# -*- coding: utf-8 -*-
"""
Tristimulus Values, CIE xyY Colourspace and Chromaticity Coordinates
====================================================================
Defines the *CIE xyY* colourspace transformations:
- :func:`colour.XYZ_to_xyY`
- :func:`colour.xyY_to_XYZ`
- :func:`colour.xyY_to_xy`
- :func:`colour.xy_to_xyY`
- :func:`colour.XYZ_to_xy`
- :func:`colour.xy_to_XYZ`
See Also
--------
`CIE xyY Colourspace Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/models/cie_xyy.ipynb>`_
References
----------
- :cite:`Lindbloom2003e` : Lindbloom, B. (2003). XYZ to xyY. Retrieved
February 24, 2014, from http://www.brucelindbloom.com/Eqn_XYZ_to_xyY.html
- :cite:`Lindbloom2009d` : Lindbloom, B. (2009). xyY to XYZ. Retrieved
February 24, 2014, from http://www.brucelindbloom.com/Eqn_xyY_to_XYZ.html
- :cite:`Wikipedia2005` : Wikipedia. (2005). CIE 1931 color space. Retrieved
February 24, 2014, from http://en.wikipedia.org/wiki/CIE_1931_color_space
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.colorimetry import ILLUMINANTS
from colour.constants import DEFAULT_FLOAT_DTYPE
from colour.utilities import (as_float_array, from_range_1, to_domain_1,
tsplit, tstack)
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2019 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = [
'XYZ_to_xyY', 'xyY_to_XYZ', 'xy_to_xyY', 'xyY_to_xy', 'XYZ_to_xy',
'xy_to_XYZ'
]
[docs]def XYZ_to_xyY(
XYZ,
illuminant=ILLUMINANTS['CIE 1931 2 Degree Standard Observer']['D65']):
"""
Converts from *CIE XYZ* tristimulus values to *CIE xyY* colourspace and
reference *illuminant*.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values.
illuminant : array_like, optional
Reference *illuminant* chromaticity coordinates.
Returns
-------
ndarray
*CIE xyY* colourspace array.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``XYZ`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``xyY`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Lindbloom2003e`, :cite:`Wikipedia2005`
Examples
--------
>>> XYZ = np.array([0.20654008, 0.12197225, 0.05136952])
>>> XYZ_to_xyY(XYZ) # doctest: +ELLIPSIS
array([ 0.5436955..., 0.3210794..., 0.1219722...])
"""
XYZ = to_domain_1(XYZ)
X, Y, Z = tsplit(XYZ)
xy_w = as_float_array(illuminant)
XYZ_n = np.zeros(XYZ.shape)
XYZ_n[..., 0:2] = xy_w
xyY = np.where(
np.all(XYZ == 0, axis=-1)[..., np.newaxis],
XYZ_n,
tstack([X / (X + Y + Z), Y / (X + Y + Z),
from_range_1(Y)]),
)
return xyY
[docs]def xyY_to_XYZ(xyY):
"""
Converts from *CIE xyY* colourspace to *CIE XYZ* tristimulus values.
Parameters
----------
xyY : array_like
*CIE xyY* colourspace array.
Returns
-------
ndarray
*CIE XYZ* tristimulus values.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``xyY`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``XYZ`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Lindbloom2009d`, :cite:`Wikipedia2005`
Examples
--------
>>> xyY = np.array([0.54369557, 0.32107944, 0.12197225])
>>> xyY_to_XYZ(xyY) # doctest: +ELLIPSIS
array([ 0.2065400..., 0.1219722..., 0.0513695...])
"""
x, y, Y = tsplit(xyY)
Y = to_domain_1(Y)
XYZ = np.where(
(y == 0)[..., np.newaxis],
tstack([y, y, y]),
tstack([x * Y / y, Y, (1 - x - y) * Y / y]),
)
return from_range_1(XYZ)
[docs]def xyY_to_xy(xyY):
"""
Converts from *CIE xyY* colourspace to *xy* chromaticity coordinates.
``xyY`` argument with last dimension being equal to 2 will be assumed to be
a *xy* chromaticity coordinates argument and will be returned directly by
the definition.
Parameters
----------
xyY : array_like
*CIE xyY* colourspace array or *xy* chromaticity coordinates.
Returns
-------
ndarray
*xy* chromaticity coordinates.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``xyY`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Wikipedia2005`
Examples
--------
>>> xyY = np.array([0.54369557, 0.32107944, 0.12197225])
>>> xyY_to_xy(xyY) # doctest: +ELLIPSIS
array([ 0.54369557..., 0.32107944...])
>>> xy = np.array([0.54369557, 0.32107944])
>>> xyY_to_xy(xy) # doctest: +ELLIPSIS
array([ 0.54369557..., 0.32107944...])
"""
xyY = as_float_array(xyY)
# Assuming ``xyY`` is actually a *xy* chromaticity coordinates argument and
# returning it directly.
if xyY.shape[-1] == 2:
return xyY
xy = xyY[..., 0:2]
return xy
[docs]def xy_to_xyY(xy, Y=1):
"""
Converts from *xy* chromaticity coordinates to *CIE xyY* colourspace by
extending the array last dimension with :math:`Y` Luminance.
``xy`` argument with last dimension being equal to 3 will be assumed to be
a *CIE xyY* colourspace array argument and will be returned directly by the
definition.
Parameters
----------
xy : array_like
*xy* chromaticity coordinates or *CIE xyY* colourspace array.
Y : numeric, optional
Optional :math:`Y` Luminance value used to construct the *CIE xyY*
colourspace array, otherwise the :math:`Y` Luminance will be set to 1.
Returns
-------
ndarray
*CIE xyY* colourspace array.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``xy`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``xyY`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
- This definition is a convenient object provided to implement support of
illuminant argument *luminance* value in various :mod:`colour.models`
package objects such as :func:`colour.Lab_to_XYZ` or
:func:`colour.Luv_to_XYZ`.
References
----------
:cite:`Wikipedia2005`
Examples
--------
>>> xy = np.array([0.54369557, 0.32107944])
>>> xy_to_xyY(xy) # doctest: +ELLIPSIS
array([ 0.5436955..., 0.3210794..., 1. ])
>>> xy = np.array([0.54369557, 0.32107944, 1.00000000])
>>> xy_to_xyY(xy) # doctest: +ELLIPSIS
array([ 0.5436955..., 0.3210794..., 1. ])
>>> xy = np.array([0.54369557, 0.32107944])
>>> xy_to_xyY(xy, 100) # doctest: +ELLIPSIS
array([ 0.5436955..., 0.3210794..., 100. ])
"""
xy = as_float_array(xy)
Y = to_domain_1(Y)
shape = xy.shape
# Assuming ``xy`` is actually a *CIE xyY* colourspace array argument and
# returning it directly.
if shape[-1] == 3:
return xy
x, y = tsplit(xy)
Y = np.full(x.shape, from_range_1(Y), DEFAULT_FLOAT_DTYPE)
xyY = tstack([x, y, Y])
return xyY
[docs]def XYZ_to_xy(
XYZ,
illuminant=ILLUMINANTS['CIE 1931 2 Degree Standard Observer']['D65']):
"""
Returns the *xy* chromaticity coordinates from given *CIE XYZ* tristimulus
values.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values.
illuminant : array_like, optional
Reference *illuminant* chromaticity coordinates.
Returns
-------
ndarray
*xy* chromaticity coordinates.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``XYZ`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Wikipedia2005`
Examples
--------
>>> XYZ = np.array([0.20654008, 0.12197225, 0.05136952])
>>> XYZ_to_xy(XYZ) # doctest: +ELLIPSIS
array([ 0.5436955..., 0.3210794...])
"""
return xyY_to_xy(XYZ_to_xyY(XYZ, illuminant))
[docs]def xy_to_XYZ(xy):
"""
Returns the *CIE XYZ* tristimulus values from given *xy* chromaticity
coordinates.
Parameters
----------
xy : array_like
*xy* chromaticity coordinates.
Returns
-------
ndarray
*CIE XYZ* tristimulus values.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``xy`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``XYZ`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Wikipedia2005`
Examples
--------
>>> xy = np.array([0.54369557, 0.32107944])
>>> xy_to_XYZ(xy) # doctest: +ELLIPSIS
array([ 1.6933366..., 1. , 0.4211574...])
"""
return xyY_to_XYZ(xy_to_xyY(xy))