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

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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°).

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Constants

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.

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Matrix types

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.

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Angle types

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.

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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

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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