Plotting a multi-function surface?

I have the following system:

f = ln(1/x) + 3 for when 1<x

f = 3 for when 0<=x<=1

What I want to do is effectively plot this 2D system as a surface in cylindrical coordinates, 'spinning' the line round as to create something resembling a flat-topped cone. Unfortunately, my limited knowledge of of both the surf and mesh functions leave me unsure of how to do this. Any help would greatly appreciated. Thanks.

Answer 1

[Star Strider]

Is this what you want to do? If not, experiment with it. This should get you started.

f = @(x) 3.*((x >= 0) & (x <= 1)) + (log(1./x) + 3).*(x > 1);   % Function

x = linspace(0, 5, 25);                                         % Change upper Limit & Vector Length

[Xc,Yc,Zc] = cylinder(f(x), 25);                                % Create Cylinder With ‘f’ Describing Radius

figure(1)
surf(Xc, Yc, Zc)                                                % Plot Resulting Cylinder
grid on

[Jack Smith]

Thanks. This is great, but what I'm trying to do is 'spin' this round:

[Star Strider]

It took me a while to figure out how to invert that. In the end it was straightforward (but then everything is in retrospect):

f = @(x) 3.*((x >= 0) & (x <= 1)) + (log(1./x) + 3).*(x > 1);   % Function
finv = @(x) exp(f(x));

x = linspace(0, 20, 25);                                        % Change upper Limit & Vector Length

[Xc,Yc,Zc] = cylinder(finv(x), 25);                             % Create Cylinder With ‘f’ Describing Radius

figure(1)
surf(Xc, Yc, 3.1*Zc)                                            % Plot Resulting Cylinder
grid on
axis equal

It doesn’t look exactly like your posted plot because I set axis equal so that I could verify it. Your plot would look like a cross-section of mine if you did the same on your plot.

[Jack Smith]

Brilliant. Thanks!

[Star Strider]

My pleasure!

That was definitely a challenge!