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MathGroup Archive 2002

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RE: how to extract parameter values

  • To: mathgroup at smc.vnet.net
  • Subject: [mg37320] RE: [mg37310] how to extract parameter values
  • From: "David Park" <djmp at earthlink.net>
  • Date: Wed, 23 Oct 2002 02:56:59 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Jan,

Why do you want the t values? They are only an artifact of Mathematica's
plot making? If what you really want is the points then here is an example
of what you can do. We extract the graphics, g, and the points, pts, from
the Line in g. Then show them both.

curve[t_] := {t, Sin[t]}

g = First[
      ParametricPlot[Evaluate[curve[t]], {t, 0, 2Pi},
        DisplayFunction -> Identity]];
pts = Cases[g, Line[a_] -> a, Infinity] // First;

Show[Graphics[
      {g,
        AbsolutePointSize[5], Point /@ pts}],
    Frame -> True,
    ImageSize -> 450];

In general you could solve for t from the x or y point coordinates (trivial
in my example) but the method you propose is better. Add Compiled -> False
to eliminate the error message and don't worry about the extra time because
you are asking for extra information. I don't think there is actually
significant extra time.

list = {};
ParametricPlot[(AppendTo[list, t]; curve[t]), {t, 0, 2Pi}, Compiled ->
False];

For our example, the two methods give the same t values, but list is not in
order. If you look at the two set of t values you can see how the
Mathematica plotting routine backtracks to fill in regions of high
curvature.

(First /@ pts) == Sort[list]
True

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

From: Jan Mangaldan [mailto:jajem at yahoo.com]
To: mathgroup at smc.vnet.net

I'd like to know how I can extract the parameter
values used by ParametricPlot in plotting a curve,
e.g. if ParametricPlot used points corresponding to
parameter values 2, 4, 6, etc... I need a way to get
the list {2, 4, 6, ...}.

One solution I know is this:

list={};
ParametricPlot[(AppendTo[list,t]; {f[t]
g[t]}),{t,tmin,tmax}];

The problem with this is that I get an error that
ParametricPlot cannot compile the function, and that
the plotting time is considerably slowed down.
especially if I have a high PlotPoints setting.

Any ideas?

                                   Jan Mangaldan (~_~)

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