Algorithm 9 Initialization of a path α on between q0, q1 ∈ .
1:	Let α(0) = q0. Let k be the number of steps along the discretized path.
2:	f = q1 − 〈q1, q0〉q0, $f=\frac{f}{\langle f,f\rangle }$
3:	for all τ = 1 to k do
4:	$\alpha \left(\frac{\tau }{k}\right)={\chi }_{\frac{\tau }{k}}(q_0,f)$
5:	Project $\alpha \left(\frac{\tau }{k}\right)$ into using Algorithm 1.
6:	end for