Visibility queries in a polygonal region

Quickest Visibility Queries in Polygonal Domains

Let s be a point in a polygonal domain P of h−1 holes and n vertices. We consider the following quickest visibility query problem. Given a query point q in P, the goal is to find a shortest path in P to move from s to see q as quickly as possible. Previously, Arkin et al. (SoCG 2015) built a data structure of size O(n22α(n) logn) that can answer each query in O(K log2 n) time, where α(n) is the...

OpenGL-assisted Visibility Queries of Large Polygonal Models

We present an OpenGL-assisted visibility culling algorithm to improve the rendering performance of large polygonal models. Using a combination of OpenGL-assisted frustum culling, hierarchical model-space partitioning, and OpenGL based occlusion culling, we achieve a significant better performance on general polygonal models than previous approaches. In contrast to these approaches, we only expl...

Visibility-Based Pursuit-Evasion in a Polygonal Region by a Searcher

We consider the most basic visibility-based pursuit-evasion problem defined as follows: Given a polygonal region, a searcher with 360 vision, and an unpredictable intruder that is arbitrarily faster than the searcher, plan the motion of the searcher so as to see the intruder. In this paper, we present simple necessary and sufficient conditions for a polygon to be searchable, which settles a dec...

Visibility graphs of polygonal rings

Weak visibility queries of line segments in simple polygons and polygonal domains

In this paper we consider the problem of computing the weak visibility polygon of any query line segment pq (or WVP(pq)) inside a given polygon P . Our first non-trivial algorithm runs in simple polygons and needs O(n log n) time and O(n) space in the preprocessing phase to report WVP(pq) of any query line segment pq in time O(log n + |WVP(pq)|). We also give an algorithm to compute the weak vi...