Algorithm 1 Projection of q ∈ to
1:	Initialize l(q)i = 1n. Let ε > 0.
2:	while ‖l(q)‖ > ε do
3:	Compute l(q)i = −i(q), i = 1, …, n.
4:	Calculate the Jacobian matrix, Ji,j = 〈∇i(q), ∇j(q)〉 as follows, $$J_{ij}=3{\int }_0^{2\pi }{q}_i(s)q_j(s)ds,i=1,\dots ,n$$ .
5:	Solve the equation J(q)xT = lT(q) for x.
6:	Update $q=q+{\sum }_{i=1}^n{x}_i\nabla {\mathcal{G}}_i(q)\delta$, δ > 0.
7:	$q=\frac{q}{\sqrt{{\langle q,q\rangle }_q}}$
8:	end while