基于坐标变换的曲线曲面求交算法  

Intersection algorithm based on coordinate transformation

作　　者：陈晓霞[1] 雍俊海[2] 陈玉健[2] 刘辉 

机构地区：[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　　处：《计算机集成制造系统》2005年第9期1327-1332,共6页Computer Integrated Manufacturing Systems

基　　金：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。~~

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。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.

关 键 词：曲线曲面求交 坐标变换 拉格朗日乘子法 最小距离 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]