An Efficient Algorithm to Calculate the Center of the Biggest Inscribed Circle in an Irregular Polygon

Abstract

In this paper, an efficient algorithm to find the center of the biggest circle inscribed in a given polygon is described. This work was inspired by the publication of Daniel Garcia-Castellanos & Umberto Lombardo and their algorithm used to find a landmass' poles of inaccessibility. Two more efficient algorithms were found, one of them only applicable when the problem can be described as a linear problem, like in the case of a convex polygon. Keywords: distance geometry, euclidean distance, inscribed circle, irregular polygon, algorithm, mathematical optimization, Monte Carlo, linear programming, maximin