On the interpolation of non-iso-parametric curves

Abstract

Exact curve interpolation has frequently been addressed in a variety of modeling domains. The suggested solutions uniformly assume the interpolated curve to be iso-parametric along one or the other of the parameter lines controlling the interpolating surface. However, once this assumption is abandoned, the difficulty of this problem rises to a degree that no known method is currently in existence which is able to solve this problem efficiently enough for practical purposes. In this context, this paper presents an algorithm capable of embedding a cubic B-spline curve within a regular quad-based Catmull-Clark subdivision surface along any arbitrary direction not necessarily along any of the parameter lines controlling the surface.