# Licensed under a 3-clause BSD style license - see LICENSE.rst # -*- coding: utf-8 -*- # pylint: disable=invalid-name """ 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 astropy import units as u from .core import Model from .parameters import Parameter, InputParameterError 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' ] 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. """ class Pix2SkyProjection(Projection): """Base class for all Pix2Sky projections.""" n_inputs = 2 n_outputs = 2 _input_units_strict = True _input_units_allow_dimensionless = True def __init__(self, *args, **kwargs): super().__init__(*args, **kwargs) self.inputs = ('x', 'y') self.outputs = ('phi', 'theta') @property def input_units(self): return {self.inputs[0]: u.deg, self.inputs[1]: u.deg} @property def return_units(self): return {self.outputs[0]: u.deg, self.outputs[1]: u.deg} class Sky2PixProjection(Projection): """Base class for all Sky2Pix projections.""" n_inputs = 2 n_outputs = 2 _input_units_strict = True _input_units_allow_dimensionless = True def __init__(self, *args, **kwargs): super().__init__(*args, **kwargs) self.inputs = ('phi', 'theta') self.outputs = ('x', 'y') @property def input_units(self): return {self.inputs[0]: u.deg, self.inputs[1]: u.deg} @property def return_units(self): return {self.outputs[0]: u.deg, self.outputs[1]: u.deg} 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 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 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) @classmethod def evaluate(cls, x, y, mu, gamma): return _projections.azpx2s(x, y, mu, _to_orig_unit(gamma)) Pix2Sky_AZP = Pix2Sky_ZenithalPerspective 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) @classmethod def evaluate(cls, phi, theta, mu, gamma): return _projections.azps2x( phi, theta, mu, _to_orig_unit(gamma)) Sky2Pix_AZP = Sky2Pix_ZenithalPerspective 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) @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 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) @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 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() @classmethod def evaluate(cls, x, y): return _projections.tanx2s(x, y) Pix2Sky_TAN = Pix2Sky_Gnomonic 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() @classmethod def evaluate(cls, phi, theta): return _projections.tans2x(phi, theta) Sky2Pix_TAN = Sky2Pix_Gnomonic 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() @classmethod def evaluate(cls, x, y): return _projections.stgx2s(x, y) Pix2Sky_STG = Pix2Sky_Stereographic 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() @classmethod def evaluate(cls, phi, theta): return _projections.stgs2x(phi, theta) Sky2Pix_STG = Sky2Pix_Stereographic 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) @classmethod def evaluate(cls, x, y, xi, eta): return _projections.sinx2s(x, y, xi, eta) Pix2Sky_SIN = Pix2Sky_SlantOrthographic 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) @classmethod def evaluate(cls, phi, theta, xi, eta): return _projections.sins2x(phi, theta, xi, eta) Sky2Pix_SIN = Sky2Pix_SlantOrthographic 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() @classmethod def evaluate(cls, x, y): return _projections.arcx2s(x, y) Pix2Sky_ARC = Pix2Sky_ZenithalEquidistant 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() @classmethod def evaluate(cls, phi, theta): return _projections.arcs2x(phi, theta) Sky2Pix_ARC = Sky2Pix_ZenithalEquidistant 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() @classmethod def evaluate(cls, x, y): return _projections.zeax2s(x, y) Pix2Sky_ZEA = Pix2Sky_ZenithalEqualArea 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() @classmethod def evaluate(cls, phi, theta): return _projections.zeas2x(phi, theta) Sky2Pix_ZEA = Sky2Pix_ZenithalEqualArea 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) @classmethod def evaluate(cls, x, y, theta_b): return _projections.airx2s(x, y, theta_b) Pix2Sky_AIR = Pix2Sky_Airy 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) @classmethod def evaluate(cls, phi, theta, theta_b): return _projections.airs2x(phi, theta, theta_b) Sky2Pix_AIR = Sky2Pix_Airy class Cylindrical(Projection): r"""Base class for Cylindrical projections. Cylindrical projections are so-named because the surface of projection is a cylinder. """ _separable = True 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) @classmethod def evaluate(cls, x, y, mu, lam): return _projections.cypx2s(x, y, mu, lam) Pix2Sky_CYP = Pix2Sky_CylindricalPerspective 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) @classmethod def evaluate(cls, phi, theta, mu, lam): return _projections.cyps2x(phi, theta, mu, lam) Sky2Pix_CYP = Sky2Pix_CylindricalPerspective 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 1. """ lam = Parameter(default=1) @property def inverse(self): return Sky2Pix_CylindricalEqualArea(self.lam) @classmethod def evaluate(cls, x, y, lam): return _projections.ceax2s(x, y, lam) Pix2Sky_CEA = Pix2Sky_CylindricalEqualArea 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) @classmethod def evaluate(cls, phi, theta, lam): return _projections.ceas2x(phi, theta, lam) Sky2Pix_CEA = Sky2Pix_CylindricalEqualArea 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() @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 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() @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 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() @classmethod def evaluate(cls, x, y): return _projections.merx2s(x, y) Pix2Sky_MER = Pix2Sky_Mercator 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() @classmethod def evaluate(cls, phi, theta): return _projections.mers2x(phi, theta) Sky2Pix_MER = Sky2Pix_Mercator 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 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() @classmethod def evaluate(cls, x, y): return _projections.sflx2s(x, y) Pix2Sky_SFL = Pix2Sky_SansonFlamsteed 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() @classmethod def evaluate(cls, phi, theta): return _projections.sfls2x(phi, theta) Sky2Pix_SFL = Sky2Pix_SansonFlamsteed 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() @classmethod def evaluate(cls, x, y): return _projections.parx2s(x, y) Pix2Sky_PAR = Pix2Sky_Parabolic 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() @classmethod def evaluate(cls, phi, theta): return _projections.pars2x(phi, theta) Sky2Pix_PAR = Sky2Pix_Parabolic 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() @classmethod def evaluate(cls, x, y): return _projections.molx2s(x, y) Pix2Sky_MOL = Pix2Sky_Molleweide 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() @classmethod def evaluate(cls, phi, theta): return _projections.mols2x(phi, theta) Sky2Pix_MOL = Sky2Pix_Molleweide 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() @classmethod def evaluate(cls, x, y): return _projections.aitx2s(x, y) Pix2Sky_AIT = Pix2Sky_HammerAitoff 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() @classmethod def evaluate(cls, phi, theta): return _projections.aits2x(phi, theta) Sky2Pix_AIT = Sky2Pix_HammerAitoff 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 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) @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 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) @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 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) @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 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) @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 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) @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 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) @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 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) @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 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) @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 class PseudoConic(Projection): r"""Base class for pseudoconic projections. Pseudoconics are a subclass of conics with concentric parallels. """ 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) @classmethod def evaluate(cls, x, y, theta1): return _projections.bonx2s(x, y, _to_orig_unit(theta1)) Pix2Sky_BON = Pix2Sky_BonneEqualArea 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) @classmethod def evaluate(cls, phi, theta, theta1): return _projections.bons2x(phi, theta, _to_orig_unit(theta1)) Sky2Pix_BON = Sky2Pix_BonneEqualArea 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() @classmethod def evaluate(cls, x, y): return _projections.pcox2s(x, y) Pix2Sky_PCO = Pix2Sky_Polyconic 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() @classmethod def evaluate(cls, phi, theta): return _projections.pcos2x(phi, theta) Sky2Pix_PCO = Sky2Pix_Polyconic 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 """ 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() @classmethod def evaluate(cls, x, y): return _projections.tscx2s(x, y) Pix2Sky_TSC = Pix2Sky_TangentialSphericalCube 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() @classmethod def evaluate(cls, phi, theta): return _projections.tscs2x(phi, theta) Sky2Pix_TSC = Sky2Pix_TangentialSphericalCube 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() @classmethod def evaluate(cls, x, y): return _projections.cscx2s(x, y) Pix2Sky_CSC = Pix2Sky_COBEQuadSphericalCube 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() @classmethod def evaluate(cls, phi, theta): return _projections.cscs2x(phi, theta) Sky2Pix_CSC = Sky2Pix_COBEQuadSphericalCube 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() @classmethod def evaluate(cls, x, y): return _projections.qscx2s(x, y) Pix2Sky_QSC = Pix2Sky_QuadSphericalCube 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() @classmethod def evaluate(cls, phi, theta): return _projections.qscs2x(phi, theta) Sky2Pix_QSC = Sky2Pix_QuadSphericalCube class HEALPix(Projection): r"""Base class for HEALPix projections. """ 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) @classmethod def evaluate(cls, x, y, H, X): return _projections.hpxx2s(x, y, H, X) Pix2Sky_HPX = Pix2Sky_HEALPix 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) @classmethod def evaluate(cls, phi, theta, H, X): return _projections.hpxs2x(phi, theta, H, X) Sky2Pix_HPX = Sky2Pix_HEALPix 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() @classmethod def evaluate(cls, x, y): return _projections.xphx2s(x, y) Pix2Sky_XPH = Pix2Sky_HEALPixPolar 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() @classmethod def evaluate(cls, phi, theta): return _projections.hpxs2x(phi, theta) Sky2Pix_XPH = Sky2Pix_HEALPixPolar class AffineTransformation2D(Model): """ Perform an affine transformation in 2 dimensions. Parameters ---------- matrix : array A 2x2 matrix specifying the linear transformation to apply to the inputs translation : array A 2D vector (given as either a 2x1 or 1x2 array) specifying a translation to apply to the inputs """ n_inputs = 2 n_outputs = 2 standard_broadcasting = False _separable = False matrix = Parameter(default=[[1.0, 0.0], [0.0, 1.0]]) translation = Parameter(default=[0.0, 0.0]) @matrix.validator def matrix(self, value): """Validates that the input matrix is a 2x2 2D array.""" if np.shape(value) != (2, 2): raise InputParameterError( "Expected transformation matrix to be a 2x2 array") @translation.validator def translation(self, value): """ Validates that the translation vector is a 2D vector. This allows either a "row" vector or a "column" vector where in the latter case the resultant Numpy array has ``ndim=2`` but the shape is ``(1, 2)``. """ if not ((np.ndim(value) == 1 and np.shape(value) == (2,)) or (np.ndim(value) == 2 and np.shape(value) == (1, 2))): raise InputParameterError( "Expected translation vector to be a 2 element row or column " "vector array") def __init__(self, matrix=matrix, translation=translation, **kwargs): super().__init__(matrix=matrix, translation=translation, **kwargs) self.inputs = ("x", "y") self.outputs = ("x", "y") @property def inverse(self): """ Inverse transformation. Raises `~astropy.modeling.InputParameterError` if the transformation cannot be inverted. """ det = np.linalg.det(self.matrix.value) if det == 0: raise InputParameterError( "Transformation matrix is singular; {} model does not " "have an inverse".format(self.__class__.__name__)) matrix = np.linalg.inv(self.matrix.value) if self.matrix.unit is not None: matrix = matrix * self.matrix.unit # If matrix has unit then translation has unit, so no need to assign it. translation = -np.dot(matrix, self.translation.value) return self.__class__(matrix=matrix, translation=translation) @classmethod def evaluate(cls, x, y, matrix, translation): """ Apply the transformation 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 """ if x.shape != y.shape: raise ValueError("Expected input arrays to have the same shape") shape = x.shape or (1,) # Use asarray to ensure loose the units. inarr = np.vstack([np.asarray(x).ravel(), np.asarray(y).ravel(), np.ones(x.size, x.dtype)]) if inarr.shape[0] != 3 or inarr.ndim != 2: raise ValueError("Incompatible input shapes") augmented_matrix = cls._create_augmented_matrix(matrix, translation) result = np.dot(augmented_matrix, inarr) x, y = result[0], result[1] x.shape = y.shape = shape return x, y @staticmethod def _create_augmented_matrix(matrix, translation): unit = None if any([hasattr(translation, 'unit'), hasattr(matrix, 'unit')]): if not all([hasattr(translation, 'unit'), hasattr(matrix, 'unit')]): raise ValueError("To use AffineTransformation with quantities, " "both matrix and unit need to be quantities.") unit = translation.unit # matrix should have the same units as translation if not (matrix.unit / translation.unit) == u.dimensionless_unscaled: raise ValueError("matrix and translation must have the same units.") augmented_matrix = np.empty((3, 3), dtype=float) augmented_matrix[0:2, 0:2] = matrix augmented_matrix[0:2, 2:].flat = translation augmented_matrix[2] = [0, 0, 1] if unit is not None: return augmented_matrix * unit return augmented_matrix @property def input_units(self): if self.translation.unit is None and self.matrix.unit is None: return None elif self.translation.unit is not None: return dict(zip(self.inputs, [self.translation.unit] * 2)) else: return dict(zip(self.inputs, [self.matrix.unit] * 2))