def tip_axis(coord: UnitSphericalRepresentation, axis_lon: Angle,
rot_angle: Angle) -> UnitSphericalRepresentation:
"""Perform a rotation about an axis perpendicular to the Z-axis.
The purpose of this rotation is to move the pole of the coordinate system from one place to
another. For example, transforming from a coordinate system where the pole is aligned with the
physical pole of a mount to a topocentric coordinate system where the pole is aligned with
zenith.
Note that this is a true rotation, and the same rotation is applied to all coordinates in the
originating coordinate system equally. It is not equivalent to using SkyCoord
directional_offset_by() with a fixed position angle and separation since the direction and
magnitude of the offset depend on the value of coord.
Args:
coord: Coordinate to be transformed.
axis_lon: Longitude angle of the axis of rotation.
rot_angle: Angle of rotation.
Returns:
Coordinate after transformation.
"""
rot = rotation_matrix(rot_angle,
axis=SkyCoord(axis_lon, 0 *
u.deg).represent_as('cartesian').xyz)
coord_cart = coord.represent_as(CartesianRepresentation)
coord_rot_cart = coord_cart.transform(rot)
return coord_rot_cart.represent_as(UnitSphericalRepresentation)
def ang2vec(theta, phi, lonlat=False):
"""Drop-in replacement for healpy `~healpy.pixelfunc.ang2vec`."""
lon, lat = _healpy_to_lonlat(theta, phi, lonlat=lonlat)
rep_sph = UnitSphericalRepresentation(lon, lat)
rep_car = rep_sph.represent_as(CartesianRepresentation)
return rep_car.xyz.value
# [-khat.y, khat.x, 0]])
# create 3x3 rotational matrix R using Rodrigues' rotation formula
Iden = np.identity(3)
K2 = np.matmul(K, K)
# right hand rule
R = Iden + sintheta*K + (1-np.cos(theta))*K2
# left hand rule testing
# R = Iden + np.sin(-theta)*K + (1-np.cos(-theta))*K2
# print('The rotational matrix to rotate cartesian vector A to B is')
# print(R)
return R
J2000R1 = UnitSphericalRepresentation(0*u.deg, 90*u.deg)
carJ1 = J2000R1.represent_as(CartesianRepresentation)
J2000R2 = UnitSphericalRepresentation(10*u.deg, 90*u.deg)
carJ2 = J2000R2.represent_as(CartesianRepresentation)
# Note that J2000R1 and J2000R2 give the same (x,y,z) : obviously!
# photo op event time used: 2084-11-10T07:53:35
Tref = 2451545 # reference JD for '2000-01-01T12:00:00'
Tevent = 2482539.828877315 # photo op event time used: 2084-11-10T07:53:35
MarsRRA = (317.681 - 0.106*(Tevent-Tref)/36525)
MarsRDEC = (52.887 - 0.061*(Tevent-Tref)/36525)
MarsR = UnitSphericalRepresentation(MarsRRA*u.deg, MarsRDEC*u.deg)
carM = MarsR.represent_as(CartesianRepresentation)
