Re: Some question about "Lighting and MaterialofHalo3"and "Lightmap compression in Halo 3"

Hi Sam

 

> does not produce a radially symmetric SH

In fact I am not sure to understand fully the SH math, that why I ask, 

I attached a picture showing the part of the "Lighting and MaterialofHalo3" which I will highlight.

 

The equation (4) is the projection of incoming lighting in SH.

The equation (5) is the diffuse reflectance equation used in Halo3

They sum the SH coefficient of the incoming lighting multiply by the SH coefficient of the projection of the cosine lobe.

 

As you said, this is a convolution, 

From Precomputed radiance transfer for real-time rendering in Dynamic, low-frequency lighting environments

(http://research.microsoft.com/en-us/um/people/johnsny/papers/prt.pdf) in the section "convolution" we can read:

 

"

In other words, the coefficients of the projected convolution are

simply scaled products of the separately projected functions.

Note that because h is circularly symmetric about z, its projection

coefficients are nonzero only for m=0. The convolution property

provides a fast way to convolve an environment map with a

hemispherical cosine kernel, defined as h(z) = max(z,0)

"

So I am a little lost here, I think I misunderstanding the math, 

in the case of the convolution, as said in the Halo3 paper you get a non nul result when you multiply the coefficient  for i = 0, 2 and 6 (based on order 3 SH)

so you don't need to store more than 9 SH coefficient ( 3 zonal harmonic for 3 color channel) for the incoming lighting, right ?

 

Is that statement mean that the lighting is radially symmetric SH, I am not sure.

 

> “Zonal” harmonics, where m != 0 are 0

Sorry for the unclarity of my word, I mean that A3 = 0 (notation from halo3 picture joint). 

the coefficient for A3, A4 etc... can be found in this paper (http://www.eecs.berkeley.edu/~ravir/lighting.pdf) and are not given in halo paper for order > 3

that why I said the zonal hamonic SH coefficient of the 4 band don't need to be store.

 

Thanks to enlighten me :)

 

Lagarde Sébastien

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