Add documentation for game engine math modules

docs/engines/iw_engine/camera_trait.md

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

docs/engines/iw_engine/constants.md

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

docs/engines/iw_engine/formulas.md

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