source 2006 Doche--Icart--Kohel "Efficient scalar multiplication by isogeny decompositions", page 197, middle display, plus substitution Z2=1, plus simplification, plus projectification
compute A = Y1/Z1^2-Y2/Z2^2
compute B = (X1/Z1)-(X2/Z2)
compute D = (X1/Z1) B^2
compute X3 = A^2-a B^2-D-(X2/Z2) B^2
compute Y3 = A B (D-X3)-(Y1/Z1^2) B^4
compute Z3 = B^2
compute ZZ3 = Z3^2