Shooting permanent rays among disjoint polygons in the plane

We present a data structure for ray shooting-and-insertion in the free space among disjoint polygonal obstacles with a total of n vertices in the plane, where each ray starts at the boundary of some obstacle. The portion of each query ray between the starting point and the first obstacle hit is inserted permanently as a new obstacle. Our data structure uses O(n log n) space and preprocessing time, and it supports m successive ray shooting-and-insertion queries in O(n log2 n + m log m) total time. We present two applications for our data structure: (1) Our data structure supports efficient implementation of auto-partitions in the plane i.e. binary space partitions where each partition is done along the supporting line of an input segment. If n input line segments are fragmented into m pieces by an auto-partition, then it can now be implemented in O(n log2 n + m log m) time. This improves the expected runtime of Patersen and Yao’s classical randomized auto-partition algorithm for n ...

• Type: Conference
• Year: 2009
• Where: COMPGEOM
• Authors: Mashhood Ishaque, Bettina Speckmann, Csaba D. Tóth
• Keywords: COMPGEOM 2009, Data Structure, Discrete Geometry, Disjoint Polygonal Obstacles, Ray Shooting-and-insertion