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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.
Instead of
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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