gcpy.grid_stretching_transforms

Functions to apply grid-stretching transforms.

Functions

`cartesian_to_spherical`(x, y, z)	Converts Cartesian coordinates to spherical (longitude, latitude) coordinates in radians.
`rotate_vectors`(x, y, z, k, theta)	Rotates 3D vectors about an arbitrary axis using Rodrigues' rotation formula.
`schmidt_transform`(x, y, s)	Applies the Schmidt transform to stretch a spherical grid toward a pole.
`scs_transform`(x, y, s, tx, ty)	Applies the Stretched Cubed-Sphere (SCS) transform to a longitude/latitude grid.
`spherical_to_cartesian`(x, y)	Converts spherical (longitude, latitude) coordinates in radians to Cartesian coordinates.

gcpy.grid_stretching_transforms.rotate_vectors(x, y, z, k, theta)[source]

Rotates 3D vectors about an arbitrary axis using Rodrigues’ rotation formula.

Parameters:

x (array-like) – X-components of the vectors to be rotated.
y (array-like) – Y-components of the vectors to be rotated.
z (array-like) – Z-components of the vectors to be rotated.
k (numpy.ndarray) – Unit vector defining the axis of rotation, shape (3,).
theta (float) – Angle of rotation in radians.

Returns:

x (numpy.ndarray) – X-components of the rotated vectors.
y (numpy.ndarray) – Y-components of the rotated vectors.
z (numpy.ndarray) – Z-components of the rotated vectors.

gcpy.grid_stretching_transforms.cartesian_to_spherical(x, y, z)[source]

Converts Cartesian coordinates to spherical (longitude, latitude) coordinates in radians.

Parameters:

x (array-like) – X-components of the Cartesian coordinates.
y (array-like) – Y-components of the Cartesian coordinates.
z (array-like) – Z-components of the Cartesian coordinates.

Returns:

x_sph (numpy.ndarray) – Longitude in radians, in the range [-pi, pi].
y_sph (numpy.ndarray) – Latitude in radians, in the range [-pi/2, pi/2].

gcpy.grid_stretching_transforms.spherical_to_cartesian(x, y)[source]

Converts spherical (longitude, latitude) coordinates in radians to Cartesian coordinates.

Parameters:

x (array-like) – Longitude in radians.
y (array-like) – Latitude in radians.

Returns:

x_car (numpy.ndarray) – X-components of the Cartesian coordinates.
y_car (numpy.ndarray) – Y-components of the Cartesian coordinates.
z_car (numpy.ndarray) – Z-components of the Cartesian coordinates.

gcpy.grid_stretching_transforms.schmidt_transform(x, y, s)[source]

Applies the Schmidt transform to stretch a spherical grid toward a pole.

Parameters:

x (array-like) – Longitude in radians.
y (array-like) – Latitude in radians.
s (float) – Stretch factor. Values greater than 1 compress the grid near the south pole and expand it near the north pole.

Returns:

x (array-like) – Longitude in radians (unchanged by this transform).
y (numpy.ndarray) – Stretched latitude in radians.

Notes

The Schmidt parameter D is computed as (1 - s**2) / (1 + s**2).

gcpy.grid_stretching_transforms.scs_transform(x, y, s, tx, ty)[source]

Applies the Stretched Cubed-Sphere (SCS) transform to a longitude/latitude grid. This combines a Schmidt stretch with rotations about the x- and z-axes to relocate the high-resolution region to a target longitude and latitude.

Parameters:

x (array-like) – Longitude in degrees.
y (array-like) – Latitude in degrees.
s (float) – Stretch factor. Values greater than 1 increase the resolution near the target point.
tx (float) – Target longitude in degrees. The center of the high-resolution region will be placed at this longitude.
ty (float) – Target latitude in degrees. The center of the high-resolution region will be placed at this latitude.

Returns:

x (numpy.ndarray) – Transformed longitude in degrees.
y (numpy.ndarray) – Transformed latitude in degrees.

Notes

The transform proceeds in the following steps:

Convert all angles from degrees to radians.
Apply the Schmidt transform to stretch the grid.
Convert to Cartesian coordinates.
Rotate about the y-axis by (ty - y0) to shift the target latitude.
Rotate about the z-axis by (tx - x0) to shift the target longitude.
Convert back to spherical coordinates and then to degrees.