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.

Key words: trigonometric polynomial, triangular domain, triangular patch, shape parameters, de Casteljau-type algorithm

摘要： 提出一种三角域上带三个形状参数的三角多项式基函数，基于此基函数可以生成一种三角域上的三角多项式曲面。该曲面可以构建边界为椭圆弧、抛物线弧以及圆弧的曲面。在不改变控制网格的情况下，所提出的曲面可以使用形状参数对曲面进行可预测的灵活调整。为了能够高效稳定地计算该三角多项式曲面，提出一种实用的de Casteljau-type算法。此外，还给出了连接两个三角多项式曲面的[G1]连续条件。

关键词: 三角多项式, 三角域, 三角曲面, 形状参数, de Casteljau-type算法