Interactive modeling of smooth manifold meshes with arbitrary topology: G(1) stitched bi-cubic Bezier patches

摘要

In this paper, we present a new piecewise parametric approach to obtain smooth surfaces from any given orientable 2-manifold polynomial control mesh. Our approach provides C-2 continuous Bi-Cubic Bezier patches that are guaranteed to be stitched with G(1) continuity regardless of the underlying mesh topology. A high level summary of the approach can be given as a two-step process: (1) Starting from an orientable 2-manifold mesh we apply vertex-insertion, which is remeshing algorithm of Catmull-Clark subdivision, to break that surface into a set of all quadrilateral patches. (2) for each such quadrilateral patch, we construct a Bi-Cubic Bezier patch, where the positions of the 16 control points are obtained from the limit surface of the Doo-Sabin subdivision scheme.