3.3 Symmetry and Similarity

The main goal of this work is to take advantage in storing and generating meshes of geometries with symmetries and similarities. The identification process of these properties is non-trivial but crucial. Two different geometrical properties are of interest: Symmetries and similarities. In the literature, similarities are often referred to as local symmetries or partial symmetries.

In general, the detection of symmetries and similarities is a very challenging task. One has to distinguish between exact and approximate symmetries or similarities. The first rarely occurs in practice due to numerical issues or inaccuracies in geometric modeling. The latter does not suffer from such issues. Section 3.3.1 and Section 3.3.2 covers detection of symmetries and similarities, respectively. Symmetry-aware mesh processing is discussed in Section 3.3.3.