多边形的圆可分性
Circular Separability of Polygons
摘要：
两个平面集合是圆可分的，如果存在一个包围其中一个集合的圆，并且其开放的内盘不与另一个集合相交。本文研究了与循环可分性有关的两个问题。提出了一种判定两个多边形是否圆可分的线性时间算法。该算法输出最小的分离圆。第二个问题要求在一些点和/或线约束下，在预处理的凸多边形中包含的最大圆。生成的圆必须包含查询点，并且必须位于由查询线分隔的半平面内。
英文摘要：
Two planar sets are circularly separable if there exists a circle enclosing one of the sets and whose open interior disk does not intersect the other set. This paper studies two problems related to circular separability. A linear-time algorithm is proposed to decide if two polygons are circularly separable. The algorithm outputs the smallest separating circle. The second problem asks for the largest circle included in a preprocessed, convex polygon, under some point and/or line constraints. The resulting circle must contain the query points and it must lie in the halfplanes delimited by the query lines.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
