Single-Point And Triple-Point Queries Visibility Constrained Minimum Link Paths In Simple Polygons

Abstract

Abstract We study the query version of constrained minimum link paths between two points inside a simple polygon $P$ with $n$ vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning $P$ into a number of faces of equal link distance from a point. This partitioning is essentially a link-based shortest path map. Initially, we solve this problem for two given points $s$, $t,$ and a query point $q$. Then, the proposed solution is extended to a general case for three arbitrary query points: $s$, $t$ and $q$. In the former case, we propose an algorithm with $O(n)$preprocessing time. For the latter case, we develop an algorithm with $O(n^3)$ preprocessing time. The link distance of a $q$-$visible$ path between $s$, $t$ and the path are provided in time $O(\log n)$ and $O(m+\log n)$, respectively, for the above two cases, where $m$ is the number of links.