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MathGroup Archive 2006

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Re: scalar field visualization

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66697] Re: scalar field visualization
  • From: "pf" <pfraundorf at umsl.edu>
  • Date: Sat, 27 May 2006 03:52:20 -0400 (EDT)
  • References: <e53lns$3uk$1@smc.vnet.net><e56elh$24b$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Chris,

  If your scalar field is continuous, you might also try plotting
isosurfaces.  This example* uses Mathematica's ContourPlot3D.  Motion
and interactivity of course also helps when exploring 3D objects on a
2D screen.  Mathematica's Shadow routine allows you to display
isosurface projections on the orthogonal walls at the same time.  You
may have to experiment a bit with these routines, to see if they can
give you something that is useful.

* http://www.umsl.edu/~fraundor/nanowrld/live3Dmodels/test2.html

  I'm not sure how to display the scalar field as though it were a dust
cloud reflecting light, but with a bit of effort you can also display
it as though it were a dust cloud absorbing light.  Basically, you do a
CAT scan in reverse, i.e. calculate multiangle shadows from a 3D model
rather than vice versa.  This can be done by Fourier backprojection,
ie. by taking the 3D Fourier transform of your scalar field, slicing it
through the DC peak about a given rotation axis, and then animate the
Fourier transform of the slices.  The result is a rotating shadow, like
the one illustrated at the bottom of this page**.

** http://www.umsl.edu/~fraundor/nanowrld/difaction.html

                              Cheers.  /pf


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