Surface mesh qualities

3D surface models are often stored as indexed face sets, whereas algorithms can typically treat only a subset of the so-representable surfaces. Besides this gap between "potential" input and "allowed" input, more and more algorithms specify their input requirements at a high level of abstraction (e.g. "natural" shapes), and this makes it difficult to automatically assess the appropriateness of a specific model. In this article, surface meshes are analyzed in terms of indexed face sets and are characterized based on a collection of "qualities". Qualities of a surface mesh represent the peculiarities of both the surface and its combinatorial representation, can be combined to formally define input requirements of algorithms, can be exploited to effectively estimate high-level categorizations of 3D objects in a collection, and can be used to quickly produce benchmarks for geometry processing algorithms starting from unstructured digital libraries.