Query-points visibility constraint minimum link paths in simple polygons
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We study the query version of constrained minimum link paths between two points inside a simple polygon with n vertices such that there is at least one point on the path, visible from a query point. 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, we propose an algorithm with O(n) preprocessing time. Extending this approach 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 as well as the path are provided in time O(log n) and O(k+log n), respectively, for the above two cases, where k is the number of links.
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