Clifford algebra, spin representation, and rational parameterization of curves and surfaces (Q1599371)

A representation map called Pyhtogorean Hodograph (PH) map which is a natural extension of the usual twisted adjoint representation of the spin group to a larger set of the even Clifford algebra is considered. The PH map has been used to provide a framework that unifies different known forms of PH curves [cf. \textit{R. T. Farouki} and \textit{T. Sakkalis}, IBM Res. Development 34, 736-752 (1990)]. The PH representation map in the context of the 4 dimensional Minkowski space is also been studied. In contrast to the situation in 2 or 3 dimensions where only certain special curves qualify for PH status, it is observed that every space like polynomial curve in 4 dimensional Minkowski space is a PH curve.