# Method for unique collisions between 2 subdivided ellipses

• Michel_vdg
In summary, The goal is to reduce the infinite number of possible outcomes when two equally subdivided ellipsoids collide by subdividing the ellipsoids into 3 zones, reducing rotation angles to steps of 15°, and using symmetry to cancel out duplicate collisions. The attached overview shows the different scenarios for Ellipse B in relation to Ellipse A. It is unclear if a method for this already exists or if it should be solved using a Monte Carlo method. All suggestions are welcome.
Michel_vdg
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.)

--

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).
--

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.

... seems like I better figure this out 'manually' ...

## 1. How does the method for unique collisions between 2 subdivided ellipses work?

The method involves subdividing each ellipse into smaller sections and then checking for collisions between these smaller sections. This allows for a more precise detection of unique collisions between the two ellipses.

## 2. What advantages does this method have over other collision detection methods?

This method is more accurate and efficient compared to other methods that only check for collisions between the outer boundaries of the ellipses. It also allows for detection of multiple collisions between the two ellipses.

## 3. Can this method be applied to other shapes besides ellipses?

Yes, this method can be applied to other shapes such as circles, rectangles, and polygons by subdividing them into smaller sections and checking for collisions between these sections.

## 4. What is the complexity of this method?

The time complexity of this method is O(n^2), where n is the number of subdivisions. This means that as the number of subdivisions increases, the time required for collision detection also increases.

## 5. Are there any limitations to this method?

One limitation of this method is that it may not be suitable for detecting collisions between very complex or irregularly shaped ellipses. Additionally, the accuracy of the method may be affected by the number and size of subdivisions chosen.

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