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