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

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Kevin Hanekom on 13 Oct 2021
Commented: Kevin Hanekom on 14 Oct 2021
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];

Matt J on 14 Oct 2021
See the cylinder command.
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 on 14 Oct 2021
You are a genius, Thank you!!

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