Skip to main content

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

  • 2244 Accesses

Summary

We consider geographic maps represented as plane graphs, which undergo a process of generalisation performed through sequences of local updates. Generalisation transforms a highly detailed map into one with fewer details, spanning many different scales of representation through the sequence of updates. We study intrinsic dependency relations among updates in the sequence and, on this basis, we derive a multi-scale model that supports efficient retrieval of maps at different scales, possibly variable through the domain.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. M. Bertolotto. Geometric modeling of spatial entities at multiple levels of resolution. Ph.D.Thesis, Department of Computer Science, University of Genova, DISI-TH-1998-01, 1998.

    Google Scholar 

  2. M. Bertolotto, L. De Floriani, and E. Puppo. Multiresolution topological maps, Advanced Geographic Data Modelling — Spatial Data Modelling and Query Languages for 2D and 3D Applications, M. Molenaar, S. De Hoop (eds.), Publications on Geodesy — New Series, N. 40, Netherland Geodetic Commission, pp. 179–190, 1994.

    Google Scholar 

  3. M. Bertolotto and M. J. Egenhofer. Progressive transmission of vector map data over the world wide web. GeoInformatica 5(4), pp. 345–373, 2001.

    Article  Google Scholar 

  4. B. Buttenfield. Progressive transmission of vector data on the internet: a cartographic solution. Proceedings 19th International Cartographic Conference, Ottawa, Canada, pp.581–590, 1999.

    Google Scholar 

  5. L. De Floriani and P. Magillo. Multiresolution mesh representation: models and data structures, Tutorials on Multiresolution in Geometric Modelling, A. Iske, E. Quak, M. S. Floater (eds.), Springer-Verlag, pp. 363–418, 2002.

    Google Scholar 

  6. D. H. Douglas and T. K. Pücker. 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, 1973.

    Google Scholar 

  7. P. Magillo, E. Puppo, and R. Viaña. A Multi-Scale Model for Geographic Maps. Technical Report, DISI-TR03-10, Department of Information and Computer Sciences, University of Genova, 2003.

    Google Scholar 

  8. E. Puppo and G. Dettori. Towards a formal model for multiresolution spatial maps. Advances in Spatial Databases, M. J. Egenhofer, J. R. Herring (eds.), LNCS Vol.951, Springer-Verlag, pp.152–169, 1995.

    Google Scholar 

  9. E. Puppo. Variable resolution triangulations. Computational Geometry Theory and Applications 11, pp.219–238, 1998.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Viaña, R., Magillo, P., Puppo, E. (2005). Multi-Scale Geographic Maps. In: Dodgson, N.A., Floater, M.S., Sabin, M.A. (eds) Advances in Multiresolution for Geometric Modelling. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26808-1_6

Download citation

Publish with us

Policies and ethics