Minkowski Pythagorean-hodograph preserving mappings

We state and prove the sufficient and necessary condition for a mapping to be a scaled MPH-preserving mapping which preserves the MPH property of a curve with rescaling the speed by a rational function in R2,1, and show how to produce polynomial scaled MPH-preserving mappings from given generating polynomials. We introduce s-cubic MPH-preserving mappings of the first kind, and their corresponding surfaces. We show that these mappings can be used to solve interpolation problems for C1 Hermite data-sets with admissible velocity vectors on their corresponding surfaces.