三角域上三阶T-Bézier曲面片的构造与设计

Construction and design for three order T-Bézier surface on triangular domain

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。

In computer aided geometric design, T-Bezier 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-Bezier 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 prop-erties 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.