source 2007 Bernstein--Birkner--Lange--Peters parameter c2 assume c2 = 2 c compute XX = X1^2 compute YY = Y1^2 compute ZZ = (c2 Z1)^2 compute D = XX+YY compute DD = D^2 compute H = 2 D (XX-YY) compute P = DD-YY ZZ compute Q = DD-XX ZZ compute T = H+Q compute U = H-P compute X3 = P U X1 compute Y3 = Q T Y1 compute Z3 = T U Z1