#!/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_XYZ
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2014 - 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* colourspace to *CIE Luv* colourspace.
Parameters
----------
XYZ : array_like, (3,)
*CIE XYZ* colourspace matrix.
illuminant : array_like, optional
Reference *illuminant* chromaticity coordinates.
Returns
-------
ndarray, (3,)
*CIE Luv* colourspace matrix.
Notes
-----
- Input *CIE XYZ* colourspace matrix is in domain [0, 1].
- Input *illuminant* chromaticity coordinates are in domain [0, 1].
- 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, 0.1008, 0.09558313])
>>> XYZ_to_Luv(XYZ) # doctest: +ELLIPSIS
array([ 37.9856291..., -28.7922944..., -1.3558195...])
"""
X, Y, Z = np.ravel(XYZ)
Xr, Yr, Zr = np.ravel(xy_to_XYZ(illuminant))
yr = Y / Yr
L = 116 * yr ** (1 / 3) - 16 if yr > CIE_E else CIE_K * yr
u = (13 * L * ((4 * X / (X + 15 * Y + 3 * Z)) -
(4 * Xr / (Xr + 15 * Yr + 3 * Zr))))
v = (13 * L * ((9 * Y / (X + 15 * Y + 3 * Z)) -
(9 * Yr / (Xr + 15 * Yr + 3 * Zr))))
return np.array([L, u, v])
[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* colourspace.
Parameters
----------
Luv : array_like, (3,)
*CIE Luv* colourspace matrix.
illuminant : array_like, optional
Reference *illuminant* chromaticity coordinates.
Returns
-------
ndarray, (3,)
*CIE XYZ* colourspace matrix.
Notes
-----
- Input :math:`L^*` is in domain [0, 100].
- Input *illuminant* chromaticity coordinates are in domain [0, 1].
- Output *CIE XYZ* colourspace matrix is 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([37.9856291, -28.79229446, -1.3558195])
>>> Luv_to_XYZ(Luv) # doctest: +ELLIPSIS
array([ 0.0704953..., 0.1008 , 0.0955831...])
"""
L, u, v = np.ravel(Luv)
Xr, Yr, Zr = np.ravel(xy_to_XYZ(illuminant))
Y = ((L + 16) / 116) ** 3 if L > CIE_E * CIE_K else L / CIE_K
a = 1 / 3 * ((52 * L / (u + 13 * L *
(4 * Xr / (Xr + 15 * Yr + 3 * Zr)))) - 1)
b = -5 * Y
c = -1 / 3.0
d = Y * (39 * L / (v + 13 * L *
(9 * Yr / (Xr + 15 * Yr + 3 * Zr))) - 5)
X = (d - b) / (a - c)
Z = X * a + b
return np.array([X, Y, Z])
[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 matrix.
Parameters
----------
Luv : array_like, (3,)
*CIE Luv* colourspace matrix.
illuminant : array_like, optional
Reference *illuminant* chromaticity coordinates.
Returns
-------
tuple
:math:`uv^p` chromaticity coordinates.
Notes
-----
- Input :math:`L^*` is in domain [0, 100].
- 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([37.9856291, -28.79229446, -1.3558195])
>>> Luv_to_uv(Luv) # doctest: +ELLIPSIS
(0.1508530..., 0.4853297...)
"""
X, Y, Z = np.ravel(Luv_to_XYZ(Luv, illuminant))
return 4 * X / (X + 15 * Y + 3 * Z), 9 * Y / (X + 15 * Y + 3 * Z)
[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
-------
tuple
*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 = (0.15085309882985695, 0.48532970854318019)
>>> Luv_uv_to_xy(uv) # doctest: +ELLIPSIS
(0.2641477..., 0.3777000...)
"""
return (9 * uv[0] / (6 * uv[0] - 16 * uv[1] + 12), 4 * uv[1] /
(6 * uv[0] - 16 * uv[1] + 12))
[docs]def Luv_to_LCHuv(Luv):
"""
Converts from *CIE Luv* colourspace to *CIE LCHuv* colourspace.
Parameters
----------
Luv : array_like, (3,)
*CIE Luv* colourspace matrix.
Returns
-------
ndarray, (3,)
*CIE LCHuv* colourspace matrix.
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([37.9856291, -28.79229446, -1.3558195])
>>> Luv_to_LCHuv(Luv) # doctest: +ELLIPSIS
array([ 37.9856291..., 28.8241993..., 182.6960474...])
"""
L, u, v = np.ravel(Luv)
H = 180 * np.arctan2(v, u) / np.pi
if H < 0:
H += 360
return np.array([L, np.sqrt(u ** 2 + v ** 2), H])
[docs]def LCHuv_to_Luv(LCHuv):
"""
Converts from *CIE LCHuv* colourspace to *CIE Luv* colourspace.
Parameters
----------
LCHuv : array_like, (3,)
*CIE LCHuv* colourspace matrix.
Returns
-------
ndarray, (3,)
*CIE Luv* colourspace matrix.
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([37.9856291, 28.82419933, 182.69604747])
>>> LCHuv_to_Luv(LCHuv) # doctest: +ELLIPSIS
array([ 37.9856291..., -28.7922944..., -1.3558195...])
"""
L, C, H = np.ravel(LCHuv)
return np.array([L,
C * np.cos(np.radians(H)),
C * np.sin(np.radians(H))])
Colour 0.3