C1 Hermite interpolations with RPH curves

In this paper, we study C-1 Hermite interpolation with a spatial rational Pythagorean hodograph (RPH) curve for a regular C-1 Hermite data set. In particular, we completely classify simple PH Mobius cubics and prove that there exist two scaled Enneper surfaces as a PH-preserving mapping satisfying the given C-1 Hermite data set. Also, we give the algorithm to construct RPH curves on the Enneper surface by using PH Mobius cubics and scaled PH-preserving mappings. Finally, we calculate arc-length and bending energy of these RPH curves to choice the best RPH curves on the Enneper surface, and give some examples for RPH curves.