A Spatial Access-Oriented Implementation of a 3-D GIS Topological Data Model for Urban Entities


3-D analysis in GIS is still one of the most challenging topics for research. With the goal being to model possible movement within the built environment, this paper, therefore, proposes a new approach to handling connectivity relationships among 3-D objects in urban environments in order to implement spatial access analyses in 3-D space. To achieve this goal, this paper introduces a 3-D network data model called the geometric network model (GNM), which has been developed by transforming the combinatorial data model (CDM), representing a connectivity relationship among 3-D objects using a dual graph. For the transformation, this paper presents (1) an O(n 2) algorithm for computing a straight medial axis transformation (MAT), (2) the processes for transforming phenomena from 3-D CDM to 3-D GNM, and (3) spatial access algorithms for the 3-D geometric network based upon the Dijkstra algorithm. Using the reconstructed geometric network generated from the transformations, spatial queries based upon the complex connectivity relationships between 3-D urban entities are implemented using Dijkstra algorithm. Finally, the paper presents the results of an experimental implementation of a 3-D network data model (GNM) using GIS data of an area in downtown Columbus, Ohio.

This is a preview of subscription content, access via your institution.


  1. 1.

    O. Aichholzer and F. Aurenhammer. “Straight skeletons for general polygonal figures in the plane,” Proc.Of Second Annual Intern.'96, Hong Kong, Computing and Combinatorics, Lecture Notes in Computer Science 1090, Springer-Verlag: Berlin, pp. 117–126, 1998.

    Google Scholar 

  2. 2.

    M. Batty and D. Howes. “Exploring urban development dynamics through visualization and animation,” in D. Parker (Eds.), Innovations in GIS 3, Taylor & Francis: New York, 1996.

    Google Scholar 

  3. 3.

    J. Bentley, B. Weide, and A. Yao. “Optimal expected-time algorithm for closest-point problems,” ACM Trans.Math.Software, Vol. 6:563–580, 1980.

    Google Scholar 

  4. 4.

    R. Bilien and S. Zlatanova. “3-D spatial relationships model: A useful concept for 3-D cadastre?” Computers, Environment and Urban Systems, Vol. 27:411–425, 2003.

    Google Scholar 

  5. 5.

    M. Birkin, G. Clarke, M. Clarke, and A. Wilson. Intelligent GIS: Location Decisions and Strategic Planning. Geoinfomation International, John Wiley & Sons Inc.: New York, 1996.

    Google Scholar 

  6. 6.

    H. Blum. “A transformation for extracting new description of shape,” Symp.Models for Perception of Speech and Visual Forms, MIT Press: Cambridge, MA, pp. 362–380, 1967.

    Google Scholar 

  7. 7.

    C. Bragdon, J. Juppe, and A. Georgiopoulos. “Sensory spatial systems simulation (s4) applied to the master planning process: East Coast and West Coast case studies,” Environment and Planning B: Planning and Design, Vol. 22:303–314,1995.

    Google Scholar 

  8. 8.

    K.L. Burns. “Lithologic topology and structural vector fields applied to subsurface predicting in geology,” in Proc.ofGISILIS 88, San Antonio, TX, USA, 1988.

    Google Scholar 

  9. 9.

    J. Canny and B. Donald. “Simplified Voronoi diagrams,” Discrete & Computation Geometry, Vol. 3:219–236,1988.

    Google Scholar 

  10. 10.

    E. Carlson. “Three dimensional conceptual modeling of subsurface structures,” in Proc.8th International Symposium on Computer Assisted Cartography, AutoCarto 8, Baltimore, MD, 336–345, 1987.

  11. 11.

    L.G. Chairnet, R.L. Francis, and P.B. Saunders. “Network models for building evacuation,” Management Science, Vol. 28(l):86–105,1982.

    Google Scholar 

  12. 12.

    F. Chin, J. Snoeyink, and C. Wang. “Finding the medial axis of a simple polygon in linear time,” in Proc.of 6th Annual International Symposium Algorithms Comput., Lecture Notes Computer Science 1004, Springer– Verlag: Berlin, pp. 382–391, 1995.

    Google Scholar 

  13. 13.

    K.C. Chung. “Three-dimensional analysis of airflow and contaminant particle transport in a partitioned enclosure,” Environment and Planning B: Planning and Design, Vol. 34:7–17, 1999.

    Google Scholar 

  14. 14.

    V. Coors. “3D-GIS in networking environments,” Computers, Environment and Urban Systems, Vol. 27:345–357,2003.

    Google Scholar 

  15. 15.

    J.P. Corbett. Topological Principles in Catrography, Technical Paper 48, U.S. Department of Commerce, Bureau of the Census, 1979.

  16. 16.

    T. Cormen, C. Leiserson, and R. Rivest. Introduction to Algorithms. The MIT Press: Cambridge, MA, 1985.

    Google Scholar 

  17. 17.

    M.J. Crobie. International Architecture Yearbook No.5. The Images Publishing Group Pty Ltd.: Australia, 1999.

    Google Scholar 

  18. 18.

    E.W. Dijkstra. “A note on two problems in connection with graphs,” Numer.Math., Vol. 1:269–271, 1959.

    Google Scholar 

  19. 19.

    P. Eichelberger. “3D GIS: The necessary next wave,” Geo Info System, Vol. 8(10), 1998.

  20. 20.

    M.J. Egenhofer and J.R. Herring. Categorising Topological Relations Between Regions, Lines and Points in Geographic Databases, Technical report 94–1, NCGIA, University of Maine, 1992.

  21. 21.

    ESRI. AreGIS User Guide, ESRI Press: Redlands, CA, 2001.

  22. 22.

    N.L. Faust. “The virtual reality of GIS,” Environment and Planning B: Planning and Design, Vol. 22:257–268,1995.

    Google Scholar 

  23. 23.

    N. Flanagan, C. Jennings, and C. Flanagan. “Automatic GIS data capture and conversion,” in M. Worboys (Eds.), Innovations in GISI, Taylor & Francis Ltd: Bristol, PA, 1996.

    Google Scholar 

  24. 24.

    S. Forture. “A sweepline algorithm for Voronoi diagrams,” Algorithmica, Vol. 2:153–174, 1987.

    Google Scholar 

  25. 25.

    B. Hoppe and E. Tardos. “The quickest transshipment problem,” in SODA: ACM-SIAM Symposium on Discrete Algorithms, 433–441,1995.

  26. 26.

    M. Kirn. “Medial axis transform,” Unpublished paper from Department of Computer Science, Johns Hopkins University, http://www.cs.jhu.edu/ ~ bishop/vision/medial.htm., 1998.

  27. 27.

    S. Kirkby, S. Pollitt, and P. Ekiund. “Implementing a shortest path algorithm in a 3-D GIS environment,” in M. J. Kraak and M. Moleanaar (Eds.), Advances in GIS Research II (Proc.Of the 7th International Symposium on Spatial Data Handling), Taylor & Francis Inc: London, pp. 437–448, 1997.

    Google Scholar 

  28. 28.

    A. Koninger and S. Bartel. “3D-GIS for urban purposes,” Geoinformatica, Vol. 2(l):79–103, 1998.

    Google Scholar 

  29. 29.

    M.J.T. Kniger. “An approach to built-form connectivity at an urban scale: System description and its representation,” Environment and Planning B: Planning and Design, Vol. 6:67–88, 1979.

    Google Scholar 

  30. 30.

    M.-P Kwan. “Interactive geovisualization of activity-travel patterns using 3-D GIS: A methodological exploration with a large data set,” Transportation Research C, Vol. 8:185–203, 2000.

    Google Scholar 

  31. 31.

    M.-P. Kwan and J. Lee. “Emergency response after 9/11: The potential of real-time 3-D GIS for quick emergency response in micro-spatial environments,” Computers, Environment and Urban Systems (forthcoming), 2004.

  32. 32.

    D.T. Lee. “Medial axis transformation of a planar shape,” IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-4(4):363–369,1982.

    Google Scholar 

  33. 33.

    D.T. Lee and R. Drysdale. “Generalization of Voronoi diagrams in the plane,” Siam J.Comput., Vol. 10(l):73–87,1981.

    Google Scholar 

  34. 34.

    J. Lee and M.-P. Kwan. “A 3-D object-oriented data model for representing geographic entities in built-environments,” Paper presented at the 96th AAG Annual Meeting, Pittsburgh, Pennsylvania, April 4–8, 2000.

  35. 35.

    J. Lee. “A spatial access oriented implementation of a topological data model for 3-D urban entities,” Paper presented at the 2001 University Consortium for Geographic Information Science (UCGIS), Summer Assembly, Buffalo, NY, June 21–24, 2001 a.

  36. 36.

    J. Lee. A 3-D Data Model for Representing Topological Relationships Between Spatial Entities in Built-Environments. Ph.D. Dissertation, The Ohio State University, 200 Ib.

  37. 37.

    Y.C. Lee. “Geographic information systems for urban applications: Problems and solutions,” Environment and Planning B: Planning and Design, Vol. 17:463–473, 1990.

    Google Scholar 

  38. 38.

    R.S. Liggett and W.H. Jepson. “An integrated environment for urban simulation,” Environment and Planning B: Planning and Design, Vol. 22:291–302, 1995.

    Google Scholar 

  39. 39.

    S. Liu. Object Orientation in Route Guidance Systems. Unpublished Master Thesis, The University of Calgary, 1996.

  40. 40.

    Q. Lu, Y. Hung, and S. Shekhar. “Evacuation planning: A capacity contrained routing approach,” in Proc.of the First NSFINU Symposium on Intelligence and Security Information (ISI), Tucson, Arizona, 2003.

    Google Scholar 

  41. 41.

    J.-L. Mallet. “GOCAD: A computer-aided design program for geological applications,” in A.K. Turner (Ed.), Three-Dimensional Modeling with Geoscientific Information Systems, Kluwer: Dordrecht, 1990.

    Google Scholar 

  42. 42.

    M. Molenaar. “A topology for 3-D vector maps,” ITC Journal, Vol. 1992(l):25–33, 1992.

    Google Scholar 

  43. 43.

    M. Molenaar. An Introduction to the Theory of Spatial Object Modelling for GIS. Taylor & Francis: New York, 1998.

    Google Scholar 

  44. 44.

    A. Okabe, B. Boots, K. Sugihara, and S. Chiu. Spatial Tessellations: Concepts of Applications of Voronoi Diagrams. Second edition. John Wiley & Sons, Ltd: New York, 2000.

    Google Scholar 

  45. 45.

    S. Pigot. “A topological model for a 3-D spatial information system,” in Proc.of the 5th International Symposium on Spatial Data Handling, Charleston, South Carolina, 344–359, 1992.

    Google Scholar 

  46. 46.

    S. Pigot and B. Hazelton. “The fundamentals of a topological model for a four-dimensional GIS,” in Proc.of tile 5th International Symposium on Spatial Data Handling, Charleston, South Carolina, 580–591, 1992.

    Google Scholar 

  47. 47.

    M. Pilouk. Integrated Modeling for 3-D GIS. Ph.D. Dissertation, ITC, The Netherlands, 1996.

    Google Scholar 

  48. 48.

    C. Plimpton and F. Hassan. “Social space: A determinant of house architecture,” Environment and Planning B: Planning and Design, Vol. 14:437–449, 1987.

    Google Scholar 

  49. 49.

    P.P. Preparata. “The medial axis of a simple polygon,” in Proc.of the Sixth Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, Vol. 53, Springer-Verlag: New York, pp. 443–450,1977.

    Google Scholar 

  50. 50.

    J. Raper. Multidimensional Geographic Information Science. Taylor & Francis: New York, 2000.

    Google Scholar 

  51. 51.

    R. Rikkers, M. Molenaar, and J. Stuiver. “A query oriented implementation of a topologic data structure for 3-dimensional vector maps,” INT.J.Geographical information System, Vol. 8(3):243–260, 1994.

    Google Scholar 

  52. 52.

    M.S. Scott. “The development of an optimal path algorithm in three dimensional raster space,” in Proc.'94,687–696,1994.

  53. 53.

    K.W. Seo. “Topological paths in housing evolution”. Proceedings of 4th International Space Syntax Symposium, London, 2003.

  54. 54.

    J.M. Smith. “State dependent queueing models in emergency evacuation networks,” Transportation Science: Part B, Vol. 25B(6):373–389, 1991.

    Google Scholar 

  55. 55.

    J.E. Stoter. “3-D Cadastres, state of the art: From 2-D parcels to 3-D registrations,” GIM International, the World Magazine for Geomatics, February, 12–15, 2002.

  56. 56.

    C.Y. Suen and P.S.P Wang (Eds.). Thinning Methodologies for Pattern Recognition. World Scientic, 1994.

  57. 57.

    M.F. Worboys. GIS: A Computing Perspective. Taylor & Francis: Bristol, PA, 1995.

    Google Scholar 

  58. 58.

    C. Yao and J. Rokne. “A straightforward algorithm for computing the medial axis of a simple polygon,” Intern.Computer Math., Vol. 39:51–60, 1991.

    Google Scholar 

  59. 59.

    C.K. Yap. “An 0(n log n) algorithm for the Voronoi diagram of a set of simple curve segments,” Discrete Computational Geometry, Vol. 2:365–393, 1987.

    Google Scholar 

  60. 60.

    M. Zeiler. Modeling Our World: The ESRI Guide to Geodatabase Design. ESRI Press: Redlands, CA, 1999.

    Google Scholar 

  61. 61.

    S. Zlatanova. 3-D GIS for Urban Development. Ph.D. Dissertation, ITC, The Netherlands, 2000.

    Google Scholar 

  62. 62.

    S. Zlatanova, A. Rahman, and M. Pilouk. “Trends in 3-D GIS development,” Journal of Geospatial Engineering, Vol. 4(2):l–10,2002.

    Google Scholar 

  63. 63.

    S. Zlatanova, A.A. Rahman, and W. Shi. “Topology for 3-D spatial objects,” International Symposium and Exhibition on Geoinformation 22–24 October, Kuala Lumpur, Malaysia, CDROM, 2002.

  64. 64.

    Z. Zhao, A. Saalfeld, and R. Ramirez. “A general line-following algorithm for raster maps,” Proc.'96, Denver, Colorado, 267–265, 1996.

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lee, J. A Spatial Access-Oriented Implementation of a 3-D GIS Topological Data Model for Urban Entities. GeoInformatica 8, 237–264 (2004). https://doi.org/10.1023/B:GEIN.0000034820.93914.d0

Download citation

  • 3-D GIS
  • topological data model
  • dual graph
  • spatial access
  • medial axis