Abstract
This chapter attempts to describe the role of tessellated models of space within the discipline of Geographic Information Systems (GIS). We look at some of the basic operations in GIS, including dynamic and kinetic applications. We examine issues of topology and data structures, and produced a tessellation model that may be widely applied both to traditional “object” and “field” data types. Based on this framework it can be argued that tessellation models are fundamental to our understanding and processing of geographical space, and provide a coherent framework for understanding the “space” in which we exist.
Keywords
- Geographic Information System
- Voronoi Diagram
- Delaunay Triangulation
- Voronoi Cell
- Geographic Information System Data
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Blum H (1967) A transformation for extracting new descriptors of shape. In: Whaten-Dunn W (ed) Proceedings of the Symposium on Models for the Perception of Speech and Visual Form, MIT Press, Cambridge, Mass., pp 362–380
Chew P (1989) Constrained Delaunay Triangulations, Algorithmica 4, pp 97–108
Dakowicz M, Gold CM (2002) Extracting Meaningful Slopes from Terrain Contours. In: Proceedings of the Computational Science - ICCS 2002, Amsterdam, The Netherlands, Lecture Notes in Computer Science, Vol. 2331, Springer, Berlin Heidelberg New York, pp 144–153
Dakowicz M, Gold CM (2007) Finite Difference Method Runoff Modelling Using Voronoi Cells. In: Proceedings of the 5th ISPRS Workshop on Dynamic and Multi-dimensional GIS, Urumchi, China, pp 55–60
Devillers O (1999) On deletion in Delaunay triangulations. In: Proceedings of the 15th Annual ACM Symposium on Computational Geometry, pp 181–188
Einstein A (1961). Relativity: The Special and general Theory, 15th Edition (Lawson RW, translator), NewYork, Bonanza Crown
Fortune S (1987) A sweepline algorithm for Voronoi diagrams. Algorithmica 2: 153–174
Fritts MJ, Crowley WP, Trease H (1985) The Free-Lagrange Method. Lecture Notes in Physics Vol. 238, Springer, Berlin Heidelberg New York
Gold CM (1989) Chapter 3 - surface interpolation, spatial adjacency and G.I.S. In: Raper J (ed), Three Dimensional Applications in Geographic Information Systems, Taylor and Francis, London, England, pp 21–35
Gold CM (1990) Spatial data structures - the extension from one to two dimensions. In: Pau LF (ed) Mapping and Spatial Modelling for Navigation, Springer, Berlin Heidelberg New York, pp 11–39
Gold CM (1992) The Meaning of “Neighbour”. In: Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, Lecture Notes in Computing Science No. 639, Springer, Berlin Heidelberg New York, pp 220–235
Gold CM (1994) Dynamic data structures: the interactive map. In: Advanced Geographic Data Modelling - Spatial Data Modelling and Query Languages for 2D and 3D Applications, Netherlands Geodetic Commission Publications on Geodesy (New Series) 40, pp121–128
Gold CM (1997) Simple topology generation from scanned maps. In: Proceedings of Auto-Carto 13, ACM/ASPRS, 5, pp 337–346
Gold CM (1999) Crust and anti-crust: A one-step boundary and skeleton extraction algorithm. In: Proceedings of the ACM Conference on Computational Geometry, pp 189–196
Gold CM, Anton F (2007) Minutes, 3D Geo-Information Working Group on Modelling, 3D-Geoinfo-07 Workshop, Delft, http://www.3d-geoinfo-07.nl
Gold CM, Dakowicz M (2005) The Crust and Skeleton – Applications in GIS. In: Proceedings of the 2nd International Symposium on Voronoi Diagrams in Science and Engineering, Seoul, Korea, pp 33–42
Gold CM, Dakowicz M (2006) Kinetic Voronoi - Delaunay drawing tools. In: Proceedings of the 3rd International Symposium on Voronoi Diagrams in Science and Engineering, Banff, Canada, pp 76–84
Gold CM, Snoeyink J (2001) A one-step crust and skeleton extraction algorithm. Algorithmica 30: 144–163
Gold CM, Chau M, Dzieszko M, Goralski R (2004) 3D Geographic Visualization: The Marine GIS. In: Fisher PF (ed) Developments in Spatial Data Handling - 11th International Symposium on Spatial Data Handling, Springer, Berlin Heidelberg New York, pp 17–28
Gold CM, Nantel J, Yang W (1996) Outside-in: an alternative approach to forest map digitizing. International Journal of Geographical Information Systems (IJGIS) 10: 291–310
Goodchild MF, Yuan M, Cova TJ (2007) Towards a general theory of geographic representation in GIS. International Journal of Geographical Information Science (IJGIS) 21: 239–260
Goralski IR, Gold CM (2007) Maintaining the Spatial Relationships of Marine Vessels Using the Kinetic Voronoi Diagram. In: Proceedings of the ISVD 2007, Glamorgan, UK, pp 84–90
Guibas L, Stolfi J (1985) Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. Transactions on Graphics 4: 74–123
Guibas L, Mitchell JSB, Roos T (1991) Voronoi Diagrams of moving points in the plane. In: Proceedings of the 17th International Workshop on Graph Theoretic Concepts in Computer Science, Fischbachau, Germany, Lecture Notes in Computer Science, Springer, Berlin Heidelberg New York, 70, pp 113–125
Held M (2001) VRONI: an engineering approach to the reliable and efficient computation of Voronoi Diagrams of points and line segments. Computational Geometry, Theory and Application 18: 95–123
Jones CB, Bundy GL, Ware JM (1995) Map generalization with a triangulated data structure. Cartography and Geographic Information Systems 22: 317–331
Karavelas MI (2004) A robust and efficient implementation for the segment Voronoi Diagram. In: International Symposium on Voronoi Diagrams in Science and Engineering 2004, pp 51–62
Ledoux H, Gold CM (2007) Simultaneous storage of primal and dual three dimensional subdivisions. Computers, Environment and Urban Systems 31: 393–408
Mioc D, Anton F, Gold CM, Moulin B (1999) “Time travel” Visualization in a Dynamic Voronoi Data Structure. Cartography and Geographic Information Science 26: 99–108
Mostafavi M, Gold CM (2004) A Global Spatial Data Structure for Marine Simulation. International Journal of Geographical Information Science (IJGIS) 18: 211–227
Mostafavi M, Gold CM, Dakowicz M (2003) Dynamic Voronoi/Delaunay Methods and Applications. Computers and Geosciences 29: 523–530
Okabe A, Boots B, Sugihara K, Chiu SN (2000) Spatial Tessellations - Concepts and Applications of Voronoi Diagrams (2nd edition), John Wiley and Sons, Chichester
Roos T (1990) Voronoi diagrams over dynamic scenes. In: Proceedings of the 2nd Canadian Conference on Computational Geometry, pp 209–213
Shewchuk JR (1997) Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates. Discrete and Computational Geometry 18: 305–363
Sibson R (1981) A brief description of natural neighbour interpolation. In: Barnett V (ed) Interpreting Multivariate Data, Wiley, New York, USA, pp 21–36
Sugihara K, Iri M, Inagaki H, Imai T (2000) Topology-oriented implementation – an approach to robust geometric algorithms. Algorithmica 27: 5–20
Thibault D, Gold CM (2000) Terrain reconstruction from contours by skeleton construction. GeoInformatica 4: 349–373
Winter S, Frank AU (2000) Topology in Raster and Vector Representation. GeoInformatica 4: 35–65
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Gold, C. (2009). A Common Spatial Model for GIS. In: Navratil, G. (eds) Research Trends in Geographic Information Science. Lecture Notes in Geoinformation and Cartography(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88244-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-88244-2_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88243-5
Online ISBN: 978-3-540-88244-2
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)