Matrices

Overview

3x2, 3x3, and 4x4 matrix types for 2D and 3D transformations. Matrices are stored in row-major order and support construction, multiplication, inversion, and transformation of points and vectors.

Why Use This?

Matrices are essential for combining translation, rotation, and scaling transformations, building camera view matrices, and creating projection matrices for rendering.

Types

Type	Scalar	Description
`lm2_m3x2_f64`	`double`	3x2 affine 2D transformation matrix
`lm2_m3x2_f32`	`float`	3x2 affine 2D transformation matrix
`lm2_m3x3_f64`	`double`	3x3 matrix (2D homogeneous / 3D rotation)
`lm2_m3x3_f32`	`float`	3x3 matrix
`lm2_m4x4_f64`	`double`	4x4 3D transformation matrix
`lm2_m4x4_f32`	`float`	4x4 3D transformation matrix

Matrix 3x2 Layout

Row-major, 6 elements representing a 2D affine transform:

[m00 m01 m02]   [a  c  tx]
[m10 m11 m12] = [b  d  ty]
[  0   0   1]   (implicit third row, never stored)

Access via named fields (m.m00, m.tx, m.a, …) or flat array (m.e[0] through m.e[5]).

Functions (3x2)

All functions shown with _f32 suffix. Also available with _f64.

Construction

Function	Description
`lm2_m3x2_identity_f32()`	Identity matrix
`lm2_m3x2_zero_f32()`	Zero matrix
`lm2_m3x2_make_f32(m00..m12)`	Construct from 6 values

Transformation Builders

Function	Description
`lm2_m3x2_scale_f32(scale)`	Scale by v2
`lm2_m3x2_scale_uniform_f32(s)`	Uniform scale
`lm2_m3x2_translate_f32(translation)`	Translation matrix
`lm2_m3x2_rotate_f32(angle)`	Rotation by angle (radians)
`lm2_m3x2_rotate_around_pivot_f32(angle, pivot)`	Rotation around a pivot point
`lm2_m3x2_scale_translate_f32(scale, translation)`	Combined scale + translate
`lm2_m3x2_world_transform_f32(translation, scale, rotation)`	Full TRS 2D world transform

Operations

Function	Description
`lm2_m3x2_mul_f32(a, b)`	Matrix multiplication (applies b first, then a)
`lm2_m3x2_inverse_f32(m)`	Inverse
`lm2_m3x2_determinant_f32(m)`	Determinant

Transforming Points and Vectors

Function	Description
`lm2_m3x2_transform_point_f32(m, v)`	Transform 2D point (applies translation)
`lm2_m3x2_transform_vector_f32(m, v)`	Transform 2D direction (ignores translation)
`lm2_m3x2_transform_points_f32(m, points, count)`	Transform array of points in-place
`lm2_m3x2_transform_points_src_dst_f32(m, src, dst, count)`	Transform array of points (separate output)

Extraction

Function	Description
`lm2_m3x2_get_rotation_f32(m)`	Extract rotation angle from matrix
`lm2_m3x2_get_scale_f32(m)`	Extract scale from matrix
`lm2_m3x2_get_translation_f32(m)`	Extract translation from matrix

Projection

Function	Description
`lm2_m3x2_ortho_f32(left, right, bottom, top)`	2D orthographic projection

Matrix 3x3 Layout

Row-major, 9 elements:

[m00 m01 m02]
[m10 m11 m12]
[m20 m21 m22]

Access via named fields (m.m00, …) or flat array (m.e[0] through m.e[8]).

Used for 2D homogeneous transformations (with implicit bottom row [0 0 1]) or 3D rotation matrices.

Functions (3x3)

All functions shown with _f32 suffix. Also available with _f64.

Construction

Function	Description
`lm2_m3x3_identity_f32()`	Identity matrix
`lm2_m3x3_zero_f32()`	Zero matrix
`lm2_m3x3_make_f32(m00..m22)`	Construct from 9 values

Transformation Builders

Function	Description
`lm2_m3x3_scale_f32(scale)`	Scale by v2
`lm2_m3x3_scale_uniform_f32(s)`	Uniform scale
`lm2_m3x3_translate_f32(translation)`	Translation matrix (2D homogeneous)
`lm2_m3x3_rotate_f32(angle)`	Rotation by angle (radians)
`lm2_m3x3_rotate_around_pivot_f32(angle, pivot)`	Rotation around a pivot point
`lm2_m3x3_scale_translate_f32(scale, translation)`	Combined scale + translate

Operations

Function	Description
`lm2_m3x3_mul_f32(a, b)`	Matrix multiplication
`lm2_m3x3_transpose_f32(m)`	Transpose
`lm2_m3x3_inverse_f32(m)`	Inverse
`lm2_m3x3_determinant_f32(m)`	Determinant
`lm2_m3x3_trace_f32(m)`	Trace (sum of diagonal)

Transforming Points and Vectors

Function	Description
`lm2_m3x3_transform_point_f32(m, v)`	Transform 2D point (applies translation)
`lm2_m3x3_transform_vector_f32(m, v)`	Transform 2D direction (ignores translation)
`lm2_m3x3_transform_f32(m, v)`	Transform full 3D vector
`lm2_m3x3_transform_points_f32(m, points, count)`	Transform array of 2D points in-place
`lm2_m3x3_transform_points_src_dst_f32(m, src, dst, count)`	Transform array of 2D points (separate output)

Extraction

Function	Description
`lm2_m3x3_get_rotation_f32(m)`	Extract rotation angle from matrix
`lm2_m3x3_get_scale_f32(m)`	Extract scale from matrix
`lm2_m3x3_get_translation_f32(m)`	Extract translation from matrix

[m00 m01 m02 m03]
[m10 m11 m12 m13]
[m20 m21 m22 m23]
[m30 m31 m32 m33]

Access via named fields (m.m00, m.m01, …) or flat array (m.e[0] through m.e[15]).

Functions (4x4)

Construction

Function	Description
`lm2_m4x4_identity_f32()`	Identity matrix
`lm2_m4x4_zero_f32()`	Zero matrix
`lm2_m4x4_make_f32(m00..m33)`	Construct from 16 values

Transformation Builders

Function	Description
`lm2_m4x4_scale_f32(scale)`	Scale by v3 (non-uniform)
`lm2_m4x4_scale_uniform_f32(s)`	Uniform scale
`lm2_m4x4_translate_f32(translation)`	Translation matrix
`lm2_m4x4_rotate_x_f32(angle)`	Rotation around X axis
`lm2_m4x4_rotate_y_f32(angle)`	Rotation around Y axis
`lm2_m4x4_rotate_z_f32(angle)`	Rotation around Z axis
`lm2_m4x4_rotate_axis_f32(axis, angle)`	Rotation around arbitrary axis
`lm2_m4x4_scale_translate_f32(scale, translation)`	Combined scale + translate
`lm2_m4x4_world_transform_f32(translation, scale, euler)`	Full TRS world transform

Operations

Function	Description
`lm2_m4x4_mul_f32(a, b)`	Matrix multiplication
`lm2_m4x4_transpose_f32(m)`	Transpose
`lm2_m4x4_inverse_f32(m)`	Inverse
`lm2_m4x4_determinant_f32(m)`	Determinant
`lm2_m4x4_trace_f32(m)`	Trace (sum of diagonal)

Transforming Points and Vectors

Function	Description
`lm2_m4x4_transform_point_f32(m, v)`	Transform 3D point (applies translation)
`lm2_m4x4_transform_vector_f32(m, v)`	Transform 3D direction (ignores translation)
`lm2_m4x4_transform_f32(m, v)`	Transform 4D vector
`lm2_m4x4_transform_points_f32(m, points, count)`	Transform array of points in-place
`lm2_m4x4_transform_points_src_dst_f32(m, src, dst, count)`	Transform array of points (separate output)

Extraction

Function	Description
`lm2_m4x4_get_scale_f32(m)`	Extract scale from matrix
`lm2_m4x4_get_translation_f32(m)`	Extract translation from matrix

Camera and Projection

`lm2_m4x4_look_at_f32`

Build a view matrix from eye position, target, and up vector.

Signature: lm2_m4x4_f32 lm2_m4x4_look_at_f32(lm2_v3_f32 eye, lm2_v3_f32 target, lm2_v3_f32 up)

`lm2_m4x4_perspective_f32`

Build a perspective projection matrix.

Signature: lm2_m4x4_f32 lm2_m4x4_perspective_f32(float fov_y, float aspect, float near_plane, float far_plane)

Parameters:

fov_y — Vertical field of view in radians
aspect — Width / height ratio
near_plane — Near clipping distance
far_plane — Far clipping distance

`lm2_m4x4_ortho_f32`

Build an orthographic projection matrix.

Signature: lm2_m4x4_f32 lm2_m4x4_ortho_f32(float left, float right, float bottom, float top, float near_plane, float far_plane)

Quaternion Conversions

Function	Description
`lm2_m4x4_from_quat_f32(q)`	Convert quaternion to 4x4 rotation matrix
`lm2_m4x4_to_quat_f32(m)`	Extract quaternion from rotation matrix

Example

// Build model-view-projection matrix
lm2_m4x4_f32 model = lm2_m4x4_world_transform_f32(
    lm2_v3_make_f32(0, 0, -5),     // position
    lm2_v3_splat_f32(1.0f),         // scale
    lm2_v3_make_f32(0, 0.5f, 0)    // rotation (euler)
);

lm2_m4x4_f32 view = lm2_m4x4_look_at_f32(
    lm2_v3_make_f32(0, 3, 8),
    lm2_v3_zero_f32(),
    lm2_v3_make_f32(0, 1, 0)
);

lm2_m4x4_f32 proj = lm2_m4x4_perspective_f32(1.047f, 16.0f/9.0f, 0.1f, 100.0f);

lm2_m4x4_f32 mvp = lm2_m4x4_mul_f32(
    lm2_m4x4_mul_f32(proj, view), model
);