Mediterranean Journal of Mathematics

, Volume 13, Issue 2, pp 841–855 | Cite as

A Practical Method for Generating Trigonometric Polynomial Surfaces over Triangular Domains



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 G 1 continuous smooth joining two trigonometric polynomial patches are deduced.

Mathematics Subject Classification

Primary 65D07 65D17 Secondary 41A15 42A05 42A10 


Trigonometric polynomial triangular domain triangular patch shape parameter de Casteljau-type algorithm 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsCentral South UniversityChangshaPeople’s Republic of China

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