How to plot 3D plot from polar plot

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I am looking at plotting the the slowness profiles of Titinium (Inverser of velocity) by solving the christoffell equation.
I have managed to get a polar plot of this but would like to visualise this in 3d. For my polar plot I have done.
c11 = 162000000000;
c12=92000000000;
c44=47000000000;
c13= 69000000000;
c33= 181000000000;
c66= 35000000000
rho = 4430;
C=[c11,c12,c13,0,0,0;
c12,c11,c13,0,0,0;
c13,c13,c33,0,0,0;
0,0,0,c44,0,0;
0,0,0,0,c44,0;
0,0,0,0,0,c66];
phase_vel3=zeros(1,181);
r=0;
for theta=-pi:pi/180:pi
r=r+1;
n=[cos(theta),0,sin(theta)];
L_11=(C(1,1)*n(1)^2+C(6,6)*n(2)^2+C(5,5)*n(3)^2+2*C(1,6)*n(1)*n(2)+2*C(1,5)*n(1)*n(3)+2*C(5,6)*n(2)*n(3));
L_12=(C(1,6)*n(1)^2+C(2,6)*n(2)^2+C(4,5)*n(3)^2+(C(1,2)+C(6,6))*n(1)*n(2)+(C(1,4)+C(5,6))*n(1)*n(3)+(C(4,6)+C(2,5))*n(2)*n(3));
L_13=(C(1,5)*n(1)^2+C(4,6)*n(2)^2+C(3,5)*n(3)^2+(C(1,4)+C(5,6))*n(1)*n(2)+(C(1,3)+C(5,5))*n(1)*n(3)+(C(3,6)+C(4,5))*n(2)*n(3));
L_22=(C(6,6)*n(1)^2+C(2,2)*n(2)^2+C(4,4)*n(3)^2+2*C(2,6)*n(1)*n(2)+2*C(4,6)*n(1)*n(3)+2*C(2,4)*n(2)*n(3));
L_23=(C(5,6)*n(1)^2+C(2,4)*n(2)^2+C(3,4)*n(3)^2+(C(4,6)+C(2,5))*n(1)*n(2)+(C(3,6)+C(4,5))*n(1)*n(3)+(C(2,3)+C(4,4))*n(2)*n(3));
L_33=(C(5,5)*n(1)^2+C(4,4)*n(2)^2+C(3,3)*n(3)^2+2*C(4,5)*n(1)*n(2)+2*C(3,5)*n(1)*n(3)+2*C(3,4)*n(2)*n(3));
Christoffel_mat=[L_11, L_12, L_13;
L_12,L_22,L_23;
L_13,L_23,L_33];
[ev,d]=eig(Christoffel_mat);
% eigvecs = polarisation vectors
pl=ev(:,3);
% eigvals ~ slowness (phase)
phase_vel3(r)=sqrt(rho./d(3,3)); % quasi-longitudinal
r=0;
for theta=-pi:pi/180:pi
r=r+1;
n=[cos(theta),0,sin(theta)];
L_11=(C(1,1)*n(1)^2+C(6,6)*n(2)^2+C(5,5)*n(3)^2+2*C(1,6)*n(1)*n(2)+2*C(1,5)*n(1)*n(3)+2*C(5,6)*n(2)*n(3));
L_12=(C(1,6)*n(1)^2+C(2,6)*n(2)^2+C(4,5)*n(3)^2+(C(1,2)+C(6,6))*n(1)*n(2)+(C(1,4)+C(5,6))*n(1)*n(3)+(C(4,6)+C(2,5))*n(2)*n(3));
L_13=(C(1,5)*n(1)^2+C(4,6)*n(2)^2+C(3,5)*n(3)^2+(C(1,4)+C(5,6))*n(1)*n(2)+(C(1,3)+C(5,5))*n(1)*n(3)+(C(3,6)+C(4,5))*n(2)*n(3));
L_22=(C(6,6)*n(1)^2+C(2,2)*n(2)^2+C(4,4)*n(3)^2+2*C(2,6)*n(1)*n(2)+2*C(4,6)*n(1)*n(3)+2*C(2,4)*n(2)*n(3));
L_23=(C(5,6)*n(1)^2+C(2,4)*n(2)^2+C(3,4)*n(3)^2+(C(4,6)+C(2,5))*n(1)*n(2)+(C(3,6)+C(4,5))*n(1)*n(3)+(C(2,3)+C(4,4))*n(2)*n(3));
L_33=(C(5,5)*n(1)^2+C(4,4)*n(2)^2+C(3,3)*n(3)^2+2*C(4,5)*n(1)*n(2)+2*C(3,5)*n(1)*n(3)+2*C(3,4)*n(2)*n(3));
Christoffel_mat=[L_11, L_12, L_13;
L_12,L_22,L_23;
L_13,L_23,L_33];
[ev,d]=eig(Christoffel_mat);
% eigvecs = polarisation vectors
pl=ev(:,3);
% eigvals ~ slowness (phase)
phase_vel3(r)=sqrt(rho./d(3,3)); % quasi-longitudinal
figure
polar(0:pi/180:2*pi,1./phase_vel3)
Any assistance how to visualise this in 3d would be appreciated.
Thanks
Dave :)

Accepted Answer

William Rose
William Rose on 9 Aug 2022
[moved this from Comment to Answer as I had originally intended]
Please post the simplest possible code fragment that clearly illustrates what you want to do. This is always a good idea, in order to raise the odss of getting a useful answer.
I cannot tell what you want to plot on the third dimension.
Matlab cannot directly plot in cylindrical or spherical coordinates, as far as I know. But it does have a built-in function to convert from cylindrical to Cartesian, which I use below.
z=0:200; theta=z*pi/25; r=1-z/400;
[x,y,z]=pol2cart(theta,r,z); %convert cylindrical to Cartesian coords
figure;
subplot(121); polar(theta,r); %polar plot
subplot(122); plot3(x,y,z); %3D plot
I hope that helps.
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