source 2008 Bernstein--Lange--Rezaeian Farashahi
compute w1 = X1+Y1
compute w2 = X2+Y2
compute A = X1^2+X1
compute B = Y1^2+Y1
compute C = d2 w1 w2
compute D = X2 Y2
compute X3 = Y1 + (C + d1 (w1+X2) + A (D+X2)) / (d1 + A w2)
compute Y3 = X1 + (C + d1 (w1+Y2) + B (D+Y2)) / (d1 + B w2)