cedalion.geometry.utils

Utility functions for geometric calculations.

Functions

cart2sph(x, y, z)	Convert 3D cartesian into spherical coordinates.
m_rot(angles)	Return a 4×4 homogeneous rotation matrix R = Rz(α)·Ry(β)·Rx(γ).
m_scale1(s)	Return a 4×4 homogeneous isotropic scaling matrix.
m_scale3(s)	Return a 4×4 homogeneous anisotropic scaling matrix.
m_trans(t)	Return a 4×4 homogeneous translation matrix.
pol2cart(theta, rho)	Convert 2D polar into 2D cartesian coordinates.

cedalion.geometry.utils.m_trans(t: ndarray) → ndarray

Return a 4×4 homogeneous translation matrix.

Parameters:

t – Translation vector [tx, ty, tz].

Returns:

4×4 NumPy array encoding the translation as a homogeneous transform.

cedalion.geometry.utils.m_scale3(s: ndarray) → ndarray

Return a 4×4 homogeneous anisotropic scaling matrix.

Parameters:

s – Scale factors [sx, sy, sz] for each axis independently.

Returns:

4×4 NumPy array encoding the anisotropic scaling as a homogeneous transform.

cedalion.geometry.utils.m_scale1(s: ndarray) → ndarray

Return a 4×4 homogeneous isotropic scaling matrix.

Parameters:

s – Array whose first element is the uniform scale factor applied to all axes.

Returns:

4×4 NumPy array encoding the isotropic scaling as a homogeneous transform.

cedalion.geometry.utils.m_rot(angles: ndarray) → ndarray

Return a 4×4 homogeneous rotation matrix R = Rz(α)·Ry(β)·Rx(γ).

See https://en.wikipedia.org/wiki/Rotation_matrix#General_rotations.

Parameters:

angles – Euler angles [alpha, beta, gamma] in radians, corresponding to rotations about Z, Y, and X axes respectively.

Returns:

4×4 NumPy array encoding the combined rotation as a homogeneous transform.

cedalion.geometry.utils.cart2sph(

x: ndarray,

y: ndarray,

z: ndarray,

) → tuple[ndarray, ndarray, ndarray]

Convert 3D cartesian into spherical coordinates.

Parameters:

• x – cartesian x coordinates

• y – cartesian y coordinates

• z – cartesian z coordinates

Returns:

The spherical coordinates azimuth, elevation and radius as np.ndarrays.

cedalion.geometry.utils.pol2cart(

theta: ndarray,

rho: ndarray,

) → tuple[ndarray, ndarray]

Convert 2D polar into 2D cartesian coordinates.

Parameters:

• theta – polar theta/angle coordinates

• rho – polar rho/radius coordinates

Returns:

The cartesian coordinates x and y as np.ndarrays.