2. 5 Formulation of Discrete Problems

In the former section the topological base operations were defined in order to retrieve elements which are incident with a given base element. As an example, all vertices incident with a given face can be determined. A second feature resulting from topological considerations is defined in this section, namely orientation. For each two elements of dimension $n$ and $n-1$ , an orientation function is defined that returns if these elements are consistently oriented.

Furthermore the method of association of topological data and numerical values allows to store data on elements of the underlying cell complex. These numerical values can contain geometrical information such as coordinate as well as curvature information.

In order to perform operations on functions which are based on the construction shown in the former section, a framework of base operations has to be defined, with which all necessary calculations can be carried out.