Abstract
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.
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References
Barnhill RE and Gregory JA (1975) Compatible smooth interpolation in triangles. Journal of Approximation Theory 15: 214–225
Bolstad P, Stowe T (1994) An evaluation of DEM accuracy: elevation slope and aspect. Photogrammetric Engineering and Remote Sensing 60: 1327–1332
Corripio JG (2003) Vectorial algebra algorithms for calculating terrain parameters from DEMs and solar radiation modelling in mountainous terrain. IJGIS 17: 1–23
Evans IS (1980) An integrated system of terrain analysis for slope mapping. Zeitschrift fur Geomorphologie 36: 274–295
Farin G (1985) A modified Clough-Tocher interpolant. Computer Aided Geometric Design 2: 19–27
Farin G (1997) Curves and surfaces for CAGD. A practical guide (Academic Press)
de Floriani L, Puppo E (1992) An online algorithm for constrained Delaunay triagulation. Graphical Models and Image Processing 54: 290–300
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): 51–85
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: 1165–1171
Hugentobler M (2002) Interpolation of continuous surfaces for terrain surfaces with Coons patches. In Proceedings of GISRUK 2002 (Sheffield, UK): 13–15.
Kumler M (1994) An intensive comparison of TINs and DEMs. Cartographica (Monograph 45), 31: 2
Maggioni M, Gruber U (2003) The influence of topographic parameters on avalanche release dimension and frequency. Cold Regions Science and Technology, 37: 407–419
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): 481–492
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): 7–34
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: 516–540
Schneider B (1998) Geomorphologisch plausible Rekonstruktion der digitalen Repräsentation von Geländeoberflächen aus Höhenliniendaten. PhD thesis, University of Zurich
Schneider B (2001a) On the uncertainty of local shape of lines and surfaces. Cartography and Geographic Information Science 28: 237–247
Schneider B (2001), Phenomenon-based specification of the digital representation of terrain surfaces. Transactions in GIS 5: 39–52
Schmidt J, Evans IS and Brinkmann J (2003) Comparison of polynomial models for land surface curvature calculation. IJGIS 17:797–814
Skidmore A (1989) A comparison of techniques for calculating gradient and aspect from a gridded digital elevation model. IJGIS 3: 323–334
Walker JP, Willgoose GR (1999) On the effect of digital terrain model accuracy on hydrology and geomorphology. Water Resources Research 35: 2259–2268
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): 269–97
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): 139–164
Wood J and Fisher P (1993) Assessing interpolation accuracy in elevation models. IEEE Computer Graphics & Applications: 48–56
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Hugentobler, M., Purves, R., Schneider, B. (2005). Evaluating Methods for Interpolating Continuous Surfaces from Irregular Data: a Case Study. In: Developments in Spatial Data Handling. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26772-7_9
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DOI: https://doi.org/10.1007/3-540-26772-7_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22610-9
Online ISBN: 978-3-540-26772-0
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