Interactive modeling of smooth manifold meshes with arbitrary topology: G1 stitched bi-cubic Bézier patches

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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 C2 continuous Bi-Cubic Bézier patches that are guaranteed to be stitched with G1 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 Bézier patch, where the positions of the 16 control points are obtained from the limit surface of the Doo–Sabin subdivision scheme.This approach, when combined with topological modeling, provides a framework for real-time interactive modeling of smooth manifold meshes with arbitrary topology. Based on this approach, we have developed an interactive modeling system that allows users to work with smooth surfaces in real-time by opening or closing holes, creating handles, and combining and disconnecting surfaces. The paper has three main contributions: (1) We guarantee that our method will produce only smooth manifold meshes with C2 continuous Bi-Cubic Bézier patches. (2) We guarantee visual smoothness for any arbitrary topological structure by providing geometric G1 continuity in boundaries of patches. (3) We demonstrate that smooth surfaces with arbitrary topology can be created interactively in real-time using parametric patches.