C 1 Hermite Interpolation with PH Curves Using the Enneper Surface

Abstract

We show that the geometric and PH-preserving properties of the Enneper surface allow us to find PH interpolants for all regular $C^{\mathrm{1}}$ Hermite data-sets. Each such data-set is satisfied by two scaled Enneper surfaces, and we can obtain four interpolants on each surface. Examples of these interpolants were found to be better, in terms of bending energy and arc-length, than those obtained using a previous PH-preserving mapping.