# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Implements roations, including spherical rotations as defined in WCS Paper II
[1]_
`RotateNative2Celestial` and `RotateCelestial2Native` follow the convention in
WCS Paper II to rotate to/from a native sphere and the celestial sphere.
The user interface sets and displays angles in degrees but the values are
stored internally in radians. This is managed through the parameter
setters/getters.
References
----------
.. [1] Calabretta, M.R., Greisen, E.W., 2002, A&A, 395, 1077 (Paper II)
"""
from __future__ import (absolute_import, unicode_literals, division,
print_function)
import math
import numpy as np
from .core import Model
from .parameters import Parameter, InputParameterError
__all__ = ['RotateCelestial2Native', 'RotateNative2Celestial', 'Rotation2D']
class EulerAngleRotation(Model):
"""
Base class for Euler angle rotations.
Parameters
----------
phi, theta, psi : float
Euler angles in deg
"""
n_inputs = 2
n_outputs = 2
phi = Parameter(getter=np.rad2deg, setter=np.deg2rad)
theta = Parameter(getter=np.rad2deg, setter=np.deg2rad)
psi = Parameter(getter=np.rad2deg, setter=np.deg2rad)
def __init__(self, phi, theta, psi):
super(EulerAngleRotation, self).__init__(phi, theta, psi)
[docs]class RotateNative2Celestial(EulerAngleRotation):
"""
Transformation from Native to Celestial Spherical Coordinates.
Defines a ZXZ rotation.
Parameters
----------
phi, theta, psi : float
Euler angles in deg
"""
[docs] def inverse(self):
return RotateCelestial2Native(self.phi, self.theta, self.psi)
[docs] def __call__(self, nphi, ntheta):
nphi = np.deg2rad(nphi)
ntheta = np.deg2rad(ntheta)
# TODO: Unfortunately right now this superfluously converts from
# radians to degrees back to radians again--this will be addressed in a
# future change
phi = np.deg2rad(self.phi)
psi = np.deg2rad(self.psi)
theta = np.deg2rad(self.theta)
calpha = np.rad2deg(
phi +
np.arctan2(-np.cos(ntheta) * np.sin(nphi - psi),
np.sin(ntheta) * np.cos(theta) -
np.cos(ntheta) * np.sin(theta) * np.cos(nphi - psi)))
cdelta = np.rad2deg(
np.arcsin(np.sin(ntheta) * np.sin(theta) +
np.cos(ntheta) * np.cos(theta) * np.cos(nphi - psi)))
ind = calpha < 0
if isinstance(ind, np.ndarray):
calpha[ind] += 360
elif ind:
calpha += 360
return calpha, cdelta
[docs]class RotateCelestial2Native(EulerAngleRotation):
"""
Transformation from Celestial to Native to Spherical Coordinates.
Defines a ZXZ rotation.
Parameters
----------
phi, theta, psi : float
Euler angles in deg
"""
[docs] def inverse(self):
return RotateNative2Celestial(self.phi, self.theta, self.psi)
[docs] def __call__(self, calpha, cdelta):
calpha = np.deg2rad(calpha)
cdelta = np.deg2rad(cdelta)
# TODO: Unfortunately right now this superfluously converts from
# radians to degrees back to radians again--this will be addressed in a
# future change
phi = np.deg2rad(self.phi)
psi = np.deg2rad(self.psi)
theta = np.deg2rad(self.theta)
nphi = np.rad2deg(
psi +
np.arctan2(-np.cos(cdelta) * np.sin(calpha - phi),
np.sin(cdelta) * np.cos(theta) -
np.cos(cdelta) * np.sin(theta) * np.cos(calpha - phi)))
ntheta = np.rad2deg(
np.arcsin(np.sin(cdelta) * np.sin(theta) +
np.cos(cdelta) * np.cos(theta) * np.cos(calpha - phi)))
ind = nphi > 180
if isinstance(ind, np.ndarray):
nphi[ind] -= 360
elif ind:
nphi -= 360
return nphi, ntheta
[docs]class Rotation2D(Model):
"""
Perform a 2D rotation given an angle in degrees.
Positive angles represent a counter-clockwise rotation and vice-versa.
Parameters
----------
angle : float
angle of rotation in deg
"""
n_inputs = 2
n_outputs = 2
angle = Parameter(default=0.0, getter=np.rad2deg, setter=np.deg2rad)
def __init__(self, angle=angle.default):
super(Rotation2D, self).__init__(angle)
self._matrix = self._compute_matrix(np.deg2rad(angle))
[docs] def inverse(self):
"""Inverse rotation."""
return self.__class__(angle=-self.angle)
[docs] def __call__(self, x, y):
"""
Apply the rotation to a set of 2D Cartesian coordinates given as two
lists--one for the x coordinates and one for a y coordinates--or a
single coordinate pair.
Parameters
----------
x, y : array, float
x and y coordinates
"""
x = np.asarray(x)
y = np.asarray(y)
if x.shape != y.shape:
raise ValueError("Expected input arrays to have the same shape")
shape = x.shape
inarr = np.array([x.flatten(), y.flatten()], dtype=np.float64)
if inarr.shape[0] != 2 or inarr.ndim != 2:
raise ValueError("Incompatible input shapes")
result = np.dot(self._matrix, inarr)
x, y = result[0], result[1]
if x.shape != shape:
x.shape = shape
y.shape = shape
return x, y
@staticmethod
def _compute_matrix(angle):
return np.array([[math.cos(angle), -math.sin(angle)],
[math.sin(angle), math.cos(angle)]],
dtype=np.float64)