As long as your class saves elements in memory in that order, it doesn't matter what notation your class constructor uses for matrices. As far as the OpenGL implementation is concerned, a 4x4 matrix is just 16 values grouped into 4 vectors sequentially, representing axes x, y, z and translation respectively. OpenGL literature commonly use the column-major pencil-and-paper notation, but that has no bearing how OpenGL accesses element values in a matrix. Matrix m = īut GL uses column-major matrices and column vectors, while DX uses row vectors and row-major matrices. Such notation allows a more natural mental mapping between matrix elements and values laid out flat in memory. Therefore, I'd recommend writing matrix classes that has an interface for accessing vectors in a row-major notation. If you were to read out each row sequentially in a row-major representation, from left to right, each element visited would correspond to the same sequence of values laid out linearly in memory.

Memory layout does not directly relate to row- vs column-major order - you also need to decide whether to use row or column vectors. (This is the principal source of confusion between row-major and row-vector). This can be seen from the matrix identity (AB) T = B TA T.įinal note, it is possible to have row-major matrices and column vectors and vice versa but you'll almost always see row-major ordering used with row-vectors and column-major ordering with column-vectors due to the convenience of having your matrices be laid out as arrays of vectors in memory. (This is also the case if going from row-major to column-major, one of the sources of confusion). Note that this means when going from row-vectors to column-vectors the matrices will need to be transposed to get the same matrix-vector product. Whereas with row-vectors the order of operations is: | a11 a12 a13 |

When using column-vectors the order of operations is: Ax = b

$zmatrix coordinate system$

The image says 'assuming you use the row-major order convention' but this is making the very common mistake of conflating the term row-major which relates to the ordering of matrix elements in memory and row-vector which relates to the ordering of matrix-vector operations.

Zmatrix coordinate system