How to rotate a 2d plot about the z axis to create a 3d object

Good afternoon everyone,

My goal with the code bellow is to somehow transfer the use of using a roation matrix to rotate my 2d plot about the z axis to hopefully create a closed, convex surface. The issue im having trouble with is how can this be accomplished, since originally we dont have a z coord? would we have to plot the snips of the rotation in spherical coords, then at the end transfer the spherical coords to rectangular? The code bellow will rotate a given vector about (0,0) with given degrees in 2d, how can I implement this in 3d? The 3d rotation matrix for the z axis will be at the bottom of the doc if it helps.

Thank you for the time!

Please, Please, let me know if you see anywhere I can improve my code, make it more efficent, faster, anything!

Yieldstr = 1000; % KPa, Sets the str for all following 2d Plots 

minValue = -4*Yieldstr;
maxValue = 4*Yieldstr;
fidelity = Yieldstr/125; %able to use much higher fidelity in 2d
  
sigx = minValue:fidelity:maxValue;
sigy = sigx.';

VM = (1/(sqrt(2)) .* sqrt((sigx-sigy).^2 + (sigy).^2 +(-sigx).^2));   
[x,y,~] = find(VM<Yieldstr);
PStress = [sigx(y).' sigy(x)];

A = boundary(PStress,0);

FirstC = PStress(A,1);
SecC = PStress(A,2); %all this block of code is doing is finding the boundary of our Pstress
Var = [FirstC SecC]; %then assigning it to a variable, I think it'll make it a bit easier in the future
Var = Var';

Num = length(Var(1,:));


for theta = 0:45:45
    for i = 1:1:Num
    
    S(1,1) = Var(1,i);
    S(2,1) = Var(2,i);
%     S(3,1) = 0;
    
    Rz = [cosd(theta) -sind(theta); sind(theta) cosd(theta)];
    P = Rz*S;
   
    X(1,:) = P(1,:);
    Y(2,:) = P(2,:);

    scatter(X,Y);
    hold on
    end
end
 
hold off

%here is the rotation matrix for rotating about the z axis
%Rz = [cosd(theta) -sind(theta) 0 ; sind(theta) cosd(theta) 0; 0 0 1];

Answer 1

[Matt J]

See the cylinder command.

https://www.mathworks.com/help/matlab/ref/cylinder.html

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


plot(r,t), xlim([0,3])

surf(X,Y,Z)

[Kevin Hanekom]

You are a genius, Thank you!!