Parametric surface interpolation

Abstract

A survey comparing methods for constructing smooth parametric surfaces to interpolate vertices and normal vectors of a triangulated polyhedron is presented. Particular attention is paid to the quality or fairness of the fit, measured by examining how curvature is distributed over the surface. The methods surveyed all generate surfaces composed of one or more surface patches per triangular facet of the input polyhedron. The approaches require an analysis of the number of constraints versus the number of degrees of freedom. Constraints include not only the interpolation conditions, but also continuity conditions imposed where adjacent surface patches abutt. Once the constraints are satisfied, there are generally surplus degrees of freedom. It is shown that the setting of these remaining free parameters can dramatically affect the shape of the surface, so the various methods are classified according to how they assign values to the free parameters.<>