Introduction to Spherical Harmonics for Graphics Programmers

https://gpfault.net/posts/sph.html

#HackerNews #SphericalHarmonics #GraphicsProgramming #MathTechniques #ComputerGraphics #ProgrammingResources

Very glad of this new collaborative work "Herglotz-NET: Implicit Neural Representation of Spherical Data with Harmonic Positional Encoding" with Théo Hanon, Nicolas Mil-Homens Cavaco, John Kiely, Laurent Jacques https://arxiv.org/html/2502.13777v1

In this work, we propose Herglotz-NET (HNET), a novel INR architecture that employs a harmonic positional encoding based on complex Herglotz mappings. This encoding yields a well-posed representation on the sphere with interpretable and robust spectral properties. Moreover, we present a unified expressivity analysis showing that any spherical-based INR satisfying a mild condition exhibits a predictable spectral expansion that scales with network depth. Our results establish HNET as a scalable and flexible framework for accurate modeling of spherical data.

#INR #SphericalHarmonics #HarmonicAnalysis #Sphere

An online interactive viewer based on Minute Physics's video on atomic orbitals by @[email protected]

https://asliceofcuriosity.pagesperso-orange.fr/assets/atom/orbitalsApp-1M.html

#orbitals #electrons #sphericalHarmonics # Atoms