Re: Contour lines, etc.

[PHRP@FHSUVM.FHSU.EDU (Roger A. Pruitt)]

> On Mon, 5 May 97 LUDWIK KOWALSKI wrote:
>
> > ... Creating a contour plot map is trivial (I wrote my own program for
> > this yesterday) when a complete set of data is available, that is when
> > a value of Z is assigned to every possible x,y location.
>
> This is not true. Interpolational ambiguities also exist after a value of
> Z is assigned to every possible mesh point. The origin of data (formulas
> versus a measurements) is no longer significant at this point. Here is an
> illustration.
>
> Suppose we want a contour plot for potentials between Z1=100 and Z2=101.
> (A range of Z must be given to define a contour line. Keep in mind that
> a too narrow range may miss all data). Cells populated with a chosen
> range will not not always be adjacent mesh cells. In fact two points
> belonging to a single contour line can be separated by numerous cells
> belonging to other contour lines. Pattern recognition dilemmas must be
> always solved to avoid misinterpretations. Can this be done without
> introducing large errors?

Both Surfer and AUXUM will allow any number (within reason) of contour
levels between 100 and 102. Additionally, the AUXUM routine seems to do a
certain amount of smoothing of the contour.

I have my students use the AUXUM program to plot equipotential contours.
Students make potential measurements on a 2 cm x 2 cm grid for various
electrode configurations. These are entered into the AUXUM program which
then produces a two dimensional contour plot. With just a few changes the
program will plot a three dimension set of contours--these are the same
contours but in 3-D. A few more changes and the program will plot a three
dimensional potential surface for the electrode configuration. I find this
all more satisfying than the usual way equipotential contours are obtained
in a beginning lab. Further, the results always look better than when
students do it the older way, and they are much less frustrated. 

The students can see the potential surface. They can then see how the
contours relate to the surface when they view the 3-dimensional contour
graph. Finally, they can see how the 2-dimensional contour plot relates to
the other two graphs.

Another reason for doing the equipotential contours this way is because this
is the way real science is done. Meteorologists use the same techniques for
plotting isobars or isotherms on a synoptic surface graph. Geologists plot
height contours on maps using the same type of contour program. Our
department uses Surfer for this. They also have a magnetometer and use the
program to plot magnetic field contours from data that has been collected in
the field. 

What I would like to know is the algorithm used to do this. I thought that
was what you were after too, Ludwig.

Roger
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Roger A. Pruitt, PhD
Professor of Physics
Fort Hays State University
Hays, KS  67601
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