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

摘要

This paper derives an approximation algorithm for multi-degree reduction of a degree n triangular Bézier surface with corners continuity in the norm L2. 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 C0 continuity. Finally several numerical examples are presented to validate the effectiveness of this algorithm.