Evaluating Methods for Interpolating Continuous Surfaces from Irregular Data: a Case Study

  • M. Hugentobler
  • R.S. Purves
  • B. Schneider
Conference paper


An artificial and ‘real’ set of test data are modelled as continuous surfaces by linear interpolators and three different cubic interpolators. Values derived from these surfaces, of both elevation and slope, are compared with analytical values for the artificial surface and a set of independently surveyed values for the real surface. The differences between interpolators are shown with a variety of measures, including visual inspection, global statistics and spatial variation, and the utility of cubic interpolators for representing curved areas of surfaces demonstrated.


Test Area Continuous Surface Artificial Surface Terrain Surface Control Dataset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Barnhill RE and Gregory JA (1975) Compatible smooth interpolation in triangles. Journal of Approximation Theory 15: 214–225CrossRefGoogle Scholar
  2. Bolstad P, Stowe T (1994) An evaluation of DEM accuracy: elevation slope and aspect. Photogrammetric Engineering and Remote Sensing 60: 1327–1332Google Scholar
  3. Corripio JG (2003) Vectorial algebra algorithms for calculating terrain parameters from DEMs and solar radiation modelling in mountainous terrain. IJGIS 17: 1–23Google Scholar
  4. Evans IS (1980) An integrated system of terrain analysis for slope mapping. Zeitschrift fur Geomorphologie 36: 274–295Google Scholar
  5. Farin G (1985) A modified Clough-Tocher interpolant. Computer Aided Geometric Design 2: 19–27Google Scholar
  6. Farin G (1997) Curves and surfaces for CAGD. A practical guide (Academic Press)Google Scholar
  7. de Floriani L, Puppo E (1992) An online algorithm for constrained Delaunay triagulation. Graphical Models and Image Processing 54: 290–300Google Scholar
  8. Gallant JC and Wilson JP (2000) Primary Topographic Attributes, In Terrain Analysis: Principles and Applications edited by Wilson, J.P. and Gallant, J.C (Wiley): 51–85Google Scholar
  9. Giles P, Franklin S (1996) Comparison of derivative topographic surfaces of a DEM generated from stereoscopic spot images with field measurements. Photogrammetric Engineering and Remote Sensing 62: 1165–1171Google Scholar
  10. Hugentobler M (2002) Interpolation of continuous surfaces for terrain surfaces with Coons patches. In Proceedings of GISRUK 2002 (Sheffield, UK): 13–15.Google Scholar
  11. Kumler M (1994) An intensive comparison of TINs and DEMs. Cartographica (Monograph 45), 31: 2Google Scholar
  12. Maggioni M, Gruber U (2003) The influence of topographic parameters on avalanche release dimension and frequency. Cold Regions Science and Technology, 37: 407–419CrossRefGoogle Scholar
  13. Mitas L, Mitasova H (1999) Spatial interpolation. In Geographical Information Systems edited by P. Longley, M.F. Goodchild, D.J. Maguire, and D.W. Rhind (Longman): 481–492Google Scholar
  14. Moore ID, Grayson RB, Landson AR (1993) Digital terrain modelling: A review of hydrological, geomorphological and biological applications. In Terrain Analysis and Distributed Modelling in Hydrology edited by Beven, K.J. and Moore, I.D (Wiley): 7–34Google Scholar
  15. Peucker TK, Fowler RJ, Little JJ, Mark DM (1978) The Triangulated Irregular Network, Proceedings of the American Society of Photogrammetry: Digital Terrain Models (DTM) Symposium, St. Louis, Missouri, May 9–11, 1978: 516–540Google Scholar
  16. Schneider B (1998) Geomorphologisch plausible Rekonstruktion der digitalen Repräsentation von Geländeoberflächen aus Höhenliniendaten. PhD thesis, University of ZurichGoogle Scholar
  17. Schneider B (2001a) On the uncertainty of local shape of lines and surfaces. Cartography and Geographic Information Science 28: 237–247Google Scholar
  18. Schneider B (2001), Phenomenon-based specification of the digital representation of terrain surfaces. Transactions in GIS 5: 39–52Google Scholar
  19. Schmidt J, Evans IS and Brinkmann J (2003) Comparison of polynomial models for land surface curvature calculation. IJGIS 17:797–814Google Scholar
  20. Skidmore A (1989) A comparison of techniques for calculating gradient and aspect from a gridded digital elevation model. IJGIS 3: 323–334Google Scholar
  21. Walker JP, Willgoose GR (1999) On the effect of digital terrain model accuracy on hydrology and geomorphology. Water Resources Research 35: 2259–2268CrossRefGoogle Scholar
  22. Weibel R, Heller M (1991) Digital terrain modeling. In GIS: Principles and Applications edited by Maguire, D.J., Goodchild, M.F. and Rhind, D.W. (Wiley, New York): 269–97Google Scholar
  23. Wise S (1997) The effect of GIS interpolation errors on the use of digital elevation models in geomorphology. In Landform monitoring, modelling and analysis edited by S. Lane, K. Richards, and J. Chandler (Wiley): 139–164Google Scholar
  24. Wood J and Fisher P (1993) Assessing interpolation accuracy in elevation models. IEEE Computer Graphics & Applications: 48–56Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • M. Hugentobler
    • 1
  • R.S. Purves
    • 1
  • B. Schneider
    • 2
  1. 1.GIS Division, Department of GeographyUniversity of ZürichZürichSwitzerland
  2. 2.Department of GeosciencesUniversity of BaselBaselSwitzerland

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