Plotting two surfaces in cylindrical coordinates

Hello,

I need to plot the following surfaces given by:

,

where ρ is the radius, z is the height and ϕthe azimuth. are constants with .

The first surface denotes a torus.

[Gautam Chettiar]

I hope i understood your question properly

Answer 1

[Gautam Chettiar]

theta = linspace(0, 10 * pi); 
z = linspace(0, 5);

[Theta, Z] = meshgrid(theta, z);

% Set the constants
% c >= a
a = 5;
c = 10;

r = sqrt(c ^ 2 - a ^ 2 - z .^ 2) + c;

[x, y, z] = pol2cart(Theta, r, Z);

mesh(x, y, z); 
axis equal

[Thanos Pol]

So to print the second surface, I should do the something like the following?(which produces an error)

r=sqrt(tan(theta)*2*a.*z-z.^2+a^2);
[x, y, z] = pol2cart(Theta, r, Z);
mesh(x, y, z); 

[Gautam Chettiar]

I implemented it, but I faced the complex datatype issue, so I used abs() to fix it, if its wrong then please choose appropriate parameters for the same:

clc
clear all
close all

theta = linspace(0, 2 * pi); 
z = linspace(0, 5);
[Theta, Z] = meshgrid(theta, z);

% Set the constants
% c >= a
a = 10;
c = 10;
phi0 = 0;

r = abs(sqrt(2 * a * z .* tan(theta - phi0) - z .^ 2 + a ^ 2)) ;

[x, y, z] = pol2cart(Theta, r, Z);

mesh(x, y, z); 
axis equal