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

• To: mathgroup at smc.vnet.net
• Subject: [mg129672] Re: Any way to get gradient lines as well as contour lines?
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sun, 3 Feb 2013 20:21:16 -0500 (EST)
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```Grad[Sin[x + y^2], {x, y}]

{Cos[x + y^2], 2*y*Cos[x + y^2]}

Plot3D[Sin[x + y^2], {x, -Pi, Pi}, {y, -2, 2},
MeshFunctions -> {
Cos[#1 + #2^2] &,
2 #2 Cos[#1 + #2^2] &},
Mesh -> {10, 20},
PlotPoints -> 35]

Bob Hanlon

On Sun, Feb 3, 2013 at 2:48 AM, 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
>
>

```

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