Skip to main content

Generalization of spatial data: Principles and selected algorithms

  • Chapter
  • First Online:
Algorithmic Foundations of Geographic Information Systems (CISM School 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1340))

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bär, H.R. (1995): Interaktive Bearbeitung von Gehindeoberflächen — Konzepte, Methoden, Versuche. (Ph.D. Dissertation) Geoprocessing Series, Department of Geography, University of Zurich, vol. 25, 140 pgs.

    Google Scholar 

  • Beard, K. (1991): Theory of the Cartographic Line Revisited: Implications for Automated Generalization. Cartographica, 28(4): 32–58.

    Google Scholar 

  • Brassel, K.E. and Weibel, R. (1988). A Review and Framework of Automated Map Generalization. International Journal of Geographical Information Systems, 2(3): 229–44.

    Google Scholar 

  • Buttenfield, B.P. (1985): Treatment of the Cartographic Line. Cartographica, 22(2): 1–26.

    Google Scholar 

  • Buttenfield, B.P. and McMaster, R.B. (1991, eds.): Map Generalization: Making Rules for Knowledge Representation. London: Longman.

    Google Scholar 

  • Clinton, W.J. (1994): Coordinating Geographic Data Acquisition and Access: The National Spatial Data Infrastructure. Federal Register, 13 April 1994, Executive Order 12906, 59(71): 17671–17674.

    Google Scholar 

  • Cromley, R.G. (1991): Hierarchical Methods of Line Simplification. Cartography and Geographic Information Systems, 18(2): 125–131.

    Google Scholar 

  • Cromley, R.G., and Campbell, G.M. (1991): Noninferior Bandwidth Line Simplification: Algorithm and Structural Analysis. Geographical Analysis, 23(1), 25–38.

    Google Scholar 

  • Cromley, R.G., and Campbell, G.M. (1992): Integrating Quantitative and Qualitative Aspects of Digital Line Simplification. The Cartographic Journal, 29(1), 25–30.

    Google Scholar 

  • De Berg, M., van Kreveld, M. and Schirra, S. (1995): A New Approach to Subdivision Simplification. ACSM/ASPRS Annual Convention and Exposition, Vol. 4 (Pros. Auto-Carto 12): 79–88.

    Google Scholar 

  • Devogele, T., Trevisan, J. and Raynal, L. (1996): Building a Multi-Scale Database with Scale-Transition Relationships. In: Kraak, M.J. and Molenaar, M. (eds.): Advances in GIS research II (Proceedings 7th International Symposium on Spatial Data Handling), London: Taylor & Francis: 6.19–6.33

    Google Scholar 

  • Douglas, D.H., and Peucker, Th.K. (1973): Algorithms for the Reduction of the Number of Points Required to Represent a Digitized Line or its Caricature. The Canadian Cartographer, 10(2): 112–122.

    Google Scholar 

  • Duda, R. and Hart, P. (1973): Pattern Classification and Scene Analysis. New York: John Wiley.

    Google Scholar 

  • Dutton, G. (1996a): Encoding and Handling Geospatial Data with Hierarchical Triangular Meshes. In: Kraak, M.J. and Molenaar, M. (eds.): Advances in GIS research II (Proceedings 7th International Symposium on Spatial Data Handling), London: Taylor & Francis: 8B.15–8B.28. 2

    Google Scholar 

  • Fisher, P.F. and Mackaness, W.A. (1987): Are Cartographic Expert Systems Possible? Proc. Auto-Carto 8 (8th Int. Symposium on Computer-Assisted Cartography), Baltimore, MD: 530–534.

    Google Scholar 

  • EUROGI (1996): GI2000 — Towards a European Policy Framework for Geographic Information. Discussion Paper, European Umbrella Organisation for Geographic Information (EUROGI).

    Google Scholar 

  • Fritsch, E. and Lagrange, J.-P. (1995): Spectral Representations of Linear Features for Generalisation. In: Frank, A.U. and Kuhn, W. (eds.): Spatial Information Theory — A Theoretical Basis for GIS (Proceedings COSIT '95). Lecture Notes in Computer Science 988, Berlin, Springer-Verlag: 157–71

    Google Scholar 

  • Grünreich, D. (1985): Computer-Assisted Generalization. Papers CERCO Cartography Course. Institut für Angewandte Geodäsie, Frankfurt a. M.

    Google Scholar 

  • Grünreich, D. (1992): ATKIS — A Topographic Information System as a Basis for GIS and Digital Cartography in Germany. In: Vinken, R. (ed.): From Digital Map Series in Geosciences to Geo-Information Systems. Geologisches Jahrbuch Series A, Vol. 122. Hannover: Federal Institute of Geosciences and Resources: 207–216.

    Google Scholar 

  • Hake, G. (1975): Zum Begriffssystem der Generalisierung. Nachrichten aus dem Karten-und Vermessungswesen, Sonderheft zum 65. Geburtstag von Prof Knorr: 53–62.

    Google Scholar 

  • Heller, M. (1990): Triangulation Algorithms for Adaptive Terrain Modeling. Proceedings Fourth International Symposium on Spatial Data Handling, Zurich, July 1990, 1: 163–174.

    Google Scholar 

  • Hershberger, J. and Snoeyink, J. (1992): Speeding Up the Douglas-Peucker Line-Simplification Algorithm. Proceedings 5th International Symposium on Spatial Data Handling, Charleston, SC, 134–143.

    Google Scholar 

  • Hess, M. (1995): Erweiterung von Methoden zur automatischen Erzeugung panoramischer Ansichten. MSc Thesis, Department of Geography, University of Zurich.

    Google Scholar 

  • Horton, R.E. (1945): Erosional Development of Streams and their Drainage Basins — Hydrophysical Approach to Quantitative Morphology. Geological Society of America Bulletin, 56: 275–370.

    Google Scholar 

  • ICA (International Cartographic Association) (1973): Multilingual Dictionary of Technical Terms in Cartography. Wiesbaden: Franz Steiner Verlag.

    Google Scholar 

  • Imai, H. and Iri, M. (1988): Polygonal Approximations of a Curve — Formulations and Algorithms. In: Toussaint, G.T. (ed.): Computational Morphology. Elsevier Science Publishers, 71–86.

    Google Scholar 

  • Jäger, E. (1991): Investigations on Automated Feature Displacement for Small Scale Maps in Raster Format. Proceedings 15th International Cartographic Conference, Bournemouth (UK): 245–256.

    Google Scholar 

  • Jones, C.B., Bundy, G.Ll. and Ware, J.M. (1995): Map Generalization with a Triangulated Data Structure. Cartography and Geographic Information Systems, 22(4): 317–331.

    Google Scholar 

  • Kidner, D.B. and Jones, C.B. (1994): A Deductive Object-Oriented GIS for Handling Multiple Representations. In: Waugh T.C. and Healey, R.G. (eds.): Advances in GIS research (Proceedings Sixth Interna tional Symposium on Spatial Data Handling), London: Taylor & Francis: 882–900

    Google Scholar 

  • Lang, T. (1969): Rules for the Robot Draughtsmen. The Geographical Magazine, 42(1): 50–51.

    Google Scholar 

  • Leberl, F.W. (1986): ASTRA — A System for Automated Scale Transition. Photogrammetric Engineering and Remote Sensing, 52(2): 251–258.

    Google Scholar 

  • Lecordix, F., Plazanet, C. and Lagrange, J.-P. (1996): Place: A Platform for Research in Generalization. Application to Caricature. GeoInformatica, 1(1).

    Google Scholar 

  • Lee, D. (1995): Experiment on Formalizing the Generalization Process. In: Müller, J-C., Lagrange, J.-P., and Weibel, R. (eds.): GIS and Generalization: Methodological and Practical Issues, London: Taylor & Francis, 219–234.

    Google Scholar 

  • Li, Z., and Openshaw, S. (1992): Algorithms for Automated Line Generalization Based on a Natural Principle of Objective Generalization. International Journal of Geographical Information Systems, 6(5): 373–389.

    Google Scholar 

  • Lichtner, W. (1979): Computer-Assisted Processes of Cartographic Generalization in Topographic Maps. Geo-Processing, 1: 183–199.

    Google Scholar 

  • MSC Mapping Science Committee (1993): Toward a Coordinated Spatial Data Infrastructure for the Nation. Washington, DC: National Research Council, National Academy Press.

    Google Scholar 

  • Marino, J.S. (1979): Identification of Characteristics along Naturally Occurring Lines: An Empirical Study. The Canadian Cartographer, 16(1): 70–80.

    Google Scholar 

  • McMaster, R.B. (1983): A Quantitative Analysis of Mathematical Measures in Linear Simplification. Ph.D. Thesis, Dept. of Geography and Meteorology, University of Kansas, Lawrence, Kansas.

    Google Scholar 

  • McMaster, R.B. (1987a): Automated Line Generalization, Cartographica, 24(2): 74–111.

    Google Scholar 

  • McMaster, R.B. (1987b): The Geometric Properties of Numerical Generalization. Geographical Analysis, 19(4): 330–346.

    Google Scholar 

  • McMaster, R.B. (1989): The Integration of Simplification and Smoothing Algorithms in Line Generalization. Cartographica, 26(1): 101–121.

    Google Scholar 

  • McMaster, R.B. and Monmonier, M. (1989): A Conceptual Framework for Quantitative and Qualitative Raster-Mode Generalization. Proceedings GIS/LIS '89, Orlando, FL: 390–403.

    Google Scholar 

  • McMaster, R.B., and Shea, K.S. (1992): Generalization in Digital Cartography. (Resource Publications in Geography). Washington, D.C.: Association of American Geographers.

    Google Scholar 

  • Misund, G. (1996): Varioscale TIN Based Surfaces. In: Kraak, M.J. and Molenaar, M. (eds.): Advances in GIS research II (Proceedings 7th International Symposium on Spatial Data Handling), London: Taylor & Francis: 6.36–6.45.

    Google Scholar 

  • Molenaar, M. (1996a, ed.): Methods for the Generalization of Geo-Databases. Publications on Geodesy, New Series, Delft: Netherlands Geodetic Commission, 43.

    Google Scholar 

  • Molenaar, M. (1996b): The role of topologic and hierarchical spatial object models in database generalization. In: Molenaar, M. (ed.): Methods for the Generalization of Geo-Databases. Publications on Geodesy, New Series, Delft, Netherlands Geodetic Commission 43: 13–36.

    Google Scholar 

  • Monmonier, M.S. and McMaster, R.B. (1991): The Sequential Effects of Geometric Operators in Cartographic Line Generalization. International Yearbook of Cartography.

    Google Scholar 

  • Muller, J.-C. (1990): The Removal of Spatial Conflicts in Line Generalization. Cartography and Geographic Information Systems, 17(2): 141–149.

    Google Scholar 

  • Muller, J.-C. (1991): Generalization of Spatial Databases. In: Maguire, D.J., Goodchild, M.F., and Rhind, D.W. (eds.): Geographical Information Systems: Principles and Applications. London: Longman, 1: 457–475.

    Google Scholar 

  • Müller, J.-C., Lagrange, J.-P., and Weibel, R. (1995a, eds.): GIS and Generalization: Methodological and Practical Issues. London: Taylor & Francis.

    Google Scholar 

  • Müller, J.-C., Weibel, R., Lagrange, J.-P., and Salgé, F. (1995b): Generalization: State of the Art and Issues. In: Müller, J-C., Lagrange, J.-P., and Weibel, R. (eds.): GIS and Generalization: Methodological and Practical Issues, London: Taylor & Francis, 3–17.

    Google Scholar 

  • Nickerson, B.G. (1988): Automated Cartographic Generalization for Linear Features. Cartographica, 25(3), 15–66.

    Google Scholar 

  • Opheim, H. (1982): Fast Reduction of a Digitized Curve. Geo-Processing, 2: 33–40.

    Google Scholar 

  • Perkal, J. (1966): An Attempt at Objective Generalization. Michigan Inter-University Community of Mathematical Geographers, Discussion Paper 10, Ann Arbor: University of Michigan, Department of Geography.

    Google Scholar 

  • Peucker, T.K. (1975): A Theory of the Cartographic Line. International Yearbook of Cartography, 16: 134–143.

    Google Scholar 

  • Plazanet, C. (1995): Measurements, Characterization, and Classification for Automated Line Feature Generalization. ACSM/ASPRS Annual Convention and Exposition, Vol. 4 (Proc. Auto-Carto 12): 59–68.

    Google Scholar 

  • Plazanet, C., Affholder, J.-G. and Fritsch, E. (1995): The Importance of Geometric Modeling in Linear Feature Generalization. Cartography and Geographic Information Systems, 22(4): 291–305.

    Google Scholar 

  • Plazanet, C. (1996): Analyse de la géométrie des objets linéaires pour l'enrichissement des bases de données. Intégration dans le processus de généralisation cartographique des routes. PhD Thesis, Université Marne la Vallée.

    Google Scholar 

  • Ramer, U. (1972): An Iterative Procedure for the Polygonal Approximation of Plane Curves. Computer Graphics and Image Processing, 1: 244–256.

    Google Scholar 

  • Reumann, K. and Witkam, A.P.M. (1974): Optimizing Curve Segmentation in Computer Graphics. International Computing Symposium. Amsterdam: North Holland; 467–472.

    Google Scholar 

  • Richardson, D.E. (1994): Generalization of Spatial and Thematic Data Using Inheritance and Classification and Aggregation Hierarchies. In: Waugh T.C. and Healey, R.G. (eds.): Advances in GIS research (Pro ceedings Sixth International Symposium on Spatial Data Handling), London: Taylor & Francis: 901–20

    Google Scholar 

  • Rieger, M. and Coulson, M. (1993): Consensus or Confusion: Cartographers' Knowledge of Generalization. Cartographica, 30(1): 69–80.

    Google Scholar 

  • Rogers, D.F. and Adams, J.A. (1990): Mathematical Elements for Computer Graphics. Second Edition. New York et al.: McGraw-Hill.

    Google Scholar 

  • Roos, T. (1996): Voronoi Methods in GIS. This volume.

    Google Scholar 

  • Ruas, A. (1995a): Multiple Representations and Generalization. Lecture Notes for 1995 Nordic Cartography Seminar. St.-Mandé: Institut Géographique National. Available as PostScript document from anonymous ftp.

    Google Scholar 

  • Ruas, A. (1995b): Multiple Paradigms for Automating Map Generalization: Geometry, Topology, Hierarchical Partitioning and Local Triangulation. AGSM/ ASPRE Annual Convention and Exposition, Vol. 4 (Proc. Auto-Carto 12): 69–78.

    Google Scholar 

  • Ruas, A. and Lagrange, J.-P. (1995): Data and Knowledge Modelling for Generalization. In: Müller, J-C., Lagrange, J.-P., and Weibel, R. (eds.): GIS and Generalization: Methodological and Practical Issues, London: Taylor & Francis, 73–90.

    Google Scholar 

  • Ruas, A. and Plazanet, C. (1996): Strategies for Automated Generalization. In: Kraak, M.J. and Molenaar, M. (eds.): Advances in GIS research II (Proceedings 7th International Symposium on Spatial Data Handling), London: Taylor & Francis: 6.1–6.18.

    Google Scholar 

  • Rusak Mazur, E., and Castner, H.W. (1990): Horton's Ordering Scheme and the Generalisation of River Networks. The Cartographic Journal, 27: 104–112.

    Google Scholar 

  • Schlegel, A., and Weibel (1995): Extending a General-Purpose GIS for Computer-Assisted Generalization. 17th International Cartographic Congress of the ICA, Barcelona (E), 2211–2220.

    Google Scholar 

  • Schylberg, L. (1993): Computational Methods for Generalization of Cartographic Data in a Raster Environment. PhD Thesis, Department of Photogrammetry, Royal Institute of Technology, Stockholm.

    Google Scholar 

  • Shreve, R.L. (1966): Statistical Law of Stream Number. Journal of Geology, 74: 17–37.

    Google Scholar 

  • Spiess, E. (1995): The Need for Generalization in a GIS Environment. In: Müller, J-C., Lagrange, J.-P., and Weibel, R. (eds.): GIS and Generalization: Methodological and Practical Issues, London: Taylor & Francis, 31–46.

    Google Scholar 

  • Strahler, A.N. (1957): Quantitative Analysis of Watershed Geomorphology. Transactions of the American Geophysical Union, 8(6): 913–920.

    Google Scholar 

  • Swiss Society of Cartography (1977): Cartographic Generalization — Topographic Maps. Cartographic Publication Series, vol. 2. Zurich: Swiss Society of Cartography.

    Google Scholar 

  • Töpfer, F. (1974): Kartographische Generalisierung. Gotha, Leipzig: VEB Hermann Haack.

    Google Scholar 

  • van Kreveld, M. (1997): Digital Elevation Models: Overview and Selected TIN Algorithms. This volume.

    Google Scholar 

  • van Oosterom, P. and van den Bos, J. (1989): An Object-Oriented Approach to the Design of Geographic Information Systems. Computers & Graphics, 13: 409–418.

    Google Scholar 

  • van Oosterom, P. and Schenkelaars, V. (1995): The Development of an Interactive Multiscale GIS. International Journal of Geographical Information Systems, 9(5): 489–507.

    Google Scholar 

  • Visvalingam, M., and Whyatt, J.D. (1993): Line Generalisation by Repeated Elimination of Points. Cartographic Journal, 30(1): 46–51.

    Google Scholar 

  • Visvalingam, M. and Williamson, P.J. (1995): Simplification and Generalization of Large Scale Data for Roads: A Comparison of Two Filtering Algorithms. Cartography and Geographic Information Systems, 22(4): 264–275.

    Google Scholar 

  • Ware, J.M., Jones, C.B. and Bundy, G.Ll. (1995): A Triangulated Spatial Model for Cartographic Generalisation of Areal Objects. In: Frank, A.U. and Kuhn, W. (eds.): Spatial Information Theory — A The oretical Basis for GIS (Proceedings COSIT '95). Lecture Notes in Computer Science 988, Berlin, Springer-Verlag: 173–192.

    Google Scholar 

  • Ware, J.M. and Jones, C.B. (1996): A Spatial Model for Detecting (and Resolving) Conflict Caused by Scale Reduction. In: Kraak, M.J. and Molenaar, M. (eds.): Advances in GIS research II (Proceedings 7th International Symposium on Spatial Data Handling), London: Taylor & Francis: 9A.15–9A.26.

    Google Scholar 

  • Weibel, R. (1991): Amplified Intelligence and Rule-Based Systems. In: Buttenfield, B.P., and McMaster, R.B. (eds.): Map Generalization — Making Rules for Knowledge Representation. London: Longman, 172–186.

    Google Scholar 

  • Weibel, R. (1992): Models and Experiments for Adaptive ComputerAssisted Terrain Generalization. Cartography and Geographic Information Systems, 19(3): 133–153.

    Google Scholar 

  • Weibel, R. (1995a): Map Generalization. Special Issue of Cartography and Geographic Information Systems, 22(4).

    Google Scholar 

  • Weibel, R. (1995b): Three Essential Building Blocks for Automated Generalisation. In: Müller, J-C., Lagrange, J.-P., and Weibel, R. (eds.): GIS and Generalization: Methodological and Practical Issues, London: Taylor & Francis, 56–69.

    Google Scholar 

  • Weibel, R. and Ehrliholzer, R. (1995): An Evaluation of MGE Map Generalizer. Internal Report, Department of Geography, University of Zurich, 36 + 18 pgs.

    Google Scholar 

  • Weibel, R., Keller, St., and Reichenbacher, T. (1995): Overcoming the Knowledge Acquisition Bottleneck in Map Generalization: The Role of Interactive Systems and Computational Intelligence. In: Frank, A.U. and Kuhn, W. (eds.): Spatial Information Theory — A Theoretical Basis for GIS (Proceedings COSIT '95). Lecture Notes in Computer Science 988, Berlin, Springer-Verlag: 139–156.

    Google Scholar 

  • Weibel, R. (1996): A Typology of Constraints to Line Simplification. In: Kraak, M.J. and Molenaar, M. (eds.): Advances in GIS research II (Proceedings 7th International Symposium on Spatial Data Handling), London: Taylor & Francis: 9A.1–9A.14.

    Google Scholar 

  • Werschlein, T. (1996): Frequenzbasierte Linienreprdsentationen für die kartographische Generalisierung. MSc Thesis, Department of Geography, University of Zurich.

    Google Scholar 

  • White, E.R. (1985): Assessment of Line Generalization Algorithms Using Characteristic Points. The American Cartographer, 12(1): 17–28.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Marc van Kreveld Jürg Nievergelt Thomas Roos Peter Widmayer

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Weibel, R. (1997). Generalization of spatial data: Principles and selected algorithms. In: van Kreveld, M., Nievergelt, J., Roos, T., Widmayer, P. (eds) Algorithmic Foundations of Geographic Information Systems. CISM School 1996. Lecture Notes in Computer Science, vol 1340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63818-0_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-63818-0_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63818-6

  • Online ISBN: 978-3-540-69653-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics