A topological data model for spatial databases
SSD '90 Proceedings of the first symposium on Design and implementation of large spatial databases
Dimension-independent modeling with simplicial complexes
ACM Transactions on Graphics (TOG)
Rounding arrangements dynamically
Proceedings of the eleventh annual symposium on Computational geometry
Realms: A Foundation for Spatial Data Types in Database Systems
SSD '93 Proceedings of the Third International Symposium on Advances in Spatial Databases
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Simplicial complexes are used to model topology in Geographic Information Systems (GIS). Line intersection is an essential operation to update them. We introduce a finite-resolution line intersection method, called Zero Order Intersection, and apply it to simplicial complexes. Any reliable implementation of a line intersection algorithm has to address the limitations of a discrete computational environment. If handled improperly, finite representation can cause drifting lines and similar effects in otherwise topologically consistent data. The Zero Order Intersection method is designed to avoid such inconsistencies. Its application to simplicial complexes results in the Discrete Simplicial Data Model which guarantees consistency and reliability of topological queries within a GIS.