Description Usage Arguments Value References Examples

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.

1 | ```
frustum_of_simplex(a, z0)
``` |

`a` |
A |

`z0` |
The scalar that defines the half-space. |

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

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.

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

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