Re: Contour line colors from z coord of a 3D plot

• To: mathgroup at smc.vnet.net
• Subject: [mg117194] Re: Contour line colors from z coord of a 3D plot
• From: Heike Gramberg <heike.gramberg at gmail.com>
• Date: Fri, 11 Mar 2011 04:32:56 -0500 (EST)

```The lack of a plot along the negative real axis comes from the fact that Log[] has a
branch cut along the negative real axis. Since the default setting for the Exclusions
option in ContourPlot is Automatic, these points are excluded from the plot.
If you want to include those points, you could set Exclusions->{} in ContourPlot.

Heike.

On 10 Mar 2011, at 21:04, Kevin J. McCann wrote:

> If you use a ListPlot3D and ListContourPlot instead, it will get rid of
> the annoying and puzzling lack of a plot along the negative real axis.
>
> On 3/10/2011 6:43 AM, Bob Hanlon wrote:
>> Module[{f, ch = Purple, cl = Yellow},
>>  f[x_, y_] := Log[x + I y];
>>  logre = Show[
>>    Plot3D[Re[f[x, y]],
>>     {x, -2.4, 2.4}, {y, -2, 2},
>>     PlotStyle ->  Opacity[0.7],
>>     PlotRange ->  {-3, 1.5},
>>     ColorFunction ->
>>      (Blend[{cl, ch}, #3]&),
>>     MeshStyle ->  Darker[Gray]],
>>    Graphics3D[
>>     ContourPlot[Re[f[x, y]],
>>        {x, -2.4, 2.4}, {y, -2, 2},
>>        Axes ->  False,
>>        Contours ->  Table[z, {z, -1, 1, .25}],
>>        ContourStyle ->
>>         Table[
>>          Blend[{cl, ch}, (z + 1)/2],
>>          {z, -1, 1, .25}]][[1]] /.
>>      {x_Real, y_Real} ->  {x,
>>        y, -3}],
>>    ViewPoint ->  {2.2, -4, 1.3},
>>    ImageSize ->  400]]
>>
>>
>> Bob Hanlon
>>
>> ---- recmath<recmath99 at gmail.com>  wrote:
>>
>> ==========================
>> Hi there,
>>
>> I'm trying to reproduce this very cool figure:
>> http://en.wikipedia.org/wiki/File:NaturalLogarithmRe.png
>>
>> Problem: I can't get the contour lines color-matched to the 3D
>> surface, which is colored according to it's height. My code is below,
>> can anyone help?
>>
>>
>> Module[{f}, f[x_, y_] := Log[x + I y];
>>
>>  logre = Show[Plot3D[Re[f[x, y]], {x, -2.4, 2.4}, {y, -2, 2},
>>     PlotStyle ->  Opacity[0.7], Axes ->  True, Boxed ->  True,
>>     PlotRange ->  {Automatic, Automatic, {-3, 4}},
>>     ColorFunction ->  (Blend[{Yellow, Purple}, #3]&)],
>>    Graphics3D[
>>     ContourPlot[Re[f[x, y]], {x, -2.4, 2.4}, {y, -2, 2},
>>        Axes ->  False, ContourShading ->  None,
>>        ContourStyle ->  Purple][[
>>       1]] /. {x : _Real, y : _Real} ->  {x, y, -3}],
>>    ViewPoint ->  {2.2, -4, 1.3}, ImageSize ->  300
>>    ]
>>  ]
>>
>>
>

```

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