#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
CIE Luv Colourspace
===================
Defines the *CIE Luv* colourspace transformations:
- :func:`XYZ_to_Luv`
- :func:`Luv_to_XYZ`
- :func:`Luv_to_uv`
- :func:`Luv_uv_to_xy`
- :func:`Luv_to_LCHuv`
- :func:`LCHuv_to_Luv`
See Also
--------
`CIE Luv Colourspace IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/models/cie_luv.ipynb>`_ # noqa
References
----------
.. [1] Wikipedia. (n.d.). CIELUV. Retrieved February 24, 2014, from
http://en.wikipedia.org/wiki/CIELUV
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.colorimetry import ILLUMINANTS
from colour.constants import CIE_E, CIE_K
from colour.models import xy_to_xyY, xyY_to_XYZ
from colour.utilities import tsplit, tstack
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2015 - 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_Luv',
'Luv_to_XYZ',
'Luv_to_uv',
'Luv_uv_to_xy',
'Luv_to_LCHuv',
'LCHuv_to_Luv']
[docs]def XYZ_to_Luv(XYZ,
illuminant=ILLUMINANTS.get(
'CIE 1931 2 Degree Standard Observer').get('D50')):
"""
Converts from *CIE XYZ* tristimulus values to *CIE Luv* colourspace.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values.
illuminant : array_like, optional
Reference *illuminant* *xy* chromaticity coordinates or *CIE xyY*
colourspace array.
Returns
-------
ndarray
*CIE Luv* colourspace array.
Notes
-----
- Input *CIE XYZ* tristimulus values are in domain [0, 1].
- Input *illuminant* *xy* chromaticity coordinates or *CIE xyY*
colourspace array are in domain [0, :math:`\infty`].
- Output :math:`L^*` is in domain [0, 100].
References
----------
.. [2] Lindbloom, B. (2003). XYZ to Luv. Retrieved February 24, 2014,
from http://brucelindbloom.com/Eqn_XYZ_to_Luv.html
Examples
--------
>>> XYZ = np.array([0.07049534, 0.10080000, 0.09558313])
>>> XYZ_to_Luv(XYZ) # doctest: +ELLIPSIS
array([ 37.9856291..., -28.7922944..., -1.3558195...])
"""
X, Y, Z = tsplit(XYZ)
X_r, Y_r, Z_r = tsplit(xyY_to_XYZ(xy_to_xyY(illuminant)))
y_r = Y / Y_r
L = np.where(y_r > CIE_E, 116 * y_r ** (1 / 3) - 16, CIE_K * y_r)
u = (13 * L * ((4 * X / (X + 15 * Y + 3 * Z)) -
(4 * X_r / (X_r + 15 * Y_r + 3 * Z_r))))
v = (13 * L * ((9 * Y / (X + 15 * Y + 3 * Z)) -
(9 * Y_r / (X_r + 15 * Y_r + 3 * Z_r))))
Luv = tstack((L, u, v))
return Luv
[docs]def Luv_to_XYZ(Luv,
illuminant=ILLUMINANTS.get(
'CIE 1931 2 Degree Standard Observer').get('D50')):
"""
Converts from *CIE Luv* colourspace to *CIE XYZ* tristimulus values.
Parameters
----------
Luv : array_like
*CIE Luv* colourspace array.
illuminant : array_like, optional
Reference *illuminant* *xy* chromaticity coordinates or *CIE xyY*
colourspace array.
Returns
-------
ndarray
*CIE XYZ* tristimulus values.
Notes
-----
- Input :math:`L^*` is in domain [0, 100].
- Input *illuminant* *xy* chromaticity coordinates or *CIE xyY*
colourspace array are in domain [0, :math:`\infty`].
- Output *CIE XYZ* tristimulus values are in domain [0, 1].
References
----------
.. [3] Lindbloom, B. (2003). Luv to XYZ. Retrieved February 24, 2014,
from http://brucelindbloom.com/Eqn_Luv_to_XYZ.html
Examples
--------
>>> Luv = np.array([37.98562910, -28.79229446, -1.35581950])
>>> Luv_to_XYZ(Luv) # doctest: +ELLIPSIS
array([ 0.0704953..., 0.1008 , 0.0955831...])
"""
L, u, v = tsplit(Luv)
X_r, Y_r, Z_r = tsplit(xyY_to_XYZ(xy_to_xyY(illuminant)))
Y = np.where(L > CIE_E * CIE_K, ((L + 16) / 116) ** 3, L / CIE_K)
a = 1 / 3 * ((52 * L / (u + 13 * L *
(4 * X_r / (X_r + 15 * Y_r + 3 * Z_r)))) - 1)
b = -5 * Y
c = -1 / 3.0
d = Y * (39 * L / (v + 13 * L *
(9 * Y_r / (X_r + 15 * Y_r + 3 * Z_r))) - 5)
X = (d - b) / (a - c)
Z = X * a + b
XYZ = tstack((X, Y, Z))
return XYZ
[docs]def Luv_to_uv(Luv,
illuminant=ILLUMINANTS.get(
'CIE 1931 2 Degree Standard Observer').get('D50')):
"""
Returns the :math:`uv^p` chromaticity coordinates from given *CIE Luv*
colourspace array.
Parameters
----------
Luv : array_like
*CIE Luv* colourspace array.
illuminant : array_like, optional
Reference *illuminant* *xy* chromaticity coordinates or *CIE xyY*
colourspace array.
Returns
-------
ndarray
:math:`uv^p` chromaticity coordinates.
Notes
-----
- Input :math:`L^*` is in domain [0, 100].
- Input *illuminant* *xy* chromaticity coordinates or *CIE xyY*
colourspace array are in domain [0, :math:`\infty`].
- Output :math:`uv^p` chromaticity coordinates are in domain [0, 1].
References
----------
.. [4] Wikipedia. (n.d.). The forward transformation. Retrieved February
24, 2014, from
http://en.wikipedia.org/wiki/CIELUV#The_forward_transformation
Examples
--------
>>> Luv = np.array([37.98562910, -28.79229446, -1.35581950])
>>> Luv_to_uv(Luv) # doctest: +ELLIPSIS
array([ 0.1508531..., 0.4853297...])
"""
X, Y, Z = tsplit(Luv_to_XYZ(Luv, illuminant))
uv = tstack((4 * X / (X + 15 * Y + 3 * Z),
9 * Y / (X + 15 * Y + 3 * Z)))
return uv
[docs]def Luv_uv_to_xy(uv):
"""
Returns the *xy* chromaticity coordinates from given *CIE Luv* colourspace
:math:`uv^p` chromaticity coordinates.
Parameters
----------
uv : array_like
*CIE Luv u"v"* chromaticity coordinates.
Returns
-------
ndarray
*xy* chromaticity coordinates.
Notes
-----
- Input :math:`uv^p` chromaticity coordinates are in domain [0, 1].
- Output *xy* is in domain [0, 1].
References
----------
.. [5] Wikipedia. (n.d.). The reverse transformation. Retrieved from
http://en.wikipedia.org/wiki/CIELUV#The_reverse_transformation
Examples
--------
>>> uv = np.array([0.15085309882985695, 0.48532970854318019])
>>> Luv_uv_to_xy(uv) # doctest: +ELLIPSIS
array([ 0.2641477..., 0.3777000...])
"""
u, v = tsplit(uv)
xy = tstack((9 * u / (6 * u - 16 * v + 12),
4 * v / (6 * u - 16 * v + 12)))
return xy
[docs]def Luv_to_LCHuv(Luv):
"""
Converts from *CIE Luv* colourspace to *CIE LCHuv* colourspace.
Parameters
----------
Luv : array_like
*CIE Luv* colourspace array.
Returns
-------
ndarray
*CIE LCHuv* colourspace array.
Notes
-----
- :math:`L^*` is in domain [0, 100].
References
----------
.. [6] Lindbloom, B. (2003). Luv to LCH(uv). Retrieved February 24, 2014,
from http://www.brucelindbloom.com/Eqn_Luv_to_LCH.html
Examples
--------
>>> Luv = np.array([37.98562910, -28.79229446, -1.35581950])
>>> Luv_to_LCHuv(Luv) # doctest: +ELLIPSIS
array([ 37.9856291..., 28.8241993..., 182.6960474...])
"""
L, u, v = tsplit(Luv)
H = np.array(180 * np.arctan2(v, u) / np.pi)
H[np.array(H < 0)] += 360
LCHuv = tstack((L, np.sqrt(u ** 2 + v ** 2), H))
return LCHuv
[docs]def LCHuv_to_Luv(LCHuv):
"""
Converts from *CIE LCHuv* colourspace to *CIE Luv* colourspace.
Parameters
----------
LCHuv : array_like
*CIE LCHuv* colourspace array.
Returns
-------
ndarray
*CIE Luv* colourspace array.
Notes
-----
- :math:`L^*` is in domain [0, 100].
References
----------
.. [7] Lindbloom, B. (2006). LCH(uv) to Luv. Retrieved February 24, 2014,
from http://www.brucelindbloom.com/Eqn_LCH_to_Luv.html
Examples
--------
>>> LCHuv = np.array([37.98562910, 28.82419933, 182.69604747])
>>> LCHuv_to_Luv(LCHuv) # doctest: +ELLIPSIS
array([ 37.9856291..., -28.7922944..., -1.3558195...])
"""
L, C, H = tsplit(LCHuv)
Luv = tstack((L, C * np.cos(np.radians(H)), C * np.sin(np.radians(H))))
return Luv
Colour 0.3