基于μ基有理可展曲面的参数化

陈晓华; 陈玉福; 申立勇

doi:10.7523/j.issn.2095-6134.2012.3.001

中国科学院大学学报 >

2012 >Issue 3: 289 - 293

DOI: https://doi.org/10.7523/j.issn.2095-6134.2012.3.001

数学与物理学

基于μ基有理可展曲面的参数化

陈晓华 ,
陈玉福 ,
申立勇

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中国科学院研究生院数学科学学院, 北京 100049

收稿日期: 2011-01-14

修回日期: 2011-04-13

网络出版日期: 2012-05-15

基金资助

Supported by National Natural Science Fund of China(10901163),and the President Fund of GUCAS

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Parametrization of a rational developable surface using the μ-basis

CHEN Xiao-Hua ,
CHEN Yu-Fu ,
SHEN Li-Yong

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School of Mathematical Sciences, Graduate University, Chinese Academy of Sciences, Beijing 100049, China

Received date: 2011-01-14

Revised date: 2011-04-13

Online published: 2012-05-15

Supported by

Supported by National Natural Science Fund of China(10901163),and the President Fund of GUCAS

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摘要

针对工程设计中常用的可展曲面,给出其有理参数化算法. 给定一个隐式曲面,首先根据几何性质判定它是否是可展曲面,并给出判定算法;然后应用近年来新兴发展的隐式化代数工具——μ基方法,得到可展曲面的μ基的次数界. 在此基础上,设计计算隐式曲面μ基的算法,并通过计算其对偶曲面的重新参数化,得到原隐式曲面的参数表示. 结合已有的参数曲面隐式化算法,给出了有理可展曲面的代数交换算法图.

关键词： 参数化; μ基; 零点分解

本文引用格式

陈晓华 , 陈玉福 , 申立勇 . 基于μ基有理可展曲面的参数化[J]. 中国科学院大学学报, 2012 , (3) : 289 -293 . DOI: 10.7523/j.issn.2095-6134.2012.3.001

Abstract

Finding parametrization of a given curve or surface is an essential problem in CAGD and CG. It is still open to design an algorithm for a general given curve or surface. In this paper, we focus on rational developable surfaces which are widely used in manufacturing.

Key words： parametrization; μ-basis; zero decomposition

参考文献

[1] Chen F,Shen L,Deng J.Implicitization and parametrization of quadractic and cubic surfaces by μ-bases[J].Computing,2006,5:131-142.
[2] 彭家贵,陈卿. 微分几何[M]. 北京:高等教育出版社,2002.
[3] Deng J, Chen F, Shen L. Computing μ-bases of rational curves and surfaces using polynomial matrix factorization //Proceeding of ISSAC. 2005: 132-139.
[4] Chen F, Zheng J, Sederberg T W. The μ-basis of a rational ruled surface[J]. Computer Aided Geometric Design, 2001, 18: 61-72.
[5] Goldman Ron. Curvature formulas for implicit curves and surfaces[J]. Computer Aided Geometric Design, 2005, 22: 632-658.
[6] 吴文俊. 数学机械化[M]. 北京:科学出版社,2003.

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