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Aotomobile Tyre

       0<a<pi       , a(step)=pi/10

   pi/2<b<3/2*pi , b(step)=pi/5

Fx(a,b)=2*sin(b)

Fy(a,b)=2*(2-cos(b))*sin(a)

Fz(a,b)=2*(2-cos(b))*cos(a)

 

Tyre Carrier

       0<a<pi       , a(step)=pi/10

   pi/2<b<3/2*pi , b(step)=pi/5

Fx(a,b)=2*sin(b)

Fy(a,b)=2*(2-cos(b)^2)*sin(a)

Fz(a,b)=2*(2-cos(b)^2)*cos(a)

Slide

   -2*pi<a<2*pi  , a(step)=pi/10

        0<b<2*pi  , b(step)=pi/10

Fx(a,b)=2*(2-cos(b)^2)*sin(a)

Fy(a,b)=2*(2-cos(b)^2)*cos(a)

Fz(a,b)=2*sin(b)+a

Firizbi

   0<a<pi   , a(step)=pi/20

   0<b<pi   , b(step)=pi/20

   0<k<0.3 , k(step)=0.3

Fx(a,b)=5*sin(b)*(0.5+sin(a))

Fy(a,b)=cos(6*a)/2+k

Fz(a,b)=5*cos(b)*(0.5+sin(a))

Dome

Half Sphere

   0<a<pi , a(step)=pi/10

   0<b<pi , b(step)=pi/10

Fx(a,b)=R*cos(a)

Fy(a,b)=R*cos(b)*sin(a)

Fz(a,b)=R*sin(b)*sin(a)+4

         R=5

Cylinder

   0<a<2*pi , a(step)=pi/10

   2<z<4 , b(step)=2

Fx(a,b)=R*cos(a)

Fy(a,b)=R*sin(a)

Fz(a,b)=z

         R=5

 

Church Window (Top Part)

   0<a<pi/2 , a(step)=pi/10

   0<b<pi    , b(step)=pi/10

   0<x<1      , x(step)=1

Fx(a,b,x)=R*cos(a)+x

Fy(a,b,x)=R*cos(b)*sin(a)

Fz(a,b,x)=R*sin(b)*sin(a)+4

           R=5

Flowerpot

   0<t<2*pi , a(step)=pi/20

   0<z<3     , b(step)=0.2

Fx(t,z)=R*cos(t)

Fy(t,z)=R*sin(t)

Fz(t,z)=3*z

        R=3*[sin(z^0.5)+sin(3*z^0.5)/2]

Pot 

   0<a<pi        , a(step)=pi/10

   0<b<7/4*pi , b(step)=pi/10

Fx(a,b)=R*sin(a)*(1-sin(b))

Fy(a,b)=R*cos(a)*(1-sin(b))

Fz(a,b)=[b<pi]*R*cos(b)+b

Vase

   0<a<7/4*pi , a(step)=pi/10

   0<b<2*pi    , b(step)=pi/10

Fx(a,b)=4*sin(b)*sin(a)

Fy(a,b)=2.5*sin(a)*a

Fz(a,b)=4*cos(b)*sin(a)

Demijohn

   0<a<7/4*pi , a(step)=pi/10

   0<b<2*pi    , b(step)=pi/10

Fx(a,b)=4*sin(b)*sin(a)

Fy(a,b)=2.5*sin(2*a)*a

Fz(a,b)=4*cos(b)*sin(a)

Klein Bottle

Loop variables

   0<u<2*pi , a(step)=pi/20

  pi<v<2*pi , b(step)=pi/20

Top

Fx(u,v)=(2.5 + 1.5*cos(v))*cos(u)

Fy(u,v)=(2.5 + 1.5*cos(v))*sin(u)

Fz(u,v)=-2.5 *sin(v)

Middle (body)

Fx(u,v)=(2.5 + 1.5*cos(v))*cos(u)

Fy(u,v)=(2.5 + 1.5*cos(v))*sin(u)

Fz(u,v)=3*v - 6 * Pi

Handle

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

Fy(u,v)=cos(u)

Fz(u,v)=3*v - 6 * Pi

Bottom 

Fx(u,v)=2 + (2 + 2*cos(u))*cos(v)

Fy(u,v)=sin(u)

Fz(u,v)=-3*Pi + (2 + 2*cos(u))*sin(v)

Klein Bottle 2 (in a single piece )

-> Covered with Polygons

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Last modified: 15/09/2002.