This paper defines the area measure of the quality of approximate convex hulls and proposes two new approximate convex hull algorithms. The first one is superior to known techniques under the area measure and comparable under the distance measure and time complexity. The second algorithm is superior to all known algorithms in both area and distance measures (including the first algorithm) while...

Divide-and-conquer is one of the most frequently used methods for the design or” fast algorithms. The most common application of the technique involves breaking a problem of size N into two subproblems of size N/2, solving these subproblems, then doing work proportional to N to “marry” the partial answers into a solution for the entire problem; this scheme leads to algorithms of O(N log N) wors...

A problem in distance geometry is to find the location of an unknown point in a given convex set in Rk such that its farthest distance to n fixed points is minimum. In this paper we present an algorithm based on subgradient method and convex hull computation for solving this problem. A recent improvement of Quickhull algorithm for computing the convex hull of a finite set of planar points is ap...

This paper describes a quick 3D-to-2D point matching algorithm. Our major contribution is to substitute a new O(2n) algorithm for the traditional N ! method by introducing a convex hull based enumerator. Projecting a 3D point set into a 2D plane yields a corresponding 2D point set. In some cases, matching information is lost. Therefore, we wish to recover the 3D-to-2D correspondence in order to...

The parallel complexity of the problem of constructing the convex hull of a sorted planar point set is studied. For any point p in the plane, let x(p) and y(p) denote the xand y-coordinate of p. A planar point set S = {p1, p2, . . . , pN} is said to be x-sorted if the points of S are given by increasing x-coordinate, i.e., x(pi) ≤ x(pi+1) for all i ∈ {1, 2, . . . , N − 1}. The following two res...

This paper presents an alternative GPU-accelerated convex hull algorithm and a novel S orting-based P reprocessing A pproach (SPA) for planar point sets. The proposed convex hull algorithm termed as CudaChain consists of two stages: (1) two rounds of preprocessing performed on the GPU and (2) the finalization of calculating the expected convex hull on the CPU. Those interior points locating ins...

We present a hybrid algorithm to compute the convex hull of points in three or higher dimensional spaces. Our formulation uses a GPU-based interior point filter to cull away many of the points that do not lie on the boundary. The convex hull of remaining points is computed on a CPU. The GPU-based filter proceeds in an incremental manner and computes a pseudo-hull that is contained inside the co...

Given a graph G = (V,E), the closed interval of a pair of vertices u, v ∈ V , denoted by I[u, v], is the set of vertices that belongs to some shortest (u, v)-path. For a given S ⊆ V , let I[S] = ⋃ u,v∈S I[u, v]. We say that S ⊆ V is a convex set if I[S] = S. The convex hull Ih[S] of a subset S ⊆ V is the smallest convex set that contains S. We say that S is a hull set if Ih[S] = V . The cardina...

Color gamut characterization is an essential step in the ICC profile generation for imaging devices. It is also needed as part of evaluation and comparison of image quality achievable by different imaging systems. A novel technique is presented for characterizing the color gamut of an imaging device via ray tracing in the CIELAB color space. Initially, the convex hull of the set of measurement ...

A polytope is the bounded intersection of a nite set of halfspaces of R d. Every polytope can also be represented as the convex hull conv V of its vertices (or extreme points) V. The convex hull problem is to convert from the vertex representation to the halfspace representation or (equivalently by geometric duality) vice-versa. Given an ordering v 1 : : : v n of the input vertices, after some ...