Fast 3D-vector matrix transformation using SSE4

In this blog-post we'd like to show how to efficiently transform multiple 3D vectors using an affine transformation matrix. Each vector has three coordinates (x, y and z) and the matrix consists of three rows each with 4 elements (3 for rotation/scale + 1 for translation). In order to multiply a 3-element vector with a 3x4 matrix, we add an additional 1 at the end of the 3D vector: