disjointarcs

Test whether a set of arcs are pairwise strictly disjoint.

arc disjointness

In each odd dimension is a convex body - the polar zonoid - whose generating functions are trigonometric polynomials. The polar zonoid is a straightforward generalization of the polar zonohedron in dimension 3, as defined by Chilton and Coxeter (1963) <doi:10.2307/2313051>. The package has some applications of the polar zonoid, including the properties of configuration spaces of arcs on the circle and 3x3 rotation matrices. There is also a root solver for trigonometric polynomials.

Glenn Davis

polarzonoid

Compute Maps and Properties of Polar Zonoids

arc disjointness function

<dl><dt>arcmat</dt>
<dd>an Nx2 matrix with an arc definition in each row;
so the total number of arcs is N.
The 1st number in the row is the center of the arc,
and the 2nd number is the length of the arc;
both in radians. 
The length can be 0 or \(2\pi\),
defining the empty arc and the full circle respectively.
For these improper arcs, there must be only 1 row,
and the center is ignored.</dd></dl>

Arguments

arc disjointness — arc disjointness

<dl>

<dt>arcmat</dt>
<dd>an Nx2 matrix with an arc definition in each row;
so the total number of arcs is N.
The 1st number in the row is the center of the arc,
and the 2nd number is the length of the arc;
both in radians. 
The length can be 0 or \(2\pi\),
defining the empty arc and the full circle respectively.
For these improper arcs, there must be only 1 row,
and the center is ignored.</dd>

</dl>

arc disjointness: arc disjointness

Description

Usage

Value

Arguments

See Also