计算机工程与应用 ›› 2010, Vol. 46 ›› Issue (15): 142-145.DOI: 10.3778/j.issn.1002-8331.2010.15.042

• 图形、图像、模式识别 • 上一篇    下一篇

带最多独立形状参数的三阶三次均匀B样条曲线

王树勋1,2,叶正麟1,陈作平3   

  1. 1.西北工业大学 理学院,西安 710072
    2.陕西理工学院 数学系,陕西 汉中 723001
    3.香港理工大学 工业中心,中国 香港
  • 收稿日期:2010-01-19 修回日期:2010-03-12 出版日期:2010-05-21 发布日期:2010-05-21
  • 通讯作者: 王树勋

Three order cubic polynomial uniform B-spline curve with most independent shape parameters

WANG Shu-xun1,2,YE Zheng-lin1,CHEN Zuo-ping3   

  1. 1.College of Science,Northwestern Polytechnical University,Xi’an 710072,China
    2.Department of Mathematics,Shaanxi University of Technology,Hanzhong,Shaanxi 723001,China
    3.Industrial Centre,The Hong Kong Polytechnic University,Hong Kong,China
  • Received:2010-01-19 Revised:2010-03-12 Online:2010-05-21 Published:2010-05-21
  • Contact: WANG Shu-xun

摘要: 构造了三阶三次等距结点的多项式B样条参数曲线,给出了de Boor控制顶点与分段三次Bézier控制顶点的关系式。该曲线具有一些类似于二次B样条曲线的性质:关于参变量为C1连续,每个样条区间上的曲线由三个de Boor控制顶点的线性组合表示,具有仿射变换下的不变性,包含了二次均匀B样条曲线等。还具有形状可调性质:调配函数中含有形状参数,具有明显的几何意义,可用于调控曲线的形状或变形。给出了其具有凸包性、对de Boor控制多边形保形性等性质及其条件,讨论了形状参数对曲线形状的影响。

关键词: 样条曲线, 调配函数, 形状参数, 仿射不变性

Abstract: This paper constructs three order cubic equidistant-knot polynomial B-spline parameter curve,and relationship function of de Boor control point and segment cubic Bézier control point.This curve has the property similar to quadratic B-spline curve:C1-continuous with respect to parametric variable,curves at each spline intervals represented by linear combinations of three de Boor control points,with invariability under affine transformation,including quadratic uniform B-spline curve,etc;And property of shape adjustability:blending function including shape parameter,and with explicit geometric significance,be able applying to control the shape or transform of the curve.And provide the properties and conditions of convex hull property,conformal property of de Boor control polygon,discuss the impact of shape parameter to curve shape.

Key words: spline curve, blending function, shape parameter, affine invariant

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