QG-L3: The QG-Centroids Line

The QG-Centroids Line is the line connecting the 1st and 2nd QG-Quasi Centroids in a Quadrigon.
This line is also called the Seebach-Walser Line. See Ref-44.

This line also can be obtained in another way: Qi divides PiPi+1 with ratio r, Ri divides Pi Pi-1 with ratio r. The sides QiRi yield a Wittenbauer type of parallelogram. The locus of diagonal crosspoints of these parallelograms with variable r, will be QG-L3. See Ref-66, QPG#496 and Ref-67.
Coefficients:
• (r (p + 2 q + r) : (p - r) (p + q + r) : -p (p + 2 q + r))
• ((q - r) (p + q + r) : r (2 p + q + r) : -q (2 p + q + r))
• (q (p + q + 2 r) : -p (p + q + 2 r) : (p - q) (p + q + r))
• (l (m - n) (l m + l n - m n) : m (l - n) (-l m + 2 m2 + l n - m n) : -(l - m) n (l m - l n - m n))
• (l (m - n) (l m + l n - m n) : -m (l - n) (l m - l n + m n) : (-l + m) n (l m - l n - m n + 2 n2))
• (-l (m - n) (2 l2 - l m - l n + m n) : -m (l - n) (l m - l n + m n) : -(l - m) n (l m - l n - m n))

• (r2 (-p2 - q2 + r2) : 0 : p2 (-p2 + q2 + r2))
• (0 : r2 (p2 + q2 - r2) : q2 (-p2 + q2 - r2))
• (q2 (p2 - q2 + r2) : p2 (p2 - q2 - r2) : 0)