The result file (*.gdr) is opened in the Result Viewer after the computation is finished. Under the Results-Report subtab the four Minkowski Parameters characterize the mathematical topology of the structure:

The parameter Volume is the volume occupied of the chosen Material ID. Its percentage is also given by Volume Fraction.

The Surface area is the boundary between the chosen Material ID and all other Material IDs. It is computed as in Algorithm 2 of the Estimate Surface Area command (see also J. Ohser, F. Mücklich).

The Integral of mean curvature describes the mean curvature of the selected Material ID, given by the following formula

where is the chosen Material ID, is a surface element of the chosen Material ID and the parameters and are defined as the radii of the two principal curvatures and from the respective surface element.

The Integral of total curvature describes the total curvature of the selected Material ID:

The surface area and the curvature values are given additionally as specific values, which are normalized by the total volume of the structure.

The Euler characteristic () is a topological number, that describes to what extent the structure is connected. It equals times the integral of total curvature. This results in , where is the number of objects, is the number of loops and is the number of cavities.If symmetric boundary conditions are used (Periodic Structure not checked), the staggered grid leads to half-cells at the domain boundary. Therefore, non-integer Euler characteristics might occur.

The screenshot shows the computed Minkowski parameters for the pore space (here Material ID00, on the left), and the solid material (ID01, right) of the structure shown above.