       Re: two graphs have different color on surface

• To: mathgroup at smc.vnet.net
• Subject: [mg95685] Re: two graphs have different color on surface
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Sun, 25 Jan 2009 06:48:48 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <gleth7\$4pe\$1@smc.vnet.net>

In article <gleth7\$4pe\$1 at smc.vnet.net>,
Steven Siew <stevensiew2 at gmail.com> wrote:

> I have tried to produce a graph where the color on the surface depends
> on the value of z. When I tried doing it in two different ways, the
> color are different on the two graphs even though as far as I can fee
> they should be the same. The code are as below
>
> ComplexColorPlot[func_, {xmin_, xmax_}, {ymin_, ymax_},
>   opts___?OptionQ] := Module[{x, y},
>   Plot3D[Re[func[x + I y]], {x, xmin, xmax}, {y, ymin, ymax}, opts,
>    ColorFunction -> (ColorData["Rainbow"][
>        Re@func[#1 + I*#2]] &)     ]  ]
>
> ComplexColorPlot2[func_, {xmin_, xmax_}, {ymin_, ymax_},
>   opts___?OptionQ] := Module[{x, y},
>   Plot3D[Re[func[x + I y]], {x, xmin, xmax}, {y, ymin, ymax}, opts,
>    ColorFunction -> (ColorData["Rainbow"][#3] &)     ]  ]
>
> ComplexColorPlot[Sqrt, {-1, 1}, {-1, 1},
>  ViewPoint -> {1.227, -1.942, 3.028}, PlotPoints -> {50, 50}]
>
> ComplexColorPlot2[Sqrt, {-1, 1}, {-1, 1},
>  ViewPoint -> {1.227, -1.942, 3.028}, PlotPoints -> {50, 50}]
>
> I expect the functions ComplexColorPlot2 and ComplexColorPlot to
> produce identical color graphs when given identical inputs but they
> dont. And I'm at loss as to why they dont.
>
> My ultimate objective is to have the color reflect the value of Im[func
> [x+I*y]] but I'm great difficulties in achieving it.

The issue might be due to color scaling, assuming that both color
functions are really the same thing but written differently. Set the
option ColorFunctionScaling to True or False in both plot functions to
see how the graphs are rendered.

ComplexColorPlot[func_, {xmin_, xmax_}, {ymin_, ymax_},
opts___?OptionQ] :=
Module[{x, y},
Plot3D[Re[func[x + I y]], {x, xmin, xmax}, {y, ymin, ymax}, opts,
ColorFunction -> (ColorData["Rainbow"][Re@func[#1 + I*#2]] &),
ColorFunctionScaling -> False]]

ComplexColorPlot2[func_, {xmin_, xmax_}, {ymin_, ymax_},
opts___?OptionQ] :=
Module[{x, y},
Plot3D[Re[func[x + I y]], {x, xmin, xmax}, {y, ymin, ymax}, opts,
ColorFunction -> (ColorData["Rainbow"][#3] &),
ColorFunctionScaling -> False]]

ComplexColorPlot[Sqrt, {-1, 1}, {-1, 1},
ViewPoint -> {1.227, -1.942, 3.028}, PlotPoints -> {50, 50}]

ComplexColorPlot2[Sqrt, {-1, 1}, {-1, 1},
ViewPoint -> {1.227, -1.942, 3.028}, PlotPoints -> {50, 50}]

HTH,
--Jean-Marc

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