Getting curvatures in certain directions

Precision Farming Project goddard at
Fri Dec 20 14:04:41 EST 1996

Hello GRASS-people:
  Before I start, I wish everyone happy holidays.

A while ago, I and some of my colleagues spent some very
enjoyable days driving around fields in a 4x4 pickup (so we
wouldn't get stuck), acquiring positioning information
via differential GPS.  Now we are trying to generate "true"
digital elevation models of the surfaces we drove over.
Building a DEM of the surface traversed by the GPS antenna is
not too difficult (just a zillion runs with trying
to find "optimal" values for the tension and smoothing
parameters), correcting the positions for the height/attitude
of the truck appears to be more problematic.

I can get enough information out of the various files produced
by to calculate normal surface vectors at all the
points in the sitelist.  So most of the elevation correction
is easily possible.  The part of the position correction due to
the truck travelling over a curved surface (thereby changing the
ground clearance) is more difficult.  I don't see any way for
GRASS to tell me the curvature of the surface in particular
directions (the heading of the vehicle), but I may be wrong on 
that.  I think the solution is to fit a smoothing spline to the
height as a function of arc length, but how does one relate the
tension and smoothing parameters of TPS working in 3 dimensions
to an "ordinary" spline working in 2?

(Rough calculations give the curvature correction as being
about the same magnitude as the error in the GPS coordinates,
so places where high curvature are seen need the correction.)

Ideas?  Opinions?  I'll offer a virtual beer to all comers.

Gordon Haverland
Precision Farming Project
Alberta Agriculture
goddard at

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