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recreating a mathematical 3D shape

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antenna_beginner

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Hello, I am trying to recreate a shape shown in the attached photo, from the attached article
I have tried to create this shape in MATLAB as shown in the code bellow ,
from this formula i get a 2D shape and not the shown 3D shape , how to create this 3D shape?
Thanks

Code: 
theta_0=15;
alpha=60;
delta=90;
r0=2.3;
D=15.2;
a=sin(theta_0)/(tan(alpha));
r1=r0*exp(a*phi);
r1=r0*exp(a*phi-pi);

Capture.JPG
 

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