math::rotation

math::rotation

The rotation module provides 3D rotation utilities: ZYX Euler-angle conversion, matrix application, composition, and inverse. All angles are in radians and matrices are 3x3 Mat<number> values.

Import

use std::math::rotation

Convention

ZYX Euler convention: R = Rz(alpha) * Ry(beta) * Rx(gamma). Alpha is yaw (Z), beta is pitch (Y), gamma is roll (X).

Functions

rotation::euler_to_matrix(alpha, beta, gamma) -> Mat<number>

Build a 3x3 rotation matrix from ZYX Euler angles.

use std::math::rotation

let identity = rotation::euler_to_matrix(0.0, 0.0, 0.0)

rotation::matrix_to_euler(m) -> Array<number>

Extract [alpha, beta, gamma] ZYX Euler angles from a 3x3 rotation matrix. Handles gimbal lock when beta is near +/- pi/2.

let m = rotation::euler_to_matrix(0.1, 0.2, 0.3)
let angles = rotation::matrix_to_euler(m)
// angles ~ [0.1, 0.2, 0.3]

rotation::rotation_apply(rot, points) -> Mat<number>

Apply a rotation matrix to a set of points (Nx3 matrix, each row is a point). Returns an Nx3 matrix of rotated points.

rotation::rotation_inverse(rot) -> Mat<number>

Inverse of a rotation matrix. For orthogonal rotation matrices, the inverse equals the transpose.

rotation::rotation_compose(r1, r2) -> Mat<number>

Compose two rotations. The result applies r2 first, then r1.

rotation::rotation_from_rows(rows) -> Mat<number>

Construct a Mat<number> from an array of row arrays (e.g. [[1,0,0], [0,1,0], [0,0,1]]).

rotation::normalize_euler(angles) -> Array<number>

Wrap each angle to [-pi, pi].

let wrapped = rotation::normalize_euler([7.0, -7.0, 0.0])

See Also

• math::linalg — vector operations
• math::interpolation — grid interpolation
• physics — physics primitives that consume rotation matrices