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## Parameterized polyhedra representation

Polylib manipulates rational polyhedra as seen in the previous chapters. There are two dual representations of polyhedra: the implicit representation, as a set of constraints, and the Minkowski representation, as a set of lines, rays and vertices.

A parameterized polyhedron is defined in the implicit form by a finite number of inequalities and equalities, the difference from the classical approach being that the constant part depends linearly on a parameter vector for both equalities and inequalities:

where is a integer matrix, a integer matrix, is an integer -vector, is a integer matrix, a integer matrix and is an integer -vector.

The Minkowski representation, as a set of lines, rays, and vertices, of a parameterized polyhedron is:

where is the matrix containing the lines, the matrix containing the rays, and the matrix depending on the parameters containing the vertices of the polyhedron.

Polylib includes an algorithm computing the vertices of a parameterized polyhedron.

Next: Parameterized vertices representation Up: Theoretical background Previous: Theoretical background   Contents
Sorin Olaru 2002-04-24