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From: PeterPike Sloan <peter_pike_sloan@ho...>  20100201 21:44:52

Hi, I believe the source of confusion is that in this equation (5) things are expressed in the local coordinate frame, the fact that they show 3 coefficients implies they are using quadratic SH (so when rotated into the local frame and integrated against a clamped cosine function you only need the 3 ZH coefficients.) The general case (where you don't know the coordinate frame, or you want to evaluate for any normal) requires all 9 coefficients. I think the "5*3" comes from the compression mentioned in Hao's slides (linear SH + RGB for directional light in "optimal linear" direction. Which is 5*3 scalars.) The compression work is Wang et al, I think Yaohua's slides are more indicative of what was actually used... PeterPike Sloan Date: Fri, 29 Jan 2010 16:28:57 +0100 From: sebastien.lagarde@... To: gdalgorithmslist@... Subject: [Algorithms] Some question about "Lighting and Material of Halo3" and "Lightmap compression in Halo 3" 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/Chapter01ChenLighting_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/TR2006152.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 
From: Sam Martin <sam.martin@ge...>  20100201 21:26:17

Hi Sébastien, Yeah, the maths is a bit of a headache... I think I see where you might be getting stuck. The clamped cosine, projected into SH, is a radially symmetric SH (ie. a zonal harmonic with no rotation). But the fact it is radially symmetric is a requirement if the convolution to produce another SH as an output. Convolving two arbitrary SH functions together doesn't actually produce another SH  it produces a higher dimensional object, which isn't so useful. It's only when one (or both) of the SH are radially symmetric that the result is still an SH. And by a similar argument, both SH need to be radially symmetric to get a radially symmetric output (in general). Convolution with a clamped cosine has some additional properties though. The 'clamp' part of the function produces a lot* of high frequency harmonics, but only evennumbered ones  all the oddnumbered levels vanish apart from L1. The coefficients also tail off very quickly so you don't need to store anything beyond L2 in practice (L3 is 0 anyway). The very best way to test this is to completely ignore the maths, and show people screenshots with different versions. You can see there is a difference, but it's extremely hard to tell which one is the mathematically more accurate version. They all look good, just different. Completely separate to that, you can sometimes represent a nonradially symmetric spherical function by accumulating several independently rotated radially symmetric functions. It's not all that different from storing a list of separate directional lights in some sense. I don't know if this what Halo are doing, although I'll probably have to read that paper now :) It's also worth making the distinction between incoming radiance, which is high frequency and isn't well represented by any kind of SH, and diffuse irradiance, which has the cosine integrated in already. SH are really great at diffuse stuff, but don't handle complexity well. Hope that helps! Thanks, Sam * = nonrigorous terminology :) From: Sébastien Lagarde [mailto:sebastien.lagarde@...] Sent: 01 February 2010 17:55 To: Game Development Algorithms Subject: Re: [Algorithms] Some question about "Lighting andMaterialofHalo3"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 realtime rendering in Dynamic, lowfrequency lighting environments (http://research.microsoft.com/enus/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 
From: David Neubelt <david@re...>  20100201 19:45:16

Hi, I can't access that paper as the website seems to be down right now but I can talk about convolving the signal with a cosine function. Check out the paper "An Effecient Representation for Irradiance Environment Maps" by Ravi Ramamoorthi and Pat Hanrahan. As Sam pointed out while the cosine function is circularly symmetric the input lighting is very complex. You can think of the cosine function as a low pass filter. It leaves you with a nonsymmetric function. Now, where I think you are getting confused is how coefficients are getting through when the odd terms > 1 are 0 for the cosine coefficients projected against the associated legendre functions. The derivation is in the environment map paper so I won't explain it here but the key equation is (7). $E(\theta, \phi) = \sum _l_m [A_l * L_l_m * Y_l_m(\theta, \phi)]$ (you can copy the above LaTeX equation into an online viewer such as http://www.codecogs.com/components/equationeditor/equationeditor.php if you can't read LaTeX) Notice, how l is defined for l <= 2 and it does contribute to the equation and as l gets higher it quickly dampens the function. As you can see for the first 9 coefficients cosine will not zero out any terms. Mind you this is 9 coefficients for just one color channel multiply that by 3 for RGB. = Dave From: Sébastien Lagarde [mailto:sebastien.lagarde@...] Sent: Monday, February 01, 2010 9:55 AM To: Game Development Algorithms Subject: Re: [Algorithms] Some question about "Lighting andMaterialofHalo3"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 realtime rendering in Dynamic, lowfrequency lighting environments (http://research.microsoft.com/enus/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 
From: Sébastien Lagarde <sebastien.lagarde@do...>  20100201 17:55:39

From: Francis Boivin <francis.boivin@ub...>  20100201 15:40:04

FWIW there here is a new compression scheme to be presented @ I3D 2010 http://www.cg.tuwien.ac.at/research/publications/2010/Habel2010EIN/ @inproceedings\{Habel2010EIN, title = "Efficient Irradiance Normal Mapping", author = "Ralf Habel and Michael Wimmer", year = "2010", abstract = "Irradiance normal mapping is a method to combine two popular techniques, light mapping and normal mapping, and is used in games such as HalfLife 2 or Halo 3. This combination allows using lowresolution light caching on surfaces with only a few coefficients which are evaluated by normal maps to render spatial highfrequency changes in the lighting. Though there are dedicated bases for this purpose such as the HalfLife 2 basis, higher order basis functions such as quadratic Spherical Harmonics are needed for an accurate representation. However, a full spherical basis is not needed since the irradiance is stored on the surface of a scene. In order to represent the irradiance signals efficiently, we propose a novel polynomial, hemispherically orthonormal basis function set that is specifically designed to carry a directional irradiance signal on the hemisphere and which makes optimal use of the number of coefficients. To compare our results with previous work, we analyze the relations and attributes of previously proposed basis systems and show that 6 coefficients are sufficient to accurately represent an irradiance signal on the hemisphere. To create the necessary irradiance signals, we use Spherical Harmonics as an intermediate basis due to their fast filtering capabilities.", pages = "%pages_from%%pages_to%", month = feb, location = "Washington D.C.", booktitle = "Proceedings of I3D 2010", keywords = "realtime rendering, irradiance, lightmap, normal mapping", URL = "http://www.cg.tuwien.ac.at/research/publications/2010/Habel2010EIN/";, } From: Sébastien Lagarde [mailto:sebastien.lagarde@...] Sent: Friday, January 29, 2010 10:29 AM To: gdalgorithmslist@... Subject: [Algorithms] Some question about "Lighting and Material of Halo3" and "Lightmap compression in Halo 3" 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/Chapter01ChenLighting_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/TR2006152.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 
From: Sam Martin <sam.martin@ge...>  20100201 15:06:52

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:sebastien.lagarde@...] 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:jwatte@...] 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 falloff 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 <sebastien.lagarde@...> 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/Chapter01ChenLighting_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/TR2006152.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  The Planet: dedicated and managed hosting, cloud storage, colocation Stay online with enterprise data centers and the best network in the business Choose flexible plans and management services without longterm contracts Personal 24x7 support from experience hosting pros just a phone call away. http://p.sf.net/sfu/theplanetcom _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist 
From: Sébastien Lagarde <sebastien.lagarde@do...>  20100201 12:42:01

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:jwatte@...] 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 falloff 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 <sebastien.lagarde@...> 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/Chapter01ChenLighting_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/TR2006152.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  The Planet: dedicated and managed hosting, cloud storage, colocation Stay online with enterprise data centers and the best network in the business Choose flexible plans and management services without longterm contracts Personal 24x7 support from experience hosting pros just a phone call away. http://p.sf.net/sfu/theplanetcom _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist 