Abstract
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.
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Ho¨lbling, W., Kuhn, W. & Frank, A.U. Finite-Resolution Simplicial Complexes. GeoInformatica 2, 281–298 (1998). https://doi.org/10.1023/A:1009773822002
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DOI: https://doi.org/10.1023/A:1009773822002