# frustum_of_simplex: Compute the percentage of the volume of the simplex that is... In volesti: Volume Approximation and Sampling of Convex Polytopes

## Description

A half-space H is given as a pair of a vector a\in R^d and a scalar z0\in R s.t.: a^Tx≤q z0. This function calls the Ali's version of the Varsi formula to compute a frustum of the simplex.

## Usage

 1 frustum_of_simplex(a, z0) 

## Arguments

 a A d-dimensional vector that defines the direction of the hyperplane. z0 The scalar that defines the half-space.

## Value

The percentage of the volume of the simplex that is contained in the intersection of a given half-space and the simplex.

## References

Varsi, Giulio, “The multidimensional content of the frustum of the simplex,” Pacific J. Math. 46, no. 1, 303–314, 1973.

Ali, Mir M., “Content of the frustum of a simplex,” Pacific J. Math. 48, no. 2, 313–322, 1973.

## Examples

 1 2 3 4 # compute the frustum of H: -x1+x2<=0 a=c(-1,1) z0=0 frustum = frustum_of_simplex(a, z0) 

volesti documentation built on July 14, 2021, 5:11 p.m.