Multi-degree reduction of triangular Bézier surfaces with boundary constraints

Authors:
Lizheng Lu;Guozhao Wang
Affiliations:
Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, China;Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, China
Venue:
Computer-Aided Design
Year:
2006

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Abstract

Given a triangular Bezier surface of degree n, the problem of multi-degree reduction by a triangular Bezier surface of degree m with boundary constraints is investigated. This paper considers the continuity of triangular Bezier surfaces at the three corners, so that the boundary curves preserve endpoints continuity of any order @a. The l"2- and L"2-norm combined with the constrained least-squares method are used to get the matrix representations for the control points of the degree reduced surfaces. Both methods can be applied to piecewise continuous triangular patches or to only a triangular patch with the combination of surface subdivision. And the resulting piecewise approximating patches are globally C^0 continuous. Finally, error estimation is given and numerical examples demonstrate the effectiveness of our methods.