In some cases it is necessary to determine the volume of a cell. For instance, many formulae for distinct integrals lead to a formulation which contains the original volume. In the following case the calculation of the volume is shown for a tetrahedron. A typical formulation of the volume of a general simplex can be defined as follows.

(2.60) |

For the determination of this determinant value it is necessary to obtain one definite vertex from the set of incident vertices . This can be easily provided by a first vertex function which returns only one vertex of the cell. Furthermore, it is necessary to remove the respective vertex from the set of vertices . Using the operator, a matrix can be provided. The vector value quantity contains the coordinate of the vertices.

(2.61) |

The expression evaluates the coordinate of the first of the incident vertices passed by the function. The accumulation forms a vector in which the resulting vectors of the subtractions are inserted.

Michael 2008-01-16