+1 for introducing them as real-valued functions over cartesian coordinates!
Typically, spherical harmonics are introduced as a complex function over spherical coordinates, which makes them much easier to derive, but imo hides their beauty.
The real-valued, cartesian form of regular spherical harmonics is also called "solid harmonics" or "harmonic polynomials", in case you want to dig deeper.
> spherical harmonics can have uses beyond lighting
This math is also used in Ambisonic surround sound though newer techniques use planewave expansion.
For games, the full-sphere encoding of Ambisonic B-format can be decoded for arbitrary speaker locations and the soundfield rotated around any axis. I'm not sure if its ever been used for a game though.
For sure that's a big reason but it's also a useful basis for doing lighting calculations because of their sphere like nature. They are quite efficient in dynamic scenes and historically used in a lot of precalc to do something akin to real time Global Illumination
Typically, spherical harmonics are introduced as a complex function over spherical coordinates, which makes them much easier to derive, but imo hides their beauty.
The real-valued, cartesian form of regular spherical harmonics is also called "solid harmonics" or "harmonic polynomials", in case you want to dig deeper.
This math is also used in Ambisonic surround sound though newer techniques use planewave expansion.
For games, the full-sphere encoding of Ambisonic B-format can be decoded for arbitrary speaker locations and the soundfield rotated around any axis. I'm not sure if its ever been used for a game though.
https://en.wikipedia.org/wiki/Ambisonics#Higher-order_ambiso...
https://en.wikipedia.org/wiki/Atomic_orbital#Orbitals_table
...and the same patterns appear on the unit disk with the Zernike polynomials, used to describe optical aberrations and more.
https://en.wikipedia.org/wiki/Zernike_polynomials
Like, if you know the third order harmonics that's only 16 values you have to pass around