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RE: Re: filled plot on part of x-interval


>-----Original Message-----
>From: AES/newspost [mailto:siegman at stanford.edu]
To: mathgroup at smc.vnet.net
>Sent: Thursday, November 20, 2003 9:16 AM
>To: mathgroup at smc.vnet.net
>Subject: [mg44699] [mg44664] Re: filled plot on part of x-interval
>
>
>I'll still assert that something like:
>
>    Needs["Graphics`Graphics`"];
>    Needs["Graphics`Colors`"];
>    Needs["Graphics`FilledPlot`"];
>
>    DisplayTogether[
>        FilledPlot[{Sin[x], Sin[x]}, {x,2,8}],
>        Plot[Sin[x], {x,0,10}, PlotStyle->Red]];
>
>is clear, simple, flexible, and readable -- and allows you to easily 
>modify the styles (linewidths, colors) of the different components of 
>the plot independently, as done here, and add additional stuff if you 
>like.
>
>DisplayTogether is your friend -- haven't run into a headache with it 
>yet.
>


Dear Professor Siegman,

my principal objection is illustrated by the (exaggerated) example:

DisplayTogether[
    FilledPlot[Sin[x], {x, 2, 8}, Fills -> {{{1, Axis}, Yellow}}, 
      PlotPoints -> 5, PlotDivision -> 2], 
    Plot[Sin[x], {x, 0, 10}, PlotStyle -> Red, PlotPoints -> 5, 
      PlotDivision -> 2]];



Compare this to:

filled = FilledPlot[Sin[t], {t, 2, 8}, Fills -> Yellow, PlotStyle -> Red, 
      PlotPoints -> 5, PlotDivision -> 2, DisplayFunction -> Identity];
plow = Plot[Sin[t], {t, 0, 2}, PlotStyle -> Red, PlotPoints -> 2, 
      PlotDivision -> 2, DisplayFunction -> Identity];
plhi = Plot[Sin[t], {t, 8, 10}, PlotStyle -> Red, PlotPoints -> 2, 
      PlotDivision -> 2, DisplayFunction -> Identity];

Show[plow, filled, plhi, DisplayFunction -> $DisplayFunction, 
    AxesFront -> True];

This effectively also is David Park proposal (packend in a convenient, yet
non standard interface)



My "cute" Theta, however, turns out to be flawed differently, as seen by:

\[Theta]1[t_, {min_, max_}] := 1 /; t < min || t > max
\[Theta]2[t_, {min_, max_}] := 1 /; min <= t <= max
\[Theta][t_, {min_, max_}] := Through[{\[Theta]1, \[Theta]2}[t, {min, max}]]
Off[Plot::"plnr"]

FilledPlot[Sin[t]*\[Theta][t, {2, 8}], {t, 0, 10}, 
  Fills -> {{{2, Axis}, Yellow}}, PlotStyle -> Red, PlotPoints -> 5, 
  PlotDivision -> 2, PlotRange -> All]

Because t=2 and t=8 are not (necessarily) sampled, but enforcing that makes
theta superfluous, Sorry.


--
Hartmut Wolf


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