6 Decompositions and Symmetries

In this chapter, decomposition methods of geometries for templated structures are presented and discussed. A special focus is laid on geometries with symmetries. Taking care of issues and dependencies for templated structures in mesh generation and adaptation algorithms is complicated for objects with general similarities (cf. Chapter 5). However, for objects with symmetries, most of these issues and dependencies are much easier to handle.

Section 6.1 covers general identification methods for mesh and geometry decompositions. Special circumstances and algorithms for reflective symmetries and rotational symmetries are presented and discussed in Section 6.2 and Section 6.3, respectively. Finally, Section 6.4 covers combinations of symmetries.