Obligatory useful SH paper for 3d rendering: http://www.ppsloan.org/publications/StupidSH36.pdf Also lots of other cool research around SH in rendering, e.g. the recent ZH3 paper.
Thanks for sharing this! Linked it on the website.
Spherical Harmonics
31–40 of 65 posts
Re: Spherical Harmonics
#32Anyone know a good explanation of what spherical harmonics are?
They are just eigen states of the angular momentum operator.
Re: Spherical Harmonics
#33Anyone know a good explanation of what spherical harmonics are?
a vibrating string make sine waves, a vibrating bubble make spherical harmonics.
Re: Spherical Harmonics
#34If anyone is curious about applications - these can be used to approximate low-frequency components of a point's surroundings. They were used in Halo 3 to do real-time HDRI lighting and shadowing (see "Lighting and Material of Halo 3" from Siggraph 2008). After the success of this method, there was a fairly long stretch of researchers looking for a better orthonormal basis (such as 2D Haar wavelents, as spherical har…
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Re: Spherical Harmonics
#35If anyone is curious about applications - these can be used to approximate low-frequency components of a point's surroundings. They were used in Halo 3 to do real-time HDRI lighting and shadowing (see "Lighting and Material of Halo 3" from Siggraph 2008). After the success of this method, there was a fairly long stretch of researchers looking for a better orthonormal basis (such as 2D Haar wavelents, as spherical har…
I wonder if Cartesian-basis multipole expansion could get the best of both worlds of GS and SH, as the former basis captures anisotropy but not detail while the latter captures detail but not anisotropy, whereas Cartesian multipole expansion naturally captures both right from the low orders, and is much easier to align to game worlds.
(to be precise, both can be captured by either if you include enough orders, what I mean is mainly how the information distribution scales with respect to each attribute)
Also, the age-old physics question: what is the minimum order of spherical harmonics required to approximate a cow?
Re: Spherical Harmonics
#36Obligatory useful SH paper for 3d rendering: http://www.ppsloan.org/publications/StupidSH36.pdf Also lots of other cool research around SH in rendering, e.g. the recent ZH3 paper.
Stupid sexy harmonics.
Re: Spherical Harmonics
#37If anyone is curious about applications - these can be used to approximate low-frequency components of a point's surroundings. They were used in Halo 3 to do real-time HDRI lighting and shadowing (see "Lighting and Material of Halo 3" from Siggraph 2008). After the success of this method, there was a fairly long stretch of researchers looking for a better orthonormal basis (such as 2D Haar wavelents, as spherical har…
Another application is Ambisonic sound spatialisation formats, where a finite set of signals corresponding to spherical harmonics are used to encode spatial sound fields. https://en.wikipedia.org/wiki/Ambisonics
Re: Spherical Harmonics
#38Shameless plug, in 140 bytes https://www.dwitter.net/h/wikimedia
Re: Spherical Harmonics
#39See also the “cubic harmonics”, which is an equivalent basis to spherical harmonics but they are real instead of complex, and also more natural to use in cubic crystals due to their symmetries.
I have also seen “triangular harmonics”, “zonal harmonics”, etc. in use in other materials.
Re: Spherical Harmonics
#40Anyone know a good explanation of what spherical harmonics are?
a vibrating string make sine waves, a vibrating bubble make spherical harmonics.
Love it, that's a fantastic image for these. As a musician intimately aware of how vibrating strings work, the vibrating bubble is a perfect analogy, it seems.