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From: Alen Ladavac <alenlml@cr...>  20060424 06:02:23

Monday, April 24, 2006, 2:08:20 AM, Tom wrote: >> c3*(2z*z1) > I think this should be c3*(3*z*z1). A three, not a two. Yes. Right. Another typo. Looks like I should be more careful when retyping from C into pseudocode. Alen 
From: Tom Forsyth <tom.gdalgo@ee...>  20060424 00:08:29

> c3*(2z*z1) I think this should be c3*(3*z*z1). A three, not a two. TomF. > Original Message > From: gdalgorithmslistadmin@...=20 > [mailto:gdalgorithmslistadmin@...] On=20 > Behalf Of Alen Ladavac > Sent: 23 April 2006 12:25 > To: gdalgorithmslist@... > Subject: Re[4]: [Algorithms] Cubemap to spherical harmonics (again) >=20 >=20 > Oh I see. Makes sense, of course. I thought it was something more > complicated. >=20 > I'm not using this for cube>sh (not anymore at least), I'm using > those factors for directional light. But now that I understand some > stuff here better, I started getting curious about how exactly does > the directional light to sh conversion works. But it's all snapping > into place now. Thanks for all your help. >=20 > I only list 5 numbers as the 9 polymonials repeat the same 5 > coefficients, so no need to repeat them. The polynomials are in fact: >=20 > c0 > c1*y > c1*z > c1*x > c2*x*y > c2*y*z > c3*(2z*z1) > c2*x*z > c4*(x*xy*y) >=20 > Do you see a problem there, or is it all ok? >=20 > Thanks, > Alen >=20 >=20 >=20 > Sunday, April 23, 2006, 5:57:33 PM, you wrote: >=20 > > The Pi*16/17 factors comes from the notion of a normalized=20 > ([0,1] space) > > directional light. It is derived by solving for a scale factor that > > given a normal pointed in Z with a directional light=20 > shining right on it > > and unit albedo would reflect 1.0. But I don't think you=20 > need this  > > you just need to integrate the RGB values against the raw SH basis > > functions (there should be 9 through the cubics  not sure=20 > why you are > > just showing 5 below and they are polynomials of the normalized > > direction.) >=20 > > PeterPike Sloan >=20 > > Original Message > > From: gdalgorithmslistadmin@... > > [mailto:gdalgorithmslistadmin@...] On=20 > Behalf Of Alen > > Ladavac > > Sent: Saturday, April 22, 2006 11:12 AM > > To: PeterPike Sloan > > Cc: gdalgorithmslist@... > > Subject: Re[2]: [Algorithms] Cubemap to spherical harmonics (again) >=20 > > Thanks a bunch! This does the trick. The reference I was using for > > differential angle obviously got it wrong, plus I didn't do the cos > > kernel convolution correctly. >=20 > > For an additional note, r^(3/2) is not quite correct in=20 > this context. > > I messed that while retyping C into pcode. It should be=20 > only r^3. The > > full expression from that Mathworld article is (x^2+y^2+z^2)^(3/2), > > but since r is already length, not length squared, the square root > > should be dropped. So the differential angle for a point on a > > (1,+1)^3 cube is r^3. With this formulation, sum(diffangle * > > pointarea) / numpoints approaches 4*PI, so it seems to be correct. >=20 > > Now that my cubemap to SH code is fine, I'm getting curious about my > > directional light to SH formulae. They work perfectly, but I don't > > understand why. :) >=20 > > I use the coefficients mentioned before: >=20 > >> 0.282095*0.282095 * PI*16/17 * 1, > >> 0.488603*0.488603 * PI*16/17 * 2/3, > >> 1.092548*1.092548 * PI*16/17 * 1/4, > >> 0.315392*0.315392 * PI*16/17 * 1/4, > >> 0.546274*0.546274 * PI*16/17 * 1/4 >=20 > > The decimal numbers are from the SH basis (1/2*sqrt(pi)=20 > etc). They are > > squared to save on one more multiplication at runtime. The=20 > 1, 2/3 and > > 1/4 factors are from the cosine convolution. I reckon PI is=20 > because I > > need to transform irradiance integral into outgoing radiance. But I > > still don't know what's 16/17 doing there. I recall that it=20 > supposedly > > has something to do with 17/16*4 being the sum of 1 + 3*2/3 + 5*1/4. > > But why is that sum used here, and not when cosine kernel=20 > is added to > > the cubemap projection. And what about the 4? Any=20 > explanation or clue > > on this are warmly welcome. :) >=20 > > Thanks, > > Alen >=20 >=20 > > Saturday, April 22, 2006, 2:27:00 AM, you wrote: >=20 > >> I think you are mixing a couple of things up (directional=20 > lights and > >> projection.) It's much easier to just think of this as=20 > projection  > > in > >> that case you get: >=20 > >> sum =3D 0 // vector of SH coeffs for each color channel > >> wt =3D 0 >=20 > >> For each face > >> For each pixel > >> =20 > >> vdir =3D position on cube (domain is (1,+1)^3) > >> r =3D len(vdir); > >> vdir /=3D r; >=20 > >> da =3D 24.0*r^(3/2) > >> wt +=3D da > >> rgb =3D sample the pixel value > >> rgb *=3D da; > >> =20 > >> addtoSHC(rgb,vdir,sum) > >> =20 >=20 > >> sum *=3D 4*Pi/wt >=20 > >> addtoSHC should just evaluate the SH basis functions in=20 > direction dir. >=20 > >> wt/num_pixels should equal 4*Pi (but it won't be exactly=20 > on the CPU, > > so > >> I tend to do this normalization), so you can just not=20 > accumulate the > >> total weight and instead just divide sum by the # of pixels. >=20 > >> The addtoSHC should literally just be evaluating the basis=20 > functions > > (if > >> you want to convolve with the normalized cosine kernel=20 > just scale the > >> bands by 1,2/3,1/4,0,etc.) >=20 > >> PeterPike Sloan >=20 > >> (the differential solid angle term is where the r(3/2)=20 > comes from  > >> it's commonly used when computing form factors in radiosity, a > >> derivation is here: >=20 > >> http://mathworld.wolfram.com/SolidAngle.html=20 >=20 > >> for what amounts to a cube map. A factor of 4.0 is used in the > >> numerator of a single face, where 24 can be used for the full cube > > (it's > >> just the area of the cube so that when you divide by the number of > >> samples you get the correct fraction of 4*Pi  if you do the > >> normalization yourself this doesn't matter of course since it just > >> cancels out...) ) >=20 > >> Original Message > >> From: gdalgorithmslistadmin@... > >> [mailto:gdalgorithmslistadmin@...] On Behalf Of > > Alen > >> Ladavac > >> Sent: Friday, April 21, 2006 9:10 AM > >> To: gdalgorithmslist@... > >> Subject: [Algorithms] Cubemap to spherical harmonics (again) >=20 > >> Hi list, >=20 > >> I believe that this issue, even though discussed a lot, was never > >> completely clarified in one place. So as my implementation=20 > is a kind > >> of a Frankenstein creation stitched from fragments of math that I > >> understand and pieces that still make by head steam, I=20 > guess it can't > >> hurt to run the actual result by some people that comprehend the SH > >> math better than me. >=20 > >> The reason I ask is that when I run it on a cube that has=20 > upper half > >> pure red and lower half pure green, I get something that I=20 > don't quite > >> expect. Upon evaluating the resulting SH in various=20 > directions, I get > >> mostly yellow everywhere, with just a tiny bit of red/green in the > >> up/down directions. >=20 > >> Even with the cosine term, I'd expect the straight up/down=20 > directions > >> to be pure red/green. Is my expectation wrong, or is the=20 > problem in my > >> implementation? >=20 > >> Here is the pcode: >=20 > >> correction =3D 1/(PI*16/17) > >> pixelarea =3D 4/(sizeU*sizeV) >=20 > >> for each face on the cube > >> for each pixel on the face >=20 > >> vdir =3D position on cube (domain is (1,+1)^3) > >> r =3D len(vdir); > >> vdir /=3D r; >=20 > >> da =3D pixelarea*r^(3/2) >=20 > >> rgb =3D sample the pixel value > >> rgb *=3D angle * correction; > >> addtoSHC(rgb,dir) >=20 > >> Where "addtoSHC()" is the one normally used by the=20 > directional light. > >> I.e. it uses the squared factors with extra corrections: >=20 > >> 0.282095*0.282095 * PI*16/17 * 1, > >> 0.488603*0.488603 * PI*16/17 * 2/3, > >> 1.092548*1.092548 * PI*16/17 * 1/4, > >> 0.315392*0.315392 * PI*16/17 * 1/4, > >> 0.546274*0.546274 * PI*16/17 * 1/4 >=20 > >> I also tried using the plain set of factors for adding (without the > >> squaring and the corrections), but I get even stranger results. >=20 > >> Thanks in advance for any insight, >=20 > >> Alen >=20 >=20 >=20 >=20 > >>  > >> Using Tomcat but need to do more? Need to support web services, > >> security? > >> Get stuff done quickly with preintegrated technology to=20 > make your job > >> easier > >> Download IBM WebSphere Application Server v.1.0.1 based on Apache > >> Geronimo > >> > >=20 > http://sel.asus.falkag.net/sel?cmd=3Dlnk&kid=3D120709&bid=3D263057&; > dat=3D121642 > >> _______________________________________________ > >> GDAlgorithmslist mailing list > >> GDAlgorithmslist@... > >> https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > >> Archives: > >> http://sourceforge.net/mailarchive/forum.php?forum_id=3D6188 >=20 >=20 > >>  > >> Using Tomcat but need to do more? Need to support web services, > > security? > >> Get stuff done quickly with preintegrated technology to=20 > make your job > > easier > >> Download IBM WebSphere Application Server v.1.0.1 based on Apache > > Geronimo > >> = http://sel.asus.falkag.net/sel?cmdlnk&kid=120709&bid&3057&dat=121642 > >> _______________________________________________ > >> GDAlgorithmslist mailing list > >> GDAlgorithmslist@... > >> https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > >> Archives: > >> http://sourceforge.net/mailarchive/forum.php?forum_ida88 >=20 >=20 >=20 >=20 >=20 >=20 > =20 > Best regards, > Alen mailto:alenlml@... >=20 >=20 >=20 >  > Using Tomcat but need to do more? Need to support web=20 > services, security? > Get stuff done quickly with preintegrated technology to make=20 > your job easier > Download IBM WebSphere Application Server v.1.0.1 based on=20 > Apache Geronimo > http://sel.asus.falkag.net/sel?cmd=3Dk&kid=120709&bid&3057&dat=121642 > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_ida88 >=20 