Approximating tensor product Bézier surfaces with tangent plane continuity

Authors:
Lizheng Lu
Affiliations:
College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

We present a simple method for degree reduction of tensor product Bezier surfaces with tangent plane continuity in L"2-norm. Continuity constraints at the four corners of surfaces are considered, so that the boundary curves preserve endpoints continuity of any order @a. We obtain matrix representations for the control points of the degree reduced surfaces by the least-squares method. A simple optimization scheme that minimizes the perturbations of some related control points is proposed, and the surface patches after adjustment are C^~ continuous in the interior and G^1 continuous at the common boundaries. We show that this scheme is applicable to surface patches defined on chessboard-like domains.