POV-Ray : Newsgroups : povray.general : Slightly faster VRand_On/In_Sphere() : Re: Slightly faster VRand_On/In_Sphere() Server Time
4 Nov 2024 17:34:01 EST (-0500)
  Re: Slightly faster VRand_On/In_Sphere()  
From: Wolfgang Wieser
Date: 8 Nov 2003 04:14:40
Message: <3facb400@news.povray.org>
Warp wrote:
> "JC (Exether)" <no### [at] spamfr> wrote:
>> I think we can agree that if Frank's VRand_On_Sphere is uniform on the
>> sphere then VRand_In_Sphere is uniform within the sphere.
> 
>   Well, I think this is not automatic, but needs proof. :)
> 
I think my posting from yesterday proofs it. 
The vector is rotated by a random amount around the Y axis, so it 
is sufficient to prove that the probability for the vector being 
in a certain latitude range is equal to the area covered by it 
(divided by 4pi, of course). Now read on in my previous posting. 

Wolfgang


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