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

• To: mathgroup at smc.vnet.net
• Subject: [mg129690] Re: Any way to get gradient lines as well as contour lines?
• From: Christopher Young <cy56 at comcast.net>
• Date: Mon, 4 Feb 2013 01:21:37 -0500 (EST)
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```On Feb 3, 2013, at 2:18 PM, Bob Hanlon <hanlonr357 at gmail.com> wrote:

> 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

Thanks, I'm getting the contour lines with this but the other mesh lines
aren't in general at right angles to the contour lines.

I'm wondering if the mesh complex functions could be used to get both
contour lines and gradient lines in some cases.

In the cases shown, though, they're not quite contours and gradients,
although they are conjugate sets of curves, i.e., at right angles to
each other.

\$TrigFunctions =
{
Sin, Cos, Sec, Csc, Tan, Cot,
ArcSin, ArcCos, ArcSec, ArcCsc, ArcTan, ArcCot,

Sinh, Cosh, Sech, Csch, Tanh, Coth,
ArcSinh, ArcCosh, ArcSech, ArcCsch, ArcTanh, ArcCoth
};

plots = Table[
Plot3D[
Abs[f[x + I y]],

{x, -2, 2}, {y, -2, 2},

MeshFunctions ->
Function @@@ {
{{x, y, z}, Re[f[x + I y]]},
{{x, y, z}, Im[f[x + I y]]}},

MeshStyle -> {Orange, Green},
PlotLabel -> f,
Ticks -> None
],

{f, \$TrigFunctions}
];

Chris Young

```

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