Smooth Ternary Subdivision of Triangle Meshes

Standard binary subdivision operators may generate surfaces with unbounded curvatures at points corresponding to ex- traordinary vertices. This defect can be removed by manipulating the eigenvalues of the subdivision operator to impose a bounded curvature spectrum. This procedure may enlarge the support of an extraordi- nary vertex beyond its two-ring. In the ternary subdivision setting, where mesh edges are split 3 to 1, no such enlargement occurs. In this paper, we generalize ternary subdivision of C 2 quartic box splines to arbitrary triangulations. The resulting subdivision algorithm has bounded curvatures and is designed to maintain the convex hull prop- erty.