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Re: Extracting points from a contour plot
*To*: mathgroup at smc.vnet.net
*Subject*: [mg90408] Re: Extracting points from a contour plot
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Tue, 8 Jul 2008 07:48:12 -0400 (EDT)
*Organization*: The Open University, Milton Keynes, UK
*References*: <g4v34e$ihi$1@smc.vnet.net>
ajfriend at gmail.com wrote:
> I'm using ContourPlot to plot the curve of zeros of a function of two
> variables within a range of vales (0 < x < 1, 0 < y < 1). Now, what I
> really want is the list of points that it generates. I've tried
> playing with Solve and NSolve, but these are either not working or are
> taking too long. What is the easiest way of getting at the list of
> points that ContourPlot has generated? Do I have to do something like
> InputForm[%] and then cut and paste the list that I want, or is there
> some easier way of doing it?
>
> Or, maybe there is a way of getting the points that I want without
> using ContourPlot that I haven't come across yet, or maybe I'm just
> not using Solve correctly.
Say we want to investigate the following equation. Looking at the
*FullForm* of the graph, we can see that the points computed by
ContourPlot are the first element (list of lists) of a GraphicsComplex
structure. We use *Cases* to extract the list of pairs and check that
the sampled points are indeed roots of the equation.
(Note that we can also use *Reduce* to get a set of analytic solutions.)
g = ContourPlot[Cos[x] + Cos[y] == 0, {x, 0, 2 Pi}, {y, 0, 2 Pi}]
FullForm[g]
pts = First@Cases[g, x_GraphicsComplex :> First[x]]
MapThread[Chop[Cos[#1] + Cos[#2]] == 0 &, Transpose@pts]
Reduce[Cos[x] + Cos[y] == 0 && 0 <= x <= 2 Pi && 0 <= y <= 2 Pi, {x,
y}]
Regards,
-- Jean-Marc
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