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.
This research was partially funded by grants from NSF under No. IST 86-09123 and Digital Equipment Corporation (Principal Investigator: Andrew U. Frank). Jeffrey P. Jackson was supported by an Undergraduate Research Experience grant from NSF under No. IRI 86-09123. The support from NSF for the NCGIA under grant number SES 88-10917 is gratefully acknowledged.
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Egenhofer, M.J., Frank, A.U., Jackson, J.P. (1990). A topological data model for spatial databases. In: Buchmann, A.P., Günther, O., Smith, T.R., Wang, YF. (eds) Design and Implementation of Large Spatial Databases. SSD 1989. Lecture Notes in Computer Science, vol 409. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52208-5_32
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