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?