POV-Ray: Newsgroups: povray.off-topic: Bounding circle intersection: Re: Bounding circle intersection

POV-Ray : Newsgroups : povray.off-topic : Bounding circle intersection : Re: Bounding circle intersection		Server Time 4 Sep 2024 23:21:13 EDT (-0400)

From: bart
Date: 11 Dec 2009 12:25:51
Message: <4b22809f$1@news.povray.org>

On 12/11/2009 02:43 AM, Slime wrote:
>> Have you tried this condition?
>>
>> ((distSq<  (radius1Sq+radius2Sq))
>> or (4*radius1Sq*radius2Sq>  (distSq - (radius1Sq+radius2Sq))^2))
>
> Smart. I feel stupid now! =) I see the equivalence, but I'm curious how long
> you took to come up with that. Was it obvious?
>
>   - Slime
>   [ http://www.slimeland.com/ ]
>
>
Well, it comes naturally from
distSq < radius1Sq + radius2Sq + 2 * radius1 * radius2
=>
distSq - (radius1Sq + radius2Sq ) <  2 * radius1 * radius2
=>
(distSq - (radius1Sq + radius2Sq ))^2 <  4 * radius1Sq * radius2Sq,

but the downside is that you have an overflow risk here to check

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