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How does Mathematica create contour plots (or density plots)?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112398] How does Mathematica create contour plots (or density plots)?
  • From: AES <siegman at stanford.edu>
  • Date: Tue, 14 Sep 2010 05:13:20 -0400 (EDT)

How does Mathematica create contour plots (or density plots)?

More specifically, suppose I want a contour plot (with maybe 10 contour 
lines) or a density plot of a function that has just one primary peak 
located somewhere in an otherwise vast and featureless (i.e., flat) 
plane with value z=0.  (Or maybe a narrow ridge running diagonally 
across the plane.)  But:

*  I don't know in advance where this peak is --  or, it moves with 
time, and I want to make multiple plots and follow its motion.

*  The function it represents is somewhat costly to calculate.

*  And I'd like to get a moderately detailed (but maybe not super 
resolved) portrayal of the substructure within that peak.

*  And all this with reasonably fast response (e.g., inside a 
Manipulate).

To obtain this, does Mathematica have to calculate a cast array of 
finely spaced pixel values covering the entire plane, then derive the 
contours from this?

Or does it use some kind of smart algorithm that does a (random?) search 
for non-zero points, then rapidly homes in on areas of interest?

Or, is there some way I can help it find the regions of interest?


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