Abstract: In computer aided geometric design, T-Bézier curve and surface is viewed as new free form curve and surface modeling tools have been widely studied, but the surface is all tensor product. In order to further study T-Bézier in non-polynomial space and perfect the theory of triangular domain, a kind of trigonometric basis for trigonometric polynomial space over triangular domain is proposed. The constructed basis over triangular domain has been proved to have nice properties such as positivity, partition of unity, symmetry, boundary representation and linear independence and so on. Some properties of the corresponding surface are also proved. Finally, some applications of the proposed basis are shown.

Key words: computer aided geometric design, T-Bézier basis, trigonometric polynomial, triangular domain

摘要： 在计算机辅助几何设计中，T-Bézier曲线曲面被视为一种新的自由曲线曲面造型工具得到广泛研究，然而其曲面都是张量积形式的，为了进一步研究非多项式空间中的T-Bézier基，完善其关于三角域部分的理论，构造了满足正性、权性、对称性、边界性质和线性无关性的基函数，并证明了三角域上相应曲面的一些性质；最后给出了一些应用。

关键词: 计算机辅助几何设计, T-Bé, zier基函数, 三角多项式, 三角域