Spherical_Harmonics

by Crys in Modifier Setups

The Spherical Harmonics node

Spherical harmonics (SH) are a set of functions that can be used to represent a wide variety of physical phenomena, such as the distribution of temperature or the gravitational potential on the surface of a sphere. They are a special type of complex function that are defined on the surface of a sphere and are based on the mathematical concept of harmonics, which are solutions to certain types of wave equations. Spherical harmonics are often used in physics, astronomy, and engineering to model and analyze data that is collected on the surface of a sphere.
SH are mathematically defined as

where is the Legendre polynomial.

Two nodes already market as asset are available in the proposed file. To use them, just put the file in your asset librairies
• The first (and main) node is called Spherical_Harmonics. It is a node which generate the spherical harmonics
• The second node is allows to sum different spherical harmonics

Spherical_Harmonics :

• l : integer value (up to 10)
• m : integer value with -l ≤ m ≤ l
• Material_1 : material for positive values of SH • Material_2 : material for negative values of SH • subdivision : mesh subdivision
• scale : scale of the generated mesh

SumSH :

• SH1 : First spherical harmonic mesh
• SH2 : Second spherical harmonic mesh
• Fields : fields of random values
• A1 : real number
• A2 : real number
• switch : (rarely) a bug may appear during the generation of the mesh. This is due to a desynchronization between the angle values between the two meshes. The switch button allows to change the origin


Some coments
• For operations on Spherical Harmonics, you must have the same subdivision value for all nodes
• The operations generate the sum of the absolute Ylm values and not the sum of the Ylm

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Spherical harmonics