Liner Swapping

  0<a<2*pi   ,  a(step)=pi/20

  0<b<2*pi   ,  b(step)=pi/20

Fx(a,b) = R2*sin(b)

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

Fz(a,b) = R2*cos(b)

         R = 2*sin(2*a)

       R2 = 5 + R*sin(a)

  0<a<2*pi   ,  a(step)=pi/40

Fx(a) = R*sin(a) + 5

Fy(a) = R*cos(a)

Fz(a) = 0

      R = 2*sin(2*a)

  0<b<2*pi   ,  b(step)=pi/40

Fx(b) = R2*sin(b)

Fy(b) = 0

Fz(b) = R2*cos(b)

      R2 = 5

Liner Swapping

(Torus)

  0<a<2*pi   ,  a(step)=pi/10

  0<b<2*pi   ,  b(step)=pi/10

Fx(a,b) = R2*sin(b)

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

Fz(a,b) = R2*cos(b)

         R = 2

       R2 = 5 + R*sin(a)

  0<a<2*pi   ,  a(step)=pi/40

Fx(a) = R*sin(a) + 5

Fy(a) = R*cos(a)

Fz(a) = 0

      R = 2

  0<b<2*pi   ,  b(step)=pi/40

Fx(b) = R2*sin(b)

Fy(b) = 0

Fz(b) = R2*cos(b)

      R2 = 5

Liner Swapping

(Cylinder - pipe )

   0<a<2*pi   ,  a(step)=pi/10

  -8<z<8       ,  z(step)=0.5

Fx(a,z) = R*sin(a)

Fy(a,z) = R*cos(a)

Fz(a,z) = z

         R = 2

   0<a<2*pi   ,  a(step)=pi/40

Fx(a) = R*sin(a)

Fy(a) = R*cos(a)

Fz(a) = 0

      R = 2

  -8<z<2*8i   ,  z(step)=0.25

Fx(z) = 0

Fy(z) = 2

Fz(z) = z

Rotation Swapping

(Sphare)

  0<a<pi      ,  a(step)=pi/10

  0<b<2*pi   ,  b(step)=pi/10

Fx(a,b) = r2*sin(b)

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

Fz(a,b) = r2*cos(b)

         R =  4

        r2 =  R*sin(a)

  0<a<pi     ,  a(step)=pi/40

Fx(a) = R*sin(a)

Fy(a) = R*cos(a)

Fz(a) = 0

      R = 4

  0<b<2*pi   ,  b(step)=pi/40

Fx(b) = r2*sin(b)

Fy(b) = 0

Fz(b) = r2*cos(b)

      r2 = 4

Liner Swapping

(Plane Surface)

  -8<x<8   ,  x(step)=0.5

  -8<z<8   ,  z(step)=0.5

Fx(x,z)= x

Fy(x,z)= sin(x) + cos(z)   (->addition)

Fz(x,z)= z

  -8<z<8   ,  z(step)=0.5

Fx(z)= pi/2

Fy(z)= cos(z)+1

Fz(z)= z

  -8<x<8   ,  x(step)=0.5

Fx(x)= x

Fy(x)= sin(x)+1

Fz(x)= 0

Liner Swapping

(Plane Surface)

  -8<x<8   ,  x(step)=0.5

  -8<z<8   ,  z(step)=0.5

Fx(x,z)= x

Fy(x,z)= sin(x) * cos(z)   (->multiply )

Fz(x,z)= z

  -8<z<8   ,  z(step)=0.5

Fx(z)= pi/2

Fy(z)= cos(z)

Fz(z)= z

  -8<x<8   ,  x(step)=0.5

Fx(x)= x

Fy(x)= sin(x)

Fz(x)= 0

Liner Swapping

(Plane Surface)

  -8<x<8   ,  x(step)=0.25

  -8<z<8   ,  z(step)=0.25

Fx(x,z)= x

Fy(x,z)= k1 + k2  

Fz(x,z)= z

n=2, y=sin(n*x) , y2=cos(n*z)

k1=sgn(y)     (-> or k2=(y>0) - (y<0) )

k2=sgn(y2)   (-> or k2=(y2>0) - (y2<0) )

  -8<x<8   ,  x(step)=0.125

Fx(x)= x

Fy(x)= k1 + 1

Fz(x)= z

n=2, y=sin(n*x)

k1=sgn(y)     (-> or k2=(y>0) - (y<0) )

  -8<z<8   ,  z(step)=0.125

Fx(z)= pi/4

Fy(z)= k2 + 1

Fz(z)= z

n=2,  y2=cos(n*z)

k2=sgn(y2)   (-> or k2=(y2>0) - (y2<0) )

Nane Sekeri

  0<a<pi      ,  a(step)=pi/10

  0<b<2*pi   ,  b(step)=pi/10

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

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

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

         R =  4

  0<a<pi     ,  a(step)=pi/40

Fx(a) = R*sin(a)

Fy(a) = R*cos(a)

Fz(a) = 0

      R = 4

  0<b<2*pi   ,  b(step)=pi/40

Fx(b) = R*sin(b)

Fy(b) = 0

Fz(b) = R*cos(b)

      R = 4

(umbrella)

 -8<x<8     ,  x(step)=0.5

  0<a<pi    ,  a(step)=pi/10

Fx(x,a) = R*sin(a)

Fy(x,a) = cos(x)

Fz(x,a) = R*cos(a)

         R =  x

  -8<x<8     ,  a(step)=pi/40

Fx(a) = x

Fy(a) = cos(x)

Fz(a) = 0

  0<a<2*pi   ,  a(step)=pi/40

Fx(b) = R*sin(a)

Fy(b) = 0

Fz(b) = R*cos(a)

      R = 3/2*pi

Liner Swapping

(Spiral Tube)

   0<a<2*pi   ,  a(step)=pi/10

  -9<z<9    ,  z(step)=0.1

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

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

Fz(a,z) = z + sin(a)

         R = 5 + cos(a)

  -10<z<10   ,  z(step)=0.1

Fx(a) = R*cos(z)

Fy(a) = R*sin(z)

Fz(a) = 0

      R = 5

   0<a<2*pi   ,  a(step)=pi/10

Fx(z) = R*cos(z)

Fy(z) = R*sin(z)

Fz(z) = z + sin(a)

      z = - 10

      R = 5 + cos(a)