| Comparing meshes [message #50013] |
Thu, 07 September 2006 08:08 |
James Kuyper
Messages: 425
Registered: March 2000
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Senior Member |
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I have two seperate sets of two-dimensional arrays of latitude,
longitude, and altitude. For the first set, the latitude, longitude,
and altitude are supposed to be a good approximation of the point on
the surface of the earth at the center of an image pixel. For the
second set, the longitude, latitude, and altitude are supposed to be a
good approximation to weighted averages integrated over the entire
pixel. Note that this means the latitudes and longitudes of the second
set are not exactly the same as those of the first set.
The spacing of the latitudes and longitudes varies smoothly from 1k to
4km, due to foreshortening and range effects, and also varies
irregularly due to terrain correction. The vector difference has an
average with a magnitude of 18 centimeters, but an RMS value of 38
meters, and a maximum magnitude of 2011 meters; these are plausible
values given the nature of the data and the algorithm used.
Because of the averaging, the second set is expected to make a smoother
surface than the first set. I'm trying to figure out two things:
a) is there any mathematical measure of surface smoothness that I can
apply to an irregular grid like this?
b) what's the best way to display the surfaces so that the greater
smoothness of the second one is clearly visible? I've not attempted to
visualize it yet, but I'd expect a difference of 38 meters to be hard
to see when the grid spacing is 1000 meters.
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