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