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