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Hölbling Werner

The Discrete Simplicial Data Model.

This work is an extension for finite implementations of the Simplicial Data Model. The Simplicial Data Model belongs to the class of complete topological data models for GIS. Any implementation of geometric data models has to address the problem of finite representation, i.e., the fact that computer geometry is always grid geometry. If handled improperly, finite representations can cause disturbing effects (i.e., drifting line segments) in otherwise topologically consistent data. Greene and Yao have proposed a method which solves the problem of the complete intersection of a set of line segments in the discrete plane. Part one of this thesis tries to integrate the Greene and Yao approach with the Simplicial Data Model, showing that this is not worth the effort, because topological inconsistencies still remain. Part two develops the Discrete Line Intersection and successfully applies it to simplicial complexes. The resulting Discrete Simplicial Data Model is algebraically specified and implemented as a prototype in the GOFER functional programming language.

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