3D Transformation [Translation, Rotation and Scaling] in C/C++

In a three-dimensional homogeneous coordinates representation, a point is translated from position P = (x, y, z) to position P’ = (x’, y’, z’) with the following equations.

To generate a rotation transformation for an object, we must designate an axis of rotation (about which the the object is to be rotated) and the amount of angular rotation. Unlike 2D applications, where all transformations are carried out in the xy plane, a three-dimensional rotation can be specified around any line in space. I will cover rotation about arbitrary axis in another post, here the discussion is restricted to rotation about coordinate axes.