Recreating a mathematical 3D shape

[dan_smith]

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?
Thankstheta_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)

 

[KataKoniK]

%for the other half of the shape
phi=linspace(-pi/2,pi/2,100); %phi can be changed to create different shapes

%convert to cartesian coordinates
x=r1.*cos(phi);
y=r1.*sin(phi);

%plot the shape
figure
plot(x,y,'LineWidth',2)
xlabel('x')
ylabel('y')
axis equal

%to create a 3D shape, we can add a z-coordinate
z=D*phi+delta;

%plot the 3D shape
figure
plot3(x,y,z,'LineWidth',2)
xlabel('x')
ylabel('y')
zlabel('z')
axis equal

%we can also rotate the shape to get different views
figure
rotate3d on
plot3(x,y,z,'LineWidth',2)
xlabel('x')
ylabel('y')
zlabel('z')
axis equal

%to add color to the shape, we can use the 'surf' command
figure
surf(x,y,z,'FaceColor','red','EdgeColor','none')
xlabel('x')
ylabel('y')
zlabel('z')
axis equal

%we can also add transparency to the shape
figure
surf(x,y,z,'FaceColor','red','EdgeColor','none','FaceAlpha',0.5)
xlabel('x')
ylabel('y')
zlabel('z')
axis equal

%to create a smoother surface, we can increase the number of points in phi
phi=linspace(-pi/2,pi/2,1000);

%plot the smoother 3D shape
figure
plot3(x,y,z,'LineWidth',2)
xlabel('x')
ylabel('y')
zlabel('z')
axis equal