Shape Modification of Cubic Quasi-B&#233;zier Curve

韩西安 1; 2; 马逸尘 1; 黄希利 3

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Shape Modification of Cubic Quasi-Bézier Curve

更新时间：2025-12-08

- Shape Modification of Cubic Quasi-Bézier Curve
- Vol. 41, Issue 8, Pages: 903-906(2007)
- 作者机构：
  
  1. 西安交通大学理学院,西安,710049
  2. 装备指挥技术学院基础部,北京,101416
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP391.4
- Online First：10 August 2007，
  
  Published：2007
- 稿件说明：
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韩西安 1, 2, 马逸尘 1, et al. Shape Modification of Cubic Quasi-Bézier Curve[J]. 2007, 41(8): 903-906.
DOI：

韩西安 1, 2, 马逸尘 1, et al. Shape Modification of Cubic Quasi-Bézier Curve[J]. 2007, 41(8): 903-906. DOI：

摘要

对于Bézier曲线的形状调整问题

给出了一组含有2个参数的四次多项式基函数

它是三次Bernstein基函数的扩展.基于该组基函数定义的带形状参数的曲线

称为三次拟Bézier(三次Q-Bézier)曲线

其优点是在保持控制多边形不变的情况下

可以通过改变形状参数来调整曲线形状.研究基于几何约束的形状调整

通过改变形状参数来满足给定的约束条件

得到形状参数简洁的计算公式

具有明显的几何意义.计算实例表明

该方法是有效的

可以广泛地应用于计算机辅助设计中对曲线形状调整.

Abstract

For modifying the shape of Bézier curve

a class of quartic polynomial basis functions with two adjustable shape parameters is presented

which can be regarded as an extension to classical cubic Bernstein basis functions. A polynomial curve called cubic quasi-Bézier(cubic Q-Bézier)curve with shape parameters is defined to outperform general cubic Bézier curves with the inherent flexibility. The shape of the cubic Q-Bézier curve can be adjusted by altering the shape parameters when the control polygon remains unchanged. The shape modification of the cubic Q-Bézier curve by geometric constrains is investigated. A new method is presented by changing the shape parameters to satisfy the given constrains

and the corresponding simple computational formulae of the shape parameters with unambiguous geometric significance are proposed. Some practical examples verify the applicability.

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references

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梁锡坤. Bernstein-Bézier 类曲线和Bézier曲线重新参数化方法[J]. 计算机研究与发展, 2004, 41(6): 1016-1021.

Liang Xikun. Bernstein-Bézier class carves and a reparametrization method of Bézier curve[J]. Journal of Computer Research and Development, 2004,41(6):1016-1021.

韩旭里,胡奇辉,彭丰富. 广义Bézier 曲线[J]. 计算机辅助设计与图形学学报, 2006, 18(3): 406-409.

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徐立,陈玉健,胡毓宁. 基于约束优化的 Bézier 曲线的形状修改[J].软件学报,2002,13(6):1069-1074.

Xu Li, Chen Yujian, Hu Yuning. Shape modification of Bézier curves by constrained optimization [J].Journal of Software, 2002,13(6): 1069-1074.

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Hu Shimin, Li Youfu, Ju Tao, et al. Modifying the shape of NURBS surfaces with geometric constraints[J].Computer Aided Design,2001,33(12):903-912.

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Related Institution

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Shape Modification of Cubic Quasi-Bézier Curve

DOI：

摘要

Abstract

关键词

Keywords

references