Adaptive Algorithms for Planar Convex Hull Problems

Sweep Line Algorithm for Convex Hull Revisited

Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...

Adaptive (Analysis of) Algorithms for Convex Hulls and Related Problems

Adaptive analysis is a well known technique in computational geometry, which re nes the traditional worst case analysis over all instances of xed input size by taking into account some other parameters, such as the size of the output in the case of output sensitive analysis. We present two adaptive techniques for the computation of the convex hull in two and three dimensions and related problem...

Algorithms for distance problems in planar complexes of global nonpositive curvature

CAT(0) metric spaces and hyperbolic spaces play an important role in combinatorial and geometric group theory. In this paper, we present efficient algorithms for distance problems in CAT(0) planar complexes. First of all, we present an algorithm for answering single-point distance queries in a CAT(0) planar complex. Namely, we show that for a CAT(0) planar complex K with n vertices, one can con...

Adaptive Planar Convex Hull Algorithm for a Set of Convex Hulls

In-Place Planar Convex Hull Algorithms

An in-place algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. In this paper we describe three in-place algorithms for computing the convex hull of a planar point set. All three algorithms are optimal, some more so than others. . .