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From: "John D'Errico" <woodchips@rochester.rr.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: level curves
Date: Thu, 8 Jan 2009 13:02:01 +0000 (UTC)
Organization: John D'Errico (1-3LEW5R)
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"m y" <ailojee@gmail.com> wrote in message <gk4rkc$94k$1@fred.mathworks.com>...
> Hi dears
> How to plot a level curve and the exact point of intersection between two different level curves.
> I ploted the level curves and their point of intersection but that is not exact.
> 
> f(x,y)=m   (first level curve with m as a parameter)
> g(x,y)=n   (second level curve with n as a parameter)
> in both cases x and y varies from 0 to 1.
> one way is
> We will fix one level curve (say for m=0.5), and check the level curve intersection for n zero to 1. similarly we change m and again check the point of intersection b/W these level curves. 
> 
> I am interested in the tangential situation,I need those values of (x,y)where both curves are tangent to eachother. 

This will be somewhat difficult to solve in general.

Most simple tools that will generate a level curve
will do so in a piecewise linear form. For example, a
contour plot uses a piecewise linear approximation.
How will you find a shared tangent for a pair of
piecewise linear curves that are piecewise linear?

So if you are to make this work, you must use
splines for the curves. This will take some work,
since now you must do a nonlinear search for a
shared tangent between two splines. Since that
optimization will surely have multiple local minima,
you will need to use a global search.

There are many things in mathematics that are
easy to state yet will take some effort to accomplish.
This would seem to be one of them.

John