2

I have this ParametricPlot3D 

sigma = 10;
rho = 27;
beta = 8/3;
sol = NDSolve[{x'[t] == sigma (y[t] - x[t]), 
    y'[t] == x[t] (rho - z[t]) - y[t], z'[t] == x[t] y[t] - beta z[t],
     x[0] == 0, y[0] == 1, z[0] == 1.05}, {x, y, z}, {t, 0, 100}, 
   MaxSteps -> 30000];
p = ParametricPlot3D[Evaluate[{x[t], y[t], z[t]} /. sol], {t, 0, 100},
   ColorFunction -> Function[{x, y, z}, Hue[x]], PlotPoints -> 250]

enter image description here

I would like to extract the data points in the form of a list {{x1,y1,z1},{x2,y2,z2},...} and so I did this

data = Cases[p, GraphicsComplex[x__] -> x, {1}][[1]];

But the points do not seem to be in the right order, in fact the first number is not my inizial value (0,1,1.05), nor is the last one. If I do

Graphics3D@Line@data

this is the result

enter image description here

which is all messed up. How can I extract the points from the plot in the right order?

Emmet
  • 356
  • 1
  • 6
  • 4
    Try this: data = Cases[Normal[p], Line[pts_] :> pts, ∞][[1]]. – J. M.'s missing motivation Mar 24 '17 at 15:28
  • Wow, that worked, thank you very much! Could you explain your code a little bit, what is Normal doing exactly and why using RuleDelayed instead of the usual rule? – Emmet Mar 24 '17 at 15:34
  • Have you seen this? – J. M.'s missing motivation Mar 24 '17 at 15:44
  • @J.M. Very good, thank you. – Emmet Mar 24 '17 at 15:49
  • 2
    maybe missing the point of the question, but you can ge the points right from the NDSolve result: Graphics3D@Line[Transpose[Through[{x, y, z}["ValuesOnGrid"]] /. First@sol ]] – george2079 Mar 24 '17 at 15:52
  • @george2079 I didn't know. But isn't some adaptive sampling performed by Plot? For example I used PlotPoints -> 250 but I could have used more. How can I specify that in your code? – Emmet Mar 24 '17 at 15:58
  • Well, NDSolve[] integrates adaptively as well, so for visualization purposes, george's proposal would often suffice. (I actually did that here.) – J. M.'s missing motivation Mar 24 '17 at 16:06
  • @J.M. Good to know, very informative. – Emmet Mar 24 '17 at 16:12
  • 2
    Plot can give you fewer points as needed to generate a smooth curve. (Example if you set a small MaxStepSize in NDSolve, Plot will just take the points it needs.). In this case about the same.. I kind of like having the actual calculated points, not interpolated. – george2079 Mar 24 '17 at 16:13
  • 1
    @george2079 I see, good point. If anybody is curious, in this case using data2 = Transpose[Through[{x, y, z}["ValuesOnGrid"]] /. First@sol] I get 12520 points while data = Cases[Normal[p], Line[pts_] :> pts, ∞][[1]] gives me 13110. – Emmet Mar 24 '17 at 16:23

0 Answers0