Line Simplification in the Presence of Non-Planar Topological Relationships

  • Padraig Corcoran
  • Peter Mooney
  • Michela Bertolotto
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)


A main objective of many line simplification methods is to progressively reduce the scale of shape properties and, in turn, provide a more explicit representation of global shape properties. However, current simplification methods which attempt to achieve this objective, while also maintaining non-planar topological relationships, are restricted and cannot always achieve an optimal result. In this paper, we present a line simplification method which removes these restrictions. This is achieved through the use of a computable set of topological invariants, which is complete and allows the topological consistency of an arbitrary simplification to be determined.


Line simplification Map generalisation Topology 


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Research presented in this paper was funded by the Irish Research Council for Science Engineering and Technology (IRCSET) EMPOWER program, the Irish Environmental Protection Agency (EPA) STRIVE programme (Grant 2008-FS-DM-14-S4) and a Strategic Research Cluster Grant (07/SRC/I1168) from Science Foundation Ireland under the National Development Plan.


  1. Agrawala, M. and Stolte, C., 2001. Rendering effective route maps: improving usability through generalization. In: SIGGRAPH New York: ACM, pp. 241–249.Google Scholar
  2. Clementini, E. and Di Felice, P., 1998. Topological invariants for lines. IEEE Transactions on Knowledge and Data Engineering, 10 (1), pp. 38 –54.Google Scholar
  3. Corcoran, P., Mooney, P., and Winstanley, A., 2011. Planar and non-planar topologically consistent vector map simplification. International Journal of Geographical Information Science, 25 (10), pp. 1659–1680.Google Scholar
  4. de Berg, M., van Kreveld, M. and Schirra, S., 1998. Topologically correct subdivision simplication using the bandwidth criterion. Cartography and Geographic Information Science, 25 (4), pp. 243-257.Google Scholar
  5. Douglas, D. and Peucker, T., 1973. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. The Canadian Cartographer, 10 (2), pp. 112–122.Google Scholar
  6. Egenhofer, M.J., 1991. Reasoning about Binary Topological Relations. In: Proceedings of the Second International Symposium on Advances in Spatial Databases, SSD’91 London, UK: Springer-Verlag, pp. 143–160.Google Scholar
  7. Jones, C.B., 1997. Geographical information systems and computer cartography. Prentice Hall.Google Scholar
  8. Kopf, J., et al., 2010. Automatic generation of destination maps. ACM Transactions on Graphics, 29 (6), pp. 1–12.Google Scholar
  9. Kulik, L., Duckham, M., and Egenhofer, M., 2005. Ontology-Driven Map Generalization. Journal of Visual Languages and Computing, 16 (3), pp. 245–267.Google Scholar
  10. Latecki, L.J. and Lakmper, R., 1999. Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution. Computer Vision and Image Understanding, 73 (3), pp. 441–454.Google Scholar
  11. Lonergan, M. and Jones, C.B., 2001. An Iterative Displacement Method for Conflict Resolution in Map Generalization. Algorithmica, 30, pp. 287–301.Google Scholar
  12. Mortenson, M., 2007. Geometric transformations for 3d modeling. 2nd New York, NY, USA: Industrial Press, Inc.Google Scholar
  13. Nollenburg, M.; Wolff, A., 2011. Drawing and Labeling High-Quality Metro Maps by Mixed-Integer Programming. IEEE Transactions on Visualization and Computer Graphics, 17 (5), pp. 626 – 641.Google Scholar
  14. Saalfeld, A., 1999. Topologically Consistent Line Simplification with the Douglas-Peucker Algorithm. Cartography and Geographic Information Science, 26 (1), pp. 7–18.Google Scholar
  15. Stott, J., et al., 2011. Automatic Metro Map Layout Using Multicriteria Optimization. Visualization and Computer Graphics, IEEE Transactions on, 17 (1), pp. 101–114.Google Scholar
  16. Weibel, R., 1996. A Typology of Constraints to Line Simplification. In: Advances in GIS Research II (Proceedings 7th International Symposium on Spatial Data Handling), 533–546 London: Taylor & Francis.Google Scholar
  17. Weihua, D., 2008. Generating On-Demand Web Mapping through Progressive Generalization. In: Education Technology and Training, Vol. 2, Dec, pp.163–166.Google Scholar
  18. Wilson, D., Bertolotto, M., and Weakliam, J., 2010. Personalizing map content to improve task completion efficiency. International Journal of Geographical Information Science, 24 (5), pp. 741–760.Google Scholar
  19. Wise, S., 2002. GIS Basics. CRC Press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Padraig Corcoran
    • 1
  • Peter Mooney
    • 2
  • Michela Bertolotto
    • 1
  1. 1.School of Computer Science and InformaticsUniversity College DublinDublinIreland
  2. 2.Department of Computer ScienceNational University of Ireland MaynoothMaynoothIreland

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