约束双圆弧插值  

Constrained Interpolation with Biarcs

作　　者：刘续征[1] 雍俊海[1] 郑国勤[1] 孙家广[1] 

机构地区：[1]清华大学软件学院

出　　处：《计算机辅助设计与图形学学报》2007年第1期1-7,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60403047;60533070);国家"九七三"重点基础研究发展规划项目(2004CB719400);全国优秀博士学位论文作者专项资金(200342);教育部"新世纪优秀人才支持计划"(NCET-04-0088).

摘　　要：提出一种构造C-型双圆弧和S-型双圆弧的算法,该双圆弧的2个端点为给定的点,在端点处的2个切向量为给定的切向量,且完全位于一条给定直线的一侧.对于C-型双圆弧,分12种情况给出不等式直接判断双圆弧是否满足位于给定直线一侧的约束条件.如果存在多个同时满足插值条件和直线约束条件的双圆弧,则通过求解一个最小值问题选出最优的双圆弧;否则,通过添加一个额外的点构造2段双圆弧.对于S-型双圆弧也给出一些带直线约束的插值结果.An algorithm to construct biarcs that not only match the interpolation requirement of the point positions and tangent vectors but also lie on one side of the constraint line is proposed. For C-type biarc interpolation with the line constraint, firstly twelve inequalities in total are provided according to different position relationships between the constraint line and the interpolation requirement. These inequalities are used to check if blares lie on one side of the constraint line. If there exist many biarcs satisfying both the interpolation requirement and the line constraint, the optimal biarc can be obtained by solving a minimum problem. Otherwise, one extra point is added to make it possible to obtain biarcs. For S-type biarc interpolation with the line constraint, some results are also listed.

关 键 词：约束插值 双圆弧 直线约束 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]