Comments for post 2011-04-14-spherical-harmonics-wtf

[tommadams]

Comments for blog post 2011-04-14-spherical-harmonics-wtf

[tommadams]

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David said on 2011-04-14 15:09:16:

Hey,

I went through the same struggles. Having his images not be gamma correct made me doubt my results. Though, there are a couple things you can do to make sure your results are correct.

For example, if your image is all white then if you sample your normal anywhere you can make sure that the convolution is going to be 1.0

I hate the Ravi Rammaoorthi paper that everyone references because it really provides no explanation behind the math. It kept me severely confused for a long time. Though, the second paper you linked and his phd thesis http://graphics.stanford.edu/papers/ravir_thesis/
are really good.

I learned a lot from his PhD thesis and it cleared up a lot of issues for me.

-= Dave

[tommadams]

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Tom Madams said on 2011-04-14 15:51:59:

Thanks for the link to the thesis, I hadn't found that and it looks pretty comprehensive. It'll make for good bedtime reading.

I did just what you described with the all white images. What's nice about that is that when you convert to an irradiance map, the values become pi, which is what you'd expect from the integral of a Lambertian BRDF. That was the moment I decided that I was right and the paper was wrong :)

[tommadams]

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Robin Green said on 2011-04-15 18:01:28:

Been doing a lot of looking into spherical basis functions generally and have come to the conclusion that SH functions are pretty much the wrong thing to use in most all cases. The Ravi Rampossibletospell's paper is truly obtuse, right up there with Schröder & Sweldens implenetrable paper on "Spherical Wavelets". It's heartening to see just how quickly the astrophysics world note the cite and it's deficiencies and move on to better things.

[tommadams]

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Miles said on 2011-04-16 01:57:51:

Also Insomniac's "Useful results in Spherical Harmonics" is a nice summary:

http://www.insomniacgames.com/assets/files/128707735545510.pdf

@robin can you provide any pointers to alternatives or what the astrophysics world uses instead?

[tommadams]

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David Neubelt said on 2011-04-17 17:29:40:

I can't speak for Robin but I've been doing the same research and came to the same conclusion.

I'd refer you to look into spherical radial basis functions. http://www.cse.cuhk.edu.hk/~ttwong/papers/srbf/srbf.html

[tommadams]

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Robin Green said on 2011-04-22 20:34:58:

Hoping to drop the results in a future Siggraph and GDC paper and tutorial. It's been a long, 4-year journey into the depths of basis functions, Riesz and Hilbert spaces and the fundamental nature of orthogonality. A short post wouldn't cover it.

[tommadams]

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Nivedita Goswami said on 2013-06-20 13:58:29:

I am looking into spherical harmonic lighting for my masters project (C++, OpenGL). I have found Robin's paper quite useful so far. I get uto the point of computing the SH but I am a bit lost when it comes to the lighting equation. Can somebody point me to some code that will make things clearer?
Thanks

[tommadams]

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Neil Gatenby said on 2014-01-14 05:47:36:

http://www.insomniacgames.com/useful-results-in-spherical-harmonics-mainly-2-band/ is the up-to-date IG link. Hope that helps.

[tommadams]

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ekflame said on 2014-08-20 01:54:56:

hello~ I'm studying SH Light with http://www.cs.columbia.edu/~cs4162/slides/spherical-harmonic-lighting.pdf

hmm... I have two question about it.. first is..

1. Equation 4. Mapping [0..1,0..1] random numbers into spherical coordinates.

in above E4. theta is mapped to '2arccos( root( 1 - deltaX) ).. but I can't understand where come from that... why don't use phi*deltaX ?

2. Equation 7. Integrating the product of two SH functions by evaluating a dot product of their coefficients.

I have known, funcY ( SH basis function ) is orthonormal, so P0xP1 = 0. P1xP1->1 but I can't prove Equation 7....

I need help... thank you...

[tommadams]

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Tom Madams said on 2014-08-20 08:31:34:

1. If you use π*ξ_x you won't get a uniform sampling of points over the hemisphere, you'll get a much higher density of points near the top of your hemisphere. Equation 4 corrects for this; try plotting the points, it should be clear to see.

2. Hmm, I'm not sure I can help you here. Sorry, it's been a long time since I thought about this and my maths is quite rusty.

[tommadams]

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ekflame said on 2014-08-21 05:05:19:

thanks,

1. I guess it too... but I don't know what that equation come from...

2. I solved it, I misunderstood , y1(s)y1(s) = 1, y1(s)y2(0) = 0.
   It's not on multiplying, it's on integrating...

thanks for your help. about question (1), I need more thinking ..

[tommadams]

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Raul said on 2016-08-18 02:53:01:

It should be noted that the values reported in Figure 2 of the Siggraph paper are scaled by multiplying by 10 for the Grace Cathedral and dividing by 10 for the Eucalyptus Grove (rnl_probe) and St. Peters Basilica.