Zadatak 02
MAT 02 - Kriva u prostoru
MAT 02 - Kriva u prostoru
MAT 02 - Kriva u prostoru
Re: MAT 02 - Kriva u prostoru
Definisati parametarski i prikazati graficki linije u prostoru.
Za ovaj zadatak koristiti sledece programe:
Function Grapher
(File, new, 3D graph...)
Fun3D
(Edit, New U Curve)
ili programe po izboru koji podrzavaju graficko predstavljanje parametarski definisanih linija u prostoru.
Odgovor: Re: MAT 02 - Kriva u prostoru
Function Grapher
Odgovor: Re: MAT 02 - Kriva u prostoru
Dodatak
x=(2+sin(2pi*v)sin(2pi*u))sin(3pi*v),
y=sin(2pi*v)cos(2pi*u)+4v-2,
z=(2+sin(2pi*v)sin(2pi*u))cos(3pi*v),
x=(2+sin(2pi*v)sin(2pi*u))sin(3pi*v),
y=sin(2pi*v)cos(2pi*u)+4v-2,
z=(2+sin(2pi*v)sin(2pi*u))cos(3pi*v),
Re: Odgovor: Re: MAT 02 - Kriva u prostoru
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Odgovor: Re: Odgovor: Re: MAT 02 - Kriva u prostoru
Sta treba da uradim?
Odgovor: Re: Odgovor: Re: MAT 02 - Kriva u prostoru
3D Grapher
x=1*sin(v)-cos(v)*4
y=1*cos(v)+sin(v)*4
z=0
x=2*cos(v)+sin(v)*4
y=2*sin(v)-cos(v)*4
z=0
x=3*cos(v)+sin(v)*4
y=3*sin(v)-cos(v)*4
z=0
x=4*sin(v)-cos(v)*4
y=4*cos(v)+sin(v)*4
z=0
x=5*sin(v)-cos(v)*4
y=5*cos(v)+sin(v)*4
z=0
x=6*sin(v)-cos(v)*4
y=6*cos(v)+sin(v)*4
z=0
min v= -10 max v= 10 steps= 20
min u= -10 max u= 10 steps= 20
x=1*sin(v)-cos(v)*4
y=1*cos(v)+sin(v)*4
z=0
x=2*cos(v)+sin(v)*4
y=2*sin(v)-cos(v)*4
z=0
x=3*cos(v)+sin(v)*4
y=3*sin(v)-cos(v)*4
z=0
x=4*sin(v)-cos(v)*4
y=4*cos(v)+sin(v)*4
z=0
x=5*sin(v)-cos(v)*4
y=5*cos(v)+sin(v)*4
z=0
x=6*sin(v)-cos(v)*4
y=6*cos(v)+sin(v)*4
z=0
min v= -10 max v= 10 steps= 20
min u= -10 max u= 10 steps= 20
Re: MAT 02 - Kriva u prostoru
3D GRAPHER
X=0.5*sin(v)-cos(v)*0.5; Y=0.5*cos(v)+sin(v)*0.5; Z=v
X=1*sin(v)-cos(v)*1; Y=1*cos(v)+sin(v)*1; Z=v
X=1.5*sin(v)-cos(v)*1.5; Y=1.5*cos(v)+sin(v)*1.5; Z=v
X=2*sin(v)-cos(v)*2; Y=2*cos(v)+sin(v)*2; Z=v
X=2.5*sin(v)-cos(v)*2.5; Y=2.5*cos(v)+sin(v)*2.5; Z=v
X=3*sin(v)-cos(v)*3; Y=3*cos(v)+sin(v)*3; Z=v
X=3.5*sin(v)-cos(v)*3.5; Y=3.5*cos(v)+sin(v)*3.5; Z=v
X=4*sin(v)-cos(v)*4; Y=4*cos(v)+sin(v)*4; Z=v
X=0.5*sin(v)-cos(v)*0.5; Y=0.5*cos(v)+sin(v)*0.5; Z=v
X=1*sin(v)-cos(v)*1; Y=1*cos(v)+sin(v)*1; Z=v
X=1.5*sin(v)-cos(v)*1.5; Y=1.5*cos(v)+sin(v)*1.5; Z=v
X=2*sin(v)-cos(v)*2; Y=2*cos(v)+sin(v)*2; Z=v
X=2.5*sin(v)-cos(v)*2.5; Y=2.5*cos(v)+sin(v)*2.5; Z=v
X=3*sin(v)-cos(v)*3; Y=3*cos(v)+sin(v)*3; Z=v
X=3.5*sin(v)-cos(v)*3.5; Y=3.5*cos(v)+sin(v)*3.5; Z=v
X=4*sin(v)-cos(v)*4; Y=4*cos(v)+sin(v)*4; Z=v
Re: MAT 02 - Kriva u prostoru
program je 3D math explorer
funkcije su:
fx=y*cos(a)
fy=y*sin(a)
fz=x
a=y*x
funkcije su:
fx=y*cos(a)
fy=y*sin(a)
fz=x
a=y*x
Re: MAT 02 - Kriva u prostoru
1.X=4*u*cos(2*u) Y=4*u*sin(2*u) Z=u*u
2.X=4*u*cos(2*u) Y=4*u*sin(2*u*)-5 Z=u*u
3.X=4*u*cos(2*u) Y=4*u*sin(2*u)-10 Z=u*u
4.X=4*u*cos(2*u) Y=4*u*sinj(2*u)+5 Z=u*u
koristla sam fun3d
Re: MAT 02 - Kriva u prostoru
Koriscen program: 3DMath
Funkcije:
fx:R*sin(a)*cos(b)*1/2;
fy:R*cos(a)*3;
fz:R*sin(a)*sin(b);
R=7;
Funkcije:
fx:R*sin(a)*cos(b)*1/2;
fy:R*cos(a)*3;
fz:R*sin(a)*sin(b);
R=7;
Odgovor: Re: MAT 02 - Kriva u prostoru
3D Grapher
x=cos(6*u)+sin(2*u)
y=sin(2*t)+cos(2*v)
z=sin(4*t)+cos(3*u)
x=cos(6*u)+sin(2*u)
y=sin(2*t)+cos(2*v)
z=sin(4*t)+cos(3*u)
Odgovor: Re: MAT 02 - Kriva u prostoru
3dMathExplorer
I funkcija: fx: tgt
fy: sin(2*t)+cos(2*t)
fz: t
v:t, s,e: -17,17, step: 0,05, red
II funkcija: fx: ctgt
fy: sin(3*t)*cos(t)
fz: t
v:t, s,e: -17,17, step: 0,1, silver
III funkcija: fx: tg3*t
fy: sin(2*t)*cos(t)
fz:t
v:t, s,e: -17,17, step: 0.1, gray
nadam se da je sad ok
I funkcija: fx: tgt
fy: sin(2*t)+cos(2*t)
fz: t
v:t, s,e: -17,17, step: 0,05, red
II funkcija: fx: ctgt
fy: sin(3*t)*cos(t)
fz: t
v:t, s,e: -17,17, step: 0,1, silver
III funkcija: fx: tg3*t
fy: sin(2*t)*cos(t)
fz:t
v:t, s,e: -17,17, step: 0.1, gray
nadam se da je sad ok
Re: MAT 02 - Kriva u prostoru
3d grapher
x=sin(v),y=cos(3*u),z=sin(3*v)+cos(2*u)
x=sin(2*u)+cos(v),y=sin(v),z=cos(3*v)
x=sin(u),y=sin(2*u),z=cos(2*v)
Odgovor: Re: MAT 02 - Kriva u prostoru
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: Odgovor: Re: MAT 02 - Kriva u prostoru
?
Odgovor: Re: Odgovor: Re: MAT 02 - Kriva u prostoru
u -30 30 0.5
fx=6*sin(u)+2*cos(u)
fy=2*cos(u)+8*sin(u)
fz=5*sin(u)
u -20 20 0.5
fx=5*sin(u)+3*cos(u)
fy=cos(u)+4*sin(u)
sin(u)
u -10 10 0.5
fx=10*sin(u)+cos(u)
fy=2*cos(u)+2*sin(u)
fz=4*cos(u)
u -40 40 0.5
fx=2*sin(u)+6*cos(u)
fy=7*cos(u)+3*sin(u)
fz=2*cos(u)
u -10 10 0.5
fx=3*sin(u)+cos(u)
fy=2*sin(u)+9*cos(u)
fz=1
Re: MAT 02 - Kriva u prostoru
X(u,v,t)=cos(u^2)+sin(v*3)
Y(u,v,t)=sin(u)*3+cos(v)*3
Z(u,v,t)=cos(u)^2-sin(v)*4
Y(u,v,t)=sin(u)*3+cos(v)*3
Z(u,v,t)=cos(u)^2-sin(v)*4
Re: MAT 02 - Kriva u prostoru
Function grapher
Odgovor: Re: MAT 02 - Kriva u prostoru
ispravljena kriva u prostoru
radjeno je u fun3du
model
X(u)=cos(u)
Y(u)=u
Z(u)=cos(u)
Maximum Umax Value 10
Maximum Umin Value 10
Minimum Umax value -10
Minumum Umin value -10
Step fpr Umax value 1
Step for Umin value 1
Umax 10
Umin -10
Udens 30
atana
X(u)=cos(u)
Y(u)=u
Z(u)=u
Maximum Umax Value 10
Maximum Umin Value 10
Minimum Umax value -10
Minumum Umin value -10
Step fpr Umax value 1
Step for Umin value 1
Umax 10
Umin -10
Udens 30
konj
X(u)=cos(u)
Y(u)=u
Z(u)=2u
Maximum Umax Value 10
Maximum Umin Value 10
Minimum Umax value -10
Minumum Umin value -10
Step fpr Umax value 1
Step for Umin value 1
Umax 10
Umin -10
Udens 30
nja
X(u)=-sin(u)
Y(u)=u
Z(u)=-2cos(u)
Maximum Umax Value 10
Maximum Umin Value 10
Minimum Umax value -10
Minumum Umin value -10
Step fpr Umax value 1
Step for Umin value 1
Umax 10
Umin -10
Udens 30
radjeno je u fun3du
model
X(u)=cos(u)
Y(u)=u
Z(u)=cos(u)
Maximum Umax Value 10
Maximum Umin Value 10
Minimum Umax value -10
Minumum Umin value -10
Step fpr Umax value 1
Step for Umin value 1
Umax 10
Umin -10
Udens 30
atana
X(u)=cos(u)
Y(u)=u
Z(u)=u
Maximum Umax Value 10
Maximum Umin Value 10
Minimum Umax value -10
Minumum Umin value -10
Step fpr Umax value 1
Step for Umin value 1
Umax 10
Umin -10
Udens 30
konj
X(u)=cos(u)
Y(u)=u
Z(u)=2u
Maximum Umax Value 10
Maximum Umin Value 10
Minimum Umax value -10
Minumum Umin value -10
Step fpr Umax value 1
Step for Umin value 1
Umax 10
Umin -10
Udens 30
nja
X(u)=-sin(u)
Y(u)=u
Z(u)=-2cos(u)
Maximum Umax Value 10
Maximum Umin Value 10
Minimum Umax value -10
Minumum Umin value -10
Step fpr Umax value 1
Step for Umin value 1
Umax 10
Umin -10
Udens 30
Re: MAT 02 - Kriva u prostoru
3D grapher
x=sin(v)
y=cos(3*u)
z=sin(3*v)+cos(2*u)
x=sin(v)
y=cos(3*u)
z=sin(3*v)+cos(2*u)
Re: MAT 02 - Kriva u prostoru
nadam se da je sada ok...
3d grapher
X=0.5*sin(v)-cos(v)*0.5; Y=0.5*cos(v)+sin(v)*0.5; Z=v
X=1.5*sin(v)-cos(v)*1.5; Y=1.5*cos(v)+sin(v)*1.5; Z=v
X=2.5*sin(v)-cos(v)*2.5; Y=2.5*cos(v)+sin(v)*2.5; Z=v
min x=-3, max x =3, steps=20
min y=-3, max y=3, steps 20
min t=-3, max t=3, steps 100
3d grapher
X=0.5*sin(v)-cos(v)*0.5; Y=0.5*cos(v)+sin(v)*0.5; Z=v
X=1.5*sin(v)-cos(v)*1.5; Y=1.5*cos(v)+sin(v)*1.5; Z=v
X=2.5*sin(v)-cos(v)*2.5; Y=2.5*cos(v)+sin(v)*2.5; Z=v
min x=-3, max x =3, steps=20
min y=-3, max y=3, steps 20
min t=-3, max t=3, steps 100
Re: MAT 02 - Kriva u prostoru
3D Grapher
Cartesian
X=cos(u)+sin(2*v)
Y=cos(v)+sin(2*t)
Z=cos(t)+sin(2*u)
Re: MAT 02 - Kriva u prostoru
Re: MAT 02 - Kriva u prostoru
3D GRAPHER
1)X=0.5*sin(v)-cos(v)*0.5; Y=v; Z=0.5*cos(v)+sin(v)*0.5
2)X=1*sin(v)-cos(v)*1; Y=v; Z=1*cos(v)+sin(v)*1
3)X=1.5*sin(v)-cos(v)*1.5; Y=v; Z=1.5*cos(v)+sin(v)*1.5
4)X=2*sin(v)-cos(v)*2; Y=v; Z=2*cos(v)+sin(v)*2
5)X=2.5*sin(v)-cos(v)*2.5; Y=v; Z=2.5*cos(v)+sin(v)*2.5
6)X=3*sin(v)-cos(v)*3; Y=v; Z=3*cos(v)+sin(v)*3;
7)X=3.5*sin(v)-cos(v)*3.5; Y=v; Z=3.5*cos(v)+sin(v)*3.5
8)X=4*sin(v)-cos(v)*4; Y=v; Z=4*cos(v)+sin(v)*4
minU=-10; maxU=10; steps=20
minV=-10; maxU=10; steps=20
1)X=0.5*sin(v)-cos(v)*0.5; Y=v; Z=0.5*cos(v)+sin(v)*0.5
2)X=1*sin(v)-cos(v)*1; Y=v; Z=1*cos(v)+sin(v)*1
3)X=1.5*sin(v)-cos(v)*1.5; Y=v; Z=1.5*cos(v)+sin(v)*1.5
4)X=2*sin(v)-cos(v)*2; Y=v; Z=2*cos(v)+sin(v)*2
5)X=2.5*sin(v)-cos(v)*2.5; Y=v; Z=2.5*cos(v)+sin(v)*2.5
6)X=3*sin(v)-cos(v)*3; Y=v; Z=3*cos(v)+sin(v)*3;
7)X=3.5*sin(v)-cos(v)*3.5; Y=v; Z=3.5*cos(v)+sin(v)*3.5
8)X=4*sin(v)-cos(v)*4; Y=v; Z=4*cos(v)+sin(v)*4
minU=-10; maxU=10; steps=20
minV=-10; maxU=10; steps=20
Re: MAT 02 - Kriva u prostoru
3D Grapher:Spherical
a(u,v,t)=5*u+sin(v)
b(u,v,t)=cos(v)*v
R(u,v,t)=0.3+sin(v*4+t)
a(u,v,t)=5*u+sin(v)
b(u,v,t)=cos(v)*v
R(u,v,t)=0.3+sin(v*4+t)
Odgovor: Re: MAT 02 - Kriva u prostoru
3D Math Explorer
fx = C*cos(a)*sin(sin(b))
fy = C*sin(a)*sin(sin(b))
fz = C*cos(sin(b))
C=2*a
Re: MAT 02 - Kriva u prostoru
1.cartesian
X=u Y=v Z=-(u^2+v^2) u=v=[-10,10] steps 50,50
2.cartesian
X=u Y=v Z=u^2*v^2 u=v=[-10,10] steps 50,50
X=u Y=v Z=-(u^2+v^2) u=v=[-10,10] steps 50,50
2.cartesian
X=u Y=v Z=u^2*v^2 u=v=[-10,10] steps 50,50
Re: MAT 02 - Kriva u prostoru
3D grapher
Coordinates-spherical
a=sin(t)+cos(t)*(u) b=sin(t)+cos(t)*(v) R=2;0;2;4
a=sin(t)+cos(t)*(u) b=sin(t)+cos(t)*(v) R=2;0;2;4
a=sin(t)+cos(t)*(u) b=sin(t)+cos(t)*(v) R=2;4;6;8
Coordinates-spherical
a=sin(t)+cos(t)*(u) b=sin(t)+cos(t)*(v) R=2;0;2;4
a=sin(t)+cos(t)*(u) b=sin(t)+cos(t)*(v) R=2;0;2;4
a=sin(t)+cos(t)*(u) b=sin(t)+cos(t)*(v) R=2;4;6;8
Re: MAT 02 - Kriva u prostoru
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Odgovor: Re: MAT 02 - Kriva u prostoru
3D Grapher
Coordinates: Cylindrical
a(u,v,t)=5*sin(2*u)-cos(2*u)
R(u,v,t)=5*sin(2*u)-cos(2*u)
Z(u,v,t)=u
a(u,v,t)=5*sin(2*u)-cos(2*u)
R(u,v,t)=5*sin(2*u)-cos(2*u)+3
Z(u,v,t)=u
a(u,v,t)=5*sin(2*u)-cos(2*u)
R(u,v,t)=5*sin(2*u)-cos(2*u)+5
Z(u,v,t)=u
Min U:-5 Max U:5 Steps:50
Min V:-5 Max V:5 Steps:50
P.S. Nadam se da je novi primer ispravan.
Odgovor: Re: MAT 02 - Kriva u prostoru
3D math explorer
parametri:
fx: 8*sin(t/2)*cos(t/5)
fy: cos(8*t)*(t-15)
fz: 8*cos(t/5)*cos(t/5)
i kriva:
parametri:
fx: 8*sin(t/2)*cos(t/5)
fy: cos(8*t)*(t-15)
fz: 8*cos(t/5)*cos(t/5)
i kriva:
Re: MAT 02 - Kriva u prostoru
FUN 3D
Re: MAT 02 - Kriva u prostoru
3D Grapher
X= cos(v); Y=sin(v); Z=v
X=sin(v)- cos(v); Y=sin(v)- cos(v); Z=v
X=sin(v)-2*cos(v); Y=sin(v)-2*cos(v); Z=v
X=sin(v)-3*cos(v); Y=sin(v)-3*cos(v); Z=v
X=sin(v)-4*cos(v); Y=sin(v)-4*cos(v); Z=v
X=sin(v)-5*cos(v); Y=sin(v)-5*cos(v); Z=v
Za sve v:
Min U=-10;Max U=10;Steps:20
Min V=-10;Max V=10;Steps:20
X= cos(v); Y=sin(v); Z=v
X=sin(v)- cos(v); Y=sin(v)- cos(v); Z=v
X=sin(v)-2*cos(v); Y=sin(v)-2*cos(v); Z=v
X=sin(v)-3*cos(v); Y=sin(v)-3*cos(v); Z=v
X=sin(v)-4*cos(v); Y=sin(v)-4*cos(v); Z=v
X=sin(v)-5*cos(v); Y=sin(v)-5*cos(v); Z=v
Za sve v:
Min U=-10;Max U=10;Steps:20
Min V=-10;Max V=10;Steps:20
Re: MAT 02 - Kriva u prostoru
3D grapher
x=sin(2*u)+cos(v)
y=sin(v)
z=cos(3*v)
x=sin(2*u)+cos(v)
y=sin(v)
z=cos(3*v)
Re: MAT 02 - Kriva u prostoru
???
Re: MAT 02 - Kriva u prostoru
3D Grapher
X = 8*cos(v)-sin(v)*8; Y = sin(v)+cos(v); Z = v
X = 7*cos(v)-sin(v)*7; Y = 2*sin(v)+cos(v); Z = v
X = 6*cos(v)-sin(v)*6; Y = 3*sin(v)+cos(v); Z = v
X = 5*cos(v)-sin(v)*5; Y = 4*sin(v)+cos(v); Z = v
X = 4*cos(v)-sin(v)*4; Y = 5*sin(v)+cos(v); Z = v
X = 3*cos(v)-sin(v)*3; Y = 6*sin(v)+cos(v); Z = v
X = 2*cos(v)-sin(v)*2; Y = 7*sin(v)+cos(v); Z = v
X = cos(v)-sin(v); Y = 8*sin(v)+cos(v); Z = v
Min U:-10 Max U:10 Steps:20
Min V:-10 Max V:10 Steps:20
X = 8*cos(v)-sin(v)*8; Y = sin(v)+cos(v); Z = v
X = 7*cos(v)-sin(v)*7; Y = 2*sin(v)+cos(v); Z = v
X = 6*cos(v)-sin(v)*6; Y = 3*sin(v)+cos(v); Z = v
X = 5*cos(v)-sin(v)*5; Y = 4*sin(v)+cos(v); Z = v
X = 4*cos(v)-sin(v)*4; Y = 5*sin(v)+cos(v); Z = v
X = 3*cos(v)-sin(v)*3; Y = 6*sin(v)+cos(v); Z = v
X = 2*cos(v)-sin(v)*2; Y = 7*sin(v)+cos(v); Z = v
X = cos(v)-sin(v); Y = 8*sin(v)+cos(v); Z = v
Min U:-10 Max U:10 Steps:20
Min V:-10 Max V:10 Steps:20
Re: MAT 02 - Kriva u prostoru
evo i mene kasnim 15 minuta xD
program 3D Grapher
X(u,v,t)= cos(v)+sin(v)
Y(u,v,t)= sin(3*u)+cos(u)
Z(u,v,t)= cos(2*u)+sin(v)
program 3D Grapher
X(u,v,t)= cos(v)+sin(v)
Y(u,v,t)= sin(3*u)+cos(u)
Z(u,v,t)= cos(2*u)+sin(v)
Re: MAT 02 - Kriva u prostoru
Coordinates: Spherical
a=cos(2*u)+cos(2*v)
b=sin(4*t)+sin(4*v)+sin(4*t)
R=tan(6*v)+tan(6*v)+tan(6*t)
Min U:-60(-50) Max U:20(50) Steps:30
Min V:-40(-50) Max V:20(50) Steps:20(30)
*iste funkcije samo se razlikuju po br,varijacija...
a=cos(2*u)+cos(2*v)
b=sin(4*t)+sin(4*v)+sin(4*t)
R=tan(6*v)+tan(6*v)+tan(6*t)
Min U:-60(-50) Max U:20(50) Steps:30
Min V:-40(-50) Max V:20(50) Steps:20(30)
*iste funkcije samo se razlikuju po br,varijacija...
Re: MAT 02 - Kriva u prostoru
3D Math Explorer
fx=7*sin(2.5*b)
fy=6*(1.5-cos(2*b))*cos(a)
fz=7*(0.5-sin(b))*sin(2*a)
fx=7*sin(2.5*b)
fy=6*(1.5-cos(2*b))*cos(a)
fz=7*(0.5-sin(b))*sin(2*a)
Re: MAT 02 - Kriva u prostoru
???
Re: MAT 02 - Kriva u prostoru
Nadam se da je ovo dobro:
Cartesian
1. X=v
Y=2*cos(u)*1.5*sin(v)
Z=1.5*sin(v)*u
2.X=v
Y=3*cos(u)*2*sin(v)
Z=sin(u)*v
3.X=v
Y=4*cos(u)*2.5*sin(v)
Z=cos(v)*1.5*u
4.X=v
Y=3.5*cos(u)*3*sin(v)
Z=1.5*cos(v)*1.5*u
5.X=v
Y=4.5*cos(u)*2.5*sin(2*v)
Z=cos(2*v)*2*u
Min U: -10 Max U: 10 steps: 20
Min V: -10 Max V: 10 steps: 20
Cartesian
1. X=v
Y=2*cos(u)*1.5*sin(v)
Z=1.5*sin(v)*u
2.X=v
Y=3*cos(u)*2*sin(v)
Z=sin(u)*v
3.X=v
Y=4*cos(u)*2.5*sin(v)
Z=cos(v)*1.5*u
4.X=v
Y=3.5*cos(u)*3*sin(v)
Z=1.5*cos(v)*1.5*u
5.X=v
Y=4.5*cos(u)*2.5*sin(2*v)
Z=cos(2*v)*2*u
Min U: -10 Max U: 10 steps: 20
Min V: -10 Max V: 10 steps: 20
Re: MAT 02 - Kriva u prostoru
t, 0, 35, 0.05
fx=x = 0.3 * t * t * cos(120*t)
fy=y = 0.3 * t * t * sin(120*t)
fz=z = 10*t
fx=x = 0.3 * t * t * cos(120*t)
fy=y = 0.3 * t * t * sin(120*t)
fz=z = 10*t
Re: MAT 02 - Kriva u prostoru
3d Grapher
X = 0.1*cos(v)+0.1*sin(v)+0.1; Y = 0.1*cos(v)-0.1*sin(v)-0.1 ; Z = v
X = 0.2*cos(v)+0.2*sin(v)+0.2; Y = 0.2*cos(v)-0.2*sin(v)-0.2 ; Z = v
X = 0.3*cos(v)+0.3*sin(v)+0.3; Y = 0.3*cos(v)-0.3*sin(v)-0.3 ; Z = v
X = 0.4*cos(v)+0.4*sin(v)+0.4; Y = 0.4*cos(v)-0.4*sin(v)-0.4; Z = v
X = 0.5*cos(v)+0.5*sin(v)+0.5; Y = 0.5*cos(v)-0.5*sin(v)-0.5 ; Z = v
X = 0.6*cos(v)+0.6*sin(v)+0.6; Y = 0.6*cos(v)-0.6*sin(v)-0.6 ; Z = v
X = 0.7*cos(v)+0.7*sin(v)+0.7; Y = 0.7*cos(v)-0.7*sin(v)-0.7 ; Z = v
X = 0.9*cos(v)+0.9*sin(v)+0.9; Y = 0.9*cos(v)-0.9*sin(v)-0.9 ; Z = v
X = 1.2*cos(v)+1.2*sin(v)+1.2; Y = 1.2*cos(v)-1.2*sin(v)- 1.2 ; Z = v
X = 1.7*cos(v)+1.7*sin(v)+1.2; Y = 1.7*cos(v)-1.7*sin(v)- 1.7 ; Z = v
X = 2.2*cos(v)+2.2*sin(v)+2.2; Y = 2.2*cos(v)-2.2*sin(v)- 2.2 ; Z = v
Granice za V su u svakoj od ovih funkcija :
Vmin = -10
Vmax = 10
Re: MAT 02 - Kriva u prostoru
fx=R*sin(a)+R*cos(2*t)
fy=R*cos(a)*2+sin(2*a)
fz=0
R=5*(sin(a)+cos(10*a))
fy=R*cos(a)*2+sin(2*a)
fz=0
R=5*(sin(a)+cos(10*a))
Odgovor: Re: MAT 02 - Kriva u prostoru
3D grapher
1)X=0.5*sin(v)-cos(v)*0.5; Y=v; Z=0.5*cos(v)+sin(v)*0.5
2)X=1*sin(v)-cos(v)*1; Y=v; Z=1*cos(v)+sin(v)*1
3)X=1.5*sin(v)-cos(v)*1.5; Y=v; Z=1.5*cos(v)+sin(v)*1.5
4)X=2*sin(v)-cos(v)*2; Y=v; Z=2*cos(v)+sin(v)*2
5)X=2.5*sin(v)-cos(v)*2.5; Y=v; Z=2.5*cos(v)+sin(v)*2.5
6)X=3*sin(v)-cos(v)*3; Y=v; Z=3*cos(v)+sin(v)*3;
7)X=3.5*sin(v)-cos(v)*3.5; Y=v; Z=3.5*cos(v)+sin(v)*3.5
8)X=4*sin(v)-cos(v)*4; Y=v; Z=4*cos(v)+sin(v)*4
minU=-10; maxU=10; steps=20
minV=-10; maxU=10; steps=20
1)X=0.5*sin(v)-cos(v)*0.5; Y=v; Z=0.5*cos(v)+sin(v)*0.5
2)X=1*sin(v)-cos(v)*1; Y=v; Z=1*cos(v)+sin(v)*1
3)X=1.5*sin(v)-cos(v)*1.5; Y=v; Z=1.5*cos(v)+sin(v)*1.5
4)X=2*sin(v)-cos(v)*2; Y=v; Z=2*cos(v)+sin(v)*2
5)X=2.5*sin(v)-cos(v)*2.5; Y=v; Z=2.5*cos(v)+sin(v)*2.5
6)X=3*sin(v)-cos(v)*3; Y=v; Z=3*cos(v)+sin(v)*3;
7)X=3.5*sin(v)-cos(v)*3.5; Y=v; Z=3.5*cos(v)+sin(v)*3.5
8)X=4*sin(v)-cos(v)*4; Y=v; Z=4*cos(v)+sin(v)*4
minU=-10; maxU=10; steps=20
minV=-10; maxU=10; steps=20
Re: MAT 02 - Kriva u prostoru
3D Grapher
a=v;R=cos(t);Z=0
a=v;R=2*cos(t);Z=1.5
a=v;R=2*cos(v)+2*cos(v);Z=3
a=v;R=4*cos(t);Z=4.5
a=v;R=2*cos(v)+2*cos(v));Z=3
a=v;R=2*cos(v)+2*cos(v));Z=-3
a=v;R=2*cos(t);Z=-1.5;
a=v;R=4*cos(t);Z=-4.5
a=v;R=cos(t);Z=0
a=v;R=2*cos(t);Z=1.5
a=v;R=2*cos(v)+2*cos(v);Z=3
a=v;R=4*cos(t);Z=4.5
a=v;R=2*cos(v)+2*cos(v));Z=3
a=v;R=2*cos(v)+2*cos(v));Z=-3
a=v;R=2*cos(t);Z=-1.5;
a=v;R=4*cos(t);Z=-4.5
Re: MAT 02 - Kriva u prostoru
3d grapher
x=0.5*u*cos(sqrt(u))
y=-0.4*u*sin(6*u)
z=sqrt(u)
min u: -20
max u: 20
step: 500
Re: MAT 02 - Kriva u prostoru
3D grapher
a=sin(u)
R=2*sin(u)*sin(v)
Z=v
minU=-10 maxU=10 Steps=10
minV=-10 naxV=10 Steps=20
svaki sledeci graph se razlikuje za parametar koji mnozi sinus
a=sin(u)
R=2*sin(u)*sin(v)
Z=v
minU=-10 maxU=10 Steps=10
minV=-10 naxV=10 Steps=20
svaki sledeci graph se razlikuje za parametar koji mnozi sinus
Odgovor: Re: MAT 02 - Kriva u prostoru
5*sin(t*500)
9*cos(900*t)
13*sin(130*t)
3*cos(30*t)
5*sin(54*t)
7*cos(78*t)
7*cos(t*7)
8*cos(8*t)
9*cos(9*t)
var t
start 5
end 200
step 40
karakus.
Re: MAT 02 - Kriva u prostoru
x=1.2*sin(v)-cos(v)*1,2; y=1.2*cos(v)+sin(v)*1.2; z=v
x=1.4*sin(v)-cos(v)*1.4; y=cos(v)*1.4+sin(v)*1.4; z=v
x=1.6*sin(v)-cos(v)*1.6; y=cos(v)*1.6+sin(v)*1.6; z=v
x=1.8*sin(v)-cos(v)*1.8; y=cos(v)*1.8+sin(v)*1.8; z=v
x=2*sin(v)-cos(v)*2; y=cos(v)*2+sin(v)*2; z=v
x=2.2*sin(v)-cos(v)*2.2; y=cos(v)*2.2+sin(v)*2.2; z=v
x=2.4*sin(v)-cos(v)*2.4; y=cos(v)*2.4+sin(v)*2.4; z=v
min U:-10; max U:10; steps:50
min V:-10; max V:10; steps:50
x=1.4*sin(v)-cos(v)*1.4; y=cos(v)*1.4+sin(v)*1.4; z=v
x=1.6*sin(v)-cos(v)*1.6; y=cos(v)*1.6+sin(v)*1.6; z=v
x=1.8*sin(v)-cos(v)*1.8; y=cos(v)*1.8+sin(v)*1.8; z=v
x=2*sin(v)-cos(v)*2; y=cos(v)*2+sin(v)*2; z=v
x=2.2*sin(v)-cos(v)*2.2; y=cos(v)*2.2+sin(v)*2.2; z=v
x=2.4*sin(v)-cos(v)*2.4; y=cos(v)*2.4+sin(v)*2.4; z=v
min U:-10; max U:10; steps:50
min V:-10; max V:10; steps:50
Re: MAT 02 - Kriva u prostoru
3D Grapher
1.
x=u+2
y=cos(3*v)
z=sin(3*v)+cos(t)
2.
x=u+1
y=cos(3*v)
z=sin(3*v)+cos(t)+1
1.
x=u+2
y=cos(3*v)
z=sin(3*v)+cos(t)
2.
x=u+1
y=cos(3*v)
z=sin(3*v)+cos(t)+1
Re: MAT 02 - Kriva u prostoru
fx=3*cos(t)-2*sin(5*t)
fy=3*sin(t)+2*cos(5*t)
fz=cos(t*6)
t 0 3*pi pi/100
fy=3*sin(t)+2*cos(5*t)
fz=cos(t*6)
t 0 3*pi pi/100
Re: MAT 02 - Kriva u prostoru
Ispravljeno:
Variable: a;
Start: -10;
End: 10;
Step: 0.1;
fx=3*cos(a*15);
fy=3*cos(a*3);
fz=a;
Variable: a;
Start: -10;
End: 10;
Step: 0.1;
fx=3*cos(a*15);
fy=3*cos(a*3);
fz=a;
Odgovor: Re: MAT 02 - Kriva u prostoru
3d grapher
x=25(log(u)+sin(2u))
y=2log(u)+5sin(u)
z=5cos(2u)
minU=-20 maxU=100
x=25(log(u)+sin(2u))
y=2log(u)+5sin(u)
z=5cos(2u)
minU=-20 maxU=100
Re: MAT 02 - Kriva u prostoru
X=sin(v)*cos(v); Y=sin(v)*cos(v); Z=sin(v);
X=3sin(v)*cos(v); Y=3sin(v)*cos(v); Z=sin(v);
X=5sin(v)*cos(v); Y=5sin(v)*cos(v); Z=5sin(v);
X=5cos(v)*sin(v) Y=5cos(v)*sin(v); Y=5cos(v);
X=5cos(v); Y=5cos(v)*sin(v); Z=5cos(v)*sin(v);
X=5cos(v); Y=5cos(v); Z=5cos(v)*sin(v);
X=3sin(v)*cos(v); Y=3sin(v)*cos(v); Z=sin(v);
X=5sin(v)*cos(v); Y=5sin(v)*cos(v); Z=5sin(v);
X=5cos(v)*sin(v) Y=5cos(v)*sin(v); Y=5cos(v);
X=5cos(v); Y=5cos(v)*sin(v); Z=5cos(v)*sin(v);
X=5cos(v); Y=5cos(v); Z=5cos(v)*sin(v);
Re: MAT 02 - Kriva u prostoru
3D GRAPHER
Prva funkcija
A=16*v
b=3*cos(v)
R=3*sin(t)+cos(v)
Druga funkcija
A=20*v
B=4*cos(v)
R=9*sin(t)+cos(v)
Prva funkcija
A=16*v
b=3*cos(v)
R=3*sin(t)+cos(v)
Druga funkcija
A=20*v
B=4*cos(v)
R=9*sin(t)+cos(v)
Re: MAT 02 - Kriva u prostoru
3D Graph
X=sin(2*u)+cos(v) Y=sin(2*u)*v Z=-2;0;2;4
X=sin(3*u)+cos(v) Y=sin(3*u)*v Z=3;0;-3;-4
X=sin(4*u)+cos(v) Y=sin(4*u)*v Z=-4;0;4;8
X=sin(5*u)+cos(v) Y=sin(5*u)*v Z=5;0;-5;-8
Min U= -10
Max U= 10
Steps: 20
X=sin(2*u)+cos(v) Y=sin(2*u)*v Z=-2;0;2;4
X=sin(3*u)+cos(v) Y=sin(3*u)*v Z=3;0;-3;-4
X=sin(4*u)+cos(v) Y=sin(4*u)*v Z=-4;0;4;8
X=sin(5*u)+cos(v) Y=sin(5*u)*v Z=5;0;-5;-8
Min U= -10
Max U= 10
Steps: 20
Re: MAT 02 - Kriva u prostoru
variable: a
start: -10
end: 10
step: 0.1
fx: 3*sin(a*10)
fy: 3*cos(a*10)
fz: a
start: -10
end: 10
step: 0.1
fx: 3*sin(a*10)
fy: 3*cos(a*10)
fz: a
Re: MAT 02 - Kriva u prostoru
x=2*sin(u)-cos(v)
y=4*cos(u)+3*sin(u)
z=u
min u=-5 max u=10 steps=25
min v=-7 max v=3 steps=30
x=6*cos(v)+6*sin(v)
y=1.5*cos(u)-0.5sin(v)
z=v
min u=-4 max u=11 steps=33
min v=-10 max v=13 steps=33
Re: MAT 02 - Kriva u prostoru
x=sin(u)*cos(u)*u*10
y=u*u
--------------
x=u*u
y=u
-----------
x=-u*u
y=u
Re: MAT 02 - Kriva u prostoru
PRIKAZ LINIJA U PROSTORU
3d grapher
cartesian
x=3*sin(v)+cos(v) ; y=6*sin(v)-cos(v) ; z=v
x=2*sin(v)+cos(v) ; y=4*sin(v)-cos(v) ; z=v
x=4*sih(v)+cos(v) ; y=8*sin(v)-cos(v) ; z=v
x=5*sin(v)+vos(v) ; y=10*sin(v)-cos(v) ; z=v
min U= -10 max U= 10 Steps=100
min V= -10 max V= 10 Steps=100
Re: MAT 02 - Kriva u prostoru
3D Math Explorer
---------------------------------
x=sin(u)
y=cos(u)
z=cos(U)/SIN(U)
Re: MAT 02 - Kriva u prostoru
X=2*sin(v)-cos(v)*2; Y=2*cos(v)+sin(v)*2; Z=v
X=2.3*sin(v)-cos(v)*2.3; Y=2.3*cos(v)+sin(v)*2.3; Z=v
X=2.5*sin(v)-cos(v)*2.5; Y=2.5*cos(v)+sin(v)*2.5; Z=v
X=2.8*sin(v)-cos(v)*2.8; Y=2.8*cos(v)+sin(v)*2.8; Z=v
X=3.1*sin(v)-cos(v)*3.1; Y=3.1*cos(v)+sin(v)*3.1; Z=v
X=3.4*sin(v)-cos(v)*3.4; Y=3.4*cos(v)+sin(v)*3.4; Z=v
X=3.7*sin(v)-cos(v)*3.7; Y=3.7*cos(v)+sin(v)*3.7; Z=v
Min U=-8, Max U=8, Steps=50;
Min V=-8, Max V=8, Steps=50;
Sve sam radio u 3D GRAPHER-u
izvinjavam se sto sam kasnio
X=2.3*sin(v)-cos(v)*2.3; Y=2.3*cos(v)+sin(v)*2.3; Z=v
X=2.5*sin(v)-cos(v)*2.5; Y=2.5*cos(v)+sin(v)*2.5; Z=v
X=2.8*sin(v)-cos(v)*2.8; Y=2.8*cos(v)+sin(v)*2.8; Z=v
X=3.1*sin(v)-cos(v)*3.1; Y=3.1*cos(v)+sin(v)*3.1; Z=v
X=3.4*sin(v)-cos(v)*3.4; Y=3.4*cos(v)+sin(v)*3.4; Z=v
X=3.7*sin(v)-cos(v)*3.7; Y=3.7*cos(v)+sin(v)*3.7; Z=v
Min U=-8, Max U=8, Steps=50;
Min V=-8, Max V=8, Steps=50;
Sve sam radio u 3D GRAPHER-u
izvinjavam se sto sam kasnio
Re: MAT 02 - Kriva u prostoru
3D GRAPHER
x=sin(u)+cos(u), y=sin(u)-cos(u), z=u
x=sin(2u)+cos(2u), y=sin(2u)-cos(2u), z=2u
x=sin(3u)+cos(3u), y=sin(3u)-cos(3u), z=3u
x=sin(4u)+cos(4u), y=sin(4u)-cos(4u), z=4u
x=sin(5u)+cos(5u), y=sin(5u)-cos(5u), z=5u
x=sin(6u)+cos(6u), y=sin(6u)-cos(6u), z=6u
x=sin(7u)+cos(7u), y=sin(7u)-cos(7u), z=7u
x=sin(8u)+cos(8u), y=sin(8u)-cos(8u), z=8u
x=sin(9u)+cos(9u), y=sin(9u)-cos(9u), z=9u
x=sin(10u)+cos(10u), y=sin(10u)-cos(10u), z=10u
umin=-10, umax=10
x=sin(u)+cos(u), y=sin(u)-cos(u), z=u
x=sin(2u)+cos(2u), y=sin(2u)-cos(2u), z=2u
x=sin(3u)+cos(3u), y=sin(3u)-cos(3u), z=3u
x=sin(4u)+cos(4u), y=sin(4u)-cos(4u), z=4u
x=sin(5u)+cos(5u), y=sin(5u)-cos(5u), z=5u
x=sin(6u)+cos(6u), y=sin(6u)-cos(6u), z=6u
x=sin(7u)+cos(7u), y=sin(7u)-cos(7u), z=7u
x=sin(8u)+cos(8u), y=sin(8u)-cos(8u), z=8u
x=sin(9u)+cos(9u), y=sin(9u)-cos(9u), z=9u
x=sin(10u)+cos(10u), y=sin(10u)-cos(10u), z=10u
umin=-10, umax=10
Re: MAT 02 - Kriva u prostoru
3d grapher:
spherical
a=2.8*sin(v)-cos(v)*2.8, b =2.8*cos(v)+sin(v)*2.8, r=u ;
a=4*sin(v)-cos(v)*4, b= 2.3*cos(v)+sin(v)*2.3, r = u ;
a=1.5*sin(v)-cos(v)*2; b= 1.5*cos(v)+sin(v)*2 ; r = u ;
max u,v= 6 ;min u,v= -2 , 20 steps
cylindrical
a=sin(v) ; r=u ; z=sin(3*v)+cos(2*u) ;
a=sin(t)+cos(t)*(u) ; r=sin(t)+cos(t)*(v); z=2;0;2;4;
max u,v= 10 ;min u,v= -10 , 20 steps
detalj:
spherical
a=2.8*sin(v)-cos(v)*2.8, b =2.8*cos(v)+sin(v)*2.8, r=u ;
a=4*sin(v)-cos(v)*4, b= 2.3*cos(v)+sin(v)*2.3, r = u ;
a=1.5*sin(v)-cos(v)*2; b= 1.5*cos(v)+sin(v)*2 ; r = u ;
max u,v= 6 ;min u,v= -2 , 20 steps
cylindrical
a=sin(v) ; r=u ; z=sin(3*v)+cos(2*u) ;
a=sin(t)+cos(t)*(u) ; r=sin(t)+cos(t)*(v); z=2;0;2;4;
max u,v= 10 ;min u,v= -10 , 20 steps
detalj:
Odgovor: Re: MAT 02 - Kriva u prostoru
X=0,5*sin(v)
Y=0,5*cos(v)+sin(v)*0.5
Z=v
minV=-100
maxV=100
steps=200
X=1*sin(v)-cos(v)*1
Y=1*cos(v)
Z=v
minV=-100
maxV=100
steps=200
Y=0,5*cos(v)+sin(v)*0.5
Z=v
minV=-100
maxV=100
steps=200
X=1*sin(v)-cos(v)*1
Y=1*cos(v)
Z=v
minV=-100
maxV=100
steps=200
Re: MAT 02 - Kriva u prostoru
3D Grapher
a=cos(u);r=4*sin(v+u)*cos(u);z=1;
min u=-6 max u=-4; min v=-6 max v=-4; steps20
a=cos(u);r=6*sin(v+u)*cos(u);z=0;
min u=-2 max u=0; min v=-2 max v=0; steps20
a=cos(u);r=8*sin(v+u)*cos(u);z=-1;
min u=0 max u=2; min v=0 max v=2; steps20
a=cos(u);r=10*sin(v+u)*cos(u);z=-2;
min u=2 max u=4; min v=2 max v=4; steps20
a=cos(u);r=12*sin(v+u)*cos(u);z=-3;
min u=4 max u=6; min v=4 max v=6; steps20
a=cos(u);r=14*sin(v+u)*cos(u);z=-4;
min u=6 max u=8; min v=6 max v=8; steps20
a=cos(u);r=16*sin(v+u)*cos(u);z=-5;
min u=8 max u=10; min v=8 max v=10; steps20
a=cos(u);r=18*sin(v+u)*cos(u);z=-6;
min u=10 max u=12; min v=10 max v=12; steps20
a=cos(u);r=20*sin(v+u)*cos(u);z=-7;
min u=12 max u=14; min v=12 max v=14; steps20
a=cos(u);r=22*sin(v+u)*cos(u);z=-8;
min u=14 max u=16; min v=14 max v=16; steps20
a=cos(u);r=4*sin(v+u)*cos(u);z=1;
min u=-6 max u=-4; min v=-6 max v=-4; steps20
a=cos(u);r=6*sin(v+u)*cos(u);z=0;
min u=-2 max u=0; min v=-2 max v=0; steps20
a=cos(u);r=8*sin(v+u)*cos(u);z=-1;
min u=0 max u=2; min v=0 max v=2; steps20
a=cos(u);r=10*sin(v+u)*cos(u);z=-2;
min u=2 max u=4; min v=2 max v=4; steps20
a=cos(u);r=12*sin(v+u)*cos(u);z=-3;
min u=4 max u=6; min v=4 max v=6; steps20
a=cos(u);r=14*sin(v+u)*cos(u);z=-4;
min u=6 max u=8; min v=6 max v=8; steps20
a=cos(u);r=16*sin(v+u)*cos(u);z=-5;
min u=8 max u=10; min v=8 max v=10; steps20
a=cos(u);r=18*sin(v+u)*cos(u);z=-6;
min u=10 max u=12; min v=10 max v=12; steps20
a=cos(u);r=20*sin(v+u)*cos(u);z=-7;
min u=12 max u=14; min v=12 max v=14; steps20
a=cos(u);r=22*sin(v+u)*cos(u);z=-8;
min u=14 max u=16; min v=14 max v=16; steps20
Re: MAT 02 - Kriva u prostoru
X=3*cos(u); Y=sin(2*u-t)+cos(2*u-t); Z=4*sin(u) minU=-5 maxU=5 steps 25
X=3.5*cos(u); Y=sin(2*u-t)+cos(2*u-t); Z=4.5*sin(u) minU=-5, maxU=5 steps 25
X=4*cos(u); Y=sin(2*u-t)+cos(2*u-t); Z=5*sin(u) minU=-10, maxU=10 steps 50
X=4.5*cos(1.5*u); Y=sin(2*u-t)+cos(2*u-t); Z=5.5*sin(1.5*u) minU=-10, maxU=10 steps 75
X=5*cos(1.6*u); Y=sin(2*u-t)+cos(2*u-t); Z=6*sin(1.6*u) minU=-10, maxU=10 steps 80
Re: MAT 02 - Kriva u prostoru
3D Math Explorer
t, od 0 do 2*pi, step=pi/50
fx= 4*cos(2*t)+cos(t)
fy= 8*sin(4*t)+sin(t)
fz= 4*cos(t)
Re: MAT 02 - Kriva u prostoru
Koristila sam 3DGrapher
a=v,R=cos(t),Z=1
a=v,R=2*cos(t),Z=0
a=v,R=2*cos(v)+2*cos(v),Z=3
a=v,R=-(2*cos(v)+2*cos(v)),Z=-3
a=v,R=-(3*cos(v)+2*cos(v)),Z=6
a=v,R=cos(t),Z=1
a=v,R=2*cos(t),Z=0
a=v,R=2*cos(v)+2*cos(v),Z=3
a=v,R=-(2*cos(v)+2*cos(v)),Z=-3
a=v,R=-(3*cos(v)+2*cos(v)),Z=6
Re: MAT 02 - Kriva u prostoru
3D grapher
sin(2*u)+cos(4*v)
cos(u)+sin(t)
cos(2*u)
cylindrical i cartesian
Re: MAT 02 - Kriva u prostoru
evo ga, kasnim a i nisam se najbolje snasla u izradi... nadam se da je koliko toliko dovoljno :/
3d grapher je u pitanju
3d grapher je u pitanju
Re: MAT 02 - Kriva u prostoru
1.X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Cartesian
X=0.5*sin(v)-cos(v)*0.5
Y=v
Z=0.5*cos(v)+sin(v)*0.5
U: [-6,6] (30)
V: [-6,6] (30)
X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Cartesian
X=1.5*sin(v)-cos(v)*1.5
Y=v
Z=1.5*cos(v)+sin(v)*1.5
U: [-6,6] (30)
V: [-6,6] (30)
X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Cartesian
X=2*sin(v)-cos(v)*2
Y=v
Z=2*cos(v)+sin(v)*2
U: [-6,6] (30)
V: [-6,6] (30)
X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Cartesian
X=3*sin(v)-cos(v)*3
Y=v
Z=3*cos(v)+sin(v)*3
U: [-6,6] (30)
V: [-6,6] (30)
X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
cartesian
X=4*sin(v)-cos(v)*4
Y=v
Z=4*cos(v)+sin(v)*4
U: [-6,6] (35)
V: [-6,6] (35)
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Cartesian
X=0.5*sin(v)-cos(v)*0.5
Y=v
Z=0.5*cos(v)+sin(v)*0.5
U: [-6,6] (30)
V: [-6,6] (30)
X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Cartesian
X=1.5*sin(v)-cos(v)*1.5
Y=v
Z=1.5*cos(v)+sin(v)*1.5
U: [-6,6] (30)
V: [-6,6] (30)
X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Cartesian
X=2*sin(v)-cos(v)*2
Y=v
Z=2*cos(v)+sin(v)*2
U: [-6,6] (30)
V: [-6,6] (30)
X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
Cartesian
X=3*sin(v)-cos(v)*3
Y=v
Z=3*cos(v)+sin(v)*3
U: [-6,6] (30)
V: [-6,6] (30)
X: [-10,10]
Y: [-10,10]
Z: [-10,10]
T: [0,0] (0)
cartesian
X=4*sin(v)-cos(v)*4
Y=v
Z=4*cos(v)+sin(v)*4
U: [-6,6] (35)
V: [-6,6] (35)
Re: MAT 02 - Kriva u prostoru
x=0.5*cos(v)-sin(v)*0.5, y=0.5*cos(v)-sin(v)*0.5, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=1*cos(v)-sin(v)*1, y=1*cos(v)-sin(v)*1, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=1.5*cos(v)-sin(v)*1.5, y=1.5*cos(v)-sin(v)*1.5, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=2*cos(v)-sin(v)*2, y=2*cos(v)-sin(v)*2, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=2.5*cos(v)-sin(v)*2.5, y=2.5*cos(v)-sin(v)*2.5, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=3*cos(v)-sin(v)*3, y=3*cos(v)-sin(v)*3, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=3.5*cos(v)-sin(v)*3.5, y=3.5*cos(v)-sin(v)*3.5, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=4*cos(v)-sin(v)*4, y=4*cos(v)-sin(v)*4, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=4.5*cos(v)-sin(v)*4.5, y=4.5*cos(v)-sin(v)*4.5, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=5*cos(v)-sin(v)*5, y=5*cos(v)-sin(v)*5, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=1*cos(v)-sin(v)*1, y=1*cos(v)-sin(v)*1, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=1.5*cos(v)-sin(v)*1.5, y=1.5*cos(v)-sin(v)*1.5, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=2*cos(v)-sin(v)*2, y=2*cos(v)-sin(v)*2, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=2.5*cos(v)-sin(v)*2.5, y=2.5*cos(v)-sin(v)*2.5, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=3*cos(v)-sin(v)*3, y=3*cos(v)-sin(v)*3, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=3.5*cos(v)-sin(v)*3.5, y=3.5*cos(v)-sin(v)*3.5, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=4*cos(v)-sin(v)*4, y=4*cos(v)-sin(v)*4, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=4.5*cos(v)-sin(v)*4.5, y=4.5*cos(v)-sin(v)*4.5, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
x=5*cos(v)-sin(v)*5, y=5*cos(v)-sin(v)*5, z=v minU=-10 MaxU=10 Steps=100 Minv=-10 MaxV=10 Steps=100
Re: MAT 02 - Kriva u prostoru
X=0.5*cos(u)-cos(u)*2; Y=0.5*sin(u)+sin(u)*2; Z=2*cos(u)
X=1*cos(u)-cos(u)*2.5; Y=1*sin(u)+sin(u)*2.5; Z=2.5*cos(u)
X=1.5*cos(u)-cos(u)*3; Y=1.5*sin(u)+sin(u)*3; Z=3*cos(u)
X=2*cos(u)-cos(u)*3.5; Y=2*sin(u)+sin(u)*3.5; Z=3.5*cos(u)
X=2.5*cos(u)-cos(u)*4; Y=2.5*sin(u)+sin(u)*4; Z=4*cos(u)
Min U=-3; Max U=3
Min V=-3; Max V=3
X=1*cos(u)-cos(u)*2.5; Y=1*sin(u)+sin(u)*2.5; Z=2.5*cos(u)
X=1.5*cos(u)-cos(u)*3; Y=1.5*sin(u)+sin(u)*3; Z=3*cos(u)
X=2*cos(u)-cos(u)*3.5; Y=2*sin(u)+sin(u)*3.5; Z=3.5*cos(u)
X=2.5*cos(u)-cos(u)*4; Y=2.5*sin(u)+sin(u)*4; Z=4*cos(u)
Min U=-3; Max U=3
Min V=-3; Max V=3
Re: MAT 02 - Kriva u prostoru
X(u,v,t)=2*u+cos(u)*0.5
Y(u,v,t)=sin(2*u)+1
Z(u,v,t)=cos(u/2)
a(u,v,t)=2*u+6*sin(u)-cos(u)*0.5
R(u,v,t)=4*cos(u)*sin(u/2)
Z(u,v,t)=1/2*sin(2*u)*u
X(u,v,t)=cos(4*u)*0.5
Y(u,v,t)=3*sin(u/2)*cos(u)
Z(u,v,t)=2*sin(2*u)/3*u
X(u,v,t)=cos(4*u)
Y(u,v,t)=7*cos(u)+u
Z(u,v,t)=sin(u/2)/5*u
Min U: -5 Max U: 5 Steps: 100
Min V: -5 Max V: 5 Steps: 100
Odgovor: Re: MAT 02 - Kriva u prostoru
Cylindrical
x=3*sin(u*6)
r=8*cos(u*t)
z=3*sin(u*t)
u(-10-10), 120
v(-10-10), 120
x=3*sin(u*6)
r=8*cos(u*t)
z=3*sin(u*t)
u(-10-10), 120
v(-10-10), 120
Odgovor: Re: MAT 02 - Kriva u prostoru
1. X=sin(u); Y=sin(u); Z=cos(u)
2. X=-sin(u)/2; Y=sin(u)/2; Z=-cos(u)
3. X=sin(u)*cos(u); Y=cos(u); Z=sin(u)
min u=-10; max u=10; steps=20
uradjeno u programu 3D grapher
2. X=-sin(u)/2; Y=sin(u)/2; Z=-cos(u)
3. X=sin(u)*cos(u); Y=cos(u); Z=sin(u)
min u=-10; max u=10; steps=20
uradjeno u programu 3D grapher
Odgovor: Re: MAT 02 - Kriva u prostoru
X=10*cos(v)-sin(v)*4, Y=sin(v)+cos(v), Z=v;
X=8*cos(v)-sin(v)*2, Y=sin(v)+cos(v), Z=v;
X=6*cos(v)-sin(v)*2, Y=sin(v)+cos(v), Z=v;
X=4*cos(v)-sin(v)*2, Y=sin(v)+cos(v), Z=v;
X=2*cos(v)-sin(v)*2, Y=sin(v)+cos(v), Z=v;
X=cos(v)-sin(v)*2, Y=sin(v)+cos(v), Z=v;
X=12*cos(v)-sin(v)*4, Y=2*sin(v)+cos(v), Z=v.
X=8*cos(v)-sin(v)*2, Y=sin(v)+cos(v), Z=v;
X=6*cos(v)-sin(v)*2, Y=sin(v)+cos(v), Z=v;
X=4*cos(v)-sin(v)*2, Y=sin(v)+cos(v), Z=v;
X=2*cos(v)-sin(v)*2, Y=sin(v)+cos(v), Z=v;
X=cos(v)-sin(v)*2, Y=sin(v)+cos(v), Z=v;
X=12*cos(v)-sin(v)*4, Y=2*sin(v)+cos(v), Z=v.
Odgovor: Re: MAT 02 - Kriva u prostoru
3D Grapher
cyilindrical
a(u,v,t)= sin(u)
R(u,v,t)=4*cos(u+t)-sin(u+v)
Z(u,v,t)=-1
min u: -10 max u: 10 steps: 20
min v: -10 max v: 10 steps: 20
cyilindrical
a(u,v,t)= sin(u)
R(u,v,t)=4*cos(u+t)-sin(u+v)
Z(u,v,t)=-1
min u: -10 max u: 10 steps: 20
min v: -10 max v: 10 steps: 20
Odgovor: Re: MAT 02 - Kriva u prostoru
a=v, R=cos(t), z=0;
a=v, R=1,2*cos(t), z=0;
a=v, R=2*cos(t), z=0;
a=v, R=1/2*cos(v)+1/2, z=1/2;
a=v, R=3*cos(t)+2*cos(v), z=2;
a=v, R=5*cos(t)+4*cos(v), z=4;
a=v, R=2/3*cos(t)+2/3*cos(v), z=2/3;
Min U=-10, Max U=10, Steps=20;
Min V=-10, Max V=10, Steps=20.
a=v, R=1,2*cos(t), z=0;
a=v, R=2*cos(t), z=0;
a=v, R=1/2*cos(v)+1/2, z=1/2;
a=v, R=3*cos(t)+2*cos(v), z=2;
a=v, R=5*cos(t)+4*cos(v), z=4;
a=v, R=2/3*cos(t)+2/3*cos(v), z=2/3;
Min U=-10, Max U=10, Steps=20;
Min V=-10, Max V=10, Steps=20.
Odgovor: Re: MAT 02 - Kriva u prostoru
3D GRAPHER
X=0.5*sin(v)-cos(v)*0.5; Y=0.5*cos(v)+sin(v)*0.5; Z=v
X=1*sin(v)-cos(v)*1; Y=1*cos(v)+sin(v)*1; Z=v
X=1.5*sin(v)-cos(v)*1.5; Y=1.5*cos(v)+sin(v)*1.5; Z=v
X=2*sin(v)-cos(v)*2; Y=2*cos(v)+sin(v)*2; Z=v
X=2.5*sin(v)-cos(v)*2.5; Y=2.5*cos(v)+sin(v)*2.5; Z=v
X=3*sin(v)-cos(v)*3; Y=3*cos(v)+sin(v)*3; Z=v
X=3.5*sin(v)-cos(v)*3.5; Y=3.5*cos(v)+sin(v)*3.5; Z=v
X=4*sin(v)-cos(v)*4; Y=4*cos(v)+sin(v)*4; Z=v
granice za v:
Min U=-3, Max U=3, Steps=20
Min V-3, Max V=3, Steps=20;
isto sa steps=100:
Re: MAT 02 - Kriva u prostoru
Program je 3D Grapher
coordinates: cylindrical
a(u,v,t)=sin(2*u)+cos(v)
R(u,v,t)=sin(2*u)*v
Z(u,v,t)=-2;0;2;4
coordinates: cylindrical
a(u,v,t)=sin(2*u)+cos(v)
R(u,v,t)=sin(2*u)*v
Z(u,v,t)=-2;0;2;4
Re: MAT 02 - Kriva u prostoru
3D Grapher
Re: MAT 02 - Kriva u prostoru
prva f-ja: sin(2*v)
sin(3*v)
sin(3*v)
druga f-ja: sin(2*v)
-sin(3*v)
sin(3*v)
Odgovor: MAT 02 - Kriva u prostoru
I funkcija: cos(5*v)
cos(3*v)
sin(3*v) + cos(v)
II funkcija: cos(5*v)
-cos(3*v)
sin(3*v) + cos(t)
III funkcija: sin(2*v)+cos(v)
sin(2*u)*v
sin(v)*cos(v)*5
Re: MAT 02 - Kriva u prostoru
3D Grapher
1. f-ja
sin(v)*cos(5*v)
cos(3*v) * 6
sin(3*v) + cos(v)
2. f-ja
sin(5*v)
-cos(3*v)
sin(3*v) + cos(t) + tan(v)
3. f-ja
sin(5*v)
cos(3*v)
sin(3*v) + cos(t) + tan(v)
Re: MAT 02 - Kriva u prostoru
3DMath Explorer
fx: R*cos(a)
fy: R*sin(a)
fz: (z-a)+z
R=(3+sin(9*a))*cos(z)
Odgovor: MAT 02 - Kriva u prostoru
evo mog rada...
Odgovor: MAT 02 - Kriva u prostoru
evo ispravke mog rada, ovaj prethodni se odnosio na ravan u prostoru, pa se izvinjavam zbog greske.....nadam se da je sada ok....to su sledece krive u prostoru:
variabila: t; od -12 do 12; step 0.1
fx: sin(t)+sin(t+1)
fy: 5*cos(t)
fz:t
variabila: x; od -12 do 12; step 0.1
fx: sin(x+1)*sin(x)
fy: 4*cos(x)
fz: x
variabila: v; od -12 do 12; step 0.1
fx: sin(v)*sin(v+1)
fy: 3*cos(v)
fz:v
variabila: m; od -12 do 12; step 0.1
fx: sin(m)*sin(m+1)
fy: cos(m)
fz: m
variabila: n; od -12 do 12; step 0.1
fx: sin(n)*sin(n+1)
fy: 2*cos(n)
fz: n
variabila: t; od -12 do 12; step 0.1
fx: sin(t)+sin(t+1)
fy: 5*cos(t)
fz:t
variabila: x; od -12 do 12; step 0.1
fx: sin(x+1)*sin(x)
fy: 4*cos(x)
fz: x
variabila: v; od -12 do 12; step 0.1
fx: sin(v)*sin(v+1)
fy: 3*cos(v)
fz:v
variabila: m; od -12 do 12; step 0.1
fx: sin(m)*sin(m+1)
fy: cos(m)
fz: m
variabila: n; od -12 do 12; step 0.1
fx: sin(n)*sin(n+1)
fy: 2*cos(n)
fz: n
Re: MAT 02 - Kriva u prostoru
1.cartesian
x=u y=v z=u^2+v^2 u.v [-1,1] steps 50,50
2.cartesian
x=u y=v z=u^2*v^2 u.v [-1,1] steps 50,50
3.cylindrical
x=u y=v -((u^2+v^2+t)^0.5) u.v [-1,1] steps 50,50
Re: MAT 02 - Kriva u prostoru
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=-2;0;2;4
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=2;0;-2;-4
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=-4;0;4;8
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=4;0;-4;-8
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=2;0;-2;-4
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=-4;0;4;8
X=sin(2*u)+cos(v); Y=sin(2*u)*v; Z=4;0;-4;-8
Odgovor: MAT 02 - Kriva u prostoru
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 y=v z=2*sin(v)-cos(v)*2
x=1.5*cos(v)+sin(v)*1.5 y=v z=1.5*sin(v)-cos(v)*1.5
x=1*cos(v)+sin(v)*1 y=v z=1*sin(v)-cos(v)*1
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 y=v z=2*sin(v)-cos(v)*2
x=1.5*cos(v)+sin(v)*1.5 y=v z=1.5*sin(v)-cos(v)*1.5
x=1*cos(v)+sin(v)*1 y=v z=1*sin(v)-cos(v)*1
Odgovor: MAT 02 - Kriva u prostoru
poboljsana varijanta :)
1. x=4*cos(v)+sin(v)*4 y=v z=4*sin(v)-cos(v)*4
2. x=3.5*cos(v)+sin(v)*3.5 y=v z=3.5*sin(v)-cos(v)*3.5
3. x=3*cos(v)+sin(v)*3 y=v z=3*sin(v)-cos(v)*3
4. x=2.5*cos(v)+sin(v)*2.5 y=v z=2.5*sin(v)-cos(v)*2.5
5. x=2*cos(v)+sin(v)*2 y=v z=2*sin(v)-cos(v)*2
6. x=1.5*cos(v)+sin(v)*1.5 y=v z=1.5*sin(v)-cos(v)*1.5
7. x=1*cos(v)+sin(v)*1 y=v z=1*sin(v)-cos(v)*1
vazi za sve:
minU=-10 maxU=10 steps=200
minV=-10 maxV=10 steps=200
1. x=4*cos(v)+sin(v)*4 y=v z=4*sin(v)-cos(v)*4
2. x=3.5*cos(v)+sin(v)*3.5 y=v z=3.5*sin(v)-cos(v)*3.5
3. x=3*cos(v)+sin(v)*3 y=v z=3*sin(v)-cos(v)*3
4. x=2.5*cos(v)+sin(v)*2.5 y=v z=2.5*sin(v)-cos(v)*2.5
5. x=2*cos(v)+sin(v)*2 y=v z=2*sin(v)-cos(v)*2
6. x=1.5*cos(v)+sin(v)*1.5 y=v z=1.5*sin(v)-cos(v)*1.5
7. x=1*cos(v)+sin(v)*1 y=v z=1*sin(v)-cos(v)*1
vazi za sve:
minU=-10 maxU=10 steps=200
minV=-10 maxV=10 steps=200
Re: MAT 02 - Kriva u prostoru
3d max explorer
fx:5*(1+cos(b))+b
fy:5*cos(a)*(1-sin(b))
fz:5*sin(a)*(1-sin(b))*(1+sin(b))
fx:5*(1+cos(b))+b
fy:5*cos(a)*(1-sin(b))
fz:5*sin(a)*(1-sin(b))*(1+sin(b))
Re: MAT 02 - Kriva u prostoru
X=sin(2*u)*v; Y=sin(2*u)+cos(v); Z=-3;0;3;6 -cartesian
X=sin(2*u)*v; Y=sin(2*u)+cos(v); Z=3;0;-3;6 -cartesian
X=sin(2*u)*v; Y=sin(2*u)+cos(v); Z=-6;0;6;12 - cartesian
X=sin(2*u)*v; Y=sin(2*u)+cos(v); Z=6;0;-6;12 -cartesian
X=sin(2*u)*v; Y=sin(2*u)+cos(v); Z=3;0;-3;6 -cartesian
X=sin(2*u)*v; Y=sin(2*u)+cos(v); Z=-6;0;6;12 - cartesian
X=sin(2*u)*v; Y=sin(2*u)+cos(v); Z=6;0;-6;12 -cartesian
Re: MAT 02 - Kriva u prostoru
Koristila sam 3D Max Explorer.
fx=R*cos(a)
fy=R*sin(a)
fz=(z*u)+(z-u)
R=(5+sin(4*a))
fx=R*cos(a)
fy=R*sin(a)
fz=(z*u)+(z-u)
R=(5+sin(4*a))
Re: MAT 02 - Kriva u prostoru
?
Re: MAT 02 - Kriva u prostoru
Ispravka:
3D Grapher
X=v; Y=0.5*sin(v)-cos(v)*0.5; Z=0.5*cos(v)+sin(v)*0.5
X=v; Y=1*sin(v)-cos(v)*1; Z=1*cos(v)+sin(v)*1
X=v; Y=2*sin(v)-cos(v)*2; Z=2*cos(v)+sin(v)*2
X=v; Y=2.5*sin(v)-cos(v)*2.5; Z=2.5*cos(v)+sin(v)*2.5
X=v; Y=3.5*sin(v)-cos(v)*3.5; Z=3.5*cos(v)+sin(v)*3.5
X=v:Y=4*sin(v)-cos(v)*4; Z=4*cos(v)+sin(v)*4
X=v:Y=4.5*sin(v)-cos(v)*4.5; Z=4.5*cos(v)+sin(v)*4.5
X=v:Y=5*sin(v)-cos(v)*5; Z=5*cos(v)+sin(v)*5
Min V:-10
Max V:10
Steps:20
3D Grapher
X=v; Y=0.5*sin(v)-cos(v)*0.5; Z=0.5*cos(v)+sin(v)*0.5
X=v; Y=1*sin(v)-cos(v)*1; Z=1*cos(v)+sin(v)*1
X=v; Y=2*sin(v)-cos(v)*2; Z=2*cos(v)+sin(v)*2
X=v; Y=2.5*sin(v)-cos(v)*2.5; Z=2.5*cos(v)+sin(v)*2.5
X=v; Y=3.5*sin(v)-cos(v)*3.5; Z=3.5*cos(v)+sin(v)*3.5
X=v:Y=4*sin(v)-cos(v)*4; Z=4*cos(v)+sin(v)*4
X=v:Y=4.5*sin(v)-cos(v)*4.5; Z=4.5*cos(v)+sin(v)*4.5
X=v:Y=5*sin(v)-cos(v)*5; Z=5*cos(v)+sin(v)*5
Min V:-10
Max V:10
Steps:20
Odgovor: MAT 02 - Kriva u prostoru
u pitanju je 3D GRAPHER...
I fumkcija koja se koristi je: a=0.5*sin(v)+0.5*cos(v); R=5*sin(v)+5*cos(v); Z=0.5*sin(v)+0.5*cos(v)
s tim sto se broj kod Z funkcije koji se mnozi sa sinusom i kosinusom u svakoj sledecoj funkciji povecava za 0.5... Ukupno ima 12 takvih funkcija...
Re: MAT 02 - Kriva u prostoru
3dfun
Re: MAT 02 - Kriva u prostoru
...
Re: MAT 02 - Kriva u prostoru
?
Re: MAT 02 - Kriva u prostoru
x:0.2*cos(v)+0.2*sin(v)+0.2, y:0.2*cos(v)-0.2*sin(v)-0.2, z:v
x:0.4*cos(v)+0.4*sin(v)+0.4, y:0.4*cos(v)-0.4*sin(v)-0.4, z:v
x:0.8*cos(v)+0.8*sin(v)+0.8, y0.8*cos(v)-0.8*sin(v)-0.8, z:v
x:1*cos(v)+1*sin(v)+1, y:1*cos(v)+1*sin(v)+1, z:v
x:1.2*cos(v)+1.2*sin(v)+1.2, y:1.2*cos(v)-1.2*sin(v)-1.2, z:v
x:1.4*cos(v)+1.4*sin(v)+1.4, y:1.4*cos(v)-1.4*sin(v)-1.4, z:v
x:1.8*cos(v)+1.8*sin(v)+1.8, y:1.8*cos(v)-1.8*sin(v)-1.8, z:v
x:2*cos(v)+2*sin(v)+2, y:2*cos(v)-2*sin(v)-2, z:v
x:2*cos(v)+2*sin(v)+2, y:2*cos(v)-2*sin(v)-2, z:v
minV:-10 maxV:10
Re: MAT 02 - Kriva u prostoru
Koristila sam 3D Math explorer...
Re: MAT 02 - Kriva u prostoru
Tek sam sad videla da nisam upisala parametre... Evo ih sada:
f(x)=x*sin(a)
f( y )=(2*x^2+4*x-16)/(x^2+2*x-3)
f(z)=x*cos(a)
x: start 0, end 15, step 0.4
y: start 0, end 2*pi, step 0.2
f(x)=x*sin(a)
f( y )=(2*x^2+4*x-16)/(x^2+2*x-3)
f(z)=x*cos(a)
x: start 0, end 15, step 0.4
y: start 0, end 2*pi, step 0.2
Re: MAT 02 - Kriva u prostoru
?
Re: MAT 02 - Kriva u prostoru
- 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; y=v; z=2*sin(v)-cos(v)*2
- x=1.5*cos(v)+sin(v)*1.5; y=v; z=1.5*sin(v)-cos(v)*1.5
- x=cos(v)+sin(v); y=v; z=sin(v)-cos(v)
minU=-10; maxU=10; Steps=200
minV=-10; maxU=10; Steps=200
Re: MAT 02 - Kriva u prostoru
Program je 3D Grapher
coordinates: cylindrical
a(u,v,t)=sin(2*u)+cos(v)
R(u,v,t)=sin(2*u)*v
Z(u,v,t)=-2;0;2;4
Re: MAT 02 - Kriva u prostoru
3D Grapher
Coordinates: Cylindrical
a= 4*sin(u)
R= v
Z= sin(u)+cos(45)*cos(u)
Min U: -10 Max U: 10 Steps: 10
Min V: -10 Max V: 10 Steps: 20
Coordinates: Cylindrical
a= sin(-u)
R= sin(v)*sin(u)
Z= v
Min U: -10 Max U: 10 Steps: 14
Min V: -10 Max V: 10 Steps: 8
Re: MAT 02 - Kriva u prostoru
3d grapher
cilindrical
a=5*u+sin(v)
R=cos(u)*v
Z=0.02+sin(v*4+t)
cilindrical
a=5*u+sin(v)
R=cos(u)*v
Z=0.02+sin(v*4+t)
Re: MAT 02 - Kriva u prostoru
?
Re: MAT 02 - Kriva u prostoru
tabela
X= sin(u)+cos(u*u) Y= cos(u*u)-sin(u) Z= u*u
X= 2.5*sin(u)+cos(u*u)*2.5 Y= 2.5*cos(u*u)-sin(u)*2.5 Z= u*u
X= 3.5*sin(u)+cos(u*u)*3.5 Y= 3.5*cos(u*u)-sin(u)*3.5 Z= u*u
X= 4*sin(u)+cos(u*u)*4 Y= 4*cos(u*u)-sin(u)*4 Z= u*u
X= 4.1*sin(u)+cos(u*u)*4.1 Y= 4.1*cos(u*u)-sin(u)* 4.1 Z= u*u
X= 4.2*sin(u)+cos(u*u)*4.2 Y= 4.2*cos(u*u)-sin(u)*4.2 Z= u*u
X= 4.3*sin(u)+cos(u*u)*4.3 Y= 4.3*cos(u*u)-sin(u)*4.3 Z= u*u
X= 4.4*sin(u)+cos(u*u)*4.4 Y= 4.4*cos(u*u)-sin(u)*4.4 Z= u*u
X= 4.5*sin(u)+cos(u*u)*4.5 Y= 4.5*cos(u*u)-sin(u)*4.5 Z= u*u
X= 5*sin(u)+cos(u*u)*5 Y= 5*cos(u*u)-sin(u)*5 Z= u*u
X= 6*sin(u)+cos(u*u)*6 Y= 6*cos(u*u)-sin(u)*6 Z= u*u
Min U= -7 Max U= 7 Steps= 30
Min V= -7 Max V= 7 Steps= 30
i prostorna slika :)
X= sin(u)+cos(u*u) Y= cos(u*u)-sin(u) Z= u*u
X= 2.5*sin(u)+cos(u*u)*2.5 Y= 2.5*cos(u*u)-sin(u)*2.5 Z= u*u
X= 3.5*sin(u)+cos(u*u)*3.5 Y= 3.5*cos(u*u)-sin(u)*3.5 Z= u*u
X= 4*sin(u)+cos(u*u)*4 Y= 4*cos(u*u)-sin(u)*4 Z= u*u
X= 4.1*sin(u)+cos(u*u)*4.1 Y= 4.1*cos(u*u)-sin(u)* 4.1 Z= u*u
X= 4.2*sin(u)+cos(u*u)*4.2 Y= 4.2*cos(u*u)-sin(u)*4.2 Z= u*u
X= 4.3*sin(u)+cos(u*u)*4.3 Y= 4.3*cos(u*u)-sin(u)*4.3 Z= u*u
X= 4.4*sin(u)+cos(u*u)*4.4 Y= 4.4*cos(u*u)-sin(u)*4.4 Z= u*u
X= 4.5*sin(u)+cos(u*u)*4.5 Y= 4.5*cos(u*u)-sin(u)*4.5 Z= u*u
X= 5*sin(u)+cos(u*u)*5 Y= 5*cos(u*u)-sin(u)*5 Z= u*u
X= 6*sin(u)+cos(u*u)*6 Y= 6*cos(u*u)-sin(u)*6 Z= u*u
Min U= -7 Max U= 7 Steps= 30
Min V= -7 Max V= 7 Steps= 30
i prostorna slika :)
Re: MAT 02 - Kriva u prostoru
Radjeno u 3d math-u.
variable: x; start: -15; end: 15; step: 0,01
fx: cos(x+1)
fy: sin(x+1-1)
fz: x
variable: x; start: -15; end: 15; step: 0,01
fx: cos(x+1)
fy: sin(x+1-1)
fz: x
Odgovor: MAT 02 - Kriva u prostoru
3D Grapher
Odgovor: MAT 02 - Kriva u prostoru
3D Grapher
1.a=cos(5*v)
b=-cos(3*v)
R=sin(3*v)+cos(t)
2.X=sin(2*v)
Y=sin(3*v)
Z=sin(9*v)
3.X=9*sin(v)*sin(v)
Y=5*sin(v)
Z=4*sin(v)*cos(v)
1.a=cos(5*v)
b=-cos(3*v)
R=sin(3*v)+cos(t)
2.X=sin(2*v)
Y=sin(3*v)
Z=sin(9*v)
3.X=9*sin(v)*sin(v)
Y=5*sin(v)
Z=4*sin(v)*cos(v)
Odgovor: MAT 02 - Kriva u prostoru
1.X=4*sin(v)-cos(v)*4
Y=3.5*cos(v)+sin(v)*3.5
Z=v
Min V=-5;Max V=5;steps=20
2.X=2*sin(v)-cos(v)*2
Y=2*cos(v)+sin(v)*2
Z=v
Min V=-11;Max V=11
3.X=3.5*sin(v)-cos(v)*3.5
Y=2.5*cos(v)+sin(v)*2.5
Z=v
Min V=-10;Max V=10;Steps=20
4.X=4*sin(v)-cos(v)*3
Y=4*cos(v)+sin(v)*3
Z=v
Min V=-10;Max V=10;Steps=20
Y=3.5*cos(v)+sin(v)*3.5
Z=v
Min V=-5;Max V=5;steps=20
2.X=2*sin(v)-cos(v)*2
Y=2*cos(v)+sin(v)*2
Z=v
Min V=-11;Max V=11
3.X=3.5*sin(v)-cos(v)*3.5
Y=2.5*cos(v)+sin(v)*2.5
Z=v
Min V=-10;Max V=10;Steps=20
4.X=4*sin(v)-cos(v)*3
Y=4*cos(v)+sin(v)*3
Z=v
Min V=-10;Max V=10;Steps=20
Re: MAT 02 - Kriva u prostoru
3d math explorer
x=10*cos(b)+2*sin(b)+cos(a)
y=11+cos(a)*sin(b)
z=11*sin(a)*sin(b)
Re: MAT 02 - Kriva u prostoru
3D Math Explorer
fx:cos(t)+sin(90*t)-4*cos(t)
fy:cos(2*t)+0.5*(t)+sin(t)
fz:sin(t)+cos(12*t)+cos(t)
variable start end step
t 0 2*pi pi/90
a 0 2*pi pi/10
fx:cos(t)+sin(90*t)-4*cos(t)
fy:cos(2*t)+0.5*(t)+sin(t)
fz:sin(t)+cos(12*t)+cos(t)
variable start end step
t 0 2*pi pi/90
a 0 2*pi pi/10
Re: MAT 02 - Kriva u prostoru
a=v
r=sin(u)
z=u
Min U= -10
min V= -10
Max U= 10
Max V= 10
Steps=20
Steps=20
Program je 3d grapher
r=sin(u)
z=u
Min U= -10
min V= -10
Max U= 10
Max V= 10
Steps=20
Steps=20
Program je 3d grapher
Re: MAT 02 - Kriva u prostoru
varijabila start end step
v -4, 12, 0.1
1.3*cos(3*v)
1.3*sin(3*v)
5*v
varijabila start end step
u -8, 100, 0,1
5*sin(u)
5*cos(u)
2.2*u
varijabila start end step
t -7, 32, 0,1
2*sin(4*t)
2*cos(4*t)
5*t
v -4, 12, 0.1
1.3*cos(3*v)
1.3*sin(3*v)
5*v
varijabila start end step
u -8, 100, 0,1
5*sin(u)
5*cos(u)
2.2*u
varijabila start end step
t -7, 32, 0,1
2*sin(4*t)
2*cos(4*t)
5*t
Re: MAT 02 - Kriva u prostoru
1:v- t, s-0 ,e-10, s-0.3, fx-3*sin(t,) fy- 3*cos(t), fz-3
2: v-t ,s- 0, e-10, s- 0.3, fx-4*sin(t), fy- 4*cos(t), fz- 4
3: v-t ,s- 0 ,e-10 ,s- 0.3, fx- 5*sin(t), fy- 5*cos(t), fz- 5
4:v- t, s-0, e-10, s- 0.3, fx- 6*sin(t), fy-6*cos(t), fz- 6
5: v-t, s-0, e-10, s- 0.3, fx-2*sin(t), fy- 2*cos(t), fz- 2
6: v-t, s--15, e- 15, s- 0.2, fx-tgt, fy- sin(s*t(+cos(2*t), fz-t
Re: MAT 02 - Kriva u prostoru
1:v- t, s--15 ,e-15, s-0.2, fx-tgt, fy- sin(2*t)+cos(2*t), fz-t
2: v-t ,s--15, e-15, s- 0.2, fx-ctg, fy- 2*(sin(4*t)+cos(4*t)), fz-t
3: v-t ,s--15 ,e-15 ,s- 0.5, fx- 3*(sin(5*t)+cos(5*t), fy- tgt, fz- t
Re: MAT 02 - Kriva u prostoru
1.X=0.1*cos(v)+0.1*sin(v)+0.1
Y=0.2*cos(v)-0.2*sin(v)-0.2
Z=v
Min V=-10;Max V=15;Steps=200
2. X= 1.7*cos(v)+1.7*sin(v)+1.2
Y= 2.2*cos(v)-2.2*sin(v)- 2.2
Z=v
Min V=-10;Max V=10;Steps=200
3.X=5*sin(u)
Y=5*cos(u)
Z=2.2*u
Min U=-10;Max U+10;Steps=200
4.X=1.3*cos(3*v)
Y=1.3*sin(3*v)
Z=5*v
Min V=-10;Max V=10;Steps=200
Y=0.2*cos(v)-0.2*sin(v)-0.2
Z=v
Min V=-10;Max V=15;Steps=200
2. X= 1.7*cos(v)+1.7*sin(v)+1.2
Y= 2.2*cos(v)-2.2*sin(v)- 2.2
Z=v
Min V=-10;Max V=10;Steps=200
3.X=5*sin(u)
Y=5*cos(u)
Z=2.2*u
Min U=-10;Max U+10;Steps=200
4.X=1.3*cos(3*v)
Y=1.3*sin(3*v)
Z=5*v
Min V=-10;Max V=10;Steps=200
Odgovor: MAT 02 - Kriva u prostoru
3D GRAPHER
I funkcija> x=u; y=v; z=sin((u*4+v*2)*0.70)*2
II funkcija> x=u; y=v; z=2*sin((u*4+v*2)*0.70)*2
III funkcija> x=u; y=v; z=-sin((u*4+v*2)*0.70)*2
u,v(-1, 1)
steps: 20
I funkcija> x=u; y=v; z=sin((u*4+v*2)*0.70)*2
II funkcija> x=u; y=v; z=2*sin((u*4+v*2)*0.70)*2
III funkcija> x=u; y=v; z=-sin((u*4+v*2)*0.70)*2
u,v(-1, 1)
steps: 20
Re: MAT 02 - Kriva u prostoru
3d grapher
coordinates: cylindrical
a=t
r=sin(u)
z=v
min u=10 max u=10 steps=20
min u=10 max u=10 steps=20
nisam bila u mogucnosti par dana da okacim, jer nije radio sajt... ne znam zbog cega... :(
coordinates: cylindrical
a=t
r=sin(u)
z=v
min u=10 max u=10 steps=20
min u=10 max u=10 steps=20
nisam bila u mogucnosti par dana da okacim, jer nije radio sajt... ne znam zbog cega... :(
Re: MAT 02 - Kriva u prostoru
X(u)=u*sin(u)-cos(u)
Y(u)=u*cos(u)
Z(u)=u
Umax=10
Umin=-10
Step for Umax=2
Step for Umin=1
Potoji 6 funkcija cije su formule date.
Menjana je pozicija X,Y,Z za po jedan, da bi se dobila ovakva kompozicija...
Nadam se da cete da oprostite kasnjenje, posto sam bila u Parizu...
Y(u)=u*cos(u)
Z(u)=u
Umax=10
Umin=-10
Step for Umax=2
Step for Umin=1
Potoji 6 funkcija cije su formule date.
Menjana je pozicija X,Y,Z za po jedan, da bi se dobila ovakva kompozicija...
Nadam se da cete da oprostite kasnjenje, posto sam bila u Parizu...
Odgovor: Re: MAT 02 - Kriva u prostoru
Cartesian
X=0.5*sin(v)-cos(v)*0.5
Y=0.5*cos(v)+sin(v)*0.5
Z=v
U: [-3,3] (200)
V: [-3,3] (200)
Cartesian
X=4*sin(v)-cos(v)*2
Y=2*cos(v)+sin(v)*2
Z=2*cos(v)+sin(v)*2
U: [-3,3] (20)
V: [-3,3] (20)
X=0.1*cos(v)+0.1*sin(v)+0.1
Y=0.1*cos(v)-0.1*sin(v)-0.1
Z=v
U: [-10,10] (20)
V: [-10,10] (20)
Cartesian
X=0.9*cos(v)+0.9*sin(v)+0.9
Y=0.9*cos(v)-0.9*sin(v)-0.9
Z=v
U: [-10,10] (20)
V: [-10,10] (20)
Cartesian
X=0.9*cos(v)-0.9*sin(v)-0.9
Y=0.9*cos(v)+0.9*sin(v)+0.9
Z=v
U: [-10,10] (20)
V: [-10,10] (20)
Cartesian
X=3.5*sin(v)-cos(v)*3.5
Y=v
Z=3.5*cos(v)+sin(v)*3.
U: [-10,10] (20)
V: [-10,10] (20)
X=0.5*sin(v)-cos(v)*0.5
Y=0.5*cos(v)+sin(v)*0.5
Z=v
U: [-3,3] (200)
V: [-3,3] (200)
Cartesian
X=4*sin(v)-cos(v)*2
Y=2*cos(v)+sin(v)*2
Z=2*cos(v)+sin(v)*2
U: [-3,3] (20)
V: [-3,3] (20)
X=0.1*cos(v)+0.1*sin(v)+0.1
Y=0.1*cos(v)-0.1*sin(v)-0.1
Z=v
U: [-10,10] (20)
V: [-10,10] (20)
Cartesian
X=0.9*cos(v)+0.9*sin(v)+0.9
Y=0.9*cos(v)-0.9*sin(v)-0.9
Z=v
U: [-10,10] (20)
V: [-10,10] (20)
Cartesian
X=0.9*cos(v)-0.9*sin(v)-0.9
Y=0.9*cos(v)+0.9*sin(v)+0.9
Z=v
U: [-10,10] (20)
V: [-10,10] (20)
Cartesian
X=3.5*sin(v)-cos(v)*3.5
Y=v
Z=3.5*cos(v)+sin(v)*3.
U: [-10,10] (20)
V: [-10,10] (20)
Re: MAT 02 - Kriva u prostoru
3D MATH EXPLORER
Variable:t
Start:-11
End:11
Step:0.2
f(x): 7*cos(t)/sin(3*t);
f(y): 6*sin(t)/cos(3*t);
f(z): 5-cos(t)/sin(t);
3/sin(t)/cos(t);
cos(5*t)/sin(t);
sin(t)/cos(2*t);
Variable:t
Start:-11
End:11
Step:0.2
f(x): 7*cos(t)/sin(3*t);
f(y): 6*sin(t)/cos(3*t);
f(z): 5-cos(t)/sin(t);
3/sin(t)/cos(t);
cos(5*t)/sin(t);
sin(t)/cos(2*t);
Re: MAT 02 - Kriva u prostoru
t;-15,15;0.05;red
fx:ctgt, fy:sin(2*t)+sin(4*t), fz:t
t;-10,10;0.1;silver
fx:ctgt, fy:cos(2*t)+cos(4*t), fy:t
t;-15,15;0.1;teal
fx:t, fy:cos(2*t)*sin(2*t), fz:cos(4*t)+cos(2*t)
t;-20,20;0.05;silver
fx:t, fy:sin(2*t)*sin(4*t), fz:cos(2*t)
t;-15,15;0.1;maroon
fx:cos(4*t), fy:t, fz:sin(2*t)+sin(4*t)
t;-15,15;0.05;teal
fx:sin(4*t)+sin(2*t), fy:t, fz:cos(2*t)*cos(4*t)
t;-15,15;0.05;red
fx:t, fy:cos(2*t)*cos(2*t), sin(2*t)
t;-20,20;0.05;silver
fx:sin(4*t)*sin(4*t), fy:t, fz:sin(2*t)*cos(4*t)
t;-15,15;0.1;teal
fx:sin(2*t)*cos(2*t), fy:sin(4*t), fz:t
Re: MAT 02 - Kriva u prostoru
cylindrical
a=v
R=sin(U)*sin(v)*u
Z=v
min U= -10 max U=10 steps=30
min U= -10 max U=10 steps=30
a=v
R=sin(U)*sin(v)*u
Z=v
min U= -10 max U=10 steps=30
min U= -10 max U=10 steps=30
Re: MAT 02 - Kriva u prostoru
3D Grapher
X(u,v,t)=sin(1*u)+cos(v); sin(1*u)+cos(v); sin(1*u)+cos(v); sin(3*u)+cos(v); sin(3*v)*cos(v)
Y(u,v,t)=sin(1*u)*v; sin(1*u)*v; sin(3*u)*v; sin(3*u)*v; sin(3*v)*cos(v)*u
Z(u,v,t)=-2;0;2;4; 3;0;-3;-4; -4;0;4;8;5;0 ;-5;-8;2; -5;6;5
Min U: -10
Max U: 10
Steps: 20
Steps: 20
X(u,v,t)=sin(1*u)+cos(v); sin(1*u)+cos(v); sin(1*u)+cos(v); sin(3*u)+cos(v); sin(3*v)*cos(v)
Y(u,v,t)=sin(1*u)*v; sin(1*u)*v; sin(3*u)*v; sin(3*u)*v; sin(3*v)*cos(v)*u
Z(u,v,t)=-2;0;2;4; 3;0;-3;-4; -4;0;4;8;5;0 ;-5;-8;2; -5;6;5
Min U: -10
Max U: 10
Steps: 20
Steps: 20
Re: MAT 02 - Kriva u prostoru
3D Grapher
a(u,v,t): v; v; sin(2*u)+cos(v); v*u; v*u;
R(u,v,t): sin(u)*cos(v)*0.5; sin(u)*cos(v)*1; sin(2*u)*v; sin(u)*cos(v)*0.10; sin(u)*1;
Z(u,v,t): u*2; u*3; 2;0;2;4; u*4; v
Min U: -10
Max U: 10
Steps: 20
Steps: 20
a(u,v,t): v; v; sin(2*u)+cos(v); v*u; v*u;
R(u,v,t): sin(u)*cos(v)*0.5; sin(u)*cos(v)*1; sin(2*u)*v; sin(u)*cos(v)*0.10; sin(u)*1;
Z(u,v,t): u*2; u*3; 2;0;2;4; u*4; v
Min U: -10
Max U: 10
Steps: 20
Steps: 20
Re: MAT 02 - Kriva u prostoru
X=1*sin(v)-cos(v)*0.5 ; Y=1*cos(v)+sin(v)*0.5 ; Z=v
X=1*sin(v)-cos(v)*2 ; Y=1*cos(v)+sin(v)*2 ; Z=v
X=1*sin(v)-cos(v)*3 ; Y=1*cos(v)+sin(v)*3 ; Z=v
X=4*sin(v)-cos(v)*2 ; Y=4*cos(v)+sin(v)*2 ; Z=v
X=4*sin(v)-cos(v)*3 ; Y=4*cos(v)+sin(v)*3 ; Z=v
X=6*sin(v)-cos(v)*3 ; Y=6*cos(v)+sin(v)*3 ; Z=v
X=6*sin(v)-cos(v)*4 ; Y=6*cos(v)+sin(v)*4 ; Z=v
X=8*sin(v)-cos(v)*3 ; Y=8*cos(v)+sin(v)*3 ; Z=v
X=8*sin(v)-cos(v)*4 ; Y=8*cos(v)+sin(v)*4 ; Z=v
min U: -10 max U: 10 steps: 20
min V: -10 max V: 10 steps: 20
program je 3D Grapher
primer osnove i 3d projekcije...izvinjavam se na kasnjenju...
X=1*sin(v)-cos(v)*2 ; Y=1*cos(v)+sin(v)*2 ; Z=v
X=1*sin(v)-cos(v)*3 ; Y=1*cos(v)+sin(v)*3 ; Z=v
X=4*sin(v)-cos(v)*2 ; Y=4*cos(v)+sin(v)*2 ; Z=v
X=4*sin(v)-cos(v)*3 ; Y=4*cos(v)+sin(v)*3 ; Z=v
X=6*sin(v)-cos(v)*3 ; Y=6*cos(v)+sin(v)*3 ; Z=v
X=6*sin(v)-cos(v)*4 ; Y=6*cos(v)+sin(v)*4 ; Z=v
X=8*sin(v)-cos(v)*3 ; Y=8*cos(v)+sin(v)*3 ; Z=v
X=8*sin(v)-cos(v)*4 ; Y=8*cos(v)+sin(v)*4 ; Z=v
min U: -10 max U: 10 steps: 20
min V: -10 max V: 10 steps: 20
program je 3D Grapher
primer osnove i 3d projekcije...izvinjavam se na kasnjenju...
Re: MAT 02 - Kriva u prostoru
Coordinates: Cartesian
X(u,v,t)=2*(log(u)+sin(u))
Y(u,v,z)=5+sin(u)*6
Z(u,v,t)=v*sin(2)*150
Domain of variables:
Min U: -3
Min V:9
Max U:6
Max V:-10
Steps:200
Steps: 200
X(u,v,t)=2*(log(u)+sin(u))
Y(u,v,z)=5+sin(u)*6
Z(u,v,t)=v*sin(2)*150
Domain of variables:
Min U: -3
Min V:9
Max U:6
Max V:-10
Steps:200
Steps: 200
Odgovor: MAT 02 - Kriva u prostoru
Funkcije su:
1 - x=3.14*sin(3*v)
2 - y=v*cos(v)
3 - z=v
Kriva je radjena u 3D Grapher-u
1 - x=3.14*sin(3*v)
2 - y=v*cos(v)
3 - z=v
Kriva je radjena u 3D Grapher-u
Re: MAT 02 - Kriva u prostoru
3d math explorer
Za promenljivu uzeto (b) i to od 0 do 2*pi, a za Step pi/20.
Fx=5*sin(2*b)
Fy=5*(1-cos(b))
Fz=5*(1-sin(b))
Posle dobijene krive ostale su uradjene istom funkcijom samo je u Fy dodavano -0.5, -1
Re: MAT 02 - Kriva u prostoru
x=tan(3*u)*5*sin(4*u)
y=45*cos(8*u)*sin(u)-10
z=u*u
Umin=-6
Umax=3
koristila sam FUN3D
y=45*cos(8*u)*sin(u)-10
z=u*u
Umin=-6
Umax=3
koristila sam FUN3D
Re: MAT 02 - Kriva u prostoru
3D Grapher
Coordinates : Cylindrical
Funkcija:
X (u,v,t) = sin(u)*3
Y (u,v,t) = cos(v)*5
Z (u,v,t) = sin(u)*3+cos(v)*5+sin(cos(t))*7
Domain of variables:
Min U : 10
Max U : 15
Steps : 30
Min V : 15
Max V : 30
Steps : 45
Points - braon
Lines - plava
Coordinates : Cylindrical
Funkcija:
X (u,v,t) = sin(u)*3
Y (u,v,t) = cos(v)*5
Z (u,v,t) = sin(u)*3+cos(v)*5+sin(cos(t))*7
Domain of variables:
Min U : 10
Max U : 15
Steps : 30
Min V : 15
Max V : 30
Steps : 45
Points - braon
Lines - plava
Re: MAT 02 - Kriva u prostoru
3d math
variable:t
start:0
end:12.6
step:0.1
fx=4*sin(8*t) fx=4*sin(8*t)
fy=4*cos(8*t) fy=4*cos(8*t)
fz=4*t fz=-8*t
variable:t
start:0
end:12.6
step:0.1
fx=4*sin(8*t) fx=4*sin(8*t)
fy=4*cos(8*t) fy=4*cos(8*t)
fz=4*t fz=-8*t
Re: MAT 02 - Kriva u prostoru
cynildrical
a=sin(V)
R=tan(v)*sin(U)+v
Z=U
minU=-10 maxU=10 steps 30
minV=-10 maxv=10
Re: MAT 02 - Kriva u prostoru
3d max explorer
fx:5*(1+cos(b))+b
fy:5*cos(a)*(1-sin(b))
fz:5*sin(a)*(1-sin(b))*(1+sin(b))
fx:5*(1+cos(b))+b
fy:5*cos(a)*(1-sin(b))
fz:5*sin(a)*(1-sin(b))*(1+sin(b))
Re: MAT 02 - Kriva u prostoru
x=4*cos(u)*sin(v) y=4*u*sin(v) z=4*u
x=9*cos(u)*sin(v) y=9*u*sin(v) z=9*u
x=2*cos(u)*sin(v) y=2*u*sin(v) z=2*u
x=12*cos(u)*sin(v) y=12*u*sin(v) z=12*u
min U=-10 maxU=10
min V=-10 maxV=10
STEPS:20
Re: MAT 02 - Kriva u prostoru
X=u*sin(3*u), Y=u*cos(3*u), Z=u*u+u
X=3*u*sin(3*u), Y=2*u*cos(3*u), Z=u*u+u
X=5*u*sin(3*u), Y=3*u*cos(3*u), Z=u*u+u
X=8*u*sin(3*u), Y=4*u*cos(3*u), Z=u*u+u
maxU=7, minU=-7
Re: MAT 02 - Kriva u prostoru
x=4*u*cos(2*u)
y=4*u*sin(2*u)
z=u*u+3
x=4*u*cos(2*u)
y=4*u*sin(2*u)
z=u*u+1
x=4*u*cos(2*u)
y=4*u*sin(2*u)
z=u*u
x=4*u*cos(2*u)
y=4*u*sin(2*u)
z=u*u-1
y=4*u*sin(2*u)
z=u*u+3
x=4*u*cos(2*u)
y=4*u*sin(2*u)
z=u*u+1
x=4*u*cos(2*u)
y=4*u*sin(2*u)
z=u*u
x=4*u*cos(2*u)
y=4*u*sin(2*u)
z=u*u-1
Odgovor: MAT 02 - Kriva u prostoru
u -30 30 0.5fx=6*sin(u)+2*cos(u)fy=2*cos(u)+8*sin(u)fz=5*sin(u)u -20 20 0.5fx=5*sin(u)+3*cos(u)fy=cos(u)+4*sin(u)sin(u)u -10 10 0.5fx=10*sin(u)+cos(u)fy=2*cos(u)+2*sin(u)fz=4*cos(u)u -40 40 0.5fx=2*sin(u)+6*cos(u)fy=7*cos(u)+3*sin(u)fz=2*cos(u)u -10 10 0.5fx=3*sin(u)+cos(u)fy=2*sin(u)+9*cos(u)fz=1
Odgovor: MAT 02 - Kriva u prostoru
X(u,v,t)=sin(1*u)+cos(v); sin(1*u)+cos(v); sin(1*u)+cos(v); sin(3*u)+cos(v); sin(3*v)*cos(v)
Y(u,v,t)=sin(1*u)*v; sin(1*u)*v; sin(3*u)*v; sin(3*u)*v; sin(3*v)*cos(v)*u
Z(u,v,t)=-2;0;2;4; 3;0;-3;-4; -4;0;4;8;5;0 ;-5;-8;2; -5;6;5
Min U: -10
Max U: 10
Steps: 20
Steps: 20
Y(u,v,t)=sin(1*u)*v; sin(1*u)*v; sin(3*u)*v; sin(3*u)*v; sin(3*v)*cos(v)*u
Z(u,v,t)=-2;0;2;4; 3;0;-3;-4; -4;0;4;8;5;0 ;-5;-8;2; -5;6;5
Min U: -10
Max U: 10
Steps: 20
Steps: 20
Odgovor: MAT 02 - Kriva u prostoru
a(u,v,t): v; v; sin(2*u)+cos(v); v*u; v*u;
R(u,v,t): sin(u)*cos(v)*0.5; sin(u)*cos(v)*1; sin(2*u)*v; sin(u)*cos(v)*0.10; sin(u)*1;
Z(u,v,t): u*2; u*3; 2;0;2;4; u*4; v
Min U: -10
Max U: 10
Steps: 20
Steps: 20
R(u,v,t): sin(u)*cos(v)*0.5; sin(u)*cos(v)*1; sin(2*u)*v; sin(u)*cos(v)*0.10; sin(u)*1;
Z(u,v,t): u*2; u*3; 2;0;2;4; u*4; v
Min U: -10
Max U: 10
Steps: 20
Steps: 20
Odgovor: MAT 02 - Kriva u prostoru
u 3d grapheru rađeno...
Cylindrical
a=sin(v);
R=u;
Z=sin(3*v)+cos(2*u);
MinU: -10 MaxU: 10 Steps: 20
MinV: -10 MaxV: 10 Steps: 20
Spherical
a= 1.5*sin(v)-cos(v)*2;
b= 1.5*cos(v)+sin(v)*2;
R= u;
MinU: -2 MaxU: 6 Steps: 20
MinV: -2 MaxV: 6 Steps: 20
Spherical
a= 4*sin(v)-cos(v)*4;
b= 2.3*cos(v)+sin(v)*2.3;
R= u;
MinU: -2 MaxU: 6 Steps: 20
MinV: -2 MaxV: 6 Steps: 20
Cylindrical
a=sin(v);
R=u;
Z=sin(3*v)+cos(2*u);
MinU: -10 MaxU: 10 Steps: 20
MinV: -10 MaxV: 10 Steps: 20
Spherical
a= 1.5*sin(v)-cos(v)*2;
b= 1.5*cos(v)+sin(v)*2;
R= u;
MinU: -2 MaxU: 6 Steps: 20
MinV: -2 MaxV: 6 Steps: 20
Spherical
a= 4*sin(v)-cos(v)*4;
b= 2.3*cos(v)+sin(v)*2.3;
R= u;
MinU: -2 MaxU: 6 Steps: 20
MinV: -2 MaxV: 6 Steps: 20
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Odgovor: MAT 02 - Kriva u prostoru
x=4*sin(v)-cos(v)*4; y=2sin(v)-cos(v)*4; z=0
x=3*cos(v)+sin(v)*4; y=2*cos(v)+sin(v)*4; z=0
x=6*sin(v)-cos(v)*4; y=5*cos(v)+sin(v)*4; z=0
x=1*sin(v)-cos(v)*4; y=1*cos(v)+sin(v)*4; z=0
x=1*cos(v)+sin(v)*4; y=4*cos(v)+sin(v)*4; z=0
x=3*cos(v)+sin(v)*4; y=2*cos(v)+sin(v)*4; z=0
x=6*sin(v)-cos(v)*4; y=5*cos(v)+sin(v)*4; z=0
x=1*sin(v)-cos(v)*4; y=1*cos(v)+sin(v)*4; z=0
x=1*cos(v)+sin(v)*4; y=4*cos(v)+sin(v)*4; z=0
Odgovor: MAT 02 - Kriva u prostoru
3d grapher
x=25(log(u)+sin(2u))
y=2log(u)+5sin(u)
z=5cos(2u)
minU=-20 maxU=100
x=25(log(u)+sin(2u))
y=2log(u)+5sin(u)
z=5cos(2u)
minU=-20 maxU=100
Odgovor: MAT 02 - Kriva u prostoru
.1.X=4*u*cos(2*u) Y=4*u*sin(2*u) Z=u*u
2.X=4*u*cos(2*u) Y=4*u*sin(2*u*)-5 Z=u*u
3.X=4*u*cos(2*u) Y=4*u*sin(2*u)-10 Z=u*u
4.X=4*u*cos(2*u) Y=4*u*sinj(2*u)+5 Z=u*u
2.X=4*u*cos(2*u) Y=4*u*sin(2*u*)-5 Z=u*u
3.X=4*u*cos(2*u) Y=4*u*sin(2*u)-10 Z=u*u
4.X=4*u*cos(2*u) Y=4*u*sinj(2*u)+5 Z=u*u
Odgovor: MAT 02 - Kriva u prostoru
3D GRAPHER
a(u,v,t)=(u) R(u,v,t)=1*cos(u)+sin(u)*1 Z(u,v,t)=sin(u) minU,minV=-10; maxU,maxV=10 steps20 green
a(u,v,t)=(u) R(u,v,t)=2*cos(u)+sin(u)*2 Z(u,v,t)=2*sin(u) minU,minV=-10; maxU,maxV=10 steps 20 blue
a(u,v,t)=(u) R(u,v,t)=2*cos(u)+sin(u)*2 Z(u,v,t)=2*sin(u) minU,minV=-10; maxU,maxV=10 steps 30 blue
a(u,v,t)=(u) R(u,v,t)=7*cos(u) Z(u,v,t)=3*sin(u) minU,minV=-10; maxU,maxV=10 steps20 violet
a(u,v,t)=(u) R(u,v,t)=7*cos(u) Z(u,v,t)=3*sin(u) minU,minV=-10; maxU,maxV=10 steps 30 violet
Odgovor: MAT 02 - Kriva u prostoru
Odgovor: MAT 02 - Kriva u prostoru
3D Grapher
coordinates : spherical;
a(u,v,t)=3*sin(v/3)+3*sin(v/3);
b(u,v,t)=3*v;
R(u,v,t)=3*cos(v/3)+3*cos(v/3);
min v : -65;
max v : 65;
steps : 540;
Upitanju je ista prostorna kriva, prikazana iz razlicitih uglova iz kojih se vidi postojanje odredjenih pravilnosti.