Zadatak 03
MAT 03 - Površ u prostoru
MAT 03 - Površ u prostoru
Re: MAT 03 - Površ u prostoru
Pomoću jednog od programa korišćenih u prošlom zadatku:
3D Grapher
3D Math Explorer
Function Grapher
parametarski definisati i prikazati grafički izabranu površ u prostoru (jednu ili više). U tekstu dati parametarski oblik svih površi koje se nalaze na slici, kao i granice u i v.
3D Grapher
3D Math Explorer
Function Grapher
parametarski definisati i prikazati grafički izabranu površ u prostoru (jednu ili više). U tekstu dati parametarski oblik svih površi koje se nalaze na slici, kao i granice u i v.
Re: MAT 03 - Površ u prostoru
primer uradjen u 3d grapher-u
1. a=4*sin(u)*cos(v)
R=u*5*v
Z=16*u
Min U:-3; Max U:3
Min V:-3; Max V:3
steps 200
2. a=sin(v)*cos(u)
R=v*5*u
Z=5*u
Min U:-1; Max U:1
Min V:-1; Max V:1
steps 100
1. a=4*sin(u)*cos(v)
R=u*5*v
Z=16*u
Min U:-3; Max U:3
Min V:-3; Max V:3
steps 200
2. a=sin(v)*cos(u)
R=v*5*u
Z=5*u
Min U:-1; Max U:1
Min V:-1; Max V:1
steps 100
Re: MAT 03 - Površ u prostoru
3D Grapher
Cylindrical
a=5*sin(v)*sin(u)+10*t
R=25*tan(u)+5*v
Z=15*u+cos(15*u)
Min U:-6 Max U:3 Steps:800
Min V:-6 Max V:3 Steps:800
Cartesian
X=10*sin(u)*cos(v)
Y=u*5*v+sin(20*u)
Z=15*u
Min U:-2 Max U:1 Steps:400
Min V:-2 Max V:1 Steps:100
Cylindrical
a=5*sin(v)*sin(u)+10*t
R=25*tan(u)+5*v
Z=15*u+cos(15*u)
Min U:-6 Max U:3 Steps:800
Min V:-6 Max V:3 Steps:800
Cartesian
X=10*sin(u)*cos(v)
Y=u*5*v+sin(20*u)
Z=15*u
Min U:-2 Max U:1 Steps:400
Min V:-2 Max V:1 Steps:100
Re: MAT 03 - Površ u prostoru
3d grapher
a=cos(u)*sin(v)*3,R=5*sin(v),Z=sin(u)*(6) steps 50
a=4*sin(u),R=cos(v),Z=2*sin(v) steps 100
Re: MAT 03 - Površ u prostoru
3D Grapher
a=4*cos(u)*sin(v)
R=u*5*v
Z=16*u
MinU=-3 MaxU=3 Steps=200
MinV=-3 MaxV=3 Steps=200
a=10*sin(u)*cos(v)
R=u*5*v+sin(20*u)
Z=15*u
MinU=-2 MaxU=1 Steps=200
MinV=-2 MaxV=1 Steps=200
a=4*cos(u)*sin(v)
R=u*5*v
Z=16*u
MinU=-3 MaxU=3 Steps=200
MinV=-3 MaxV=3 Steps=200
a=10*sin(u)*cos(v)
R=u*5*v+sin(20*u)
Z=15*u
MinU=-2 MaxU=1 Steps=200
MinV=-2 MaxV=1 Steps=200
Re: MAT 03 - Površ u prostoru
u; 0; 100; pi/15;
v; 0; 100; pi/15;
fx=u
fy=v
fz=max
SU=sin(u)
SV=cos(v)
max=(SU>=SV)*SU - (SU>SV)*SV
v; 0; 100; pi/15;
fx=u
fy=v
fz=max
SU=sin(u)
SV=cos(v)
max=(SU>=SV)*SU - (SU>SV)*SV
Re: MAT 03 - Površ u prostoru
3D Grapher
Cartesian
1. x=5*sin(v)-cos(u)*5, Y=cos(v), Z=v
2. x=5*sin(u)-cos(v)*5, Y=sin(u), Z=u
MinU:-10 MaxU:10 Steps:200
MinV:-10 MaxV:10 Steps:200
Re: MAT 03 - Površ u prostoru
3d math explorer
fx=u
fy=v
fz=sin(x)+cos(y)
u: -7, 7; step 0.3
v: -7, 7; step 0.3
fx=u
fy=v
fz=sin(x)+cos(y)
u: -7, 7; step 0.3
v: -7, 7; step 0.3
Re: MAT 03 - Površ u prostoru
3D Grapher
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=v
Umin = 0; U max = 4; vmin = 0, Vmax = 4
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=v
Umin = -4; U max =0; vmin = -4, Vmax = 0
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=v
Umin = 0; U max = 8 vmin = 0, Vmax = 8
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=v
Umin = -8; U max =0; vmin = -8, Vmax = 0
X=sin(2*u)+cos(v)+1; Y=sin(2*u)*v+1; Z=v
Umin = 0; U max = 4; vmin = 0, Vmax = 4
X=sin(2*u)+cos(v)+1; Y=sin(2*u)*v+1; Z=v
Umin = -4; U max = 0; vmin = -4, Vmax = 0
X=sin(2*u)+cos(v)-1; Y=sin(2*u)*v-1; Z=v
Umin =0; U max = 4; vmin = 0, Vmax = 4
X=sin(2*u)+cos(v)-1; Y=sin(2*u)*v-1; Z=v
Umin = -4; U max = 0 ; vmin = -4, Vmax = 0
Odgovor: Re: MAT 03 - Površ u prostoru
a=5*cos(2*u)*sin(3*v)
R=5*u+6*cos(v)
z=10*u
minU:-1 maxU:1, step: 180
minV:-1 maxV:1 step:180
a=3*sin(2*u)*cos(v)
R=sin(3*v)+5*u
Z=10*u
minU:-5 maxU:5 step: 220
minV:-5 maxV:5 step: 220
3D Grapher
R=5*u+6*cos(v)
z=10*u
minU:-1 maxU:1, step: 180
minV:-1 maxV:1 step:180
a=3*sin(2*u)*cos(v)
R=sin(3*v)+5*u
Z=10*u
minU:-5 maxU:5 step: 220
minV:-5 maxV:5 step: 220
3D Grapher
Re: MAT 03 - Površ u prostoru
3D Grapher
a(u,v,t)= 2*cos(v)*sin(v), R(u,v,t)=sin(v)+u, Z(u,v,t)=4*v
Min U=-10, Max U=10, Steps=100
Min V-10, Max V=10, Steps=100;
a(u,v,t)= 4*cos(v)*sin(v), R(u,v,t)=sin(v)+u, Z(u,v,t)=4*v
Min U=-5, Max U=5, Steps=100
Min V-5, Max V=5, Steps=100;
a(u,v,t)= 6*cos(v)*sin(v), R(u,v,t)=sin(v)+u, Z(u,v,t)=4*v
Min U=-3, Max U=3, Steps=100
Min V-3, Max V=3, Steps=100;
coordinates: cartesian
a(u,v,t)= 2*cos(v)*sin(v), R(u,v,t)=sin(v)+u, Z(u,v,t)=4*v
Min U=-10, Max U=10, Steps=100
Min V-10, Max V=10, Steps=100;
a(u,v,t)= 4*cos(v)*sin(v), R(u,v,t)=sin(v)+u, Z(u,v,t)=4*v
Min U=-5, Max U=5, Steps=100
Min V-5, Max V=5, Steps=100;
a(u,v,t)= 6*cos(v)*sin(v), R(u,v,t)=sin(v)+u, Z(u,v,t)=4*v
Min U=-3, Max U=3, Steps=100
Min V-3, Max V=3, Steps=100;
coordinates: cartesian
Odgovor: Re: MAT 03 - Površ u prostoru
A=cos(v)*sin(v)+sin(2*v)
R=u*5*sin(v)
Z=16*u+v
MinU=-5 MaxU=5 Steps=200
MinV=-5
A=5*sin(6*u)*sin(v)
R=u*5*v-sin(u)
Z=15*u-sin(v)
MinU=-4 MaxU=1 Steps=200
MinV=-4 MaxV=1 Steps=200
R=u*5*sin(v)
Z=16*u+v
MinU=-5 MaxU=5 Steps=200
MinV=-5
A=5*sin(6*u)*sin(v)
R=u*5*v-sin(u)
Z=15*u-sin(v)
MinU=-4 MaxU=1 Steps=200
MinV=-4 MaxV=1 Steps=200
Re: MAT 03 - Površ u prostoru
Cylindrical
a=20*cos(u)*sin(v)
R=v*5*u
Z=15*u
min u=-2 max u=1 steps 200
min v=-2 max v=1 steps 200
Cylindrical
a=4*cos(u)*sin(v)
R=u*5*v
Z=20*u
min u=-2 max u=2 steps 200
min v=-2 max v=2 steps 200
a=20*cos(u)*sin(v)
R=v*5*u
Z=15*u
min u=-2 max u=1 steps 200
min v=-2 max v=1 steps 200
Cylindrical
a=4*cos(u)*sin(v)
R=u*5*v
Z=20*u
min u=-2 max u=2 steps 200
min v=-2 max v=2 steps 200
Re: MAT 03 - Površ u prostoru
3D Grapher
1. a=2*sin(v)*cos(u)
R=v*U
Z=5*u+t
Min U:-3 Max U:2 Steps:100
Min V:-3 Max V:3 steps:100
2. a=sin(v)*cos(u)
R=v*5*u
Z=%*u
Min U=-10 Max U:1 Steps 200
Min V:10 Max V:1 Steps 200
1. a=2*sin(v)*cos(u)
R=v*U
Z=5*u+t
Min U:-3 Max U:2 Steps:100
Min V:-3 Max V:3 steps:100
2. a=sin(v)*cos(u)
R=v*5*u
Z=%*u
Min U=-10 Max U:1 Steps 200
Min V:10 Max V:1 Steps 200
Odgovor: Re: MAT 03 - Površ u prostoru
a: start 0, end p, step pi/100
b: start o, end 2*pi, step pi/100
fx:R*cos(b)
fy:R*sin(a)*sin(a)
fz:R*cos(a)
R=cos(13*a)*sin(20*b)+10
b: start o, end 2*pi, step pi/100
fx:R*cos(b)
fy:R*sin(a)*sin(a)
fz:R*cos(a)
R=cos(13*a)*sin(20*b)+10
Re: MAT 03 - Površ u prostoru
3D Grapher
Cylindrical
a=u
R=2*v
Z=sin(7*v-t)/(1+v)^2
Min u=0 Max u=6.2832 Steps 60
Min v=0 Max v=4 Steps 60
Cylindrical
a=u
R=2*v
Z=sin(7*v-t)/(1+v)^2
Min u=0 Max u=6.2832 Steps 60
Min v=0 Max v=4 Steps 60
Re: MAT 03 - Površ u prostoru
3D grapher
Cartesian
x cos(u)*sin(v)
y u*v*4
z 16*u
minU -4 maxU4 steps 100
minV=-4 maxV=4 steps=100
Re: MAT 03 - Površ u prostoru
Radio sam u 3D Grapheru.
Spherical
a=v+t
b=cos(u+v+t)
R=cos(u+v)
U: [-10,10] (60)
V: [-10,10] (60)
Odgovor: Re: MAT 03 - Površ u prostoru
ovo je ono sto smo svi greskom uradili za prosli zadatak?
3D math explorer
a - 0 - 5 - 0.4
b - 0 - 6 - 0.4
fx=sin(b)*r*cos(b)
fy=cos(b)*r*sin(a)
fz=r+r*sin(b)
r=10*sin(a)
Re: MAT 03 - Površ u prostoru
Cyllindrical
a=2*sin(v)*cos(u)
R=v*U
Z=5*u+t
U:-3 Max U:2 Steps:100
V:-3 Max V:3 steps:100
Cartesian
X=10*sin(u)*cos(v)
Y=u*5*v+sin(10*u)
Z=13*u
U: [-10,10] (100)
V: [-10,10] (100)
Cartesian
X=25*tan(u)+5*v
Y=25*u+cos(15*u)
Z=25*sin(v)*sin(u)+10*t
U: [-3,2] (100)
V: [-3,3] (100)
a=2*sin(v)*cos(u)
R=v*U
Z=5*u+t
U:-3 Max U:2 Steps:100
V:-3 Max V:3 steps:100
Cartesian
X=10*sin(u)*cos(v)
Y=u*5*v+sin(10*u)
Z=13*u
U: [-10,10] (100)
V: [-10,10] (100)
Cartesian
X=25*tan(u)+5*v
Y=25*u+cos(15*u)
Z=25*sin(v)*sin(u)+10*t
U: [-3,2] (100)
V: [-3,3] (100)
Re: MAT 03 - Površ u prostoru
a=5*sin(v)*cos(u)
b=v*10*u
R=15*u
min U:-3; max U:3; steps:99
min V:-3; max V:3; steps:77
a=7*sin(u)*cos(v)
R=u*4*v+sin(15*u)
z=20*u
min U:-2; max U:2; steps:200
min V:-2; max V:2; steps:200
b=v*10*u
R=15*u
min U:-3; max U:3; steps:99
min V:-3; max V:3; steps:77
a=7*sin(u)*cos(v)
R=u*4*v+sin(15*u)
z=20*u
min U:-2; max U:2; steps:200
min V:-2; max V:2; steps:200
Re: MAT 03 - Površ u prostoru
1.x=sin(2*u)+cos(v)+2-7-9+4
y=sin(2*u)*v-9+9-5+9-6+4
z=v-3+3+3+8
minu=-19
minv=-10
maxu=9
maxv=2
steps=45
steps=180
y=sin(2*u)*v-9+9-5+9-6+4
z=v-3+3+3+8
minu=-19
minv=-10
maxu=9
maxv=2
steps=45
steps=180
Re: MAT 03 - Površ u prostoru
3DMath
Variable: a
Start: 0
End: Pi
Step: pi/20
Variable: b
Start: 0
End: 4*Pi
Step: pi/20
fx:R*sin(a)*sin(b)*10
fy:R*cos(a)*12
fz:R*sin(a)*cos(b)*10
R=cos(2*a);
Variable: a
Start: 0
End: Pi
Step: pi/20
Variable: b
Start: 0
End: 4*Pi
Step: pi/20
fx:R*sin(a)*sin(b)*10
fy:R*cos(a)*12
fz:R*sin(a)*cos(b)*10
R=cos(2*a);
Re: MAT 03 - Površ u prostoru
3d grapher
1.a:9*cos(u)*sin(v)
R:u*5*v+sin(25*u)
Z:16*u
minu:-2 maxu:1 speps:200
minv:-2 maxv:1 steps:200
2.a:5*sin(u)*cos(v)
R:u*6*v*sin(v)
Z:15*u
minu:-3 maxu:3 speps:200
minv:-3 maxv:3 steps:200
1.a:9*cos(u)*sin(v)
R:u*5*v+sin(25*u)
Z:16*u
minu:-2 maxu:1 speps:200
minv:-2 maxv:1 steps:200
2.a:5*sin(u)*cos(v)
R:u*6*v*sin(v)
Z:15*u
minu:-3 maxu:3 speps:200
minv:-3 maxv:3 steps:200
Re: MAT 03 - Površ u prostoru
3d grapher
a=4*cos(u)*sin(v)
R=u*v*5
Z=16*u
MINU = -3 MAXU=3 STEPS=200
MINV=-3 MAXV=3 STEPS=200
a=10*sin(u)*cos(v)
R=u*5*v+sin(20*u)
Z=15*u
MINU=-2 MAXU=1 STEPS=200
MINV=-2 MAXV=1 STEPS=200
Odgovor: Re: MAT 03 - Površ u prostoru
3d grapher
x=4*log(0.5*u)
y=v
z=2*(sin(u)*cos(v))
minU=-10 maxU=30
minV=-10 maxV=10
x=4*log(0.5*u)
y=v
z=2*(sin(u)*cos(v))
minU=-10 maxU=30
minV=-10 maxV=10
Re: MAT 03 - Površ u prostoru
FORMULE
x=a*cos(r)
y=a*sin(r)
z=3*a/sin(r)
a(od 0 do 4*pi),step 0.1
r(od 0 do 6),step 0.2
Re: MAT 03 - Površ u prostoru
X=3*cos(u)*sin(v)
Y=3*u*sin(v)
Z=3*u
minU=-10 maxU=10 steps=180
minV=-10 maxU=10 steps=180
program je 3d grapher
Y=3*u*sin(v)
Z=3*u
minU=-10 maxU=10 steps=180
minV=-10 maxU=10 steps=180
program je 3d grapher
Re: MAT 03 - Površ u prostoru
Ovo sam pogresno postavila na prethodni zadatak kao i svi ostali
3d grapher
X=cos(6*u)+sin(2*u)
Y=0
Z=sin(3*v)+cos(2*u)
3d grapher
X=cos(6*u)+sin(2*u)
Y=0
Z=sin(3*v)+cos(2*u)
Re: MAT 03 - Površ u prostoru
prva povrs
a=3*sin(v)*cos(u)
R=5*u*v
Z=18*u
druga povrs
a=sin(u)*cos(v)
b=4*u*v
R=4*u
a=3*sin(v)*cos(u)
R=5*u*v
Z=18*u
druga povrs
a=sin(u)*cos(v)
b=4*u*v
R=4*u
Re: MAT 03 - Površ u prostoru
3D GRAPHER
Prva funkcija:
Cylindrical
a=4*cos(u)*sin(v)
R=u*v
Z=16*u
Druga funkcija
Cylindrical
a=4*cos(u)*sin(v)
R=u*v
Z=8*u+sin(v)
Prva funkcija:
Cylindrical
a=4*cos(u)*sin(v)
R=u*v
Z=16*u
Druga funkcija
Cylindrical
a=4*cos(u)*sin(v)
R=u*v
Z=8*u+sin(v)
Re: MAT 03 - Površ u prostoru
3D Graph
X=3*cos(u)*sin(v)
Y=3*u*sin(v)
Z=3*u
X=4*cos(u)*sin(v)
Y=4*u*sin(v)
Z=4*u
X=5*cos(u)*sin(v)
Y=5*u*sin(v)
Z=5*u
minU=-10 maxU=10 steps=50
minV=-10 maxU=10 steps=50
X=3*cos(u)*sin(v)
Y=3*u*sin(v)
Z=3*u
X=4*cos(u)*sin(v)
Y=4*u*sin(v)
Z=4*u
X=5*cos(u)*sin(v)
Y=5*u*sin(v)
Z=5*u
minU=-10 maxU=10 steps=50
minV=-10 maxU=10 steps=50
Re: MAT 03 - Površ u prostoru
3d grapher
I
x=sin(2*u)+cos(v)
y=sin(2*u)*v
z=u
minU=-10, maxU=10 steps 40
minV=-15, maxV=15 steps 40
II
x=sin(2*u)+cos(v)+1
y=sin(2*u)*v+1
z=v
minU=-5, maxU=5 steps 40
minV=-40, maxV=40 steps 40
III
x=sin(2*u)+cos(v)+3
y=sin(2*u)*v
z=v
minU=-10, maxU=10 steps 40
minV=-5, maxV=5 steps 40
I
x=sin(2*u)+cos(v)
y=sin(2*u)*v
z=u
minU=-10, maxU=10 steps 40
minV=-15, maxV=15 steps 40
II
x=sin(2*u)+cos(v)+1
y=sin(2*u)*v+1
z=v
minU=-5, maxU=5 steps 40
minV=-40, maxV=40 steps 40
III
x=sin(2*u)+cos(v)+3
y=sin(2*u)*v
z=v
minU=-10, maxU=10 steps 40
minV=-5, maxV=5 steps 40
Re: MAT 03 - Površ u prostoru
a:4*sin(u)*2*cos(v); b:15*cos(t); R:15*tan(u)
U: -3,3; 400
V: -3,3; 400
X:2*sin(u)*4*cos(v); Y:4*cos(u); Z:16*cos(v)
U:-5,5; 300
V: -5,5; 300
X:6*cos(v)*cos(u); Y:3*sin(v); Z:cos(u)*2*cos(u)
U: -5,5; 100
V: -5,5; 100
X:sin(u)*8*sin(v); Y:3*cos(u); Z:sin(u)
U: -3,3; 100
V: -3,3; 100
3D Grapher
U: -3,3; 400
V: -3,3; 400
X:2*sin(u)*4*cos(v); Y:4*cos(u); Z:16*cos(v)
U:-5,5; 300
V: -5,5; 300
X:6*cos(v)*cos(u); Y:3*sin(v); Z:cos(u)*2*cos(u)
U: -5,5; 100
V: -5,5; 100
X:sin(u)*8*sin(v); Y:3*cos(u); Z:sin(u)
U: -3,3; 100
V: -3,3; 100
3D Grapher
Re: MAT 03 - Površ u prostoru
variable: a
start: 0
end: 3*Pi
step: pi/20
variable: b
start: 0
end: 2*Pi
step: pi/20
fx: R*sin(a)*sin(b)*15
fy: R*cos(a)*6
fz: R*sin(a)*cos(b)*15
R=sin(4*a);
start: 0
end: 3*Pi
step: pi/20
variable: b
start: 0
end: 2*Pi
step: pi/20
fx: R*sin(a)*sin(b)*15
fy: R*cos(a)*6
fz: R*sin(a)*cos(b)*15
R=sin(4*a);
Re: MAT 03 - Površ u prostoru
a=sin(u+v)+2*cos(u)
b=u
R=sin(v)+sin(u)
-7,12,25
-13,13,25
3d grapher
spherical
Re: MAT 03 - Površ u prostoru
3D Math Explorer
fx: 4*cos(a)+b+b+b
fy: 3*cos(a)
fz: 2*(sin(b)+sin(a))+cos(b)+cos(b)
a 0 5 0.1
b 0 5 0.1
fx: 4*cos(a)+b+b+b
fy: 3*cos(a)
fz: 2*(sin(b)+sin(a))+cos(b)+cos(b)
a 0 5 0.1
b 0 5 0.1
Re: MAT 03 - Površ u prostoru
3d grapher
x=4*sin(v)
y=1.5*cos(u)+1.5*v
z=3*sin(u)
min u: -10
max u: 10
steps: 50
min v: -10
max u: 10
steps: 50
Re: MAT 03 - Površ u prostoru
3D Grapher
1. a=2*sin(v)*cos(u)
R=v*U
Z=5*u+t
Min U:-3 Max U:2 Steps:70
Min V:-3 Max V:3 steps:70
02. a=sin(v)*cos(u)
R=v*5*u
Z=5*u
Min U=-10 Max U:1 Steps 70
Min V:10 Max V:1 Steps 70
1. a=2*sin(v)*cos(u)
R=v*U
Z=5*u+t
Min U:-3 Max U:2 Steps:70
Min V:-3 Max V:3 steps:70
02. a=sin(v)*cos(u)
R=v*5*u
Z=5*u
Min U=-10 Max U:1 Steps 70
Min V:10 Max V:1 Steps 70
Re: MAT 03 - Površ u prostoru
3D Math Explorer
-------------------------
x=sin(u)*100
y=cos(u)*v
z=cos(U)/SIN(U)
Re: MAT 03 - Površ u prostoru
POVRS U PROSTORU
3d graph
cartasain
x=2*sin(v)+cos(u)*2 ; y=4*sin(v)-cos(u)*4 ; z=v
min U= -10 max U=10 Steps=100
min V= -10 max V=10 Steps=100
Re: MAT 03 - Površ u prostoru
3D Grapher
- Cylindrical
a=5*cos(v)*sin(u)
R=v*5*u
Z=16*u
minu=-8 maxu=8 steps 500
minv=-8 maxv=8 steps 500
- Cylindrical
a= cos(u)*sin(v)
R= 5*u*v+sin(15*v)
Z= 15*v
minu=-10 maxu=10 steps 300
minv=-10 maxv=10 steps 500
- Cartesian
X= 10*sin(u)*cos(v)
Y= u*5*v+sin(10*u)
Z=15*v
minu=-2 maxu=2 steps 200
minv=-2 max=2 steps 200
Re: MAT 03 - Površ u prostoru
3D Grapher
Cylindrical
1.a=sin(u)*v
R=cos(v)*u
Z=u*v
Min U: -3 Max U: 3
Min V: -3 Max V: 3
Steps: 100
2.a=u*2*sin(v)
R=2*cos(v)*2*sin(u)
Z=u*v*3
Min U: -4 Max U:4
Min V: -4 Max V:4
Steps: 150
3.a=sin(u)*cos(v)
R=2*(u)*sin(v)
Z=v*2*u
Min U: -5 Max U: 5
Min V: -5 Max V: 5
Steps: 120
Cylindrical
1.a=sin(u)*v
R=cos(v)*u
Z=u*v
Min U: -3 Max U: 3
Min V: -3 Max V: 3
Steps: 100
2.a=u*2*sin(v)
R=2*cos(v)*2*sin(u)
Z=u*v*3
Min U: -4 Max U:4
Min V: -4 Max V:4
Steps: 150
3.a=sin(u)*cos(v)
R=2*(u)*sin(v)
Z=v*2*u
Min U: -5 Max U: 5
Min V: -5 Max V: 5
Steps: 120
Re: MAT 03 - Površ u prostoru
3d max explorer
x 0 10 0.4
a 0 2*pi 0.2
fx x*sin(a)+sin(b)*x
fy (2*x^2+4*x-16)/(x^2+2*x-3)*x-3
fz x*sin(a)*cos(a)
Odgovor: Re: MAT 03 - Površ u prostoru
X=1*cos(u)+1*cos(v)
Y=1*cos(v)-1*cos(u)
Z=u
minU=-10 maxU=10
minV=-10 maxV=10
Y=1*cos(v)-1*cos(u)
Z=u
minU=-10 maxU=10
minV=-10 maxV=10
Re: MAT 03 - Površ u prostoru
3d Grapher
a=sin(u)+sin(v) r=cos(v)-2 z=cos(v)
min u=-10 max u=-6; min v=-10 max v=-6; steps 20
a=sin(u)+sin(v) r=cos(v)+2 z=cos(v)
min u=-10 max u=-6; min v=-10 max v=-6; steps 20
a=sin(u)+sin(v) r=cos(v)-4 z=cos(v)
min u=-10 max u=-6; min v=-10 max v=-6; steps 20
a=sin(u)+sin(v) r=cos(v)+4 z=cos(v)
min u=-10 max u=-6; min v=-10 max v=-6; steps 20
a=sin(u)+sin(v) r=cos(v)-6 z=cos(v)
min u=-10 max u=-6; min v=-10 max v=-6; steps 20
a=sin(u)+sin(v) r=cos(v)+6 z=cos(v)
min u=-10 max u=-6; min v=-10 max v=-6; steps 20
a=sin(u)+sin(v) r=cos(v)-2 z=cos(v)
min u=-10 max u=-6; min v=-10 max v=-6; steps 20
a=sin(u)+sin(v) r=cos(v)+2 z=cos(v)
min u=-10 max u=-6; min v=-10 max v=-6; steps 20
a=sin(u)+sin(v) r=cos(v)-4 z=cos(v)
min u=-10 max u=-6; min v=-10 max v=-6; steps 20
a=sin(u)+sin(v) r=cos(v)+4 z=cos(v)
min u=-10 max u=-6; min v=-10 max v=-6; steps 20
a=sin(u)+sin(v) r=cos(v)-6 z=cos(v)
min u=-10 max u=-6; min v=-10 max v=-6; steps 20
a=sin(u)+sin(v) r=cos(v)+6 z=cos(v)
min u=-10 max u=-6; min v=-10 max v=-6; steps 20
Re: MAT 03 - Površ u prostoru
3D Grapher
X(u,v,t)=u-v*cos(v)^sin(t)
Y(u,v,t)=cos(u)*v
Z(u,v,t)=sin(u*u)^cos(v)
MinU=-6 MaxU=6 Steps=50
MinV=-6 MaxV=6 Speps=50
X(u,v,t)=u-v*cos(v)^sin(t)
Y(u,v,t)=cos(u)*v
Z(u,v,t)=sin(u*u)^cos(v)
MinU=-6 MaxU=6 Steps=50
MinV=-6 MaxV=6 Speps=50
Re: MAT 03 - Površ u prostoru
X(u,v,t)=4*sin(u)-cos(v)
Y(u,v,t)=2*sin(u)+3*cos(v)
Z(u,v,t)=u+2
Min U: -20
Max U: 20
steps: 20
Min V: -20
Max V:20
steps: 20
Y(u,v,t)=2*sin(u)+3*cos(v)
Z(u,v,t)=u+2
Min U: -20
Max U: 20
steps: 20
Min V: -20
Max V:20
steps: 20
Re: MAT 03 - Površ u prostoru
a=4*cos(u)*sin(v)
R=u*5*v
Z=16*u
min(u,v)= -3, max(u,v)= 3
steps(u,v)=400
x=cos(u*2)+sin(v*3)
y=2*sin(u)
z=3*cos(v)
min(u,v)= -3, max(u,v)= 3
steps(u,v)=200
R=u*5*v
Z=16*u
min(u,v)= -3, max(u,v)= 3
steps(u,v)=400
x=cos(u*2)+sin(v*3)
y=2*sin(u)
z=3*cos(v)
min(u,v)= -3, max(u,v)= 3
steps(u,v)=200
Re: MAT 03 - Površ u prostoru
3D Grapher
a = 3*cos(u)*sin(v)
R = u*3*v
Z = 13*u
MinU:-5 MaxU:5 Steps:1000
MinV:-5 MaxV:5 Steps:1000
a = 7*sin(u)*cos(v)
R = u*5*v+sin(8*u)
Z = 9*u
MinU:-3 MaxU:1 Steps:500
MaxV:-3 MaxV:1 Steps:500
Re: MAT 03 - Površ u prostoru
3d grapher
spherical
a=cos(v)+1
b=cos(u)*sin(u)+1
c=cos(v)*cos(u)+1
domain of variables:
min u =-6 max u=6 steps 210
min v=-12 max v=12 steps 210
Re: MAT 03 - Površ u prostoru
a=u+t
b=cos(t)*sin(v)
R=4*v
min U:-7 max U: 9
min V: -3 max V:10
steps: 190
steps:190
Odgovor: Re: MAT 03 - Površ u prostoru
3D Grapher
x=8*sin(u)*cos(v)
y=8*sin(u)*cos(v)
z=18*u
U=(5,3), V=(5,3), steps= 100
x=3*sin(u)*cos(v)
y=9*v*u-sin(15*u)
z=50*u
U=(5,3), V=(5,3), steps= 100
Odgovor: Re: MAT 03 - Površ u prostoru
t od -10 do 10 step 0.5
z od -4pi do 4pi step 0.5
fx=t*cos(z)
fy=sin(t)
tz=z
z od -4pi do 4pi step 0.5
fx=t*cos(z)
fy=sin(t)
tz=z
Re: MAT 03 - Površ u prostoru
3D Grapher
cartesian
a(u,v,t)=(sin(u+v+t))^2
R(u,v,t)=u*v^2+3*sin(t)
Z(u,v,t)=t^7-v^7
MinU=-7
MaxU=7
MinV=-7
MaxV=7
steps U 190
steps V 190
cartesian
a(u,v,t)=(sin(u+v+t))^2
R(u,v,t)=u*v^2+3*sin(t)
Z(u,v,t)=t^7-v^7
MinU=-7
MaxU=7
MinV=-7
MaxV=7
steps U 190
steps V 190
Re: MAT 03 - Površ u prostoru
3D GRAPHER
1.funkcija
cartesian
a=8*sin(u)*cos(v), R=5*v*u+sin(20*u), Z=18*u
Umin=-5, Umax=3, steps: 120
Vmin=-5, Vmax=3 steps:120
2.funkcija
cylindrical
a=3*sin(u)*cos(v), R=9*v*u-sin(15*u), Z=50*u
Umin=-5, Umax=3, steps: 120
Vmin=-5, Vmax=3 steps:120
1.funkcija
cartesian
a=8*sin(u)*cos(v), R=5*v*u+sin(20*u), Z=18*u
Umin=-5, Umax=3, steps: 120
Vmin=-5, Vmax=3 steps:120
2.funkcija
cylindrical
a=3*sin(u)*cos(v), R=9*v*u-sin(15*u), Z=50*u
Umin=-5, Umax=3, steps: 120
Vmin=-5, Vmax=3 steps:120
Re: MAT 03 - Površ u prostoru
3D Math Explorer
u 0-10, step 0,1
v 0-10, step 0,1
fx: 10*sin(u)+v
fx: 10*cos(u)+2*v
fx: 5*cos(v)+sin(u)+5*sin(v)
u 0-10, step 0,1
v 0-10, step 0,1
fx: 10*sin(u)+v
fx: 10*cos(u)+2*v
fx: 5*cos(v)+sin(u)+5*sin(v)
Re: MAT 03 - Površ u prostoru
-7<x<7 step=0.125
-7<y<7 step=0.125
f(x)=x
f(y)=y
f(z)=cos(mesafe*Pi/2)-2
mesafe=(x^2+y^2)^0.65
Re: MAT 03 - Površ u prostoru
1. Function
a(u,v,t)=2*sin(v)*cos(u)
R(u,v,t)=v*u
Z(u,v,t)+5*u+t
Min U: -10 Max U: 10 Steps: 200
Min V: -10 Max V: 10 Steps: 200
2. Function
a(u,v,t)=2*sin(v)*cos(u)
R(u,v,t)= -v*u
Z(u.v.t)=5*u+t
Min U:-10 Max U: 10 Steps: 200
Min U:-10 Max V: 10 Steps: 200
a(u,v,t)=2*sin(v)*cos(u)
R(u,v,t)=v*u
Z(u,v,t)+5*u+t
Min U: -10 Max U: 10 Steps: 200
Min V: -10 Max V: 10 Steps: 200
2. Function
a(u,v,t)=2*sin(v)*cos(u)
R(u,v,t)= -v*u
Z(u.v.t)=5*u+t
Min U:-10 Max U: 10 Steps: 200
Min U:-10 Max V: 10 Steps: 200
Re: MAT 03 - Površ u prostoru
X= 5*cos(u)*sin(v)
Y= u*4*v
Z= 13*u
Mmin U= -5 maxU= 5 steps= 200
Mmin U=-5 maxU= 5 steps= 200
X=10*sin(u)*cos(v)
Y= u*5*v+sin(20*u)
Z= 15*u
Mmin U= -6 maxU= 6 steps= 150
Mmin U=-3 maxU= 3 steps= 150
X=4*sin(u)+cos(v)
Y=u*3*v+sin(20*u)
Z= 12*u
Mmin U= -3 maxU= 6 steps= 200
Mmin U=-3 maxU= 6 steps= 200
Y= u*4*v
Z= 13*u
Mmin U= -5 maxU= 5 steps= 200
Mmin U=-5 maxU= 5 steps= 200
X=10*sin(u)*cos(v)
Y= u*5*v+sin(20*u)
Z= 15*u
Mmin U= -6 maxU= 6 steps= 150
Mmin U=-3 maxU= 3 steps= 150
X=4*sin(u)+cos(v)
Y=u*3*v+sin(20*u)
Z= 12*u
Mmin U= -3 maxU= 6 steps= 200
Mmin U=-3 maxU= 6 steps= 200
Re: MAT 03 - Površ u prostoru
x,-20,20,0.25
y,-20,20,0.25
f(x)=x
f(y)=y
f(z)=-2/(x*x+1)+ 1/(y*y+1)+0.5*sin(5*a)/a
a=(x*x+y*y)^0.5
y,-20,20,0.25
f(x)=x
f(y)=y
f(z)=-2/(x*x+1)+ 1/(y*y+1)+0.5*sin(5*a)/a
a=(x*x+y*y)^0.5
Re: MAT 03 - Površ u prostoru
uradjeno u 3d grapher-u
1. a=4*atan(u)*cos(2*v)
R=u*5*v
Z=16*u
Min U:-3; Max U:3
Min V:-3; Max V:3
steps 150
1. a=4*atan(u)*cos(2*v)
R=u*5*v
Z=16*u
Min U:-3; Max U:3
Min V:-3; Max V:3
steps 150
Re: MAT 03 - Površ u prostoru
fx = C*cos(a)*sin(sin(b))
fy = C*sin(a)*sin(sin(b))
fz = C*cos(sin(b))
C=2*a
fy = C*sin(a)*sin(sin(b))
fz = C*cos(sin(b))
C=2*a
Re: MAT 03 - Površ u prostoru
a=cos(u)*sin(v)*4
R=4*sin(v)
Z=sin(u)*(4)
min U= -10 max U=10 steps:25
min V= -10 max V=10 steps:25
a=5*sin(u)
R=cos(v)
Z=3*sin(v)
min U= -10 max U=10 steps:15
min V= -10 max V=10 steps:15
R=4*sin(v)
Z=sin(u)*(4)
min U= -10 max U=10 steps:25
min V= -10 max V=10 steps:25
a=5*sin(u)
R=cos(v)
Z=3*sin(v)
min U= -10 max U=10 steps:15
min V= -10 max V=10 steps:15
Re: MAT 03 - Površ u prostoru
primer uradjen u 3D grapher-u
cartesian
X=10*sin(u)*cos(v)
Y=u*5*v+sin(20*u)
Z=15*u
Min U=-2 Max U=1 Steps=300
Min V=-2 Min V=1 Steps=100
cartesian
X=5*sin(v)-cos(u)*5
Y=cos(v)
Z=v
Min U=-10 Max U=10 Steps=200
Min V=-10 Min V=10 Steps=300
cartesian
X=10*sin(u)*cos(v)
Y=u*5*v+sin(20*u)
Z=15*u
Min U=-2 Max U=1 Steps=300
Min V=-2 Min V=1 Steps=100
cartesian
X=5*sin(v)-cos(u)*5
Y=cos(v)
Z=v
Min U=-10 Max U=10 Steps=200
Min V=-10 Min V=10 Steps=300
Re: MAT 03 - Površ u prostoru
3D grapher
spherical:
a=sin(u+v)+2*cos(u)
b=u+1
R=sin(v)+sin(u)
Min U=-7 Max U=14 steps=30
Min v=-13 Max V=20 steps=25
spherical:
a=sin(u+v)+2*cos(u)
b=u+1
R=sin(v)+sin(u)
Min U=-7 Max U=14 steps=30
Min v=-13 Max V=20 steps=25
Odgovor: Re: MAT 03 - Površ u prostoru
Cartesian
x=u/(1+v)^2
y=v
z=sin(7*v-t)/(1+v)^2
u(0-6.2832), 60
v(0-4), 60
x=u/(1+v)^2
y=v
z=sin(7*v-t)/(1+v)^2
u(0-6.2832), 60
v(0-4), 60
Odgovor: Re: MAT 03 - Površ u prostoru
1. cylindrical; a=u*sin(v); R=v*cos(v); Z=v
2. cartesian; X=u/2; Y=v/2; Z=sin(u)
min u=-10; max u=10; steps=20
min v=-10; max v=10; steps=20
uradjeno u programu 3D grapher
2. cartesian; X=u/2; Y=v/2; Z=sin(u)
min u=-10; max u=10; steps=20
min v=-10; max v=10; steps=20
uradjeno u programu 3D grapher
Odgovor: Re: MAT 03 - Površ u prostoru
3d grapher
a= 2*sin(v)*cos(u)
R= v*u
Z= 6*u+t
Umin= -10 Umax=10 steps=200
Vmin= -10 Vmax=10 steps=200
a= 2*sin(v)*cos(u)
R= v*u
Z= 6*u+t
Umin= -10 Umax=10 steps=200
Vmin= -10 Vmax=10 steps=200
Odgovor: Re: MAT 03 - Površ u prostoru
3D Grapher
1. Cylindrical
a=9*cos(u)*sin(v)
R=u*5*v+sin(25*u)
Z=16*u
minU=-2 maxU=1 Steps= 200
minV=-2 maxV=1 Steps= 200
2. Cylindrical
a=4*cos(u)*sin(v)
R=v*u*6
Z=14*u
minU=-3 maxU=3 Steps= 180
minV=-3 maxV=3 Steps= 180
1. Cylindrical
a=9*cos(u)*sin(v)
R=u*5*v+sin(25*u)
Z=16*u
minU=-2 maxU=1 Steps= 200
minV=-2 maxV=1 Steps= 200
2. Cylindrical
a=4*cos(u)*sin(v)
R=v*u*6
Z=14*u
minU=-3 maxU=3 Steps= 180
minV=-3 maxV=3 Steps= 180
Odgovor: Re: MAT 03 - Površ u prostoru
Povrs u prostoru,radjena u 3d grapher-u
name:1
coordinates: Cartesian
Function:
X(u,v,t)=u+u+v+t
Y(u,v,t)=v+u+u+u+u+u+u+u+u+u+u+u+u
Z(u,v,t)=t+t+sin(t)+v+u+u+u+u+cos(u+u)
Min U=-10 Max U=10 Steps 20
Min V=-10 Max V=10 Steps 20
Name: New Graph
coordinates: Cartesian
Function:
X(u,v,t)=cos(u)+sin(v+t)-cos(u+u)
Y(u,v,t)=sin(v)
Z(u,v,t)=cos(t)+t+u+v+sin(v+t)
Min U=-10 Max U=10 Steps 20
Min V=-10 Max V=10 Steps 20
name:1
coordinates: Cartesian
Function:
X(u,v,t)=u+u+v+t
Y(u,v,t)=v+u+u+u+u+u+u+u+u+u+u+u+u
Z(u,v,t)=t+t+sin(t)+v+u+u+u+u+cos(u+u)
Min U=-10 Max U=10 Steps 20
Min V=-10 Max V=10 Steps 20
Name: New Graph
coordinates: Cartesian
Function:
X(u,v,t)=cos(u)+sin(v+t)-cos(u+u)
Y(u,v,t)=sin(v)
Z(u,v,t)=cos(t)+t+u+v+sin(v+t)
Min U=-10 Max U=10 Steps 20
Min V=-10 Max V=10 Steps 20
Re: MAT 03 - Površ u prostoru
Prva f-ja: x,y od -5 do 5 ; step=0.25
f(x)=x
f(y)=y
f(z)=1/(x*x+1) - 2/(y*y+1) - 0.5*sin(5*r)/r
r=-(x*x+y*y)^0.5
Druga f-ja: x,y od -5 do 5 ; step=0.25
f(x)=x
f(y)=y
f(z)=-1/(x*x+1) + 2/(y*y+1) + 0.5*sin(5*r)/r
r=+(x*x+y*y)^0.5
f(x)=x
f(y)=y
f(z)=1/(x*x+1) - 2/(y*y+1) - 0.5*sin(5*r)/r
r=-(x*x+y*y)^0.5
Druga f-ja: x,y od -5 do 5 ; step=0.25
f(x)=x
f(y)=y
f(z)=-1/(x*x+1) + 2/(y*y+1) + 0.5*sin(5*r)/r
r=+(x*x+y*y)^0.5
Odgovor: MAT 03 - Površ u prostoru
3D Grapher
1. cartesian
x=25*tan(u)+5*v
y=25*u+cos(15*u)
z=25*sin(v)*sin(u)+10*t
minU:-10 maxU:5 steps:800
minU:-10 maxU:5 steps:800
2. cartesian
x=25*sin(v)*sin(u)-10*t
y=25*u+cos(15*u)
z=25*tan(u)+5*v
minU:-10 maxU:5 steps:800
minU:-10 maxU:5 steps:800
1. cartesian
x=25*tan(u)+5*v
y=25*u+cos(15*u)
z=25*sin(v)*sin(u)+10*t
minU:-10 maxU:5 steps:800
minU:-10 maxU:5 steps:800
2. cartesian
x=25*sin(v)*sin(u)-10*t
y=25*u+cos(15*u)
z=25*tan(u)+5*v
minU:-10 maxU:5 steps:800
minU:-10 maxU:5 steps:800
Re: MAT 03 - Površ u prostoru
f(x)= 1.5*cos(a)*(k=2)
f ( y )= b*cos(b)*sin(a)*k
f(z)= b*sin(b)*sin(a)*k
a: start 0, end Pi, step 0.1
b: start 0, end 2*Pi, step 0.1
f ( y )= b*cos(b)*sin(a)*k
f(z)= b*sin(b)*sin(a)*k
a: start 0, end Pi, step 0.1
b: start 0, end 2*Pi, step 0.1
Re: MAT 03 - Površ u prostoru
3dmath explorer
fx:2*sin(b)
fy:3*(3-cos(b))*sin(a)*sin(b)+3*(3-cos(b))+a+a+a+cos(a)
fz:2*(2-cos(a))*cos(a)+b+2*(2-cos(a))*cos(a)+b+b+b
Re: MAT 03 - Površ u prostoru
3d grapher
1. a=5*cos(v)*sin(u)
r=v*5*u
z=13*u
minu=-10 maxu=10 steps 500
minv=-10 maxv=10 steps 500
2. a=cos(u)*sin(v)
r=5*u*v+sin(15*v)
15*v
minu=-10 maxu=10 steps 200
minv=-10 maxv=1- steps 200
3.x=5*sin(v)*cos(u)
y=5*u*t
z=15*v
minu=-10 maxu=10 steps 20
minv=-10 max=10 steps 20
4. x=10*sin(u)*cos(v)
y=u*5*v+sin(10*u)
z=13*u
minu=-3 maxu=1 steps 200
minv=-3 maxv=1 steps 200
1. a=5*cos(v)*sin(u)
r=v*5*u
z=13*u
minu=-10 maxu=10 steps 500
minv=-10 maxv=10 steps 500
2. a=cos(u)*sin(v)
r=5*u*v+sin(15*v)
15*v
minu=-10 maxu=10 steps 200
minv=-10 maxv=1- steps 200
3.x=5*sin(v)*cos(u)
y=5*u*t
z=15*v
minu=-10 maxu=10 steps 20
minv=-10 max=10 steps 20
4. x=10*sin(u)*cos(v)
y=u*5*v+sin(10*u)
z=13*u
minu=-3 maxu=1 steps 200
minv=-3 maxv=1 steps 200
Re: MAT 03 - Površ u prostoru
1. x=u+v
y=u*v
z=cos(u+v)-v
minU:-5; maxu:5; steps:120
minv:-5; maxv:5; steps 120
2. a=sin(v*u)-cos(u)*u*2
b=5*v
R=5*u*v
minu:-5; maxu:5; steps 150
minv:-5; maxv:5; steps 150
3. x=cos(u*2)+sin(v*3)
y=2*sin(u)
z=3*cos(v)
minu:-10; maxu:10; steps:100
minv:-10; maxv:10; steps:100
3d grapher
y=u*v
z=cos(u+v)-v
minU:-5; maxu:5; steps:120
minv:-5; maxv:5; steps 120
2. a=sin(v*u)-cos(u)*u*2
b=5*v
R=5*u*v
minu:-5; maxu:5; steps 150
minv:-5; maxv:5; steps 150
3. x=cos(u*2)+sin(v*3)
y=2*sin(u)
z=3*cos(v)
minu:-10; maxu:10; steps:100
minv:-10; maxv:10; steps:100
3d grapher
Odgovor: MAT 03 - Površ u prostoru
3D Grapher
1.a=cos(v)*sin(v)+sin(2*v)
R=u*5*sin(v)
Z=16*v+u
Min U,V=-5;Max U,V=5;Steps=200
2.a=4*sin(u)*cos(v)
R=u*5*u
Z=16*u
Min U,V=-3;Max U,V=4;Steps=200
3.X=5*cos(v)*sin(u)
Y=v*5*u
Z=13*u
Min U,V=-10;Max U,V=10;Steps=200
1.a=cos(v)*sin(v)+sin(2*v)
R=u*5*sin(v)
Z=16*v+u
Min U,V=-5;Max U,V=5;Steps=200
2.a=4*sin(u)*cos(v)
R=u*5*u
Z=16*u
Min U,V=-3;Max U,V=4;Steps=200
3.X=5*cos(v)*sin(u)
Y=v*5*u
Z=13*u
Min U,V=-10;Max U,V=10;Steps=200
Re: MAT 03 - Površ u prostoru
X=4*cos(u)*sin(2*v)
Y=u*5*v
Z=16*u
X=10*sin(u)*cos(v)
Y=u*5*v+sin(15*u)
Z=15*u
X=6*cos(v)*sin(v)
Y=sin(v)+2*u
Z=4*v
Y=u*5*v
Z=16*u
X=10*sin(u)*cos(v)
Y=u*5*v+sin(15*u)
Z=15*u
X=6*cos(v)*sin(v)
Y=sin(v)+2*u
Z=4*v
Odgovor: MAT 03 - Površ u prostoru
3D grapher
1)cylindrical
a=1*u
R=20*sin(u)*cos(v)
Z=u*5*v+sin(15*u)
minU=-3; maxU=3; steps=200
minV=-3; maxU=3; steps=200
2)cylindrical
a=u*2*v
R=20*u
Z=20*cos(u)*sin(v)
minU=-3; maxU=3; steps=200
minV=-3; maxU=3; steps=200
3)cylindrical
a=1*sin(u)*cos(v)
R=u*15*v+sin(5*u)
Z=5*u
minU=-3; maxU=3; steps=200
minV=-3; maxU=3; steps=200
1)cylindrical
a=1*u
R=20*sin(u)*cos(v)
Z=u*5*v+sin(15*u)
minU=-3; maxU=3; steps=200
minV=-3; maxU=3; steps=200
2)cylindrical
a=u*2*v
R=20*u
Z=20*cos(u)*sin(v)
minU=-3; maxU=3; steps=200
minV=-3; maxU=3; steps=200
3)cylindrical
a=1*sin(u)*cos(v)
R=u*15*v+sin(5*u)
Z=5*u
minU=-3; maxU=3; steps=200
minV=-3; maxU=3; steps=200
Re: MAT 03 - Površ u prostoru
3d grapher
coordinates:spherical
a=cos(v)+1
b=cos(u)*sin(u)+1
c=cos(v)*cos(u)+1
domain of variables:
min u =-5 max u=5 steps 200
min v=-10 max v=10 steps 200
Re: MAT 03 - Površ u prostoru
3D Grapher
1. 2.
coordinates:cartesian coordinates:cartesian
function function
X(u,v,t)=10*sin(u)*cos(v) X(u,v,t)=15*sin(u)*cos(v)
Y(u,v,t)=u*5*v+sin(20*u) Y(u,v,t)=u*5*v+sin(20*u)
Z(u,v,t)=35*u Z(u,v,t)=30*u
domain of variables: domain of variables:
min U: -5 max U:1 steps: 250 min U: -10 max U:1 steps:230
min V: -5 max V: 1 steps: 250 min V: -10 max V:1 steps:230
Re: MAT 03 - Površ u prostoru
3D Grapher
X: v Y: u Z: u^2+v^2
X: v Y: u Z: -((v^2+u^2+t)^1)
min U: -10 max U: 10
min V: -10 max V: 10
X: v Y: u Z: u^2+v^2
X: v Y: u Z: -((v^2+u^2+t)^1)
min U: -10 max U: 10
min V: -10 max V: 10
Odgovor: MAT 03 - Površ u prostoru
3D grapher
funkcija1:
a=u*v R=u/v Z=v minU=-3 maxU=3 steps=60 minV=-10 maxV=10 steps=20
funkcija2:
a=u*v R=u/v Z=v minU=-2 maxU=2 steps=90 minV=-10 maxV=10 steps=20
Re: MAT 03 - Površ u prostoru
3D Math Explorer
fx: R*cos(theta)
fy: R*sin(theta)
fz: 2*b*t
theta=t+b*2
k=1
R=cos(t*k)*b
t- 0,Pi,Pi/20
b-0,10,Pi/20
Odgovor: MAT 03 - Površ u prostoru
X od 1 do 20 sa korakom od 0.0895
f(x)=sin(20*x)
f(y)=sin(20*x)*cos(20*x)
f(z)=cos(20*x)
PS
Tek danas sam shvatio da slika koju sam postavio kao odgovor na drugi zadatak u stvari apsolutno nije adekvatna za njega, već odgovara ovoj temi, pa evo limka i do nje. Link
f(x)=sin(20*x)
f(y)=sin(20*x)*cos(20*x)
f(z)=cos(20*x)
PS
Tek danas sam shvatio da slika koju sam postavio kao odgovor na drugi zadatak u stvari apsolutno nije adekvatna za njega, već odgovara ovoj temi, pa evo limka i do nje. Link
Re: MAT 03 - Površ u prostoru
3D Grapher
Coordinates: Cylindrical
a= 3*sin(v)
R= 4*cos(60)*sin(u)+cos(u)
Z= u
Min U: -10 Max U: 10 Steps: 10
Min V: -10 Max V: 10 Steps: 20
Odgovor: MAT 03 - Površ u prostoru
I funkcija> Cylindrical
a=u^2+v^2 u (-1, 1) steps: 20
R=3*v^2 v(-1, 1) steps: 90
Z=4*u^2
II funkcija> Cylindrical
a=2*u^2+v^2 u (-1, 1) steps: 20
R=4.5*v^2 v (-1, 1) steps: 90
Z=5.5*u^2
II funkcija> Cylindrical
a=4*u^2 u(-1, 1) steps: 56
R=u^2+v^2 v(-1, 1) steps:120
Z=3*v^2
a=u^2+v^2 u (-1, 1) steps: 20
R=3*v^2 v(-1, 1) steps: 90
Z=4*u^2
II funkcija> Cylindrical
a=2*u^2+v^2 u (-1, 1) steps: 20
R=4.5*v^2 v (-1, 1) steps: 90
Z=5.5*u^2
II funkcija> Cylindrical
a=4*u^2 u(-1, 1) steps: 56
R=u^2+v^2 v(-1, 1) steps:120
Z=3*v^2
Re: MAT 03 - Površ u prostoru
3d grapher
cylindrical
a=13*sin(t)*sin(v)
R=v*10*u+sin(15*t)
Z=10*v
min U=-5 max U=20 steps=200
min U=-5 max U=20 steps=200
cartesian
a=10*sin(t)*sin(v)
R=v*17*u+sin(12*t)
Z=10*v
min U=-4 max U=3 steps=300
min U=-4 max U=3 steps=300
nadam se da je dobro :)
cylindrical
a=13*sin(t)*sin(v)
R=v*10*u+sin(15*t)
Z=10*v
min U=-5 max U=20 steps=200
min U=-5 max U=20 steps=200
cartesian
a=10*sin(t)*sin(v)
R=v*17*u+sin(12*t)
Z=10*v
min U=-4 max U=3 steps=300
min U=-4 max U=3 steps=300
nadam se da je dobro :)
Re: MAT 03 - Površ u prostoru
a(u,v,t)=(sin(u+v+t))^2
R(u,v,t)=u*v^2+3*sin(t)
Z(u,v,t)=t^5-v^5
MinU=-5
MaxU=5
MinV=-5
MaxV=5
steps U 200
steps V 200
R(u,v,t)=u*v^2+3*sin(t)
Z(u,v,t)=t^5-v^5
MinU=-5
MaxU=5
MinV=-5
MaxV=5
steps U 200
steps V 200
Re: MAT 03 - Površ u prostoru
Povrs 1
a ; 0 ; Pi ; pi/80
b ; 0 ; 2*Pi ; pi/80
Fx: R*sin(a)*cos(b)
Fy: R*sin(a)*sin(b)
Fz: R*cos(a)
R=cos(20*a)*sin(15*b)+10
Re: MAT 03 - Površ u prostoru
Povrs 2
t ; 0 ; Pi ; pi/20
b ; 0 ; 20 ; pi/20
Fx=R*cos(theta)
Fy=R*sin(theta)
Fz=3*b
theta=t+b*3
k=1
R=cos(t*k)*b
Odgovor: Re: MAT 03 - Površ u prostoru
3D Grapher
Cylindrical
a=sin(v)*cos(u)
R=u*v*4
Z=5*u+t
U: [-3,2] (20)
V: [-3,3] (20)
Cylindrical
a=20*cos(u)*sin(v)
R=v*5*u
Z=15*u
U: [-2,1] (200)
V: [-2,1] (200)
Cylindrical
a=sin(v)*cos(u)
R=u*v*4
Z=5*u+t
U: [-3,2] (20)
V: [-3,3] (20)
Cylindrical
a=20*cos(u)*sin(v)
R=v*5*u
Z=15*u
U: [-2,1] (200)
V: [-2,1] (200)
Re: MAT 03 - Površ u prostoru
3D MATH EXPLORER
f(x): x*sin(a)
f(y): (2*x^2+4*x-16)((x^2+2*x-3)
f(z): xcos(a)
vName1: x
vStart1: 0
vEnd1: 10
vStep1: 0.4
vName2: a
vStart2: 0
vEnd2: 2*Pi
vStep2: 0.2
f(x): x*sin(a)
f(y): (2*x^2+4*x-16)((x^2+2*x-3)
f(z): xcos(a)
vName1: x
vStart1: 0
vEnd1: 10
vStep1: 0.4
vName2: a
vStart2: 0
vEnd2: 2*Pi
vStep2: 0.2
Re: MAT 03 - Površ u prostoru
cylindrical
a=5(u)*cos(v)
R=v*5*u*v
Z=4*v+(t*u)
minU=-10 maxU=10 steps=200
x=4*cos*(v)
y=4*sin*(u)+t
Z=7*v
minU=-10 maxU=10 steps=300
a=5(u)*cos(v)
R=v*5*u*v
Z=4*v+(t*u)
minU=-10 maxU=10 steps=200
x=4*cos*(v)
y=4*sin*(u)+t
Z=7*v
minU=-10 maxU=10 steps=300
Re: MAT 03 - Površ u prostoru
3D Grapher
1. Cylindicar
a(u,v,t)=2*sin(v)*cos(u)
R(u,v,t)=v*u
Z(u,v,t)=5*u+t
U(-3; 5), Steps(100)
V(-4; 4), Steps(100)
2. Cartesian
X(u,v,t)=10*sin(u)*cos(v)
Y(u,v,t)=u*5*v+sin(10*u)
Z(u,v,t)=13*u
U(-10; 10), Steps(200)
V(-10; 10), Steps(200)
3. Cartesian
X(u,v,t)=25*tan(u)+5*v
Y(u,v,t)=25*u+cos(15*u)
Z(u,v,t)=25*sin(v)*sin(u)+10*t
U(-3; 1), Steps(100)
V(-3; 2), Steps(100)
1. Cylindicar
a(u,v,t)=2*sin(v)*cos(u)
R(u,v,t)=v*u
Z(u,v,t)=5*u+t
U(-3; 5), Steps(100)
V(-4; 4), Steps(100)
2. Cartesian
X(u,v,t)=10*sin(u)*cos(v)
Y(u,v,t)=u*5*v+sin(10*u)
Z(u,v,t)=13*u
U(-10; 10), Steps(200)
V(-10; 10), Steps(200)
3. Cartesian
X(u,v,t)=25*tan(u)+5*v
Y(u,v,t)=25*u+cos(15*u)
Z(u,v,t)=25*sin(v)*sin(u)+10*t
U(-3; 1), Steps(100)
V(-3; 2), Steps(100)
Re: MAT 03 - Površ u prostoru
3D Grapher
1. Cylindrical
a=8*sin(v)*cos(u)
R=3*u*v
Z=5*v
U(-3,3); Steps:100
V(-3,2); Steps:100
2.Cylindrical
a=5*sin(v)*cos(u)
R=3*u*v
Z=5*u
U(-10,10); Steps:20
V(-10,10); Steps:20
3.Cartesian
X=2*sin(v)*cos(u)
Y=u*7*v
Z=1*v
U(-3,1); Steps:100
V(-3,3); Steps:100
1. Cylindrical
a=8*sin(v)*cos(u)
R=3*u*v
Z=5*v
U(-3,3); Steps:100
V(-3,2); Steps:100
2.Cylindrical
a=5*sin(v)*cos(u)
R=3*u*v
Z=5*u
U(-10,10); Steps:20
V(-10,10); Steps:20
3.Cartesian
X=2*sin(v)*cos(u)
Y=u*7*v
Z=1*v
U(-3,1); Steps:100
V(-3,3); Steps:100
Re: MAT 03 - Površ u prostoru
-7<x<7 step 0.05
-7<y<7 step 0.05
fx: x
fy: y
fz: e^(-r/10)*sin(3*r)
r=(x*x+y*y)^0.6
-7<y<7 step 0.05
fx: x
fy: y
fz: e^(-r/10)*sin(3*r)
r=(x*x+y*y)^0.6
Re: MAT 03 - Površ u prostoru
a=1*cos(u)*sin(v)*1 ; R=u*4*v ; Z=3*v
min U: -2 ; max U: 2 ; steps: 200
a=2*cos(u)*sin(v)*2 ; R=u*10*v*cos(u) ; Z=16*v
min U: -1 ; max U: 1 ; steps: 150
3D Grapher
min U: -2 ; max U: 2 ; steps: 200
a=2*cos(u)*sin(v)*2 ; R=u*10*v*cos(u) ; Z=16*v
min U: -1 ; max U: 1 ; steps: 150
3D Grapher
Re: MAT 03 - Površ u prostoru
Cylindrical
a(u,v,t)= 16*cos(u)*sin(v)
R(u,v,t)= u*5*sin(v)
Z(u,v,t)= 8*u+v
max U: -10 max V: 19 steps 200
min U: -5 min V: 2 steps 100
a(u,v,t)= 16*cos(u)*sin(v)
R(u,v,t)= u*5*sin(v)
Z(u,v,t)= 8*u+v
max U: -10 max V: 19 steps 200
min U: -5 min V: 2 steps 100
Re: MAT 03 - Površ u prostoru
cylindrical
a=5*sin(v)*cos(u)
R=v*u
Z=5*u
minU=-5 maxU=5 steps 50
minV=-5 maxV=5 steps 50
Re: MAT 03 - Površ u prostoru
3d grapher
x= 5*sin(u)-cos(u)*5
y= cos(v)
z=v
minU=-10
minV=-10
maxU=10
maxV=10
steps=200
steps=200
x= 5*sin(u)-cos(u)*5
y= cos(v)
z=v
minU=-10
minV=-10
maxU=10
maxV=10
steps=200
steps=200
Re: MAT 03 - Površ u prostoru
3d grapher
x:6*sin(u)*2*cos(v)
Y:u*10*v
z:20*u
min U:-4
min V:-4
max U:5
max V:5
Re: MAT 03 - Površ u prostoru
Cylindrical
a=2*u
R=20*sin(u)*cos(v)
Z=u*5*v+sin(15*u)
Min U=-3 Max U=5 Steps=200
Min V=-3 Max V=5 Steps=200
Re: MAT 03 - Površ u prostoru
3d grapher
spherical:
a:sin(2*u)+cos(v)+2; b=sin(2*u) r=u
max u,v=15 min u,v= -6 , steps=150
spherical:
a:sin(2*u)+cos(v)+2; b=sin(2*u) r=u
max u,v=15 min u,v= -6 , steps=150
Re: MAT 03 - Površ u prostoru
cartesian
X=(4+1.5*cos(4*u))*cos(v)
Y=(4+2*cos(6*u))*sin(v)
Z=2*sin(u)*2*cos(v)
minU=-10 maxU=10 steps 40
minV=-3.5 maxV=-3.5 steps 30
Re: MAT 03 - Površ u prostoru
3D Grapher
Cartesian:
X = 8*cos(v)*sin(u)
Y = v*u
Z = u*15
Min U:-10 Max U:50 Steps:500
Min V:-10 Max U:50 Steps:500
Cartesian:
X = 8*cos(v)*sin(u)
Y = v*u
Z = u*15
Min U:-10 Max U:50 Steps:500
Min V:-10 Max U:50 Steps:500
Re: MAT 03 - Površ u prostoru
3D GRAPHER
1.
a=8*sin(u)*cos(v), R=5*v*u+sin(20*u), Z=18*u
Umin=-5, Umax=3, steps: 100
Vmin=-5, Vmax=3 steps:100
2.
a=3*sin(u)*cos(v), R=9*v*u-sin(15*u), Z=50*u
Umin=-5, Umax=3, steps: 100
Vmin=-5, Vmax=3 steps:100
1.
a=8*sin(u)*cos(v), R=5*v*u+sin(20*u), Z=18*u
Umin=-5, Umax=3, steps: 100
Vmin=-5, Vmax=3 steps:100
2.
a=3*sin(u)*cos(v), R=9*v*u-sin(15*u), Z=50*u
Umin=-5, Umax=3, steps: 100
Vmin=-5, Vmax=3 steps:100
Re: MAT 03 - Površ u prostoru
3D Grapher
prva povrs druga povrs
coordinates:cartesian coordinates:cartesian
function function
X(u,v,t)=10*sin(u)*cos(v) X(u,v,t)=15*sin(u)*cos(v)
Y(u,v,t)=u*5*v+sin(20*u) Y(u,v,t)=u*5*v+sin(20*u)
Z(u,v,t)=35*u Z(u,v,t)=30*u
domain of variables: domain of variables:
min U: -5 max U:1 steps: 250 min U: -10 max U:1 steps:230
min V: -5 max V: 1 steps: 250 min V: -10 max V:1 steps:230
Re: MAT 03 - Površ u prostoru
cylindrical
a=4*cos(v)*sin(v)
r=(3*sin(9*u))*cos(v)
z=(v)
minU=0 maxU=7 steps=100
minV=-5 maxV=5 steps=50
cylindrical
a=5*sin(v)-cos(u)*4
r=cos(u)
z=(U)
minU=-10 maxU=10 steps 100
minV=-10 maxV=10 steps 100
a=4*cos(v)*sin(v)
r=(3*sin(9*u))*cos(v)
z=(v)
minU=0 maxU=7 steps=100
minV=-5 maxV=5 steps=50
cylindrical
a=5*sin(v)-cos(u)*4
r=cos(u)
z=(U)
minU=-10 maxU=10 steps 100
minV=-10 maxV=10 steps 100
Re: MAT 03 - Površ u prostoru
3D Grapher
X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Cylindrical
a=20*cos(u)*sin(v)
R=v*5*u
Z=15*u
U: [-2,1] (200)
V: [-2,1] (200)
X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Cylindrical
a=20*cos(u)*sin(v)
R=v*5*u
Z=15*u
U: [-2,1] (200)
V: [-2,1] (200)
Re: MAT 03 - Površ u prostoru
cartesian
x=sin(u)*cos(v)/sin(v)
y=v-cos(v)
z=v
minV=-10 maxV=10 minU=-10 maxU=10
steps 20 steps 20
speherical
a=u
b=6+cos(v)*sin(u)
r=u+sin(v)
minU=-10 mixU=10
minV=o maxU=7
steps 100 steps 100
x=sin(u)*cos(v)/sin(v)
y=v-cos(v)
z=v
minV=-10 maxV=10 minU=-10 maxU=10
steps 20 steps 20
speherical
a=u
b=6+cos(v)*sin(u)
r=u+sin(v)
minU=-10 mixU=10
minV=o maxU=7
steps 100 steps 100
Re: MAT 03 - Površ u prostoru
3d grapher
Cylindrical
a=2*sin(v)*cos(u)
R=3*u+t
Z=5*u+t
U: [-10,10] (20)
V: [-10,10] (20)
Cylindrical
a=2*sin(v)*cos(u)
R=v*u
Z=5*u+t
U: [-3,2] (50)
V: [-3,3] (100)
Re: MAT 03 - Površ u prostoru
a=sin(3*u)*cos(t)*log(v)
R=cos(t)*3*cos(u)
Z=sin(v)*sin(3*t)
minU=-3 maxU=3 steps=130
minV=-1 maxV=10 steps=200
R=cos(t)*3*cos(u)
Z=sin(v)*sin(3*t)
minU=-3 maxU=3 steps=130
minV=-1 maxV=10 steps=200
Re: MAT 03 - Površ u prostoru
3D Grapher
Cylindrical
a: 2*cos(u)*cos(v)
R: 2*u
Z: u
Min U: -4 Max U: 4 Step: 150
Min V: -4 Max V: 4 Step: 150
a: sin(u)+v
R: cos(u)
Z: 2*u+t
Min U: -10 Max U: 10 Step: 100
Min V: -10 Max V: 10 Step: 100
Cylindrical
a: 2*cos(u)*cos(v)
R: 2*u
Z: u
Min U: -4 Max U: 4 Step: 150
Min V: -4 Max V: 4 Step: 150
a: sin(u)+v
R: cos(u)
Z: 2*u+t
Min U: -10 Max U: 10 Step: 100
Min V: -10 Max V: 10 Step: 100
Re: MAT 03 - Površ u prostoru
a=4*cos(u)*sin(v)
b=u*5*v
c=16*u
minu=-3 maxu=4 steps 300
minv=-4 maxv=3 steps 300
b=u*5*v
c=16*u
minu=-3 maxu=4 steps 300
minv=-4 maxv=3 steps 300
Re: MAT 03 - Površ u prostoru
Coordinates: CARSTESIAN
Color : face - plava
lines - roze
Function:
X(u,v,t)= v*(3+sin(u))+v
Y(u,v,t)= (u*(5+sin(u))*v)+(u*sin(u)*v)
Z(u,v,t)= 7*sin(u-v)*sin(v+u)+7*sin(u-v)*sin(v+u)
Domain of variables
Min U :-4
Max U : 1
Steps : 200
Min V :-8
Max V : 8
Steps : 200
Color : face - plava
lines - roze
Function:
X(u,v,t)= v*(3+sin(u))+v
Y(u,v,t)= (u*(5+sin(u))*v)+(u*sin(u)*v)
Z(u,v,t)= 7*sin(u-v)*sin(v+u)+7*sin(u-v)*sin(v+u)
Domain of variables
Min U :-4
Max U : 1
Steps : 200
Min V :-8
Max V : 8
Steps : 200
Re: MAT 03 - Površ u prostoru
3D Grapher
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=v
Umin = 0; U max = 4; vmin = 0, Vmax = 4
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=v
Umin = -4; U max =0; vmin = -4, Vmax = 0
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=v
Umin = 0; U max = 8 vmin = 0, Vmax = 8
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=v
Umin = -8; U max =0; vmin = -8, Vmax = 0
X=sin(2*u)+cos(v)+1; Y=sin(2*u)*v+1; Z=v
Umin = 0; U max = 4; vmin = 0, Vmax = 4
X=sin(2*u)+cos(v)+1; Y=sin(2*u)*v+1; Z=v
Umin = -4; U max = 0; vmin = -4, Vmax = 0
X=sin(2*u)+cos(v)-1; Y=sin(2*u)*v-1; Z=v
Umin =0; U max = 4; vmin = 0, Vmax = 4
X=sin(2*u)+cos(v)-1; Y=sin(2*u)*v-1; Z=v
Umin = -4; U max = 0 ; vmin = -4, Vmax = 0
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=v
Umin = 0; U max = 4; vmin = 0, Vmax = 4
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=v
Umin = -4; U max =0; vmin = -4, Vmax = 0
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=v
Umin = 0; U max = 8 vmin = 0, Vmax = 8
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=v
Umin = -8; U max =0; vmin = -8, Vmax = 0
X=sin(2*u)+cos(v)+1; Y=sin(2*u)*v+1; Z=v
Umin = 0; U max = 4; vmin = 0, Vmax = 4
X=sin(2*u)+cos(v)+1; Y=sin(2*u)*v+1; Z=v
Umin = -4; U max = 0; vmin = -4, Vmax = 0
X=sin(2*u)+cos(v)-1; Y=sin(2*u)*v-1; Z=v
Umin =0; U max = 4; vmin = 0, Vmax = 4
X=sin(2*u)+cos(v)-1; Y=sin(2*u)*v-1; Z=v
Umin = -4; U max = 0 ; vmin = -4, Vmax = 0
Re: MAT 03 - Površ u prostoru
3D Grapher
1. cartesian
x=25*tan(u)+5*v
y=25*u+cos(15*u)
z=25*sin(v)*sin(u)+10*t
minU:-10 maxU:5 steps:800
minU:-10 maxU:5 steps:800
2. cartesian
x=25*sin(v)*sin(u)-10*t
y=25*u+cos(15*u)
z=25*tan(u)+5*v
minU:-10 maxU:5 steps:800
minU:-10 maxU:5 steps:800
1. cartesian
x=25*tan(u)+5*v
y=25*u+cos(15*u)
z=25*sin(v)*sin(u)+10*t
minU:-10 maxU:5 steps:800
minU:-10 maxU:5 steps:800
2. cartesian
x=25*sin(v)*sin(u)-10*t
y=25*u+cos(15*u)
z=25*tan(u)+5*v
minU:-10 maxU:5 steps:800
minU:-10 maxU:5 steps:800
Re: MAT 03 - Površ u prostoru
3D GRAPHER
x=8*cos(v)*sin(u)
y=v*u
z=u*15
u=(-10,10)
v=(-10,10)
steps 500
Re: MAT 03 - Površ u prostoru
Radjeno u 3d Grapheru...
1. Cylindrical
a= 2*sin(v)*cos(u)
R= 2*v*u
Z= 4*u+t
Min U= -3 Max U=1 Steps=50
Min V= -3 Max V=1 Steps=100
2. Cylindrical
a= sin(u)*cos(u)
R= v*2+u
Z= u*v*v
Min U= -10 Max U= 3 Steps= 200
Min V= -11 Max V= 4 Steps= 40
1. Cylindrical
a= 2*sin(v)*cos(u)
R= 2*v*u
Z= 4*u+t
Min U= -3 Max U=1 Steps=50
Min V= -3 Max V=1 Steps=100
2. Cylindrical
a= sin(u)*cos(u)
R= v*2+u
Z= u*v*v
Min U= -10 Max U= 3 Steps= 200
Min V= -11 Max V= 4 Steps= 40
Re: MAT 03 - Površ u prostoru
3d grapher
1)cylindrical
a(u,v,t)=u*2*v
R(u,v,t)=20*u
Z(u,v,t)=12*u*v
Min U:-3 Max:3 steps:200
Min V:-3 Max:3 steps:200
2)cylindrical
a(u,v,t)=u*2*v*2
R(u,v,t)=24*u
Z(u,v,t)=22*u
Min U:-2 Max:3 steps:777
Min V:-2 Max:3 steps:777
Re: MAT 03 - Površ u prostoru
Spherical
a(u,v,t)=sin(v)*u
b(u,v,t )=cos(v)
R(u,v,t )=3*u
V:
Min U=-3;Max U=3;Steps:20
Min V=-3;Max V=3;Steps:20
a(u,v,t)=sin(v)*u
b(u,v,t )=cos(v)
R(u,v,t )=3*u
V:
Min U=-3;Max U=3;Steps:20
Min V=-3;Max V=3;Steps:20
Re: MAT 03 - Površ u prostoru
3D Grapher
Cartesian
x=8*sin(u)*cos(v)
y=7*v*u+sin(20*u)
z=20*u
minU=-5 maxU=3 steps 120
minV=-5 maxV=3 steps 120
x=4*sin(u)*cos(v)
y=4*v*u+sin(20*u)
z=18*u
minU=-7 maxU=2 steps 150
minV=-7 maxV=2 steps 150
Cartesian
x=8*sin(u)*cos(v)
y=7*v*u+sin(20*u)
z=20*u
minU=-5 maxU=3 steps 120
minV=-5 maxV=3 steps 120
x=4*sin(u)*cos(v)
y=4*v*u+sin(20*u)
z=18*u
minU=-7 maxU=2 steps 150
minV=-7 maxV=2 steps 150
Re: MAT 03 - Površ u prostoru
Cylindrical
a= 5*cos(u)*sin(v)
R= v*50*u
Z= 15*u
Min U= -3 Max U= 1 Steps=200
Min V= -3 Max V= 1 Steps=200
a= 5*cos(u)*sin(v)
R= v*50*u
Z= 15*u
Min U= -3 Max U= 1 Steps=200
Min V= -3 Max V= 1 Steps=200
Re: MAT 03 - Površ u prostoru
Cartesian coordinates
x=log(sin(u))*cos(3*u)*3*u
y=u*5*v*cos(v)*u
z=v*20*sin(u)
-1<u<1 steps 200
-3<u<3 steps 200
Re: MAT 03 - Površ u prostoru
cartesian
X=sin(u)*cos(cos(u))
Y=v*u*sin(v)
Z=cos(v)
Min U:-1 Max U:1 steps:100
Min V:-2 Max V:2 steps:100
X=sin(u)*cos(cos(u))
Y=v*u*sin(v)
Z=sin(v)
Min U:-1 Max U:1 steps:100
Min V:-2 Max V:2 steps:100
X=sin(u)*cos(cos(u))
Y=v*u*sin(v)*sin(v)*0.3
Z=cos(v)*0.3
Min U:-1 Max U:1 steps:100
Min V:-2 Max V:2 steps:100
X=sin(u)*cos(cos(u))
Y=v*u*sin(v)
Z=cos(v)
Min U:-1 Max U:1 steps:100
Min V:-2 Max V:2 steps:100
X=sin(u)*cos(cos(u))
Y=v*u*sin(v)
Z=sin(v)
Min U:-1 Max U:1 steps:100
Min V:-2 Max V:2 steps:100
X=sin(u)*cos(cos(u))
Y=v*u*sin(v)*sin(v)*0.3
Z=cos(v)*0.3
Min U:-1 Max U:1 steps:100
Min V:-2 Max V:2 steps:100
Re: MAT 03 - Površ u prostoru
cylindrical
a=2*V
R=4*sin(V)*coS(U)
z=5*U
minU=-4 maxU=3 STEPS 200
minV=-4 maxV=3
a=cos(V)+sin(V)
R=tan(U)*V*U
Z=5*U
minU=-3 maxU=2 STEPS 100
minV=-3 maxV=2
Re: MAT 03 - Površ u prostoru
X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Selected:
New Graph (1/1)
Cartesian
X=5*sin(v)
Y=2.5*cos(u)+2.5*v
Z=4*sin(u)
U: [-10,10] (60)
V: [-10,10] (60)
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Selected:
New Graph (1/1)
Cartesian
X=5*sin(v)
Y=2.5*cos(u)+2.5*v
Z=4*sin(u)
U: [-10,10] (60)
V: [-10,10] (60)
Re: MAT 03 - Površ u prostoru
Min U:-6 Max U:6 Steps:150
Min V:-6 Max V:6 Steps:150
1.
x(u,v,t):sin(u)+sin(v)*u
y(u,v,t):u
z(u,v,t):v*u
2.
x(u,v,t):-sin(u)+sin(v)*u
y(u,v,t):-u
z(u,v,t):-v*u
3.
x(u,v,t):u
y(u,v,t):v*u
z(u,v,t):sin(u)+sin(v)*u
Min V:-6 Max V:6 Steps:150
1.
x(u,v,t):sin(u)+sin(v)*u
y(u,v,t):u
z(u,v,t):v*u
2.
x(u,v,t):-sin(u)+sin(v)*u
y(u,v,t):-u
z(u,v,t):-v*u
3.
x(u,v,t):u
y(u,v,t):v*u
z(u,v,t):sin(u)+sin(v)*u
Re: MAT 03 - Površ u prostoru
x=sin(2*u)+cos(v)*5
y=sin(2*u)*v
z=2*v
min U=-5 max U=20 steps=20
min V=0 max V=5 steps=20
x=sin(2*u)+cos(v)
y=2*v
z=sin(2*u)*v
min U=-5 max U=15 steps=20
min V=-5 max V=15 steps=20
x=2*v
y=2*v
z=sin(2*u)*v+sin(2*u)+cos(v)
min U=-5 max U=0 steps=20
min V=-5 max V=0 steps=20
x=v
y=sin(2*u)+cos(v)*3
z=sin(2*u)*v
min U=0 max U=6 steps=20
min V=0 max V=10 steps=20
x=2*v
y=-2*v
z=sin(2*u)*v+sin(2*u)+cos(v)
min U=-5 max U=0 steps=20
min V=-5 max V=0 steps=20
y=sin(2*u)*v
z=2*v
min U=-5 max U=20 steps=20
min V=0 max V=5 steps=20
x=sin(2*u)+cos(v)
y=2*v
z=sin(2*u)*v
min U=-5 max U=15 steps=20
min V=-5 max V=15 steps=20
x=2*v
y=2*v
z=sin(2*u)*v+sin(2*u)+cos(v)
min U=-5 max U=0 steps=20
min V=-5 max V=0 steps=20
x=v
y=sin(2*u)+cos(v)*3
z=sin(2*u)*v
min U=0 max U=6 steps=20
min V=0 max V=10 steps=20
x=2*v
y=-2*v
z=sin(2*u)*v+sin(2*u)+cos(v)
min U=-5 max U=0 steps=20
min V=-5 max V=0 steps=20
Re: MAT 03 - Površ u prostoru
Izvinjavam se na kasnom odgovoru na zadatak
3D Grapher- Cylindrical
2*cos(u)*cos(v)
2*sin(v)
v
-10 10 200; -10 10 200
3D Grapher- Cylindrical
2*cos(u)*cos(v)
2*sin(v)
v
-10 10 200; -10 10 200
Re: MAT 03 - Površ u prostoru
Cylindrical
a=10*sin(v)*cos(u), r=5*u*v, z=6*v
Cylindrical
x=10*sin(v)*cos(v), y=10*u*v, z=10*u
Cylindrical
a=2*sin(v)*cos(u), r=v*u, z=5*u+t
Odgovor: MAT 03 - Površ u prostoru
Cylindrical
a=5*sin(v)*sin(u)+10*t
R=25*tan(u)+5*v
Z=15*u+cos(15*u)
min U: -6 maxU: 3 steps: 800
min V: -6 max V: 3 steps:800
Cartesian
X=10*sin(u)*cos(v)
Y=u*5*v+sin(20*u)
Z=15*u
min U: -2 max U: 1 steps: 400
min U: -2 max : 1 steps : 400
Odgovor: MAT 03 - Površ u prostoru
1. a=4*sin(u)*cos(v)
R=u*5*v
Z=16*u
Min U:-3; Max U:3
Min V:-3; Max V:3
steps 200
2. x=10*sin(u)*cos(v)*sin(v)*t
y=u*5*v+sin(20*u)*cos(u)*2*t
15*u*v/3*t
minU:-2 maxU:1 steps:400
minV:-2 maxV:1 steps:100
Odgovor: MAT 03 - Površ u prostoru
U 3D grapheru rađeno
a=2*cos(u)*sin(v)*2;
R=u*10*v*cos(u) ;
Z=16*v;
min U: -1;
max U: 1;
steps: 150;
a=1*cos(u)*sin(v)*1;
R=u*4*v ;
Z=3*v
min U: -2;
max U: 2;
steps: 200;
a=2*cos(u)*sin(v)*2;
R=u*10*v*cos(u) ;
Z=16*v;
min U: -1;
max U: 1;
steps: 150;
a=1*cos(u)*sin(v)*1;
R=u*4*v ;
Z=3*v
min U: -2;
max U: 2;
steps: 200;
Odgovor: MAT 03 - Površ u prostoru
3D Grapher
a=4*cos(u)*sin(u*u)
R=u*5*v
Z=16*u
MinU=-3 MaxU=3 Steps=200
MinV=-3 MaxV=3 Steps=200
a=10*sin(u)*cos(v)
R=u*5*v+sin(20*u)
Z=17*u
MinU=-2 MaxU=1 Steps=200
MinV=-2 MaxV=1 Steps=200
Odgovor: MAT 03 - Površ u prostoru
1. a=4*atan(u)*cos(2*v)
R=u*5*v
Z=16*u
Min U:-3; Max U:3
Min V:-3; Max V:3
steps 150
3d grapher
Odgovor: MAT 03 - Površ u prostoru
povrs u prostoru nastala u fun 3d programu.
Odgovor: MAT 03 - Površ u prostoru
Cartesian
Odgovor: MAT 03 - Površ u prostoru
X=cos(3*v)+sin(u); Y=cos(3*v)*u; Z=u
Umin = 0; U max = 5; vmin = 0, Vmax = 5
X=cos(3*v)+sin(u); Y=cos(3*v)*u; Z=u
Umin = -5; U max =0; vmin = -5, Vmax = 0
X=cos(3*v)+sin(u); Y=cos(3*v)*u; Z=u
Umin = 0; U max = 10 vmin = 0, Vmax = 10
X=cos(3*v)+sin(u); Y=cos(3*v)*u; Z=u
Umin = -10; U max =0; vmin = -10, Vmax = 0
X=cos(3*v)+sin(u)+1; Y=cos(3*v)*u+1; Z=u
Umin = 0; U max = 5; vmin = 0, Vmax = 5
X=cos(3*v)+sin(u)-1; Y=cos(3*v)*u-1; Z=u
Umin = -5; U max = 0; vmin = -5, Vmax = 0
X=cos(3*v)+sin(u)+1; Y=cos(3*v)*u-1; Z=u
Umin =0; U max = 10; vmin = 0, Vmax = 10
X=cos(3*v)+sin(u)+1; Y=cos(3*v)*u-1; Z=u
Umin = -10; U max = 0 ; vmin = -10, Vmax = 0
Odgovor: MAT 03 - Površ u prostoru
iz nekog razloga ja ovo nisam okacila a uradila sam odavno... ne razumem sta se desilo tek sam sada to videla
shvatam ako ne moze da se uvazi ali ipak cu okaciti
shvatam ako ne moze da se uvazi ali ipak cu okaciti
