"""
CIE 1960 UCS Colourspace
========================
Defines the *CIE 1960 UCS* colourspace transformations:
- :func:`colour.XYZ_to_UCS`
- :func:`colour.UCS_to_XYZ`
- :func:`colour.UCS_to_uv`
- :func:`colour.uv_to_UCS`
- :func:`colour.UCS_uv_to_xy`
- :func:`colour.xy_to_UCS_uv`
References
----------
- :cite:`Wikipedia2008` : Wikipedia. (2008). CIE 1960 color space. Retrieved
February 24, 2014, from http://en.wikipedia.org/wiki/CIE_1960_color_space
- :cite:`Wikipedia2008c` : Wikipedia. (2008). Relation to CIE XYZ. Retrieved
February 24, 2014, from
http://en.wikipedia.org/wiki/CIE_1960_color_space#Relation_to_CIE_XYZ
"""
from __future__ import annotations
from colour.algebra import sdiv, sdiv_mode
from colour.hints import ArrayLike, NDArrayFloat
from colour.utilities import (
as_float_scalar,
from_range_1,
full,
to_domain_1,
tsplit,
tstack,
)
__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_UCS",
"UCS_to_XYZ",
"UCS_to_uv",
"uv_to_UCS",
"UCS_uv_to_xy",
"xy_to_UCS_uv",
]
[docs]
def XYZ_to_UCS(XYZ: ArrayLike) -> NDArrayFloat:
"""
Convert from *CIE XYZ* tristimulus values to *CIE 1960 UCS* colourspace.
Parameters
----------
XYZ
*CIE XYZ* tristimulus values.
Returns
-------
:class:`numpy.ndarray`
*CIE 1960 UCS* colourspace array.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``XYZ`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``UVW`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Wikipedia2008c`, :cite:`Wikipedia2008`
Examples
--------
>>> import numpy as np
>>> XYZ = np.array([0.20654008, 0.12197225, 0.05136952])
>>> XYZ_to_UCS(XYZ) # doctest: +ELLIPSIS
array([ 0.1376933..., 0.1219722..., 0.1053731...])
"""
X, Y, Z = tsplit(to_domain_1(XYZ))
UVW = tstack([2 / 3 * X, Y, 1 / 2 * (-X + 3 * Y + Z)])
return from_range_1(UVW)
[docs]
def UCS_to_XYZ(UVW: ArrayLike) -> NDArrayFloat:
"""
Convert from *CIE 1960 UCS* colourspace to *CIE XYZ* tristimulus values.
Parameters
----------
UVW
*CIE 1960 UCS* colourspace array.
Returns
-------
:class:`numpy.ndarray`
*CIE XYZ* tristimulus values.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``UVW`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``XYZ`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Wikipedia2008c`, :cite:`Wikipedia2008`
Examples
--------
>>> import numpy as np
>>> UVW = np.array([0.13769339, 0.12197225, 0.10537310])
>>> UCS_to_XYZ(UVW) # doctest: +ELLIPSIS
array([ 0.2065400..., 0.1219722..., 0.0513695...])
"""
U, V, W = tsplit(to_domain_1(UVW))
XYZ = tstack([3 / 2 * U, V, 3 / 2 * U - (3 * V) + (2 * W)])
return from_range_1(XYZ)
[docs]
def UCS_to_uv(UVW: ArrayLike) -> NDArrayFloat:
"""
Return the *uv* chromaticity coordinates from given *CIE 1960 UCS*
colourspace array.
Parameters
----------
UVW
*CIE 1960 UCS* colourspace array.
Returns
-------
:class:`numpy.ndarray`
*uv* chromaticity coordinates.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``UVW`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Wikipedia2008c`
Examples
--------
>>> import numpy as np
>>> UVW = np.array([0.13769339, 0.12197225, 0.10537310])
>>> UCS_to_uv(UVW) # doctest: +ELLIPSIS
array([ 0.3772021..., 0.3341350...])
"""
U, V, W = tsplit(to_domain_1(UVW))
U_V_W = U + V + W
with sdiv_mode():
uv = tstack([sdiv(U, U_V_W), sdiv(V, U_V_W)])
return uv
[docs]
def uv_to_UCS(uv: ArrayLike, V: float = 1) -> NDArrayFloat:
"""
Return the *CIE 1960 UCS* colourspace array from given *uv* chromaticity
coordinates.
Parameters
----------
uv
*uv* chromaticity coordinates.
V
Optional :math:`V` *luminance* value used to construct the
*CIE 1960 UCS* colourspace array, the default :math:`V` *luminance* is
set to 1.
Returns
-------
:class:`numpy.ndarray`
*CIE 1960 UCS* colourspace array.
References
----------
:cite:`Wikipedia2008c`
Examples
--------
>>> import numpy as np
>>> uv = np.array([0.37720213, 0.33413508])
>>> uv_to_UCS(uv) # doctest: +ELLIPSIS
array([ 1.1288911..., 1. , 0.8639104...])
"""
u, v = tsplit(uv)
V = as_float_scalar(to_domain_1(V))
with sdiv_mode():
UVW = tstack(
[V * sdiv(u, v), full(u.shape, V), -V * sdiv(u + v - 1, v)]
)
return from_range_1(UVW)
[docs]
def UCS_uv_to_xy(uv: ArrayLike) -> NDArrayFloat:
"""
Return the *CIE xy* chromaticity coordinates from given *CIE 1960 UCS*
colourspace *uv* chromaticity coordinates.
Parameters
----------
uv
*CIE UCS uv* chromaticity coordinates.
Returns
-------
:class:`numpy.ndarray`
*CIE xy* chromaticity coordinates.
References
----------
:cite:`Wikipedia2008c`
Examples
--------
>>> import numpy as np
>>> uv = np.array([0.37720213, 0.33413508])
>>> UCS_uv_to_xy(uv) # doctest: +ELLIPSIS
array([ 0.5436955..., 0.3210794...])
"""
u, v = tsplit(uv)
d = 2 * u - 8 * v + 4
with sdiv_mode():
xy = tstack([sdiv(3 * u, d), sdiv(2 * v, d)])
return xy
[docs]
def xy_to_UCS_uv(xy: ArrayLike) -> NDArrayFloat:
"""
Return the *CIE 1960 UCS* colourspace *uv* chromaticity coordinates from
given *CIE xy* chromaticity coordinates.
Parameters
----------
xy
*CIE xy* chromaticity coordinates.
Returns
-------
:class:`numpy.ndarray`
*CIE UCS uv* chromaticity coordinates.
References
----------
:cite:`Wikipedia2008c`
Examples
--------
>>> import numpy as np
>>> xy = np.array([0.54369555, 0.32107941])
>>> xy_to_UCS_uv(xy) # doctest: +ELLIPSIS
array([ 0.3772021..., 0.3341350...])
"""
x, y = tsplit(xy)
d = 12 * y - 2 * x + 3
with sdiv_mode():
uv = tstack([sdiv(4 * x, d), sdiv(6 * y, d)])
return uv