橢圓雙曲面

x(u,v)

=

asqrt(1+u^2)cosv

y(u,v)

=

bsqrt(1+u^2)sinv

z(u,v)

=

cu

v in [0,2pi)

x(u,v)

=

a(cosu∓vsinu)

y(u,v)

=

b(sinu+/-vcosu)

z(u,v)

=

+/-cv,

x(u,v)

=

acoshvcosu

y(u,v)

=

bcoshvsinu

z(u,v)

=

csinhv.

E

=

(a^2cos^2v+b^2sin^2v)/(4u)-1

F

=

1/4(b^2-a^2)sin(2v)

G

=

u(a^2sin^2v+b^2cos^2v),

e

=

(ab)/(2usqrt(a^2b^2+2u(a^2+b^2)+2(b^2-a^2)ucos(2v)))

f

=

0

g

=

(2abu)/(sqrt(a^2b^2+2u(a^2+b^2)+2(b^2-a^2)ucos(2v))).

K

=

(4a^2b^2)/([a^2b^2+2u(a^2+b^2)+2(b^2-a^2)ucos(2v)]^2)

H

=

(ab(a^2+b^2+4u))/([a^2b^2+2u(a^2+b^2)+2(b^2-a^2)ucos(2v)]^(3/2)).

K(x,y,z)

=

-(a^6b^6c^2)/((a^4b^4-a^2b^4x^2-b^4c^2x^2-a^4b^2y^2-a^4c^2y^2)^2)

=

-(a^6b^2c^6)/((a^4c^4-a^2c^4x^2+b^2c^4x^2+a^4b^2z^2+a^4c^2z^2)^2)

=

-(a^2b^6c^6)/((b^4c^4+a^2c^4y^2-b^2c^4y^2+a^2b^4z^2+b^4c^2z^2)^2).

x

=

asinhucosv

y

=

bsinhusinv

z

=

c+/-coshu.

x

=

acoshucoshv

y

=

bsinhucoshv

z

=

csinhv.

K(x,y,z)

=

(a^6b^6c^2)/((a^4b^4+a^2b^4x^2+b^4c^2x^2+a^4b^2y^2+a^4c^2y^2)^2)

=

(a^6b^2c^6)/((a^4c^4+a^2c^4x^2-b^2c^4x^2-a^4b^2z^2-a^4c^2z^2)^2)

=

(a^2b^6c^6)/((b^4c^4-a^2c^4y^2+b^2c^4y^2-a^2b^4z^2-b^4c^2z^2)^2).