An extension of the Bezier model

作者：Yan Lanlan^*; Liang Jiongfeng

来源：Applied Mathematics and Computation, 2011, 218(6): 2863-2879.

DOI：10.1016/j.amc.2011.08.030

• Bernstein basis function
• Bernstein polynomial
• Bezier curve
• Bernstein-Bezier surface
• Shape parameter
• De Casteljau algorithm

In this paper, we first construct a new kind of basis functions by a recursive approach. Based on these basis functions, we define the Bezier-like curve and rectangular Bezier-like surface. Then we extend the new basis functions to the triangular domain, and define the Bernstein-Bezier-like surface over the triangular domain. The new curve and surfaces have most properties of the corresponding classical Bezier curve and surfaces. Moreover, the shape parameter can adjust the shape of the new curve and surfaces without changing the control points. Along with the increase of the shape parameter, the new curve and surfaces approach the control polygon or control net. In addition, the evaluation algorithm for the new curve and triangular surface are provided.

• 出版日期2011-11-15
• 单位东华理工大学