The “convex hull problem” is a catch-all phrase for computing various descriptions of a polytope that is either specified as the convex hull of a finite point set in R or as the intersection of a finite number of halfspaces. We first define the various problems and discuss their mutual relationships (Section 26.1). We discuss the very special case of the irredundancy problem in Section 26.2. We...

Problem of defining convexity of a digital region is considered. Definition of DL− (digital line) convexity is proposed, and it is shown to be stronger than the other two definitions, T−(triangle) convexity and L−(line) convexity. In attempt to connect the convexity of digital sets, to the fact that digital set can be a fuzzy set, the notion of convexity of the membership function is introduced...

Consider the classification task of assigning a test object to one of two or more possible groups, or classes. An intuitive way to proceed is to assign the object to that class, to which the distance is minimal. As a distance measure to a class, we propose here to use the distance to the convex hull of that class. Hence the name Nearest Convex Hull (NCH) classification for the method. Convex-hu...

In this paper we address the problem of computing a minimal H-representation of the convex hull of the union of k H-polytopes in R. Our method applies the reverse search algorithm to a shelling ordering of the facets of the convex hull. Efficient wrapping is done by projecting the polytopes onto the two-dimensional space and solving a linear program. The resulting algorithm is polynomial in the...

This note concerns the computation of the convex hull of a given set P = {p1, p2, . . . , pn} of n points in the plane. Let h denote the size of the convex hull, ie the number of its vertices. The value h is not known beforehand, and it can range anywhere from a small constant to n. We hav e already seen that any convex hull algorithm requires at least Ω(n lg n) time in the worst case, and have...

In this paper we determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(logn) time per operation. The space usage of the data structure is O(n). The data structure supports extreme point queries in a given direction, tangen...

Convex hull calculation, which is one of the important topics computer aided geometric design, constitutes starting point this study. hull, has many definitions in literature, was calculated with convex combination approach our From definition all possible sets for given set [13], a body consisting n points obtained. In addition to mathematics and geometry, relationship between special generali...

Problem 1: Evaluating Convex Polygons This write-up presents several simple algorithms for determining whether a given set of twodimensional points defines a convex polygon (i.e., a convex hull). In Section 1.1, we introduce the notion of regular polygons and provide examples of both convex and non-convex point sets. Section 1.2 presents an algorithm for ordering a set of points such that a cou...