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>> 4.Plane Curves

-5<x<5  x(step)=0.25

-5<y<5  y(step)=0.25

Fx(x,y)= x

Fy(x,y)= y

Fz(x,y)= -1/(x*x+1) + 2/(y*y+1) + 0.5*sin(5*r)/r

r=(x*x+y*y)^0.5

-6<x<6  x(step)=0.25

-6<y<6  y(step)=0.25

Fx(x,y)=x

Fy(x,y)=y

Fz(x,y)=x/(x*x+1) - y/(y*y+1) + 2*(r-1)/((r-1)*(r-1)+1)

r=(x*x+y*y)^0.5

 50

-40<x<40  x(step)=1

-40<y<40  y(step)=1

Fx(x,y)=x

Fy(x,y)=y

Fz(x,y)=2*[ cos(((x+0)^2+(y+0)^2)^(1/2)) +

cos(((x+.913*2*pi)^2+(y+0)^2)^(1/2)) +

cos(((x-.913*2*pi)^2+(y+0)^2)^(1/2))  ]

-6<x<6  x(step)=1/4

-6<y<6  y(step)=1/4

Fx(x,y)=x

Fy(x,y)=y

Fz(x,y)=(cos(y)+sin(x))*sin(y+x)

-1<x<1  x(step)=1/20

-2<y<2  y(step)=1/20

Fx(x,y)=x

Fy(x,y)=y

Fz(x,y)=cos(f1*12)/(2*(f1*6.28+1))

f1=x^2+ y^2

-7<x<7  x(step)=0.25

-7<y<7  y(step)=0.25

Fx(x,y)=x

Fy(x,y)=y

Fz(x,y)=Cos(mesafe*Pi/2) -2

mesafe=(x^2+y^2)^0.5

-3<x<3  x(step)=0.1

-3<z<6  z(step)=0.1

Fx(x,z)=2*x

Fy(x,z)=2*y

Fz(x,z)=2*z

y=([9*(x^2-z^2)^2]^(1/3) - (x^2 + z^2) )^(1/3)

-3<x<3  x(step)=0.1

-3<z<6  z(step)=0.1

Fx(x,z)=2*x

Fy(x,z)=2*y

Fz(x,z)=0

y=([9*(x^2-z^2)^2]^(1/3) - (x^2 + z^2) )^(1/3)

-3<x<3  x(step)=0.2

-3<y<3  y(step)=0.2

Fx(x,y)=x

Fy(x,y)=y

Fz(x,y)=[8*x^2*y^2*e^(0-r)] / r

r=x^2+y^2

Half Sphere

-8<x<8  x(step)=1

-8<y<8  y(step)=1

Fx(x,y)=x

Fy(x,y)=y

Fz(x,y)=(64 - x^2 - y^2)^(1/2)

-3<x<3  x(step)=0.25

-3<y<3  y(step)=0.25

Fx(x,y)=x

Fy(x,y)=y

Fz(x,y)=[z=e^[(x^2+y^2)^(1/2)]-5] * [1/(z<8)]

-10<x<10  x(step)=0.2

-10<y<10  y(step)=0.2

Fx(x,y)=x

Fy(x,y)=1/(sin(x)+sin(y)<0) * y

Fz(x,y)=0

-10<x<10  x(step)=0.2

-10<y<10  y(step)=0.2

Fx(x,y)=x

Fy(x,y)=1/(sin(x)+sin(y)>0) * y

Fz(x,y)=0

-20<x<20  x(step)=0.2

-20<y<20  y(step)=0.2

Fx(x,y)=x

Fy(x,y)=1/(x*sin(x)+y*sin(y)<0) * y

Fz(x,y)=0

-8<x<14  x(step)=0.5

-8<y<14  y(step)=0.5

Fx(x,y)=x

Fy(x,y)=y

Fz(x,y)=30/[2^10 + x^10 + y^10]^(1/10)

A simple unequality graph

y=x^3

-8<x<10  x(step)=0.3

-10<y<10  y(step)=0.3

Fx(x,y)=x

Fy(x,y)=1/(y<x^3) * y

Fz(x,y)=0

Inner Twisted Wave

-5<x<5  x(step)=0.2

-5<y<5  y(step)=0.2

Fx(x,y)=x

Fy(x,y)=y

Fz(x,y)=1/(1+r)*[x*sin(4*r)+y*cos(4*r)]

r=(x*x+y*y)^0.5

Water drop wave

-7<x<7  x(step)=0.2

-7<y<7  y(step)=0.2

Fx(x,y)=x

Fy(x,y)=y

Fz(x,y)=e^(-r/4)*sin(3*r)

r=(x*x+y*y)^0.5

Mexican sombrero 1

(defined with a simple square plane curve)

-5<x<5    , x(step)=0.25

-5<x<5   , y(step)=0.25

Fx(x,y)=x

Fy(x,y)=y

Fz(x,y)=12*cos((x^2+y^2)/4)/(3+x^2+y^2)

Mexican sombrero 2

(**defined with a cyclical plane curve)

0<r<6.25    , r(step)=0.25

0<a<2*pi   , a(step)=pi/20

Fx(r,a)= x=r*cos(a)

Fy(r,a)= y=r*sin(a)

Fz(r,a)= z=12*cos((x^2+y^2)/4)/(3+x^2+y^2)

Straw Hat 1

(defined with a simple square plane curve)

Straw Hat 2

(**defined with a cyclical plane curve)

Moebious Strip 1

0<u<2*pi   , u(step)=pi/20

-0.3<v<0.3    , v(step)=0.2

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

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

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

k= 5  (-> k only zooms the object (here it zooms 5 times))

Moebious Strip2

0<u<2*pi   , u(step)=pi/20

-0.8<v<0.8    , v(step)=0.2

Fx(u,v)= sin(u)*(2-v*sin(t*u/2))

Fy(u,v)= cos(u)*(2-v*sin(t*u/2))

Fz(u,v)= v*cos(t*u/2)

t=1   (->parameter t shows how many times

we twist the strip)

Moebious Strip when parameter t = 4

(4 times twisted strip.

*the twisting number is an even number so the strip has 2 surface.)

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