Matematika u arhitekturi 2

Program: 3D Grapher

1. Coordinate: Spherical

Function:

a(u,v,t)=v*sin(u))*4

b(u,v,t)=u*(sin(v))*3

R(u,v,t)=u*3+v*3

Domain of variables:

Min U:-1; Max U:1; Steps: 70

MinV:-1; Max V:1; Steps: 70

2.Coordinate: Cylindrical

Function:

a(u,v,t)=u+v+t

R(u,v,t)=3*sin(7*u)

Z(u,v,t)=3*cos(7*u)

Domain of variables:

Min U:-10; Max U:10; Steps:30

MinV:-10; Max V:10; Steps: 30

3D Grapher

Korišćeni program - 3D Grapher

Coordinates: Cartesian

X (u,v,t) = 3*v*cos(2*u)
 
Y (u,v,t) = 2*v* sin(u)*3

Z (u,v,t) = 2*v

Domain of variables:

Min U : -10 Max U : 10 Steps: 60

Min V : -10 Max V : 10 Steps: 60

3D Grapher

Coordinates: Cartesian

Podaci su na slici za X,Y i Z koordinate.

MinU: -10, MaxU: 10, Steps: 111

Program: 3D Grapher

Coordinates: Spherical

a(u,v,t)= v*(sin(u))^3

b(u,v,t)= u*(sin(v))^2

R(u,v,t)= u^2+v^3

Min U: -2  Max U: 2  Steps: 70

Min V: -2  Max V: 2  Steps: 70

program: 3d grapher

parametri:
x= 0.5*cos(u); y= 0.5*u; z= 0.5*sin(u); 
x= cos(u); y= u; z= sin(u);
x= 1.5*cos(u); y= 1.5*u; z= 1.5*sin(u);
x= 2*cos(u); y= 2*u; z= 2*sin(u);
x= 2.5*cos(u); y= 2.5*u; z= 2.5*sin(u);
x= 3*cos(u); y= 3*u; z= 3*sin(u);
x= 3.5*cos(u); y= 3.5*u; z= 3.5*sin(u);
x= 4*cos(u); y= 4*u; z= 4*sin(u);
x= 4.5*cos(u); y= 4.5*u; z= 4.5*sin(u);
x= 5*cos(u); y= 5*u; z= 5*sin(u);
x= 5.5*cos(u); y= 5.5*u; z= 5.5*sin(u);
x= 6*cos(u); y= 6*u; z= 6*sin(u);
x= 6.5*cos(u); y= 6.5*u; z= 6.5*sin(u);
x= 7*cos(u); y= 7*u; z= 7*sin(u);
x=7.5*cos(u); y=7.5*u; z=7.5*sin(u);
x=8*cos(u);; y=8*u; z=8*sin(u);
x=8.5*cos(u); y=8.5*u; z=8.5*sin(u)

granice:
minU= -10; maxU:10; steps: 600

3d grapher

Spherical
a=u*sin(7*v*v)
b=cos(v)*v
R=sin(v)*sin(v)
U: [-10,10] (30)
V: [-10,10] (30)

3D Grapher

Graficki prikazane krive u prostoru koriscenjem programa 3D Grapher.

3D Grapher

coordinates: cartesian

x=2*sin(u):y=10*v*sin(u)*1:z=7*v steps 30/45

x=3*sin(u);y=20*v*sin(u);z=7*cos(u) steps 45/60

x=2*v*cos(u);y=10*cos(u);z=10*sin(u) steps 45/45

x=3*v*cos(u);y=10*cos(u);z=10*sin(u) steps 45/45

Min U; -10   Max U; 10

Min V; -10   Max V; 10

3D Grapher

X: [-10,10]

Y: [-10,10]

Z: [-10,10]

T: [0,0] (0)

Selected: New Graph (1/1)

Spherical

a=v*(sin(u))^6

b=u*(sin(v))^4

R=u^2-v^3

U: [-2.2,2.2] (100)

V: [2.2,-2.2] (100)

parametri su navedeni u grafickom prikazu.

ime programa 3d grapher

Program: 3D Grapher

X: [-10,10]

Y: [-10,10]

Z: [-10,10]

T: [0,0] (0)

Selected:

11 (1/1)

Spherical

a=15*cos(t)-sin(u)

b=8*cos(v)

R=7*sin(v)

U: [-2,12] (25)

V: [-2,12] (25)

Program: 3D Grapher

Coordinates: Spherical

Function:

a=v*(sin(u))^4

b=u*(sin(v))^3

R=u^3+v^3

Min U: -1 Max U: 1 Steps: 70

Min V: -1 Max V: 1 Steps: 70

Program: 3D Grapher

Coordinates: Spherical

Function

a(u,v,t)=sin(u)

b(u,v,t)=cos(u)+v

R(u,v,t)=0.5*u

Domain of variables

Min U: -4 Max U: 8 Steps: 40

Min V: -6 Max V: 20 Steps: 40

Radjeno u programu 3D Grapher

Coordinates  -   "Cartesian"

Funkcije:

X(u,v,t)=2*v*(cos(4*u))^2

Y(u,v,t)=5*v*(sin(2*u))

Z(u,v,t)=3*v

Domen:

Min U : -2      ;     Max U: 8     ;    Steps: 50

Min V : -2      ;     Max V: 8     ;    Steps: 50

Coordinates-Cartesain

Name -funkcija 1

X=cos(3*t)-sin(2*u)

Y=tan(2*v)+3*cos(t)

Z=sin(3*v)-4*cos(u)

MinU=-10

MaxU=10

Steps=20

Name -Funkcija2

X=cos(4t)-sin(5*u)

Y=tan(v)+3*cos(2*v)

Z=sin(3*v)-4*cos(u)

MinU=-10

MaxU=10

Steps=20

Name -funkcija 3

X=cos(2*t)-sin(u)

Y=tan(2*v)3*cos(3v)

Z=sin(2*v)-2*cos(2*u)

Min U =-10

Max U=10

Steps=20

Name-Funkcija4

X=7*sin(3*u)-4*cos(u)

Y=2*tan(v)+4*sin(u)

Z=sin(4t)-2*cos(5t)

MinU=-10

MaxU=10

Steps=20

Program: 3D GRAPHER

Cordinates: Cartesian

Function:

X(u, v, t)=

 15*v* sin (2*u);                             15*v*sin(2*u)           10*v                                   10*v

Y(U, V, T)=

 20*v*sin(u)*3;                               20*v*sin(u)*3           15*v*sin(2*u)                      15*v*sin(2*u)

Z(u, v, t)= 

10*v;                                             10*v                         20*v*sin (u)*3                     20*v*sin (u)*3

Domain of variables:

Min U:0                                                        -10                          -10                                    0

Min V: 0                                                        -10                          -10                                    0

Max U:10                                                      0                             0                                       10

Max V: 10                                                     0                             0                                       10

Steps:600                                                     600                         500                                    500

Steps: 60                                                      60                           50                                      50

*cos(u);b(u,v,t)*sin(u);R(u,v,t)=*u3

Min U/V=-aomaxU/V=10steps=250

a(u,v,t)=0,7*cos(u);b(u,v,t)=0.8sin(u);R(u,v,t)=0.01*u^3

min U/V=-10maxU/V=10steps=150

a(u,v,t)=1.1*cos(u);b(u,v,t)=0.5*sin(u);R(u,v,t)=0.01*u^3

min U/V=-1omaxU/V=10steps=150

a(u,v,t)=1.9*cos(u);b(u,v,t)=0,8*sin(u)R(u,v,t)=0.01*u^3

min U/V=-10maxU/V=10steps=150

u(u,v,t)=1,4*cos(u);b(u,v,t)=1sin(t);R(u,v,t)=-0.01*u^3

min U/V=-10maxU/V=10steps=150

3D Grapher

X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Selected:
New Graph (1/1)
Cartesian
X=5*u*(sin(v))
Y=3*u*(cos(v))
Z=2*u
U: [-23,23] (50)
V: [-23,23] (50)

3D Grapher
cordinates:cylindrical
function
a(u,v,t)=u
R(u,v,t)=sin(v-u)
Z(u,v,t)=v
domain of variables
min u=-5 max u=10 steps=30
min v=-5 max v=10 steps=30

program: 3D grapher

Coordinates: Spherical

x(u,v,t)=0.5*cos(u);   y(u,v,t)=0.3*sin(u);   z(u,v,t)=0.01*u^3, 

min U/V: -10 maxU/V: 10 steps: 250/250

x(u,v,t)=0.5*cos(u);   y(u,v,t)=0.3*sin(u);   z(u,v,t)=0.01*u^3, 

min U/V: -10 maxU/V: 10 steps: 150/20

x(u,v,t)=0.6*cos(u);   y(u,v,t)=0.5*sin(u);   z(u,v,t)=-0.01*u^6

min U/V: -10 maxU/V: 10 steps: 150/150

x(u,v,t)=0.9*cos(u);   y(u,v,t)=0.8*sin(u);   z(u,v,t)=0.01*u^3

min U/V: -10 maxU/V: 10 steps: 150/150

x(u,v,t)=0.7*cos(u);   y(u,v,t)=0.7*sin(u);   z(u,v,t)=0.01*u^3

min U/V: -10 maxU/V: 10 steps: 150/150

x(u,v,t)=1.1*cos(u);   y(u,v,t)=0.4*sin(u);   z(u,v,t)=-0.01*u^6

min U/V: -10 maxU/V: 10 steps: 100/100

x(u,v,t)=1.1*cos(u);   y(u,v,t)=0.4*sin(u);   z(u,v,t)=-0.01*u^6

min U/V: -10 maxU/V: 10 steps: 100/100

x(u,v,t)=0.9*cos(u);   y(u,v,t)=0.2*sin(u);   z(u,v,t)=0.01*u^6

min U/V: -10 maxU/V: 10 steps: 100/100

x(u,v,t)=1.1*cos(u);   y(u,v,t)=0.6*sin(u);   z(u,v,t)=-0.01*u^6

min U/V: -10 maxU/V: 10 steps: 100/100

x(u,v,t)=1.1*cos(u);   y(u,v,t)=0.2*sin(u);   z(u,v,t)=-0.01*u^6

X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Cartesian
X=cos(v)
Y=cos(v)+sin(v)
Z=6
U: [-10,10] (20)
V: [-10,10] (20)

X=cos(v)*2 Y=cos(v)+sin(v)*2 Z=7

X=cos(v)*3 Y=cos(v)+sin(v)*3 Z=8

X=cos(v)*4 Y=4.2*cos(v)+sin(v)*4.2  Z=cos(v)+sin(v)*4

X=4*sin(v)-cos(v)*4  Y=4*cos(v)+sin(v)*4 Z=0.01*v^3*2

X=3.5*sin(v)-cos(v)*3.5 Y=3.5*cos(v)+sin(v)*3.5 Z=0.01*v^3*2

X=3*sin(v)-cos(v)*3 Y=3*cos(v)+sin(v)*3 Z=0.01*v^3

X=2*sin(v)-cos(v)*2  Y=2*cos(v)+sin(v)*2 Z=0.01*v^3

3D Grapher

X:[-10,10]          Y:[-10,10]                 Z:[-10,10]

Selected: 1ng (1/1)         Cartesian

X=2*u*(sin(3*v))          Y=3*u*(cos(v))           Z=2*u

U: [-11,10] (40)             V:[-11,10] (40)

3D Grapher

Coordinates: Cartesian

MinU: -10, MaxU: 10, Steps: 150

X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Selected:
New Graph (1/1)
Cylindrical
a=u-v
R=sin(v-u)*u
Z=v
U: [-5,10] (30)
V: [-5,10] (30)

Program: 3D Grapher

Coordinates: Spherical

a= v*sin(u)^0.8

b= u*(cos(v))^0.4

R= (u^2+v^2)^0.8

MinU: -4   MaxU: 4   Steps: 100

MinV: -4   MaxV: 4   Steps: 100

X:[-10,10]

Y:[-10,10]

Z:[-10,10]

T:[0,0] (0)

Cartesian

X:v*(sin(u))^3

Y:u*(sin(v))^2

Z:u^2+v^3

U:[-3,3] (70)

V: [-3,3] (70)

3D grapher

Program: 3D Grapher

1. Coordinate: Spherical

Function:

a(u,v,t)=cos(u)+t

b(u,v,t)=sin(u)+v

R(u,v,t)=0.1*u

Domain of variables:

Min U:-10; Max U:10; Steps: 50

MinV:-10; Max V:10; Steps: 50

Program:3D Grapher

Coordinates:Spherical

a(u,v,t)=v*(cos(u))^2

b(u,v,t)=3+5+sin(u)

R(u,v,t)=4+sin(v)*u

Min U=-3; max U=4; Steps=70

Min V=-3; max V=4; Steps=70

Program: 3D Grapher

Coordinates: cartesian

X(u,v,t)= 4*cos(v)+sin(u); Y(u,v,t)= 4*cos(v)*2*u; Z(u,v,t)= 2*sin(v)

X(u,v,t)= 2*sin(u)+cos(v); Y(u,v,t)= sin(u)*4*v; Z(u,v,t)= cos(v)

Min U: -8; Max: 9; Steps 46

Min V: -9; Max: 8; Steps 46

X=cos(v)*sin(u)

Y=sin(u)+cos(t)

Z=sin(v)

MIN U: -10 MAX U :20 STEPS:40

MIN V:-10 MAX V :20 STEPS:40

Program: 3D Grapher

3D Grapher

Coordinates:Spherical

a(u,v,t)=v*(sin(u))^5

b(u,v,t)=u*(sin(v))^5

R(u,v,t)=u^2+v^3

Min U:-2 Max U:2 Steps:60 Min V:-2 Max V:2 Steps:80

3D Grapher

Coordinates:Spherical

a(u,v,t)=cos(u)

b(u,v,t)=cos(u)+v

R(u,v,t)=0.5*u

Min U: 2           Max U: 10         Steps:100

Min V: 1           Max V: 10          Steps:100

Coordinates: Cartesian
X (u,v,t) = 3*v*cos(u)*2
Y (u,v,t) = 2*v* sin(u)*3
Z (u,v,t) = 2*v
Domain of variables:
Min U : -10 Max U : 10 Steps: 52
Min V : -10 Max V : 10 Steps: 52

X: [-10,10]

Y: [-10,10]

Z: [-10,10]

T: [0,0] (0)

Selected: New Graph (1/1)

Spherical

a=v*(sin(u))^6

b=u*(sin(v))^7

R=u^2-v^5

U: [-2.5,2.5] (100)

V: [2.5,-2.5] (100)

x=3*cos(s)+cos(t)*cos(s)

y=3*sin(s)+cos(t)*sin(s)

z=sin(t)

smin=0

smax=2*pi

tmin=0

tmax=2*pi

zmin=-4

zmax=4

ymin=-4

ymax=4

xmin=-4

xmax=4

grid: 14 by 14
Parametric Surfaces (version 1.2)

3D grapher

coordinates: spherical

a=1.2*sin(v)

b=cos(v)*v

R=5+sin(v)

U: -9, 10   steps:100

V: -10, 10   steps:100

Program: 3D grapher

step:0.15,start:-20,end:20.

fx=2*t*cos(2*t),fy=2*t*sin(3*t),fz=3*t.

start:-15,end:15,step:0.10.

fx=cos(t*6)*2*t,fy=sin(2*t)*4*t,fz=5*t.

start:-30,end:30,step:0.3.

fx=cos(t)*6*t,fy=sin(t)*5*t,fz=3*t.

step:0.05,start:-15,end:15.

fx=8*t,fy=7*t*sin(2*t),fz=6*t.

3D math explorer.

3d grapher

x=v*(sin(u))^8+5

y=u*(sin(v))^9

z=u*2+v^3

minu-3 maxu3 steps50

minv-4 maxv3 steps90

3D Grapher

Coordinates: Cartesian

X(u,v,t)= 3*v*sin(3*u)

Y(u,v,t)= 11*v* sin(u)*0.5

Z(u,v,t)= 2*v*5

Min U: -10;   Max U: 10;  Steps: 60

Min V: -10;   Max V: 10;  Steps: 60

Coordinates: Cylindrical

a(u,v,t)=  u*01

R(u,v,t)= cos(u-v)

Z(u,v,t)= v*0.75

Min U: -10;   Max U: 10;  Steps: 20

Min V: -10;   Max V: 10;  Steps: 20

Coordinates: Spherical

a(u,v,t)= sin(u)*cos(u)-3

b(u,v,t)= cos(u)+v*3

R(u,v,t)= 0.75*u

Min U: 10;   Max U: 5;  Steps: 200

Min V: 1;   Max V: 40;  Steps: 100

Coordinates: Spherical a(u,v,t)= v*(sin(u))*4 b(u,v,t)= u*(sin(v))*3 R(u,v,t)= u*3+v*3 Min U: -1; Max U: 1; Steps: 70 Min V: -1; Max V: 1; Steps: 70

Coordinates: Spherical

a(u,v,t)= 1*u

b(u,v,t)= cos(u)+v

R(u,v,t)= 0.1*u

Min U: -10;   Max U: 1;  Steps: 50

Min V: -10;   Max V: 10;  Steps: 50

Coordinates: Cartesian

Function: X(u,v,t)= 4*v*sin(cos(u)*4)^2

          Y(u,v,t)= 4*v*cos(sin(u))^2

          Z(u,v,t)= 2*v^2

Domain of variables:

          MinU: -10   MaxU: 10   Steps: 100

          MinV: -10   MaxV: 10   Steps: 100

PROGRAM : 3D Grapher

Cylindrical

Function

a(u,v,t)=cos(u)*v-2

R(u,v,t)=tan(u)

Z(u,v,t)=1

Domain of variables

Min U: -10 Max U: 10 Steps: 10

Min V: -10 Max V: 10 Steps: 60

Program: 3d Grapher

a=sin(v)-cos(u)

R=4*sin(v)+cos(u)

z=u

Domain of variables:

min U: -20,max U: 30,Steps: 30

min V: -10,max V: 30,Steps: 30

3D Grapher

3D Grapher 
Coordinates:

Spherical a=v*(sin(u))^2

b=u*(sin(v))^2

R=u^3+v^3

Min U:-2

Max U:2

Steps:80

Min V:-2

Max V:2

Steps:80

X=2*cos(u)-0.5*v+u

Y=3*sin(v)+0.5*u+u

Z=sin(v)+cos(u)

Min U -5 Max U 5 Steps 50

Min V -5 Max V 5 Steps 50

Krive u prostoru

Predstava krivih u prostoru

3d graper 

coordinates: spherical

a(u,v,t)=cos(u)+v

b(u,v,t)=sin(u) 

R(u,v,t)=0.1*u

min u: -5 max u: 5 steps:60

min v:-12 max v: 12 steps:60

Program: 3D Grapher

Coordinate: Spherical

Function:

a(u,v,t)=2*sin(v)+2*cos(t)

b(u,v,t)=sin(u)+v

R(u,v,t)=0.2*u

Domain of variables:

Min U:20; Max U:5; Steps: 5

MinV:5; Max V:10; Steps: 200

3D Grapher

Spherical

a(u,v,t)= tan(t)-sin(u);
b(u,v,t)= 3*cos(v);
R(u,v,t)= v;

a(u,v,t)= tan(t)-sin(u);
b(u,v,t)= 3*cos(v); 
R(u,v,t)=v;

Cylindrical

a(u,v,t)= tan(t)-sin(u);
R(u,v,t)= 3*cos(v);
Z(u,v,t)=v.

x=4*cos(u)*sin(u)

y=0.3*u^3

z=2.4*cos(u)

x=4.3*cos(u)*sin(u)

y=0.3*u^3

z=2.6*cos(u)

x=4.6*cos(u)*sin(u)

y=0.3*u^3

z=2.8*cos(u)

x=4.9*cos(u)*sin(u)

y=0.3*u^3

z=3.0*cos(u)

U=-20,20 steps=40

V=-20,20 steps=40

x=1.0*cos(u)

y=2.0*sin(u)*cos(u)

z=u^2

x=1.2*cos(u)

y=2.2*sin(u)*cos(u)

z=u^2

U=-25,50 steps=50

V=-25,50 steps=50

3D Grapher

Spherical

Krive u prostoru
Program 3D Grapher
coordinates Spherical

a(u,v,t)= v*(cos(v))^2

b(u,v,t)=u*(cos(u))^3

R(u,v,t)=v^2+u^3

Min U : -1 Max U : 1 Steps: 40

Min V: -1 Max V:1 steps:40

3d Grapher

Choordinates: Spherical

Functions:

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

b(u,v,t,)= cos(u)+v*3

R(u,v,t,)= 1*u

Domain of variables:

Min U: -10    Max U: 10     Steps: 150

Min V: -10    Max V: 50     Steps: 100

3D grapher

X=1*sin(v)*cos(v) Y=1*cos(v)*tan(v)*sin(v) Z=1*cos(v)
X=2*sin(v)*cos(v) Y=2*cos(v)*tan(v)*sin(v) Z=2*cos(v)
X=3*sin(v)*cos(v) Y=3*cos(v)*tan(v)*sin(v) Z=3*cos(v)
X=4*sin(v)*cos(v) Y=4*cos(v)*tan(v)*sin(v) Z=4*cos(v)
X=5*sin(v)*cos(v) Y=5*cos(v)*tan(v)*sin(v) Z=5*cos(v)
X=6*sin(v)*cos(v) Y=6*cos(v)*tan(v)*sin(v) Z=6*cos(v)

min U:-10 min V:-10  steps:950

max U:10   max V:10   steps:950

Korišćeni program - 3D Grapher

Coordinates: Cartesian

X (u,v,t) = 2.5^u*sin(3*u)
 
Y (u,v,t) =2.5^u*cos(3*u)

Z (u,v,t) = u+v

Domain of variables:

Min U : -20 Max U : 20 Steps: 400

Min V : -5 Max V : 5 Steps: 20

Program : 3d grapher

Program 3D Grapher

3D GRAPHER

Coordinates: Cylindrical

a(u,v,t)=sin(u)

R(u,v,t)=sin(u)+v

Z(u,v,t)=0,5*u

Min U : -10     Max U : 10     Steps : 20 

Min V : -10     Max V : 10     Steps : 20

3D GRAPHER

Coordinater :  Spherical

a(u,v,t) = cos(u)

R(u,v,t) = cos(u)+v

Z(u,v,t) = 0,5*u

Min U : 2    Max U : 10     Steps : 100 

Min V : 1    Max V : 10     Steps : 100

3D Grapher

Coordinates: Cylindrical

a(u,v,t)= cos(u)-t

R(u,v,t)= sin(u)+v+cos(t)

Z(u,v,t)= 0.01*u

Min U: -45         Max U: 50           Steps: 60

Min V: -25         Max V: 30           Steps: 70

X= 3*v*cos(2*u)

Y=2*v*sin(u)*3

Z=2*v

Min U = -1

Min V= -1

Max U = 1

Max V = 1 

Steps = 50

Steps = 50

X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Selected:
New Graph (1/1)
Cartesian
X=sin(v+u)
Y=sin(u)
Z=cosh(v)
U: [-5,10] (10)
V: [-5,10] (10)

3D Grapher

Podaci su na slici

3D Grapher

Spherical

a=3+1,3*cos(u)

b=cos(u)+v

R=0,9*u

minU=2, maxU=10, steps=200

minV=1, maxV=10, steps=150

Krive u prostoru 

3D grapher

1. X= 1*sin(v)*cos(v); Y=1*sin(v)^2*tan(v)*cos(v); Z=1*cos(v)
2. X= 2*sin(v)*cos(v); Y=1*sin(v)^2*tan(v)*cos(v); Z=2*cos(v)
3. X= 3*sin(v)*cos(v); Y=1*sin(v)^2*tan(v)*cos(v); Z=3*cos(v)
4. X= 4*sin(v)*cos(v); Y=1*sin(v)^2*tan(v)*cos(v); Z=4*cos(v)
5. X= 5*sin(v)*cos(v); Y=1*sin(v)^2*tan(v)*cos(v); Z=5*cos(v)
6. X= 6*sin(v)*cos(v); Y=1*sin(v)^2*tan(v)*cos(v); Z=6*cos(v)
7. X= 7*sin(v)*cos(v); Y=1*sin(v)^2*tan(v)*cos(v); Z=7*cos(v)

min U:-10  min V:10  steps:200

max U:-10  max V:10  steps:200

3D Grapher

Cartesian

X=u*sin(u)
Y=v*cos(v)
Z=u+v

U: [-10,10] (100)
V: [-5,5] (100)

Program: 3D Grapher

cylindrical

a (u,v,t) = 3*v*sin(3*u)
R(u,v,t) = 7*v* sin(u)*1
Z(u,v,t)= 2*v*7
min U= -10  max U = 10 Steps = 60
min U= -10  max U = 10 Steps = 60

Spherical
a (u,v,t) = u*02
R(u,v,t) = cos(u-v)
Z(u,v,t)= v*0.9
min U= -10  max U = 10 Steps = 2
min U= -10  max U = 10 Steps = 2

3D Grapher

X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Selected:
123 (1/1)
Spherical
a=cos(u)+t+t
b=sin(u)+v+v
R=2*u
U: [-8,12] (35)
V: [-8,12] (50)

3D Grapher

Coordinates: Spherical

Function: 

a=v*(sin(u))ˆ2*u

b=u*(sin(v))ˆ5*v

R=uˆ2+vˆ2

domain of variables:

Min U:-2      Max U:0.5      Steps:100

Min V:-2      Max V:0.5      Steps:100

3D grapher

3D Grapher

Coordinates: Spherical

Function: 

a=v*(sin(u))ˆ8*u

b=u*(sin(v))ˆ3*v

R=uˆ2+vˆ2

domain of variables:

Min U:-2      Max U:0.5      Steps:100

Min V:-2      Max V:0.5      Steps:100

3D grapher

Coordinates: Cartesian

x=2*cos(u)  y=2*u  z=2*sin(u)

x=0.9*cos(u)  y=0.8*sin(u)  z=0.01*u^3

x=0.6*cos(u)  y=0.5*sin(u)  z=0.01*u^3

x=4.5*cos(u)  y=4.5*sin(u)  z=2*cos(u)

x=5.5*cos(u)  y=5.5*sin(u)  z=2*cos(u)

x=5*cos(u)  y=5*sin(u)  z=1*cos(u)

x=0.6*cos(u)  y=0.6*sin(u)  z=0.05*u^3

x=0.75*cos(u)  y=0.75*sin(u)  z=0.05*u^3

x=0.4*cos(u)  y=0.4*sin(u)  z=0.05*u^3

x=2.2*cos(u)  y=2.2*u  z=2*sin(u)

x=2.5*cos(u)  y=2.5*u  z=2*sin(u)

x=2.8*cos(u)  y=2.8*u  z=2*sin(u)

Min U,V -10/-10

Max U,V 10/10

Steps 150/150

Program: 3D Grapher

Coordinates: Cylindrical

a(u,v,t) = cos(60*v)

R(u,v,t) = sin(u)

Z = 2*v

Min U: -10  Max U: 10  Steps: 40

Min V: -10  Max V: 10  Steps: 40

Korišćeni program: 3D Grapher

Coordinates: Spherical

Function:

a(u,v,t)= 7+cos(1.5*u)^4

b(u,v,t)= 1*v*sin(v+v)

R(u,v,t)= 1.2*v

Domain of variables:

Min U: 7          Max U: 15            Steps: 20

Min V: 5          Max V: 10            Steps: 40

Korišćeni program - 3D GRAPHER

Coordinates: CARTESIAN

X (u,v,t) = sin(u)*cos(u)-4
 
Y (u,v,t) = cos(u)+v*3

Z (u,v,t) = 0.95*u

Domain of variables:

Min U : -10 Max U : 5 Steps: 200

Min V : -1 Max V : 30 Steps: 90

Program: 3D Grapher

1. Coordinate: Cartesian

Function:

X(u,v,t)=v*sin(v))^3

Y(u,v,t)=v*(cos(u))

Z(u,v,t)=v*u

Domain of variables:

Min U:-10; Max U:10; Steps: 150

MinV:-10; Max V:10; Steps: 150

X(u,v,t)=v*(sin(u))^5*v

Y(u,v,t)=u*(sin(v))^5*u

Z(u,v,t)=u^5+v^5

MinU = -2 MaxU = 1,5 Steps = 95

MinV = -2 MaxV = 1,5 Steps = 95

Spherical

a= v(sin(u-2))3

b= u(sin(v-3))3

R= 3u + 3v

Domen:

min u= -1 max u= 2 steps= 50

min v = -1 max v = 1 steps= 70

3D Grapher

Cartesian

Function:

X=v*cos(u)

Y=u*cos(v)

Z=0.3*u

Variables

MinU:2

MinV:6

MaxU:8

MaxV:10

Steps:100

Steps:100

Program:3D Grapher

Coordinates: Cartesian

Function:

x(u,v,t)=3*V*cos(2*u)

y(u,v,t)=2*V*sin(u)*3

z(u,v,t)=2*V*4

Domain of variables:

Min U: -9   Max U: 10   Steps: 50

Min V: -10   Max V: 9   STEPS: 50

3D GRAPHER

Coordinates: Cartesian

1)      X(u,v,t)= 1*sin(u);   Y(u,v,t)= 2* cos(u);   Z(u,v,t)=  0.01*u^3;

2)      X(u,v,t)= 1.25*sin(u);   Y(u,v,t)=  2.25*cos(u);   Z(u,v,t)=  0.01*u^3;

3)      X(u,v,t)= 1.5*sin(u);   Y(u,v,t)=  2.5cos(u);   Z(u,v,t)=  0.01*u^3;

4)      X(u,v,t)= 1.75*sin(u);   Y(u,v,t)=  2.75*cos(u);   Z(u,v,t)=  0.01*u^3;

5)      X(u,v,t)= 2*sin(u);   Y(u,v,t)=  3*cos(u);   Z(u,v,t)=  0.01*u^3;

6)      X(u,v,t)= 2*sin(u);   Y(u,v,t)=  1*cos(u);   Z(u,v,t)=  0.01*u^5;

7)      X(u,v,t)= 2.25*sin(u);   Y(u,v,t)=  1.25cos(u);   Z(u,v,t)=  0.01*u^5;

8)      X(u,v,t)= 2.5*sin(u);   Y(u,v,t)=  1.5*cos(u);   Z(u,v,t)=  0.01*u^5;

9)      X(u,v,t)= 2.75*sin(u);   Y(u,v,t)= 1.75* cos(u);   Z(u,v,t)=  0.01*u^5;

10)   X(u,v,t)= 3*sin(u);   Y(u,v,t)=  2*cos(u);   Z(u,v,t)=  0.01*u^5;

11)   X(u,v,t)= 3.25*sin(u);   Y(u,v,t)=  2.25*cos(u);   Z(u,v,t)=  0.01*u^5;

Min U/Min V: -10

MaxU/MaxV: 10

Steps: 100

Line width:  1-4

Coordinates: Cartesian

x ( u, v, t)= 5*v*(cos(7*u))^4;   y ( u, v, t)= 2*sin(7*u)^4;   z ( u, v, t)= 2*v;

Domain of variables: min U: -5, max U: 15, steps: 30;   min V: -5, max V: 15, steps: 30; 

Program: 3D Grapher

 3D Grapher

Coordinates: shperical

X (u,v,t) =cos(u)
 
Y (u,v,t) = cos(u)+v

Z (u,v,t) =6*cos(v)

Domain of variables:

Min U : -20 Max U : 10 Steps: 50

Min V : -10 Max V : 100 Steps: 100

saljem 2 slike istog sistema krivih u prostoru gledano sa prednje i sa zadnje strane

Program 3D Grapher
Coordinates: Spherical
Function:
a(u,v,t)=2*(sin(u))
b(u,v,t)=cos(u)-sin(v)
R(u,v,t)=sin(v)
Domain of variables:
Min U:-12 Max U:14 Steps:50
Min V:-7 Max V:14 Steps:60

Program 3D Grapher
Coordinates: Spherical
Function:
a(u,v,t)=sin(v)
b(u,v,t)=cos(u)+v
R(u,v,t)=2*u
Domain of variables:
Min U:-5 Max U:4 Steps:70
Min V:-11 Max V:12 Steps:70

Program: 3D grapher

Coordinates: Cartesian

X(u,v,t)= 3*cos(u)

Y(u,v,t)= 2*v* sin(u)

Z(u,v,t)= 5*v

Min U: - 10    Max U: 10   Steps:80

Min V: - 10    Max V: 10    Steps:70

coordinates:cylindrical

Funcrion:

a(u,v,t)=2*v*cos(u)

R(u,v,t)=u*sin(v)

Z(u.v.t)=u*v

Min U: -3

MacU: 15

Steps: 350

Min V: -25

Max V: 14

Steps: 40

coordinates:cylindrical

Funcrion:

a(u,v,t)=2*v*cos(u)

R(u,v,t)=u*sin(v)

Z(u.v.t)=u*v

Min U: -6

MaxU: 12

Steps: 400

Min V: -50

Max V: 12

Steps: 40

Program: 3D Grapher

Coordinates: Spherical

Function:

a(u,v,t)=0.8*cos(u) b(u,v,t)=0.5*sin(u) R(u,v,t)=0.3*cos(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 100/100

a(u,v,t)=0.8*cos(u) b(u,v,t)=0.5*sin(u) R(u,v,t)=0.8*cos(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 100/100

a(u,v,t)=0.8*cos(u) b(u,v,t)=0.5*sin(u) R(u,v,t)=0.8*cos(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 180/180

a(u,v,t)=0.8*cos(u) b(u,v,t)=0.5*sin(u) R(u,v,t)=0.2*cos(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 100/100

a(u,v,t)=0.08*cos(u) b(u,v,t)=0.05*sin(u) R(u,v,t)=0.02*cos(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 250/200

a(u,v,t)=0.08*cos(u) b(u,v,t)=0.05*sin(u) R(u,v,t)=0.02*cos(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 250/200

a(u,v,t)=0.1*cos(u) b(u,v,t)=0.2*sin(u) R(u,v,t)=0.02*sin(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 250/200

a(u,v,t)=0.3*cos(u) b(u,v,t)=0.3*sin(u) R(u,v,t)=0.02*sin(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 250/200

a(u,v,t)=0.5*cos(u) b(u,v,t)=0.5*sin(u) R(u,v,t)=0.3*cos(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 250/200

a(u,v,t)=0.5*cos(u) b(u,v,t)=0.5*sin(u) R(u,v,t)=0.5*cos(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 250/200

a(u,v,t)=0.8*cos(u) b(u,v,t)=0.7*sin(u) R(u,v,t)=0.7*tan(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 200/200

a(u,v,t)=1.8*cos(u) b(u,v,t)=1.7*sin(u) R(u,v,t)=1.7*tan(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 200/200

a(u,v,t)=2.8*cos(u) b(u,v,t)=2.7*sin(u) R(u,v,t)=2.7*tan(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 200/200

a(u,v,t)=3.8*cos(u) b(u,v,t)=3.7*sin(u) R(u,v,t)=3.7*tan(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 200/200

a(u,v,t)=4.8*cos(u) b(u,v,t)=4.7*sin(u) R(u,v,t)=4.7*tan(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 200/200

a(u,v,t)=5.8*cos(u) b(u,v,t)=5.7*sin(u) R(u,v,t)=5.7*tan(u) MinU=-10 MaxU=10 MinV=10 MaxV=10 Steps: 200/200

Program: 3D Grapher

Coordinates: Spherical

Function:
a(u,v,t)= (5*sin(u)-2*sin(v))*0.2
b(u,v,t)= sin(u)*cos(v)
c(u,v,t)= u*3+t

Domain of variables:
MinU: 2; MaxU:10; Steps:80;
MinV:2; MaxV:10; Steps:30;

Program: 3D grapher
Coordinates: Cartesian
Function
X(u,v,t)=cos(u); Y(u,v,t)=sin(u); Z(u,v,t)=0.5*u^9;
MinU/V: -9; MaxU/V: 9; Steps: 200
X(u,v,t)=1.25*cos(u); Y(u,v,t)=1.25*sin(u); Z(u,v,t)=0.5*u^11;
MinU/V: -10; MaxU/V: 10; Steps: 200
X(u,v,t)=1.5*cos(u); Y(u,v,t)=1.5*sin(u); Z(u,v,t)=0.5*u^13;
MinU/V: -12; MaxU/V: 12; Steps: 200
X(u,v,t)=1.75*cos(u); Y(u,v,t)=1.75*sin(u); Z(u,v,t)=0.5*u^15;
MinU/V: -13; MaxU/V: 13; Steps: 200
X(u,v,t)=2*cos(u); Y(u,v,t)=2*sin(u); Z(u,v,t)=0.5*u^17;
MinU/V: -14; MaxU/V: 14; Steps: 200
X(u,v,t)=6.5*cos(u); Y(u,v,t)=6.5*sin(u); Z(u,v,t)=3*cos(u);
MinU/V: -10; MaxU/V: 10; Steps: 100
X(u,v,t)=8.5*cos(u); Y(u,v,t)=8.5*sin(u); Z(u,v,t)=3*cos(u);
MinU/V: -10; MaxU/V: 10; Steps: 100
X(u,v,t)=10*cos(u); Y(u,v,t)=10*sin(u); Z(u,v,t)=3*cos(u);
MinU/V: -10; MaxU/V: 10; Steps: 100
X(u,v,t)=0.3*cos(u); Y(u,v,t)=0.3*sin(u); Z(u,v,t)=0.05*u^3;
MinU/V: -50; MaxU/V: 50; Steps: 100
X(u,v,t)=0.5*cos(u); Y(u,v,t)=0.5*sin(u); Z(u,v,t)=0.05*u^3;
MinU/V: -50; MaxU/V: 50; Steps: 100
X(u,v,t)=0.7*cos(u); Y(u,v,t)=0.7*sin(u); Z(u,v,t)=0.05*u^3;
MinU/V: -50; MaxU/V: 50; Steps: 100
X(u,v,t)=0.85*cos(u); Y(u,v,t)=0.85*sin(u); Z(u,v,t)=0.05*u^3;
MinU/V: -50; MaxU/V: 50; Steps: 100
X(u,v,t)=1.3*cos(u); Y(u,v,t)=1.3*sin(u); Z(u,v,t)=0.05*u^3;
MinU/V: -50; MaxU/V: 50; Steps: 100
X(u,v,t)=3*cos(u); Y(u,v,t)=3*sin(u); Z(u,v,t)=0.05*u^3;
MinU/V: -7; MaxU/V: 7; Steps: 100
X(u,v,t)=3.5*cos(u); Y(u,v,t)=3.5*sin(u); Z(u,v,t)=0.05*u^3;
MinU/V: -6; MaxU/V: 6; Steps: 100
X(u,v,t)=4*cos(u); Y(u,v,t)=4*sin(u); Z(u,v,t)=0.05*u^3;
MinU/V: -5; MaxU/V: 5; Steps: 100
X(u,v,t)=4.5*cos(u); Y(u,v,t)=4.5*sin(u); Z(u,v,t)=0.05*u^3;
MinU/V: -4; MaxU/V: 4; Steps: 100
X(u,v,t)=0.5*cos(u); Y(u,v,t)=0.5*sin(u); Z(u,v,t)=0.01*u^3
MinU/V: -10; MaxU/V: 10; Steps: 250
X(u,v,t)=0.7*cos(u); Y(u,v,t)=0.7*sin(u); Z(u,v,t)=0.01*u^3
MinU/V: -10; MaxU/V: 10; Steps: 250
X(u,v,t)=0.9*cos(u); Y(u,v,t)=0.9*sin(u); Z(u,v,t)=0.01*u^3
MinU/V: -10; MaxU/V: 10; Steps: 250
X(u,v,t)=1.1*cos(u); Y(u,v,t)=1.1*sin(u); Z(u,v,t)=0.01*u^3
MinU/V: -10; MaxU/V: 10; Steps: 250
X(u,v,t)=1.3*cos(u); Y(u,v,t)=1.3*sin(u); Z(u,v,t)=0.01*u^3
MinU/V: -10; MaxU/V: 10; Steps: 250

Program: 3D grapher
Coordinates: Cartesian
Function
X(u,v,t)=2*cos(u); Y(u,v,t)=2*sin(u); Z(u,v,t)=0.6*u^3;
MinU/V: -6; MaxU/V: 6; Steps: 100
X(u,v,t)=3*cos(u); Y(u,v,t)=3*sin(u); Z(u,v,t)=0.6*u^3;
MinU/V: -6; MaxU/V: 6; Steps: 100
X(u,v,t)=4*cos(u); Y(u,v,t)=4*sin(u); Z(u,v,t)=0.6*u^3;
MinU/V: -6; MaxU/V: 6; Steps: 100
X(u,v,t)=5*cos(u); Y(u,v,t)=5*sin(u); Z(u,v,t)=0.6*u^3;
MinU/V: -6; MaxU/V: 6; Steps: 100
X(u,v,t)=3.25*cos(u); Y(u,v,t)=3.25*sin(u); Z(u,v,t)=0.5*u^2;
MinU/V: -6; MaxU/V: 6; Steps: 100
X(u,v,t)=3.75*cos(u); Y(u,v,t)=3.75*sin(u); Z(u,v,t)=0.5*u^2;
MinU/V: -5; MaxU/V: 5; Steps: 100
X(u,v,t)=4.25*cos(u); Y(u,v,t)=4.25*sin(u); Z(u,v,t)=0.5*u^2;
MinU/V: -5; MaxU/V: 5; Steps: 100
X(u,v,t)=5.25*cos(u); Y(u,v,t)=5.25*sin(u); Z(u,v,t)=0.5*u^2;
MinU/V: -8; MaxU/V: 8; Steps: 100
X(u,v,t)=0.5*cos(u); Y(u,v,t)=0.5*sin(u); Z(u,v,t)=0.1*u^3;
MinU/V: -10; MaxU/V: 10; Steps: 100
X(u,v,t)=0.7*cos(u); Y(u,v,t)=0.7*sin(u); Z(u,v,t)=-0.1*u^3;
MinU/V: -10; MaxU/V: 10; Steps: 100
X(u,v,t)=0.9*cos(u); Y(u,v,t)=0.9*sin(u); Z(u,v,t)=0.1*u^3;
MinU/V: -10; MaxU/V: 10; Steps: 100
X(u,v,t)=1.1*cos(u); Y(u,v,t)=1.1*sin(u); Z(u,v,t)=-0.1*u^3;
MinU/V: -10; MaxU/V: 10; Steps: 100
X(u,v,t)=1.3*cos(u); Y(u,v,t)=1.3*sin(u); Z(u,v,t)=-0.1*u^3;
MinU/V: -10; MaxU/V: 10; Steps: 100

3D Grapher

Program: 3D Grapher

Coordinates: Cartesian
X(u,v,t)= 2*v*cos(u)

Y(u,v,t)= 4*sin(u)*cos(v)+2*(u)

Z(u,v,t)= u*v

Min U: -6     Max U: 20     Steps: 250

Min V: -6      Max V: 5       Steps: 120

x=4*cos(v)+sin(v)*4 ; y=v z= 4*sin(v)-cos(v)*4

x=3.5*cos(v)+sin(v)*3.5 ; y=v z= 3.5*sin(v)-cos(v)*3.5

x=3*cos(v)+sin(v)*3 ; y=v z= 3*sin(v)-cos(v)*3

x=2.5*cos(v)+sin(v)*2.5 ; y=v z= 2.5*sin(v)-cos(v)*2.5

x=2*cos(v)+sin(v)*2.5 ; y=v  z= 2*sin(v)-cos(v)*2.5

x=4.5*cos(v)+sin(v)*4 ; y=v  z= 4.5*sin(v)-cos(v)*4

x=6*cos(v)+sin(v)*4 ; y=v z= 6*sin(v)-cos(v)*4

x=5*cos(v)+sin(v)*4 ; y=v z= 5*sin(v)-cos(v)*4

x=8*cos(v)+sin(v)*4 ; y=v z= 8*sin(v)-cos(v)*4

x=7*cos(v)+sin(v)*4 ; y=v z= 7*sin(v)-cos(v)*4

minU= -10 max U= 10 steps : 200

minV=-10 maxU= 10  steps : 200

Program: 3D Grapher

X(u,v,t) 4*v*cos(2*u)

Y(u,v,t) 3*v* sin(u)*3

Z(u,v,t  )2*v

min U: 10                    max U: -10                  Steps: 65

MIN V: 1                      max V: -10                  Steps: 65

Program: 3D Grapher
Koordinatni sistem: Cartesian

1.

X=2*sin(u+1.5)^4
Y=2*cos(u-2)
Z=u/5
U: [0,50] (200)
V: [0,0] (0)

2.

X=2*sin(u-1.5)^2
Y=2*cos(u+2)
Z=u/5
U: [0,50] (200)
V: [0,0] (0)

3.

X=2*sin(u+2.7)
Y=2*cos(u-3.5)
Z=(u^2)/100
U: [0,50] (200)
V: [0,0] (0)

4.-12.

X=a*cos(u); a=[5, 5, 4.5, 4, 3.5, 3, 2.5, 2]
Y=b*sin(u); b=[2, 2, 2.5, 3, 3.5, 4, 4.5, 5]
Z=c; c={0,1,2,3,...,8}
U: [0,20] (200)
V: [0,0] (0)

program: 3D Grapher

parametri:

coordinates: cartesian

x = cos(u)

y = sin(v)

z = v-u

u (-10, 10)

v (-10,10)

Program: 3D Grapher

Coordinates: Cartesian

X(u,v,t)= 2*sin(u)

Y(u,v,t)= 10*v*sin(u)*2

Z(u,v,t)=u^3+v^3

Min U: -2  Max U: 2  Steps: 50

Min V: -2  Max V: 2  Steps: 50

X(u,v,t)= 10*v*sin(u)

Y(u,v,t)= u*(sin(v))*2

Z(u,v,t)= t*sin(u))^3

Min U: -3  Max U: 3  Steps: 30

Min V: -3  Max V: 3  Steps: 30

program: 3D grapher

coordinates:spherical

a(u,v,t)=5*sin(v)+cos(t)

b(u,v,t)=8*sin(8*u)+cos(t)

R(u,v,t)=sin(v)

U min -20  max 20 steps 20

V min -15  max 15 steps 15

krive u prostoru 

3D Grapher

Coordinates: Spherical

Functions:     a(u,v,t) = v*(sin(u))*4

                      b(u,v,t) = u*(sin(v))*3

                      R(u,v,t) = u*3 + v*3

Domain of variables:

Min U: -1  Max U: 1   Steps: 100

Min V: -1  Max U: 2   Steps: 100

3D Grapher

Program: 3D Grapher

Coordinates: spherical

Functions:

a(u,v,t)= cos(u)*sin(v)

b(u,v,t)= 2*v+cos(t)

R(u,v,t)=cos(u)+v

Domain variables:

MinU: 10 MaxU: 5 steps:10 

MinV: 1 MaxV: 10 steps:120

Name: Kriva u prostoru 

Coordinates: Spherical

Function

a(u,v,t)= cos(v)+u

b(u,v,t)=sin(u)

R(u,v,t)=v

Domain of variables

Min U: 1 Max U:10 Steps:100

Min V:2 Max V: 10 Steps: 50

Program - 3D Grapher

Coordinate - Cylindrical

Funkcija - 
a (u,v,t) = v*cos(u)*5
R (u,v,t) = sin(v)*5+cos(t)
Z (u,v,t) = t*3+sin(u)

Domain of variables -

Min U:-1; Max U:1; Steps:20
MinV:-1; Max V:1; Steps: 20

3d grapher

a(u,v,t):  v*(sin(u))^3*v
R(u,v,t): (sin(v))^2.5*v
Z(u,v,t): (sin(u))^3

MinU: -4 MinV: -4  MaxU: 2   MaxV:2
Steps:120
Steps:100
Coordinate: Cylindrical

3D Grapher

Cylindrical

a=5*sin(3*u)*cos(v)

R=cos(v)

Z=5*sin(3*u)

U: [-10, 10] (256)

V: [-10, 10] (36)

Program: 3D Grapher

Coordinates: Spherical

a(u,v,t)= 2*v*(cos(u))^2;

b(u,v,t)=0.5*u*(sin(v))^2;

R(u,v,t)=2*v^2+0.5*u^2+0.8*t^2;

Domain of variables:

min U:-2, max U:2, steps:50;

min V:-2, max V:2, steps:50.

3D Graph

Program: 3D Grapher

Coordinates: Spherical

Function:

a(u,v,t)=0.1*u*sin(u)

b(u,v,t)=0.1*v*cos(v)

R(u,v,t)=0.1*u*v

Domain of variables:

Min U:-10; Max U:10; Steps:100

Min V:-10; Max V:10; Steps:100

Za ovaj zadatak kostila sam program 3DGrapher.

3d grapher

Program: 3D Grapher

coordinates: cartesian
x=u*cos(u)
y=sin(u)
z=u^3
u:[-10,10] steps=60

coordinates: cartesian
x=cos(u)^2
y=sin(u)
z=u^2
u:[-5,5] steps=60

coordinates: cylindrical
a=u
R=sin(u)
Z=u
u:[-10,10] steps=60

coordinates: spherical
a=u
b=u
R=5*cos(u)
u:[-5,5] steps=100

Coordinates: Cartesian

slika sa dva prikaza i parametrima.

a = 6*u
b = 6*v
R = 6
spherical

x = sin(u) + cos(v)
y = cos(v) + sin(v)
z = u+v
cartesian

3D Grapher

Coordinates: Spherical

Function

a(u,v,t)=0.1*cos(u)  b(u,v,t)=0.2*sin(u)  R(u,v,t)=0.01*u^3

a(u,v,t)=0.2*cos(u)  b(u,v,t)=0.5*sin(u)  R(u,v,t)=0.01*u^3

a(u,v,t)=0.1*cos(u)  b(u,v,t)=0.4*sin(u)  R(u,v,t)=0.01*u^3

a(u.v.t)=0.2*cos(u)  b(u,v,t)=0.1*sin(u)  R(u,v,t)=0.01*u^3

a(u,v,t)=0.3*cos(u)  b(u,v,t)=0.6*sin(u)  R(u,v,t)=0.01*u^3

a(u,v,t)=0.3*cos(u)  b(u,v,t)=0.1*sin(u)  R(u,v,t)=-0.02*u^3

a(u,v,t)=0.2*cos(u)  b(u,v,t)=0.3*sin(u)  R(u,v,t)=-0.02*u^3

a(u,v,t)=0.4*cos(u)  b(u,v,t)=0.2*sin(u)  R(u,v,t)=-0.02*u^3

a(u,v,t)=0.1*cos(u)  b(u,v,t)=0.4*sin(u)  R(u,v,t)=-0.02*u^3

a(u,v,t)=0.5*cos(u)  b(u,v,t)=0.3*sin(u)  R(u,v,t)=-0.02*u^3

Min U: -10 Max U: 10 Steps: 100

Min V: -10  Max V: 10 Steps: 100

3D Grapher

Coordinates: Spherical

Function:

a(u,v,t)=10*cos(u)

b(u,v,t)=cos(u)

R(u,v,t)=0.5*u

minU: 2   maxU: 10  Steps:100

minV: 2   maxV: 10  Steps: 100

Korisceni program: 3d grapher

X( u,v,t)=4*v*sin(3*v)

Y (u,v,t)= 3*v*cos*(v)*2

Z ( u,v,t)= 3*v

Domain of variables

min U=-10; max U=10

min V=-10; max V=10

steps: 60

steps: 60

Coordinates: Catesian

X(u,v,t)=3*v*cos(4*v)

Y(u,v,t)=3*v*sin(u)*3

Z(u,v,t)=3*v

Domain of variables:

Min U= -10    Max U= 10    Steps= 40

Min V= -10    Max U= 10    Steps= 40

Coordinates: Cartesian

Function:

X(u,v,t)=1.5*v*sin(3*u)-3*v

Y(u,v,t)=4*v*cos(u)*2

Z(u,v,t)=4*v

Domain of variables:

Min U: -10     Max U: 10     Steps: 60

Min V: -10     Max V: 10     Steps: 60

3D grapher

Coordinates:cylindrical

Function:

a=4v*sin(2u)*2

R=4*cos(v)

Z=0.1*u*v

 Domain of variables

Min u:-10   Max u:6   steps:30

Min v:-1     Max v:5    steps:30

3D grapher

4.2*sin(v)^5+cos(2*u)

sin(v)*2*u

cos(2*u)

-5; 25; 250

-5; 25; 250

3D Grapher

3D Grapher

coordinates: cartesian

X(u,v,t) = 3*sin(u)-cos(u)*2

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

Z(u,v,t) = 2*cos(u)*sin(u)*2

min U: -50    maxU: 50     steps: 20

min V: 50     maxV: 50     steps: 20

3D Grapher

coordinates:cylindrical

Funcrion:

a(u,v,t)=2*v*cos(u)

R(u,v,t)=u*sin(v)

Z(u.v.t)=u*v

Min U: -3

MacU: 10

Steps: 100

Min V: -3

Max V: 10

Steps: 100

3D Grapher

Coordinates: Spherical

Function

a(u,v,t)=sin(u)

b(u,v,t)=cos(u)+v

R(u,v,t)=0.4*u

Domain of variables

Min U: -2 Max U: 10 Steps: 40

Min V: -6 Max V: 24 Steps: 40

X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Selected:
New Graph (1/1)
Cartesian
X=v*cos(2*u)
Y=v*sin(u)
Z=1.5*u
U: [-10,10] (90)
V: [-10,10] (15)

zadatak 02

3D Grapher 

a(u,v,t)= 7*u

R(u,v,t)=3*v

Z(u,v,t)=10*v

min U: -20       max U:10             Steps:300

min V:-20        max V: 10            Steps:100

3D Graph

Coordinates: Cartesian

X(u,v,t)=0.2*cos(u)  Y(u,v,t)=0.2*cos(u)  Z(u,v,t)=0.05*u^3  MinU:-7  MaxU:7  Steps:100

X(u,v,t)=2.2*cos(u)  Y(u,v,t)=2.2*cos(u)  Z(u,v,t)=0.05*u^3  MinU:-7  MaxU:7  Steps:100

X(u,v,t)=4.2*cos(u)  Y(u,v,t)=4.2*cos(u)  Z(u,v,t)=0.05*u^3  MinU:-7  MaxU:7  Steps:100

X(u,v,t)=6.2*cos(u)  Y(u,v,t)=6.2*cos(u)  Z(u,v,t)=0.05*u^3  MinU:-7  MaxU:7  Steps:100

 X(u,v,t)=1*cos(u)  Y(u,v,t)=1*cos(u)  Z(u,v,t)=0.5*u^2  MinU:-7  MaxU:7  Steps:100

X(u,v,t)=3*cos(u)  Y(u,v,t)=3*cos(u)  Z(u,v,t)=0.5*u^2  MinU:-7  MaxU:7  Steps:100

X(u,v,t)=5*cos(u)  Y(u,v,t)=5*cos(u)  Z(u,v,t)=0.5*u^2  MinU:-7  MaxU:7  Steps:100

X(u,v,t)=7*cos(u)  Y(u,v,t)=7*cos(u)  Z(u,v,t)=0.5*u^2  MinU:-7  MaxU:7  Steps:100

X(u,v,t)=2*cos(u)  Y(u,v,t)=2*cos(u)  Z(u,v,t)=3*cos(u)  MinU:-7  MaxU:7  Steps:100

X(u,v,t)=4*cos(u)  Y(u,v,t)=4*cos(u)  Z(u,v,t)=3*cos(u)  MinU:-7  MaxU:7  Steps:100

X(u,v,t)=6*cos(u)  Y(u,v,t)=6*cos(u)  Z(u,v,t)=3*cos(u)  MinU:-7  MaxU:7  Steps:100

X(u,v,t)=8*cos(u)  Y(u,v,t)=8*cos(u)  Z(u,v,t)=3*cos(u)  MinU:-7  MaxU:7  Steps:100

Program: 3D Grapher

Coordinates: Cartesian

x = 3*sin(4*u)-cos(v)

y = cos(u)

z = sin(2*u)

MinU: -10 MaxU:  10  Steps 50

MinV:  -10 MaxV: 10  Steps 30

261

program: 3D Grapher

coordinates: spherical

function:
a(u,v,t)=v*(sin(u))^4
b(u,v,t)=u*(sin(v))^3
R(u,v,t)=u^3+v^3

domain of variables:
min U: -2        max U: 1       steps: 70
min V: -2        max V: 1       steps: 70

3D Grapher

koordinate i funkcije su date u grafičkom prikazu

3D Grapher

Coordinates: Cylindrical

a (u,v,t): 6*u

R (u,v,t): 4*v

Z (u,v,t): 12*v

Min U: -40           Max U: 40             Steps: 200

Min V: -20           Max V: 20             Steps: 150

X, Y, Z= 1

3D Grapher

x = 10*cos(u) 
y = 1*sin(v)
z = v*cos(u)

Min U -10,      Max U 10     steps   40

Min V -10       Max v 10      steps    40

program - 3D grapher

coordinates - Spherical

a(u,v,t)- v*(cos(u))^2+2

b(u,v,t)- u*(sin(v))^5+3

R(u,v,t)- u^5+v+t^3

min U- -1,  min V- -1

max U- 1,   max V- 1

steps- 80,  steps- 80

Program: 3D Grapher

Coordinate: Cylindrical

Function:

a(u,v,t)=sin(u)*u*cos(v)

R(u,v,t)=4*sin(u)*sin(v)*cos(t)

Z(u,v,t)=5*u

Domain of variables:

Min U:-10; Max U:5; Steps: 300

MinV:-10; Max V:5; Steps: 300

Program: 3D Grapher

Coordinate: Cartesian

Function:

X(u,v,t)=7*sin(u)*sin(v)*cos(t)

Y(u,v,t)=cos(u)*sin(v)

Z(u,v,t)=5*v

Domain of variables:

Min U:-10; Max U:7; Steps: 200

MinV:-11; Max V:5; Steps: 200

Program: 3D Grapher

zadatak  - krive u prostoru 

Coordinates: Special

Funkcije:

X(u,v,t)=v*(sin(u))^3*u

Y(u,v,t)=u*(sin(v))^6*u

Z(u,v,t)=u^3+u^3

Domen:

U:(-2,1.5)  ( 90 )

V:(-2, 1.5)  (90 )

3D Grapher

Spherical

a=v*(sin(u))^2

b=u*(sin(v))^3

R=(v^3-u^2)^3

U: [-3,3] (300)

V: [-3,3] (300)

3D Grapher

a=1*u

b=cos(u)+v

R=0.1*u

U: [-10,1] (50)

V: [-10,10] (50)

3D Grapher

Koriscen program: 3D Grapher

Coordinates: Spherical

a: v*(sin(u))^3

b: u*(sin(v))^3

R: u^3+v^3

Min U: -2 Max U: 2 Steps: 60

Min V: -2 Max V: 2 Steps: 60

3D Grapher

Coordinates : Cylindrical

Function :

a=(10-2)*cos(u)

R=(2-10)*sin(u)

Z=(u)/6*(10-2)

Domain of variables :

U: [-10,10] (1000)

V: [-10,10] (1000)

3D Grapher

Coordinates: Spherical

Function:

a(u,v,t)= -0.1*u*sin(u)

b(u,v,t)= 0.1*v*cos(v)

R(u,v,t)= 0.1*u*0.1*v*6

Min U:-8    Max U:8    Steps:60

Min V:-6    Max V:6    Steps:30

3D Grapher

Coordinates: Spherical

Function: a(u,v,t)= v*(cos(u))^2+1

                b(u,v,t)= u*(sin(v))*4+3

                R(u,v,t)= u^3+v+t^3^v^1

Domain of variables: minU: -1 maxU: 1     Steps: 100

                                 minV: -1 maxV: 3     Steps: 100

Program: 3D Grapher

1. Coordinate: Spherical

Function:

a(u,v,t)=15*cos(t)*sin(u)*6

b(u,v,t)=8*cos(u)

R(u,v,t)=7*sin(u)

Domain of variables:

Min U:-10; Max U:10; Steps: 50

MinV:-10; Max V:10; Steps:20

2.Coordinate: Spehrical

Function:

a(u,v,t)=15*cos(t)*sin(u)*6

R(u,v,t)=7*sin(u)

Z(u,v,t)=8*cos(u)

Domain of variables:

Min U:-10; Max U:10; Steps:70

MinV:-10; Max V:10; Steps: 20

3.Coordinate: Spehrical

Function:

a(u,v,t)=15*cos(t)*sin(u)*6

R(u,v,t)=8*cos(u)*5

Z(u,v,t)=7*sin(u)

Domain of variables:

Min U:-10; Max U:10; Steps:50

MinV:-10; Max V:10; Steps: 30

Program 3D Grapher

Coordinates: Cartesian

X (u,v,t) = 4*cos(u)

Y (u,v,t) = 3*v*sin(u)*3

Z (u,v,t) = 3*v*v*v*v*sin(u)

Domain of variables:

Min U : -10 Max U : 10 Steps: 40

Min V : -10 Max V : 10 Steps: 40

Coordinates: Cartesian

X (u,v,t) = 9*cos(u)
 
Y (u,v,t) = 9*v*sin(u)*4

Z (u,v,t) = 3*v*v*v*sin(u)

Domain of variables:

Min U : -10 Max U : 10 Steps: 60

Min V : -10 Max V : 10 Steps: 60

program 3D Grapher

X(u,v,t)=2*v*sin(3*u)-3*v

Y(u,v,t)=3*v*cos(v)*2

Z(u,v,t)=u*v

U:  min=-20;  max=20    steps=90

V:  min=-20;  max=20    steps=90

Program 3D Grapher
Coordinates: Cartesian
X(u,v,t)=2*cos(u); Y(u,v,t)=2*sin(u); Z(u,v,t)=0.01*u^3
MinU/V: -10; MaxU/V: 10; Steps: 300
X(u,v,t)=2.7*cos(u); Y(u,v,t)=2.7*sin(u); Z(u,v,t)=0.01*u^3
MinU/V: -10; MaxU/V: 10; Steps: 300
X(u,v,t)=2.9*cos(u); Y(u,v,t)=2.9*sin(u); Z(u,v,t)=0.01*u^3
MinU/V: -10; MaxU/V: 10; Steps: 300
X(u,v,t)=3.1*cos(u); Y(u,v,t)=3.1*sin(u); Z(u,v,t)=0.01*u^3
MinU/V: -10; MaxU/V: 10; Steps: 300

X(u,v,t)=cos(u); Y(u,v,t)=sin(u); Z(u,v,t)=0.7*u^10;
MinU/V: -8; MaxU/V: 8; Steps: 150
X(u,v,t)=-1.5*cos(u); Y(u,v,t)=-1.5*sin(u); Z(u,v,t)=0.7*u^10;
MinU/V: -8; MaxU/V: 8; Steps: 150
X(u,v,t)=1.7*cos(u); Y(u,v,t)=1.7*sin(u); Z(u,v,t)=0.7*u^10;
MinU/V: -8; MaxU/V: 8; Steps: 150
X(u,v,t)=-2.2*cos(u); Y(u,v,t)=-2.2*sin(u); Z(u,v,t)=-0.7*u^10;
MinU/V: -8; MaxU/V: 8; Steps: 150
X(u,v,t)=2.4*cos(u); Y(u,v,t)=2.4*sin(u); Z(u,v,t)=0.7*u^10;
MinU/V: -8; MaxU/V: 8; Steps: 150
X(u,v,t)=-2.9*cos(u); Y(u,v,t)=-2.9*sin(u); Z(u,v,t)=0.7*u^10;
MinU/V: -8; MaxU/V: 8; Steps: 150

X(u,v,t)=3*cos(u); Y(u,v,t)=3*sin(u); Z(u,v,t)=0.5*u^4;
MinU/V: -3; MaxU/V: 3; Steps: 200
X(u,v,t)=5*cos(u); Y(u,v,t)=5*sin(u); Z(u,v,t)=0.5*u^4;
MinU/V: -5; MaxU/V: 5; Steps: 200
X(u,v,t)=-7*cos(u); Y(u,v,t)=-7*sin(u); Z(u,v,t)=-0.5*u^4;
MinU/V: -7; MaxU/V: 7; Steps: 200
X(u,v,t)=-9*cos(u); Y(u,v,t)=-9*sin(u); Z(u,v,t)=-0.5*u^4;
MinU/V: -9; MaxU/V: 9; Steps: 200

X(u,v,t)=v*(sin(u))^2
Y(u,v,t,)=u*(sin(v))^5

Z(u,v,t)=u^3+v^6

min U=-2 max U=2 steps=100

min V=-2 max V= steps=100

3d grapsher

3D Grapher

x=sin(t)-2*cos(u)

y=sin(v)*cos(v)

z=sin (v)+cos (v)

u:[-10,10]*(100)

v:[-10,10]*(1)

3D Grapher.

X(u,v,t)= 0.1*sin(u)    Y(u,v,t)= 0.2*cos(u)    Z(u,v,t)= 0.3*u^3

X(u,v,t)= 0.2*sin(u)    Y(u,v,t)= 0.3*cos(u)    Z(u,v,t)= 0.4*u^3

X(u,v,t)= 0.3*sin(u)    Y(u,v,t)= 0.4*cos(u)    Z(u,v,t)= 0.5*u^3

X(u,v,t)= 0.4*sin(u)    Y(u,v,t)= 0.5*cos(u)    Z(u,v,t)= 0.6*u^3

X(u,v,t)= 0.5*sin(u)    Y(u,v,t)= 0.6*cos(u)    Z(u,v,t)= 0.7*u^3

X(u,v,t)= 0.6*sin(u)    Y(u,v,t)= 0.7*cos(u)    Z(u,v,t)= 0.8*u^3

X(u,v,t)= 0.7*sin(u)    Y(u,v,t)= 0.8*cos(u)    Z(u,v,t)= 0.9*u^3

X(u,v,t)= 0.8*sin(u)    Y(u,v,t)= 0.9*cos(u)    Z(u,v,t)= 1*u^3

X(u,v,t)= 0.9*sin(u)    Y(u,v,t)= 1*cos(u)       Z(u,v,t)= 1.1*u^3

X(u,v,t)= 1*sin(u)       Y(u,v,t)= 1.1*cos(u)    Z(u,v,t)= 1.2*u^3

X(u,v,t)= 1*sin(u)       Y(u,v,t)= 1.1*cos(u)    Z(u,v,t)= 0.21*u^3

X(u,v,t)= 1*sin(u)       Y(u,v,t)= 1.1*cos(u)    Z(u,v,t)= 0.23*u^3

X(u,v,t)= 1*sin(u)       Y(u,v,t)= 1.1*cos(u)    Z(u,v,t)= 0.25*u^3

X(u,v,t)= 1*sin(u)       Y(u,v,t)= 1.1*cos(u)    Z(u,v,t)= 0.27*u^3

X(u,v,t)= 1*sin(u)       Y(u,v,t)= 1.1*cos(u)    Z(u,v,t)= 0.29*u^3

X(u,v,t)= 1*sin(u)       Y(u,v,t)= 1.1*cos(u)    Z(u,v,t)= 0.31*u^3

X(u,v,t)= 1*sin(u)       Y(u,v,t)= 1.1*cos(u)    Z(u,v,t)= 0.33*u^3

X(u,v,t)= 1*sin(u)       Y(u,v,t)= 1.1*cos(u)    Z(u,v,t)= 0.35*u^3

X(u,v,t)= 1*sin(u)       Y(u,v,t)= 1.1*cos(u)    Z(u,v,t)= 0.37*u^3

X(u,v,t)= 1*sin(u)       Y(u,v,t)= 1.1*cos(u)    Z(u,v,t)= 0.39*u^3

X(u,v,t)= 1*sin(u)       Y(u,v,t)= 1.1*cos(u)    Z(u,v,t)= 0.41*u^3

X(u,v,t)= 1*sin(u)       Y(u,v,t)= 1.1*cos(u)    Z(u,v,t)= 0.43*u^3

minU: -10,

maxU: 10,

Steps: 100

Radjeno u 3D Math Explorer-u

fx = C*cos(a)*sin(sin(b)) 
fy = C*sin(a)*sin(sin(b)) 
fz = C*cos(sin(b)) 
C=2*a

3D Grapher

3D Grapher

Korisceni program - 3D Grapher

Coordinates: Cartesian

X (u,v,t) = 5*v*cos(2*u)
 
Y (u,v,t) = 5*v* tan(3*u)

Z (u,v,t) = 2*v

Domain of variables:

Min U : -10 Max U : 10 Steps: 30

Min V : -10 Max V : 10 Steps: 60

program: 3d graph

X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Selected:
New Graph (1/1)
Cartesian
X=3*v*cos(3*u)
Y=5*v* sin(u)*3
Z=3*v
U: [-10,10] (50)
V: [-10,10] (60)

Krive u prostoru

Program: 3D Grapher

3D grapher

3D Grapher

Coordinates: Spherical
Function:
a(u,v,t)= cos(u)*4
b(u,v,t)= max(t;+5)
R(u,v,t)= log(v)*3

Min U: -10    Max U: 20      Steps: 100
Min V: -10    Max V: 20       Steps: 100

Program: 3D Grapher

3D grapher

x(u,v)= c3*cos(u)+(c2(c8cos(u)c5sin(v)

y(u,v)=c3sin(u)*(c2*(c8cos(u)c4+sin(v)

z(u,v)=c3sin(sin(3*u/2)+(c2sin(v)c7)c8)

c1=10

c2=2

c3=ca(cos*(3*u/2)+3/4

c4=c3sin(u)3c1sin(3u2)cos

R(u,v)=(sin(u)+1)*50

G(u,v)=(cos(u)+1)*50

B(u,v)=(sin(u,v)+1)*50

Z rotate 325

Scale 95%

program SD Grapher

Cylindrical

a(u,v,t)=v

R(u,v,t)=u

Z(u,v,t)=t

minu=-40,maxU=180,steps=200

minV=-15,maxV=-10,steps=20

3D Grapher

Coordinates: Spherical

Function

a(u,v,t)=sin(u)

b(u,v,t)=cos(u)+v

R(u,v,t)=0.2*u

Domain of variables

Min U: -2 Max U: 10 Steps: 40

Min V: -6 Max V: 24 Steps: 40

3D grapher
spherical

a=cos(8*u)
R=sin(2*v)
Z=cos(2*v)sin(4*t)
U:[-10,10] (20)
V:[-10,10](20)