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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