Tessellate a plane of points

Question

I have a file filled with 3d points. The points form a plane. Here is an example file:

25
1 -1 0
1 -0.5 0
1 0 0
1 0.5 0
1 1 0
0.5 -1 0
0.5 -0.5 0
0.5 0 0
0.5 0.5 0
0.5 1 0
0 -1 0
0 -0.5 0
0 0 0
0 0.5 0
0 1 0
-0.5 -1 0
-0.5 -0.5 0
-0.5 0 0
-0.5 0.5 0
-0.5 1 0
-1 -1 0
-1 -0.5 0
-1 0 0
-1 0.5 0
-1 1 0

Edit: Since my example set of points was too simple, here is a more complex example.

30
-0.298858 -0.816497 1.11536
0.0546949 -0.816497 0.761802
0.408248 -0.816497 0.408248
0.761802 -0.816497 0.0546949
1.11536 -0.816497 -0.298858
-0.462158 -0.489898 0.952056
-0.108604 -0.489898 0.598502
0.244949 -0.489898 0.244949
0.598502 -0.489898 -0.108604
0.952056 -0.489898 -0.462158
-0.625457 -0.163299 0.788756
-0.271904 -0.163299 0.435203
0.0816497 -0.163299 0.0816497
0.435203 -0.163299 -0.271904
0.788756 -0.163299 -0.625457
-0.788756 0.163299 0.625457
-0.435203 0.163299 0.271904
-0.0816497 0.163299 -0.0816497
0.271904 0.163299 -0.435203
0.625457 0.163299 -0.788756
-0.952056 0.489898 0.462158
-0.598502 0.489898 0.108604
-0.244949 0.489898 -0.244949
0.108604 0.489898 -0.598502
0.462158 0.489898 -0.952056
-1.11536 0.816497 0.298858
-0.761802 0.816497 -0.0546949
-0.408248 0.816497 -0.408248
-0.0546949 0.816497 -0.761802
0.298858 0.816497 -1.11536

These points are plotted like so:

This file states that there are 25 points in the plane, and lists the points. The points are regularly spaced. Based on this information, how could I form triangles out of the point data and store it in a std::vector<Tri> where Tri is a

struct Tri 
{
  double x1, y1, z1;
  double x2, y2, z2;
  double x3, y3, z3;
};

Note also: Problem restrictions: External libraries are not allowed. The use of C++0X is not allowed (compiler: g++ 4.5.2).

Answer 1

read the first line, call it N. Read the rest of the points into an array A.

Point xdir = A[1] - A[0];
int xdim = 2;
while (A[xdim] - A[xdim-1] == xdir) xdim++;
int ydim = N / xdim;
for (int y = 0; y < ydim-1; y++) {
   for (int x = 0; x < xdim-1; x++) {
      addTriangle(A[y*xdim+x],A[(y+1)*xdim+x],A[(y+1)*xdim+(x+1)]);
      addTriangle(A[y*xdim+x],A[y*xdim+(x+1)],A[(y+1)*xdim+(x+1)]);
   }
}

Of course, this assumes you're really getting all of your points in grid order. If not, sort them first.