Omnidimensional Convex Polytopes

Convex Polytopes

The study of convex polytopes in Euclidean space of two and three dimensions is one of the oldest branches of mathematics. Yet many of the more interesting properties of polytopes have been discovered comparatively recently, and are still unknown to the majority of mathematicians. In this paper we shall survey the subject, mentioning some of the most recent results, and stating the more importa...

Basic Properties of Convex Polytopes

Convex polytopes are fundamental geometric objects that have been investigated since antiquity. The beauty of their theory is nowadays complemented by their importance for many other mathematical subjects, ranging from integration theory, algebraic topology, and algebraic geometry (toric varieties) to linear and combinatorial optimization. In this chapter we try to give a short introduction, pr...

Barycentric coordinates for convex polytopes

An extension of the standard barycentric coordinate functions for simplices to arbitrary convex polytopes is described. The key to this extension is the construction, for a given convex polytope, of a unique polynomial associated with that polytope. This polynomial, the adjoint of the polytope, generalizes a previous two-dimensional construction described by Wachspress. The barycentric coordina...

Domain Triangulation Between Convex Polytopes

In this paper, we propose a method for solving the problem triangulation of a domain between convex polyhedrons in ddimensional space using Delaunay triangulation in O(N) time. Novelty of our work is in using a modified Delaunay triangulation algorithm with constraints.

Combinatorial Aspects of Convex Polytopes