Templated meshes and geometries have been defined in Section 4.1. The definitions and lemmas provide solid and abstract mechanisms for geometries and meshes with symmetries and/or similarities.
As discussed in Section 4.2, issues arise at locations where two template instances meet (cf. Lemma 4.2). The conformity has to be ensured at these locations. To identify and handle these issues in algorithms, the boundary patch partition (cf. Section 4.3) has been developed.
Additional issues arise for templated structures with irregular instance graphs as some mesh generation and adaptation algorithms get more intricate (cf. Section 5.1.2 and Section 5.2.2)
However, for objects with reflecting symmetries, there are no issues or restrictions as shown in Section 6.2 (cf. Lemma 6.1) and Section 6.4.1 (cf. Lemma 6.2), which is also true for objects which have rotational and reflective symmetries (cf. Section 6.4.2). Conformity issues potentially occur for objects with rotational symmetries on instance interfaces of slice templates. However, the boundary patch partition is much easier to determine for such objects and the resulting instance graph is regular (cf. Section 6.3).
florian
2016-11-21
