"""
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`
References
----------
- :cite:`CIETC1-482004h` : CIE TC 1-48. (2004). CIE 015:2004 Colorimetry,
3rd Edition. In CIE 015:2004 Colorimetry, 3rd Edition. Commission
Internationale de l'Eclairage. ISBN:978-3-901906-33-6
- :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 annotations
import numpy as np
from colour.hints import ArrayLike, NDArrayFloat
from colour.utilities import (
as_float_array,
from_range_1,
to_domain_1,
tsplit,
tstack,
zeros,
)
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "BSD-3-Clause - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__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: ArrayLike) -> NDArrayFloat:
"""
Convert from *CIE XYZ* tristimulus values to *CIE xyY* colourspace.
Parameters
----------
XYZ
*CIE XYZ* tristimulus values.
Returns
-------
:class:`numpy.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:`CIETC1-482004h`, :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)
xyY = zeros(XYZ.shape)
xyY[..., 0:2] = 0
m_xyY = ~np.all(XYZ == 0, axis=-1)
X_Y_Z = (X + Y + Z)[m_xyY]
xyY[m_xyY] = (
tstack(
[
X[m_xyY] / X_Y_Z,
Y[m_xyY] / X_Y_Z,
from_range_1(Y[m_xyY]),
]
),
)
return xyY
[docs]
def xyY_to_XYZ(xyY: ArrayLike) -> NDArrayFloat:
"""
Convert from *CIE xyY* colourspace to *CIE XYZ* tristimulus values.
Parameters
----------
xyY
*CIE xyY* colourspace array.
Returns
-------
:class:`numpy.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:`CIETC1-482004h`, :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...])
"""
xyY = as_float_array(xyY)
x, y, Y = tsplit(xyY)
Y = to_domain_1(Y)
XYZ = zeros(xyY.shape)
m_XYZ = ~(y == 0)
Y_y = Y[m_XYZ] / y[m_XYZ]
XYZ[m_XYZ] = tstack([x[m_XYZ] * Y_y, Y[m_XYZ], (1 - x[m_XYZ] - y[m_XYZ]) * Y_y])
return from_range_1(XYZ)
[docs]
def xyY_to_xy(xyY: ArrayLike) -> NDArrayFloat:
"""
Convert from *CIE xyY* colourspace to *CIE xy* chromaticity coordinates.
``xyY`` argument with last dimension being equal to 2 will be assumed to be
a *CIE xy* chromaticity coordinates argument and will be returned directly
by the definition.
Parameters
----------
xyY
*CIE xyY* colourspace array or *CIE xy* chromaticity coordinates.
Returns
-------
:class:`numpy.ndarray`
*CIE xy* chromaticity coordinates.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``xyY`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`CIETC1-482004h`, :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 *CIE 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: ArrayLike, Y: NDArrayFloat = np.array(1)) -> NDArrayFloat:
"""
Convert from *CIE xy* chromaticity coordinates to *CIE xyY* colourspace by
extending the array last dimension with given :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
*CIE xy* chromaticity coordinates or *CIE xyY* colourspace array.
Y
Optional :math:`Y` *luminance* value used to construct the *CIE xyY*
colourspace array, the default :math:`Y` *luminance* value is 1.
Returns
-------
:class:`numpy.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:`CIETC1-482004h`, :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 = as_float_array(to_domain_1(Y))
# Assuming ``xy`` is actually a *CIE xyY* colourspace array argument and
# returning it directly.
if xy.shape[-1] == 3:
return xy
x, y = tsplit(xy)
xyY = tstack([x, y, np.resize(Y, x.shape)])
return from_range_1(xyY, np.array([1, 1, 100]))
[docs]
def XYZ_to_xy(XYZ: ArrayLike) -> NDArrayFloat:
"""
Return the *CIE xy* chromaticity coordinates from given *CIE XYZ*
tristimulus values.
Parameters
----------
XYZ
*CIE XYZ* tristimulus values.
Returns
-------
:class:`numpy.ndarray`
*CIE xy* chromaticity coordinates.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``XYZ`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`CIETC1-482004h`, :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))
[docs]
def xy_to_XYZ(xy: ArrayLike) -> NDArrayFloat:
"""
Return the *CIE XYZ* tristimulus values from given *CIE xy* chromaticity
coordinates.
Parameters
----------
xy
*CIE xy* chromaticity coordinates.
Returns
-------
:class:`numpy.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:`CIETC1-482004h`, :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))