Principal Directions with surf.ls
Thanks. I was hoping that either there were an existing function or the components of the output of surf.ls were sufficiently documented to allow one to do it oneself. surf.ls seems to do all the real work in a C function and I don't relish having to go through that but since its just a regression I guess I can ditch surf.ls and use lm in which case I can get the coefficients explicitly and figure it out from there.
On 3/14/07, Roger Bivand <Roger.Bivand at nhh.no> wrote:
On Wed, 14 Mar 2007, Gabor Grothendieck wrote:
Suppose we plot a quadratic surface as in: library(spatial) example(surf.ls) How can we plot lines on the graph to show the principal directions/axes of the elliptical contours and how do we get them?
In the example there are no closed ellipses, with an open, north-facing depression with flow from the west, south-west, south, south-east and east towards the north at the centre of the northern edge. The contour lines can be retrieved with contourLines() on the same object as contour() is used on. However, they are just a generalised visualisation of the surface represented by the matrix. The underlying question might then be: what is the aspect and slope of the surface, in this case a smoothed surface, what are the plan and especially profile curvatures, and what are their length attributes (ie. patches of similar aspect along a profile curvature. In GIS terms this would involve geomorphometrics, often computed using a 3 x 3 filter, and then flow analysis to find the directions (on a digital elevation model, these would be similar to predicting drainage channel networks. Landslip and avalanche studies often need slope length too, which involves measuring patch characteristics in aspect and profile curvature - that is extracting patches with interesting pattern signatures, and checking whether the patch is "straight" in some sense, and longer than a minimum accumulation threshold to feed mass movement. These are general observations in the case that we don't have a smoothed surface. But here we have a model, and I'd guess that the underlying model could be used, rather than its predictions. I couldn't see a package with a vector field plot, there was a suggestion in: http://finzi.psych.upenn.edu/R/Rhelp02a/archive/35933.html but you'd still need the slope and aspect to get the length and direction of the arrows (for display only). A classic reference is: Horn, B. K. P. (1981). Hill Shading and the Reflectance Map, Proceedings of the IEEE, 69(1): 14-47 and Horn's algorithm has stood the test of time, as has Zevenbergen and Thorne: Zevenbergen, L. W., Thorne, C. R. 1987. Quantitative analysis of land surface topography. Earth Surface Processes and Landforms, 12 (1), 4756. It could well be that the surface you are considering is something other than elevation (temperature, etc.), but getting further would depend on the specific characteristics of the study, and whether the surface is a fitted trend surface or not. With a fitted trend surface model, it ought to be possible to use the model. If thinking in terms of geomorphometrics is unhelpful, please accept that geographers "see" things in those kinds of ways! Hope this helps, Roger
Thanks.
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-- Roger Bivand Economic Geography Section, Department of Economics, Norwegian School of Economics and Business Administration, Helleveien 30, N-5045 Bergen, Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43 e-mail: Roger.Bivand at nhh.no