def intrinsic_to_extrinsic_coords(point_intrinsic):
"""Convert point from intrinsic to extrensic coordinates.
Convert the parameterization of a point in the hyperbolic space
from its intrinsic coordinates, to its extrinsic coordinates
in Minkowski space.
Parameters
----------
point_intrinsic : array-like, shape=[..., n_disk, dim]
Point in intrinsic coordinates.
Returns
-------
point_extrinsic : array-like, shape=[..., n_disks, dim + 1]
Point in extrinsic coordinates.
"""
n_disks = point_intrinsic.shape[1]
point_extrinsic = gs.stack(
[
_Hyperbolic.change_coordinates_system(
point_intrinsic[:, i_disk, ...], "intrinsic", "extrinsic")
for i_disk in range(n_disks)
],
axis=1,
)
return point_extrinsic
def intrinsic_to_extrinsic_coords(self, point_intrinsic):
"""Convert from intrinsic to extrinsic coordinates.
Parameters
----------
point_intrinsic : array-like, shape=[..., dim]
Point in the embedded manifold in intrinsic coordinates.
Returns
-------
point_extrinsic : array-like, shape=[..., dim + 1]
Point in the embedded manifold in extrinsic coordinates.
"""
if self.dim != point_intrinsic.shape[-1]:
raise NameError("Wrong intrinsic dimension: " +
str(point_intrinsic.shape[-1]) + " instead of " +
str(self.dim))
return _Hyperbolic.change_coordinates_system(point_intrinsic,
"intrinsic", "extrinsic")
def extrinsic_to_intrinsic_coords(self, point_extrinsic):
"""Convert from extrinsic to intrinsic coordinates.
Parameters
----------
point_extrinsic : array-like, shape=[..., dim + 1]
Point in the embedded manifold in extrinsic coordinates,
i. e. in the coordinates of the embedding manifold.
Returns
-------
point_intrinsic : array-like, shape=[..., dim]
Point in intrinsic coordinates.
"""
belong_point = self.belongs(point_extrinsic)
if not gs.all(belong_point):
raise NameError("Point that does not belong to the hyperboloid "
"found")
return _Hyperbolic.change_coordinates_system(point_extrinsic,
"extrinsic", "intrinsic")