Representing geometric structures in d dimensions: topology and order
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
Simplicial mesh generation with applications
Simplicial mesh generation with applications
High Resolution Forward And Inverse Earthquake Modeling on Terascale Computers
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
Gridfields: model-driven data transformation in the physical sciences
Gridfields: model-driven data transformation in the physical sciences
Algebraic manipulation of scientific datasets
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Survey of graph database models
ACM Computing Surveys (CSUR)
A polyhedron representation for computer vision
AFIPS '75 Proceedings of the May 19-22, 1975, national computer conference and exposition
GrAL-the grid algorithms library
Future Generation Computer Systems
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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 ImG-Complexes. ImG-Complex can support a wide range of application domains. We introduce optional and application-specific 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.