Journal of Computer Applications

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New method of curve modeling based on continuity for extension-Bézier curves

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  • Received:2007-07-23 Revised:2007-09-13 Online:2008-01-01 Published:2008-01-01
  • Contact: Gang HU

基于扩展Bézier曲线拼接的曲线造型新方法

胡钢 刘哲 徐华楠   

  1. 西安理工大学理学院应用数学系 西北工业大学理学院应用数学系 西北工业大学理学院应用数学系
  • 通讯作者: 胡钢

Abstract: The extension of Bézier curves with shape control parameters has become the hot spot in computer aided geometric design. A new method of curve modeling based on continuity for Extension-Bézier curves was presented in this paper. This method first constructed a class polynomial curves called cubic extension (CE) Bézier curves with three shape parameter α, β, γ. CE-Bézier curves not only inherit the outstanding properties of cubic Bézier curve, but also are adjustable in shape and fit close to the control polygon. In order to overcome shortcomings that the circular arc and ellipse could not be accurately represented by CE-Bézier curves, this method used the continuity condition of CE-Bézier curves and C-Bézier curves to resolve the representation of circular arc and ellipse in CE-Bézier curve modeling. In addition, some applications of this method in curve and surface design were also discussed. The modeling examples illustrate that this method is valuable for computer aided geometric design.

Key words: curve modeling, Bézier curve, C-Bézier, shape parameter, extension, continuity

摘要: 提出了一种基于扩展Bézier曲线拼接的曲线造型新方法。该方法首先构造了一种具有优良形状可调性和更好逼近性的带3个形状参数α, β, γ的三次扩展Bézier曲线(CE-Bézier曲线);并针对CE-Bézier曲线无法精确表示圆弧和椭圆弧等二次曲线的缺点,利用CE-Bézier曲线与C-Bézier曲线间的拼接技术,解决了CE-Bézier曲线造型中圆弧和椭圆弧的表示问题。最后讨论了该方法在曲线曲面设计中的应用。造型实例表明,该方法在计算机辅助几何设计中具有一定的应用价值。

关键词: 曲线造型, Bézier曲线, C-Bézier, 形状参数, 扩展, 拼接