The Discrete Simplicial Data Model.
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.