A detailed view on the implementation of the topological data structures is given in . The discussed environment comprises a topology library (GTL) that is based on the properties of a single cell and on the properties of a the cell complex. By single cell properties the internal structure of one single cell can be determined. For instance, a triangle consists of three bounding edges and three bounding vertices. Typically, the cell topological properties for all cells are identical within a cell complex. The complex properties, however, contain the incidence information of topological elements of different cells, for instance the set of all cells incident to a vertex. Once cell and complex properties are obtained, all different traversal mechanisms can be obtained.
Next, methods for the storage of quantities (data access) are introduced. This container provides associative data access with two different keys, namely with topological elements, such as vertices and cells, and with quantity keys. One quantity (section) is defined on various topological elements of the same quantity key. Furthermore, it is possible to access all quantity values which are associated with the same topological element.
Benchmarks of the topological library are given that show that the performance of the provided libraries is in the same order of magnitude as comparable conventionally designed special purpose libraries. A comparison of incidence traversal operations to the boost graph library shows that on most platforms the GTL yields higher performance than an equivalent implementation of the boost graph library. The functional library is compared to the imperative specification of the respective expression. This library is comparable to state of the art highly specialized libraries .