Determining wire-phi correspondance
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![DC stereo.png](/./images/d/d4/DC_stereo.png)
![PhiCone.png](/./images/5/50/PhiCone.png)
![Projection side view.png](/./images/8/8c/Projection_side_view.png)
![Projection Rear view.png](/./images/4/48/Projection_Rear_view.png)
![Conic section.png](/./images/e/ef/Conic_section.png)
![Ellipse.png](/./images/9/9b/Ellipse.png)
![DC stereo.png](/./images/d/d4/DC_stereo.png)
Using Mathematica, we can produce a 3D rendering of how the sectors for Level 1 would have to interact with a steady angle theta with respect to the beam line, as angle phi is rotated through 360 degrees.
![PhiCone.png](/./images/5/50/PhiCone.png)
Looking just at sector 1, we can see that the intersection of level 1 and the cone of constant angle theta forms a conic section.
![Projection side view.png](/./images/8/8c/Projection_side_view.png)
![Projection Rear view.png](/./images/4/48/Projection_Rear_view.png)
Following the rules of conic sections we know that the eccentricity of the conic is given by:
Where β is the angle of the plane, and α is the slant of the cone.
If the conic is an circle, e=0
If the conic is an parabola, e=1
If the conic is an ellipse,
![Conic section.png](/./images/e/ef/Conic_section.png)
For ellipses centered at (h,k):
where
![Ellipse.png](/./images/9/9b/Ellipse.png)
Where
For a parabola:
where
p = distance from vertex to focus (or directrix)