It would be nice if the grid can be usid with a function like:

check(x, y, z);

so it can report if there is a point or not on that position,

maybe an boolean array you can set true or false. and then check ?

I tried the following in Processing
Code:

void setup(){
  size(400,400);
  int d = 400;
  int x[][][]  = new int[d][d][d];
  println("DONE");
}
 

A 3D array with 64,000,000 integers and each requires 4 bytes - so the array requires 256,000,000 bytes (244.14Mb). Initially Processing refused to create the array but you can increase it in the Preferences option. I set aside 256Mb and it accepted it. If you only need to know it exists the Cedric's boolean array is good since Java requires just 1 byte of RAM per boolean.

So it seems possible to create such large arrays but doing the calculations on 64million elements would be time consuming.
This is particularly true with multidimensional arrays for instance the 3D array created above is actually an array of arrays of arrays.

One possible solution is to use a single dimensional array and calculate the offsets for the dimensions. See thread http://processing.org/discourse/yabb2/num_1262269249.html