Optimal multi-degree reduction of triangular Bézier surfaces with corners continuity in the norm L2

Authors:
Qian-Qian Hu;Guo-Jin Wang
Affiliations:
Department of Mathematics, State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, PR China;Department of Mathematics, State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

This paper derives an approximation algorithm for multi-degree reduction of a degree n triangular Bezier surface with corners continuity in the norm L"2. The new idea is to use orthonormality of triangular Jacobi polynomials and the transformation relationship between bivariate Jacobi and Bernstein polynomials. This algorithm has a very simple and explicit expression in matrix form, i.e., the reduced matrix depends only on the degrees of the surfaces before and after degree reduction. And the approximation error of this degree-reduced surface is minimum and can get a precise expression before processing of degree reduction. Combined with surface subdivision, the piecewise degree-reduced patches possess global C^0 continuity. Finally several numerical examples are presented to validate the effectiveness of this algorithm.