Affordable Access

Publisher Website

Optimal multi-degree reduction of triangular Bézier surfaces with corners continuity in the norm [formula omitted]

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
215
Issue
1
Identifiers
DOI: 10.1016/j.cam.2007.04.022
Keywords
  • Triangular Bézier Surface
  • Multi-Degree Reduction
  • Boundary Constraint
  • Bivariate Bernstein Polynomial
  • Bivariate Jacobi Polynomial
Disciplines
  • Computer Science

Abstract

Abstract 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.

There are no comments yet on this publication. Be the first to share your thoughts.