Generation of Interpolatory Smooth Bézier Patches over Quadrilateral Mesh Based on C-C Subdivision

Constructing smooth surface over arbitrary topological quadrilateral mesh is an important issue in CAGD.This paper presents an algorithm for generating smoothly connected Bézier patches that interpolate the mesh vertices over a quadrilateral mesh based on C-C subdivision.The input quadrilateral mesh is taken as the initial control mesh of C-C subdivision,and the limit surface of C-C subdivision is converted into Bézier patches.For each facet of the quadrilateral mesh,a Bézier patch is obtained.The Bézier patches are G¹-continuous along boundaries connecting to extraordinary points and C²-continuous everywhere else.For resolving the shrinking problem of C-C subdivision,a recursive method to expand the initial control mesh is proposed based on the deviation analysis.The final surface generated from the expanded mesh interpolates the vertices of the input quadrilateral mesh.The experimental data show that the presented algorithm is effective and the constructed surface has good smoothness and continuity.It can be well applied to reconstruct smooth surface from quadrilateral mesh.