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Proceedings of CAD'16, 2016, 322-326
Subdivision Based Piecewise C2 Surfaces Construction for Meshes of Arbitrary Topology
Abstract. It has been a long desire and a long effort of the computer graphics and geometric design community to have a nice approach to construct smooth surfaces from meshes of arbitrary topology. A nice approach should satisfy the following requirements: (1) simple: no linear or non-linear system needs to be solved; (2) local: changes to a control mesh only affect the resulting surface locally; (3) smooth: the resulting surface is C2 everywhere, including at any extra-ordinary points; (4) convex: the resulting surface satisfies the convex hull property; and (5) explicit: the resulting surface has an explicit expression of the form WMG for each patch, where W is a parameter vector, M is a constant matrix and G is the control point vector, so that surface evaluation, and computation of the first and second derivatives, normal and curvature at any point can be easily done from the simple representation. When the degree (valence) of each vertex of the given mesh is 4, the algorithm for generating tensor product B-spline surfaces is such a nice approach. However, for meshes not in this category, as far as we know, there is no such an approach reported in the literature yet, although there are approaches that satisfy almost all of the above requirements.
Keywords. Subdivision Surface, C2 Smooth Surface, 3D Modeling