Computer Engineering and Applications ›› 2019, Vol. 55 ›› Issue (22): 195-200.

### Practical Method for Generating Trigonometric Polynomial Surfaces over Triangular Domains

WANG Kai, ZHANG Guicang, SU Jinfeng

1. School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
• Online:2019-11-15 Published:2019-11-13

### 三角域上生成三角多项式曲面的实用方法

1. 西北师范大学 数学与统计学院，兰州 730070

Abstract: A class of trigonometric polynomial basis functions over triangular domain with three shape parameters is constructed in this paper. Based on these new basis functions, a kind of trigonometric polynomial patch over triangular domain, which can be used to construct some surfaces whose boundaries are arcs of ellipse or parabola, is proposed. Without changing the control points, the shape of the trigonometric polynomial patch can be adjusted flexibly in foreseeable way by using the shape parameters. For computing the proposed trigonometric polynomial patch stably and efficiently, a practical de Casteljau-type algorithm is developed. Moreover, the conditions for [G1] continuous smooth joining two trigonometric polynomial patches are deduced.