Intersections and circuits in sets of line segments
Publication Date
11-1-2022
Document Type
Article
Publication Title
Journal of Combinatorial Optimization
Volume
44
Issue
4
DOI
10.1007/s10878-021-00731-3
First Page
2302
Last Page
2323
Abstract
Sets of straight line segments with special structures and properties appear in various applications of geometric modeling, such as scientific visualization, computer-aided design, and medical image processing. In this paper, we derive sharp upper and lower bounds on the number of intersection points and closed regions that can occur in sets of line segments with certain structure, in terms of the number of segments. In particular, we consider sets of segments whose underlying planar graphs are Halin graphs, cactus graphs, maximal planar graphs, and triangle-free planar graphs, as well as randomly produced segment sets.
Funding Number
1603823
Funding Sponsor
National Science Foundation
Keywords
Cactus graph, Circuits, Halin graph, Intersection points, Maximal planar graph, Triangle-free planar graph
Department
Mathematics and Statistics
Recommended Citation
Boris Brimkov, Jesse Geneson, Alathea Jensen, Jordan Broussard, and Pouria Salehi Nowbandegani. "Intersections and circuits in sets of line segments" Journal of Combinatorial Optimization (2022): 2302-2323. https://doi.org/10.1007/s10878-021-00731-3
