Re: extracting points plotted by ContourPlot
- To: mathgroup at smc.vnet.net
- Subject: [mg3396] Re: [mg3356] extracting points plotted by ContourPlot
- From: penny at edu-suu-scf.sc.suu.edu (Des Penny)
- Date: Sun, 3 Mar 1996 02:25:38 -0500
- Sender: owner-wri-mathgroup at wolfram.com
>Hi!
>
>Can someone help me with the following problem. After doing a
>
> figure = ContourPlot[f[x,y], ..., Contours ->{0}],
>
>I want to extract the set of points actually plotted - ie a set of {x,y}
>where f[x,y] == 0 for some additional processing.
>
>The command TextForm[InputForm[Graphics[ figure ]]] gives me a text
>string which has a series of Line commands that actually contains the
>{x,y} values that are plotted.
>
>Now what I want to know is this: can someone tell me a nice (or even
>ugly but workable!) way of extracting the list(s) of points plotted by
>the Line command(s)?
>
>If so I would be very grateful!
>
>Richard
*************************************************************************
Hi Richard:
A good reference for graphics questions is "Mathematica Graphics" by Tom
Wickham-Jones. Pages 632-643 discuss ContourPlot.
The contour plot function generates a rectangular array of heights.
Consider for example:
f[x_,y_] := y-x^2
contour = ContourPlot[f[x,y], {x,0,2},{y,0,4}, Contours->{0},
PlotPoints->5, ContourShading->False];
MatrixForm[ contour[[1]] ]
This gives the rectangular array from which a surface can be drawn as follows:
ListPlot3D[ contour[[1]] ]
The ContourPlot function draws the contours as explained on P633 of
"Mathematica Graphics".
****************************************************************************
**********
In order to abstract the xy data of the curve f[x,y]=0, we proceed as
follows. We first convert the ContourGraphics object to a Graphics object
and take the first part of it:
contour=ContourPlot[f[x,y], {x,-2,2},{y,0,4}, PlotPoints->30,
ContourShading->False, Contours->{0}];
contourLine=First[ Graphics[contour] ];
If you look at the contents of contourLine, you will see it has Line
primitives that can be plotted by:
Show[Graphics[contourLine]];
We can now abstract the desired xydata of the curve f[x,y]=0:
xyData=contourLine[[1,3,1]];
We can now manipulate this xyData as desired. We can plot it again if needed:
ListPlot[xyData];
Hope this helps,
Cheers,
Des Penny
==========================
Des Penny
Physical Science Dept.
Southern Utah University
Cedar City, UT 84720
VOICE: (Office): (801) 586-7708
(Home) : (801) 586-2286
FAX: (801) 865-8051
e-mail: penny at suu.edu
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