Exporting data from a Plot3D

Question

In Maple, I can get data from a plot3d like this,

restart;
Eq1:=diff(u(eta,t),t)=diff(u(eta,t),eta$2);
BCs := {u(0,t)=sin(t), u(10,t)=0};
ICs := {u(eta,0)=0};
sys:={Eq1};
pds:= pdsolve(sys,ICs union BCs,numeric,time=t,range=0..10);
p1:= pds:-plot3d(u(eta,t),t=0..35,eta=0..10,grid=[360,360]):

Here is the command for exporting data from plot p1

A:= op([1,3],p1):
  a,b:= op(op([1,1],p1)):
  c,d:= op(op([1,2],p1)):
  m:= rhs(rtable_dims(A)[1]):
  n:= rhs(rtable_dims(A)[2]):
  for i from 1 to m do
   for j from 1 to n do
     X:= ((m-i)*a + (i-1)*b)/(m-1);
     Y:= ((n-j)*c + (j-1)*d)/(n-1);
     fprintf("C:/tcdata/SL1.txt",
         "%f  %f  %f\n",Y,X,A[i,j]);
   end do
  end do:
  close("C:/tcdata/SL1.txt"):

This gives me data in the desired format, which I can later use in another software. The format is

0.000000  0.000000  0.000000
0.097493  0.000000  0.102694
0.194986  0.000000  0.200925
0.292479  0.000000  0.294693
0.389972  0.000000  0.383998
0.487465  0.000000  0.468841
0.584958  0.000000  0.549221
0.682451  0.000000  0.625138
0.779944  0.000000  0.696593
0.877437  0.000000  0.763584
..............

How can I get data from Plot3D in the same format (see above) in Mathematica?

ClearAll["Global`*"];

pdeset = {Derivative[1, 0][U][t, x] == Derivative[0, 2][U][t, x]}

ics = {U[0, x] == 0};

bcs = {U[t, 0] == Sin[t], U[t, 10] == 0};    

bcAll = Flatten[{ics, bcs}, 1];    

sol = NDSolve[{pdeset, bcAll}, {U}, {t, 0, 35}, {x, 0, 10}];

Plot3D[(U /. First@sol)[t, x],  {t, 0, 35}, {x, 0, 10},
 PlotRange -> All]

Answer 1

No need to extract the points from the plot as you have the generating function already, unless this is exactly what you want

Export["pts-plot.dat", Plot3D[(U /. First@sol)[t, x], {t, 0, 35}, {x, 0, 10}, 
PlotRange -> All][[1, 1]], "Table"]

Otherwise, use Table or its parallel version to obtain as many points as you want:

pts = Flatten[ParallelTable[{t, x, (U /. First@sol)[t, x]}, {t, 0, 35, 0.5}, {x,0, 10, 0.5}], 1]:
Export["pts.dat", pts, "Table"]

Answer 2

If you name your Plot

pic=Plot3D[(U /. First@sol)[t, x],  {t, 0, 35}, {x, 0, 10},PlotRange -> All]

you can pick the plotted points with

p=Flatten[Cases[bild, _GraphicsComplex , Infinity][[;; , 1]], 1]
Show[pic, Graphics3D[Point[p]]]

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