X(u, v) = (u, v, u^2 + v^2)

q = (0.000000, 0.000000)
Xu = (1.000000, 0.000000, 0.000000)  Xv = (0.000000, 1.000000, 0.000000)
N = (0.000000, 0.000000, 1.000000)  Xuu = (0.000000, 0.000000, 2.000000)
Xvv = (0.000000, 0.000000, 2.000000)  Xuv = (0.000000, 0.000000, 0.000000)

E = 1.000000  F = 0.000000   G = 1.000000
e = 2.000000  f = 0.000000   g = 2.000000
K = 4.000000   H = 2.000000   k1 = 2.000000   k2 = 2.000000

Ponto umbilico
Ponto eliptico

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X(u, v) = (u, v, u^2 - v^2)

q = (0.000000, 0.000000)
Xu = (1.000000, 0.000000, 0.000000)  Xv = (0.000000, 1.000000, 0.000000)
N = (0.000000, 0.000000, 1.000000)  Xuu = (0.000000, 0.000000, 2.000000)
Xvv = (0.000000, 0.000000, -2.000000)  Xuv = (0.000000, 0.000000, 0.000000)

E = 1.000000  F = 0.000000   G = 1.000000
e = 2.000000  f = 0.000000   g = -2.000000
K = -4.000000   H = 0.000000   k1 = -2.000000   k2 = 2.000000

Ponto hiperbolico
Direcao principal w1 = (0.000000, 1.000000, 0.000000)= Xv - 0.000000 Xu
Direcao principal w2 = (1.000000, 0.000000, 0.000000) = Xu - 0.000000 Xv

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X(u, v) = (u, v, u^3 - v^3)

q = (0.000000, 0.000000)
Xu = (1.000000, 0.000000, 0.000000)  Xv = (0.000000, 1.000000, -0.000000)
N = (-0.000000, 0.000000, 1.000000)  Xuu = (0.000000, 0.000000, 0.000000)
Xvv = (0.000000, 0.000000, 0.000000)  Xuv = (0.000000, 0.000000, 0.000000)

E = 1.000000  F = -0.000000   G = 1.000000
e = 0.000000  f = 0.000000   g = 0.000000
K = 0.000000   H = 0.000000   k1 = 0.000000   k2 = 0.000000

Ponto umbilico
Ponto planar

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X(u, v) = (uv - 1, v^3, vu^3 - v^2 + 1)

q = (1.000000, 1.000000)
Xu = (1.00000, 0.000000, 3.000000)  Xv = (1.00000, 3.000000, -1.00000)
N = (-9.000000, 4.000000, 3.000000)  Xuu = (0.000028, 0.000000, 6.000083)
Xvv = (0.000028, 6.000083, -2.000028)  Xuv = (1.00000, 0.000000, 3.000000)

E = 10.00000  F = -2.000000   G = 11.000000
e = 18.000000  f = -0.000000   g = 18.000000
K = 3.056604   H = 1.783019   k1 = 1.432944   k2 = 2.133094

Ponto eliptico

Direcao principal w1 = (-0.280776, -3.842329, 4.280776)= Xu - 1.280776 Xv
Direcao principal w2 = (1.780776, 2.342329, 2.219224) = Xu + 0.780776 Xv