Construction of three-dimensional improved-quality triangulations using local transformations
SIAM Journal on Scientific Computing
A Topological Data Model for Spatial Databases
SSD '89 Proceedings of the First Symposium on Design and Implementation of Large Spatial Databases
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Proceedings of the nineteenth annual symposium on Computational geometry
Simplification and improvement of tetrahedral models for simulation
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Streaming computation of Delaunay triangulations
ACM SIGGRAPH 2006 Papers
Modelling 3D spatial objects in a geo-DBMS using a 3D primitive
Computers & Geosciences
Flipping to robustly delete a vertex in a delaunay tetrahedralization
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
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COSIT'05 Proceedings of the 2005 international conference on Spatial Information Theory
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Delaunay refinement algorithms for triangular mesh generation
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GIScience '08 Proceedings of the 5th international conference on Geographic Information Science
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Computers & Geosciences
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This paper introduces a new compact topological 3D data structure. The proposed method models the real world as a complete decomposition of space and this subdivision is represented by a constrained tetrahedral network (TEN). Operators and definitions from the mathematical field of simplicial homology are used to define and handle this TEN structure. Only tetrahedrons need to be stored explicitly in a (single column) database table, while all simplexes of lower dimensions, constraints and topological relationships can be derived in views. As a result the data structure is relatively compact and easy to update, while it still offers favourable characteristics from a computational point of view as well as presence of topological relationships.