volesti: Volume Approximation and Sampling for Convex Polytopes in R

Random Polytopes, Convex Bodies, and Approximation

Assume K ⊂ R is a convex body and Xn ⊂ K is a random sample of n uniform, independent points from K. The convex hull of Xn is a convex polytope Kn called random polytope inscribed in K. We are going to investigate various properties of this polytope: for instance how well it approximates K, or how many vertices and facets it has. It turns out that Kn is very close to the so called floating body...

Feasible Region Approximation Using Convex Polytopes

A new technique for polytope approximation of the feasible region for a design is presented. This method is computationally less expensive than the simplicial approximation method [1]. Results on several circuits are presented, and it is shown that the quality of the polytope approximation is substantially better than an ellipsoidal approximation.

Linear time approximation of 3D convex polytopes

Fine Approximation of Convex Bodies by Polytopes

We prove that for every convex body K with the center of mass at the origin and every ε ∈ ( 0, 12 ) , there exists a convex polytope P with at most eO(d)ε− d−1 2 vertices such that (1− ε)K ⊂ P ⊂ K.

Hausdorff approximation of 3D convex polytopes

Let P be a convex polytope in R, d = 3 or 2, with n vertices. We present linear time algorithms for approximating P by simpler polytopes. For instance, one such algorithm selects k < n vertices of P whose convex hull is the approximating polytope. The rate of approximation, in the Hausdorff distance sense, is best possible in the worst case. An analogous algorithm, where the role of vertices is...