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

✍ Scribed by Qian-Qian Hu; Guo-Jin Wang

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
723 KB
Volume
215
Category
Article
ISSN
0377-0427

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✦ Synopsis

This paper derives an approximation algorithm for multi-degree reduction of a degree n triangular Bézier 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.

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✍ Lizheng Lu; Guozhao Wang 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 1014 KB

Given a triangular Bézier surface of degree n, the problem of multi-degree reduction by a triangular Bézier surface of degree m with boundary constraints is investigated. This paper considers the continuity of triangular Bézier surfaces at the three corners, so that the boundary curves preserve endp