Re: ContourPlot and finite approximation to level sets

*To*: mathgroup at smc.vnet.net*Subject*: [mg68653] Re: [mg68629] ContourPlot and finite approximation to level sets*From*: "Chris Chiasson" <chris at chiasson.name>*Date*: Mon, 14 Aug 2006 06:44:39 -0400 (EDT)*References*: <200608130952.FAA06266@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Let my bumbling converted to experience be your guide: It is possible to extract contours from graphs, though you should remember that the contour lines are only approximate. If your function is complicated, you may want to try a numerical solution for the contour. Also, be careful that you aren't trying to obtain a contour from a (fine grained) discrete function that doesn't actually take on the value of your contour. Here is an example of contour extraction: In[1]:= f[x_,y_]=((x-1)/3)^2+((y-1)/2)^2 In[2]:= Reap[Graphics@ ContourPlot[f[x,y],{x,-5,6},{y,-5,5},Contours\[Rule]{2}, ContourShading\[Rule]False]/.xpr:Line[___]\[RuleDelayed] Sow[xpr]][[2]] You may also want to look at InequalityPlot and ImplicitPlot. On 8/13/06, dkjk at bigpond.net.au <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? > > Thanks very much in advance, > > James > > -- http://chris.chiasson.name/

**References**:**ContourPlot and finite approximation to level sets***From:*dkjk@bigpond.net.au