volesti (version 1.1.2-9)

inner_ball: Compute an inscribed ball of a convex polytope

Description

For a H-polytope described by a \(m\times d\) matrix \(A\) and a \(m\)-dimensional vector \(b\), s.t.: \(P=\{x\ |\ Ax\leq b\} \), 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 \(i=1, \dots ,d\). Then the ball centered at the origin with radius \(r/ \sqrt{d}\) is an inscribed ball.

Usage

inner_ball(P)

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.

Arguments

P

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

Examples

# 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)