| Re: How to detect ellipse intersection [message #70846] |
Sat, 08 May 2010 11:58 |
ben.bighair
Messages: 221
Registered: April 2007
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Senior Member |
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On May 7, 10:25 am, pp <pp.pente...@gmail.com> wrote:
> On May 7, 11:10 am, Paolo <pgri...@gmail.com> wrote:
>
>> first, select pairs that could possible have an intersection
>> (i.e. distance between centers less or equal the larger of the
>> two semimajor axes) - no point in bothering with far apart pairs.
>
> No, the distance should be less or equal to the sum of the two
> semimajor axes.
>
> Another selection which may also reduce the number for which the
> complicated test is needed is to find those with distances less than
> the sum of the two semiminor axes, since these intercept regardless of
> their orientation.
Hi,
You might be able to adapt this description for intercepting circles
in a plane.
http://local.wasp.uwa.edu.au/~pbourke/geometry/2circle/
Cheers,
ben
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| Re: How to detect ellipse intersection [message #70853 is a reply to message #70846] |
Fri, 07 May 2010 07:25  |
penteado
Messages: 866
Registered: February 2018
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Senior Member
Administrator |
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On May 7, 11:10 am, Paolo <pgri...@gmail.com> wrote:
> first, select pairs that could possible have an intersection
> (i.e. distance between centers less or equal the larger of the
> two semimajor axes) - no point in bothering with far apart pairs.
No, the distance should be less or equal to the sum of the two
semimajor axes.
Another selection which may also reduce the number for which the
complicated test is needed is to find those with distances less than
the sum of the two semiminor axes, since these intercept regardless of
their orientation.
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| Re: How to detect ellipse intersection [message #70854 is a reply to message #70853] |
Fri, 07 May 2010 07:24 |
pgrigis
Messages: 436
Registered: September 2007
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Senior Member |
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On May 7, 10:10 am, Paolo <pgri...@gmail.com> wrote:
> On May 7, 4:53 am, oupin <hhb1...@gmail.com> wrote:
>
>> I have hundreds and thousands ellipse, which includes center
>> coordinates and major/minor axis and azimuth of major axis. Now I want
>> to detect which pairs ellipse intersect, how can I realize this
>> program using IDL?
>
> first, select pairs that could possible have an intersection
> (i.e. distance between centers less or equal the larger of the
> two semimajor axes) - no point in bothering with far apart pairs.
^^^^^^^^^^^^^^^^^^^^
times 2 of course :)
>
> second, find the intersection points. I guess they are given by
> a 4th degree equation (since each ellipse is 2nd degree, and there
> can obviously be from 0 to 4 intersections), so you should be
> able to solve it exactly... but some smart geometer may have a better
> approach :)
>
> Ciao,
> Paolo
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| Re: How to detect ellipse intersection [message #70855 is a reply to message #70854] |
Fri, 07 May 2010 07:10 |
pgrigis
Messages: 436
Registered: September 2007
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Senior Member |
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On May 7, 4:53 am, oupin <hhb1...@gmail.com> wrote:
> I have hundreds and thousands ellipse, which includes center
> coordinates and major/minor axis and azimuth of major axis. Now I want
> to detect which pairs ellipse intersect, how can I realize this
> program using IDL?
first, select pairs that could possible have an intersection
(i.e. distance between centers less or equal the larger of the
two semimajor axes) - no point in bothering with far apart pairs.
second, find the intersection points. I guess they are given by
a 4th degree equation (since each ellipse is 2nd degree, and there
can obviously be from 0 to 4 intersections), so you should be
able to solve it exactly... but some smart geometer may have a better
approach :)
Ciao,
Paolo
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