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Gauss Map in Local Coordinates<br />
From here on, all parameterizations x : U ⊂<br />
R 2 → S are assumed to be compatible with<br />
the orientation N of S; that is, in x(U),<br />
N = xu × xv<br />
|xu × xv|<br />
Let x(u, v) be a parameterization at a point<br />
p ∈ S, and let α(t) = x(u(t), v(t)) be a parameterized<br />
curve in S, with α(0) = p.