基于坐标变换的曲线曲面求交算法

• 论文 •

基于坐标变换的曲线曲面求交算法

陈晓霞，雍俊海, 陈玉健，刘辉

1. 兰州理工大学机电学院，甘肃兰州 730050； 2. 清华大学软件学院，北京 100084;3.兰州炼油化工仪表厂，甘肃兰州 730050

出版日期:2005-09-15 发布日期:2005-09-25

Intersection algorithm based on coordinate transformation

CHEN Xiao-xia, YONG Jun-hai , CHEN Yu-jian，LIU Hui

1. Sch. of Mechanical & Electronic Eng., Lanzhou Univ. of S & T, Lanzhou 730050, China;2. Sch. of Software, Tsinghua Univ., Beijing 100084, China；3.Lanzhou Petrochemical Instrument Plant,Lanzhou 730050,China

Online:2005-09-15 Published:2005-09-25

摘要/Abstract

摘要： 利用坐标变换的方法，给出了二次曲线和二次曲面求交的解析算法。利用拉格朗日乘子法求解二次曲线和二次曲面之间的最小距离，给出了曲线与曲面相切的条件。算法表明，坐标变换可以简化求交运算表达式，使求交算法易于实现。根据得出的相切条件，可以有效地判断曲线、曲面是否有交，对相切情况的计算结果进行修正，可提高奇异情况下的求交稳定性。算法已在清软英泰公司开发的自主版权3维CAD软件GEMS中得到应用。

关键词: 曲线曲面求交, 坐标变换, 拉格朗日乘子法, 最小距离

Abstract: A method to solve the intersection of conic and conicoid based on the coordinate transformation was presented. With the Lagrange multiplier method, the minimum distance of the center of a circle and a quadric surface was provided and the tangency condition of curve and surface was given. Experience showed that the coordinate transformation could significantly simplify the method to intersection calculation. The location of the tangent point was revised by using the tangency condition. It could improve the stability of the intersection of given curves and surfaces in singularity cases. The new algorithm was applied in a three-dimensional Computer Aided Design (CAD) software, GEMS, which was produced by Tsinghua University.

Key words: curve and surface intersection, coordinate transformation, Lagrange multiplier method, minimum distance

中图分类号:

TP391.41

陈晓霞,, 雍俊海, 陈玉健，刘辉. 基于坐标变换的曲线曲面求交算法[J]. .

CHEN Xiao-xia,, YONG Jun-hai , CHEN Yu-jian，LIU Hui. Intersection algorithm based on coordinate transformation[J]. .

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