Source code for colour.models.cie_luv

#!/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]  http://en.wikipedia.org/wiki/CIELUV
        (Last accessed 24 February 2014)
"""

from __future__ import division, unicode_literals

import math
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] http://brucelindbloom.com/Eqn_XYZ_to_Luv.html (Last accessed 24 February 2014) Examples -------- >>> XYZ_to_Luv(np.array([0.92193107, 1, 1.03744246])) # doctest: +ELLIPSIS array([ 100. , -20.0430424..., -19.8167603...]) """ 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] http://brucelindbloom.com/Eqn_Luv_to_XYZ.html (Last accessed 24 February 2014) Examples -------- >>> Luv = np.array([100, -20.04304247, -19.81676035]) >>> Luv_to_XYZ(Luv) # doctest: +ELLIPSIS array([ 0.9219310..., 1. , 1.0374424...]) """ 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 *u"v"* 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 *u"v"* chromaticity coordinates. Notes ----- - Input :math:`L^*` is in domain [0, 100]. - Output *u"v"* chromaticity coordinates are in domain [0, 1]. References ---------- .. [4] http://en.wikipedia.org/wiki/CIELUV#The_forward_transformation (Last accessed 24 February 2014) Examples -------- >>> Luv = np.array([100, -20.04304247, -19.81676035]) >>> Luv_to_uv(Luv) # doctest: +ELLIPSIS (0.1937414..., 0.4728316...) """ 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 *u"v"* chromaticity coordinates. Parameters ---------- uv : array_like *CIE Luv u"v"* chromaticity coordinates. Returns ------- tuple *xy* chromaticity coordinates. Notes ----- - Input *u"v"* chromaticity coordinates are in domain [0, 1]. - Output *xy* is in domain [0, 1]. References ---------- .. [5] http://en.wikipedia.org/wiki/CIELUV#The_reverse_transformation (Last accessed 24 February 2014) Examples -------- >>> uv = (0.2033733344733139, 0.3140500001549052) >>> Luv_uv_to_xy(uv) # doctest: +ELLIPSIS (0.2233388..., 0.1532803...) """ 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] http://www.brucelindbloom.com/Eqn_Luv_to_LCH.html (Last accessed 24 February 2014) Examples -------- >>> Luv = np.array([100, -20.04304247, -19.81676035]) >>> Luv_to_LCHuv(Luv) # doctest: +ELLIPSIS array([ 100. , 28.1855910..., 224.6747382...]) """ L, u, v = np.ravel(Luv) H = 180 * math.atan2(v, u) / math.pi if H < 0: H += 360 return np.array([L, math.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] http://www.brucelindbloom.com/Eqn_LCH_to_Luv.html (Last accessed 24 February 2014) Examples -------- >>> LCHuv = np.array([100, 28.18559104, 224.6747382]) >>> LCHuv_to_Luv(LCHuv) # doctest: +ELLIPSIS array([ 100. , -20.0430424..., -19.8167603...]) """ L, C, H = np.ravel(LCHuv) return np.array([L, C * math.cos(math.radians(H)), C * math.sin(math.radians(H))])