Database Support for Unstructured Meshes

Despite ubiquitous usage of unstructured mesh in many application domains (e.g., computer aided design, scientific simulation, climate modeling, etc.), there is no specialized mesh database which supports storing and querying such data structures. Existing mesh libraries use file-based APIs which do not support declarative querying and are difficult to maintain. A mesh database can benefit these domains in several ways such as: declarative query language, ease of maintenance, query optimization, etc. In this thesis work, the core idea is to have a very general model which can represent objects from different domains and specialize it to smaller object classes using combinatorial constraints. We propose the Incidence multi-Graph Complex (ImG-Complex) data model for storing combinatorial aspect of meshes in a database. We extend incidence graph (IG) representation with multi-incidence information (ImG) to represent a class of objects which we call ImGComplexes. ImG-Complex can support a wide range of application domains. We introduce optional and applicationspecific constraints to restrain the general ImG model to specific object classes or specific geometric representations. The constraints check validity of meshes based on the properties of the modeled object class. Finally, we show how graph databases can be utilized and reused to query some combinatorial mesh queries based on the (possibly constrained) ImG model. In particular, we show the strengths and limitations of a graph-only query language in expressing combinatorial mesh queries.