Re: overlapping area of two ellipses
- From: Uwe Schmitt <rocksportrocker@xxxxxxxxxxxxxx>
- Date: Wed, 3 Sep 2008 04:20:57 -0700 (PDT)
On 3 Sep., 10:13, fatih.arslan....@xxxxxxxxx wrote:
hello guys,
I have two ellipses, which I know their centers, axis a and axis b and
rotations for each of them. Is there any analytical formula for
calculating overlapping region?
Like Ellips1: center(x,y)=(10,20) axis a=5 axis b=4 rotation=30 degree
Ellps2: center(x,y)=(20,30) axis a=4 axis b=5 rotation=40
degree
(rotation is clockwise)
PS1: Even if I could not find the exact area, a solution which
approximates the overlapping area is ok. Because I am writing a C++
code, and I just have to compare the overlapping areas of different
ellipses...So if I can find a reasonable approximation, it is ok...
PS2:If you do not have time or patience to write, you can give me
references...It will be very good...
Thank you
You may try montecarlo methods:
http://www.nrbook.com/a/bookcpdf/c7-6.pdf
http://www.taygeta.com/rwalks/node5.html
http://en.wikipedia.org/wiki/Monte_Carlo_integration
This may be slow, but can be acclerated by using
quasi random numbers.
Greetings, Uwe
Ask if you have further questions.
.
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