       Re: Re: Question in ParametricPlot

• To: MathGroup at christensen.cybernetics.net
• Subject: [mg264] Re: [mg249] Re: [mg227] Question in ParametricPlot
• From: Jeffrey Adams <jeff at tiag.com>
• Date: Thu, 1 Dec 94 16:48:02 -0500

```>The algorithm that Mathematica uses to generate plots is described

>in a number of places; I know of no way short of duplicating that

>algorithm explicitly to get one's hands on the list {t1, t2, ...}

Here is a method of easily getting a list of the independent variable
as Mathematica generates a plot.

The credit for this "trick" goes to Tom Wickam-Jones at Wolfram
Research, (at least he was the first person I've seen that
illustrated this technique).

Example:
========
--------------------------------------
lst = {}

Plot[ AppendTo[lst, x]; x^2, {x,0,1}]
--------------------------------------

Now lst holds the values of x that were used by Mathematica to make
the plot.

And so for any Parametric Plot you can get the same results for the
independent variable:

Example:
========
--------------------------------------
lst = {}

ParametricPlot[
AppendTo[lst, t];
{Sin[t], Sin[2 t]}, {t,0,2Pi},
Compiled ->False]
--------------------------------------

Now lst holds a list of the independent values of t used to make the
plot.  Notice the use of Compiled -> False to remove a warning
message about Mathematica not being able to compile this function
because of AppendTo being in there.

A very simple and elegant way of getting the values after you realize
that as Mathematica has to evaluate the value of the function at each
point it uses, you know the entire first argument of the plotting
function will evaluate, in this case, the AppendTo as well.