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Thread Subject:
Ellipse-ellipse intersection area

Subject: Ellipse-ellipse intersection area

From: Sébastien MAILFERT

Date: 21 Jul, 2011 15:18:09

Message: 1 of 4

Hi,

I'm trying to find a solution to calculate the intersection area between two ellipse with different areas and rotated between them.

The solution of this probelm is a little bit tricky or I'm really not good in Mathematics...!

Thanks for your help!

Sebastien

Subject: Ellipse-ellipse intersection area

From: Roger Stafford

Date: 21 Jul, 2011 16:26:11

Message: 2 of 4

"Sébastien MAILFERT" wrote in message <j09fvh$p2f$1@newscl01ah.mathworks.com>...
> Hi,
>
> I'm trying to find a solution to calculate the intersection area between two ellipse with different areas and rotated between them.
>
> The solution of this probelm is a little bit tricky or I'm really not good in Mathematics...!
>
> Thanks for your help!
>
> Sebastien
- - - - - - - - - -
  You haven't said how you determine your two ellipses, but I would suppose you have them located within some coordinate system and are able to find their two points (if any) of intersection in terms of these coordinates. If a line connects these two points, it divides the intersection area into two parts, each one a segment of one of the ellipses. So your problem now is to find the areas of the two ellipse segments.

  Provided you can determine each of their major and minor axes, in each case you can expand the ellipse, along with the two intersection points, along the line of a minor axis until the ellipse becomes a circle. Then determine the area of the resulting circular segment using the standard formula for that. Then divide the answer by the expansion factor used in each case, and that will give you each elliptical segment's actual area.

Roger Stafford

Subject: Ellipse-ellipse intersection area

From: Florin Neacsu

Date: 21 Jul, 2011 19:22:08

Message: 3 of 4

Hi,

If you are looking for non-analytical solution :

plot the 2 ellipses, assign to all the interior pixels 1 and 2 respectively and then superimpose them and look for pixels=3.

Regards,
Florin

Subject: Ellipse-ellipse intersection area

From: Gary Hughes

Date: 29 Jul, 2011 16:44:13

Message: 4 of 4

Hi Sebastien,
Well, the solution to the problem is tricky, as you note! Probably the most common approach is to approximate the overlap area with polygons. Recently, there is a post that finds the area using Gauss-Green formula, once the points of intersection of the two ellipses are known. See http://works.bepress.com/gbhughes/17/, which also gives c-code.
--Gary Hughes

"Sébastien MAILFERT" wrote in message <j09fvh$p2f$1@newscl01ah.mathworks.com>...
> Hi,
>
> I'm trying to find a solution to calculate the intersection area between two ellipse with different areas and rotated between them.
>
> The solution of this probelm is a little bit tricky or I'm really not good in Mathematics...!
>
> Thanks for your help!
>
> Sebastien

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