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