Crate tang 

tang — Math library for physical reality

Unified math foundation for geometry kernels, physics engines, and differentiable simulation. Generic over scalar type to support f32, f64, dual numbers (autodiff), and interval arithmetic from the same code.

Design principles

• Generic over Scalar type (f32, f64, Dual, Interval)
• #[repr(C)] everywhere for GPU interop
• No nalgebra dependency — full control of the stack
• Block-structured spatial matrices (no 6x6 index gymnastics)
• Dir3 derefs to Vec3 (no .as_ref() pain)

Structs

Dir3

A normalized direction vector in 3D space.

Dual

Forward-mode automatic differentiation via dual numbers.

Mat3

3x3 matrix, column-major storage.

Mat4

4x4 matrix, column-major storage.

Point2

A point in 2D space (distinct from Vec2 — points have position, vectors have direction).

Point3

A point in 3D space (distinct from Vec3 — points have position, vectors have direction).

Quat

Quaternion: w + xi + yj + zk

SpatialInertia

Spatial inertia — compact representation.

SpatialMat

6x6 spatial matrix, stored as four 3x3 blocks.

SpatialTransform

Spatial transform: Plücker coordinate transform.

SpatialVec

Spatial (6D) vector — represents either a twist (motion) or wrench (force).

Transform

Rigid body transform (isometry): rotation + translation.

Vec2

Vec3

Vec4

Constants

GRAVITY

Traits

Scalar

Trait for scalar types that can be used throughout kern-math.

Functions

skew

Cross-product matrix [v]× such that [v]× w = v × w