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Topic: Scientific Visualization: The Mathematical Content
Replies: 1   Last Post: Feb 9, 1993 3:19 PM

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Gene Klotz

Posts: 30
Registered: 12/3/04
Scientific Visualization: The Mathematical Content
Posted: Feb 9, 1993 1:40 PM
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Scientific Visualization: Mathematical Content

THE QUEST

Scientific visualization now lies somewhere between a growth industry and
a buzz word. It's become an important tool for the scientific research
community, is rapidly becoming one in undergraduate education, and has
captured the imagination of the (semi)popular press. There are a lot of
mathematicians involved in GEOMETRIC visualization, yet I don't know
MATHEMATICIANS who know much about the mathematical content of SCIENTIFIC
visualization. And I think this could be important, as I'll explain
below.

My guess is that scientific visualization uses
--three-dimensional analytic geometry (but what?),
--occasional pieces of other areas of classical mathematics, such as
differential geometry,
--new geometry, in particular computational geometry,
--multivariate statistics,
plus things I just don't know about.

WHY THIS COULD BE IMPORTANT

--Three-dimensional geometry has just about disappeared from the
college and from the school curriculum. We've all noticed the "splat"
students make when they bump into having to visualize simple
three-dimensional objects in several variable calculus. I'd argue that
some parts of three-dimensional geometry are very important for the
college curriculum, but I'm not sure exactly what parts. It might be
useful to look at what is needed in scientific visualization. Certainly
I'd expect the new geometric visualization software being developed at
the Geometry Center and other places might be very helpful in deciding
how to teach three-dimensional geometry. This time around, we might even
be able to make it an interesting course!

--Moreover, we just might find some interesting mathematics we should
be teaching future scientists, and we might find some cogent arguments
for the mathematics we're now teaching.

--There are at least some instances of fruitful collaboration between
mathematicians and scientists(!) in scientific visualization, and I think
this deserves to be more widely known.

--At least some areas of scientific visualization appear to be fertile
breeding grounds for new mathematics. We should be preparing students
for this. (Incidentally, has computational geometry, our most recent
child, been completely abandoned to its foster-parent computer science,
or is it still nurtured in some math departments?)

--In general, some of the mathematics used in scientific visualization
may be important for mathematics and for mathematics education, and this
mathematics may not yet be recognized as important.

MY STRATEGY

The Media Magic catalog (mentioned several times before on the Forum)
has, among other things, an imposing list of books on scientific
visualization, none of which are in our local library. The prices are
imposing, too, but I've just been given some unattached research funds
which were equal to the task. I plan to look through a batch of books
and let you know what I find of interest relating to the above. "Review"
would be too strong a word, since I won't have time to examine them in
real detail, but perhaps I can inspire others to take a more careful look
and report their findings.

THE BOOKS

Brodlie, K.W. et al (Eds.), "Scientific Visualization Techniques and
Applications, Springer-Verlag, '91

Kaufman and Nielson, (Eds.), "Proceedings of Visualization '92", IEEE
Press, '92

Keller and Keller, "Visual Cues", '92

Patrikalakis,N.M. (Ed.), "Scientific Visualization of Physical
Phenomena", Springer-Verlag, '91

Thalman, Daniel (Ed.), "Scientific Visualization and Graphics
Simulation", Wiley, '90

There are other books available, but from two-paragraph descriptions
these appeared to have the best chance of having at least a little bit of
mathematical content, and not be entirely gee-whiz pictures.

WHAT I'D LIKE FROM YOU

Help! Do you know or know people who know anything about the
mathematical content of scientific visualization? Would you like to look
over and report on a book? Do you know other important sources which
should be considered? Etc?

Also, please do comment about this project (how's my jousting technique?
have I picked a good windmill?), and on the book reports I'll soon be
giving. What could I do to make the project more worthwhile?





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