[MUG] Animation of drawing a function point-by-point

[MUG] Re: Animation of drawing a function point-by-point
Author: Maple User Group    Posted: Mon, 4 Nov 2002 10:23:49 -0500 (
>> From: Maple User Group "maple_gr" From: "Sandy Yates" "S.Yates" | I am not very experienced with Maple (v7). I am trying to ANIMATE | drawing an (x, f(x) ) function where for each iteration I would like to | draw more of the function, i.e, incrementing x for each step animation | step. -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Fri, 1 Nov 2002 08:46:35 -0800 (PST) From: Robert Israel "israel" To: "maple-list" Subject: Animation of drawing a function point-by-point > with(plots): display([seq(plot(f(t),t=0..20*j, numpoints=3*j), j=1..30)], insequence=true); Robert Israel "israel" Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: "Dr Francis J. Wright" "F.J.Wright" To: "S.Yates" Subject: Animation of drawing a function point-by-point Date: Fri, 1 Nov 2002 17:14:43 -0000 I discuss this type of animation in my book "Computing with Maple"; see http://centaur.maths.qmul.ac.uk/CwM/ for details. I suggest you take a look at the cardioid animation under "Graphics examples" on that web page. If that does essentially what you want, then you might like to download the solutions to the exercises for Chapter 3, which are available as a Maple 6 worksheet under "Exercise solutions". (Of course, I would also encourage you to buy the book!) This worksheet also runs in Maple 7. (In fact, I have just fixed a problem in it caused by the fact that Maple 7 will not accept a zero-length parametric curve, whereas Maple 6 would.) Francis --- Dr Francis J. Wright School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK Tel: 020 7882 5453 (direct); Fax: 020 8981 9587 (dept.) "F.J.Wright" http://centaur.maths.qmul.ac.uk/ -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Fri, 01 Nov 2002 09:42:23 -0800 To: "maple-list" From: David Harrington "dharr" Subject: Animation of drawing a function point-by-point A little crude because the moving point is connected to the axis (discont = true seems not to work here): with(plots):animate( sin(x)*Heaviside(t-x),x=0..10,t=0..10,frames=50,numpoints=100); Your function is harder to do because of overflow problems -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Fri, 01 Nov 2002 11:09:11 -0800 From: Allan Wittkopf "awittkop" Subject: Animation of drawing a function point-by-point To: "maple-list" The following is quite short and will give you what you need: f:= t -> exp(-t/100)*cos(t); nf := 11: plots[display]([ seq( plot(f(t),t=0..(i-1)/(nf-1)*600+1e-15, numpoints=max(2,trunc(1+(i-1)/(nf-1)*400))), i=1..nf) ],insequence=true); In the above 'nf' is the number of frames, and can be adjusted to suit - the 600 is the last time value, and the 400 is the number of points in the last frame - notice, they are defined as ratios of the final values in terms of '(i-1)/(nf-1)'. This can be made more efficient, but it is much less elegant. - Allan -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Fri, 1 Nov 2002 15:30:26 -0500 (EST) From: Denis Sevee "dsevee" To: "maple-list" "maple-list" Subject: Animation of drawing a function point-by-point Here's one way: >f:=t->sin(t): >for i to 10 do p[i]:=plot(f(t),t=0...2*i,color=black) od: >plots[display]([seq(p[i],i=1..10)], insequence=true); The second line creates the frames of the animation (in this case 10 frames). The third line displays them as an animation. Denis Sevee -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Sat, 2 Nov 2002 03:40:38 -0500 (EST) From: Carl Devore "devore" To: "maple-list" Subject: Animation of drawing a function point-by-point The range 0..600 seems much too big to do justice to this graph, but if that's what you really want: plots[animate]( `if`(t<x, f(t), undefined) ,t= 0..600 ,x= 0..600 ,numpoints= 400 ,frames= 100 ); Of course, you can change the ranges and the number of frames to whatever you want. -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Sun, 3 Nov 2002 07:04:15 -0500 (EST) From: Carl Devore "devore" To: "maple-list" Subject: Animation of drawing a function point-by-point Here is another solution in addition to the one that I just posted. This one works much, much faster and gives a smoother animation, but it is more difficult to understand for a new user. TracePlot:= proc(P::specfunc(anything, PLOT)) local A,C,C0,Cn,Pn,np,chunk,fr,f; fr:= 16; # Defaukt number of frames hasoption([args[2..-1]], 'frames', 'fr'); C:= op(1,P); C0:= op(0,C); A:= op(1,C); Cn:= op(2..-1,C); Pn:= op(2..-1,P); np:= nops(A); chunk:= np/fr; PLOT(ANIMATE(seq([C0(A[1..trunc(chunk*f)], Cn), Pn], f= 0..fr))) end proc: And call it as: TracePlot( plot(exp(-t/100)*cos(t), t= 0..100, numpoints= 400) ,frames= 100 ); -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Mon, 04 Nov 2002 11:04:01 +0100 From: Koch-Beuttenmueller "Heike.Koch-Beuttenmueller" To: "maple-list" Subject: Animation of drawing a function point-by-point May-be animatecurve( .... ) is the function you need ? (after with(plots) ) Best regards, Heike Koch-Beuttenmueller

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