Code Documentation

Welcome! This page provides a structured overview of the spherical-inr toolbox. Modules are grouped by purpose.

Conventions

Spherical coordinates are represented as (theta, phi) in radians, with tensors of shape (..., 2):

• theta ∈ [0, π] (polar angle)

• phi   ∈ [-π, π] (azimuth)

Cartesian coordinates are represented as tensors of shape (..., 3) in \(\mathbb{R}^3\).

Core modules

Models

Ready-to-use networks combining an encoding and a backbone:

• INR — generic composition wrapper

• SirenNet — Fourier features on angles + sine MLP

• HerglotzNet — Herglotz map + sine MLP

• SphericalSirenNet — spherical harmonics on angles + sine MLP

Positional encodings

Coordinate-to-feature mappings used by models or custom compositions:

• FourierPE

• SphericalHarmonicsPE

• HerglotzPE

MLP backbones

Pointwise networks applied to encoded coordinates:

• ReLUMLP

• SineMLP

Coordinate transforms

Utilities for converting between spherical and Cartesian representations:

• tp_to_r3()

• r3_to_tp()

• rtp_to_r3()

• r3_to_rtp()

Differential operators

Autograd-based operators for implicit functions (Cartesian, spherical, and \(\mathbb{S}^2\) variants):

• cartesian_gradient()

• cartesian_divergence()

• cartesian_laplacian()

• spherical_gradient()

• spherical_divergence()

• spherical_laplacian()

• s2_gradient()

• s2_divergence()

• s2_laplacian()