The methdology is outlined in http://www-stat.wharton.upenn.edu/~buja/PAPERS/paper-dyn-proj-algs.pdf and http://www-stat.wharton.upenn.edu/~buja/PAPERS/paper-dyn-proj-math.pdf, and the code follows the notation outlined in those papers:
geodesic_info(Fa, Fz, epsilon = 1e-06)
starting frame, will be orthonormalised if necessary
target frame, will be orthonormalised if necessary
epsilon used to determine if an angle is effectively equal to 0
p = dimension of data
d = target dimension
F = frame, an orthonormal p x d matrix
Fa = starting frame, Fz = target frame
Fa'Fz = Va lamda Vz' (svd)
Ga = Fa Va, Gz = Fz Vz
tau = principle angles