Abstract
The concept of duality is used to understand and characterise how geographical objects are spatially related. It has been used extensively in 2D to qualify the boundaries between different types of terrain, and in 3D for navigation inside buildings, among others. In this chapter, we explore duality in four dimensions, in the context where space and other characteristics (e.g. time) are modelled as being in four dimensional space. We explain what duality in 4D entails, and we present two data structures that can be used to store the dual graph of a set of 4D objects. We also discuss applications where such data structures could be useful in the future.
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Notes
- 1.
Also called a 4-polytope or a 4-polyhedron.
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Acknowledgments
This research is supported by the Ministry of Higher Education in Malaysia (vote no. 02H97, Universiti Teknologi Malaysia) and by the Dutch Technology Foundation STW, which is part of the Netherlands Organisation for Scientific Research (NWO), and partly funded by the Ministry of Economic Affairs, Agriculture and Innovation. (Project code: 11300)
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Arroyo Ohori, K., Boguslawski, P., Ledoux, H. (2013). Representing the Dual of Objects in a Four-Dimensional GIS. In: Abdul Rahman, A., Boguslawski, P., Gold, C., Said, M. (eds) Developments in Multidimensional Spatial Data Models. Lecture Notes in Geoinformation and Cartography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36379-5_2
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