Question

can anyone assist me in finding the proper formula for quad normalization ?

using c++ with opengl.

thank you!

Answer 1

Assuming that you want the normal vector for a quad, this pseudo-code works

Vector3d vertex[4] = { ... }
Vector3d normal(0,0,0) ;

for (int i=0; i<4; i++)
{
    normal += cross (vertex[i], vertex[(i+1)%4]) ; // cross product
}
normalize (normal) ;
// normal is the unit normal to the quad

This gives you the formula n=A/|A|, where A = v0xv1 + v1xv2 + v2xv3 + v3xv0 and vi=vertex[i]). |A|/2 is also the area of the polygon. This can be generalized to arbitrary polygons, and will even give reasonable results for non-planar polygons, as long as they aren’t too non-planar.

One reference is http://softsurfer.com/Archive/algorithm_0101/algorithm_0101.htm

If you know that the quad/polygon is planar, you only have to calculate the normal of the triangle formed by the first three vertices. This is A1/|A1|, where A1 = (v1-v0)x(v2-v0) = v0xv1 + v1xv2 + v2xv0.

If by “quad normalization” you meant something else, just ignore this answer.

EDIT: I found this related question: Get the Surface Area of a Polyhedron (3D object)