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Re: Adding Colorfunction causing poor plot quality

  • To: mathgroup at smc.vnet.net
  • Subject: [mg101288] Re: Adding Colorfunction causing poor plot quality
  • From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
  • Date: Tue, 30 Jun 2009 06:32:57 -0400 (EDT)
  • References: <h29cc0$bct$1@smc.vnet.net>

John Fultz already explained it in this thread:

http://groups.google.com/group/comp.soft-sys.math.mathematica/
browse_frm/thread/a956d8eee41f8923# (http://tinyurl.com/l44dmm)

Cheers -- Sjoerd


On Jun 29, 5:28 am, Porscha Louise McRobbie <pmcro... at umich.edu>
wrote:
> Hi,
>
> I want to understand why adding a ColorFunction seems to worsen the
> resolution of my graphics.  I have two side-by-side animations, one of
> which is a complex function Psi, where the shape is the square modulus
> and the ColorFunction is Arg[Psi].
>
> I have the following:
>
> Clear[Psi, X, anima, dx0, dk, k0]
> DynamicModule[{dk, k0, Psi, anima}, dk = .5; dx0 = 0.5/dk;
>
>   Psi[x_, k0_, t_] :=
>    1/((4 Pi^2 dk^2)^(1/4)) (
>     2 E^((k0^2 t - 2 k0 x - 2 I dk^2 x^2)/(2 I - 4 dk^2 t))
>       Sqrt[Pi])/Sqrt[1/dk^2 + 2 I t];
>
>   anima[x_, k0_] :=
>    Animate[
>
>     GraphicsRow[{Plot[Abs[Psi[x, k0, t]]^2, {x, -20, 20},
>        PlotRange -> {{-20, 20}, {0, 1.1}}, Filling -> Axis,
>        ColorFunction -> (Hue[(Arg[Psi[#1, k0, t]])/(2 Pi)] &),
>        ColorFunctionScaling -> False, PerformanceGoal -> "Quality=
",
>        PlotPoints -> 10, MaxRecursion -> 3],
>
>       Show[
>        Plot[Sqrt[1 + T^2/(4 dx0^4)], {T, 0, t},
>         PlotStyle -> {Thick, Blue}, PlotRange -> {{0, 15}, {0, 7.=
5}}],
>        Plot[dk T/dx0, {T, 0, 15},
>         PlotStyle -> {Black, Dashed, Thick}]]}, ImageSize -> 600]=
,
>
>     {t, 0.0001, 15}, AnimationRunning -> False];
>
>   Manipulate[anima[x, k0],
>    Style["Wavepacket Center", Bold,
>     16], {{k0, 0,
>      Style["\!\(\*SubscriptBox[\"k\", \"0\"]\)", 14]}, -1.25, 1.25,
>     Appearance -> "Labeled", ImageSize -> Small},
>    ControlPlacement -> Left, SaveDefinitions -> True]]
>
> The resolution on both plots isn't great. I've tried adjusting both
> PlotPoints and MaxRecursion, but it doesn't seem to improve the
> quality at all, it only makes the animation controls (Play/Pause) more
> slow to respond when clicked. I see the same problems if I change the
> ColorFunction to something simpler like "Rainbow".
>
> However, if I remove the options ColorFunction and
> ColorFunctionScaling, the plots are not jagged, the resolution is
> great, and the animation smoother.
>
> 1. Is there another way to add a ColorFunction to such a filled plot?
> 2. Why should adding a colorfunction to the first element of my
> GraphicsRow (which worsens the resolution), also worsen the resolution
> of the second element of my GraphicsRow?
>
> Thanks in advance,
> Porscha



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