Calculate normal vector of a polygon - Newells Method

Question

I'm trying to calculate the surface normal of a 2D polygon. I am using Newell's method from the OpenGL wiki to calculate the surface normal. https://www.opengl.org/wiki/Calculating_a_Surface_Normal From my understanding the normal should be in the y direction but it always returns [0, 0, 0]. The y value gets changed to -1 on the second iteration and back to zero on the fourth iteration.

p = [[0, 0, 0]
    [1, 0, 0]
    [0, 0, 1]
    [1, 0, 1]]

function calcNormal(p) {
    var normal = [0, 0, 0];
    for(var i = 0; i < p.length; i++) {
        var j = (i + 1) % (p.length);       
        normal[0] += (p[i][1] - p[j][1]) * (p[i][2] + p[j][2]);
        normal[1] += (p[i][2] - p[j][2]) * (p[i][0] + p[j][0]);
        normal[2] += (p[i][0] - p[j][0]) * (p[i][1] + p[j][1]);
    }
    return normal;
}

Answer 1

You're using a degenerate polygon for testing. If you draw it in the xz-plane, with the vertices numbered from 0 to 3, it looks like this:

2 ---- 3
 \    /
  \  /
   \/
   /\
  /  \
 /    \
0 ---- 1

This polygon does not have a well defined normal, since it changes orientation in the middle, and folds over itself.

If you swap the last two vertices:

p = [[0, 0, 0]
     [1, 0, 0]
     [1, 0, 1]
     [0, 0, 1]]

It will look like this, and you should get much more meaningful results:

3 ---- 2
|      |
|      |
|      |
0 ---- 1