C2 continuous spline surfaces over catmull-clark meshes

Abstract

An efficient method for generating a C2 continuous spline surface over a Catmull-Clark mesh is presented in this paper. The spline surface is the same as the Catmull-Clark limit surface except in the immediate neighborhood of the irregular mesh points. The construction process presented in this paper consists of three steps: subdividing the initial mesh at most twice using the Catmull-Clark subdivision rules; generating a bi-cubic Bézier patch for each regular face of the resultant mesh; generating a C2 Gregory patch around each irregular vertex of the mesh. The union of all patches forms a C2 spline surface. Differing from the previous methods proposed by Loop, DeRose and Peters, this method achieves an overall C2 smoothness rather than only a C1 continuity. © Springer-Verlag Berlin Heidelberg 2005.