计算直线平面内直线凸形障碍物的骨架
Computing skeletons for rectilinearly-convex obstacles in the rectilinear plane
摘要：
我们引入了障碍骨架的概念，这是一组线段内的多边形障碍$ω$，可用于在地方的$ω$进行交叉测试时，避障网络问题的平面。与原始障碍物的边界中的线段的数量相比，骨架可以具有显著更少的线段，并且因此对骨架（而不是原始障碍物）执行相交测试可以显著减少用于计算避障问题的解决方案的算法所需的CPU时间。最小骨架是具有尽可能少的线段数的骨架。我们提供了一个精确的$O(n^2)$算法计算最小骨架的直线障碍物在直线平面是直线凸。我们表明，在一个最小的骨架的边缘的数量通常是非常小的边缘的数量相比，在原始障碍物的边界，通过随机直凸障碍与多达1000个顶点进行实验。
英文摘要：
We introduce the concept of an obstacle skeleton which is a set of line segments inside a polygonal obstacle $ω$ that can be used in place of $ω$ when performing intersection tests for obstacle-avoiding network problems in the plane. A skeleton can have significantly fewer line segments compared to the number of line segments in the boundary of the original obstacle, and therefore performing intersection tests on a skeleton (rather than the original obstacle) can significantly reduce the CPU time required by algorithms for computing solutions to obstacle-avoidance problems. A minimum skeleton is a skeleton with the smallest possible number of line segments. We provide an exact $O(n^2)$ algorithm for computing minimum skeletons for rectilinear obstacles in the rectilinear plane that are rectilinearly-convex. We show that the number of edges in a minimum skeleton is generally very small compared to the number of edges in the boundary of the original obstacle, by performing experiments on random rectilinearly-convex obstacles with up to 1000 vertices.
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