One of the most popular mathematical tools in fields of robotics, mechanisms and computer graphics is the 4x4 homogeneous transformation matrix. In previous work we applied this matrix to the optical domains of flat and spherical surfaces for: (1) skew ray tracing to determine the paths of skew rays being reflected/refracted; (2) sensitivity analysis to determine by direct mathematical analysis the differential change of incident point and reflected/refracted vector with respect to change in incident light source. The present work extends our previous work to include the case of parabaloidal boundary surfaces.