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中文摘要：
为了进一步研究非多项式空间的拟Bézier基,完善其关于三角域部分的理论,将5阶三角多项式空间G=span{1,sint,cost,sin2t,cos2t}上的基推广到三角域上,构造出满足正性、权性、对称性、边界性质和线性无关性的拟Bézier基,使得相应的三角曲面不用有理形式就可以表示球面片.实例结果表明,使用这组基可以精确地造型出整球面.
英文摘要：
To extend the Bézier-stype basis from the traditional polynomial space to other common spaces such as triangular domains, in this paper a basis for trigonometric polynomial space F= span{1, sin t, cos t, sin 2t, cos 2t } of order 5 in triangular domain is proposed. The constructed Bézier-type basis in triangular domain have been proved to have the nice properties including positivity, partition of unity, symmetry, boundary representation and linear independence. Its corresponding surfaces of triangular domain can exactly represent spherical patches without rational form. The results of the practical examples shows the representative power of this new basis.
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