陈文喻 汪国昭. 代数三角混合的样条曲线[J]. 计算机研究与发展, 2006, 43(4): 679-687.
 引用本文: 陈文喻 汪国昭. 代数三角混合的样条曲线[J]. 计算机研究与发展, 2006, 43(4): 679-687.
Chen Wenyu and Wang Guozhao. Algebraic-Trigonometric Splines[J]. Journal of Computer Research and Development, 2006, 43(4): 679-687.
 Citation: Chen Wenyu and Wang Guozhao. Algebraic-Trigonometric Splines[J]. Journal of Computer Research and Development, 2006, 43(4): 679-687.

## Algebraic-Trigonometric Splines

• 摘要: B样条曲线能对多项式参数曲线提供有效的控制,但是它不能表示一些超越曲线，因此，很多文献提供了新的模型来构造曲线，但是这些模型要么只能表示低阶曲线，要么不能表示圆的渐开线和圆锥螺线.对此，在空间Ω\-k=spancost,sint,tcost,tsint,1,t,t\+2,…,t\+\k-1\(k≥5)中构造一类曲线，称为节点序列T上的代数三角混合的k阶样条曲线(代数三角样条曲线)，该类曲线具有很多与B样条曲线类似的性质，利用这些性质可以通过嵌入新节点对曲线进行逼近，并且可以精确表示圆锥螺线、圆的渐开线等超越曲线.

Abstract: The B-spline provides a free control of the parametric polynomial, but it cannot deal with some transcendent curves. Therefore, lots of research works present all kinds of new models. However, these models can encompass neither high order curves nor conical solenoids and involutes of the circle. Thus a new kind of splines generated over the space spanned by cost,sint,tcost,tsint,1,t,t\+2,…,t\+\k-5\(k≥5) are presented, which are called non-uniform algebraic-trigonometric splines of order k with regard to the given node sequence T. The algebraic-trigonometric splines have most of their properties similar to that of the B-splines in the polynomial space. After inserting new nodes to the node sequence, the sequence of the control polygons converts to the spline. Apparently, algebraic-trigonometric splines can encompass conical solenoids, involutes of circles and some other transcendent curves.

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