astropy:docs

Source code for astropy.modeling.rotations

# 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)

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