All geometry in computer graphics are transformed by position * transform matrix; The issue is the fact that position is a vector with 3 components (x,y,z); And transform matrix is a 4 by 4 with one column that can be dumped(at least in my case). So my transform matrix is now a 3 by 4 matrix:
axis x { x, y, z }
axis y { x, y, z }
axis z { x, y, z }
position axis { x, y, z }
multiplied with position vector { x, y ,z }
If I dump position axis this can be done with standard formula of matrix multiplication. But it does not transform it. I can make the position vector with 4 components { x, y, z, w } but don't know what to do with the w? My only solution is a slow one, put position vector in a new transform matrix in position axis and multiply them. But it is computationally expensive. How to approach such problem?