Re: Contour maps, etc.

["Prof. John P. Ertel (wizard)" <jpe@nadn.navy.mil>]

Sorry, the contour plot for the data that you have listed is a single flat
surface at Z=10 --- the iso-Z curve is completely undetermined.

If you want to know how to properly do a contour plot, check out the
description given by Wolfram's people in their Mathematica guide, or in
the MAPLE User's Guide, in an old document from IBM called on its SSP
(Scientific Subroutine Package), the User's Ref. Man. from DEC on it's
RGLFEP (REGIS Graphic Library - FORTRAN Enhancement Package), etc.

They all describe two versions (one quick & easy / another slower and more
involved).  In the first case, simple bubble sorting routines are used to
"pre-condition" the array of date triplets so that a "connect the dots"
routine can draw the contours.  The "3-color conjecture" technique is used
to try to make sure that there are no crossing lines of iso-Z.  The next
method actually tries to interpolate and thereby smooth the iso-Z contours
using predictor-corrector like methods which try an approximate a set of
iso-Z contours, check for self consistency, then correct and iterate.



On Sat, 3 May 1997, LUDWIK KOWALSKI wrote:

> How are contour lines created by computers? Suppose the following data 
> are given to you; they represent values of Z (such as elevations of a
> terrrain, temperatures, magnetic fields, etc.) over a rectangular grid. 
> Use these data to create a scatter plot. It will be a square with a 
> "dent in its roof". A computer will plot the same shape by connecting
>    x    y    Z      points in the order in which they are presented;
>   -------------     for example, all Z=10 linked in red, all Z=20 in blue,
>    1    1   10      etc. But now suppose that the order in which data are
>    2    1   10      presented is random. The scatter-points shape remains
>    3    1   10      unique but several "equipotential" lines can be drawn
>    3    2   10      through it, one with "the dent in the roof", one with 
>    3    3   10      "the dent in the floor", etc.
>    2  2.6   10
>    1    3   10      Now imagine a more complicated terrain and a lot of
>    1    2   10      data presented in RANDOM ORDER. I suspect that some
>                     commercial programs may not be reliable for maping
> COMPLICATED contour lines (multi-fold ridges and valeys with irregular 
> ziz-zag shapes, or their meteorologic equivalents). Why should we trust 
> a computer when we suspect that a unique solution does not exist? 
> Several VERY DIFFERENT maps may often match a given set of descrete data. 
> How do computers deal with this?
>
> Where can I learn about algarithms used to construct contour maps? I want 
> to write a program which gives the "error analysis" of its solution (for
> my summer research project).
>                                                  Ludwik Kowalski

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