计算机工程与应用 ›› 2007, Vol. 43 ›› Issue (35): 39-43.

• 学术探讨 • 上一篇    下一篇

Bezier分形曲线的细分叠加生成方法

王 睿1,叶正麟1,赵红星1,2   

  1. 1.西北工业大学 理学院,西安 710072
    2.榆林学院,陕西 榆林 719000
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2007-12-11 发布日期:2007-12-11
  • 通讯作者: 王 睿

Subdivision-and-adding Bernstein-polynomial method of constructing Bezier fractal curves

WANG Rui1,YE Zheng-lin1,ZHAO Hong-xing1,2   

  1. 1.School of Sciences,Northwestern Polytechnical University,Xi’an 710072,China
    2.Yulin College,Yulin,Shaanxi 719000,China
  • Received:1900-01-01 Revised:1900-01-01 Online:2007-12-11 Published:2007-12-11
  • Contact: WANG Rui

摘要: 给出了一种由Bezier曲线生成分形曲线的细分叠加方法。将参数二周期化后的Bezier曲线进行递归细分,得到细分曲线序列,再依次将此细分曲线序列无限叠加,构造出处处连续而处处不可微的分形曲线,具有某种自相似性。此Bezier分形曲线可表示为原Bezier曲线控制顶点的线性组合,其调配函数由参数二周期化后的Bernstein基函数无限细分叠加生成,处处连续而处处不可微,且有某种自相似性。数值实验表明此细分叠加方法所生成的曲线具有分形特征。

关键词: Bezier曲线, 细分叠加, 分形

Abstract: In this paper,a subdivision-and-adding scheme of constructing fractal curves from Bezier-curves is created.First,we gain subdivided curve sequence by subdividding parameter-2-perioded Bezier curves recursively,then we add these subdivided curve sequence in file infinitely,by this means,we construct continuous and non-differentiable fractal curves,these curves have the property of self-similitude.The Bezier fractal curve can be indicated as linear combination of control-vertex of the original Bezier curve,the mixed function is created by adding parameter-2-perioded Bernstein basis function infinitely,it has the properties of continuity and non-differentiable and self-similitude.Numerical experiments indicate that curves created by this subdivision-and-adding scheme have fractal character.

Key words: Bezier curve, subdivision-and-adding, fractal