minkowskisum {zonohedra}

Minkowski sum of Two zonotopes

Description

A zonotope can be viewed as a Minkowski sum of line segments, with one endpoint at 0. Therefore, the Minkowski sum of two zonotopes (in the same dimension) is also a zonotope.

Usage

## S3 method for class 'zonotope'
minkowskisum( zono1, zono2, e0=0, e1=1.e-6, e2=1.e-10, ground=NULL, ... )

## S3 method for class 'zonotope'
zono1 %+% zono2

Arguments

zono1

a zonotope object - a zonohedron, a zonogon, or a zonoseg

zono2

a zonotope object with the same dimension as zono1

e0

see zonohedron()

e1

see zonohedron()

e2

see zonohedron()

ground

the ground set of the returned zonotope. If ground is NULL, it is set to the ground set of zono1 followed by the ground set of zono2 translated sufficiently to not intersect that of zono1.

...

not used

Details

After verifying that zono1 and zono2 are the same dimension, it takes the 2 matrices, cbinds them, and passes the new matrix to the appropriate constructor, along with the other arguments. There are no special optimizations.

Value

minkowskisum() returns a zonotope of the same dimension as zono1 and zono2.
%+% is a more convenient binary operator that calls minkowskisum(), but without the flexibility of the extra arguments.
In case of error, the function returns NULL.

References

Zonohedron - Wikipedia.
https://en.wikipedia.org/wiki/Zonohedron.

See Also

zonohedron(), zonogon(), zonoseg()