How can I graph the following parametric functions on a 3d graph?

Hi everyone! The three functions are as follows:

• x=r*cos(theta)sin(phi)
• y=r*sin(theta)sin(phi)
• z=4r

the three equations should make a hemisphere. This is what I have:

theta=[0:0.1:6.28];
phi=[0:0.1:6.28];
r=[0:0.1:2];
[THETA,PHI]=meshgrid(theta,phi);
X2=R.*cos(THETA).*sin(PHI);
Y2=R.*sin(THETA).*sin(PHI);
Z2=R.*cos(PHI);
mesh(X2,Y2,Z2)

I know that's obviously not right, but I don't know what to do to make it right. Any help would be appreciated! Thanks!

Answer 1

[Marco Castelli]

If R is a constant the code is:

theta=[0:0.1:6.28];
phi=[0:0.1:6.28];
R=2;
[THETA,PHI]=meshgrid(theta,phi);
X2=R.*cos(THETA).*sin(PHI);
Y2=R.*sin(THETA).*sin(PHI);
Z2=R.*cos(PHI);
mesh(X2,Y2,Z2)

In this case , if you want to see how the surface changes with r, you can use subplot to plot more picture in one window:

theta=[0:0.1:6.28];
phi=[0:0.1:6.28];
R=1;
[THETA,PHI]=meshgrid(theta,phi);
X1=R.*cos(THETA).*sin(PHI);
Y1=R.*sin(THETA).*sin(PHI);
Z1=R.*cos(PHI);
R=2;
[THETA,PHI]=meshgrid(theta,phi);
X2=R.*cos(THETA).*sin(PHI);
Y2=R.*sin(THETA).*sin(PHI);
Z2=R.*cos(PHI);
mesh(X2,Y2,Z2)
figure
hold on
subplot(1,2,1)
mesh(X1,Y1,Z1)
axis([-2 2 -2 2 -2 2])
subplot(1,2,2)
mesh(X2,Y2,Z2)
axis([-2 2 -2 2 -2 2])

Answer 2

[Carlos Guerrero García]

And...what about an animation?

[THETA,PHI]=meshgrid(0:2*pi/60:2*pi,0:pi/60:pi);
for R=0.1:0.01:2;
    mesh(R.*cos(THETA).*sin(PHI),R.*sin(THETA).*sin(PHI),R.*cos(PHI));
    title(['R=',num2str(R)]);
    axis equal;
    axis([-2 2 -2 2 -2 2]);
    drawnow;
end