Re: [Algorithms] More SH exponentiation questions

[Ben Y. <shu...@gm...>]

Sorry, hit enter a bit prematurely.

Regarding Figure 3, I wanted to also ask how the values for AB were derived
for multiple overlapping spheres. It's basically what I'm trying to
accomplish...



On Wed, Nov 11, 2009 at 12:04 PM, Ben Yeoh <shu...@gm...> wrote:

> Hi Peter,
>
> Thanks for chiming in!
>
> Okay, let me elaborate a bit.
>
> Basically, I'm trying to avoid doing any factorization to reduce the log
> magnitude (besides DC isolation) in the pixel shader for performance
> reasons. It still looks prohibitively expensive even with 3rd order SHs and
> John's code generator. I was hoping that the artifacts arising with just the
> OL approach with overlapping sphere occluders would be similar to what is
> shown in the bunny example in Figure 9 in the paper, which looks to me like
> fainter shadows. I think I'm willing to live with that if that's the case...
>
> So the pure OL approach (fit to a single sphere) with 1 sphere occluder in
> the scene works fine. But when I have multiple overlapping spheres though as
> in the bunny example, there's some pretty objectionable "shadow
> saturation"/ringing artifacts when those overlapping spheres are "close" to
> the receiver. In fact, it looks very different compared to the Figure 9
> example. I'm guessing that's because the OL approximation in Figure 9 was
> fit to multiple spheres (ie, 63 spheres for the bunny?), wheares I was only
> fitting to a single sphere. Am I right to assume this?
>
> Now, going along this line, I've tried a couple of things to "fit" the AB
> table to multiple sphere occluders (which didn't work) :
>
> 1. Multiply the log visibility coeffs by 2 (for 2 sphere occluders) and use
> that to find AB instead.
>
> 2. Do a triple product on the sphere visibility coeffs (ie, F * F) and use
> that to find the log and AB.
>
>
>
>
>
>
>
> On Wed, Nov 11, 2009 at 2:29 AM, Peter-Pike Sloan <
> pet...@ho...> wrote:
>
>>
>> I'm not really sure what you are talking about.  You might want to email
>> John directly, I think we just computed a bunch of pairs and then built the
>> table as a function of log magnitude (after DC isolation.)
>>
>> You could pose computing the ab texture itself as a least squares problem,
>> and include training examples that were the result of multiple spheres
>> (instead of just single spheres), but I don't think we did that...
>>
>> Are you referring to figure 3 in the paper?  It is really just showing the
>> OL pretty much just works as long as the magnitude is small enough...
>>
>> Peter-Pike Sloan
>>
>> ------------------------------
>> Date: Tue, 10 Nov 2009 16:58:04 +0800
>> From: shu...@gm...
>> To: gda...@li...
>> Subject: [Algorithms] More SH exponentiation questions
>>
>> Has anyone implemented SH exponentiation AND managed to approximate the
>> optimal linear (OL) values for 2 or more sphere occluders?
>>
>> The SH paper briefly mentioned/implied that the authors managed to fit the
>> OL approximation to multiple spheres, which still has some artifacts with
>> inaccurate/lighter occlusion, but is still preferable to the single sphere
>> approximation when dealing with multiple sphere occluders, which is common
>> in most "practical" cases.
>>
>> If anyone has some idea how the fitting to multiple spheres thing is done
>> - that'll be awesome.
>>
>>
>>
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>
>