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Many views of planar point sets

Publication at Faculty of Mathematics and Physics |
2023

Abstract

Given a set P of n points in the plane and two points x and y not in P, such that their union is in general position, we say that x and y have the same view of P if the points of P are visible in the same cyclic order from x and y. We show that for every set P of n points in strong general position in the plane, there are Omega(n^4) points with mutually distinct views of P, confirming a conjecture by

Díaz-Báñez, Fabila-Monroy and Pérez-Lantero.