Considerations toward a dynamic mesh data structure

The use of 3D shapes in different domains such as in engineering, entertainment, cultural heritage or medicine, is essential for representing 3D physical reality. Regardless of whether the 3D shapes are representing physically or digitally born objects, meshes are a versatile and common representation for the 3D reality. Nonetheless, the mesh generation process does not always produce qualitative results, thus incomplete, non-orientable or non-manifold meshes frequently are the input for the domain application. The domain application itself also demands special requirements, e.g. an engineering simulation requires a volumetric mesh either tetrahedral or hexahedral, while a cultural heritage color enhancement uses a triangular or quadrangular mesh, or in both cases even hybrid meshes. Moreover, the processes applied on the meshes (e.g. modeling, simulation, visualization) need to support some operations, such as querying neighboring information or enabling dynamic changes of geometry and topology. These operations need to be robust, hence the neighboring information can be consistently updated, during the dynamic changes. Dealing with this mesh diversity usually requires dedicated data structures for performing in the given domain application. This paper compiles the considerations toward designing a data structure for dynamic meshes in a generic and robust manner, despite the type and the quality of the input mesh. These aspects enable a flexible representation of 3D shapes toward general purpose geometry processing for dynamic meshes in 2D and 3D.