# Licensed under a 3-clause BSD style license - see LICENSE.rst
# -*- coding: utf-8 -*-
"""
Implements projections--particularly sky projections defined in WCS Paper II
[1]_.
All angles are set and and displayed in degrees but internally computations are
performed in radians. All functions expect inputs and outputs degrees.
References
----------
.. [1] Calabretta, M.R., Greisen, E.W., 2002, A&A, 395, 1077 (Paper II)
"""
import abc
import numpy as np
from .core import Model
from .parameters import Parameter, InputParameterError
from astropy import units as u
from . import _projections
from .utils import _to_radian, _to_orig_unit
projcodes = [
'AZP', 'SZP', 'TAN', 'STG', 'SIN', 'ARC', 'ZEA', 'AIR', 'CYP',
'CEA', 'CAR', 'MER', 'SFL', 'PAR', 'MOL', 'AIT', 'COP', 'COE',
'COD', 'COO', 'BON', 'PCO', 'TSC', 'CSC', 'QSC', 'HPX', 'XPH'
]
__all__ = ['Projection', 'Pix2SkyProjection', 'Sky2PixProjection',
'Zenithal', 'Cylindrical', 'PseudoCylindrical', 'Conic',
'PseudoConic', 'QuadCube', 'HEALPix',
'AffineTransformation2D',
'projcodes',
'Pix2Sky_ZenithalPerspective', 'Sky2Pix_ZenithalPerspective',
'Pix2Sky_SlantZenithalPerspective', 'Sky2Pix_SlantZenithalPerspective',
'Pix2Sky_Gnomonic', 'Sky2Pix_Gnomonic',
'Pix2Sky_Stereographic', 'Sky2Pix_Stereographic',
'Pix2Sky_SlantOrthographic', 'Sky2Pix_SlantOrthographic',
'Pix2Sky_ZenithalEquidistant', 'Sky2Pix_ZenithalEquidistant',
'Pix2Sky_ZenithalEqualArea', 'Sky2Pix_ZenithalEqualArea',
'Pix2Sky_Airy', 'Sky2Pix_Airy',
'Pix2Sky_CylindricalPerspective', 'Sky2Pix_CylindricalPerspective',
'Pix2Sky_CylindricalEqualArea', 'Sky2Pix_CylindricalEqualArea',
'Pix2Sky_PlateCarree', 'Sky2Pix_PlateCarree',
'Pix2Sky_Mercator', 'Sky2Pix_Mercator',
'Pix2Sky_SansonFlamsteed', 'Sky2Pix_SansonFlamsteed',
'Pix2Sky_Parabolic', 'Sky2Pix_Parabolic',
'Pix2Sky_Molleweide', 'Sky2Pix_Molleweide',
'Pix2Sky_HammerAitoff', 'Sky2Pix_HammerAitoff',
'Pix2Sky_ConicPerspective', 'Sky2Pix_ConicPerspective',
'Pix2Sky_ConicEqualArea', 'Sky2Pix_ConicEqualArea',
'Pix2Sky_ConicEquidistant', 'Sky2Pix_ConicEquidistant',
'Pix2Sky_ConicOrthomorphic', 'Sky2Pix_ConicOrthomorphic',
'Pix2Sky_BonneEqualArea', 'Sky2Pix_BonneEqualArea',
'Pix2Sky_Polyconic', 'Sky2Pix_Polyconic',
'Pix2Sky_TangentialSphericalCube', 'Sky2Pix_TangentialSphericalCube',
'Pix2Sky_COBEQuadSphericalCube', 'Sky2Pix_COBEQuadSphericalCube',
'Pix2Sky_QuadSphericalCube', 'Sky2Pix_QuadSphericalCube',
'Pix2Sky_HEALPix', 'Sky2Pix_HEALPix',
'Pix2Sky_HEALPixPolar', 'Sky2Pix_HEALPixPolar',
# The following are short FITS WCS aliases
'Pix2Sky_AZP', 'Sky2Pix_AZP',
'Pix2Sky_SZP', 'Sky2Pix_SZP',
'Pix2Sky_TAN', 'Sky2Pix_TAN',
'Pix2Sky_STG', 'Sky2Pix_STG',
'Pix2Sky_SIN', 'Sky2Pix_SIN',
'Pix2Sky_ARC', 'Sky2Pix_ARC',
'Pix2Sky_ZEA', 'Sky2Pix_ZEA',
'Pix2Sky_AIR', 'Sky2Pix_AIR',
'Pix2Sky_CYP', 'Sky2Pix_CYP',
'Pix2Sky_CEA', 'Sky2Pix_CEA',
'Pix2Sky_CAR', 'Sky2Pix_CAR',
'Pix2Sky_MER', 'Sky2Pix_MER',
'Pix2Sky_SFL', 'Sky2Pix_SFL',
'Pix2Sky_PAR', 'Sky2Pix_PAR',
'Pix2Sky_MOL', 'Sky2Pix_MOL',
'Pix2Sky_AIT', 'Sky2Pix_AIT',
'Pix2Sky_COP', 'Sky2Pix_COP',
'Pix2Sky_COE', 'Sky2Pix_COE',
'Pix2Sky_COD', 'Sky2Pix_COD',
'Pix2Sky_COO', 'Sky2Pix_COO',
'Pix2Sky_BON', 'Sky2Pix_BON',
'Pix2Sky_PCO', 'Sky2Pix_PCO',
'Pix2Sky_TSC', 'Sky2Pix_TSC',
'Pix2Sky_CSC', 'Sky2Pix_CSC',
'Pix2Sky_QSC', 'Sky2Pix_QSC',
'Pix2Sky_HPX', 'Sky2Pix_HPX',
'Pix2Sky_XPH', 'Sky2Pix_XPH'
]
[docs]class Projection(Model):
"""Base class for all sky projections."""
# Radius of the generating sphere.
# This sets the circumference to 360 deg so that arc length is measured in deg.
r0 = 180 * u.deg / np.pi
_separable = False
@property
@abc.abstractmethod
def inverse(self):
"""
Inverse projection--all projection models must provide an inverse.
"""
[docs]class Pix2SkyProjection(Projection):
"""Base class for all Pix2Sky projections."""
inputs = ('x', 'y')
outputs = ('phi', 'theta')
_input_units_strict = True
_input_units_allow_dimensionless = True
@property
def input_units(self):
return {'x': u.deg, 'y': u.deg}
@property
def return_units(self):
return {'phi': u.deg, 'theta': u.deg}
[docs]class Sky2PixProjection(Projection):
"""Base class for all Sky2Pix projections."""
inputs = ('phi', 'theta')
outputs = ('x', 'y')
_input_units_strict = True
_input_units_allow_dimensionless = True
@property
def input_units(self):
return {'phi': u.deg, 'theta': u.deg}
@property
def return_units(self):
return {'x': u.deg, 'y': u.deg}
[docs]class Zenithal(Projection):
r"""Base class for all Zenithal projections.
Zenithal (or azimuthal) projections map the sphere directly onto a
plane. All zenithal projections are specified by defining the
radius as a function of native latitude, :math:`R_\theta`.
The pixel-to-sky transformation is defined as:
.. math::
\phi &= \arg(-y, x) \\
R_\theta &= \sqrt{x^2 + y^2}
and the inverse (sky-to-pixel) is defined as:
.. math::
x &= R_\theta \sin \phi \\
y &= R_\theta \cos \phi
"""
_separable = False
[docs]class Pix2Sky_ZenithalPerspective(Pix2SkyProjection, Zenithal):
r"""
Zenithal perspective projection - pixel to sky.
Corresponds to the ``AZP`` projection in FITS WCS.
.. math::
\phi &= \arg(-y \cos \gamma, x) \\
\theta &= \left\{\genfrac{}{}{0pt}{}{\psi - \omega}{\psi + \omega + 180^{\circ}}\right.
where:
.. math::
\psi &= \arg(\rho, 1) \\
\omega &= \sin^{-1}\left(\frac{\rho \mu}{\sqrt{\rho^2 + 1}}\right) \\
\rho &= \frac{R}{\frac{180^{\circ}}{\pi}(\mu + 1) + y \sin \gamma} \\
R &= \sqrt{x^2 + y^2 \cos^2 \gamma}
Parameters
--------------
mu : float
Distance from point of projection to center of sphere
in spherical radii, μ. Default is 0.
gamma : float
Look angle γ in degrees. Default is 0°.
"""
mu = Parameter(default=0.0)
gamma = Parameter(default=0.0, getter=_to_orig_unit, setter=_to_radian)
def __init__(self, mu=mu.default, gamma=gamma.default, **kwargs):
# units : mu - in spherical radii, gamma - in deg
# TODO: Support quantity objects here and in similar contexts
super().__init__(mu, gamma, **kwargs)
@mu.validator
def mu(self, value):
if np.any(value == -1):
raise InputParameterError(
"Zenithal perspective projection is not defined for mu = -1")
@property
def inverse(self):
return Sky2Pix_ZenithalPerspective(self.mu.value, self.gamma.value)
[docs] @classmethod
def evaluate(cls, x, y, mu, gamma):
return _projections.azpx2s(x, y, mu, _to_orig_unit(gamma))
Pix2Sky_AZP = Pix2Sky_ZenithalPerspective
[docs]class Sky2Pix_ZenithalPerspective(Sky2PixProjection, Zenithal):
r"""
Zenithal perspective projection - sky to pixel.
Corresponds to the ``AZP`` projection in FITS WCS.
.. math::
x &= R \sin \phi \\
y &= -R \sec \gamma \cos \theta
where:
.. math::
R = \frac{180^{\circ}}{\pi} \frac{(\mu + 1) \cos \theta}{(\mu + \sin \theta) + \cos \theta \cos \phi \tan \gamma}
Parameters
----------
mu : float
Distance from point of projection to center of sphere
in spherical radii, μ. Default is 0.
gamma : float
Look angle γ in degrees. Default is 0°.
"""
mu = Parameter(default=0.0)
gamma = Parameter(default=0.0, getter=_to_orig_unit, setter=_to_radian)
@mu.validator
def mu(self, value):
if np.any(value == -1):
raise InputParameterError(
"Zenithal perspective projection is not defined for mu = -1")
@property
def inverse(self):
return Pix2Sky_AZP(self.mu.value, self.gamma.value)
[docs] @classmethod
def evaluate(cls, phi, theta, mu, gamma):
return _projections.azps2x(
phi, theta, mu, _to_orig_unit(gamma))
Sky2Pix_AZP = Sky2Pix_ZenithalPerspective
[docs]class Pix2Sky_SlantZenithalPerspective(Pix2SkyProjection, Zenithal):
r"""
Slant zenithal perspective projection - pixel to sky.
Corresponds to the ``SZP`` projection in FITS WCS.
Parameters
--------------
mu : float
Distance from point of projection to center of sphere
in spherical radii, μ. Default is 0.
phi0 : float
The longitude φ₀ of the reference point, in degrees. Default
is 0°.
theta0 : float
The latitude θ₀ of the reference point, in degrees. Default
is 90°.
"""
def _validate_mu(mu):
if np.asarray(mu == -1).any():
raise ValueError(
"Zenithal perspective projection is not defined for mu=-1")
return mu
mu = Parameter(default=0.0, setter=_validate_mu)
phi0 = Parameter(default=0.0, getter=_to_orig_unit, setter=_to_radian)
theta0 = Parameter(default=90.0, getter=_to_orig_unit, setter=_to_radian)
@property
def inverse(self):
return Sky2Pix_SlantZenithalPerspective(
self.mu.value, self.phi0.value, self.theta0.value)
[docs] @classmethod
def evaluate(cls, x, y, mu, phi0, theta0):
return _projections.szpx2s(
x, y, mu, _to_orig_unit(phi0), _to_orig_unit(theta0))
Pix2Sky_SZP = Pix2Sky_SlantZenithalPerspective
[docs]class Sky2Pix_SlantZenithalPerspective(Sky2PixProjection, Zenithal):
r"""
Zenithal perspective projection - sky to pixel.
Corresponds to the ``SZP`` projection in FITS WCS.
Parameters
----------
mu : float
distance from point of projection to center of sphere
in spherical radii, μ. Default is 0.
phi0 : float
The longitude φ₀ of the reference point, in degrees. Default
is 0°.
theta0 : float
The latitude θ₀ of the reference point, in degrees. Default
is 90°.
"""
def _validate_mu(mu):
if np.asarray(mu == -1).any():
raise ValueError("Zenithal perspective projection is not defined for mu=-1")
return mu
mu = Parameter(default=0.0, setter=_validate_mu)
phi0 = Parameter(default=0.0, getter=_to_orig_unit, setter=_to_radian)
theta0 = Parameter(default=0.0, getter=_to_orig_unit, setter=_to_radian)
@property
def inverse(self):
return Pix2Sky_SlantZenithalPerspective(
self.mu.value, self.phi0.value, self.theta0.value)
[docs] @classmethod
def evaluate(cls, phi, theta, mu, phi0, theta0):
return _projections.szps2x(
phi, theta, mu, _to_orig_unit(phi0), _to_orig_unit(theta0))
Sky2Pix_SZP = Sky2Pix_SlantZenithalPerspective
[docs]class Pix2Sky_Gnomonic(Pix2SkyProjection, Zenithal):
r"""
Gnomonic projection - pixel to sky.
Corresponds to the ``TAN`` projection in FITS WCS.
See `Zenithal` for a definition of the full transformation.
.. math::
\theta = \tan^{-1}\left(\frac{180^{\circ}}{\pi R_\theta}\right)
"""
@property
def inverse(self):
return Sky2Pix_Gnomonic()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.tanx2s(x, y)
Pix2Sky_TAN = Pix2Sky_Gnomonic
[docs]class Sky2Pix_Gnomonic(Sky2PixProjection, Zenithal):
r"""
Gnomonic Projection - sky to pixel.
Corresponds to the ``TAN`` projection in FITS WCS.
See `Zenithal` for a definition of the full transformation.
.. math::
R_\theta = \frac{180^{\circ}}{\pi}\cot \theta
"""
@property
def inverse(self):
return Pix2Sky_Gnomonic()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.tans2x(phi, theta)
Sky2Pix_TAN = Sky2Pix_Gnomonic
[docs]class Pix2Sky_Stereographic(Pix2SkyProjection, Zenithal):
r"""
Stereographic Projection - pixel to sky.
Corresponds to the ``STG`` projection in FITS WCS.
See `Zenithal` for a definition of the full transformation.
.. math::
\theta = 90^{\circ} - 2 \tan^{-1}\left(\frac{\pi R_\theta}{360^{\circ}}\right)
"""
@property
def inverse(self):
return Sky2Pix_Stereographic()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.stgx2s(x, y)
Pix2Sky_STG = Pix2Sky_Stereographic
[docs]class Sky2Pix_Stereographic(Sky2PixProjection, Zenithal):
r"""
Stereographic Projection - sky to pixel.
Corresponds to the ``STG`` projection in FITS WCS.
See `Zenithal` for a definition of the full transformation.
.. math::
R_\theta = \frac{180^{\circ}}{\pi}\frac{2 \cos \theta}{1 + \sin \theta}
"""
@property
def inverse(self):
return Pix2Sky_Stereographic()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.stgs2x(phi, theta)
Sky2Pix_STG = Sky2Pix_Stereographic
[docs]class Pix2Sky_SlantOrthographic(Pix2SkyProjection, Zenithal):
r"""
Slant orthographic projection - pixel to sky.
Corresponds to the ``SIN`` projection in FITS WCS.
See `Zenithal` for a definition of the full transformation.
The following transformation applies when :math:`\xi` and
:math:`\eta` are both zero.
.. math::
\theta = \cos^{-1}\left(\frac{\pi}{180^{\circ}}R_\theta\right)
The parameters :math:`\xi` and :math:`\eta` are defined from the
reference point :math:`(\phi_c, \theta_c)` as:
.. math::
\xi &= \cot \theta_c \sin \phi_c \\
\eta &= - \cot \theta_c \cos \phi_c
Parameters
----------
xi : float
Obliqueness parameter, ξ. Default is 0.0.
eta : float
Obliqueness parameter, η. Default is 0.0.
"""
xi = Parameter(default=0.0)
eta = Parameter(default=0.0)
@property
def inverse(self):
return Sky2Pix_SlantOrthographic(self.xi.value, self.eta.value)
[docs] @classmethod
def evaluate(cls, x, y, xi, eta):
return _projections.sinx2s(x, y, xi, eta)
Pix2Sky_SIN = Pix2Sky_SlantOrthographic
[docs]class Sky2Pix_SlantOrthographic(Sky2PixProjection, Zenithal):
r"""
Slant orthographic projection - sky to pixel.
Corresponds to the ``SIN`` projection in FITS WCS.
See `Zenithal` for a definition of the full transformation.
The following transformation applies when :math:`\xi` and
:math:`\eta` are both zero.
.. math::
R_\theta = \frac{180^{\circ}}{\pi}\cos \theta
But more specifically are:
.. math::
x &= \frac{180^\circ}{\pi}[\cos \theta \sin \phi + \xi(1 - \sin \theta)] \\
y &= \frac{180^\circ}{\pi}[\cos \theta \cos \phi + \eta(1 - \sin \theta)]
"""
xi = Parameter(default=0.0)
eta = Parameter(default=0.0)
@property
def inverse(self):
return Pix2Sky_SlantOrthographic(self.xi.value, self.eta.value)
[docs] @classmethod
def evaluate(cls, phi, theta, xi, eta):
return _projections.sins2x(phi, theta, xi, eta)
Sky2Pix_SIN = Sky2Pix_SlantOrthographic
[docs]class Pix2Sky_ZenithalEquidistant(Pix2SkyProjection, Zenithal):
r"""
Zenithal equidistant projection - pixel to sky.
Corresponds to the ``ARC`` projection in FITS WCS.
See `Zenithal` for a definition of the full transformation.
.. math::
\theta = 90^\circ - R_\theta
"""
@property
def inverse(self):
return Sky2Pix_ZenithalEquidistant()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.arcx2s(x, y)
Pix2Sky_ARC = Pix2Sky_ZenithalEquidistant
[docs]class Sky2Pix_ZenithalEquidistant(Sky2PixProjection, Zenithal):
r"""
Zenithal equidistant projection - sky to pixel.
Corresponds to the ``ARC`` projection in FITS WCS.
See `Zenithal` for a definition of the full transformation.
.. math::
R_\theta = 90^\circ - \theta
"""
@property
def inverse(self):
return Pix2Sky_ZenithalEquidistant()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.arcs2x(phi, theta)
Sky2Pix_ARC = Sky2Pix_ZenithalEquidistant
[docs]class Pix2Sky_ZenithalEqualArea(Pix2SkyProjection, Zenithal):
r"""
Zenithal equidistant projection - pixel to sky.
Corresponds to the ``ZEA`` projection in FITS WCS.
See `Zenithal` for a definition of the full transformation.
.. math::
\theta = 90^\circ - 2 \sin^{-1} \left(\frac{\pi R_\theta}{360^\circ}\right)
"""
@property
def inverse(self):
return Sky2Pix_ZenithalEqualArea()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.zeax2s(x, y)
Pix2Sky_ZEA = Pix2Sky_ZenithalEqualArea
[docs]class Sky2Pix_ZenithalEqualArea(Sky2PixProjection, Zenithal):
r"""
Zenithal equidistant projection - sky to pixel.
Corresponds to the ``ZEA`` projection in FITS WCS.
See `Zenithal` for a definition of the full transformation.
.. math::
R_\theta &= \frac{180^\circ}{\pi} \sqrt{2(1 - \sin\theta)} \\
&= \frac{360^\circ}{\pi} \sin\left(\frac{90^\circ - \theta}{2}\right)
"""
@property
def inverse(self):
return Pix2Sky_ZenithalEqualArea()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.zeas2x(phi, theta)
Sky2Pix_ZEA = Sky2Pix_ZenithalEqualArea
[docs]class Pix2Sky_Airy(Pix2SkyProjection, Zenithal):
r"""
Airy projection - pixel to sky.
Corresponds to the ``AIR`` projection in FITS WCS.
See `Zenithal` for a definition of the full transformation.
Parameters
----------
theta_b : float
The latitude :math:`\theta_b` at which to minimize the error,
in degrees. Default is 90°.
"""
theta_b = Parameter(default=90.0)
@property
def inverse(self):
return Sky2Pix_Airy(self.theta_b.value)
[docs] @classmethod
def evaluate(cls, x, y, theta_b):
return _projections.airx2s(x, y, theta_b)
Pix2Sky_AIR = Pix2Sky_Airy
[docs]class Sky2Pix_Airy(Sky2PixProjection, Zenithal):
r"""
Airy - sky to pixel.
Corresponds to the ``AIR`` projection in FITS WCS.
See `Zenithal` for a definition of the full transformation.
.. math::
R_\theta = -2 \frac{180^\circ}{\pi}\left(\frac{\ln(\cos \xi)}{\tan \xi} + \frac{\ln(\cos \xi_b)}{\tan^2 \xi_b} \tan \xi \right)
where:
.. math::
\xi &= \frac{90^\circ - \theta}{2} \\
\xi_b &= \frac{90^\circ - \theta_b}{2}
Parameters
----------
theta_b : float
The latitude :math:`\theta_b` at which to minimize the error,
in degrees. Default is 90°.
"""
theta_b = Parameter(default=90.0)
@property
def inverse(self):
return Pix2Sky_Airy(self.theta_b.value)
[docs] @classmethod
def evaluate(cls, phi, theta, theta_b):
return _projections.airs2x(phi, theta, theta_b)
Sky2Pix_AIR = Sky2Pix_Airy
[docs]class Cylindrical(Projection):
r"""Base class for Cylindrical projections.
Cylindrical projections are so-named because the surface of
projection is a cylinder.
"""
_separable = True
[docs]class Pix2Sky_CylindricalPerspective(Pix2SkyProjection, Cylindrical):
r"""
Cylindrical perspective - pixel to sky.
Corresponds to the ``CYP`` projection in FITS WCS.
.. math::
\phi &= \frac{x}{\lambda} \\
\theta &= \arg(1, \eta) + \sin{-1}\left(\frac{\eta \mu}{\sqrt{\eta^2 + 1}}\right)
where:
.. math::
\eta = \frac{\pi}{180^{\circ}}\frac{y}{\mu + \lambda}
Parameters
----------
mu : float
Distance from center of sphere in the direction opposite the
projected surface, in spherical radii, μ. Default is 1.
lam : float
Radius of the cylinder in spherical radii, λ. Default is 1.
"""
mu = Parameter(default=1.0)
lam = Parameter(default=1.0)
@mu.validator
def mu(self, value):
if np.any(value == -self.lam):
raise InputParameterError(
"CYP projection is not defined for mu = -lambda")
@lam.validator
def lam(self, value):
if np.any(value == -self.mu):
raise InputParameterError(
"CYP projection is not defined for lambda = -mu")
@property
def inverse(self):
return Sky2Pix_CylindricalPerspective(self.mu.value, self.lam.value)
[docs] @classmethod
def evaluate(cls, x, y, mu, lam):
return _projections.cypx2s(x, y, mu, lam)
Pix2Sky_CYP = Pix2Sky_CylindricalPerspective
[docs]class Sky2Pix_CylindricalPerspective(Sky2PixProjection, Cylindrical):
r"""
Cylindrical Perspective - sky to pixel.
Corresponds to the ``CYP`` projection in FITS WCS.
.. math::
x &= \lambda \phi \\
y &= \frac{180^{\circ}}{\pi}\left(\frac{\mu + \lambda}{\mu + \cos \theta}\right)\sin \theta
Parameters
----------
mu : float
Distance from center of sphere in the direction opposite the
projected surface, in spherical radii, μ. Default is 0.
lam : float
Radius of the cylinder in spherical radii, λ. Default is 0.
"""
mu = Parameter(default=1.0)
lam = Parameter(default=1.0)
@mu.validator
def mu(self, value):
if np.any(value == -self.lam):
raise InputParameterError(
"CYP projection is not defined for mu = -lambda")
@lam.validator
def lam(self, value):
if np.any(value == -self.mu):
raise InputParameterError(
"CYP projection is not defined for lambda = -mu")
@property
def inverse(self):
return Pix2Sky_CylindricalPerspective(self.mu, self.lam)
[docs] @classmethod
def evaluate(cls, phi, theta, mu, lam):
return _projections.cyps2x(phi, theta, mu, lam)
Sky2Pix_CYP = Sky2Pix_CylindricalPerspective
[docs]class Pix2Sky_CylindricalEqualArea(Pix2SkyProjection, Cylindrical):
r"""
Cylindrical equal area projection - pixel to sky.
Corresponds to the ``CEA`` projection in FITS WCS.
.. math::
\phi &= x \\
\theta &= \sin^{-1}\left(\frac{\pi}{180^{\circ}}\lambda y\right)
Parameters
----------
lam : float
Radius of the cylinder in spherical radii, λ. Default is 0.
"""
lam = Parameter(default=1)
@property
def inverse(self):
return Sky2Pix_CylindricalEqualArea(self.lam)
[docs] @classmethod
def evaluate(cls, x, y, lam):
return _projections.ceax2s(x, y, lam)
Pix2Sky_CEA = Pix2Sky_CylindricalEqualArea
[docs]class Sky2Pix_CylindricalEqualArea(Sky2PixProjection, Cylindrical):
r"""
Cylindrical equal area projection - sky to pixel.
Corresponds to the ``CEA`` projection in FITS WCS.
.. math::
x &= \phi \\
y &= \frac{180^{\circ}}{\pi}\frac{\sin \theta}{\lambda}
Parameters
----------
lam : float
Radius of the cylinder in spherical radii, λ. Default is 0.
"""
lam = Parameter(default=1)
@property
def inverse(self):
return Pix2Sky_CylindricalEqualArea(self.lam)
[docs] @classmethod
def evaluate(cls, phi, theta, lam):
return _projections.ceas2x(phi, theta, lam)
Sky2Pix_CEA = Sky2Pix_CylindricalEqualArea
[docs]class Pix2Sky_PlateCarree(Pix2SkyProjection, Cylindrical):
r"""
Plate carrée projection - pixel to sky.
Corresponds to the ``CAR`` projection in FITS WCS.
.. math::
\phi &= x \\
\theta &= y
"""
@property
def inverse(self):
return Sky2Pix_PlateCarree()
[docs] @staticmethod
def evaluate(x, y):
# The intermediate variables are only used here for clarity
phi = np.array(x, copy=True)
theta = np.array(y, copy=True)
return phi, theta
Pix2Sky_CAR = Pix2Sky_PlateCarree
[docs]class Sky2Pix_PlateCarree(Sky2PixProjection, Cylindrical):
r"""
Plate carrée projection - sky to pixel.
Corresponds to the ``CAR`` projection in FITS WCS.
.. math::
x &= \phi \\
y &= \theta
"""
@property
def inverse(self):
return Pix2Sky_PlateCarree()
[docs] @staticmethod
def evaluate(phi, theta):
# The intermediate variables are only used here for clarity
x = np.array(phi, copy=True)
y = np.array(theta, copy=True)
return x, y
Sky2Pix_CAR = Sky2Pix_PlateCarree
[docs]class Pix2Sky_Mercator(Pix2SkyProjection, Cylindrical):
r"""
Mercator - pixel to sky.
Corresponds to the ``MER`` projection in FITS WCS.
.. math::
\phi &= x \\
\theta &= 2 \tan^{-1}\left(e^{y \pi / 180^{\circ}}\right)-90^{\circ}
"""
@property
def inverse(self):
return Sky2Pix_Mercator()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.merx2s(x, y)
Pix2Sky_MER = Pix2Sky_Mercator
[docs]class Sky2Pix_Mercator(Sky2PixProjection, Cylindrical):
r"""
Mercator - sky to pixel.
Corresponds to the ``MER`` projection in FITS WCS.
.. math::
x &= \phi \\
y &= \frac{180^{\circ}}{\pi}\ln \tan \left(\frac{90^{\circ} + \theta}{2}\right)
"""
@property
def inverse(self):
return Pix2Sky_Mercator()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.mers2x(phi, theta)
Sky2Pix_MER = Sky2Pix_Mercator
[docs]class PseudoCylindrical(Projection):
r"""Base class for pseudocylindrical projections.
Pseudocylindrical projections are like cylindrical projections
except the parallels of latitude are projected at diminishing
lengths toward the polar regions in order to reduce lateral
distortion there. Consequently, the meridians are curved.
"""
_separable = True
[docs]class Pix2Sky_SansonFlamsteed(Pix2SkyProjection, PseudoCylindrical):
r"""
Sanson-Flamsteed projection - pixel to sky.
Corresponds to the ``SFL`` projection in FITS WCS.
.. math::
\phi &= \frac{x}{\cos y} \\
\theta &= y
"""
@property
def inverse(self):
return Sky2Pix_SansonFlamsteed()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.sflx2s(x, y)
Pix2Sky_SFL = Pix2Sky_SansonFlamsteed
[docs]class Sky2Pix_SansonFlamsteed(Sky2PixProjection, PseudoCylindrical):
r"""
Sanson-Flamsteed projection - sky to pixel.
Corresponds to the ``SFL`` projection in FITS WCS.
.. math::
x &= \phi \cos \theta \\
y &= \theta
"""
@property
def inverse(self):
return Pix2Sky_SansonFlamsteed()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.sfls2x(phi, theta)
Sky2Pix_SFL = Sky2Pix_SansonFlamsteed
[docs]class Pix2Sky_Parabolic(Pix2SkyProjection, PseudoCylindrical):
r"""
Parabolic projection - pixel to sky.
Corresponds to the ``PAR`` projection in FITS WCS.
.. math::
\phi &= \frac{180^\circ}{\pi} \frac{x}{1 - 4(y / 180^\circ)^2} \\
\theta &= 3 \sin^{-1}\left(\frac{y}{180^\circ}\right)
"""
_separable = False
@property
def inverse(self):
return Sky2Pix_Parabolic()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.parx2s(x, y)
Pix2Sky_PAR = Pix2Sky_Parabolic
[docs]class Sky2Pix_Parabolic(Sky2PixProjection, PseudoCylindrical):
r"""
Parabolic projection - sky to pixel.
Corresponds to the ``PAR`` projection in FITS WCS.
.. math::
x &= \phi \left(2\cos\frac{2\theta}{3} - 1\right) \\
y &= 180^\circ \sin \frac{\theta}{3}
"""
_separable = False
@property
def inverse(self):
return Pix2Sky_Parabolic()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.pars2x(phi, theta)
Sky2Pix_PAR = Sky2Pix_Parabolic
[docs]class Pix2Sky_Molleweide(Pix2SkyProjection, PseudoCylindrical):
r"""
Molleweide's projection - pixel to sky.
Corresponds to the ``MOL`` projection in FITS WCS.
.. math::
\phi &= \frac{\pi x}{2 \sqrt{2 - \left(\frac{\pi}{180^\circ}y\right)^2}} \\
\theta &= \sin^{-1}\left(\frac{1}{90^\circ}\sin^{-1}\left(\frac{\pi}{180^\circ}\frac{y}{\sqrt{2}}\right) + \frac{y}{180^\circ}\sqrt{2 - \left(\frac{\pi}{180^\circ}y\right)^2}\right)
"""
_separable = False
@property
def inverse(self):
return Sky2Pix_Molleweide()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.molx2s(x, y)
Pix2Sky_MOL = Pix2Sky_Molleweide
[docs]class Sky2Pix_Molleweide(Sky2PixProjection, PseudoCylindrical):
r"""
Molleweide's projection - sky to pixel.
Corresponds to the ``MOL`` projection in FITS WCS.
.. math::
x &= \frac{2 \sqrt{2}}{\pi} \phi \cos \gamma \\
y &= \sqrt{2} \frac{180^\circ}{\pi} \sin \gamma
where :math:`\gamma` is defined as the solution of the
transcendental equation:
.. math::
\sin \theta = \frac{\gamma}{90^\circ} + \frac{\sin 2 \gamma}{\pi}
"""
_separable = False
@property
def inverse(self):
return Pix2Sky_Molleweide()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.mols2x(phi, theta)
Sky2Pix_MOL = Sky2Pix_Molleweide
[docs]class Pix2Sky_HammerAitoff(Pix2SkyProjection, PseudoCylindrical):
r"""
Hammer-Aitoff projection - pixel to sky.
Corresponds to the ``AIT`` projection in FITS WCS.
.. math::
\phi &= 2 \arg \left(2Z^2 - 1, \frac{\pi}{180^\circ} \frac{Z}{2}x\right) \\
\theta &= \sin^{-1}\left(\frac{\pi}{180^\circ}yZ\right)
"""
_separable = False
@property
def inverse(self):
return Sky2Pix_HammerAitoff()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.aitx2s(x, y)
Pix2Sky_AIT = Pix2Sky_HammerAitoff
[docs]class Sky2Pix_HammerAitoff(Sky2PixProjection, PseudoCylindrical):
r"""
Hammer-Aitoff projection - sky to pixel.
Corresponds to the ``AIT`` projection in FITS WCS.
.. math::
x &= 2 \gamma \cos \theta \sin \frac{\phi}{2} \\
y &= \gamma \sin \theta
where:
.. math::
\gamma = \frac{180^\circ}{\pi} \sqrt{\frac{2}{1 + \cos \theta \cos(\phi / 2)}}
"""
_separable = False
@property
def inverse(self):
return Pix2Sky_HammerAitoff()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.aits2x(phi, theta)
Sky2Pix_AIT = Sky2Pix_HammerAitoff
[docs]class Conic(Projection):
r"""Base class for conic projections.
In conic projections, the sphere is thought to be projected onto
the surface of a cone which is then opened out.
In a general sense, the pixel-to-sky transformation is defined as:
.. math::
\phi &= \arg\left(\frac{Y_0 - y}{R_\theta}, \frac{x}{R_\theta}\right) / C \\
R_\theta &= \mathrm{sign} \theta_a \sqrt{x^2 + (Y_0 - y)^2}
and the inverse (sky-to-pixel) is defined as:
.. math::
x &= R_\theta \sin (C \phi) \\
y &= R_\theta \cos (C \phi) + Y_0
where :math:`C` is the "constant of the cone":
.. math::
C = \frac{180^\circ \cos \theta}{\pi R_\theta}
"""
sigma = Parameter(default=90.0, getter=_to_orig_unit, setter=_to_radian)
delta = Parameter(default=0.0, getter=_to_orig_unit, setter=_to_radian)
_separable = False
[docs]class Pix2Sky_ConicPerspective(Pix2SkyProjection, Conic):
r"""
Colles' conic perspective projection - pixel to sky.
Corresponds to the ``COP`` projection in FITS WCS.
See `Conic` for a description of the entire equation.
The projection formulae are:
.. math::
C &= \sin \theta_a \\
R_\theta &= \frac{180^\circ}{\pi} \cos \eta [ \cot \theta_a - \tan(\theta - \theta_a)] \\
Y_0 &= \frac{180^\circ}{\pi} \cos \eta \cot \theta_a
Parameters
----------
sigma : float
:math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 90.
delta : float
:math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 0.
"""
@property
def inverse(self):
return Sky2Pix_ConicPerspective(self.sigma.value, self.delta.value)
[docs] @classmethod
def evaluate(cls, x, y, sigma, delta):
return _projections.copx2s(x, y, _to_orig_unit(sigma), _to_orig_unit(delta))
Pix2Sky_COP = Pix2Sky_ConicPerspective
[docs]class Sky2Pix_ConicPerspective(Sky2PixProjection, Conic):
r"""
Colles' conic perspective projection - sky to pixel.
Corresponds to the ``COP`` projection in FITS WCS.
See `Conic` for a description of the entire equation.
The projection formulae are:
.. math::
C &= \sin \theta_a \\
R_\theta &= \frac{180^\circ}{\pi} \cos \eta [ \cot \theta_a - \tan(\theta - \theta_a)] \\
Y_0 &= \frac{180^\circ}{\pi} \cos \eta \cot \theta_a
Parameters
----------
sigma : float
:math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 90.
delta : float
:math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 0.
"""
@property
def inverse(self):
return Pix2Sky_ConicPerspective(self.sigma.value, self.delta.value)
[docs] @classmethod
def evaluate(cls, phi, theta, sigma, delta):
return _projections.cops2x(phi, theta,
_to_orig_unit(sigma), _to_orig_unit(delta))
Sky2Pix_COP = Sky2Pix_ConicPerspective
[docs]class Pix2Sky_ConicEqualArea(Pix2SkyProjection, Conic):
r"""
Alber's conic equal area projection - pixel to sky.
Corresponds to the ``COE`` projection in FITS WCS.
See `Conic` for a description of the entire equation.
The projection formulae are:
.. math::
C &= \gamma / 2 \\
R_\theta &= \frac{180^\circ}{\pi} \frac{2}{\gamma} \sqrt{1 + \sin \theta_1 \sin \theta_2 - \gamma \sin \theta} \\
Y_0 &= \frac{180^\circ}{\pi} \frac{2}{\gamma} \sqrt{1 + \sin \theta_1 \sin \theta_2 - \gamma \sin((\theta_1 + \theta_2)/2)}
where:
.. math::
\gamma = \sin \theta_1 + \sin \theta_2
Parameters
----------
sigma : float
:math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 90.
delta : float
:math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 0.
"""
@property
def inverse(self):
return Sky2Pix_ConicEqualArea(self.sigma.value, self.delta.value)
[docs] @classmethod
def evaluate(cls, x, y, sigma, delta):
return _projections.coex2s(x, y, _to_orig_unit(sigma), _to_orig_unit(delta))
Pix2Sky_COE = Pix2Sky_ConicEqualArea
[docs]class Sky2Pix_ConicEqualArea(Sky2PixProjection, Conic):
r"""
Alber's conic equal area projection - sky to pixel.
Corresponds to the ``COE`` projection in FITS WCS.
See `Conic` for a description of the entire equation.
The projection formulae are:
.. math::
C &= \gamma / 2 \\
R_\theta &= \frac{180^\circ}{\pi} \frac{2}{\gamma} \sqrt{1 + \sin \theta_1 \sin \theta_2 - \gamma \sin \theta} \\
Y_0 &= \frac{180^\circ}{\pi} \frac{2}{\gamma} \sqrt{1 + \sin \theta_1 \sin \theta_2 - \gamma \sin((\theta_1 + \theta_2)/2)}
where:
.. math::
\gamma = \sin \theta_1 + \sin \theta_2
Parameters
----------
sigma : float
:math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 90.
delta : float
:math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 0.
"""
@property
def inverse(self):
return Pix2Sky_ConicEqualArea(self.sigma.value, self.delta.value)
[docs] @classmethod
def evaluate(cls, phi, theta, sigma, delta):
return _projections.coes2x(phi, theta,
_to_orig_unit(sigma), _to_orig_unit(delta))
Sky2Pix_COE = Sky2Pix_ConicEqualArea
[docs]class Pix2Sky_ConicEquidistant(Pix2SkyProjection, Conic):
r"""
Conic equidistant projection - pixel to sky.
Corresponds to the ``COD`` projection in FITS WCS.
See `Conic` for a description of the entire equation.
The projection formulae are:
.. math::
C &= \frac{180^\circ}{\pi} \frac{\sin\theta_a\sin\eta}{\eta} \\
R_\theta &= \theta_a - \theta + \eta\cot\eta\cot\theta_a \\
Y_0 = \eta\cot\eta\cot\theta_a
Parameters
----------
sigma : float
:math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 90.
delta : float
:math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 0.
"""
@property
def inverse(self):
return Sky2Pix_ConicEquidistant(self.sigma.value, self.delta.value)
[docs] @classmethod
def evaluate(cls, x, y, sigma, delta):
return _projections.codx2s(x, y, _to_orig_unit(sigma), _to_orig_unit(delta))
Pix2Sky_COD = Pix2Sky_ConicEquidistant
[docs]class Sky2Pix_ConicEquidistant(Sky2PixProjection, Conic):
r"""
Conic equidistant projection - sky to pixel.
Corresponds to the ``COD`` projection in FITS WCS.
See `Conic` for a description of the entire equation.
The projection formulae are:
.. math::
C &= \frac{180^\circ}{\pi} \frac{\sin\theta_a\sin\eta}{\eta} \\
R_\theta &= \theta_a - \theta + \eta\cot\eta\cot\theta_a \\
Y_0 = \eta\cot\eta\cot\theta_a
Parameters
----------
sigma : float
:math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 90.
delta : float
:math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 0.
"""
@property
def inverse(self):
return Pix2Sky_ConicEquidistant(self.sigma.value, self.delta.value)
[docs] @classmethod
def evaluate(cls, phi, theta, sigma, delta):
return _projections.cods2x(phi, theta,
_to_orig_unit(sigma), _to_orig_unit(delta))
Sky2Pix_COD = Sky2Pix_ConicEquidistant
[docs]class Pix2Sky_ConicOrthomorphic(Pix2SkyProjection, Conic):
r"""
Conic orthomorphic projection - pixel to sky.
Corresponds to the ``COO`` projection in FITS WCS.
See `Conic` for a description of the entire equation.
The projection formulae are:
.. math::
C &= \frac{\ln \left( \frac{\cos\theta_2}{\cos\theta_1} \right)}
{\ln \left[ \frac{\tan\left(\frac{90^\circ-\theta_2}{2}\right)}
{\tan\left(\frac{90^\circ-\theta_1}{2}\right)} \right] } \\
R_\theta &= \psi \left[ \tan \left( \frac{90^\circ - \theta}{2} \right) \right]^C \\
Y_0 &= \psi \left[ \tan \left( \frac{90^\circ - \theta_a}{2} \right) \right]^C
where:
.. math::
\psi = \frac{180^\circ}{\pi} \frac{\cos \theta}
{C\left[\tan\left(\frac{90^\circ-\theta}{2}\right)\right]^C}
Parameters
----------
sigma : float
:math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 90.
delta : float
:math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 0.
"""
@property
def inverse(self):
return Sky2Pix_ConicOrthomorphic(self.sigma.value, self.delta.value)
[docs] @classmethod
def evaluate(cls, x, y, sigma, delta):
return _projections.coox2s(x, y, _to_orig_unit(sigma), _to_orig_unit(delta))
Pix2Sky_COO = Pix2Sky_ConicOrthomorphic
[docs]class Sky2Pix_ConicOrthomorphic(Sky2PixProjection, Conic):
r"""
Conic orthomorphic projection - sky to pixel.
Corresponds to the ``COO`` projection in FITS WCS.
See `Conic` for a description of the entire equation.
The projection formulae are:
.. math::
C &= \frac{\ln \left( \frac{\cos\theta_2}{\cos\theta_1} \right)}
{\ln \left[ \frac{\tan\left(\frac{90^\circ-\theta_2}{2}\right)}
{\tan\left(\frac{90^\circ-\theta_1}{2}\right)} \right] } \\
R_\theta &= \psi \left[ \tan \left( \frac{90^\circ - \theta}{2} \right) \right]^C \\
Y_0 &= \psi \left[ \tan \left( \frac{90^\circ - \theta_a}{2} \right) \right]^C
where:
.. math::
\psi = \frac{180^\circ}{\pi} \frac{\cos \theta}
{C\left[\tan\left(\frac{90^\circ-\theta}{2}\right)\right]^C}
Parameters
----------
sigma : float
:math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 90.
delta : float
:math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and
:math:`\theta_2` are the latitudes of the standard parallels,
in degrees. Default is 0.
"""
@property
def inverse(self):
return Pix2Sky_ConicOrthomorphic(self.sigma.value, self.delta.value)
[docs] @classmethod
def evaluate(cls, phi, theta, sigma, delta):
return _projections.coos2x(phi, theta,
_to_orig_unit(sigma), _to_orig_unit(delta))
Sky2Pix_COO = Sky2Pix_ConicOrthomorphic
[docs]class PseudoConic(Projection):
r"""Base class for pseudoconic projections.
Pseudoconics are a subclass of conics with concentric parallels.
"""
[docs]class Pix2Sky_BonneEqualArea(Pix2SkyProjection, PseudoConic):
r"""
Bonne's equal area pseudoconic projection - pixel to sky.
Corresponds to the ``BON`` projection in FITS WCS.
.. math::
\phi &= \frac{\pi}{180^\circ} A_\phi R_\theta / \cos \theta \\
\theta &= Y_0 - R_\theta
where:
.. math::
R_\theta &= \mathrm{sign} \theta_1 \sqrt{x^2 + (Y_0 - y)^2} \\
A_\phi &= \arg\left(\frac{Y_0 - y}{R_\theta}, \frac{x}{R_\theta}\right)
Parameters
----------
theta1 : float
Bonne conformal latitude, in degrees.
"""
theta1 = Parameter(default=0.0, getter=_to_orig_unit, setter=_to_radian)
_separable = True
@property
def inverse(self):
return Sky2Pix_BonneEqualArea(self.theta1.value)
[docs] @classmethod
def evaluate(cls, x, y, theta1):
return _projections.bonx2s(x, y, _to_orig_unit(theta1))
Pix2Sky_BON = Pix2Sky_BonneEqualArea
[docs]class Sky2Pix_BonneEqualArea(Sky2PixProjection, PseudoConic):
r"""
Bonne's equal area pseudoconic projection - sky to pixel.
Corresponds to the ``BON`` projection in FITS WCS.
.. math::
x &= R_\theta \sin A_\phi \\
y &= -R_\theta \cos A_\phi + Y_0
where:
.. math::
A_\phi &= \frac{180^\circ}{\pi R_\theta} \phi \cos \theta \\
R_\theta &= Y_0 - \theta \\
Y_0 &= \frac{180^\circ}{\pi} \cot \theta_1 + \theta_1
Parameters
----------
theta1 : float
Bonne conformal latitude, in degrees.
"""
theta1 = Parameter(default=0.0, getter=_to_orig_unit, setter=_to_radian)
_separable = True
@property
def inverse(self):
return Pix2Sky_BonneEqualArea(self.theta1.value)
[docs] @classmethod
def evaluate(cls, phi, theta, theta1):
return _projections.bons2x(phi, theta,
_to_orig_unit(theta1))
Sky2Pix_BON = Sky2Pix_BonneEqualArea
[docs]class Pix2Sky_Polyconic(Pix2SkyProjection, PseudoConic):
r"""
Polyconic projection - pixel to sky.
Corresponds to the ``PCO`` projection in FITS WCS.
"""
_separable = False
@property
def inverse(self):
return Sky2Pix_Polyconic()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.pcox2s(x, y)
Pix2Sky_PCO = Pix2Sky_Polyconic
[docs]class Sky2Pix_Polyconic(Sky2PixProjection, PseudoConic):
r"""
Polyconic projection - sky to pixel.
Corresponds to the ``PCO`` projection in FITS WCS.
"""
_separable = False
@property
def inverse(self):
return Pix2Sky_Polyconic()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.pcos2x(phi, theta)
Sky2Pix_PCO = Sky2Pix_Polyconic
[docs]class QuadCube(Projection):
r"""Base class for quad cube projections.
Quadrilateralized spherical cube (quad-cube) projections belong to
the class of polyhedral projections in which the sphere is
projected onto the surface of an enclosing polyhedron.
The six faces of the quad-cube projections are numbered and laid
out as::
0
4 3 2 1 4 3 2
5
"""
[docs]class Pix2Sky_TangentialSphericalCube(Pix2SkyProjection, QuadCube):
r"""
Tangential spherical cube projection - pixel to sky.
Corresponds to the ``TSC`` projection in FITS WCS.
"""
_separable = False
@property
def inverse(self):
return Sky2Pix_TangentialSphericalCube()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.tscx2s(x, y)
Pix2Sky_TSC = Pix2Sky_TangentialSphericalCube
[docs]class Sky2Pix_TangentialSphericalCube(Sky2PixProjection, QuadCube):
r"""
Tangential spherical cube projection - sky to pixel.
Corresponds to the ``PCO`` projection in FITS WCS.
"""
_separable = False
@property
def inverse(self):
return Pix2Sky_TangentialSphericalCube()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.tscs2x(phi, theta)
Sky2Pix_TSC = Sky2Pix_TangentialSphericalCube
[docs]class Pix2Sky_COBEQuadSphericalCube(Pix2SkyProjection, QuadCube):
r"""
COBE quadrilateralized spherical cube projection - pixel to sky.
Corresponds to the ``CSC`` projection in FITS WCS.
"""
_separable = False
@property
def inverse(self):
return Sky2Pix_COBEQuadSphericalCube()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.cscx2s(x, y)
Pix2Sky_CSC = Pix2Sky_COBEQuadSphericalCube
[docs]class Sky2Pix_COBEQuadSphericalCube(Sky2PixProjection, QuadCube):
r"""
COBE quadrilateralized spherical cube projection - sky to pixel.
Corresponds to the ``CSC`` projection in FITS WCS.
"""
_separable = False
@property
def inverse(self):
return Pix2Sky_COBEQuadSphericalCube()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.cscs2x(phi, theta)
Sky2Pix_CSC = Sky2Pix_COBEQuadSphericalCube
[docs]class Pix2Sky_QuadSphericalCube(Pix2SkyProjection, QuadCube):
r"""
Quadrilateralized spherical cube projection - pixel to sky.
Corresponds to the ``QSC`` projection in FITS WCS.
"""
_separable = False
@property
def inverse(self):
return Sky2Pix_QuadSphericalCube()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.qscx2s(x, y)
Pix2Sky_QSC = Pix2Sky_QuadSphericalCube
[docs]class Sky2Pix_QuadSphericalCube(Sky2PixProjection, QuadCube):
r"""
Quadrilateralized spherical cube projection - sky to pixel.
Corresponds to the ``QSC`` projection in FITS WCS.
"""
_separable = False
@property
def inverse(self):
return Pix2Sky_QuadSphericalCube()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.qscs2x(phi, theta)
Sky2Pix_QSC = Sky2Pix_QuadSphericalCube
[docs]class HEALPix(Projection):
r"""Base class for HEALPix projections.
"""
[docs]class Pix2Sky_HEALPix(Pix2SkyProjection, HEALPix):
r"""
HEALPix - pixel to sky.
Corresponds to the ``HPX`` projection in FITS WCS.
Parameters
----------
H : float
The number of facets in longitude direction.
X : float
The number of facets in latitude direction.
"""
_separable = True
H = Parameter(default=4.0)
X = Parameter(default=3.0)
@property
def inverse(self):
return Sky2Pix_HEALPix(self.H.value, self.X.value)
[docs] @classmethod
def evaluate(cls, x, y, H, X):
return _projections.hpxx2s(x, y, H, X)
Pix2Sky_HPX = Pix2Sky_HEALPix
[docs]class Sky2Pix_HEALPix(Sky2PixProjection, HEALPix):
r"""
HEALPix projection - sky to pixel.
Corresponds to the ``HPX`` projection in FITS WCS.
Parameters
----------
H : float
The number of facets in longitude direction.
X : float
The number of facets in latitude direction.
"""
_separable = True
H = Parameter(default=4.0)
X = Parameter(default=3.0)
@property
def inverse(self):
return Pix2Sky_HEALPix(self.H.value, self.X.value)
[docs] @classmethod
def evaluate(cls, phi, theta, H, X):
return _projections.hpxs2x(phi, theta, H, X)
Sky2Pix_HPX = Sky2Pix_HEALPix
[docs]class Pix2Sky_HEALPixPolar(Pix2SkyProjection, HEALPix):
r"""
HEALPix polar, aka "butterfly" projection - pixel to sky.
Corresponds to the ``XPH`` projection in FITS WCS.
"""
_separable = False
@property
def inverse(self):
return Sky2Pix_HEALPix()
[docs] @classmethod
def evaluate(cls, x, y):
return _projections.xphx2s(x, y)
Pix2Sky_XPH = Pix2Sky_HEALPixPolar
[docs]class Sky2Pix_HEALPixPolar(Sky2PixProjection, HEALPix):
r"""
HEALPix polar, aka "butterfly" projection - pixel to sky.
Corresponds to the ``XPH`` projection in FITS WCS.
"""
_separable = False
@property
def inverse(self):
return Pix2Sky_HEALPix()
[docs] @classmethod
def evaluate(cls, phi, theta):
return _projections.hpxs2x(phi, theta)
Sky2Pix_XPH = Sky2Pix_HEALPixPolar