| 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C2连续，当形状参数取特殊值时可达C3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. |
| 关键词: 曲线设计 代数三角样条基 形状参数 圆锥曲线 超越曲线 |
| DOI： |
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| A kind of algebraic-trigonometric blending spline curve |
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| Abstract: |
| 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 C2continuous,and it achieved C3 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. |
| Key words: curve design algebraic-trigonometric spline basis shape parameter conic section transcendental curve |
