Revolving a curve about the y-axis to generate a 3D surface

I'm aware that the cylinder() functiond does this for revolutions about the x-axis. But is there a way to do this about the y-axis?

Answer 1

[John D'Errico]

Certainly. Just write the code yourself. Seriously, it is not difficult.

Consider the function y = f(x).

f = @(x) x.*(1-x);
fplot(f,[0,1])

We want to rotate this around the Y axis.

n = 100;
theta = linspace(0,2*pi,n).';
x0 = linspace(0,1,n);
y0 = f(x0);

x = x0.*cos(theta);
z = x0.*sin(theta);
y = repmat(y0,[n,1]);

surf(x,y,z)
xlabel x
ylabel y
zlabel z
view(20,30)

So the y axis lives at (x,z) = (0,0). The curve drawn in the original figure has been rotated around the y axis, producing this sideways cup, with a cusp at the center.

[Asser Abdelgawad]

Hello @John D'Errico. Thank you for sharing this; it helped me a lot. I have a follow-up question if you don't mind:

Is there a way to revolve the graph without using repmat? The issue is, for me, since this rotation is in the fourier domain, when i perform ifft2 to get back to spatial domain, my resultant function is essentially one-dimensional because of the repeated values from repmat. I want a 3D Gaussian from performing ifft2 on the 2D MTF here, but I get this for the PSF:

Here is my code for reference:

f = fit(freq.', MTF_fit.', 'gauss2'); %gaussian function

% rotate MTF in fourier domain

n_val = 100;

x0 = freq;

y0 = f(x0).';

theta = linspace(0,2*pi,n_val).';

x = x0.*cos(theta);

y = x0.*sin(theta);

z = repmat(y0,[n_val,1]);

MTF2 = z;

PSF2 = abs(ifftshift(ifft2(MTF2)); %back to spatial domain

surf(x,y,z) %plot top right graph

surf(PSF2) %plot bottom left graph

Ideally, the values for MTF2 wouldn't be repeated across the matrix. I've also shared what MTF2 looks like currently for refernece. What do you think?

Answer 2

[Matt J]

Why not just revole around whatever axis cylinder() acommodates and then use rotate?

Or, interchange the data when you plot, e.g.,

t = 0:pi/10:2*pi;
r = 2 + cos(t);
[X,Z,Y] = cylinder(r);

surf(X,Y,Z); 
xlabel X; ylabel Y; zlabel Z;

[Asser Abdelgawad]

Hi @Matt J I've tried the cylinder function with all 6 possible orderings of x,y, and z but I cannot get my gaussian function to go from left to right such as in this diagram.

This was acheived with @John D'Errico's solution, though my issue is the repeated values it produces because of repmat. How would you do it with your technique on a gaussian such as this? Is it possible with cylinder()?

Thank you so much for your help.

Asser