Merge pull request #102 from orange-cpp/feature/gjk_algorithm

Feature/gjk algorithm

.clang-format

@@ -56,7 +56,7 @@ SpaceBeforeParensOptions:
   AfterIfMacros: true
   AfterOverloadedOperator: false
   BeforeNonEmptyParentheses: false
-SpaceBeforeRangeBasedForLoopColon: false
+SpaceBeforeRangeBasedForLoopColon: true
 SpaceInEmptyParentheses: false
 SpacesInCStyleCastParentheses: false
 SpacesInConditionalStatement: false

.github/workflows/cmake-multi-platform.yml

@@ -19,27 +19,32 @@ jobs:
     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
+                 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 -DOMATH_BUILD_TESTS=ON
+        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 --target all
+        run: cmake --build cmake-build/build/linux-release-vcpkg --target unit_tests omath
 
       - name: Run unit_tests
         shell: bash
@@ -47,12 +52,14 @@ jobs:
 
 
 
-##############################################################################
-# 2)  Windows  –  MSVC / Ninja
-##############################################################################
+  ##############################################################################
+  # 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)
@@ -68,12 +75,48 @@ jobs:
 
       - name: Configure (cmake --preset)
         shell: bash
-        run: cmake --preset windows-release -DOMATH_BUILD_TESTS=ON
+        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 --target all
+        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

.gitmodules

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

.idea/vcs.xml

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

CMakeLists.txt

@@ -1,42 +1,75 @@
 cmake_minimum_required(VERSION 3.26)
 
-project(omath VERSION 3.5.0 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" ${PROJECT_IS_TOP_LEVEL})
+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" OFF)
+option(OMATH_ENABLE_LEGACY "Will enable legacy classes that MUST be used ONLY for backward compatibility" ON)
 
-message(STATUS "[${PROJECT_NAME}]: Building on ${CMAKE_HOST_SYSTEM_NAME}")
-message(STATUS "[${PROJECT_NAME}]: Warnings as errors ${OMATH_THREAT_WARNING_AS_ERROR}")
-message(STATUS "[${PROJECT_NAME}]: Build unit tests ${OMATH_BUILD_TESTS}")
-message(STATUS "[${PROJECT_NAME}]: 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}")
+
+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(${PROJECT_NAME} SHARED ${OMATH_SOURCES} ${OMATH_HEADERS})
 else ()
     add_library(${PROJECT_NAME} STATIC ${OMATH_SOURCES} ${OMATH_HEADERS})
 endif ()
 
+
 add_library(${PROJECT_NAME}::${PROJECT_NAME} ALIAS ${PROJECT_NAME})
 
 target_compile_definitions(${PROJECT_NAME} PUBLIC OMATH_VERSION="${PROJECT_VERSION}")
@@ -69,7 +102,7 @@ if (OMATH_SUPRESS_SAFETY_CHECKS)
 endif ()
 
 if (OMATH_ENABLE_LEGACY)
-    target_compile_options(${PROJECT_NAME} PUBLIC OMATH_ENABLE_LEGACY)
+    target_compile_definitions(${PROJECT_NAME} PUBLIC OMATH_ENABLE_LEGACY)
 endif ()
 
 set_target_properties(${PROJECT_NAME} PROPERTIES
@@ -90,19 +123,27 @@ if (OMATH_STATIC_MSVC_RUNTIME_LIBRARY)
     )
 endif ()
 
-if (CMAKE_CXX_COMPILER_ID STREQUAL "Clang")
-    target_compile_options(${PROJECT_NAME} PRIVATE -mavx2 -mfma)
+if (OMATH_USE_AVX2)
+    if (MSVC)
+        target_compile_options(${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 ()
 
 target_compile_features(${PROJECT_NAME} PUBLIC cxx_std_23)
 
-
 if (OMATH_BUILD_TESTS)
-    add_subdirectory(extlibs)
     add_subdirectory(tests)
     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 ()

CMakePresets.json

@@ -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": "clang",
-        "CMAKE_CXX_COMPILER": "clang++"
+        "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",
@@ -65,6 +112,14 @@
         "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,
@@ -72,8 +127,8 @@
       "binaryDir": "${sourceDir}/cmake-build/build/${presetName}",
       "installDir": "${sourceDir}/cmake-build/install/${presetName}",
       "cacheVariables": {
-        "CMAKE_C_COMPILER": "clang",
-        "CMAKE_CXX_COMPILER": "clang++"
+        "CMAKE_CXX_COMPILER": "clang++",
+        "CMAKE_MAKE_PROGRAM": "ninja"
       },
       "condition": {
         "type": "equals",
@@ -81,6 +136,17 @@
         "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",
@@ -89,10 +155,26 @@
         "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-debug",
+      "inherits": "darwin-base",
+      "cacheVariables": {
+        "CMAKE_BUILD_TYPE": "Release"
+      }
+    },
+    {
+      "name": "darwin-release-vcpkg",
+      "displayName": "Darwin Release",
+      "inherits": "darwin-base-vcpkg",
       "cacheVariables": {
         "CMAKE_BUILD_TYPE": "Release"
       }

CONTRIBUTING.md

@@ -18,7 +18,7 @@ In order to send code back to the official OMath repository, you must first crea
 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 developement is performed on multiple branches. Changes are then pull requested into master. By default, changes
+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

CREDITS.md

@@ -3,6 +3,8 @@
 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!
 

INSTALL.md

@@ -59,7 +59,7 @@ target("...")
    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**.
+   Use **\<platform\>-\<build configuration\>** preset to build suitable version for yourself. Like **windows-release** or **linux-release**.
 
     | Platform Name | Build Config  |
     |---------------|---------------|

LICENSE

@@ -1,7 +1,7 @@
 Copyright (C) 2024-2025 Orange++ <orange_github@proton.me>
 
 This software is provided 'as-is', without any express or implied
-warranty.  In no event will the authors be held liable for any damages
+warranty. In no event will the authors be held liable for any damages
 arising from the use of this software.
 
 Permission is granted to anyone to use this software for any purpose,
@@ -16,13 +16,44 @@ freely, subject to the following restrictions:
    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, present, or future)
+   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
+     * "Yandex.Lavka" LLC
+     * "Yandex.Telecom" LLC
+     * "Yandex.Cloud" LLC
+     * "Micromobility" LLC
+     * "MM-Tech" LLC
+     * "Carsharing" LLC
+     * "Yandex.Drive" LLC
+     * "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
+   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.

README.md

@@ -1,6 +1,6 @@
 <div align = center>
 
-![banner](.github/images/logos/omath_logo_macro.png)
+![banner](docs/images/logos/omath_logo_macro.png)
 
 ![Static Badge](https://img.shields.io/badge/license-libomath-orange)
 ![GitHub contributors](https://img.shields.io/github/contributors/orange-cpp/omath)
@@ -20,9 +20,11 @@ It provides the latest features, is highly customizable, has all for cheat devel
 
 ---
 
-**[<kbd> <br> Install <br> </kbd>][INSTALL]**
-**[<kbd> <br> Examples <br> </kbd>][EXAMPLES]**
-**[<kbd> <br> Contribute <br> </kbd>][CONTRIBUTING]**
+**[<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]** 
 
 ---
 
@@ -41,21 +43,52 @@ It provides the latest features, is highly customizable, has all for cheat devel
  </a>
 </div>
 
-## 👁‍🗨 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!
+## 🚀 Quick Example
 
+```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
+}
+```
+
+**[➡️ See more examples and tutorials][TUTORIALS]**
+
+# ✨ 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
 
 <br>
 
-[![Youtube Video](.github/images/yt_previews/img.png)](https://youtu.be/lM_NJ1yCunw?si=-Qf5yzDcWbaxAXGQ)
+[![Youtube Video](docs/images/yt_previews/img.png)](https://youtu.be/lM_NJ1yCunw?si=-Qf5yzDcWbaxAXGQ)
 
 <br>
 
@@ -69,59 +102,44 @@ It provides the latest features, is highly customizable, has all for cheat devel
 
 ![CS2 Preview]
 
+<br>
+
+![TF2 Preview]
+
 <br>
 <br>
 
+</div>
 
+## 📚 Documentation
 
-## Supported Render Pipelines
-| ENGINE   | SUPPORT |
-|----------|---------|
-| Source   | ✅YES    |
-| Unity    | ✅YES    |
-| IWEngine | ✅YES    |
-| OpenGL   | ✅YES    |
-| Unreal   | ✅YES    |
+- **[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
 
-## Supported Operating Systems
+## 🤝 Community & Support
 
-| OS             | SUPPORT |
-|----------------|---------|
-| Windows 10/11  | ✅YES    |
-| Linux          | ✅YES    |
-| Darwin (MacOS) | ✅YES    |
+- **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
 
-## ❔ Usage
-ESP example
-```c++
-omath::source_engine::Camera cam{localPlayer.GetCameraOrigin(),
-                                 localPlayer.GetAimPunch(),
-                                 {1920.f, 1080.f},
-                                 localPlayer.GetFieldOfView(),
-                                 0.01.f, 30000.f};
-
-for (auto ent: apex_sdk::EntityList::GetAllEntities())
-{
-    const auto bottom = cam.world_to_screen(ent.GetOrigin());
-    const auto top = cam.world_to_screen(ent.GetBonePosition(8) + omath::Vector3<float>{0, 0, 10});
-
-    const auto ent_health = ent.GetHealth();
-
-    if (!top || !bottom || ent_health <= 0)
-        continue;
-    // esp rendering...
-}
-```
-
-## 💘 Acknowledgments
+# 💘 Acknowledgments
 -  [All contributors](https://github.com/orange-cpp/omath/graphs/contributors)
 
 <!----------------------------------{ Images }--------------------------------->
-[APEX Preview]: .github/images/showcase/apex.png
-[BO2 Preview]: .github/images/showcase/cod_bo2.png
-[CS2 Preview]: .github/images/showcase/cs2.jpeg
-
+[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

VERSION

@@ -0,0 +1 @@
+4.2.0

benchmark/CMakeLists.txt

@@ -0,0 +1,19 @@
+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 ()

benchmark/benchmark_mat.cpp

@@ -0,0 +1,65 @@
+//
+// 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);

benchmark/benchmark_projectile_pred.cpp

@@ -0,0 +1,23 @@
+//
+// 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);

benchmark/main.cpp

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

docs/3d_primitives/box.md

@@ -0,0 +1,118 @@
+# `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*

docs/3d_primitives/plane.md

@@ -0,0 +1,98 @@
+# `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.

docs/api_overview.md

@@ -0,0 +1,527 @@
+# 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*

docs/best_practices.md

@@ -0,0 +1,532 @@
+# 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*

docs/collision/line_tracer.md

@@ -0,0 +1,181 @@
+# `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*

docs/engines/frostbite/camera_trait.md

@@ -0,0 +1,108 @@
+# `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). 

docs/engines/frostbite/constants.md

@@ -0,0 +1,59 @@
+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.

docs/engines/frostbite/pred_engine_trait.md

@@ -0,0 +1,105 @@
+// 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

docs/engines/iw_engine/camera_trait.md

@@ -0,0 +1,109 @@
+# `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).

docs/engines/iw_engine/constants.md

@@ -0,0 +1,77 @@
+# `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

docs/engines/iw_engine/formulas.md

@@ -0,0 +1,135 @@
+# `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

docs/engines/iw_engine/pred_engine_trait.md

@@ -0,0 +1,198 @@
+# `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`

docs/engines/opengl_engine/camera_trait.md

@@ -0,0 +1,110 @@
+# `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).

docs/engines/opengl_engine/constants.md

@@ -0,0 +1,78 @@
+# `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

docs/engines/opengl_engine/formulas.md

@@ -0,0 +1,140 @@
+# `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

docs/engines/opengl_engine/pred_engine_trait.md

@@ -0,0 +1,199 @@
+# `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`

docs/engines/source_engine/camera_trait.md

@@ -0,0 +1,113 @@
+# `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

docs/engines/source_engine/constants.md

@@ -0,0 +1,77 @@
+# `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

docs/engines/source_engine/formulas.md

@@ -0,0 +1,135 @@
+# `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

docs/engines/source_engine/pred_engine_trait.md

@@ -0,0 +1,198 @@
+# `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`

docs/engines/unity_engine/camera_trait.md

@@ -0,0 +1,109 @@
+# `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).

docs/engines/unity_engine/constants.md

@@ -0,0 +1,77 @@
+# `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

docs/engines/unity_engine/formulas.md

@@ -0,0 +1,135 @@
+# `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

docs/engines/unity_engine/pred_engine_trait.md

@@ -0,0 +1,198 @@
+# `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`

docs/engines/unreal_engine/camera_trait.md

@@ -0,0 +1,109 @@
+# `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).

docs/engines/unreal_engine/constants.md

@@ -0,0 +1,77 @@
+# `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

docs/engines/unreal_engine/formulas.md

@@ -0,0 +1,135 @@
+# `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

docs/engines/unreal_engine/pred_engine_trait.md

@@ -0,0 +1,200 @@
+# `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`

docs/faq.md

@@ -0,0 +1,406 @@
+# 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*

docs/getting_started.md

@@ -0,0 +1,305 @@
+# 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*

docs/index.md

@@ -0,0 +1,239 @@
+<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

docs/install.md

@@ -1,6 +1,6 @@
-# 📥Installation Guide
+# Installation
 
-## Using vcpkg
+## <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:
@@ -14,7 +14,21 @@ 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 using CMake
+## <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).
@@ -45,10 +59,10 @@ For detailed commands on installing different versions and more information, ple
    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**.
+   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 |
+   | darwin        | release/debug |

docs/linear_algebra/mat.md

@@ -0,0 +1,428 @@
+# `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*

docs/linear_algebra/triangle.md

@@ -0,0 +1,173 @@
+# `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*

docs/linear_algebra/vector2.md

@@ -0,0 +1,300 @@
+# `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*

docs/linear_algebra/vector3.md

@@ -0,0 +1,307 @@
+# `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*

docs/linear_algebra/vector4.md

@@ -0,0 +1,253 @@
+# `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*

docs/pathfinding/a_star.md

@@ -0,0 +1,188 @@
+# `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*

docs/pathfinding/navigation_mesh.md

@@ -0,0 +1,113 @@
+# `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.

docs/projectile_prediction/proj_pred_engine_avx2.md

@@ -0,0 +1,161 @@
+# `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*

docs/projectile_prediction/proj_pred_engine_legacy.md

@@ -0,0 +1,184 @@
+# `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*

docs/projectile_prediction/projectile.md

@@ -0,0 +1,96 @@
+# `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*

docs/projectile_prediction/projectile_engine.md

@@ -0,0 +1,162 @@
+# `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*

docs/projectile_prediction/target.md

@@ -0,0 +1,70 @@
+# `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*

docs/projection/camera.md

@@ -0,0 +1,270 @@
+# `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*

docs/projection/error_codes.md

@@ -0,0 +1,79 @@
+# `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.

docs/rev_eng/external_rev_object.md

@@ -0,0 +1,164 @@
+# `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*

docs/rev_eng/internal_rev_object.md

@@ -0,0 +1,142 @@
+# `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*

docs/styles/center.css

@@ -0,0 +1,4 @@
+/* docs/css/custom.css */
+.center-text {
+    text-align: center;
+}

docs/styles/custom-header.css

@@ -0,0 +1,11 @@
+/* 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;
+}

docs/trigonometry/angle.md

@@ -0,0 +1,165 @@
+# `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*

docs/trigonometry/angles.md

@@ -0,0 +1,107 @@
+# `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);
+```

docs/trigonometry/view_angles.md

@@ -0,0 +1,87 @@
+# `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.

docs/troubleshooting.md

@@ -0,0 +1,525 @@
+# 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*

docs/tutorials.md

@@ -0,0 +1,616 @@
+# 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*

docs/utility/color.md

@@ -0,0 +1,190 @@
+# `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*

docs/utility/pattern_scan.md

@@ -0,0 +1,194 @@
+# `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*

docs/utility/pe_pattern_scan.md

@@ -0,0 +1,155 @@
+# `omath::PePatternScanner` — Scan PE images for byte patterns
+
+> Header: your project’s `pe_pattern_scanner.hpp`
+> Namespace: `omath`
+> Platform: **Windows / PE (Portable Executable) images**
+> Depends on: `<filesystem>`, `<optional>`, `<cstdint>`
+> Companion: works well with `omath::PatternScanner` (same pattern grammar)
+
+`PePatternScanner` searches **Portable Executable (PE)** binaries for a hex pattern (with wildcards). You can scan:
+
+* a **loaded module** in the current process, or
+* a **PE file on disk** (by section name; defaults to **`.text`**).
+
+---
+
+## Pattern string grammar (same as `PatternScanner`)
+
+* **Hex byte**: two hex digits → one byte (`90`, `4F`, `00`, `ff`).
+* **Wildcard byte**: `?` or `??` matches **any byte**.
+* **Whitespace**: ignored (use to group tokens).
+
+✔️ `"48 8B ?? ?? 89"`, `"55 8B EC"`, `"??"`
+❌ odd digit counts, non-hex characters (besides `?` and whitespace)
+
+---
+
+## API
+
+```cpp
+namespace omath {
+
+struct PeSectionScanResult {
+  std::uint64_t virtual_base_addr;  // RVA base of the scanned section (ImageBase + SectionRVA)
+  std::uint64_t raw_base_addr;      // file offset (start of section in the file)
+  std::ptrdiff_t target_offset;     // offset from section base to the first matched byte
+};
+
+class PePatternScanner final {
+public:
+  // Scan a module already loaded in *this* process.
+  // module_base_address: HMODULE / ImageBase (e.g., from GetModuleHandle)
+  // Returns absolute address (process VA) of the first match, or nullopt.
+  static std::optional<std::uintptr_t>
+  scan_for_pattern_in_loaded_module(const void* module_base_address,
+                                    const std::string_view& pattern);
+
+  // Scan a PE file on disk, by section name (default ".text").
+  // Returns section bases (virtual + raw) and match offset within the section, or nullopt.
+  static std::optional<PeSectionScanResult>
+  scan_for_pattern_in_file(const std::filesystem::path& path_to_file,
+                           const std::string_view& pattern,
+                           const std::string_view& target_section_name = ".text");
+};
+
+} // namespace omath
+```
+
+---
+
+## Return values
+
+* **Loaded module**: `std::optional<std::uintptr_t>`
+
+    * `value()` = **process virtual address** (ImageBase + SectionRVA + match offset).
+    * `nullopt` = no match or parse/PE error.
+
+* **File scan**: `std::optional<PeSectionScanResult>`
+
+    * `virtual_base_addr` = **ImageBase + SectionRVA** of the scanned section (as if mapped).
+    * `raw_base_addr` = **file offset** of section start.
+    * `target_offset` = offset from the section base to the **first matched byte**.
+    * To get addresses:
+
+        * **Virtual (RVA)** of hit = `virtual_base_addr + target_offset`
+        * **Raw file offset** of hit = `raw_base_addr + target_offset`
+
+---
+
+## Usage examples
+
+### Scan a loaded module (current process)
+
+```cpp
+#include <windows.h>
+#include "pe_pattern_scanner.hpp"
+
+using omath::PePatternScanner;
+
+auto hMod = ::GetModuleHandleW(L"kernel32.dll");
+if (hMod) {
+  auto addr = PePatternScanner::scan_for_pattern_in_loaded_module(
+      hMod, "48 8B ?? ?? 89" // hex + wildcards
+  );
+  if (addr) {
+    // Use the absolute process VA:
+    std::uintptr_t hit_va = *addr;
+    // ...
+  }
+}
+```
+
+### Scan a PE file on disk (default section “.text”)
+
+```cpp
+#include "pe_pattern_scanner.hpp"
+using omath::PePatternScanner;
+
+auto res = PePatternScanner::scan_for_pattern_in_file(
+    R"(C:\Windows\System32\kernel32.dll)", "55 8B EC"
+);
+if (res) {
+  auto rva_hit  = res->virtual_base_addr + res->target_offset;
+  auto raw_hit  = res->raw_base_addr     + res->target_offset;
+  // rva_hit: where it would be in memory; raw_hit: file offset
+}
+```
+
+### Scan another section (e.g., “.rdata”)
+
+```cpp
+auto res = PePatternScanner::scan_for_pattern_in_file(
+  "foo.dll", "48 8D 0D ?? ?? ?? ??", ".rdata"
+);
+```
+
+---
+
+## Notes & edge cases
+
+* **PE only**: these functions assume a valid **PE/COFF** layout. Non-PE files or corrupted headers yield `nullopt`.
+* **Section name**: `scan_for_pattern_in_file` defaults to **`.text`**; pass a different name to target other sections.
+* **Alignment & RVAs**: `virtual_base_addr` is computed from section headers (RVA aligned per section alignment). The returned “virtual” base is suitable for RVA math; the **process VA** returned by the “loaded module” API already includes the image base.
+* **Architecture**: works for 32-bit and 64-bit PEs; `std::uintptr_t` size matches the build architecture.
+* **Performance**: Pattern matching is **O(N × M)** (sliding window with wildcards). For large images, prefer scanning only necessary sections.
+* **Wildcards**: Each `?` matches **one byte** (no nibble masks). If you need `A?`-style nibble wildcards, extend the parser (see `PatternScanner`).
+* **Safety**: For loaded modules, you must have access to the memory; scanning read-only sections is fine, but never write. For file scans, ensure the file path is accessible.
+
+---
+
+## Troubleshooting
+
+* **`nullopt`**: Verify the pattern (valid tokens), correct **section**, and that you’re scanning the intended module/file (check bitness and version).
+* **“Loaded module” address math**: If you need an **offset from the module base**, compute `offset = hit_va - reinterpret_cast<std::uintptr_t>(module_base_address)`.
+* **Multiple matches**: Only the **first** match is returned. If you need all matches, extend the implementation to continue scanning from `target_offset + 1`.
+
+---
+
+## See also
+
+* `omath::PatternScanner` — raw buffer/iterator scanning with the same pattern grammar.
+* `omath::Triangle`, `omath::Vector3` — math types used elsewhere in the library.
+
+---
+
+*Last updated: 31 Oct 2025*

examples/CMakeLists.txt

@@ -1,4 +1,9 @@
 project(examples)
 
-add_executable(ExampleProjectionMatrixBuilder example_proj_mat_builder.cpp)
-target_link_libraries(ExampleProjectionMatrixBuilder PRIVATE omath::omath)
+add_executable(example_projection_matrix_builder example_proj_mat_builder.cpp)
+set_target_properties(example_projection_matrix_builder PROPERTIES CXX_STANDARD 26)
+target_link_libraries(example_projection_matrix_builder PRIVATE omath::omath)
+
+add_executable(example_signature_scan example_signature_scan.cpp)
+set_target_properties(example_signature_scan PROPERTIES CXX_STANDARD 26)
+target_link_libraries(example_signature_scan PRIVATE omath::omath)

examples/example_signature_scan.cpp

@@ -0,0 +1,39 @@
+//
+// Created by Vlad on 11/8/2025.
+//
+
+#include <iostream>
+#include <omath/utility/pe_pattern_scan.hpp>
+#include <print>
+
+int main()
+{
+    std::println("OMATH Signature Scanner");
+
+    std::print("Enter path to PE file: ");
+    std::string file_path;
+    std::getline(std::cin, file_path); // allows spaces
+
+    std::print("Enter target section: ");
+    std::string section;
+    std::getline(std::cin, section);
+
+    std::print("Enter signature: ");
+    std::string signature;
+    std::getline(std::cin, signature);
+
+    std::println("[LOG] Performing scan....");
+
+    const auto result = omath::PePatternScanner::scan_for_pattern_in_file(file_path, signature, section);
+
+    if (!result)
+    {
+        std::println("[ERROR] Scan failed or signature was not found");
+        return -1;
+    }
+
+    std::println("Found at virtual 0x{:x} , raw 0x{:x}", result->virtual_base_addr + result->target_offset,
+               result->raw_base_addr + result->target_offset);
+
+    return 0;
+}

extlibs/CMakeLists.txt

@@ -1 +0,0 @@
-add_subdirectory(googletest)

include/omath/3d_primitives/box.hpp

@@ -3,8 +3,8 @@
 //
 
 #pragma once
+#include "omath/linear_algebra/triangle.hpp"
 #include "omath/linear_algebra/vector3.hpp"
-#include "omath/triangle.hpp"
 #include <array>
 
 namespace omath::primitives

include/omath/3d_primitives/mesh.hpp

@@ -0,0 +1,102 @@
+//
+// Created by Vladislav on 09.11.2025.
+//
+#pragma once
+#include "omath/linear_algebra/triangle.hpp"
+#include <omath/linear_algebra/mat.hpp>
+#include <omath/linear_algebra/vector3.hpp>
+#include <utility>
+#include <vector>
+
+namespace omath::primitives
+{
+    template<class Mat4X4, class RotationAngles, class MeshTypeTrait, class Type = float>
+    class Mesh final
+    {
+    public:
+        using NumericType = Type;
+
+    private:
+        using Vbo = std::vector<Vector3<NumericType>>;
+        using Vao = std::vector<Vector3<std::size_t>>;
+
+    public:
+        Vbo m_vertex_buffer;
+        Vao m_vertex_array_object;
+
+        Mesh(Vbo vbo, Vao vao, const Vector3<NumericType> scale = {1, 1, 1,})
+            : m_vertex_buffer(std::move(vbo)), m_vertex_array_object(std::move(vao)), m_scale(scale)
+        {
+        }
+        void set_origin(const Vector3<NumericType>& new_origin)
+        {
+            m_origin = new_origin;
+            m_to_world_matrix = std::nullopt;
+        }
+
+        void set_scale(const Vector3<NumericType>& new_scale)
+        {
+            m_scale = new_scale;
+            m_to_world_matrix = std::nullopt;
+        }
+
+        void set_rotation(const RotationAngles& new_rotation_angles)
+        {
+            m_rotation_angles = new_rotation_angles;
+            m_to_world_matrix = std::nullopt;
+        }
+
+        [[nodiscard]]
+        const Vector3<NumericType>& get_origin() const
+        {
+            return m_origin;
+        }
+
+        [[nodiscard]]
+        const Vector3<NumericType>& get_scale() const
+        {
+            return m_scale;
+        }
+
+        [[nodiscard]]
+        const RotationAngles& get_rotation_angles() const
+        {
+            return m_rotation_angles;
+        }
+
+        [[nodiscard]]
+        const Mat4X4& get_to_world_matrix() const
+        {
+            if (m_to_world_matrix)
+                return m_to_world_matrix.value();
+            m_to_world_matrix =
+                    mat_translation(m_origin) * mat_scale(m_scale) * MeshTypeTrait::rotation_matrix(m_rotation_angles);
+
+            return m_to_world_matrix.value();
+        }
+
+        [[nodiscard]]
+        Vector3<float> vertex_to_world_space(const Vector3<float>& vertex) const
+        {
+            auto abs_vec = get_to_world_matrix() * mat_column_from_vector(vertex);
+
+            return {abs_vec.at(0, 0), abs_vec.at(1, 0), abs_vec.at(2, 0)};
+        }
+
+        [[nodiscard]]
+        Triangle<Vector3<float>> make_face_in_world_space(const Vao::const_iterator vao_iterator) const
+        {
+            return {vertex_to_world_space(m_vertex_buffer.at(vao_iterator->x)),
+                    vertex_to_world_space(m_vertex_buffer.at(vao_iterator->y)),
+                    vertex_to_world_space(m_vertex_buffer.at(vao_iterator->z))};
+        }
+
+    private:
+        Vector3<NumericType> m_origin;
+        Vector3<NumericType> m_scale;
+
+        RotationAngles m_rotation_angles;
+
+        mutable std::optional<Mat4X4> m_to_world_matrix;
+    };
+} // namespace omath::primitives

include/omath/3d_primitives/plane.hpp

@@ -3,8 +3,8 @@
 //
 
 #pragma once
+#include "omath/linear_algebra/triangle.hpp"
 #include "omath/linear_algebra/vector3.hpp"
-#include "omath/triangle.hpp"
 #include <array>
 
 namespace omath::primitives

include/omath/collision/gjk_algorithm.hpp

@@ -0,0 +1,49 @@
+//
+// Created by Vlad on 11/9/2025.
+//
+
+#pragma once
+#include "mesh_collider.hpp"
+#include "omath/linear_algebra/vector3.hpp"
+#include "simplex.hpp"
+
+namespace omath::collision
+{
+    template<class ColliderType>
+    class GjkAlgorithm final
+    {
+    public:
+        [[nodiscard]]
+        static ColliderType::VertexType find_support_vertex(const ColliderType& collider_a,
+                                                            const ColliderType& collider_b,
+                                                            const ColliderType::VertexType& direction)
+        {
+            return collider_a.find_abs_furthest_vertex(direction) - collider_b.find_abs_furthest_vertex(-direction);
+        }
+
+        [[nodiscard]]
+        static bool is_collide(const ColliderType& collider_a, const ColliderType& collider_b)
+        {
+            // Get initial support point in any direction
+            auto support = find_support_vertex(collider_a, collider_b, {1, 0, 0});
+
+            Simplex<typename ColliderType::VertexType> simplex;
+            simplex.push_front(support);
+
+            auto direction = -support;
+
+            while (true)
+            {
+                support = find_support_vertex(collider_a, collider_b, direction);
+
+                if (support.dot(direction) <= 0.f)
+                    return false;
+
+                simplex.push_front(support);
+
+                if (simplex.handle(direction))
+                    return true;
+            }
+        }
+    };
+} // namespace omath::collision

include/omath/collision/line_tracer.hpp

@@ -3,8 +3,8 @@
 //
 #pragma once
 
+#include "omath/linear_algebra/triangle.hpp"
 #include "omath/linear_algebra/vector3.hpp"
-#include "omath/triangle.hpp"
 
 namespace omath::collision
 {

include/omath/collision/mesh_collider.hpp

@@ -0,0 +1,37 @@
+//
+// Created by Vlad on 11/9/2025.
+//
+
+#pragma once
+#include "omath/linear_algebra/vector3.hpp"
+
+namespace omath::collision
+{
+    template<class MeshType>
+    class MeshCollider
+    {
+    public:
+        using NumericType = typename MeshType::NumericType;
+
+        using VertexType = Vector3<NumericType>;
+        explicit MeshCollider(MeshType mesh): m_mesh(std::move(mesh))
+        {
+        }
+
+        [[nodiscard]]
+        const Vector3<float>& find_furthest_vertex(const Vector3<float>& direction) const
+        {
+            return *std::ranges::max_element(m_mesh.m_vertex_buffer, [&direction](const auto& first, const auto& second)
+                                             { return first.dot(direction) < second.dot(direction); });
+        }
+
+        [[nodiscard]]
+        Vector3<float> find_abs_furthest_vertex(const Vector3<float>& direction) const
+        {
+            return m_mesh.vertex_to_world_space(find_furthest_vertex(direction));
+        }
+
+    private:
+        MeshType m_mesh;
+    };
+} // namespace omath::collision

include/omath/collision/simplex.hpp

@@ -0,0 +1,257 @@
+#pragma once
+#include "omath/linear_algebra/vector3.hpp"
+#include <array>
+#include <cassert>
+#include <initializer_list>
+#include <type_traits>
+
+namespace omath::collision
+{
+
+    // Minimal structural contract for the vector type used by GJK.
+    template<class V>
+    concept GjkVector = requires(const V& a, const V& b) {
+        { -a } -> std::same_as<V>;
+        { a - b } -> std::same_as<V>;
+        { a.cross(b) } -> std::same_as<V>;
+        { a.point_to_same_direction(b) } -> std::same_as<bool>;
+    };
+
+    template<GjkVector VectorType = Vector3<float>>
+    class Simplex final
+    {
+        std::array<VectorType, 4> m_points{};
+        std::size_t m_size{0};
+
+    public:
+        static constexpr std::size_t capacity = 4;
+
+        constexpr Simplex() = default;
+
+        constexpr Simplex& operator=(std::initializer_list<VectorType> list) noexcept
+        {
+            assert(list.size() <= capacity && "Simplex can have at most 4 points");
+            m_size = 0;
+            for (const auto& p : list)
+                m_points[m_size++] = p;
+            return *this;
+        }
+
+        constexpr void push_front(const VectorType& p) noexcept
+        {
+            const std::size_t limit = (m_size < capacity) ? m_size : capacity - 1;
+            for (std::size_t i = limit; i > 0; --i)
+                m_points[i] = m_points[i - 1];
+            m_points[0] = p;
+            if (m_size < capacity)
+                ++m_size;
+        }
+
+        constexpr const VectorType& operator[](std::size_t i) const noexcept
+        {
+            return m_points[i];
+        }
+        constexpr VectorType& operator[](std::size_t i) noexcept
+        {
+            return m_points[i];
+        }
+
+        [[nodiscard]] constexpr std::size_t size() const noexcept
+        {
+            return m_size;
+        }
+
+        [[nodiscard]] constexpr bool empty() const noexcept
+        {
+            return m_size == 0;
+        }
+
+        [[nodiscard]] constexpr const VectorType& front() const noexcept
+        {
+            return m_points[0];
+        }
+
+        [[nodiscard]] constexpr const VectorType& back() const noexcept
+        {
+            return m_points[m_size - 1];
+        }
+
+        [[nodiscard]] constexpr const VectorType* data() const noexcept
+        {
+            return m_points.data();
+        }
+
+        [[nodiscard]] constexpr auto begin() const noexcept
+        {
+            return m_points.begin();
+        }
+
+        [[nodiscard]] constexpr auto end() const noexcept
+        {
+            return m_points.begin() + m_size;
+        }
+
+        constexpr void clear() noexcept
+        {
+            m_size = 0;
+        }
+
+        // GJK step: updates simplex + next search direction.
+        // Returns true iff the origin lies inside the tetrahedron.
+        [[nodiscard]] constexpr bool handle(VectorType& direction) noexcept
+        {
+            switch (m_size)
+            {
+            case 0:
+                return false;
+            case 1:
+                return handle_point(direction);
+            case 2:
+                return handle_line(direction);
+            case 3:
+                return handle_triangle(direction);
+            case 4:
+                return handle_tetrahedron(direction);
+            default:
+                std::unreachable();
+            }
+        }
+
+    private:
+        [[nodiscard]] constexpr bool handle_point(VectorType& direction) noexcept
+        {
+            const auto& a = m_points[0];
+            direction = -a;
+            return false;
+        }
+
+        template<class V>
+        static constexpr bool near_zero(const V& v, const float eps = 1e-7f)
+        {
+            return v.dot(v) <= eps * eps;
+        }
+
+        template<class V>
+        static constexpr V any_perp(const V& v)
+        {
+            // try cross with axes until non-zero
+            V d = v.cross(V{1, 0, 0});
+            if (near_zero(d))
+                d = v.cross(V{0, 1, 0});
+            if (near_zero(d))
+                d = v.cross(V{0, 0, 1});
+            return d;
+        }
+
+        constexpr bool handle_line(VectorType& direction)
+        {
+            const auto& a = m_points[0];
+            const auto& b = m_points[1];
+
+            const auto ab = b - a;
+            const auto ao = -a;
+
+            if (ab.point_to_same_direction(ao))
+            {
+                // ReSharper disable once CppTooWideScopeInitStatement
+                auto n = ab.cross(ao); // Needed to valid handle collision if colliders placed at same origin pos
+                if (near_zero(n))
+                {
+                    // collinear: origin lies on ray AB (often on segment), pick any perp to escape
+                    direction = any_perp(ab);
+                }
+                else
+                {
+                    direction = n.cross(ab);
+                }
+            }
+            else
+            {
+                *this = {a};
+                direction = ao;
+            }
+            return false;
+        }
+
+        [[nodiscard]] constexpr bool handle_triangle(VectorType& direction) noexcept
+        {
+            const auto& a = m_points[0];
+            const auto& b = m_points[1];
+            const auto& c = m_points[2];
+
+            const auto ab = b - a;
+            const auto ac = c - a;
+            const auto ao = -a;
+
+            const auto abc = ab.cross(ac);
+
+            // Region AC
+            if (abc.cross(ac).point_to_same_direction(ao))
+            {
+                if (ac.point_to_same_direction(ao))
+                {
+                    *this = {a, c};
+                    direction = ac.cross(ao).cross(ac);
+                    return false;
+                }
+                *this = {a, b};
+                return handle_line(direction);
+            }
+
+            // Region AB
+            if (ab.cross(abc).point_to_same_direction(ao))
+            {
+                *this = {a, b};
+                return handle_line(direction);
+            }
+
+            // Above or below triangle
+            if (abc.point_to_same_direction(ao))
+            {
+                direction = abc;
+            }
+            else
+            {
+                *this = {a, c, b}; // flip winding
+                direction = -abc;
+            }
+            return false;
+        }
+
+        [[nodiscard]] constexpr bool handle_tetrahedron(VectorType& direction) noexcept
+        {
+            const auto& a = m_points[0];
+            const auto& b = m_points[1];
+            const auto& c = m_points[2];
+            const auto& d = m_points[3];
+
+            const auto ab = b - a;
+            const auto ac = c - a;
+            const auto ad = d - a;
+            const auto ao = -a;
+
+            const auto abc = ab.cross(ac);
+            const auto acd = ac.cross(ad);
+            const auto adb = ad.cross(ab);
+
+            if (abc.point_to_same_direction(ao))
+            {
+                *this = {a, b, c};
+                return handle_triangle(direction);
+            }
+            if (acd.point_to_same_direction(ao))
+            {
+                *this = {a, c, d};
+                return handle_triangle(direction);
+            }
+            if (adb.point_to_same_direction(ao))
+            {
+                *this = {a, d, b};
+                return handle_triangle(direction);
+            }
+            // Origin inside tetrahedron
+            return true;
+        }
+    };
+
+} // namespace omath::collision

include/omath/engines/frostbite_engine/camera.hpp

@@ -0,0 +1,13 @@
+//
+// Created by Vlad on 3/22/2025.
+//
+
+#pragma once
+#include "omath/engines/frostbite_engine/constants.hpp"
+#include "omath/projection/camera.hpp"
+#include "traits/camera_trait.hpp"
+
+namespace omath::frostbite_engine
+{
+    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait>;
+} // namespace omath::unity_engine

include/omath/engines/frostbite_engine/constants.hpp

@@ -0,0 +1,25 @@
+//
+// 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
+{
+    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};
+
+    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>;
+    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>;
+} // namespace omath::frostbite_engine

include/omath/engines/frostbite_engine/formulas.hpp

@@ -0,0 +1,26 @@
+//
+// Created by Vlad on 3/22/2025.
+//
+
+#pragma once
+#include "omath/engines/frostbite_engine/constants.hpp"
+
+namespace omath::frostbite_engine
+{
+    [[nodiscard]]
+    Vector3<float> forward_vector(const ViewAngles& angles) noexcept;
+
+    [[nodiscard]]
+    Vector3<float> right_vector(const ViewAngles& angles) noexcept;
+
+    [[nodiscard]]
+    Vector3<float> up_vector(const ViewAngles& angles) noexcept;
+
+    [[nodiscard]] Mat4X4 calc_view_matrix(const ViewAngles& angles, const Vector3<float>& cam_origin) noexcept;
+
+    [[nodiscard]]
+    Mat4X4 rotation_matrix(const ViewAngles& angles) noexcept;
+
+    [[nodiscard]]
+    Mat4X4 calc_perspective_projection_matrix(float field_of_view, float aspect_ratio, float near, float far) noexcept;
+} // namespace omath::unity_engine

include/omath/engines/frostbite_engine/mesh.hpp

@@ -0,0 +1,12 @@
+//
+// Created by Vladislav on 09.11.2025.
+//
+#pragma once
+#include "constants.hpp"
+#include "omath/3d_primitives/mesh.hpp"
+#include "traits/mesh_trait.hpp"
+
+namespace omath::frostbite_engine
+{
+    using Mesh = primitives::Mesh<Mat4X4, ViewAngles, MeshTrait, float>;
+}