最小范围的良好照明
Good Illumination of Minimum Range
摘要：
若点p位于点集F的凸包内部，则点p被点集F的n个点光1-良好照明.这个概念对应于三角形保护或井覆盖。在本文中，我们考虑的照明范围的光源作为一个参数进行优化。首先，我们解决了最小化光源的照明范围以1-well照亮给定点p的问题。我们还计算了1-well以最小照明范围照亮p的光源的最小集合。其次，我们用O（n^2）算法解决了最小化光源照明范围以1-井照明线段上所有点的问题。最后，我们给出了一个O（n^2 log n）的算法来预处理数据，使之可以在O（log n）的时间内获得1-井照明线段上的一个点所需的照明范围。这些结果可以应用于解决1-井照明的轨迹接近它的多边形路径的问题。
英文摘要：
A point p is 1-well illuminated by a set F of n point lights if p lies in the interior of the convex hull of F. This concept corresponds to triangle-guarding or well-covering. In this paper we consider the illumination range of the light sources as a parameter to be optimized. First, we solve the problem of minimizing the light sources' illumination range to 1-well illuminate a given point p. We also compute a minimal set of light sources that 1-well illuminates p with minimum illumination range. Second, we solve the problem of minimizing the light sources' illumination range to 1-well illuminate all the points of a line segment with an O(n^2) algorithm. Finally, we give an O(n^2 log n) algorithm for preprocessing the data so that one can obtain the illumination range needed to 1-well illuminate a point of a line segment in O(log n) time. These results can be applied to solve problems of 1-well illuminating a trajectory by approaching it to a polygonal path.
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。
