Numerical stability of a convex hull algorithm for simple polygons

Abstract

A numerically stable and optimal O(n)-time implementation of an algorithm for finding the convex hull of a simple polygon is presented. Stability is understood in the sense of a backward error analysis. A concept of the condition number of simple polygons and its impact on the performance of the algorithm is discussed. It is shown that if the condition number does not exceed (1+O(ε))/(3 ε), then, in floating-point arithmetic with the unit roundoff ε, the algorithm produces the vertices of a convex hull for slightly perturbed input points. The relative perturbation does not exceed 3 ε(1+O(ε)). © 1993 Springer-Verlag New York Inc.