Proximity Problems on Line Segments Spanned by Points

Fast Algorithms for Collision and Proximity Problems Involving Moving Geometric Objects

Consider a set of geometric objects, such as points, line segments, or axesparallel hyperrectangles in IR, that move with constant but possibly different velocities along linear trajectories. Efficient algorithms are presented for several problems defined on such objects, such as determining whether any two objects ever collide and computing the minimum inter-point separation or minimum diamete...

An O(n log n) Algorithm for the All-Farthest-Segments Problem for a Planar Set of Points

In this paper, we propose an algorithm for computing the farthest-segment Voronoi diagram for the edges of a convex polygon and apply this to obtain an O(n logn) algorithm for the following proximity problem: Given a set P of n (>2) points in the plane, we have O(n2) implicitly defined segments on pairs of points. For each point p ∈ P , find a segment from this set of implicitly defined segment...

Finding Segments and Triangles Spanned by Points in R3

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...

Some results on convergence and existence of best proximity points

In this paper, we introduce generalized cyclic φ-contraction maps in metric spaces and give some results of best proximity points of such mappings in the setting of a uniformly convex Banach space. Moreover, we obtain convergence and existence results of proximity points of the mappings on reflexive Banach spaces