Re: Contour plots

["Andrew D. Hwang" <ahwang@mathcs.holycross.edu>]

On Fri, 28 Jan 2005, Jeffrey A. Edlund wrote:

> The data come from simulations of populations of binaries white dwarf
> stars.  I'm trying to plot the number of binary systems (z) in a given
> frequency range (x) and chirp mass range (y).  I'm not quite sure how to
> answer your question about how curved the contours will be. Nothing
> really crazy I suppose.
>
That's pretty much what I was asking. :)

> I'd definitely be willing to do some programming to get this to work
> if I had some suggestions on the right way to approach this problem.
>
A few (definitely non-expert) ideas for numerical methods:

Interpolate the data with cubic spline patches to get a C^1 surface, then

  - solve the level set equations algebraically.

  - refine the data mesh (perhaps to 100x100?) using the spline patches,
    then use piecewise-linear approximation to calculate contour points.

  - Euler's method on J(grad f) -- find a point on the desired contour,
    compute the gradient of the height function and rotate 1/4 turn,
    follow for a short interval, and repeat until the contour returns to
    its starting point or leaves the bounding box or...

I suspect there are more knowledgeable people subscribed to the list who
could suggest numerical methods that actually work. :)


> My thoughts:  Ideally I'd like something that will autoselect contour
> levels that work well (while at the same time allowing the user to set
> specific levels).  Also the contours need to be labeled in some way.
> Having an auto labeler would be nice.
>
Regarding implementation, presumably there'd be a "contour" class
containing the height of the contour, the position, orientation, and text
of the label, and linked lists of points representing the contour data
proper; and a "contour plot" class containing maximum and minimum heights,
the number of contours to plot and/or the specific heights, and a list of
contours...

--Andy

Andrew D. Hwang			ahwang@mathcs.holycross.edu
Department of Math and CS	http://math.holycross.edu/~ahwang
College of the Holy Cross	(508) 793-2458 (Office: 320 Swords)
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