpendicular(v3b)) {
std::cout << "Vectors are perpendicular\n";
}
```
**Key takeaways:**
- All vector operations are type-safe and constexpr-friendly
- Safe normalization never produces NaN
- Angle calculations use `std::expected` for error handling
---
## Tutorial 2: World-to-Screen Projection
Project 3D coordinates to 2D screen space for overlays and ESP.
### Step 1: Choose Your Game Engine
```cpp
#include <omath/omath.hpp>
// For Source Engine games (CS:GO, TF2, etc.)
using namespace omath::source_engine;
// Or for other engines:
// using namespace omath::unity_engine;
// using namespace omath::unreal_engine;
// using namespace omath::frostbite_engine;
```
### Step 2: Set Up the Camera
```cpp
using namespace omath;
using namespace omath::projection;
// Define viewport (screen dimensions)
ViewPort viewport{1920.0f, 1080.0f};
// Define field of view
auto fov = FieldOfView::from_degrees(90.0f);
// Camera position and angles
Vector3<float> camera_pos{0.0f, 0.0f, 100.0f};
ViewAngles camera_angles{
PitchAngle::from_degrees(0.0f),
YawAngle::from_degrees(0.0f),
RollAngle::from_degrees(0.0f)
};
// Create camera (using Source Engine in this example)
Camera camera(
camera_pos,
camera_angles,
viewport,
fov,
0.1f, // near plane
1000.0f // far plane
);
```
### Step 3: Project 3D Points
```cpp
// 3D world position (e.g., enemy player position)
Vector3<float> enemy_pos{150.0f, 200.0f, 75.0f};
// Project to screen
if (auto screen = camera.world_to_screen(enemy_pos)) {
std::cout << "Enemy on screen at: "
<< screen->x << ", " << screen->y << "\n";
// Draw ESP box or marker at screen->x, screen->y
// Note: screen coordinates are in viewport space (0-width, 0-height)
} else {
// Enemy is not visible (behind camera or outside frustum)
std::cout << "Enemy not visible\n";
}
```
### Step 4: Update Camera for Each Frame
```cpp
void render_frame() {
// Read current camera data from game
Vector3<float> new_pos = read_camera_position();
ViewAngles new_angles = read_camera_angles();
// Update camera
camera.update(new_pos, new_angles);
// Project all entities
for (const auto& entity : entities) {
if (auto screen = camera.world_to_screen(entity.position)) {
draw_esp_box(screen->x, screen->y);
}
}
}
```
**Key takeaways:**
- Choose the engine trait that matches your target game
- `world_to_screen()` returns `std::optional` - always check the result
- Update camera each frame for accurate projections
- Screen coordinates are in the viewport space you defined
---
## Tutorial 3: Projectile Prediction (Aim-Bot)
Calculate where to aim to hit a moving target.
### Step 1: Define Projectile Properties
```cpp
#include <omath/omath.hpp>
#include <omath/projectile_prediction/proj_pred_engine_legacy.hpp>
using namespace omath;
using namespace omath::projectile_prediction;
// Define your weapon's projectile
Projectile bullet;
bullet.origin = Vector3<float>{0, 0, 0}; // Shooter position
bullet.speed = 800.0f; // Muzzle velocity (m/s or game units/s)
bullet.gravity = Vector3<float>{0, 0, -9.81f}; // Gravity vector
```
### Step 2: Define Target State
```cpp
// Target information (enemy player)
Target enemy;
enemy.position = Vector3<float>{100, 200, 50}; // Current position
enemy.velocity = Vector3<float>{10, 5, 0}; // Current velocity
```
### Step 3: Calculate Aim Point
```cpp
// Create prediction engine
// Use AVX2 version if available for better performance:
// ProjPredEngineAVX2 engine;
ProjPredEngineLegacy engine;
// Calculate where to aim
if (auto aim_point = engine.maybe_calculate_aim_point(bullet, enemy)) {
std::cout << "Aim at: "
<< aim_point->x << ", "
<< aim_point->y << ", "
<< aim_point->z << "\n";
// Calculate angles to aim_point
Vector3<float> aim_direction = (*aim_point - bullet.origin).normalized();
// Convert to view angles (engine-specific)
// ViewAngles angles = calculate_angles_to_direction(aim_direction);
// set_aim_angles(angles);
} else {
// Cannot hit target (too fast, out of range, etc.)
std::cout << "Target cannot be hit\n";
}
```
### Step 4: Handle Different Scenarios
```cpp
// Stationary target
Target stationary;
stationary.position = Vector3<float>{100, 100, 100};
stationary.velocity = Vector3<float>{0, 0, 0};
// aim_point will equal position for stationary targets
// Fast-moving target
Target fast;
fast.position = Vector3<float>{100, 100, 100};
fast.velocity = Vector3<float>{50, 0, 0}; // Moving very fast
// May return nullopt if target is too fast
// Target at different heights
Target aerial;
aerial.position = Vector3<float>{100, 100, 200}; // High up
aerial.velocity = Vector3<float>{5, 5, -10}; // Falling
// Gravity will be factored into the calculation
```
### Step 5: Performance Optimization
```cpp
// For better performance on modern CPUs, use AVX2:
#include <omath/projectile_prediction/proj_pred_engine_avx2.hpp>
ProjPredEngineAVX2 fast_engine; // 2-4x faster than legacy
// Use the same way as legacy engine
if (auto aim = fast_engine.maybe_calculate_aim_point(bullet, enemy)) {
// Process aim point
}
```
**Key takeaways:**
- Always check if aim point exists before using
- Velocity must be in same units as position/speed
- Gravity vector points down (typically negative Z or Y depending on engine)
- Use AVX2 engine when possible for better performance
- Returns `nullopt` when target is unreachable
---
## Tutorial 4: Collision Detection
Perform ray-casting and intersection tests.
### Step 1: Ray-Plane Intersection
```cpp
#include <omath/omath.hpp>
using namespace omath;
// Define a ground plane (Z=0, normal pointing up)
Plane ground{
Vector3<float>{0, 0, 0}, // Point on plane
Vector3<float>{0, 0, 1} // Normal vector (Z-up)
};
// Define a ray (e.g., looking downward from above)
Vector3<float> ray_origin{10, 20, 100};
Vector3<float> ray_direction{0, 0, -1}; // Pointing down
// Test intersection
if (auto hit = ground.intersects_ray(ray_origin, ray_direction)) {
std::cout << "Hit ground at: "
<< hit->x << ", " << hit->y << ", " << hit->z << "\n";
// Expected: (10, 20, 0)
} else {
std::cout << "Ray does not intersect plane\n";
}
```
### Step 2: Distance to Plane
```cpp
// Calculate signed distance from point to plane
Vector3<float> point{10, 20, 50};
float distance = ground.distance_to_point(point);
std::cout << "Distance to ground: " << distance << "\n";
// Expected: 50.0 (50 units above ground)
// Negative distance means point is below the plane
Vector3<float> below{10, 20, -5};
float dist_below = ground.distance_to_point(below);
// Expected: -5.0
```
### Step 3: Axis-Aligned Bounding Box
```cpp
#include <omath/3d_primitives/box.hpp>
// Create a bounding box
Box bbox{
Vector3<float>{0, 0, 0}, // Min corner
Vector3<float>{100, 100, 100} // Max corner
};
// Test if point is inside
Vector3<float> inside{50, 50, 50};
if (bbox.contains(inside)) {
std::cout << "Point is inside box\n";
}
Vector3<float> outside{150, 50, 50};
if (!bbox.contains(outside)) {
std::cout << "Point is outside box\n";
}
// Box-box intersection
Box other{
Vector3<float>{50, 50, 50},
Vector3<float>{150, 150, 150}
};
if (bbox.intersects(other)) {
std::cout << "Boxes overlap\n";
}
```
### Step 4: Line Tracing
```cpp
#include <omath/collision/line_tracer.hpp>
using namespace omath::collision;
// Ray-triangle intersection
Vector3<float> v0{0, 0, 0};
Vector3<float> v1{100, 0, 0};
Vector3<float> v2{0, 100, 0};
Vector3<float> ray_start{25, 25, 100};
Vector3<float> ray_dir{0, 0, -1};
LineTracer tracer;
if (auto hit = tracer.ray_triangle_intersect(ray_start, ray_dir, v0, v1, v2)) {
std::cout << "Hit triangle at: "
<< hit->point.x << ", "
<< hit->point.y << ", "
<< hit->point.z << "\n";
std::cout << "Hit distance: " << hit->distance << "\n";
std::cout << "Surface normal: "
<< hit->normal.x << ", "
<< hit->normal.y << ", "
<< hit->normal.z << "\n";
}
```
**Key takeaways:**
- Plane normals should be unit vectors
- Ray direction should typically be normalized
- Signed distance indicates which side of plane a point is on
- AABB tests are very fast for broad-phase collision detection
- Line tracer provides hit point, distance, and surface normal
---
## Tutorial 5: Pattern Scanning
Search for byte patterns in memory.
### Step 1: Basic Pattern Scanning
```cpp
#include <omath/utility/pattern_scan.hpp>
#include <vector>
using namespace omath;
// Memory to search (e.g., from a loaded module)
std::vector<uint8_t> memory = {
0x48, 0x8B, 0x05, 0xAA, 0xBB, 0xCC, 0xDD,
0x48, 0x85, 0xC0, 0x74, 0x10,
// ... more bytes
};
// Pattern with wildcards (?? = match any byte)
PatternView pattern{"48 8B 05 ?? ?? ?? ?? 48 85 C0"};
// Scan for pattern
if (auto result = pattern_scan(memory, pattern)) {
std::cout << "Pattern found at offset: " << result->offset << "\n";
// Extract wildcard values if needed
// result->wildcards contains the matched bytes at ?? positions
} else {
std::cout << "Pattern not found\n";
}
```
### Step 2: PE File Scanning
```cpp
#include <omath/utility/pe_pattern_scan.hpp>
// Scan a PE file (EXE or DLL)
PEPatternScanner scanner("game.exe");
PatternView pattern{"E8 ?? ?? ?? ?? 85 C0 75 ??"};
if (auto rva = scanner.scan_pattern(pattern)) {
std::cout << "Pattern found at RVA: 0x"
<< std::hex << *rva << std::dec << "\n";
// Convert RVA to absolute address if needed
uintptr_t base_address = get_module_base("game.exe");
uintptr_t absolute = base_address + *rva;
} else {
std::cout << "Pattern not found in PE file\n";
}
```
### Step 3: Multiple Patterns
```cpp
// Search for multiple patterns
std::vector<PatternView> patterns{
PatternView{"48 8B 05 ?? ?? ?? ??"},
PatternView{"E8 ?? ?? ?? ?? 85 C0"},
PatternView{"FF 15 ?? ?? ?? ?? 48 8B"}
};
for (size_t i = 0; i < patterns.size(); ++i) {
if (auto result = pattern_scan(memory, patterns[i])) {
std::cout << "Pattern " << i << " found at: "
<< result->offset << "\n";
}
}
```
### Step 4: Pattern with Masks
```cpp
// Alternative: use mask-based patterns
// Pattern: bytes to match
std::vector<uint8_t> pattern_bytes{0x48, 0x8B, 0x05, 0x00, 0x00, 0x00, 0x00};
// Mask: 'x' = must match, '?' = wildcard
std::string mask{"xxx????"};
// Custom scan function
auto scan_with_mask = [&](const std::vector<uint8_t>& data) {
for (size_t i = 0; i < data.size() - pattern_bytes.size(); ++i) {
bool match = true;
for (size_t j = 0; j < pattern_bytes.size(); ++j) {
if (mask[j] == 'x' && data[i + j] != pattern_bytes[j]) {
match = false;
break;
}
}
if (match) return i;
}
return size_t(-1);
};
```
**Key takeaways:**
- Use `??` in pattern strings for wildcards
- PE scanner works with files and modules
- Pattern scanning is useful for finding functions, vtables, or data
- Always validate found addresses before use
- Patterns may have multiple matches - consider context
---
## Tutorial 6: Angles and View Angles
Work with game camera angles properly.
### Step 1: Understanding Angle Types
```cpp
#include <omath/omath.hpp>
using namespace omath;
// Generic angle with custom range
auto angle1 = Angle<float, 0.0f, 360.0f>::from_degrees(45.0f);
auto angle2 = Angle<float, -180.0f, 180.0f>::from_degrees(270.0f);
// Specialized camera angles
auto pitch = PitchAngle::from_degrees(-10.0f); // Looking down
auto yaw = YawAngle::from_degrees(90.0f); // Looking right
auto roll = RollAngle::from_degrees(0.0f); // No tilt
```
### Step 2: Angle Conversions
```cpp
// Create from degrees
auto deg_angle = PitchAngle::from_degrees(45.0f);
// Get as radians
float radians = deg_angle.as_radians();
std::cout << "45° = " << radians << " radians\n";
// Get as degrees
float degrees = deg_angle.as_degrees();
std::cout << "Value: " << degrees << "°\n";
```
### Step 3: View Angles (Camera)
```cpp
// Pitch: vertical rotation (-89° to 89°)
// Yaw: horizontal rotation (-180° to 180°)
// Roll: camera tilt (-180° to 180°)
ViewAngles camera_angles{
PitchAngle::from_degrees(-15.0f), // Looking slightly down
YawAngle::from_degrees(45.0f), // Facing northeast
RollAngle::from_degrees(0.0f) // No tilt
};
// Access individual components
float pitch_val = camera_angles.pitch.as_degrees();
float yaw_val = camera_angles.yaw.as_degrees();
float roll_val = camera_angles.roll.as_degrees();
```
### Step 4: Calculating Look-At Angles
```cpp
using namespace omath::source_engine; // Or your game's engine
Vector3<float> camera_pos{0, 0, 100};
Vector3<float> target_pos{100, 100, 100};
// Calculate angles to look at target
ViewAngles look_at = CameraTrait::calc_look_at_angle(camera_pos, target_pos);
std::cout << "Pitch: " << look_at.pitch.as_degrees() << "°\n";
std::cout << "Yaw: " << look_at.yaw.as_degrees() << "°\n";
std::cout << "Roll: " << look_at.roll.as_degrees() << "°\n";
```
### Step 5: Angle Arithmetic
```cpp
// Angles support arithmetic with automatic normalization
auto angle1 = YawAngle::from_degrees(170.0f);
auto angle2 = YawAngle::from_degrees(20.0f);
// Addition (wraps around)
auto sum = angle1 + angle2; // 190° → normalized to -170°
// Subtraction
auto diff = angle2 - angle1; // -150°
// Scaling
auto scaled = angle1 * 2.0f;
```
**Key takeaways:**
- Use specialized angle types for camera angles (PitchAngle, YawAngle, RollAngle)
- Angles automatically normalize to their valid ranges
- Each game engine may have different angle conventions
- Use engine traits to calculate look-at angles correctly
---
## Next Steps
Now that you've completed these tutorials, explore:
- **[API Overview](api_overview.md)** - Complete API reference
- **[Engine Documentation](engines/)** - Engine-specific features
- **[Examples](../examples/)** - More code examples
- **[Getting Started](getting_started.md)** - Quick start guide
---
*Last updated: 1 Nov 2025*

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# `omath::Color` — RGBA color with HSV helpers (C++20/23)
> Header: your project’s `color.hpp`
> Namespace: `omath`
> Inherits: `Vector4<float>` (`x=r`, `y=g`, `z=b`, `w=a`)
> Depends on: `<cstdint>`, `Vector4`, optionally ImGui (`OMATH_IMGUI_INTEGRATION`)
> Formatting: provides `std::formatter<omath::Color>`
`Color` is a tiny RGBA utility on top of `Vector4<float>`. It offers sRGB-style channel construction, HSV↔RGB conversion, in-place HSV setters, linear blending, and string/formatter helpers.
---
## Quick start
```cpp
#include "color.hpp"
using omath::Color;
// RGBA in [0,1] (r,g,b clamped to [0,1] on construction)
Color c{0.2f, 0.4f, 0.8f, 0.5f};
// From 8-bit channels
auto red = Color::from_rgba(255, 0, 0, 255);
auto green = Color::from_rgba(0, 255, 0, 160);
// From HSV (h ∈ [0,1], s ∈ [0,1], v ∈ [0,1])
auto cyan = Color::from_hsv(0.5f, 1.0f, 1.0f); // a = 1
// Read/modify via HSV
auto hsv = cyan.to_hsv(); // hue ∈ [0,1], saturation ∈ [0,1], value ∈ [0,1]
cyan.set_value(0.6f); // converts back to RGB (alpha becomes 1)
// Blend linearly (lerp)
auto mid = red.blend(green, 0.5f);
// Printable (0–255 per channel)
std::string s = std::format("{}", mid); // "[r:128, g:128, b:0, a:207]" for example
```
---
## Data model
* Inherits `Vector4<float>`:
* `x` = **red**, `y` = **green**, `z` = **blue**, `w` = **alpha**.
* Construction clamps **RGB** to `[0,1]` (via `Vector4::clamp(0,1)`), **alpha is not clamped** by that call (see notes).
---
## Construction & factories
```cpp
// RGBA in [0,1] (RGB clamped to [0,1]; alpha untouched by clamp)
constexpr Color(float r, float g, float b, float a) noexcept;
// Default
constexpr Color() noexcept;
// From 8-bit RGBA (0–255) → normalized to [0,1]
constexpr static Color from_rgba(uint8_t r, uint8_t g, uint8_t b, uint8_t a) noexcept;
// From HSV where hue ∈ [0,1], saturation ∈ [0,1], value ∈ [0,1]
struct Hsv { float hue{}, saturation{}, value{}; };
constexpr static Color from_hsv(float hue, float saturation, float value) noexcept;
constexpr static Color from_hsv(const Hsv& hsv) noexcept; // delegates to the above
// Construct from a Vector4 (RGB clamped, alpha not clamped)
constexpr explicit Color(const Vector4& vec) noexcept;
```
**HSV details**
* `from_hsv(h, s, v)`: `h` is **normalized** (`[0,1]`); it is clamped, then mapped to the 6 hue sectors; **alpha = 1.0**.
* `to_hsv()`: returns `Hsv{h,s,v}` with **`h ∈ [0,1]`** (internally computes degrees and divides by 360), `s,v ∈ [0,1]`.
---
## Mutators
```cpp
constexpr void set_hue(float h) noexcept; // h ∈ [0,1] recommended
constexpr void set_saturation(float s) noexcept; // s ∈ [0,1]
constexpr void set_value(float v) noexcept; // v ∈ [0,1]
// Linear blend: (1-ratio)*this + ratio*other, ratio clamped to [0,1]
constexpr Color blend(const Color& other, float ratio) const noexcept;
```
> ⚠️ **Alpha reset on HSV setters:** each `set_*` converts HSV→RGB using `from_hsv(...)`, which **sets alpha to 1.0** (overwriting previous `w`). If you need to preserve alpha:
>
> ```cpp
> float a = col.w;
> col.set_value(0.5f);
> col.w = a;
> ```
---
## Constants
```cpp
static constexpr Color red(); // (1,0,0,1)
static constexpr Color green(); // (0,1,0,1)
static constexpr Color blue(); // (0,0,1,1)
```
---
## String & formatting
```cpp
// "[r:R, g:G, b:B, a:A]" with each channel shown as 0–255 integer
std::string to_string() const noexcept;
std::wstring to_wstring() const noexcept;
std::u8string to_u8string() const noexcept;
// Formatter forwards to the above (char/wchar_t/char8_t)
template<> struct std::formatter<omath::Color>;
```
---
## ImGui (optional)
```cpp
#ifdef OMATH_IMGUI_INTEGRATION
ImColor to_im_color() const noexcept; // constructs from Vector4's to_im_vec4()
#endif
```
Ensure `<imgui.h>` is included somewhere before this header when the macro is enabled.
---
## Notes & caveats
* **Alpha clamping:** `Vector4::clamp(min,max)` (called by `Color` ctors) clamps **x,y,z** only in the provided `Vector4` implementation; `w` is **left unchanged**. If you require strict `[0,1]` alpha, clamp it yourself:
```cpp
col.w = std::clamp(col.w, 0.0f, 1.0f);
```
* **HSV range:** The API consistently uses **normalized hue** (`[0,1]`). Convert degrees ↔ normalized as `h_norm = h_deg / 360.f`.
* **Blend space:** `blend` is a **linear** interpolation in RGBA; it is not perceptually uniform.
---
## API summary
```cpp
struct Hsv { float hue{}, saturation{}, value{}; };
class Color final : public Vector4<float> {
public:
constexpr Color(float r, float g, float b, float a) noexcept;
constexpr Color() noexcept;
constexpr explicit Color(const Vector4& vec) noexcept;
static constexpr Color from_rgba(uint8_t r, uint8_t g, uint8_t b, uint8_t a) noexcept;
static constexpr Color from_hsv(float hue, float saturation, float value) noexcept;
static constexpr Color from_hsv(const Hsv& hsv) noexcept;
constexpr Hsv to_hsv() const noexcept;
constexpr void set_hue(float h) noexcept;
constexpr void set_saturation(float s) noexcept;
constexpr void set_value(float v) noexcept;
constexpr Color blend(const Color& other, float ratio) const noexcept;
static constexpr Color red();
static constexpr Color green();
static constexpr Color blue();
#ifdef OMATH_IMGUI_INTEGRATION
ImColor to_im_color() const noexcept;
#endif
std::string to_string() const noexcept;
std::wstring to_wstring() const noexcept;
std::u8string to_u8string() const noexcept;
};
// formatter<omath::Color> provided
```
---
*Last updated: 31 Oct 2025*

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# `omath::PatternScanner` — Fast byte-pattern search with wildcards
> Header: your project’s `pattern_scanner.hpp`
> Namespace: `omath`
> Core API: `scan_for_pattern(...)` (span or iterators)
> Errors: `PatternScanError::INVALID_PATTERN_STRING` (from `parse_pattern`)
> C++: uses `std::span`, `std::expected`, `std::byte`
`PatternScanner` scans a contiguous byte range for a **hex pattern** that may include **wildcards**. It returns an iterator to the **first match** or the end iterator if not found (or if the pattern string is invalid).
---
## Quick start
```cpp
#include "pattern_scanner.hpp"
using omath::PatternScanner;
std::vector<std::byte> buf = /* ... bytes ... */;
std::span<std::byte> s{buf.data(), buf.size()};
// Example pattern: "48 8B ?? ?? 89" (hex bytes with '?' as any byte)
auto it = PatternScanner::scan_for_pattern(s, "48 8B ?? ?? 89");
if (it != s.end()) {
// Found at offset:
auto offset = static_cast<std::size_t>(it - s.begin());
}
```
Or with iterators:
```cpp
auto it = PatternScanner::scan_for_pattern(buf.begin(), buf.end(), "DE AD BE EF");
if (it != buf.end()) { /* ... */ }
```
---
## Pattern string grammar
The pattern string is parsed into a sequence of byte **tokens**:
* **Hex byte**: two hexadecimal digits form one byte.
Examples: `90`, `4F`, `00`, `ff`
* **Wildcard byte**: `?` or `??` matches **any single byte**.
* **Separators**: any ASCII whitespace (space, tab, newline) is **ignored** and may be used to group tokens.
> ✔️ Valid: `"48 8B ?? 05 00"`, `"90 90 90"`, `"??"`
> ❌ Invalid: odd number of hex digits in a token, non-hex characters (besides `?` and whitespace)
If the string cannot be parsed into a clean sequence of tokens, `parse_pattern()` returns `std::unexpected(PatternScanError::INVALID_PATTERN_STRING)`, and the public scan function returns **end**.
---
## API
```cpp
namespace omath {
enum class PatternScanError { INVALID_PATTERN_STRING };
class PatternScanner final {
public:
// Contiguous range (span) overload
[[nodiscard]]
static std::span<std::byte>::iterator
scan_for_pattern(const std::span<std::byte>& range,
const std::string_view& pattern);
// Deleted rvalue-span overload (prevents dangling)
static std::span<std::byte>::iterator
scan_for_pattern(std::span<std::byte>&&,
const std::string_view&) = delete;
// Iterator overload
template<class IteratorType>
requires std::input_or_output_iterator<std::remove_cvref_t<IteratorType>>
static IteratorType
scan_for_pattern(const IteratorType& begin,
const IteratorType& end,
const std::string_view& pattern);
private:
[[nodiscard]]
static std::expected<std::vector<std::optional<std::byte>>, PatternScanError>
parse_pattern(const std::string_view& pattern_string);
};
} // namespace omath
```
### Return value
* On success: iterator to the **first** matching position.
* On failure / not found / invalid pattern: **`end`**.
---
## Complexity
Let `N` be the number of bytes in the range and `M` the number of **pattern tokens**.
* Time: **O(N × M)** (simple sliding window with early break).
* Space: **O(M)** for the parsed pattern vector.
---
## Examples
### Find a function prologue
```cpp
// x86-64: push rbp; mov rbp, rsp
auto it = PatternScanner::scan_for_pattern(s, "55 48 89 E5");
if (it != s.end()) {
// ... process
}
```
### Skip variable bytes with wildcards
```cpp
// mov rax, <imm32>; call <rel32>
auto it = PatternScanner::scan_for_pattern(s, "48 B8 ?? ?? ?? ?? ?? ?? ?? ?? E8 ?? ?? ?? ??");
```
### Iterator-based scan (subrange)
```cpp
auto sub_begin = buf.begin() + 1024;
auto sub_end = buf.begin() + 4096;
auto it = PatternScanner::scan_for_pattern(sub_begin, sub_end, "DE AD ?? BE EF");
```
---
## Behavior & edge cases
* **Empty or too-short**: If the effective pattern token count `M` is `0` or `M > N`, the function returns `end`.
* **Wildcards**: Each `?`/`??` token matches **exactly one** byte.
* **No exceptions**: Invalid pattern → parsed as `unexpected`, public API returns `end`.
* **No ownership**: The span overload takes `const std::span<std::byte>&` and returns a **mutable iterator** into that span. You must ensure the underlying memory stays alive. The rvalue-span overload is **deleted** to prevent dangling.
---
## Notes & caveats (implementation-sensitive)
* Although the iterator overload is constrained with `std::input_or_output_iterator`, the implementation uses `*(begin + i + j)` and arithmetic on iterators. In practice this means you should pass **random-access / contiguous iterators** (e.g., from `std::vector<std::byte>` or `std::span<std::byte>`). Using non-random-access iterators would be ill-formed.
* The inner matching loop compares a parsed token (`std::optional<std::byte>`) to the candidate byte; `std::nullopt` is treated as a **wildcard** (always matches).
* **Implementation note:** the outer scan currently derives its scan bound from the **pattern string length**; conceptually it should use the **number of parsed tokens** (hex/wildcard bytes). If you plan to accept spaces (or other non-byte characters) in the pattern string, ensure the scan window uses the parsed token count to avoid false negatives near the end of the buffer.
---
## Testing hooks
The class befriends several unit tests:
```
unit_test_pattern_scan_read_test_Test
unit_test_pattern_scan_corner_case_1_Test
unit_test_pattern_scan_corner_case_2_Test
unit_test_pattern_scan_corner_case_3_Test
unit_test_pattern_scan_corner_case_4_Test
```
Use these to validate parsing correctness, wildcard handling, and boundary conditions.
---
## Troubleshooting
* **Always returns end**: verify the pattern string is valid hex/wildcards and that you’re scanning the intended subrange. Try a simpler pattern (e.g., a single known byte) to sanity-check.
* **Crashes or compile errors with iterator overload**: use iterators that support random access (e.g., from `std::vector`), or prefer the `std::span` overload.
* **Ambiguous wildcards**: this scanner treats `?` and `??` as **byte-wide** wildcards (not per-nibble). If you need nibble-level masks, extend `parse_pattern` to support patterns like `A?`/`?F` with bitmask matching.
---
## Minimal unit test sketch
```cpp
TEST(pattern, basic) {
std::array<std::byte, 8> data{
std::byte{0x48}, std::byte{0x8B}, std::byte{0x01}, std::byte{0x02},
std::byte{0x89}, std::byte{0x50}, std::byte{0x90}, std::byte{0xCC}
};
std::span<std::byte> s{data.data(), data.size()};
auto it = omath::PatternScanner::scan_for_pattern(s, "48 8B ?? ?? 89");
ASSERT_NE(it, s.end());
EXPECT_EQ(static_cast<size_t>(it - s.begin()), 0U);
}
```
---
*Last updated: 31 Oct 2025*

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