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

[Sam M. <sam...@ge...>]

I can’t help you with the “what sh order halo 3..” question, but I think there’s a bit of confusion over the zonal harmonic part.

 

Convolving an arbitrary SH (e.g. your input lighting) against a clamped cosine SH (for the diffuse integral - which is radially symmetric) does not produce a radially symmetric SH. But it does greatly reduce the need for higher order coefficients. Diffuse lighting is very low frequency and in practice I’ve never found a need for more than L2, and L1 is often adequate for most purposes.

 

“Zonal” harmonics, where m != 0 are 0, are a bit of a special case. I’m not sure how they are used in the paper you mentioned, but in general diffuse lighting over a sphere isn’t radially symmetric. 

 

Not sure if that helps or not!

 

Ta,

Sam

 

From: Sébastien Lagarde [mailto:seb...@do...] 
Sent: 01 February 2010 12:23
To: Game Development Algorithms
Subject: Re: [Algorithms] Some question about "Lighting and MaterialofHalo3" and "Lightmap compression in Halo 3"

 

Yes, in fact I was not clear, I will sum up my questions :)

And yes you remember correctly.

 

Question:

What SH order Halo 3 uses for their SH lightmap (2 (4 coeff), 3 (9 coeff), 4 (16 coeff) ), 5 (25 coeff)  etc...) ? And what are the value stored ?

 

From the paper, it seems that they store HDR RGB value.

So multiply the number of SH coefficient by 3

but  they only need to store the integration of the diffuse equation (5) in the paper "lighting and material in halo 3"

which contain the projection of the cosine lobe in SH, which is radially symmetric.

Mean that only zonal harmonic coefficient matter (all coefficient with m != 0 are 0).

So this reduce the number of SH coefficient depend on the order:

(2 (2 coeff), 3 (3 coeff), 4 (3 coeff) ), 5 (4 coeff)  etc...) (note that order 4 zonal harmonic is 0)

So if halo 3 store 3 SH order for RGB we get: 3 *3 = 9 colored SH coefficient

and for order 4 : 3 * 4 = 12 colored SH coefficient

but they saisd that they store 5 * 3 float value, so I am lost. What represent this float value ?

 

Thanks you for any advice :)

 

Lagarde Sébastien

 

 

De : Jon Watte [mailto:jw...@gm...] 
Envoyé : samedi 30 janvier 2010 01:46
À : Game Development Algorithms
Objet : Re: [Algorithms] Some question about "Lighting and Material ofHalo3" and "Lightmap compression in Halo 3"

 

I don't quite understand your coupling between harmonic orders and coefficients.

 

If I remember correctly, spherical harmonics of order 0 is a flat value -- 1 coefficient.

Order 1 adds three cardinal directions -- 3 additional coefficients, for a total of 4.

Order 2 adds another 5, for a total of 9.

Order 3 adds another 7, for a total of 16.

Order 4 adds another 9, for a total of 25.

...

 

You may be able to omit the constant term (calculating it or assuming it) which would get a total harmonic count for order 3 of 15. Perhaps that's where the number comes from (but I have not had time to check the paper, just guessing here).

 

Generally, if you separate out the diffuse/ambient reflection/albedo texture to a "regular" texture, you don't need to store the light response in RGB channels, just like you don't use different light fall-off equations for the different color channels. (Except when you do Rayleigh scattering and similar for atmospherics, I think...)

 

Sincerely,

 

jw

--
Americans might object: there is no way we would sacrifice our living standards for the benefit of people in the rest of the world. Nevertheless, whether we get there willingly or not, we shall soon have lower consumption rates, because our present rates are unsustainable. 



2010/1/29 Sébastien Lagarde <seb...@do...>

Hello all, 

 

I tried to contact the author of this two (now old) paper, without success,:

"Lighting and Material of Halo 3" published at siggraph 2008 (http://ati.amd.com/developer/SIGGRAPH08/Chapter01-Chen-Lighting_and_Material_of_Halo3.pdf)

and GDC 2008 conference "Lightmap compression in Halo 3" (http://toomuchlogic.com/Lightmap_Compression_2008_02_22.pdf)

so I will ask some question to the list, if anyone is interested by the subject and has better understanding of math than me :)

 

1. "Lighting and Material of Halo 3"  About equation (5) the diffuse reflectance using SH basis

the diffuse reflectance using SH basis is : k_d R_d Sum Lambda_i A_i

A_i is the projection of the cosine lobe in SH, and as it is radially symetric.

all coefficient with m != 0 are 0.

After that the author give the first three term of A_i.

I wondering how many band are use for this calculation  ? (order 3, 4 or more ?)

 

I read from "Stupid spherical harmonics tricks" from Perter Pike sloan (http://www.ppsloan.org/publications/StupidSH36.pdf)

that order 3 SH is sufficient for approximate light source

but for HDR light sources he recommand order 5.

As order 4 is 0 (From paper http://www.eecs.berkeley.edu/~ravir/lighting.pdf I get the formula for A_i)

This mean 4 coefficient to store by color channel.

As I am pretty sure the author store  HDR data, can someone lighten me ?

 

2. About texture storage (which are deduced from above statement)

 

I try to figure out how are encoded the incident radiance in their SHLightmap.

From GDC 2008 conference "Lightmap compression in Halo 3" I can read that the author need to

store for each texel a vector of 5 * 3 float values.

I don't figure what are the values exactly.

 

My assumption is that "3" is for each channel color RGB,

But I can't figure what's the 5 is ?

Are they 5 first band of SH order like I suppose above (but as I said, we only need 4 coefficient in this case)

or maybe order 6 ?

 

In this same paper later I found:

A. Two DXT5 texture for each SH coefficient channel (HDR, positive/negative)

And

B. Each band of the SH coefficients (RGB) are converted to Luvw space

 

I suppose that Luvw space is what is describe in this paper "Rendering from Compressed High Dynamic Range Textures on

Programmable Graphics Hardware" by Peter Pike sloan and al.(ftp://ftp.research.microsoft.com/pub/tr/TR-2006-152.pdf)

 

What I don't understand is that A and B seem different. I can't understand what is store.

Are they storing for each band the triplet RGB of SH coeeficient, mean 3 float value for two DXT5 x order

or do they store store 5 SH coefficient for channel color R in two DXT5 ?

 

So what are the total storage cost of all the 5 * 3 float value in term of DXT5 texture ?

Cause It looks like to be pretty big.

 

Thanks for anyone interested by this post

 

Best regards

 

Lagarde Sébastien


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