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MathGroup Archive 2004

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RE: on ColorFunction and combined images?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47939] RE: [mg47930] on ColorFunction and combined images?
  • From: "David Park" <djmp at earthlink.net>
  • Date: Sat, 1 May 2004 02:43:04 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Sampo,

There is an error in the Mathematica conversion of DensityGraphics to
Graphics. It must perform this conversion to combine the two plots where one
of them is Graphics.

Consider...

Options[Raster]
{ColorFunction -> Automatic, ColorFunctionScaling -> True}

When converting to Graphics, Mathematica drops the ColorFunctionScaling
option.

Let's make a simple plot using Raster.

tab = Table[2x, {y, 0, 1, 0.2}, {x, 0, 1, 0.2}]
{{0, 0.4, 0.8, 1.2, 1.6, 2.},
 {0, 0.4, 0.8, 1.2, 1.6, 2.},
 {0, 0.4, 0.8, 1.2, 1.6, 2.},
 {0, 0.4, 0.8, 1.2, 1.6, 2.},
 {0, 0.4, 0.8, 1.2, 1.6, 2.},
 {0, 0.4, 0.8, 1.2, 1.6, 2.}}

Show[Graphics[
      {Raster[tab, {{0, 0}, {1, 1}},
          ColorFunctionScaling -> False,
          ColorFunction -> (Hue[#/2] &)]}],
    AspectRatio -> Automatic,
    Frame -> True];

Now make the same plot using DensityPlot.

plot1 =
    DensityPlot[2x, {x, 0, 1}, {y, 0, 1},
      Mesh -> False,
      ColorFunctionScaling -> False,
      ColorFunction -> (Hue[#/2] &),
      PlotPoints -> 6];

Now, lets convert plot1 to Graphics and look at the first part.

First@Graphics@plot1

Raster[{{0., 0.4, 0.8, 1.2, 1.6,
    2.}, {0., 0.4, 0.8, 1.2, 1.6,
    2.}, {0., 0.4, 0.8, 1.2, 1.6,
    2.}, {0., 0.4, 0.8, 1.2, 1.6,
    2.}, {0., 0.4, 0.8, 1.2, 1.6,
    2.}, {0., 0.4, 0.8, 1.2, 1.6,
    2.}}, {{0., 0.}, {1., 1.}}, {0., 2.},
  ColorFunction -> (Hue[#1/2] & )]

The ColorFunctionScaling option has been dropped and that is an error.

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/




From: Sampo Smolander [mailto:sampo.smolander+newsnspam at helsinki.fi]
To: mathgroup at smc.vnet.net

Intro:

If I want to combine, say, a density field plot and an overlaid
curve on it, it is rather easy:

pic1 = DensityPlot[x^2, {x, 0, 1}, {y, 0, 1}, Mesh -> False]
pic2 = Plot[x^2, {x, 0, 1}]
Show[pic1, pic2]


My Case:

But say that I am plotting a densify field that that describes, just for
an example, some carbon dioxide concentrations for which a natural scale
(in the air outdoors) is something like 350...370 rather than 0...1.

I can tell DensityPlot to feed the raw concentration values
to the ColorFunction, and I can provide it my own ColorFunction:

mycf[x_] := RGBColor[0, 0, (x - 350)/20]
pic1 = DensityPlot[350 + 20*x^2, {x, 0, 1}, {y, 0, 1},
  ColorFunctionScaling -> False, ColorFunction -> mycf, Mesh -> False]
pic2 = Plot[x^2, {x, 0, 1}]
Show[pic1, pic2]


The Problem:

There is no problem in drawing the pic1, but then when I try to
combine pic1 and pic2 with that Show, I get an error message:
"Argument in RGBColor[0, 0, -17.5] is not a real number between 0 and 1."

It apparently happens so that with Show, the pic1 is redrawn and (some
of?) the options that I gave in the original DensityPlot command are not
used anymore.

Is there a way around this problem?
How can I overlay other graphs with densityplots for which I have used my
own colorfunctions?

I think of the following: I could manually scale every function, that I
attempt to plot, to give out values only in the range 0...1. Then
I guess everything should work okay. But an easier way?

--
Sampo Smolander ............... http://www.cs.helsinki.fi/u/ssmoland/
Division of Atmospheric Sciences ............. University of Helsinki




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