Re: Pick up coordinates along different contours.

• To: mathgroup at smc.vnet.net
• Subject: [mg43418] Re: Pick up coordinates along different contours.
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Tue, 16 Sep 2003 04:36:39 -0400 (EDT)
• References: <bihpbq\$b5t\$1@smc.vnet.net>
• Reply-to: "Allan Hayes" <hay at haystack.demon.co.uk>
• Sender: owner-wri-mathgroup at wolfram.com

```"Jun Lin" <jl_03824 at yahoo.com> wrote in message
news:bihpbq\$b5t\$1 at smc.vnet.net...
> I plot a couple of 2D contours by using ContourPlot. Now, I want to
> pick up the coordinate of each point along each contour for next step
> calculation purposes. I appreciate with your any suggestion of how to
> get the coordinates of each point along a specific contour (suppose
> two contours have been created).
>
> Jun
>

Jun,

Here are some ideas

cp = ContourPlot[x*y, {x, -1, 1}, {y, -1, 1}]

-ContourGraphics-

-ContourGraphics- is a name for the actual output, cp, which we do not
normally want to see (the picture is a side effect).  We can, however, look
at it:

InputForm[cp]

We see that it is simply an array of values of the x*y at sample points
together with instructions to create a picture when operated on with Show -
no lines - these are constructed each time the picture is created.

To get explicit lines we convert  cp into a Graphics object:

gr = Graphics[cp]

-Graphics-

Again, we can look at the actual output:

InputForm[gr]

We see lines (the contour lines) and polygons (for constructing the

Now extract the lines

lns = Cases[gr, _Line, Infinity]

We may need to label the lines with their heights, especially  if there are
several contour segments  at the same height.

lns /. ln:Line[{___, {x_, y_}}] :> {x*y, ln}.

Note: we can avoid the polygons in gr by begining with

ContourPlot[x*y, {x, -1, 1}, {y, -1, 1}, ContourShading->False]

--
Allan
---------------
Allan Hayes
hay at haystack.demon.co.uk
Voice: +44 (0)116 241 8747
Fax: +44 (0)870 164 0565

```

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