Modified Jacobi–Bernstein basis transformation and its application to multi-degree reduction of Bézier curves

作者：

Highlights：

• We establish and prove the basis transformation between the modified Jacobi polynomials (MJPs) and Bernstein polynomials and vice versa.

• This transformation is merging the perfect Least-square performance of the MJPs with the geometrical insight of the Bernstein form.

• The MJPs with indexes corresponding to the number of endpoint constraints are the natural basis functions for Least-square approximation of Bezier curves.

• Several numerical results are considered.

摘要

•We establish and prove the basis transformation between the modified Jacobi polynomials (MJPs) and Bernstein polynomials and vice versa.•This transformation is merging the perfect Least-square performance of the MJPs with the geometrical insight of the Bernstein form.•The MJPs with indexes corresponding to the number of endpoint constraints are the natural basis functions for Least-square approximation of Bezier curves.•Several numerical results are considered.

论文关键词：Basis transformation,Modified Jacobi polynomials,Bernstein polynomials,Galerkin orthogonal polynomials,Multiple degree reduction of Bézier curves

论文评审过程：Received 26 December 2014, Revised 6 December 2015, Available online 1 February 2016, Version of Record 10 March 2016.

论文官网地址：https://doi.org/10.1016/j.cam.2016.01.009