Spherical Harmonics

3D printable models of spherical harmonics.

The .stl files are available on Thingiverse and in the GitHub releases (SH_optimized.zip file).

Definition

The surface of each model is defined by real spherical harmonics:

$$\text S\text H_{lm+}(\theta, \phi) = \sqrt{2}(-1)^{m}\text{Re}\left[Y_{lm}(\theta, \phi)\right]$$ $$\text S\text H_{lm-}(\theta, \phi) = \sqrt{2}(-1)^{m}\text{Im}\left[Y_{lm}(\theta, \phi)\right]$$ $$\text S\text H_{l0+}(\theta, \phi) = \text{Re}\left[Y_{lm}(\theta, \phi)\right]$$

where $l=0,1,\dots$, $m=0,1,\dots,l$, $Y_{lm}$ is the complex-valued spherical harmonic as defined in SciPy. The $+$ and $-$ signs in the $\text{SH}$ index indicate the sign of $m$ in the interval $[-l, l]$.

A small central sphere has been added to each .stl model to soften sharp edges and provide additional support for floating "leaves", improving printability.

Setup

Install all dependencies using uv:

uv sync

Generation

Run the script to generate the models:

uv run generator.py

This script generates .stl files of spherical harmonics on a regular mesh and then optimizes them using gmsh library.

License

Licensed under CC BY-NC-SA 4.0