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# -*- coding: utf-8 -*-
# Copyright (C) 2011 Association of Universities for Research in
# Astronomy (AURA)
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# 1. Redistributions of source code must retain the above
# copyright notice, this list of conditions and the following
# disclaimer.
#
# 2. Redistributions in binary form must reproduce the above
# copyright notice, this list of conditions and the following
# disclaimer in the documentation and/or other materials
# provided with the distribution.
#
# 3. The name of AURA and its representatives may not be used to
# endorse or promote products derived from this software without
# specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY AURA ``AS IS'' AND ANY EXPRESS OR
# IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL AURA BE LIABLE FOR ANY DIRECT,
# INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
# (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
# HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
# STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
# OF THE POSSIBILITY OF SUCH DAMAGE.
"""
The `sphere.vector` module contains the basic operations for handling
vectors and converting them to and from other representations.
"""
from __future__ import unicode_literals
# THIRD-PARTY
import numpy as np
__all__ = ['radec_to_vector', 'vector_to_radec', 'normalize_vector',
'rotate_around']
def radec_to_vector(ra, dec, degrees=True):
r"""
Converts a location on the unit sphere from right-ascension and
declination to an *x*, *y*, *z* vector.
Parameters
----------
ra, dec : scalars or 1-D arrays
degrees : bool, optional
If `True`, (default) *ra* and *dec* are in decimal degrees,
otherwise in radians.
Returns
-------
x, y, z : tuple of scalars or 1-D arrays of the same length
Notes
-----
Where right-ascension is *α* and declination is *δ*:
.. math::
x = \cos\alpha \cos\delta
y = \sin\alpha \cos\delta
z = \sin\delta
"""
ra = np.asanyarray(ra)
dec = np.asanyarray(dec)
if degrees:
ra_rad = np.deg2rad(ra)
dec_rad = np.deg2rad(dec)
else:
ra_rad = ra
dec_rad = dec
cos_dec = np.cos(dec_rad)
return (
np.cos(ra_rad) * cos_dec,
np.sin(ra_rad) * cos_dec,
np.sin(dec_rad))
def vector_to_radec(x, y, z, degrees=True):
r"""
Converts a vector to right-ascension and declination.
Parameters
----------
x, y, z : scalars or 1-D arrays
The input vectors
degrees : bool, optional
If `True` (default) the result is returned in decimal degrees,
otherwise radians.
Returns
-------
ra, dec : tuple of scalars or arrays of the same length
Notes
-----
Where right-ascension is *α* and declination is
*δ*:
.. math::
\alpha = \arctan2(y, x)
\delta = \arctan2(z, \sqrt{x^2 + y^2})
"""
x = np.asanyarray(x)
y = np.asanyarray(y)
z = np.asanyarray(z)
result = (
np.arctan2(y, x),
np.arctan2(z, np.sqrt(x ** 2 + y ** 2)))
if degrees:
return np.rad2deg(result[0]), np.rad2deg(result[1])
else:
return result
def normalize_vector(x, y, z, inplace=False):
r"""
Normalizes a vector so it falls on the unit sphere.
*x*, *y*, *z* may be scalars or 1-D arrays
Parameters
----------
x, y, z : scalars or 1-D arrays of the same length
The input vectors
inplace : bool, optional
When `True`, the original arrays will be normalized in place,
otherwise a normalized copy is returned.
Returns
-------
X, Y, Z : scalars of 1-D arrays of the same length
The normalized output vectors
"""
x = np.asanyarray(x)
y = np.asanyarray(y)
z = np.asanyarray(z)
l = np.sqrt(x ** 2 + y ** 2 + z ** 2)
if inplace:
x /= l
y /= l
z /= l
return (x, y, z)
else:
return (x / l, y / l, z / l)
def rotate_around(x, y, z, u, v, w, theta, degrees=True):
r"""
Rotates the vector (*x*, *y*, *z*) around the arbitrary axis defined by
vector (*u*, *v*, *w*) by *theta*.
It is assumed that both (*x*, *y*, *z*) and (*u*, *v*, *w*) are
already normalized.
Parameters
----------
x, y, z : doubles
The normalized vector to rotate
u, v, w : doubles
The normalized vector to rotate around
theta : double, or array of doubles
The amount to rotate
degrees : bool, optional
When `True`, *theta* is given in degrees, otherwise radians.
Returns
-------
X, Y, Z : doubles
The rotated vector
"""
if degrees:
theta = np.deg2rad(theta)
costheta = np.cos(theta)
sintheta = np.sin(theta)
icostheta = 1.0 - costheta
det = (-u*x - v*y - w*z)
X = (-u*det)*icostheta + x*costheta + (-w*y + v*z)*sintheta
Y = (-v*det)*icostheta + y*costheta + ( w*x - u*z)*sintheta
Z = (-w*det)*icostheta + z*costheta + (-v*x + u*y)*sintheta
return X, Y, Z
def equal_area_proj(x, y, z):
"""
Transform the coordinates to a 2-dimensional plane using the
Lambert azimuthal equal-area projection.
Parameters
----------
x, y, z : scalars or 1-D arrays
The input vectors
Returns
-------
X, Y : tuple of scalars or arrays of the same length
Notes
-----
.. math::
X = \sqrt{\frac{2}{1-z}}x
.. math::
Y = \sqrt{\frac{2}{1-z}}y
"""
scale = np.sqrt(2.0 / (1.0 - z))
X = scale * x
Y = scale * y
return X, Y
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