inner_ball {volesti}

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)

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

# 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)