intersection intersect(const ray &ray) const
{
    vector3 r_d = ray.direction, r_o = ray.origin;
    vector3 k = r_o - a.coords, e1 = b.coords - a.coords, e2 = c.coords - a.coords;
    vector3 d_e2 = r_d%e2, k_e1 = k%e1; // % is the cross product operator
    double det = d_e2*e1;
    if (det >= -DELTA && det <= DELTA)
        return intersection(); //no intersection
    else
    {
        bool inside = det < 0;
        double inv_det = 1 / det, u = inv_det*(d_e2*k);
        if (u < 0 || u > 1)
            return intersection();
        else
        {
            double v = inv_det*(k_e1*r_d);
            if (v < 0 || v>1 || u + v > 1)
                return intersection();
            else
            {
                //there is an intersection, compute t
                double t = inv_det*(k_e1*e2);
                vector3 point = r_o + t*r_d;
                vector3 temp_normal = ((b.coords - point) % (c.coords - point)).normalize();
                vector3 normal = inside ? -temp_normal : temp_normal;
                return intersection(point, normal, interpolateData(a, b, c, u, v, 1 - u - v).mat, true, inside);
            }
        }
    }
    return intersection();
}

color col = w*a.col + u*b.col + v*c.col;