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   0<s<2*pi , s(step)=pi/40

   0<t<2*pi  , t(step)=pi/40

Fx(s,t)=cos(s)*sin(2*t)*R

Fy(s,t)=cos(s)*cos(3*t)*R

Fz(s,t)=sin(2*s)*R

        R=5

 

Boy's Surface

   0<u<pi  , u(step)=pi/60

   0<v<pi  , v(step)=pi/60

Fx(u,v)=k*(2/3)*(cos(u)*cos(2*v)+2^0.5*sin(u)*cos(v))

                         *cos(u) / L

Fy(u,v)=k*(2/3)*(cos(u)*sin(2*v)-2^0.5*sin(u)*sin(v))

                        *cos(u) / L

Fz(u,v)=k*2^0.5*cos(u)^2 / L

          k=4

          L=(2^0.5 - sin(2*u)*sin(3*v))

Enneper's surface

   -2<u<2 , u(step)=0.25

   -2<v<2  , v(step)=0.25

Fx(u,v)=u-(u*u*u/3)+u*v*v

Fy(u,v)=v-(v*v*v/3)+u*u*v

Fz(u,v)=u*u-v*v

Klein Bottle 1

   0<u<2*pi  , u(step)=pi/10

   0<v<2*pi , v(step)=pi/10

Fx(u,v)=k*(a+cos(u/2)*sin(v)-sin(u/2)*sin(2*v))*cos(u)

Fy(u,v)=k*(a+cos(u/2)*sin(v)-sin(u/2)*sin(2*v))*sin(u)

Fz(u,v)=k*sin(u/2)*sin(v)+cos(u/2)*sin(2*v)

a=2

k=2

 

Klein Bottle 2

   -pi/4<u<3/2*pi  , u(step)=pi/10

         0<v<2*pi    , v(step)=pi/10

Fx(u,v)=4*k*cos(u)

Fy(u,v)=4*k*sin(u)

Fz(u,v)=4*sin(u/2)*sin(v)+cos(u/2)*sin(2*v)

a=2

k=(a+cos(u/2)*sin(v)-sin(u/2)*sin(2*v))

Klein Bottle 2

      -2<u<2    , u(step)=0.1

   -0.8<v<0.8 , v(step)=0.05

Fx(u,v)=u*v^2 + 3*v^4

Fy(u,v)=-2*u*v - 4*v^3

Fz(u,v)=u

The Famed Klein Bottle

   0<u<4*pi , u(step)=pi/10

   0<v<2*pi , v(step)=pi/10

Fx(u,v)=k*cos(u)*( cos(u/2)*(2^0.5+cos(v))

                                +sin(u/2)*sin(v)*cos(v) )

Fy(u,v)=k*sin(u)*( cos(u/2)*(2^0.5+cos(v))

                              +sin(u/2)*sin(v)*cos(v) )

Fz(u,v)=k*-1*sin(u/2)*( 2^0.5+cos(v))

                                       +cos(u/2)*sin(v)*cos(v)

k=3

 

Clifford Torus

Crosscap

Roman Surface1

Roman Surface2

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Last modified: 15/09/2002.