Interactive 3D surface explorer built with Dash and Plotly.
Ellipsoid: parametric ellipsoid scaled by axes a, b, c.
Spherical Harmonics: sphere of radius r₀ deformed by a weighted sum of real spherical harmonics: r(θ,φ) = r₀ + Σ aₗₘ Yₗᵐ(θ,φ). Coefficients aₗₘ are set per (l,m) pair up to L_max.
Orbital: polar plot of r(θ,φ) = r₀ + Σ |Yₗᵐ|·Yₗᵐ, showing the pure angular structure of the harmonics as lobes (analogous to atomic orbitals). An optional semi-transparent SH overlay can be toggled to compare the two representations.
θ and φ domain limits are shared across all modes.
pip install dash plotly numpy scipy beartype
python app.pyThen open http://127.0.0.1:8050.
| File | Purpose |
|---|---|
app.py |
Dash app, layout, callbacks |
ellipticalSurface.py |
Ellipsoid surface computation |
sphericalHarmonicSurface.py |
SH-deformed sphere |
orbitalSurface.py |
Orbital polar plot |
sphericalHarmonic.py |
Real spherical harmonic Yₗᵐ |
mesh.py |
θ/φ meshgrid utility |