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

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