Constructing an n-dimensional Cell Complex from a Soup of (n − 1)-Dimensional Faces
There is substantial value in the use of higher-dimensional (>3D) digital objects in GIS that are built from complex real-world data. This use is however hampered by the difficulty of constructing such objects. In this paper, we present a dimension independent algorithm to build an n-dimensional cellular complex with linear geometries from its isolated (n − 1)-dimensional faces represented as combinatorial maps. It does so by efficiently finding the common (n − 2)-cells (ridges) along which they need to be linked. This process can then be iteratively applied in increasing dimension to construct objects of any dimension. We briefly describe combinatorial maps, present our algorithm using them as a base, and show an example using 2D, 3D and 4D objects which was verified to be correct, both manually and using automated methods.
KeywordsGeographic Information System Cell Complex Open Geospatial Consortium Incremental Construction Identity Comparison
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- 1.Peuquet, D.J.: Representations of Space and Time. Guilford Press (2002)Google Scholar
- 2.van Oosterom, P., Meijers, M.: Towards a true vario-scale structure supporting smooth-zoom. In: Proceedings of the 14th ICA/ISPRS Workshop on Generalisation and Multiple Representation, Paris (2011)Google Scholar
- 3.Baglatzi, A., Kuhn, W.: On the formulation of conceptual spaces for land cover classification systems. In: Vandenbroucke, D., Bucher, B., Crompvoets, J. (eds.) Geographic Information Science at the Heart of Europe. Lecture Notes in Geoinformation and Cartography, pp. 173–188. Springer (2013)Google Scholar
- 4.Raper, J.: Multidimensional geographic information science. Taylor & Francis (2000)Google Scholar
- 5.Stoter, J., Ledoux, H., Meijers, M., Arroyo Ohori, K., van Oosterom, P.: 5D modeling - applications and advantages. In: Proceedings of the Geospatial World Forum 2012, p. 9 (2012)Google Scholar
- 6.Mäntylä, M.: An introduction to solid modeling. Computer Science Press, New York (1988)Google Scholar
- 7.Baumgart, B.G.: A polyhedron representation for computer vision. In: Proceedings of the National Computer Conference and Exposition, May 19-22, pp. 589–596 (1975)Google Scholar
- 9.Hatcher, A.: Algebraic Topology. Cambridge University Press (2002)Google Scholar
- 11.OGC: OpenGIS Implementation Specification for Geographic Information - Simple Feature Access - Part 1: Common Architecture. Open Geospatial Consortium, 1.2.1 edn. (May 2011)Google Scholar
- 12.Open Geospatial Consortium: OGC City Geography Markup Language (CityGML) Encoding Standard, 2.0.0 edn. (April 2012)Google Scholar
- 13.Edmonds, J.: A combinatorial representation of polyhedral surfaces. Notices of the American Mathematical Society 7 (1960)Google Scholar
- 15.Poudret, M., Arnould, A., Bertrand, Y., Lienhardt, P.: Cartes combinatoires ouverts. Technical Report 2007-01, Laboratoire SIC, UFR SFA, Université de Poitiers (October 2007)Google Scholar