Skip to main content
Log in

Object Calculus and the Object-Oriented Analysis and Design of an Error-Sensitive GIS

  • Published:
GeoInformatica Aims and scope Submit manuscript

Abstract

The use of object-oriented analysis and design (OOAD) in GIS research, development and application is now well established. However, the tendency towards informality in OOAD techniques means many of the potential benefits of object-orientation (OO) are being discounted. Recent advances in the formal representation of OO systems may help realize these benefits with respect to some of the key contemporary issues in GIS. This paper examines the application of one particular OO formalism, the ς (sigma) calculus of Abadi and Cardelli, to a long-standing unresolved research problem in GIS: the development of an error-sensitive GIS. The work indicates that significant enhancements in the exploration, verification and understanding of OO systems can be achieved through the use of ς-calculus in support of conventional OOAD techniques.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. H.J.G.L. Aalders, “Quality metrics for GIS,” in M.J. Kraak and M. Molenaar, (Eds.), Advances in GIS Research II; Proceedings Seventh International Symposium on Spatial Data Handling, Vol. 1, 5B-10, 1996.

  2. M. Abadi and L. Cardelli. “An imperative object calculus,” Theory and Practice of Object Systems, Vol. 1(3):151–166, 1995.

    Google Scholar 

  3. M. Abadi and L. Cardelli. “A theory of primitive objects: Second-order systems,” Science of Computer Programming, Vol. 25(2–3):81–116, 1995.

    Google Scholar 

  4. M. Abadi and L. Cardelli. A Theory of Objects. Springer-Verlag: New York, 1996.

    Google Scholar 

  5. M. Abadi and L. Cardelli. “A theory of primitive objects: Untyped and first-order systems,” Information and Computation, Vol. 125(2):78–102, 1996.

    Google Scholar 

  6. A. Agumya and G.J. Hunter. “Determining fitness for use of geographic information,” ITC Journal, (2):109–113, 1997.

    Google Scholar 

  7. R.J. Aspinall. “Measurement of area in GIS: A rapid method for assessing the accuracy of area measurement,” in Proceedings of the GIS Research UK 1996 Conference, 135–142, 1996.

  8. L. Becker, A. Voigtmann, and K.H. Hinrichs. “Developing applications with the object-oriented GIS-kernel Goodac,” in M.J. Kraak and M. Molenaar, (Eds.), Advances in GIS Research II; Proceedings Seventh International Symposium on Spatial Data Handling, Vol. 1, 5A1–18, 1996.

  9. G. Blaschek and J.H. Frölich. “Recursion in object-oriented programming,” Journal of Object-Oriented Programming, Vol. 11(7):29–35, 1998.

    Google Scholar 

  10. G. Booch. Object oriented analysis and desing with applications. Benjamin-Cummings: California, second edition, 1994.

    Google Scholar 

  11. J. Bowen. Formal specification and documentation using Z: A case study approach. International Thomson Computer Press: London, 1996.

    Google Scholar 

  12. C. Brunsdon and S. Openshaw. “Simulation the effects of error in GIS,” in P.M. Mather, (Ed.), Geographical Information Handling: Research and Applications. Wiley: New York, 1993.

    Google Scholar 

  13. P.A. Burrough and R.A. McDonnell. Principles of geographical information systems. Clarendon: Oxford, Second edition, 1998.

    Google Scholar 

  14. G. Campbell, L. Carker, and P. Egesborg. “A GIS-based multipurpose digital cadastre for Canada lands,” in FIG Congress XX, 1994.

  15. L. Cardelli. “A semantics of multiple inheritance,” in G. Goos and J. Hartmanis, (Eds.), Semantics of Data Types. (Number 173 in Lecture notes in computer science), 51–67. Springer-Verlag: New York, 1984.

    Google Scholar 

  16. CEN/TC287. “Draft European standard; geographic information—quality,” Technical Report prEN 287008. European Committee for Standardization, 1996.

  17. N.R. Chrisman. “The role of quality information in the long term functioning of a geographic information system,” in Proceedings Auto-Carto 6, Vol. 1:303–312, 1983.

    Google Scholar 

  18. N.R. Chrisman. “The error component in spatial data,” in D.J. Maguire, M.F. Goodchild, and D.W. Rhind, (Eds.), Geographical information systems. Longman: Essex, Vol. 1, chapter 12, 165–174, 1991.

    Google Scholar 

  19. P. Coad and E. Yourdon. Object-Oriented Analysis. Yourdon Press: New Jersey, 1991.

    Google Scholar 

  20. B. David, M. van den Herrewegen, and F. Salgé. “Conceptual models for geometry and quality of geographic information,” in P.A. Burrough and A.U. Frank, (Eds.), Geographic objects with indeterminate boundaries. GIS Data 2. Taylor and Francis: London, 1996.

    Google Scholar 

  21. D. de Champeaux and P. Faure. “A comparative study of object-oriented analysis methods,” Journal of Object-Oriented Programming, Vol. 5(1):21–33, 1992.

    Google Scholar 

  22. M. Duckham and J. Drummond. “Implementing and object-oriented approach to data quality,” in B. Gittings, (Ed.), Integrating Information Infrastructures with GI Technology, Taylor and Francis: London, 53–64, 1999.

    Google Scholar 

  23. M. Duckham and J. McCreadie. “An intelligent, distributed, error-aware object-oriented GIS,” in W. Shi, M.F. Goodchild, and P.F. Fisher, (Eds.), Proceedings 1st International Symposium on Spatial Data Quality, 596–505, 1999.

  24. M.J. Egenhofer and A.U. Frank. “Object-oriented modeling: Inheritance and propagation,” in Proceedings Auto-Carto 9 588–598, 1989.

    Google Scholar 

  25. J. Fiadeiro and T. Maibaum. “Describing, structuring and implementing objects,” in G. Goos and J. Hartmanis, (Eds.), Foundations of Object-Oriented Languages, (Number 489 in Lecture notes in computer science), 274–310. Springer-Verlag: New York, 1991.

    Google Scholar 

  26. P.F. Fisher. “Is GIS hidebound by the legacy of cartography?” Cartographic Journal, Vol. 35(1):5–9, 1998.

    Google Scholar 

  27. M. Goodchild. “Integrating GIS and spatial data analysis: Problems and possibilities,” International Journal of Geographical Information Systems, Vol. 6(5):407–423, 1992.

    Google Scholar 

  28. M.F. Goodchild. “Sharing imperfect data,” In H.J. Onsrud and G. Rushton, (Eds.), Sharing geographic information. Rutgers: Jersey, 413–425, 1995.

    Google Scholar 

  29. M.F. Goodchild. “Directions in GIS,” in Proceedings Third International Conference/Workshop on Integrating GIS and Environmental Modeling, 1996. http://www.ncgia.ucsb.edu/conf/SANTA_FD_CD-ROM/main.html

  30. M.F. Goodchild. “Measurement-based GIS,” in W. Shi, M.F. Goodchild, and P.F. Fisher, (Eds.), Proceedings of the International Symposium on Spatial Data Quality, 1–9, 1999.

  31. A.D. Gordon and G.D. Rees. “Bisimilarity for a first-order calculus of objects with subtyping,” In Proceedings 23rd Annual ACM Symposium on Principles of Programming Languages, 386–395, 1996.

  32. S.C. Guptill. “Inclusion of accuracy data in a feature based object oriented data model,” in M.F. Goodchild and S. Gopal, (Eds.), Accuracy of spatial databases. Taylor and Francis: London, chapter 8. 91–98, 1989.

    Google Scholar 

  33. W. Haythorn. “What is object-oriented design?” Journal of Object-Oriented Programming, Vol. 7(1):67–78, 1994.

    Google Scholar 

  34. J.R. Herring. “TIGRIS: a data model for an object-oriented geographic information system,” Computers and Geosciences, Vol. 18(4):443–452, 1992.

    Google Scholar 

  35. G.B.M. Heuvelink. Error propagation in quantitative spatial modelling: Applications in Geographical Information Systems. University of Utrecht, 1993.

  36. G.B.M. Heuvelink. Error propagation in environmental modelling with GIS. Research monographs in GIS, Taylor and Francis: London, 1998.

    Google Scholar 

  37. G.B.M. Heuvelink, P.A. Burrough, and A. Stein. “Propagation of errors in spatial modeling in GIS,” International Journal of Geographical Information Systems, Vol. 3(4):303–322, 1989.

    Google Scholar 

  38. B. Jacobs. “Objects and classes, co-algebraically,” in B. Freitag, C.B. Jones, C. Lengauer, and H.-J. Schek, (Eds.), Object-Orientation with Parallelism and Persistence. Kluwer: Massachusetts, 83–103, 1996.

    Google Scholar 

  39. W. Kainz. “Logical consistency,” in S.C. Guptil and J.L. Morrison, (Eds.), Elements of spatial data quality. Elsevier Science: Oxford, chapter 6, 109–137, 1995.

    Google Scholar 

  40. K. Lano. Formal object-oriented development. Springer-Verlag: Berlin, 1995.

    Google Scholar 

  41. D.P. Lanter and H. Veregin. “A research paradigm for propagating error in layer-based GIS,” Photogrammetric Engineering and Remote Sensing, Vol. 58(6):825–833, 1992.

    Google Scholar 

  42. J.A. Lewis, S.M. Henry, D.G. Kafura, and R.S. Schulman. “On the relationship between the object-oriented paradigm and software reuse: An empirical investigation,” Journal of Object-Oriented Programming, Vol. 5(4):35–41, 1992.

    Google Scholar 

  43. D.J. Maguire and J. Dangermond. “The functionality of GIS,” in D.J. Maguire, M.F. Goodchild, and D.W. Rhind, (Eds.), Geographical information systems. Longman: Essex, Vol. 1, chapter 21, 319–335, 1991.

    Google Scholar 

  44. P. Milne, S. Milton, and J.L. Smith. “Geographical object-oriented databases: A case study,” International Journal of Geographical Information Systems, Vol. 7(1):39–55, 1993.

    Google Scholar 

  45. H. Moellering, (Ed.) Spatial Database Transfer Standards 2: Characteristics for Assessing Standards and Full Descriptions of the National and International Standards in the World. Elsevier Science: Oxford, 1997.

    Google Scholar 

  46. D.E. Monarchi and G.I. Puhr. “A research typology for object-oriented analysis and design,” Communications of the ACM, Vol. 35(9):35–47, 1992.

    Google Scholar 

  47. National Committee for Digital Cartographic Data Standards. “The proposed standard for digital catographic data,” American Cartographer, Vol. 15(1):11–142, 1988.

    Google Scholar 

  48. J.M. Nerson. “Applying object-oriented anlysis and design,” Communications of the ACM, Vol. 35(9):63–74, 1992.

    Google Scholar 

  49. C. Partridge. “Modelling the real world: Are classes abstractions or objects?” Journal of Object-Oriented Programming, Vol. 7(7):39–45, 1994.

    Google Scholar 

  50. B.A. Ralston. “Object oriented spatial analysis,” in S. Fotheringham and P. Rogerson, (Eds.), Spatial analysis and GIS, Taylor and Fracis: London, 165–186, 1994.

    Google Scholar 

  51. B. Ramlal and J.E. Drummond. “A GIS uncertainty subsystem,” in Archives ISPRS Congress XVII, Vol. 29.B3:356–362, 1992.

    Google Scholar 

  52. J. Raper and D. Livingston. “Development of a geomorphological spatial model using object oriented design,” International Journal of Geographical Information Systems, Vol. 9(4):359–384, 1995.

    Google Scholar 

  53. J. Rumbaugh, M. Blaha, W. Premerlani, F. Eddy, and W. Lorensen. Object-oriented modeling and design. Prentice Hall: New Jersey, 1991.

    Google Scholar 

  54. A.Y. Tang, T.M. Adams, and E.L. Usery. “A spatial data model design for feature-based geographical information systems,” International Journal of Geographical Information Systems, Vol. 10(5):643–659, 1996.

    Google Scholar 

  55. D.J. Unwin. “Geographical information systems and the problem of error and uncertainty.” Progress in Human Geography, Vol. 19(4):549–558, 1995.

    Google Scholar 

  56. US Department of Defense. Interface standard for vector product format, 1996. MIL-STD-2407.

  57. F.J.M. van der Wel, R.M. Hootsmans, and F. Ormeling. “Visualization of data quality.” In A.M. MacEachren and D.R.F. Taylor, (Eds.), Visualization in modern cartography. Pergamon: Oxford, 313–331, 1994.

    Google Scholar 

  58. H. Veregin. “Data quality parameters,” in P.A. Longley, M.F. Goodchild, D.J. Maguire, and D.W. Rhind (Eds.), Geographical information systems. Longman: Esses, second edition, vol. 1, chapter 12, 177–189, 1999.

    Google Scholar 

  59. C.G. Wesseling and G.B.M. Heuvelink. “Manipulating qualitative attrbute accuracy in vector GIS,” in Proceedings Fourth European Conference on Geographical Information Systems, Vol. 1:675–684, 1993.

    Google Scholar 

  60. M.F. Worboys. “A generic model for planar geographical objects,” International Journal of Geographicaal Information Systems, Vol. 6(5):353–372, 1992.

    Google Scholar 

  61. M.F. Worboys. “Object-oriented approaches to geo-referenced information,” International Journal of Geographical Information Systems, Vol. 8(4):385–399, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Duckham, M. Object Calculus and the Object-Oriented Analysis and Design of an Error-Sensitive GIS. GeoInformatica 5, 261–289 (2001). https://doi.org/10.1023/A:1011434131001

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011434131001

Navigation