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