mach.geometry.spherical_to_cartesian

mach.geometry.spherical_to_cartesian#

mach.geometry.spherical_to_cartesian(
theta_rad: Real[Array, '*angles'] | float | int,
phi_rad: Real[Array, '*angles'] | float | int,
radius_m: Real[Array, '*angles'] | float | int = 1,
) → Real[Array, '*angles xyz=3'] | tuple[float, float, float]#

Convert standard spherical angle convention to a Cartesian vector.

Uses the physics convention as defined in ISO 80000-2:2019. https://en.wikipedia.org/wiki/Spherical_coordinate_system

Parameters:

  • theta_rad – Polar angle in radians - angle between the radial line and a polar axis.

  • phi_rad – Azimuthal angle in radians - angle of rotation of the radial line around the polar axis.

  • radius_m – Radial distance from the origin in meters (defaults to 1 for unit vectors).

Returns:

Wave-direction vectors in xyz-order, with norm=radius_m. For scalar inputs: returns tuple[float, float, float]. For array inputs: returns array with shape (*angles, 3).

Raises:

ValueError – If any angle has magnitude >= π/2, suggesting possible unit confusion.

Examples

>>> # Convert physics spherical coordinates
>>> import numpy as np
>>> x, y, z = spherical_to_cartesian(np.pi/4, np.pi/3, 1)
>>> print(f"Spherical to Cartesian: ({x:.3f}, {y:.3f}, {z:.3f})")
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