Re: Question in ParametricPlot

• To: MathGroup at christensen.cybernetics.net
• Subject: [mg249] Re: [mg227] Question in ParametricPlot
• From: Lou Talman <me at talmanl.mscd.edu>
• Date: Tue, 29 Nov 94 09:44:36 -0700

```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, ...} of values of the
independent variable that Mathematica actually generates in a
"ParametricPlot".  However, one can easily do something that's very close.

MyPlot = ParametricPlot[{x[t], y[t]}, {t, tmin, tmax}, opts]

use "ParametricPlot3D".

MyNonPlot = ParametricPlot3D[{t, x[t], y[t]}, {t, tmin, tmax},

opts, DisplayFunction -> Identity]

Then use Mathematica's list-handling facilities to strip off all
the stuff except for the values of t that this instruction generates:

tValues = Nest[Map[First, #]&, First[MyNonPlot], 3]

The nested "First"'s unfortunately strip off the last of the t-values--but
we know what the last one has to be and we can use "AppendTo" to put it

where it belongs:

AppendTo[tValues, N[tmax]]

One should not expect this to generate *exactly* the list of t-values that

"ParametricPlot" actually uses, but it should be a good substitute.

--------------------------------------------------------------------
Begin forwarded message:

Date: Wed, 23 Nov 1994 03:12:33 -0800 (PST)
From: Xah Y Lee  <xyl10060 at fhda.edu>
Subject: [mg227] Question in ParametricPlot
To: mathgroup at christensen.cybernetics.net
Content-Length: 0

Here is a problem I have that calls for knowing the internal algorithm

used for ParametricPlot. When we do a ParametricPlot, mma automatically

figures out which t to use to produce a smooth curve. I need the list of

t(s) used. Is there a way to get them?

I know I can get a list of points {{x[t1],y[t1]}, {x[t2], y[t2]},...} by

someplot = ParametricPlot[....];

Cases[ someplot, _Line,Infinity ] [[1]]

and solve for t, but this would be very inpractical. I am writing a

series of animation generating functions on special plane curves. With

the list of t, I can be much flexible and powerful in writing my

programs. What I want is to have mma figure out the t(s) needed to make a

smooth curve then pass them to my ploting program.

Thanks for any help.

Xah Lee
Permament email: 74631.731 at compuserve.com
good till December 10: xyl10060 at tiptoe.fhda.com
Phone: 415-965-1454
Mountain View, CA

```

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