How to make this 3D plot from parameterized function?

Dear Sir:

Attached below is a picture from the textbook. Here is the function:

w=xy+z, x=cos(t), y=sin(t), z=t

The book shows the 3D plot of this function, which is a curve living in 3D. I am wondering how to do that in MatLab.

Next is a function:

w=x+2y+z^2, x=r/s, y=r^2+lns, z=2r

Since there are two parameters, so this function is a surface living in 3D. The book doesn't show the plot, but I wish I can plot it and take a look.

I have googled and just have no clue how to do this. I know some basice plotting, like contour, surface. I know how to plot a vector field. I am always eager to learn. If you can point me the direction, that will be great.

Thank you very much! Have a nice day!

[ryecatcher]

Dear Sir:

I am using the following code to plot:

x=@(t) cos(t);

y=@(t) sin(t);

z=@(t) t;

ezplot3(x,y,z,[0,100],10000)

The figure is attached below. However, the original question is:

w=xy+z, x=cos(t), y=sin(t), z=t

I just don't know how to plot 'w=xy+z'.

Thank you very much for your help. I greatly appreciate it.

[darova]

• w=xy+z

What does it mean? Color?

• Next is a function:
• w=x+2y+z^2, x=r/s, y=r^2+lns, z=2r

What are r and s parameters? Radius and angle?

[ryecatcher]

I don't know their physical meaning. It is just a function, with 3 components(x,y,z) and 2 parameters(r, s).

Answer 1

[darova]

success?

[r,s]=meshgrid(0:0.1:2);
x=r./s;  
y=r.^2+log(s);
z=2*r;
surf(x,y,z)
axis vis3d

[ryecatcher]

Thank you very much. I greatly appreciate your help.