# inner_ball: Compute an inscribed ball of a convex polytope In volesti: Volume Approximation and Sampling of Convex Polytopes

## Description

For a H-polytope described by a m\times d matrix A and a m-dimensional vector b, s.t.: P=\{x\ |\ Ax≤q b\} , this function computes the largest inscribed ball (Chebychev ball) by solving the corresponding linear program. For both zonotopes and V-polytopes the function computes the minimum r s.t.: r e_i \in P for all i=1, … ,d. Then the ball centered at the origin with radius r/ √{d} is an inscribed ball.

## Usage

 1 inner_ball(P) 

## Arguments

 P A convex polytope. It is an object from class (a) Hpolytope or (b) Vpolytope or (c) Zonotope or (d) VpolytopeIntersection.

## Value

A (d+1)-dimensional vector that describes the inscribed ball. The first d coordinates corresponds to the center of the ball and the last one to the radius.

## Examples

 1 2 3 4 5 6 7 # compute the Chebychev ball of the 2d unit simplex P = gen_simplex(2,'H') ball_vec = inner_ball(P) # compute an inscribed ball of the 3-dimensional unit cube in V-representation P = gen_cube(3, 'V') ball_vec = inner_ball(P) 

volesti documentation built on July 14, 2021, 5:11 p.m.