Module spherical 

Spherical coordinate transformations

This module provides functions for transforming between Cartesian and spherical coordinate systems, as well as utilities for working with spherical coordinates.

Spherical coordinates use the following convention:

• r (radius): Distance from the origin to the point
• theta (polar angle): Angle from the positive z-axis (0 to π)
• phi (azimuthal angle): Angle from the positive x-axis in the xy-plane (0 to 2π)

Note: This convention (r, theta, phi) is used in physics. In mathematics, the convention (r, phi, theta) is sometimes used. We follow the physics convention.

Functions

cart_to_spherical

Converts Cartesian coordinates (x, y, z) to spherical coordinates (r, theta, phi)

cart_to_spherical_batch

Converts multiple Cartesian coordinates to spherical coordinates

geodesic_distance

Calculates the geodesic distance between two points on a sphere

spherical_to_cart

Converts spherical coordinates (r, theta, phi) to Cartesian coordinates (x, y, z)

spherical_to_cart_batch

Converts multiple spherical coordinates to Cartesian coordinates

spherical_triangle_area

Calculates the area of a spherical triangle given by three points on a unit sphere