文章摘要
一种代数三角混合样条曲线
A kind of algebraic-trigonometric blending spline curve
  
DOI:
中文关键词: 曲线设计  代数三角样条基  形状参数  圆锥曲线  超越曲线
英文关键词: curve design  algebraic-trigonometric spline basis  shape parameter  conic section  transcendental curve
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作者单位
严兰兰1,2,韩旭里2,应正卫1 1.东华理工大学 理学院, 江西 南昌 3300132.中南大学 数学与统计学院, 湖南 长沙 410083 
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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.
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 C2continuous,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.
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