plotpolygon

A zonohedron is pointed iff there is a vector n
so the inner product of all the zonohedron generators with n is positive.
In other terminology, it is pointed iff there is an open halfspace
that contains all the generators.
 
When n exists, a neighborhood of 0 can be cut by a plane
orthogonal to n and the intersection is a polygon.
Since n is not unique, the polygon is only unique up
to a 2D projective transformation.

Computes a zonohedron from real vector generators. The package also computes zonogons (2D zonotopes) and zonosegs (1D zonotopes). An elementary S3 class for matroids is included, which supports matroids with rank 3, 2, and 1. Optimization methods are taken from Heckbert (1985) <https://www.cs.cmu.edu/~ph/zono.ps.gz>.

Glenn Davis

zonohedra

Compute and Plot Zonohedra from Vector Generators

plotpolygon function

<dl><dt>x</dt>
<dd>a zonohedron object as returned by the constructor <code>zonohedron()</code>.
It must be pointed.</dd>
<dt>normal</dt>
<dd>the vector n to use - a non-zero numeric vector of length 3.
If it is given, the validity is checked and if invalid it is an error.
 
If it is <code>NULL</code>, a few canonical normals are first tested for validity.
If they are invalid, then a valid one is computed.</dd>
<dt>points</dt>
<dd>If <code>TRUE</code> then draw the vertices of the polygon</dd>
<dt>labels</dt>
<dd>If <code>TRUE</code> then draw labels,
taken from the ground set of the simplified matroid, near the vertices</dd>
</dl>

Arguments

A zonohedron is pointed iff there is a vector n
so the inner product of all the zonohedron generators with n is positive.
In other terminology, it is pointed iff there is an open halfspace
that contains all the generators.
 
When n exists, a neighborhood of 0 can be cut by a plane
orthogonal to n and the intersection is a polygon.
Since n is not unique, the polygon is only unique up
to a 2D projective transformation.

plot the generator polygon associated with a pointed zonohedron — plotpolygon

<dl>

<dt>x</dt>
<dd>a zonohedron object as returned by the constructor <code>zonohedron()</code>.
It must be pointed.</dd>


<dt>normal</dt>
<dd>the vector n to use - a non-zero numeric vector of length 3.
If it is given, the validity is checked and if invalid it is an error.
 
If it is <code>NULL</code>, a few canonical normals are first tested for validity.
If they are invalid, then a valid one is computed.</dd>


<dt>points</dt>
<dd>If <code>TRUE</code> then draw the vertices of the polygon</dd>


<dt>labels</dt>
<dd>If <code>TRUE</code> then draw labels,
taken from the ground set of the simplified matroid, near the vertices</dd>


</dl>

plotpolygon: plot the generator polygon associated with a pointed zonohedron

Description

Usage

Value

Arguments

Details

See Also