_PROGRAMMING WITH OPENGL PRIMITIVES_
by Ron Fosner

Listing One

// Pass in three points, and a vector to be filled

void  NormalVector( GLdouble p1[3], GLdouble p2[3],GLdouble p3[3], GLdouble n[3] )
{
    GLdouble v1[3], v2[3], d;
    // calculate two vectors, using the middle point
    // as the common origin    
    v1[0] = p2[0] - p1[0];
    v1[1] = p2[1] - p1[1];
    v1[2] = p2[2] - p1[2];
    v2[0] = p2[0] - p0[0];
    v2[1] = p2[1] - p0[1];
    v2[2] = p2[2] - p0[2];
   
    // calculate the crossproduct of the two vectors
    n[0] = v1[1]*v2[2] - v2[1]*v1[2];
    n[1] = v1[2]*v2[0] - v2[2]*v1[0];
    n[2] = v1[0]*v2[1] - v2[0]*v1[1];
    
   // normalize the vector
    d = ( n[0]*n[0] + n[1]*n[1] + n[2]*n[2] );
   // try to catch very small vectors
    if (  d  <  (Gldouble)0.00000001)
        {
        // error, near zero length vector
        // do our best to recover
        d = (GLdouble)100000000.0;
        }
    else // take the square root
        {
        // multiplication is faster than division
        // so use reciprocal of the length
        d = (GLdouble)1.0/ sqrt( d );
        }
    n[0] *= d;
    n[1] *= d;
    n[2] *= d;
}