Coordinate and matrix conventions

• +X is right, +Y is up, and +Z is the conventional forward axis.
• The core does not force every camera or projection to be left-handed. Projection and view builders require an explicit Handedness.
• Matrices are stored and presented by rows.
• Vector * Matrix applies a matrix using Move's row-vector convention.
• Compose(first, second) applies first and then second.
• Affine translation occupies the fourth row of Mat4 and the homogeneous fourth column is (0, 0, 0, 1).

Semantic values

• Point3 is a location. Point minus point is a displacement; adding two points is unavailable.
• Direction3 is always finite, unit length, and nonzero.
• Normal3 is a unit surface/plane covector and is distinct from direction.
• Rotation3 stores a unit quaternion. General, possibly non-unit quaternion algebra uses Quat.
• Construction that cannot preserve an invariant uses Try... and reports failure.

Transforms

• RigidTransform3 is rotation plus translation and is closed under composition and inversion.
• TrsTransform3 is an authoring/decomposition value. Arbitrary TRS composition can create shear, so its general composition result is affine.
• AffineTransform3 represents a linear transformation plus translation and is closed under composition. Inversion can fail for singular inputs.
• TransformPoint applies translation. TransformVector does not.
• A general affine direction transformation is fallible because it must restore unit length.
• TryTransformNormal uses inverse-transpose/covector semantics and preserves the transformed positive half-space under reflections.
• TryTransformOrientedSurfaceNormal transforms the cross product of an ordered tangent pair and therefore differs by a sign under reflection.

Rotations and angles

• Angles use Radians<T> and Degrees<T> wrappers.
• Euler construction requires an explicit EulerOrder; the order names the sequence applied to a local vector.
• Nlerp and Slerp take the shortest quaternion arc and clamp the amount to [0,1]. Their Unclamped variants expose extrapolation.
• Quaternion component equality is exact. IsNearlyEquivalent(Rotation3, Rotation3) treats q and -q as the same rotation.

Projection, depth, and viewport conventions

• Perspective and orthographic constructors require Handedness, ClipDepth, and DepthDirection.
• Both [0,1] and [-1,1] normalized-device depth are supported.
• Forward and reverse Z, finite and infinite far perspective, and intentional orthographic axis reversal are explicit.
• TryProjectPoint returns normalized-device coordinates and exposes invalid homogeneous division.
• Viewport conversion requires an explicit clip-depth convention; screen Y can be declared up or down.
• TryMakeViewportRay begins at the near plane and works for perspective or orthographic projections. TryMakePerspectiveViewportRay accepts the camera origin when an eye-origin ray is desired.

Geometry and culling

• Linear primitive parameters use physical distance when their direction is a Direction3.
• AABB and OBB half-extents are nonnegative. Touching boundaries intersect.
• Frustum planes point inward. Infinite-far frusta deactivate the far plane rather than storing an invalid sentinel.
• Culling is conservative. Plane-mask propagation retains only planes that intersected a parent bound.

Representations and backends

• Compute types select scalar or RTM primitives privately; backend identity is not part of ordinary public type names.
• Vec2f stays compact and scalar-backed so array loops can vectorize across values. Vec3f and Vec4f may retain SIMD-native storage.
• Packed CPU and GPU transfer representations name their exact byte layout. A compute vector is not described as universally GPU-blittable.
• Define MV_MATH_FORCE_SCALAR=1, or use XMake's force_scalar option, to select the portable scalar backend consistently for a target graph.