Designing Catmull-Clark subdivision surfaces with curve interpolation constraints

Abstract

Generating subdivision surfaces with curve interpolation constraints is needed in both computer graphics and geometric modeling applications. In the context of the Doo–Sabin subdivision scheme, this can be achieved through the use of polygonal complexes as suggested by Nasri (Presented at the Fifth Siam Conference on Geometric Design, Nashville, 1997; Comput. Aided Geom. Des. 17 (2000) 595). A polygonal complex is simply a polygonal mesh whose structure depends on the subdivision scheme used and whose limit of subdivision is a curve rather than a surface. The subdivision scheme applied to these complexes is basically the same applied to the mesh defining the surface but with possible modification of its subdivision rules. The advantage of that lies in the retention of the same subdivision coefficients, thus saving the need for any further analysis at the limit. In this paper, we propose a method for using polygonal complexes to generate Catmull–Clark subdivision surfaces with curve interpolation constraints. The polygonal complexes are embedded here in the given mesh, which can possibly interpolate intersecting curves.