Matrix3

3x3 matrix functions using arrays of 9 elements in column-major order. Rotation angles are in degrees. Functions modify the first matrix in-place for zero allocations.

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Creating Matrices

// Create a new identity matrix
var m = mat3_create();  // [1,0,0, 0,1,0, 0,0,1]

// Create and set to rotation
var rot = mat3_create();
mat3_make_rotation(rot, 45);  // 45 degrees

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Matrix Layout

Matrices are stored in column-major order:

| m[0] m[3] m[6] |
| m[1] m[4] m[7] |
| m[2] m[5] m[8] |

When using mat3_set(), arguments are in row-major order for readability:

mat3_set(m, n11, n12, n13, n21, n22, n23, n31, n32, n33);

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Functions Reference

Creation

Function	Returns	Description
mat3_create()	Array	Creates a new identity 3x3 matrix

Setters

Function	Description
mat3_set(m, n11, n12, n13, n21, n22, n23, n31, n32, n33)	Sets elements (row-major input)
mat3_identity(m)	Resets to identity matrix

Clone / Copy

Function	Returns	Description
mat3_clone(m)	Array	Returns a new independent copy
mat3_copy(dest, src)	-	Copies src values into dest

Determinant / Inversion

Function	Returns	Description
mat3_determinant(m)	number	Computes the determinant
mat3_invert(m)	-	Inverts in-place (zero matrix if singular)

Transpose

Function	Description
mat3_transpose(m)	Transposes in place
mat3_transpose_into_array(m, arr)	Writes transposed matrix to array

Equality

Function	Returns	Description
mat3_equals(m, other)	boolean	True if matrices are equal

Multiplication

Function	Description
mat3_multiply(m, other)	Post-multiply: m = m * other
mat3_premultiply(m, other)	Pre-multiply: m = other * m
mat3_multiply_matrices(dest, a, b)	Sets dest = a * b
mat3_multiply_scalar(m, s)	Multiplies all elements by scalar

2D Transform Makers (in degrees)

Function	Description
mat3_make_rotation(m, angle)	Sets to 2D rotation matrix
mat3_make_scale(m, x, y)	Sets to 2D scale matrix
mat3_make_translation(m, x, y)	Sets to 2D translation matrix

2D Transform Operations (in degrees)

Function	Description
mat3_rotate(m, angle)	Applies rotation to matrix
mat3_scale(m, sx, sy)	Applies scale to matrix
mat3_translate(m, tx, ty)	Applies translation to matrix

Extract / Convert

Function	Description
mat3_extract_basis(m, xAxis, yAxis, zAxis)	Extracts column vectors (vec3)
mat3_set_matrix4(m, m4)	Sets from upper 3x3 of 4x4 matrix
mat3_get_normal_matrix(m, m4)	Computes normal matrix (inverse transpose)

UV Transform

Function	Description
mat3_set_uv_transform(m, tx, ty, sx, sy, rotation, cx, cy)	Sets UV transform matrix

Array Conversion

Function	Returns	Description
mat3_from_array(m, array, offset?)	-	Sets from array at offset
mat3_to_array(m, array?, offset?)	Array	Copies to array at offset

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Usage Examples

Basic Operations

var m = mat3_create();

// Set specific values
mat3_set(m, 1, 2, 3, 4, 5, 6, 7, 8, 9);

// Reset to identity
mat3_identity(m);

2D Transformations

var m = mat3_create();

// Create rotation matrix (45 degrees)
mat3_make_rotation(m, 45);

// Create scale matrix
mat3_make_scale(m, 2, 3);

// Create translation matrix
mat3_make_translation(m, 10, 20);

Combining Transforms

var m = mat3_create();

// Apply multiple transforms
mat3_translate(m, 10, 20);  // First translate
mat3_rotate(m, 45);         // Then rotate
mat3_scale(m, 2, 2);        // Then scale

Matrix Multiplication

var a = mat3_create();
var b = mat3_create();

mat3_make_rotation(a, 45);
mat3_make_scale(b, 2, 2);

// a = a * b
mat3_multiply(a, b);

// Or store result in separate matrix
var result = mat3_create();
mat3_multiply_matrices(result, a, b);

Inversion

var m = mat3_create();
mat3_make_scale(m, 2, 4);

mat3_invert(m);  // Now m is [0.5, 0, 0, 0, 0.25, 0, 0, 0, 1]

Normal Matrix

// Get normal matrix from a 4x4 model matrix
var normalMatrix = mat3_create();
var modelMatrix4 = [2,0,0,0, 0,2,0,0, 0,0,2,0, 0,0,0,1];

mat3_get_normal_matrix(normalMatrix, modelMatrix4);

Extract Basis Vectors

var m = mat3_create();
mat3_make_rotation(m, 45);

var xAxis = vec3_create();
var yAxis = vec3_create();
var zAxis = vec3_create();

mat3_extract_basis(m, xAxis, yAxis, zAxis);

UV Transform

var uvMatrix = mat3_create();

// offset, repeat, rotation (degrees), center
mat3_set_uv_transform(uvMatrix, 0.5, 0.5, 2, 2, 45, 0.5, 0.5);