RE: [Algorithms] Bounding cones.

[Peter-Pike S. <pp...@wi...>]

I haven't been following this thread that closely, but pedro sander did
a very nice job of computing optimnal sphere/cone hiearchies for his
Silhouette Clipping paper:

http://pedrosander.com/publications/

(section 5 in the above paper)

-Peter-Pike Sloan

-----Original Message-----
From: gda...@li...
[mailto:gda...@li...] On Behalf Of
Jonathan Blow
Sent: Tuesday, January 27, 2004 7:27 PM
To: gda...@li...
Subject: Re: [Algorithms] Bounding cones.

> However, you might have something there. If I simply took n points=20
> around the edge of each cone, where n is about 3-6 (could even change=20
> the number according to the size of the cone - typically I will have=20
> cones of widely varying sizes, since the objects vary widely in size,=20
> and are at very different distances to the light). Then cluster them,=20
> and use that as a starting guess. As long as the initial guess is=20
> fairly accurate, I think it's true to say you can then do the=20
> one-at-a-time merging and still get a very good bounding cone at the
end.

The covariance stuff is really fast, once you have the initial values
inside the covariance matrices; you can just transform them and add them
after that.
And actually, you can compute the closed-form covariance of a cone, and
evaluating that would probably be faster than using individual points.
So my original 1000 points idea was overzealous and unnecessary.

By default when using such closed-form covariance, big cones would be
favored, but you can compensate for this just by scaling up the density
of the small cones.

I'm not saying it's the best solution for your problem, but it's worth
trying if yer gonna investigate various solutions.



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