Generate a table of data points from a surface in 3D

Question

I'm trying to extract the data points from a general 3D surface and saving the data points, in the form of the coordinate triples $\mathbf{ \{ x,y,z\} }$, in a table/array in the format: $\mathbf{\{ \{ x_1,y_1,z_1\} , \{ x_2,y_2,z_2\} , ..., \{ x_n,y_n,z_n\} \} }$.

With a cylinder this is quite easy since we know that for a cylinder:

$\mathbf{x^2+y^2=r^2}$

$\mathbf{ x=t_1}$

$\mathbf{ y=n \cdot \sqrt{r^2-t_1^2}}$

$\mathbf{ z=t_2}$

where $n$ is either +1 or -1. So for a cylinder with radius 1 and length 10 we can generate the table as:

step=0.1
data = Table[{x = t1, y = n*(1 - t1^2)^(1/2), z = t2},
{t1, -1, 1,step}, {t2, 0, 10, step}, {n,{-1,1}}];

I would like to know if there exist an easier way to do this? I have tried executing Table[plot] but that doesn't seem to save any data points it just saves the plot itself in the table as an element.

I just started learning Mathematica yesterday so I am a complete beginner, so be easy on me please.

Answer 1

Assuming the plot is

plot = With[{n = 1.},
            RegionPlot3D[x^2 + y^2 <= n + 0.1 && x^2 + y^2 >= n, 
             {x, -2, 2}, {y, -2, 2}, {z, -20, 20}, PlotPoints -> 120, ImageSize -> Large]
           ]

one can extract the discrete points it's made of by taking

points = Cases[plot, GraphicsComplex[p___] :> p, Infinity];

The first element points[[1]] is a list of points as it can be checked:

ListPointPlot3D[points[[1]]]