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I would like to know if there is a way to extract x,y,z points from ParametricPlot3D.

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ParametricPlot3D[{a1, b1, c1, d1, f1, g1, h1, i1, j1}, {t, 3, 4}, {w, 0, 2 [Pi]}, Axes -> True, AxesStyle -> {Red, Green, Blue},
AxesStyle -> {Red, Green, Blue}, PlotStyle -> {Red, LightPink}, Mesh -> None]

ParametricPlot3D[{a1, b1, c1, d1, f1, g1, h1, i1, j1}, {t, 3, 4}, {w, 0, 2 [Pi]}, Axes -> False, Boxed -> False, PlotStyle -> {Red, LightPink}, Mesh -> None]

a

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We have, for example:

plot1 = ParametricPlot3D[{Cos[u], Sin[u] + Cos[v], Sin[v]}, {u, 0, 2 \[Pi]}, {v, -\[Pi], \[Pi]}]

enter image description here

Then we can extract the points using the following:

pts=Flatten[Cases[plot1, _GraphicsComplex , Infinity][[;; , 1]], 1]

We can then superimpose them on an already existing plot:

Show[plot1, Graphics3D[Point[pts]]]

enter image description here

Or we can save them as a .txt document, in the form of a table:

Export["data.txt", pts, "Table"]

To access them in Mathematica, you can simply do, for instance:

pts[[1]]

{1., -1., -4.48799*10^-7}

I hope this helps.

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  • 1
    $\begingroup$ More directly you can get the points with plot1[[1,1]] $\endgroup$ – Ulrich Neumann Apr 23 at 10:33

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