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 a foreseeable way using the shape parameters. For computing the proposed trigonometric polynomial patch stably and efficiently, a practical de Casteljau-type algorithm is developed. Moveover, the conditions for G1 continuous smooth joining two trigonometric polynomial patches are deduced.
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