Equal Aperture Angles Curve for some Convex Sets in the Plane

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.