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