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Proceedings of CAD'15, 2015, 259-263
A G2 Interpolation Scheme for Polar Surface

Jianzhong Wang, Fuhua Cheng, University of Kentucky

Abstract. Subdivision surfaces have been widely used in CAD, gaming and computer graphics. Catmull-Clark subdivision (CCS), based on tensor product bi-cubic B-Splines, is one of the most important subdivision schemes. The surfaces generated by the scheme are C2 continuous everywhere except at extraordinary points, where they are C1 continuous. A shortcoming inherent in CCS surfaces is the ripple problem, that is, ripples tend to appear around an extraordinary point with high valence. In the past, research focused on improving curvature distribution at extraordinary points.  However, with quad mesh structure of CCS surfaces, ripples could not be avoided in high valence cases. To handle this artifact, Polar surface are studied by a number of researchers. A Polar surface has a quad/triangular mixed mesh structure. A bi-cubic Polar subdivision scheme is presented in that sets up the control mesh refinement rules for Polar configuration so that the limit surface is C1 continuous and curvature bounded. A Polar surface handles high valence cases well, but there are some issues to solve for connecting them to Catmull-Clark meshes. For instance, because of the mismatch on the mesh between radial subdivision and Catmull-Clark subdivision, given a polar vertex of valence n, at the kth level, its generalized bi-cubic subdivision scheme generates 2^k subfaces and expands the valence to n2^k.

Keywords. Interpolation, Polar subdivision, Catmull-Clark subdivision, Bezier crust, Polar embedded Catmull-Clark subdivison

DOI: 10.14733/cadconfP.2015.259-263