glMatrix

A mat2d is a 2x3 matrix used for 2D transformations. It is represented as a 6-element array containing: [a, b, c, d, tx, ty].

This is a compact representation of a 3x3 matrix:

[a, b, 0,
 c, d, 0,
 tx, ty, 1]

The last column (the third column) is ignored to optimize performance.

Check for equality between two 2x2 matrices:

• exactEquals(a, b): Returns true if the matrices have exactly the same elements in the same position (using ===).
• equals(a, b): Returns true if the matrices are approximately equal, accounting for floating-point precision using glMatrix.EPSILON.

You can derive a mat3 from other matrix types using these functions:

• fromMat4(out, a): Copies the upper-left 3x3 values from a 4x4 matrix.
• fromMat2d(out, a): Copies values from a 2D matrix.
• fromQuat(out, q): Calculates a 3x3 matrix from a quaternion.
• fromTranslation(out, v): Creates a matrix from a 2D translation vector.
• fromRotation(out, rad): Creates a matrix from a rotation angle (radians).
• fromScaling(out, v): Creates a matrix from a 2D scaling vector.

Use these functions to instantiate new 2x3 matrices or reset existing ones.

• create(): Returns a new identity mat2d.
• clone(a): Returns a new mat2d containing the values of matrix a.
• copy(out, a): Copies values from source matrix a into receiving matrix out.
• identity(out): Sets the receiving matrix out to the identity matrix.
• fromValues(a, b, c, d, tx, ty): Creates a new mat2d with the specified components.
• set(out, a, b, c, d, tx, ty): Sets the components of the receiving matrix out to the specified values.

Check for equality between vectors:

• exactEquals(a, b): Returns true if elements are exactly equal (===).
• equals(a, b): Returns true if elements are approximately equal, accounting for floating-point epsilon.
• str(a): Returns a string representation: vec2(x, y).

The forEach function allows performing an operation over an array of vec2 elements. It handles both tightly packed arrays and arrays with a stride.

Parameters:

• a: The array of vectors to iterate over.
• stride: Number of elements between the start of each vec2 (defaults to 2 if 0).
• offset: Number of elements to skip at the beginning (defaults to 0).
• count: Number of vec2s to iterate over (0 for entire array).
• fn: Function to call for each vector. Signature: fn(out, a, arg).
• arg: Additional argument passed to fn.

Use these functions for advanced matrix calculations:

• invert(out, a): Inverts the matrix. Returns null if the matrix is not invertible.
• determinant(a): Returns the determinant of the matrix.
• adjoint(out, a): Calculates the adjugate (adjoint) of the matrix.
• normalFromMat4(out, a): Calculates a 3x3 normal matrix (transpose inverse) from a 4x4 matrix. Returns null if not invertible.

The gl-matrix package provides high-performance mathematical operations for graphics programming. You can import specific modules for 2D/3D vectors, matrices, and quaternions. The main entrypoint exports the following modules:

• glMatrix: Common utilities and constants.
• mat2, mat2d, mat3, mat4: 2x2, 2D affine, 3x3, and 4x4 matrix operations.
• quat, quat2: Quaternion operations.
• vec2, vec3, vec4: 2D, 3D, and 4D vector operations.

Extract mathematical properties from a 2x2 matrix:

• determinant(a): Returns the determinant of matrix a.
• invert(out, a): Inverts matrix a and stores the result in out. Returns null if the matrix is not invertible.
• adjoint(out, a): Calculates the adjugate (adjoint) of matrix a and stores it in out.
• frob(a): Returns the Frobenius norm of matrix a.
• LDU(L, D, U, a): Factorizes matrix a into Lower triangular (L), Diagonal (D), and Upper triangular (U) matrices.