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http://dx.doi.org/10.6109/jkiice.2017.21.4.753

A Convex Layer Tree for the Ray-Shooting Problem  

Kim, Soo-Hwan (Department of Embedded Software, Busan University of Foreign Studies)
Publication Information
Journal of the Korea Institute of Information and Communication Engineering / v.21, no.4, 2017 , pp. 753-758 More about this Journal
Abstract
The ray-shooting problem is to find the first intersection point on the surface of given geometric objects where a ray moving along a straight line hits. Since rays are usually given in the form of queries, this problem is typically solved as follows. First, a data structure for a collection of objects is constructed as preprocessing. Then, the answer for each query ray is quickly computed using the data structure. In this paper, we consider the ray-shooting problem about the set of vertical line segments on the x-axis. We present a new data structure called a convex layer tree for n vertical line segments given by input. This is a tree structure consisting of layers of convex hulls of vertical line segments. It can be constructed in O(n log n) time and O(n) space and is easy to implement. We also present an algorithm to solve each query in O(log n) time using this data structure.
Keywords
Binary tree; Computational geometry; Convex hull; Ray-shooting;
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