"""
CIE 1964 U*V*W* Colourspace
===========================
Defines the *CIE 1964 U\\*V\\*W\\** colourspace transformations:
- :func:`colour.XYZ_to_UVW`
- :func:`colour.UVW_to_XYZ`
References
----------
- :cite:`Wikipedia2008a` : Wikipedia. (2008). CIE 1964 color space.
Retrieved June 10, 2014, from
http://en.wikipedia.org/wiki/CIE_1964_color_space
"""
from __future__ import annotations
from colour.algebra import sdiv, sdiv_mode, spow
from colour.colorimetry import CCS_ILLUMINANTS
from colour.hints import ArrayLike, NDArrayFloat
from colour.models import (
UCS_uv_to_xy,
XYZ_to_xy,
xy_to_UCS_uv,
xyY_to_xy,
xyY_to_XYZ,
)
from colour.utilities import from_range_100, to_domain_100, 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_UVW",
"UVW_to_XYZ",
]
[docs]
def XYZ_to_UVW(
XYZ: ArrayLike,
illuminant: ArrayLike = CCS_ILLUMINANTS[
"CIE 1931 2 Degree Standard Observer"
]["D65"],
) -> NDArrayFloat:
"""
Convert from *CIE XYZ* tristimulus values to *CIE 1964 U\\*V\\*W\\**
colourspace.
Parameters
----------
XYZ
*CIE XYZ* tristimulus values.
illuminant
Reference *illuminant* *CIE xy* chromaticity coordinates or *CIE xyY*
colourspace array.
Returns
-------
:class:`numpy.ndarray`
*CIE 1964 U\\*V\\*W\\** colourspace array.
Notes
-----
+----------------+-----------------------+-----------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+================+=======================+=================+
| ``XYZ`` | [0, 100] | [0, 1] |
+----------------+-----------------------+-----------------+
| ``illuminant`` | [0, 1] | [0, 1] |
+----------------+-----------------------+-----------------+
+----------------+-----------------------+-----------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+================+=======================+=================+
| ``UVW`` | ``U`` : [-100, 100] | ``U`` : [-1, 1] |
| | | |
| | ``V`` : [-100, 100] | ``V`` : [-1, 1] |
| | | |
| | ``W`` : [0, 100] | ``W`` : [0, 1] |
+----------------+-----------------------+-----------------+
References
----------
:cite:`Wikipedia2008a`
Examples
--------
>>> import numpy as np
>>> XYZ = np.array([0.20654008, 0.12197225, 0.05136952]) * 100
>>> XYZ_to_UVW(XYZ) # doctest: +ELLIPSIS
array([ 94.5503572..., 11.5553652..., 40.5475740...])
"""
XYZ = to_domain_100(XYZ)
xy = XYZ_to_xy(XYZ / 100)
xy_n = xyY_to_xy(illuminant)
Y = XYZ[..., 1]
uv = xy_to_UCS_uv(xy)
uv_0 = xy_to_UCS_uv(xy_n)
W = 25 * spow(Y, 1 / 3) - 17
U, V = tsplit(13 * W[..., None] * (uv - uv_0))
UVW = tstack([U, V, W])
return from_range_100(UVW)
[docs]
def UVW_to_XYZ(
UVW: ArrayLike,
illuminant: ArrayLike = CCS_ILLUMINANTS[
"CIE 1931 2 Degree Standard Observer"
]["D65"],
) -> NDArrayFloat:
"""
Convert *CIE 1964 U\\*V\\*W\\** colourspace to *CIE XYZ* tristimulus
values.
Parameters
----------
UVW
*CIE 1964 U\\*V\\*W\\** colourspace array.
illuminant
Reference *illuminant* *CIE xy* chromaticity coordinates or *CIE xyY*
colourspace array.
Returns
-------
:class:`numpy.ndarray`
*CIE XYZ* tristimulus values.
Notes
-----
+----------------+-----------------------+-----------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+================+=======================+=================+
| ``UVW`` | ``U`` : [-100, 100] | ``U`` : [-1, 1] |
| | | |
| | ``V`` : [-100, 100] | ``V`` : [-1, 1] |
| | | |
| | ``W`` : [0, 100] | ``W`` : [0, 1] |
+----------------+-----------------------+-----------------+
| ``illuminant`` | [0, 1] | [0, 1] |
+----------------+-----------------------+-----------------+
+----------------+-----------------------+-----------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+================+=======================+=================+
| ``XYZ`` | [0, 100 | [0, 1] |
+----------------+-----------------------+-----------------+
References
----------
:cite:`Wikipedia2008a`
Examples
--------
>>> import numpy as np
>>> UVW = np.array([94.55035725, 11.55536523, 40.54757405])
>>> UVW_to_XYZ(UVW)
array([ 20.654008, 12.197225, 5.136952])
"""
U, V, W = tsplit(to_domain_100(UVW))
u_0, v_0 = tsplit(xy_to_UCS_uv(xyY_to_xy(illuminant)))
Y = ((W + 17) / 25) ** 3
with sdiv_mode():
u = sdiv(U, 13 * W) + u_0
v = sdiv(V, 13 * W) + v_0
x, y = tsplit(UCS_uv_to_xy(tstack([u, v])))
XYZ = xyY_to_XYZ(tstack([x, y, Y]))
return from_range_100(XYZ)