Underlying geospatial algorithms

Saturday, 14 June, 2008

I was completing a project this week that used, in-part, a tensioned spline to interpolate across an area with no data points. My colleague had actually written a custom interpolator based upon the well used algorithm from Smith and Wessell (1). This is the algorithm used in the popular Generic Mapping Tools and seems commonly employed. I then trialled the same process in ArcGIS and noticed that the tension parameter is different between the two and therefore, not surprisingly, that the algorithms are different.

The SPLINE function that is used in Spatial Analyst and available within ArcToolBox actually calls the underlying ARC-INFO function. You won’t find details of it in the Help file. Rather you have to look in ArcDocs or online. And what you find is that they are using a method from two early papers (2,3). Now I don’t have a problem with this per se as the method appears to work reasonably well, although you do need to know what the tension parameter is actually doing. However it is interesting to note that the original Smith and Wessel algorithm has recently been updated (4). Which then begs the question as to why ESRI are still using the 1982 algorithm. Is there a sound basis for this? Or is it simply a case of “code and forget”?

1. Smith, W.H.F. & Wessel, P., 1990. Gridding with continuous curvaturesplines in tension, Geophysics, 55, 293-305.
2. Franke, R., 1982. Smooth Interpolation of Scattered Data by Local Thin Plate Splines. Comp. & Maths. with Appls. Vol. 8. No. 4. pp. 237 - 281.
3. Mitas, L., and H. Mitasova. 1988. General Variational Approach to the Interpolation Problem. Comput. Math. Applic. Vol. 16. No. 12. pp. 983-992.
4. Wessel, P. & Becker, J.M., 2008 Interpolation using a generalized Green’s function for a spherical surface spline in tension. Geophys. J. Int., 174, 21-28.

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