# Method for unique collisions between 2 subdivided ellipses

## Main Question or Discussion Point

Hello,

I would like find a way to figure out how many unique collision there are between 2 equally subdivided ellipsoids (velocity=1).

When you have 2 ellipsoids and you let them collide than you have an infinite amount of possible outcomes.

The goal is to reduce this infinite number to a manageable list of for example unique 32 collisions by:
1. Subdividing the ellipsoids, so instead of having an infinite number of points on these ellipsoids where they can hit, they are subdivided into 3 zones (I-II-III per quarter).
2. Reduce the possible rotation angles into steps of 15°
3. Using symmetry, to cancel out the collisions that are the same when A hits B vs. B hits A, and the outcome of a collision on the left side is symmetric to one on the right, or back and front etc.
(Note, the use of 3 Zones and 15° Angles is arbitrary, i guess once a method is found these could be easily changed into whatever.)

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Attached is an overview where the Ellipse A is Set and B comes flying in (see pic.), and where:
• B is shifted a couple of steps along the vertical-axis (right-top).
• B is rotated in relation to A in steps of 15° (left-bottom)
• B is rotated in relation to A in steps of 15° and B itself is rotated 15° (right-bottom)
• B is shifted a couple of steps along the horizontal-axis and B itself is rotated 105°(left-top).
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I don't know if such a method already exists or if this is perhaps something that should be solved with a Monte Carlo method or ... all suggestions are welcome to tackle this issue.

Kind regards,

m.  