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I have a plot of an implicit function. I would like to extract all the data points from the graph. The plot is done using contourplot and cannot be plot with plot command.

yode
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Aswin Rajeevan
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1 Answers1

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Here a random example plot:

plot = ContourPlot3D[x^2 + y^2 - z^2 == 1, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]

enter image description here

Surfaces in such plots are usually represented by GraphicsComplexes in compressed notation. The first entry in such a GraphicsComplex is always the list of vertex coordinates (followed by specifications of Polygons via a list of integer tuples, wrapped in Polygon).

We can extract a list of all GraphicsComplexes from a plot with

gclist = Cases[plot, _GraphicsComplex, \[Infinity]];

In this case, there is only one GraphicsComplex, so gclist has length 1. The vertex positions can thus be obtained with gclist[[1, 1]] as in the following example

Graphics3D[Point[gclist[[1, 1]]]]

enter image description here

Henrik Schumacher
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