The Ultimate Guide to Matrix Multiplication and Ordering
Matrix multiplication in graphics APIs is ridiculously confusing. People are often confused about the right order of multiplying their matrices, and about row-major, column-major, pre-multiplication, post-multiplication, row vectors and column vectors, and transposing. I plan for this to be the last resource you’ll never need to check. If matrices are so confusing, why do we even use them in the first place? Our goal with using matrices in graphics is using them to transform objects in space, or to transform space itself. If we imagine a cube with some X, Y, and Z coordinates, we can translate that cube along the X axis by 5 units by adding a constant 5: If we wanted to scale the cube by 2, we can multiply by 2: These are both very simple forms of transformations. So why go more complicated and use matrices? Well, let’s introduce rotation. Scaling and translating happen along a single axis, while rotation happens within a plane. Rotating a point around the Y axis changes the point’s va