use math — Matrices & Quaternions

Matrix and quaternion types for 3D transformations. All types are part of the math module.

See also: Scalar functions | Vectors

Mat4

4x4 matrix in column-major order (OpenGL compatible).

Struct

Constructors

fn mat4_identity

Create identity Mat4.

Signature: ( -- m:Mat4)

Example:

math::mat4_identity  // m

fn mat4_rotation_x

Create rotation Mat4 around X axis.

Signature: (angle:f64 -- m:Mat4)

Example:

1.57 math::mat4_rotation_x  // m

fn mat4_rotation_y

Create rotation Mat4 around Y axis.

Signature: (angle:f64 -- m:Mat4)

Example:

1.57 math::mat4_rotation_y  // m

fn mat4_rotation_z

Create rotation Mat4 around Z axis.

Signature: (angle:f64 -- m:Mat4)

Example:

1.57 math::mat4_rotation_z  // m

fn mat4_scaling

Create scale Mat4.

Signature: (sx:f64 sy:f64 sz:f64 -- m:Mat4)

Example:

2.0 2.0 2.0 math::mat4_scaling  // m

fn mat4_translation

Create translation Mat4.

Signature: (x:f64 y:f64 z:f64 -- m:Mat4)

Example:

1.0 2.0 3.0 math::mat4_translation  // m

fn mat4_zero

Create zero Mat4.

Signature: ( -- m:Mat4)

Example:

math::mat4_zero  // m

fn mat4_look_at

Create a look-at view matrix.

Signature: (eye:Vec3 target:Vec3 up:Vec3 -- m:Mat4)

Example:

eye target up math::mat4_look_at -> view

fn mat4_perspective

Create a perspective projection matrix.

Signature: (fov:f64 aspect:f64 near:f64 far:f64 -- m:Mat4)

Example:

1.047 1.777 0.1 100.0 math::mat4_perspective -> proj

fn mat4_orthographic

Create an orthographic projection matrix.

Signature: (left:f64 right:f64 bottom:f64 top:f64 near:f64 far:f64 -- m:Mat4)

Example:

-1.0 1.0 -1.0 1.0 0.1 100.0 math::mat4_orthographic -> proj

fn mat4_from_quat

Create rotation matrix from quaternion.

Signature: (q:Quat -- m:Mat4)

Example:

q math::mat4_from_quat -> rot_mat

Methods

fn mul

Matrix multiplication.

Signature: (m:Mat4) mul(other:Mat4 -- result:Mat4)

Example:

other m mul -> product

fn determinant

Matrix determinant.

Signature: (m:Mat4) determinant( -- result:f64)

Example:

m determinant -> det

fn inverse

Matrix inverse.

Signature: (m:Mat4) inverse( -- result:Mat4)

Example:

m inverse -> m_inv

fn transpose

Transpose this matrix.

Signature: (m:Mat4) transpose( -- result:Mat4)

Example:

m transpose  // m_t

fn transform_point

Transform a Vec3 point by this matrix (w=1).

Signature: (m:Mat4) transform_point(v:Vec3 -- result:Vec3)

Example:

point m transform_point -> transformed

fn transform_vec4

Transform a Vec4 by this matrix.

Signature: (m:Mat4) transform_vec4(v:Vec4 -- result:Vec4)

Example:

vec m transform_vec4 -> transformed

Quat

Quaternion for representing rotations. Stored as (w, x, y, z) where w is the scalar part.

Struct

Constructors

fn quat_identity

Create identity quaternion (no rotation).

Signature: ( -- q:Quat)

Example:

math::quat_identity  // q

fn quat_from_axis_angle

Create quaternion from axis and angle.

Signature: (axis:Vec3 angle:f64 -- result:Quat)

Example:

axis 1.57 math::quat_from_axis_angle -> q

fn quat_from_euler

Create quaternion from Euler angles (XYZ order).

Signature: (pitch:f64 yaw:f64 roll:f64 -- result:Quat)

Example:

0.0 1.57 0.0 math::quat_from_euler -> q

Methods

fn conjugate

Conjugate of this quaternion.

Signature: (q:Quat) conjugate( -- result:Quat)

Example:

q conjugate  // q_conj

fn dot

Dot product with another quaternion.

Signature: (q:Quat) dot(other:Quat -- result:f64)

Example:

other q dot  // d

fn length

Length (magnitude) of this quaternion.

Signature: (q:Quat) length( -- result:f64)

Example:

q length  // len

fn mul

Quaternion multiplication.

Signature: (q:Quat) mul(other:Quat -- result:Quat)

Example:

other q mul  // product

fn normalize

Normalize this quaternion to unit length.

Signature: (q:Quat) normalize( -- result:Quat)

Example:

q normalize  // unit_q

fn inverse

Inverse of this quaternion.

Signature: (q:Quat) inverse( -- result:Quat)

Example:

q inverse -> q_inv

fn length_sq

Squared length of quaternion.

Signature: (q:Quat) length_sq( -- result:f64)

Example:

q length_sq -> len_sq

fn slerp

Spherical linear interpolation to another quaternion.

Signature: (q:Quat) slerp(other:Quat t:f64 -- result:Quat)

Example:

other 0.5 q slerp -> mid

fn rotate_vec3

Rotate a Vec3 by this quaternion.

Signature: (q:Quat) rotate_vec3(v:Vec3 -- result:Vec3)

Example:

v q rotate_vec3 -> rotated