Equal Aperture Angles Curve for some Convex Sets in the Plane

2012/06/20 by Michal Kaukič, Kaukič, Michal
Computer Science · Mathematics · #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #FOS: Mathematics #Metric Geometry (math.MG) #Numerical Analysis (math.NA) #Point processes and geometric inequalities #Robotic Path Planning Algorithms

paper · pdf · doi:10.48550/arxiv.1206.4691

openalex publication_date 2012/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For given convex set K in the plane (not necessarily bounded), we can construct the curve C for which the visibility (aperture) angle of this set has the same, prescribed value. We give the implicit formula for C, discuss some issues concerning practical computations of C and bring several simple examples, when the equal visibility angle curves can be effectively computed explicitly. We conclude with some remarks about possible directions for further research in this area. Extensive use of Open Source software (Sage, Pylab, IPython,...) is a key feature of this article.

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