Re: ContourPlot and finite approximation to level sets

• To: mathgroup at smc.vnet.net
• Subject: [mg68638] Re: ContourPlot and finite approximation to level sets
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Mon, 14 Aug 2006 06:44:09 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <ebmu7p\$6q9\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```dkjk at bigpond.net.au wrote:
> Hi all,
>
> Given a real-valued function f(x,y) over {(x,y) | xmin < x < xmax, ymin
> < y < ymax}, ContourPlot can be used to generate the graph of the level
> set { (x,y) | f(x,y) = c } using
>
> ContourPlot[f[x,y],{x,xmin,xmax},{y,ymin,ymax},Contours->{c},ContourShading->False].
>
> Is there any way to access the coordinates used by Mathematica to paint
> the contour line of height c? If not, can anyone suggest an algorithm,
> such as the one used by Mathematica, to finitely approximate a level
> set?

Hi James,

The array of points (by default 25x25 points)is the first element of the
SurfaceGraphics object return by ContourPlot. For example,

cp = ContourPlot[Sin[x*y], {x, -1, 1}, {y, -1, 1}, Contours -> {0.5},
ContourShading -> False];
FullForm[cp]
Dimensions[cp[[1]]]

Best regards,
Jean-Marc

```

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