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Re: Any way to get gradient lines as well as contour lines?

• To: mathgroup at smc.vnet.net
• Subject: [mg129684] Re: Any way to get gradient lines as well as contour lines?
• From: James Stein <mathgroup at stein.org>
• Date: Sun, 3 Feb 2013 20:25:16 -0500 (EST)
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• References: <20130203074823.CADA568AF@smc.vnet.net>

Google for the two words   Mathematica relaxation    and you may find some
useful ideas, for example:
http://demonstrations.wolfram.com/RelaxationMethodForElectrostaticProblems/
HTH

On Sat, Feb 2, 2013 at 11:48 PM, Chris Young <cy56 at comcast.net> wrote:

> I'd like to be able to plot "gradient lines", i.e., lines of steepest
> descent, on plots of functions of x and y, f(x, y). The contour lines
> can be obtained via MeshFunctions, as in
>
> Plot3D[Sin[x + y^2], {x, -3, 3}, {y, -2, 2}, MeshFunctions -> {#3 &},
> Mesh -> 5].
>
> I'd like all the lines at right angles to these contours.
>
> There must be some way to use the gradient function and then integrate
> to the get the gradient lines.
>
> Maybe this is difficult to do, in general. Also, maybe in general the
> "gradient lines" wouldn't be continuous.
>
> But I wonder if it could be done for some simple examples.
>
> Any suggestions appreciated.
>
> Chris Young
> cy56 at comcast.net
>
>
>

• References:
  • Any way to get gradient lines as well as contour lines?
    • From: Chris Young <cy56@comcast.net>