中文摘要：

针对3次B样条曲线相对于其控制多边形形状固定,以及不能描述除抛物线以外的圆锥曲线的不足进行改进.通过构造一组性质良好的代数三角混合样条基,定义了一种结构类似于3次B样条曲线的新曲线.新曲线在保留3次B样条曲线主要优点的同时,既具有形状可调性,又能精确表示圆、椭圆、抛物线,正弦、余弦曲线,摆线以及圆柱螺线.对于等距节点,在一般情况下,新曲线C^2连续,当形状参数取特殊值时可达C^3连续.另外还讨论了如何选择控制顶点使新曲线与给定的多边形相切.

英文摘要：

The shape of cubic B- spline curve is fixed to its control polygon. In addition,it cannot describe the conic section besides the parabola. In order to overcome disadvantages,a set of algebraic- trigonometric blending spline basis,which enjoys many nice properties,was constructed. A kind of new curve,which structure was similar to the classical cubic B- spline curve,was defined. The new curve not only inherited the major advantages of the cubic B- spline curve,but also enjoyed shape adjustability,and it exactly expressed circle,ellipse,parabola,sine curve,cosine curve,cycloid and cylinder helix. For equidistant knots,the new curve was C^2 continuous,and it achieved C^3 continuity when taking special shape parameter. In addition,how to choose control points to make the new curve tangent to a given control polygon was discussed.