support: The Support Function for the Polar Zonoid in...

In polarzonoid: Compute Maps and Properties of Polar Zonoids

The Support Function for the Polar Zonoid in \mathbb{R}^{2n+1}

Description

This section calculates the classical support function for convex bodies, for the specific case of the polar zonoid.

Usage

support( direction )

Arguments

direction

an Rx(2n+1) matrix with non-zero direction vectors in the R rows. If the number of columns is even, a column of 0s is appended to make it odd. direction can also be a vector of length M, which is then converted to a 1xM matrix.

Details

Each direction is converted to a non-zero trignometric polynomial. The roots are computed using trigpolyroot() and the the roots are converted to arcs, and thus arcs. The function boundaryfromarcs() is then used to compute argmax, and then value.

Value

support() returns a data frame with R rows and these columns:

direction	the given matrix of directions
value	the value of the support function of the zonoid, in the given direction
argmax	the point on the boundary of the zonoid where the maximum is taken
arcs	the number of arcs for argmax. This number is always \le n.

In case of error, the function returns NULL.

See Also

boundaryfromarcs(), trigpolyroot()

polarzonoid documentation built on June 13, 2025, 9:08 a.m.