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Re: Plotting colorfunctions over multiple parametric curves

• To: mathgroup at smc.vnet.net
• Subject: [mg125200] Re: Plotting colorfunctions over multiple parametric curves
• From: "djmpark" <djmpark at comcast.net>
• Date: Tue, 28 Feb 2012 00:46:34 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <5868125.5962.1330344098277.JavaMail.root@m06>

You will obtain better responses if you supply a completely evaluable
example and not leave it up to responders to make up part of the input.


David Park
djmpark at comcast.net 
http://home.comcast.net/~djmpark/index.html 


From: Andrew Green [mailto:kiwibooga at googlemail.com] 


Hi there

I am a bit stuck with this one. I have several curves (circles in this
case) I want to plot at the same time. Each circle also has its own function
defining a unique potential as a function of theta around the curve. I want
to take advantage of Mathematica's colorfunction color scaling and show the
potential around each curve in a color scaled to the min and max values for
the entire set of circle potentials. I get about this far....

n = 5; (*number of circles*)

potential[theta_, i_] := Sin[2*i*theta];

circle[i_, theta_] := {x[i] + r[i]*Cos[theta], y[i] + r[i]*Sin[theta]};
(*x,y, and r are earlier defined vectors of coordinates, radius*)

ParametricPlot[
 Evaluate@Table[circle[i, theta], {i, 1, n}], {theta, 0, 2 Pi},  PlotStyle
-> Thick, Axes -> False,  ColorFunction ->
  Function[{x, y, theta}, ColorData["TemperatureMap"][theta]]];

I can get a nice rainbow color around each circle  but it is the same for
all because I can only seem to define one colorfunction and cannot
incorporate the potential function which varies for each circle "i".

Any help would be most appreciated.


Andrew Green