Polygon Queries for Convex Hulls of Points
Eunjin Oh, Hee-Kap Ahn

TL;DR
This paper introduces a data structure for efficiently computing convex hulls of point subsets within polygons of fixed orientations, optimizing range searching queries based on polygon shape and orientation.
Contribution
It presents a novel data structure that preprocesses points for fast convex hull queries within oriented polygons, with efficient space, construction, and query times.
Findings
Data structure supports efficient convex hull queries within oriented polygons.
Query time depends on the hull complexity and polygon size.
Perimeter and area of convex hulls can be computed quickly using the data structure.
Abstract
We study the following range searching problem: Preprocess a set of points in the plane with respect to a set of orientations % , for a constant, in the plane so that given an -oriented convex polygon , the convex hull of can be computed efficiently, where an -oriented polygon is a polygon whose edges have orientations in . We present a data structure with space and construction time, and an -time query algorithm for any query -oriented convex -gon , where is the complexity of the convex hull. Also, we can compute the perimeter or area of the convex hull of in time using the data structure.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Robotics and Sensor-Based Localization · Advanced Image and Video Retrieval Techniques
