| 基于坐标变换的曲线曲面求交算法 |
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| 引用本文： | 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].计算机集成制造系统,2005,11(9):1327-1332. |
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| 作者姓名： | 陈晓霞 雍俊海 陈玉健 刘辉 |
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| 作者单位： | 兰州理工大学,机电学院,甘肃,兰州,730050;清华大学,软件学院,北京,100084;清华大学,软件学院,北京,100084;兰州炼油化工仪表厂,甘肃,兰州,730050 |
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| 基金项目： | 国家高技术研究发展计划(2003AA4Z1010)，国家重点基础研究发展计划(2002CB312106)，留学回国人员科研启动基金(041501004)，高等学校全国优秀博士学位论文作者专项资金(200342)的资助。~~ |
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| 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。
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| 关 键 词： | 曲线曲面求交 坐标变换 拉格朗日乘子法 最小距离 |
| 文章编号： | 1006-5911(2005)09-1327-06 |
| 修稿时间： | 2004年4月6日 |
Intersection algorithm based on coordinate transformation |
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| CHEN Xiao-xia,YONG Jun-hai,CHEN Yu-jian,LIU Hui.Intersection algorithm based on coordinate transformation[J].Computer Integrated Manufacturing Systems,2005,11(9):1327-1332. |
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| Authors: | CHEN Xiao-xia YONG Jun-hai CHEN Yu-jian LIU Hui |
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| Affiliation: | CHEN Xiao-xia~ |
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| 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. |
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| Keywords: | curve and surface intersection coordinate transformation Lagrange multiplier method minimum distance |
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