Max Egenhofer, Andrew Frank, and Jeff Jackson Symposium on the Design and Implementation of Large Spatial Databases, Santa Barbara, CA,
A. Buchmann, O. Gunther, T. Smith, and Y. Wang (eds.), Lecture Notes in Computer Science, Vol. 409, Springer-Verlag, pp. 271-286, July 1989.
Abstract
There is a growing demand for engineering applications which need a
sophisticated treatment of geometric properties. Implementations of
Euclidian geometry, commonly used in current commercial Geographic
Information Systems and CAD/CAM, are impeded by the finiteness of
computers and their numbering systems. To overcome these
deficiencies a spatial data model is proposed which is based upon
the mathematical theory of simplices and simplicial complexes from
combinatorial topology and introduces completeness of
incidence and completeness of inclusion as an extension
to the closed world assumption. It guarantees the preservation of
topology under affine transformations. This model leads to
straightforward algorithms which are described. The implementation
as a general spatial framework on top of an object-oriented
database management system is discussed.
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Max Egenhofer, 
Andrew Frank, and Jeff Jackson