| 判别平面上两个椭圆位置关系的代数条件 |
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| 引用本文： | 刘洋,申立勇. 判别平面上两个椭圆位置关系的代数条件[J]. 计算机辅助设计与图形学学报, 2003, 15(5): 555-560 |
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| 作者姓名： | 刘洋 申立勇 |
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| 作者单位： | 中国科学技术大学数学系,合肥,230026 |
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| 基金项目： | 国家自然科学基金 (6960 30 0 9,199710 87)，国家“九七三”数学机械化二级子课题 (G19980 360 0 )，教育部博士点基金 (2 0 0 10 35 80 0 3) |
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| 摘 要： | 在计算机动画、计算机图形学、计算机辅助设计、机器人等领域中，经常需要检测多个实体间的位置关系．基于广义特征多项式的方法，给出判断平面上任意两个椭圆所有位置关系(分离、外切、相交、内切、内含等)的代数条件．这些代数条件表示为由两椭圆确定的广义特征多项式的根的分布情况．该判别方法简单、实用．
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| 关 键 词： | 计算机动画 计算机图形学 判别平面 椭圆位置关系 代数条件 计算机辅助设计 |
| 修稿时间： | 2002-08-28 |
An Algebraic Condition for Classifying the Positional Relationship of Two Planar Ellipses |
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| Liu Yang Shen Liyong. An Algebraic Condition for Classifying the Positional Relationship of Two Planar Ellipses[J]. Journal of Computer-Aided Design & Computer Graphics, 2003, 15(5): 555-560 |
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| Authors: | Liu Yang Shen Liyong |
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| Abstract: | In many scientific fields such as computer animation, computer graphics, computer aided geometry design and robotics, it is very common to need detecting the positional relationship of several entities Based on the generalized characteristic polynomial, we give an algebraic condition for detecting the positional relationship of two planar ellipses, namely, separation, exterior contact, intersection, interior contact or inclusion The algebraic condition can be classified by the distribution of roots of the generalized characteristic equation The criterion is simple, effective, and easier than other known methods |
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| Keywords: | positional relationship of two ellipses generalized characteristic polynomial collision detection |
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