x(u, v) = cos(v) (a + u cos(v/2)) y(u, v) = sin(v) (a + u cos(v/2)) z(u, v) = u sin(v/2)
-a^2 y - 2 a x z + x^2 y - 2 x^2 z + y^3 - 2 y^2 z + y z^2 = 0
3
g = 0
ds^2 = 1 du^2 + a^2 + 2 a u cos(v/2) + 1/2 u^2 cos(v) + (3 u^2)/4 dv^2
dA = sqrt(a^2 + 2 a u cos(v/2) + 1/2 u^2 cos(v) + (3 u^2)/4) du dv
K(u, v) = -(4 a^2)/(4 a^2 + 8 a u cos(v/2) + 2 u^2 cos(v) + 3 u^2)^2
g_(uu) = 1 g_(vv) = a^2 + 2 a u cos(v/2) + 1/2 u^2 cos(v) + (3 u^2)/4
Γ | u | | | vv = 1/4 (-4 a cos(v/2) - u (2 cos(v) + 3)) Γ | v | | | uv = (4 a cos(v/2) + u (2 cos(v) + 3))/(4 a^2 + 8 a u cos(v/2) + 2 u^2 cos(v) + 3 u^2) Γ | v | | | vu = (4 a cos(v/2) + u (2 cos(v) + 3))/(4 a^2 + 8 a u cos(v/2) + 2 u^2 cos(v) + 3 u^2) Γ | v | | | vv = -(2 u sin(v/2) (a + u cos(v/2)))/(4 a^2 + 8 a u cos(v/2) + 2 u^2 cos(v) + 3 u^2)
E(u, v) = 1 F(u, v) = 0 G(u, v) = a^2 + 2 a u cos(v/2) + 1/2 u^2 cos(v) + (3 u^2)/4
e(u, v) = 0 f(u, v) = a/sqrt(4 a^2 + 8 a u cos(v/2) + 2 u^2 cos(v) + 3 u^2) g(u, v) = (sin(v/2) (2 (a^2 + u^2) + 4 a u cos(v/2) + u^2 cos(v)))/sqrt(4 a^2 + 8 a u cos(v/2) + 2 u^2 cos(v) + 3 u^2)
left double bracketing bar x(u, v) right double bracketing bar = sqrt(a^2 + 2 a u cos(v/2) + u^2)
N^^(u, v) = ((2 sin(v/2) (-u sin(v/2) sin(v) + cos(v) a))/sqrt(3 u^2 + 2 u^2 cos(v) + 8 u cos(v/2) a + 4 a^2), (u (cos(v) + sin^2(v)) + 2 sin(v/2) sin(v) a)/sqrt(3 u^2 + 2 u^2 cos(v) + 8 u cos(v/2) a + 4 a^2), -(2 cos(v/2) (u cos(v/2) + a))/sqrt(3 u^2 + 2 u^2 cos(v) + 8 u cos(v/2) a + 4 a^2))
algebraic surfaces | cubic surfaces | nonorientable surfaces | ruled surfaces
