Algorithm 2 Projection of w ∈ Tq() into Tq()
1:	Start by projecting w into Tq() by $$\stackrel{\sim }{w}\equiv w-\langle w,q\rangle q$$ (7)
2:	Compute an orthonormal basis $\left\{{\mathbf{\text{e}}}_{\mathcal{G}(q)}^i\right\}$ for {∇i(s)}, i = 1, …, n. w.r.t. the inner product given in Eqn. 5.
3:	Then the projection of w̃ into Tq() is given as, $$w_{\mathit{\text{proj}}}\equiv \stackrel{\sim }{w}-\sum _{i=1}^n\langle \stackrel{\sim }{w},{\mathbf{\text{e}}}_{\mathcal{G}(q)}^i\rangle {\mathbf{\text{e}}}_{\mathcal{G}(q)}^i.$$ (8)