The graphene:matrix-t structure is a type that provides a 4x4 square matrix, useful for representing 3D transformations. The matrix is treated as row-major, that is, it has four vectors x, y, z, and w representing rows, and elements of each vector are a column:

⎡ m.x ⎤      ⎛ x.x  x.y  x.z  x.w ⎞
⎜ m.y ⎟  =>  ⎜ y.x  y.y  y.z  y.w ⎟
⎜ m.z ⎟      ⎜ z.x  z.y  z.z  z.w ⎟
⎣ m.w ⎦      ⎝ w.x  w.y  w.z  w.w ⎠  

It is possible to easily convert a graphene:matrix-t instance to and from an array of floating point values that can be used with other libraries.

The contents of a graphene:matrix-t instance are private, and direct access is not possible. You can modify and read the contents of a graphene:matrix-t instance only through the provided API.

Conventions

Graphene uses left-multiplication for all its operations on vectors and matrices. In other words, given a matrix A and a vector b, the result of a multiplication is going to be:

res = b × A  

Multiplying two matrices, on the other hand, will use right-multiplication. Given two matrices A and B, the result of the multiplication is going to be

res = A × B  

as the implementation will multiply each row vector of matrix A with the matrix B to obtain the new row vectors of the result matrix:

res = ⎡ A.x × B ⎤
      ⎜ A.y × B ⎟
      ⎜ A.z × B ⎟
      ⎣ A.w × B ⎦