几何迭代方法计算空间两圆之间的最近距离
The Geometric Iteration Method for Computing the Minimum Distance between Two Spatial Circles
DOI: 10.12677/CSA.2015.511050, PDF,    国家自然科学基金支持
作者: 李小武, 王林, 张明生：贵州民族大学信息工程学院，贵州 贵阳；吴志男：宜春学院，数学与计算机科学学院，江西 宜春
关键词: 空间两圆；最近距离；几何迭代方法；中心轴；Two Spatial Circles； The Minimum Distance； Geometric Iteration Method； Central Axis
摘要: 空间两圆之间的最近距离计算是计算机图形学、计算机辅助设计、计算机辅助几何设计等领域进行碰撞检测和相交计算问题的基础。本文对任意位置关系的空间两圆的最近距离进行了完整分析与讨论。空间两圆的中心轴不平行时，提出了基于几何迭代方法的空间两圆最近距离的求解算法，当空间两圆中心轴有交点时，本文给出了间两圆最近距离的两对对应点；当空间两圆的中心轴平行或重合时，本文给出两圆最近距离的解析表达式。最后通过若干例子显示本文方法的稳定性和有效性。
Abstract: Computing the minimum distance between two spatial circles is the base of collision detection and intersection in the fields of computer graphics, computer-aided design and computer-aided geo-metric design. This paper has completely analyzed and discussed the minimum distance problem between two spatial circles for their spatial position relationships. If the two central axes of two spatial circles are not paralleled, we have presented the algorithm for computing the minimum distance between two spatial circles based on the geometric iterative method. Besides, if two cen-tral axes of two spatial circles have an intersection, we also have presented two pairs of corres-ponding points of the minimum distance for two spatial circles based on the geometric iterative method; if two central axes of two spatial circles are paralleled or coincident, we have directly provided the analytical expressions for computing the minimum distance between two spatial cir-cles. Numerical examples illustrate that the algorithms are efficient and robust.
文章引用：李小武, 吴志男, 王林, 张明生. 几何迭代方法计算空间两圆之间的最近距离[J]. 计算机科学与应用, 2015, 5(11): 394-402. https://dx.doi.org/10.12677/CSA.2015.511050

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