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

• To: mathgroup at smc.vnet.net
• Subject: [mg117230] Re: Contour line colors from z coord of a 3D plot
• From: "Kevin J. McCann" <kjm at KevinMcCann.com>
• Date: Sat, 12 Mar 2011 05:08:40 -0500 (EST)
• References: <ilcq8k\$igu\$1@smc.vnet.net>

```Except that Re[Log[x+I y]] produces a number and is continuous across
the axis:
Try:

{Re[Log[-2.0 + I .0001]], Re[Log[-2.0]], Re[Log[-2.0 - I .0001]]}

There is a branch cut there or at least that is where one usually puts
it, but that does not change the real part.

Kevin

On 3/11/2011 4:33 AM, Heike Gramberg wrote:
> 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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