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Re: ListDensityPlot, ColorFunction, and associated confusions

• To: mathgroup at smc.vnet.net
• Subject: [mg49777] Re: [mg49737] ListDensityPlot, ColorFunction, and associated confusions
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Fri, 30 Jul 2004 06:02:29 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

>-----Original Message-----
>From: AES/newspost [mailto:siegman at stanford.edu]
To: mathgroup at smc.vnet.net
>Sent: Thursday, July 29, 2004 1:46 PM
>To: mathgroup at smc.vnet.net
>Subject: [mg49777] [mg49737] ListDensityPlot, ColorFunction, and associated
>confusions
>
>
>I'm trying to show some rectangular arrays in two ways by creating 
>side-by-side ListPlot3D and ListDensityPlot displays in a 
>GraphicsArray.
>
>Each of the arrays contains a primary "mountain peak" that 
>arises out of 
>a flat plane at a base elevation close to zero, plus several secondary 
>hillocks only 1/3 to 1/2 as high as the main peak -- and 
>that's how they 
>show up in the ListPlot3D,
>
>In the ListDensityPlot, however, using the standard 
>ColorFunction->Hue, 
>the tops of some of the secondary hillocks show up in the same bright 
>red as the top of the main peak, even though they appear in the 
>ListPlot3D to be less than 1/2 as high as the main peak.  It's as if 
>ColorFunctionScaling is being applied locally to each individual peak 
>somehow.
>
>What might be going on here?  (And secondarily, because of the way Hue 
>functions, the flat background plain ends up in close to the 
>same red as 
>the top of the peaks.  Any easy way to fix that?)
>
>

Well, an example might simplify discussion.  
Possibly your problems are related to: 

 Options[ListPlot3D, PlotRange]
 {PlotRange -> Automatic}


 Options[ListDensityPlot, PlotRange]
 {PlotRange -> Automatic}


Please compare:

 a=10;
 data=Table[ 1/(1+a(x^2+y^2)),{x,-1,1,.1},{y,-1,1,.1}];

 ListPlot3D[data]
 ListDensityPlot[data, ColorFunction -> Hue]

with

 ListPlot3D[data, PlotRange -> All]
 ListDensityPlot[data, ColorFunction -> Hue, PlotRange -> All]


The bottom and top are both red because Hue[0] == Hue[1] == RGBColor[1,0,0]
If you don't like that, customize your ColorFunction.


--
Hartmut Wolf