#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Correlated Colour Temperature :math:`T_{cp}`
============================================
Defines correlated colour temperature :math:`T_{cp}` computations objects:
- :func:`uv_to_CCT_Ohno2013`: Correlated colour temperature :math:`T_{cp}`
and :math:`\Delta_{uv}` computation of given *CIE UCS* colourspace *uv*
chromaticity coordinates using Ohno (2013) method.
- :func:`CCT_to_uv_Ohno2013`: *CIE UCS* colourspace *uv* chromaticity
coordinates computation of given correlated colour temperature
:math:`T_{cp}`, :math:`\Delta_{uv}` using Ohno (2013) method.
- :func:`uv_to_CCT_Robertson1968`: Correlated colour temperature
:math:`T_{cp}` and :math:`\Delta_{uv}` computation of given *CIE UCS*
colourspace *uv* chromaticity coordinates using Robertson (1968) method.
- :func:`CCT_to_uv_Robertson1968`: *CIE UCS* colourspace *uv* chromaticity
coordinates computation of given correlated colour temperature
:math:`T_{cp}` and :math:`\Delta_{uv}` using Robertson (1968) method.
- :func:`xy_to_CCT_McCamy1992`: Correlated colour temperature :math:`T_{cp}`
computation of given *CIE XYZ* colourspace *xy* chromaticity coordinates
using McCamy (1992) method.
- :func:`xy_to_CCT_Hernandez1999`: Correlated colour temperature
:math:`T_{cp}` computation of given *CIE XYZ* colourspace *xy* chromaticity
coordinates using Hernandez-Andres, Lee and Romero (1999) method.
- :func:`CCT_to_xy_Kang2002`: *CIE XYZ* colourspace *xy* chromaticity
coordinates computation of given correlated colour temperature
:math:`T_{cp}` using Kang et al. (2002) method.
- :func:`CCT_to_xy_CIE_D`: *CIE XYZ* colourspace *xy* chromaticity
coordinates computation of *CIE Illuminant D Series* from given correlated
colour temperature :math:`T_{cp}` of that *CIE Illuminant D Series*.
See Also
--------
`Colour Temperature & Correlated Colour Temperature IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/temperature/cct.ipynb>`_ # noqa
References
----------
.. [1] Wikipedia. (n.d.). Color temperature. Retrieved June 28, 2014, from
http://en.wikipedia.org/wiki/Color_temperature
"""
from __future__ import division, unicode_literals
import numpy as np
from collections import namedtuple
from colour.colorimetry import (
STANDARD_OBSERVERS_CMFS,
blackbody_spd,
spectral_to_XYZ)
from colour.models import UCS_to_uv, XYZ_to_UCS
from colour.utilities import CaseInsensitiveMapping, warning
__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__ = ['PLANCKIAN_TABLE_TUVD',
'CCT_MINIMAL',
'CCT_MAXIMAL',
'CCT_SAMPLES',
'CCT_CALCULATION_ITERATIONS',
'ROBERTSON_ISOTEMPERATURE_LINES_DATA',
'ROBERTSON_ISOTEMPERATURE_LINES_RUVT',
'ROBERTSON_ISOTEMPERATURE_LINES',
'planckian_table',
'planckian_table_minimal_distance_index',
'uv_to_CCT_Ohno2013',
'CCT_to_uv_Ohno2013',
'uv_to_CCT_Robertson1968',
'CCT_to_uv_Robertson1968',
'UV_TO_CCT_METHODS',
'uv_to_CCT',
'CCT_TO_UV_METHODS',
'CCT_to_uv',
'xy_to_CCT_McCamy1992',
'xy_to_CCT_Hernandez1999',
'CCT_to_xy_Kang2002',
'CCT_to_xy_CIE_D',
'XY_TO_CCT_METHODS',
'xy_to_CCT',
'CCT_TO_XY_METHODS',
'CCT_to_xy']
PLANCKIAN_TABLE_TUVD = namedtuple('PlanckianTable_Tuvdi',
('Ti', 'ui', 'vi', 'di'))
CCT_MINIMAL = 1000
CCT_MAXIMAL = 100000
CCT_SAMPLES = 10
CCT_CALCULATION_ITERATIONS = 6
ROBERTSON_ISOTEMPERATURE_LINES_DATA = (
(0, 0.18006, 0.26352, -0.24341),
(10, 0.18066, 0.26589, -0.25479),
(20, 0.18133, 0.26846, -0.26876),
(30, 0.18208, 0.27119, -0.28539),
(40, 0.18293, 0.27407, -0.30470),
(50, 0.18388, 0.27709, -0.32675),
(60, 0.18494, 0.28021, -0.35156),
(70, 0.18611, 0.28342, -0.37915),
(80, 0.18740, 0.28668, -0.40955),
(90, 0.18880, 0.28997, -0.44278),
(100, 0.19032, 0.29326, -0.47888),
(125, 0.19462, 0.30141, -0.58204),
(150, 0.19962, 0.30921, -0.70471),
(175, 0.20525, 0.31647, -0.84901),
(200, 0.21142, 0.32312, -1.0182),
(225, 0.21807, 0.32909, -1.2168),
(250, 0.22511, 0.33439, -1.4512),
(275, 0.23247, 0.33904, -1.7298),
(300, 0.24010, 0.34308, -2.0637),
(325, 0.24792, 0.34655, -2.4681), # 0.24702 ---> 0.24792 Bruce Lindbloom
(350, 0.25591, 0.34951, -2.9641),
(375, 0.26400, 0.35200, -3.5814),
(400, 0.27218, 0.35407, -4.3633),
(425, 0.28039, 0.35577, -5.3762),
(450, 0.28863, 0.35714, -6.7262),
(475, 0.29685, 0.35823, -8.5955),
(500, 0.30505, 0.35907, -11.324),
(525, 0.31320, 0.35968, -15.628),
(550, 0.32129, 0.36011, -23.325),
(575, 0.32931, 0.36038, -40.770),
(600, 0.33724, 0.36051, -116.45))
"""
Robertson (1968) iso-temperature lines.
ROBERTSON_ISOTEMPERATURE_LINES_DATA : tuple
(Reciprocal Megakelvin,
CIE 1960 Chromaticity Coordinate *u*,
CIE 1960 Chromaticity Coordinate *v*,
Slope)
Notes
-----
- A correction has been done by Lindbloom for *325* Megakelvin
temperature: 0.24702 ---> 0.24792
References
----------
.. [2] Wyszecki, G., & Stiles, W. S. (2000). Table 1(3.11) Isotemperature
Lines. In Color Science: Concepts and Methods, Quantitative Data and
Formulae (p. 228). Wiley. ISBN:978-0471399186
"""
ROBERTSON_ISOTEMPERATURE_LINES_RUVT = namedtuple(
'WyszeckiRobertson_ruvt', ('r', 'u', 'v', 't'))
ROBERTSON_ISOTEMPERATURE_LINES = [
ROBERTSON_ISOTEMPERATURE_LINES_RUVT(*x)
for x in ROBERTSON_ISOTEMPERATURE_LINES_DATA]
[docs]def planckian_table(uv, cmfs, start, end, count):
"""
Returns a planckian table from given *CIE UCS* colourspace *uv*
chromaticity coordinates, colour matching functions and temperature range
using Ohno (2013) method.
Parameters
----------
uv : array_like
*uv* chromaticity coordinates.
cmfs : XYZ_ColourMatchingFunctions
Standard observer colour matching functions.
start : numeric
Temperature range start in kelvins.
end : numeric
Temperature range end in kelvins.
count : int
Temperatures count in the planckian table.
Returns
-------
list
Planckian table.
Examples
--------
>>> from colour import STANDARD_OBSERVERS_CMFS
>>> from pprint import pprint
>>> cmfs = 'CIE 1931 2 Degree Standard Observer'
>>> cmfs = STANDARD_OBSERVERS_CMFS.get(cmfs)
>>> pprint(planckian_table((0.1978, 0.3122), cmfs, 1000, 1010, 10)) # noqa # doctest: +ELLIPSIS
[PlanckianTable_Tuvdi(Ti=1000.0, ui=0.4480108..., vi=0.3546249..., di=0.2537821...),
PlanckianTable_Tuvdi(Ti=1001.1111111..., ui=0.4477508..., vi=0.3546475..., di=0.2535294...),
PlanckianTable_Tuvdi(Ti=1002.2222222..., ui=0.4474910..., vi=0.3546700..., di=0.2532771...),
PlanckianTable_Tuvdi(Ti=1003.3333333..., ui=0.4472316..., vi=0.3546924..., di=0.2530251...),
PlanckianTable_Tuvdi(Ti=1004.4444444..., ui=0.4469724..., vi=0.3547148..., di=0.2527734...),
PlanckianTable_Tuvdi(Ti=1005.5555555..., ui=0.4467136..., vi=0.3547372..., di=0.2525220...),
PlanckianTable_Tuvdi(Ti=1006.6666666..., ui=0.4464550..., vi=0.3547595..., di=0.2522710...),
PlanckianTable_Tuvdi(Ti=1007.7777777..., ui=0.4461968..., vi=0.3547817..., di=0.2520202...),
PlanckianTable_Tuvdi(Ti=1008.8888888..., ui=0.4459389..., vi=0.3548040..., di=0.2517697...),
PlanckianTable_Tuvdi(Ti=1010.0, ui=0.4456812..., vi=0.3548261..., di=0.2515196...)]
"""
ux, vx = uv
shape = cmfs.shape
table = []
for Ti in np.linspace(start, end, count):
spd = blackbody_spd(Ti, shape)
XYZ = spectral_to_XYZ(spd, cmfs)
XYZ *= 1 / np.max(XYZ)
UVW = XYZ_to_UCS(XYZ)
ui, vi = UCS_to_uv(UVW)
di = np.sqrt((ux - ui) ** 2 + (vx - vi) ** 2)
table.append(PLANCKIAN_TABLE_TUVD(Ti, ui, vi, di))
return table
[docs]def planckian_table_minimal_distance_index(planckian_table):
"""
Returns the shortest distance index in given planckian table using
Ohno (2013) method.
Parameters
----------
planckian_table : list
Planckian table.
Returns
-------
int
Shortest distance index.
Examples
--------
>>> from colour import STANDARD_OBSERVERS_CMFS
>>> cmfs = 'CIE 1931 2 Degree Standard Observer'
>>> cmfs = STANDARD_OBSERVERS_CMFS.get(cmfs)
>>> table = planckian_table((0.1978, 0.3122), cmfs, 1000, 1010, 10)
>>> planckian_table_minimal_distance_index(table)
9
"""
distances = [x.di for x in planckian_table]
return distances.index(min(distances))
[docs]def uv_to_CCT_Ohno2013(uv,
cmfs=STANDARD_OBSERVERS_CMFS.get(
'CIE 1931 2 Degree Standard Observer'),
start=CCT_MINIMAL,
end=CCT_MAXIMAL,
count=CCT_SAMPLES,
iterations=CCT_CALCULATION_ITERATIONS):
"""
Returns the correlated colour temperature :math:`T_{cp}` and
:math:`\Delta_{uv}` from given *CIE UCS* colourspace *uv* chromaticity
coordinates, colour matching functions and temperature range using
Ohno (2013) method.
The iterations parameter defines the calculations precision: The higher its
value, the more planckian tables will be generated through cascade
expansion in order to converge to the exact solution.
Parameters
----------
uv : array_like
*CIE UCS* colourspace *uv* chromaticity coordinates.
cmfs : XYZ_ColourMatchingFunctions, optional
Standard observer colour matching functions.
start : numeric, optional
Temperature range start in kelvins.
end : numeric, optional
Temperature range end in kelvins.
count : int, optional
Temperatures count in the planckian tables.
iterations : int, optional
Number of planckian tables to generate.
Returns
-------
tuple
Correlated colour temperature :math:`T_{cp}`, :math:`\Delta_{uv}`.
References
----------
.. [3] Ohno, Y. (2014). Practical Use and Calculation of CCT and Duv.
LEUKOS, 10(1), 47–55. doi:10.1080/15502724.2014.839020
Examples
--------
>>> from colour import STANDARD_OBSERVERS_CMFS
>>> cmfs = 'CIE 1931 2 Degree Standard Observer'
>>> cmfs = STANDARD_OBSERVERS_CMFS.get(cmfs)
>>> uv_to_CCT_Ohno2013((0.1978, 0.3122), cmfs) # doctest: +ELLIPSIS
(6507.5470349..., 0.0032236...)
"""
# Ensuring we do at least one iteration to initialise variables.
if iterations <= 0:
iterations = 1
# Planckian table creation through cascade expansion.
for i in range(iterations):
table = planckian_table(uv, cmfs, start, end, count)
index = planckian_table_minimal_distance_index(table)
if index == 0:
warning(
('Minimal distance index is on lowest planckian table bound, '
'unpredictable results may occur!'))
index += 1
elif index == len(table) - 1:
warning(
('Minimal distance index is on highest planckian table bound, '
'unpredictable results may occur!'))
index -= 1
start = table[index - 1].Ti
end = table[index + 1].Ti
ux, vx = uv
Tuvdip, Tuvdi, Tuvdin = (table[index - 1], table[index], table[index + 1])
Tip, uip, vip, dip = Tuvdip.Ti, Tuvdip.ui, Tuvdip.vi, Tuvdip.di
Ti, di = Tuvdi.Ti, Tuvdi.di
Tin, uin, vin, din = Tuvdin.Ti, Tuvdin.ui, Tuvdin.vi, Tuvdin.di
# Triangular solution.
l = np.sqrt((uin - uip) ** 2 + (vin - vip) ** 2)
x = (dip ** 2 - din ** 2 + l ** 2) / (2 * l)
T = Tip + (Tin - Tip) * (x / l)
vtx = vip + (vin - vip) * (x / l)
sign = 1 if vx - vtx >= 0 else -1
D_uv = (dip ** 2 - x ** 2) ** (1 / 2) * sign
# Parabolic solution.
if D_uv < 0.002:
X = (Tin - Ti) * (Tip - Tin) * (Ti - Tip)
a = (Tip * (din - di) + Ti * (dip - din) + Tin * (di - dip)) * X ** -1
b = (-(Tip ** 2 * (din - di) + Ti ** 2 * (dip - din) + Tin ** 2 *
(di - dip)) * X ** -1)
c = (-(dip * (Tin - Ti) * Ti * Tin + di * (Tip - Tin) * Tip * Tin
+ din * (Ti - Tip) * Tip * Ti) * X ** -1)
T = -b / (2 * a)
D_uv = sign * (a * T ** 2 + b * T + c)
return T, D_uv
[docs]def CCT_to_uv_Ohno2013(CCT,
D_uv=0,
cmfs=STANDARD_OBSERVERS_CMFS.get(
'CIE 1931 2 Degree Standard Observer')):
"""
Returns the *CIE UCS* colourspace *uv* chromaticity coordinates from given
correlated colour temperature :math:`T_{cp}`, :math:`\Delta_{uv}` and
colour matching functions using Ohno (2013) method.
Parameters
----------
CCT : numeric
Correlated colour temperature :math:`T_{cp}`.
D_uv : numeric, optional
:math:`\Delta_{uv}`.
cmfs : XYZ_ColourMatchingFunctions, optional
Standard observer colour matching functions.
Returns
-------
tuple
*CIE UCS* colourspace *uv* chromaticity coordinates.
References
----------
.. [4] Ohno, Y. (2014). Practical Use and Calculation of CCT and Duv.
LEUKOS, 10(1), 47–55. doi:10.1080/15502724.2014.839020
Examples
--------
>>> from colour import STANDARD_OBSERVERS_CMFS
>>> cmfs = 'CIE 1931 2 Degree Standard Observer'
>>> cmfs = STANDARD_OBSERVERS_CMFS.get(cmfs)
>>> CCT = 6507.4342201047066
>>> D_uv = 0.003223690901512735
>>> CCT_to_uv_Ohno2013(CCT, D_uv, cmfs) # doctest: +ELLIPSIS
(0.1978003..., 0.3122005...)
"""
shape = cmfs.shape
delta = 0.01
spd = blackbody_spd(CCT, shape)
XYZ = spectral_to_XYZ(spd, cmfs)
XYZ *= 1 / np.max(XYZ)
UVW = XYZ_to_UCS(XYZ)
u0, v0 = UCS_to_uv(UVW)
if D_uv == 0:
return u0, v0
else:
spd = blackbody_spd(CCT + delta, shape)
XYZ = spectral_to_XYZ(spd, cmfs)
XYZ *= 1 / np.max(XYZ)
UVW = XYZ_to_UCS(XYZ)
u1, v1 = UCS_to_uv(UVW)
du = u0 - u1
dv = v0 - v1
u = u0 - D_uv * (dv / np.sqrt(du ** 2 + dv ** 2))
v = v0 + D_uv * (du / np.sqrt(du ** 2 + dv ** 2))
return u, v
[docs]def uv_to_CCT_Robertson1968(uv):
"""
Returns the correlated colour temperature :math:`T_{cp}` and
:math:`\Delta_{uv}` from given *CIE UCS* colourspace *uv* chromaticity
coordinates using *Roberston (1968)* method.
Parameters
----------
uv : array_like
*CIE UCS* colourspace *uv* chromaticity coordinates.
Returns
-------
tuple
Correlated colour temperature :math:`T_{cp}`, :math:`\Delta_{uv}`.
References
----------
.. [5] Wyszecki, G., & Stiles, W. S. (2000). DISTRIBUTION TEMPERATURE,
COLOR TEMPERATURE, AND CORRELATED COLOR TEMPERATURE. In Color
Science: Concepts and Methods, Quantitative Data and Formulae
(pp. 224–229). Wiley. ISBN:978-0471399186
.. [6] Adobe Systems. (2013). Adobe DNG Software Development Kit (SDK) -
1.3.0.0 - dng_sdk_1_3/dng_sdk/source/dng_temperature.cpp::
dng_temperature::Set_xy_coord. Retrieved from
https://www.adobe.com/support/downloads/dng/dng_sdk.html
Examples
--------
>>> uv = (0.19374137599822966, 0.31522104394059397)
>>> uv_to_CCT_Robertson1968(uv) # doctest: +ELLIPSIS
(6500.0162879..., 0.0083333...)
"""
u, v = uv
last_dt = last_dv = last_du = 0.0
for i in range(1, 31):
wr_ruvt = ROBERTSON_ISOTEMPERATURE_LINES[i]
wr_ruvt_previous = ROBERTSON_ISOTEMPERATURE_LINES[i - 1]
du = 1.0
dv = wr_ruvt.t
length = np.sqrt(1 + dv * dv)
du /= length
dv /= length
uu = u - wr_ruvt.u
vv = v - wr_ruvt.v
dt = -uu * dv + vv * du
if dt <= 0 or i == 30:
if dt > 0.0:
dt = 0.0
dt = -dt
if i == 1:
f = 0.0
else:
f = dt / (last_dt + dt)
T = 1.0e6 / (wr_ruvt_previous.r * f + wr_ruvt.r * (1 - f))
uu = u - (wr_ruvt_previous.u * f + wr_ruvt.u * (1 - f))
vv = v - (wr_ruvt_previous.v * f + wr_ruvt.v * (1 - f))
du = du * (1 - f) + last_du * f
dv = dv * (1 - f) + last_dv * f
length = np.sqrt(du * du + dv * dv)
du /= length
dv /= length
D_uv = uu * du + vv * dv
break
last_dt = dt
last_du = du
last_dv = dv
return T, -D_uv
[docs]def CCT_to_uv_Robertson1968(CCT, D_uv=0):
"""
Returns the *CIE UCS* colourspace *uv* chromaticity coordinates from given
correlated colour temperature :math:`T_{cp}` and :math:`\Delta_{uv}` using
*Roberston (1968)* method.
Parameters
----------
CCT : numeric
Correlated colour temperature :math:`T_{cp}`.
D_uv : numeric
:math:`\Delta_{uv}`.
Returns
-------
tuple
*CIE UCS* colourspace *uv* chromaticity coordinates.
References
----------
.. [7] Wyszecki, G., & Stiles, W. S. (2000). DISTRIBUTION TEMPERATURE,
COLOR TEMPERATURE, AND CORRELATED COLOR TEMPERATURE. In Color
Science: Concepts and Methods, Quantitative Data and Formulae
(pp. 224–229). Wiley. ISBN:978-0471399186
.. [8] Adobe Systems. (2013). Adobe DNG Software Development Kit (SDK) -
1.3.0.0 - dng_sdk_1_3/dng_sdk/source/dng_temperature.cpp::
dng_temperature::xy_coord. Retrieved from
https://www.adobe.com/support/downloads/dng/dng_sdk.html
Examples
--------
>>> CCT = 6500.0081378199056
>>> D_uv = 0.0083333312442250979
>>> CCT_to_uv_Robertson1968(CCT, D_uv) # doctest: +ELLIPSIS
(0.1937413..., 0.3152210...)
"""
r = 1.0e6 / CCT
for i in range(30):
wr_ruvt = ROBERTSON_ISOTEMPERATURE_LINES[i]
wr_ruvt_next = ROBERTSON_ISOTEMPERATURE_LINES[i + 1]
if r < wr_ruvt_next.r or i == 29:
f = (wr_ruvt_next.r - r) / (wr_ruvt_next.r - wr_ruvt.r)
u = wr_ruvt.u * f + wr_ruvt_next.u * (1 - f)
v = wr_ruvt.v * f + wr_ruvt_next.v * (1 - f)
uu1 = uu2 = 1.0
vv1, vv2 = wr_ruvt.t, wr_ruvt_next.t
length1 = np.sqrt(1 + vv1 * vv1)
length2 = np.sqrt(1 + vv2 * vv2)
uu1 /= length1
vv1 /= length1
uu2 /= length2
vv2 /= length2
uu3 = uu1 * f + uu2 * (1 - f)
vv3 = vv1 * f + vv2 * (1 - f)
len3 = np.sqrt(uu3 * uu3 + vv3 * vv3)
uu3 /= len3
vv3 /= len3
u += uu3 * -D_uv
v += vv3 * -D_uv
return u, v
UV_TO_CCT_METHODS = CaseInsensitiveMapping(
{'Ohno 2013': uv_to_CCT_Ohno2013,
'Robertson 1968': uv_to_CCT_Robertson1968})
"""
Supported *CIE UCS* colourspace *uv* chromaticity coordinates to correlated
colour temperature :math:`T_{cp}` computation methods.
UV_TO_CCT_METHODS : CaseInsensitiveMapping
{'Ohno 2013', 'Robertson 1968'}
Aliases:
- 'ohno2013': 'Ohno 2013'
- 'robertson1968': 'Robertson 1968'
"""
UV_TO_CCT_METHODS['ohno2013'] = UV_TO_CCT_METHODS['Ohno 2013']
UV_TO_CCT_METHODS['robertson1968'] = UV_TO_CCT_METHODS['Robertson 1968']
[docs]def uv_to_CCT(uv, method='Ohno 2013', **kwargs):
"""
Returns the correlated colour temperature :math:`T_{cp}` and
:math:`\Delta_{uv}` from given *CIE UCS* colourspace *uv* chromaticity
coordinates using given method.
Parameters
----------
uv : array_like
*CIE UCS* colourspace *uv* chromaticity coordinates.
method : unicode, optional
{'Ohno 2013', 'Robertson 1968'}
Computation method.
\*\*kwargs : \*\*
Keywords arguments.
Returns
-------
tuple
Correlated colour temperature :math:`T_{cp}`, :math:`\Delta_{uv}`.
Raises
------
ValueError
If the computation method is not defined.
Examples
--------
>>> from colour import STANDARD_OBSERVERS_CMFS
>>> cmfs = 'CIE 1931 2 Degree Standard Observer'
>>> cmfs = STANDARD_OBSERVERS_CMFS.get(cmfs)
>>> uv_to_CCT((0.1978, 0.3122), cmfs=cmfs) # doctest: +ELLIPSIS
(6507.5470349..., 0.0032236...)
"""
if method == 'Ohno 2013':
return UV_TO_CCT_METHODS.get(method)(uv, **kwargs)
else:
if 'cmfs' in kwargs:
if kwargs.get('cmfs').name != (
'CIE 1931 2 Degree Standard Observer'):
raise ValueError(
('Robertson (1968) method is only valid for '
'"CIE 1931 2 Degree Standard Observer"!'))
return UV_TO_CCT_METHODS.get(method)(uv)
CCT_TO_UV_METHODS = CaseInsensitiveMapping(
{'Ohno 2013': CCT_to_uv_Ohno2013,
'Robertson 1968': CCT_to_uv_Robertson1968})
"""
Supported correlated colour temperature :math:`T_{cp}` to *CIE UCS* colourspace
*uv* chromaticity coordinates computation methods.
CCT_TO_UV_METHODS : CaseInsensitiveMapping
{'Ohno 2013', 'Robertson 1968'}
Aliases:
- 'ohno2013': 'Ohno 2013'
- 'robertson1968': 'Robertson 1968'
"""
CCT_TO_UV_METHODS['ohno2013'] = CCT_TO_UV_METHODS['Ohno 2013']
CCT_TO_UV_METHODS['robertson1968'] = CCT_TO_UV_METHODS['Robertson 1968']
[docs]def CCT_to_uv(CCT, D_uv=0, method='Ohno 2013', **kwargs):
"""
Returns the *CIE UCS* colourspace *uv* chromaticity coordinates from given
correlated colour temperature :math:`T_{cp}` and :math:`\Delta_{uv}` using
given method.
Parameters
----------
CCT : numeric
Correlated colour temperature :math:`T_{cp}`.
D_uv : numeric
:math:`\Delta_{uv}`.
method : unicode, optional
{'Ohno 2013', 'Robertson 1968'}
Computation method.
\*\*kwargs : \*\*
Keywords arguments.
Returns
-------
tuple
*CIE UCS* colourspace *uv* chromaticity coordinates.
Raises
------
ValueError
If the computation method is not defined.
Examples
--------
>>> from colour import STANDARD_OBSERVERS_CMFS
>>> cmfs = 'CIE 1931 2 Degree Standard Observer'
>>> cmfs = STANDARD_OBSERVERS_CMFS.get(cmfs)
>>> CCT = 6507.4342201047066
>>> D_uv = 0.003223690901512735
>>> CCT_to_uv(CCT, D_uv, cmfs=cmfs) # doctest: +ELLIPSIS
(0.1978003..., 0.3122005...)
"""
if method == 'Ohno 2013':
return CCT_TO_UV_METHODS.get(method)(CCT, D_uv, **kwargs)
else:
if 'cmfs' in kwargs:
if kwargs.get('cmfs').name != (
'CIE 1931 2 Degree Standard Observer'):
raise ValueError(
('Robertson (1968) method is only valid for '
'"CIE 1931 2 Degree Standard Observer"!'))
return CCT_TO_UV_METHODS.get(method)(CCT, D_uv)
[docs]def xy_to_CCT_McCamy1992(xy):
"""
Returns the correlated colour temperature :math:`T_{cp}` from given
*CIE XYZ* colourspace *xy* chromaticity coordinates using
McCamy (1992) method.
Parameters
----------
xy : array_like
*xy* chromaticity coordinates.
Returns
-------
numeric
Correlated colour temperature :math:`T_{cp}`.
References
----------
.. [9] Wikipedia. (n.d.). Approximation. Retrieved June 28, 2014, from
http://en.wikipedia.org/wiki/Color_temperature#Approximation
Examples
--------
>>> xy_to_CCT_McCamy1992((0.31271, 0.32902)) # doctest: +ELLIPSIS
6504.3893830...
"""
x, y = xy
n = (x - 0.3320) / (y - 0.1858)
CCT = -449 * np.power(n, 3) + 3525 * np.power(n, 2) - 6823.3 * n + 5520.33
return CCT
[docs]def xy_to_CCT_Hernandez1999(xy):
"""
Returns the correlated colour temperature :math:`T_{cp}` from given
*CIE XYZ* colourspace *xy* chromaticity coordinates using
Hernandez-Andres, Lee and Romero (1999) method.
Parameters
----------
xy : array_like
*xy* chromaticity coordinates.
Returns
-------
numeric
Correlated colour temperature :math:`T_{cp}`.
References
----------
.. [10] Hernández-Andrés, J., Lee, R. L., & Romero, J. (1999).
Calculating correlated color temperatures across the entire gamut
of daylight and skylight chromaticities. Applied Optics, 38(27),
5703–5709. doi:10.1364/AO.38.005703
Examples
--------
>>> xy_to_CCT_Hernandez1999((0.31271, 0.32902)) # doctest: +ELLIPSIS
6500.0421533...
"""
x, y = xy
n = (x - 0.3366) / (y - 0.1735)
CCT = (-949.86315 +
6253.80338 * np.exp(-n / 0.92159) +
28.70599 * np.exp(-n / 0.20039) +
0.00004 * np.exp(-n / 0.07125))
if CCT > 50000:
n = (x - 0.3356) / (y - 0.1691)
CCT = (36284.48953 +
0.00228 * np.exp(-n / 0.07861) +
5.4535e-36 * np.exp(-n / 0.01543))
return CCT
[docs]def CCT_to_xy_Kang2002(CCT):
"""
Returns the *CIE XYZ* colourspace *xy* chromaticity coordinates from given
correlated colour temperature :math:`T_{cp}` using Kang et al. (2002)
method.
Parameters
----------
CCT : numeric
Correlated colour temperature :math:`T_{cp}`.
Returns
-------
tuple
*xy* chromaticity coordinates.
Raises
------
ValueError
If the correlated colour temperature is not in appropriate domain.
References
----------
.. [11] Kang, B., Moon, O., Hong, C., Lee, H., Cho, B., & Kim, Y. (2002).
Design of advanced color: Temperature control system for HDTV
applications. Journal of the Korean …, 41(6), 865–871. Retrieved
from http://cat.inist.fr/?aModele=afficheN&cpsidt=14448733
Examples
--------
>>> CCT_to_xy_Kang2002(6504.38938305) # doctest: +ELLIPSIS
(0.3134259..., 0.3235959...)
"""
if 1667 <= CCT <= 4000:
x = (-0.2661239 * 10 ** 9 / CCT ** 3 -
0.2343589 * 10 ** 6 / CCT ** 2 +
0.8776956 * 10 ** 3 / CCT +
0.179910)
elif 4000 <= CCT <= 25000:
x = (-3.0258469 * 10 ** 9 / CCT ** 3 +
2.1070379 * 10 ** 6 / CCT ** 2 +
0.2226347 * 10 ** 3 / CCT +
0.24039)
else:
raise ValueError(
'Correlated colour temperature must be in domain [1667, 25000]!')
if 1667 <= CCT <= 2222:
y = (-1.1063814 * x ** 3 -
1.34811020 * x ** 2 +
2.18555832 * x -
0.20219683)
elif 2222 <= CCT <= 4000:
y = (-0.9549476 * x ** 3 -
1.37418593 * x ** 2 +
2.09137015 * x -
0.16748867)
elif 4000 <= CCT <= 25000:
y = (3.0817580 * x ** 3 -
5.8733867 * x ** 2 +
3.75112997 * x -
0.37001483)
return x, y
[docs]def CCT_to_xy_CIE_D(CCT):
"""
Converts from the correlated colour temperature :math:`T_{cp}` of a
*CIE Illuminant D Series* to the chromaticity of that
*CIE Illuminant D Series* illuminant.
Parameters
----------
CCT : numeric
Correlated colour temperature :math:`T_{cp}`.
Returns
-------
tuple
*xy* chromaticity coordinates.
Raises
------
ValueError
If the correlated colour temperature is not in appropriate domain.
References
----------
.. [12] Wyszecki, G., & Stiles, W. S. (2000). CIE Method of Calculating
D-Illuminants. In Color Science: Concepts and Methods,
Quantitative Data and Formulae (pp. 145–146). Wiley.
ISBN:978-0471399186
Examples
--------
>>> CCT_to_xy_CIE_D(6504.38938305) # doctest: +ELLIPSIS
(0.3127077..., 0.3291128...)
"""
if 4000 <= CCT <= 7000:
x = (-4.607 * 10 ** 9 / CCT ** 3 +
2.9678 * 10 ** 6 / CCT ** 2 +
0.09911 * 10 ** 3 / CCT +
0.244063)
elif 7000 < CCT <= 25000:
x = (-2.0064 * 10 ** 9 / CCT ** 3 +
1.9018 * 10 ** 6 / CCT ** 2 +
0.24748 * 10 ** 3 / CCT +
0.23704)
else:
raise ValueError(
'Correlated colour temperature must be in domain [4000, 25000]!')
y = -3 * x ** 2 + 2.87 * x - 0.275
return x, y
XY_TO_CCT_METHODS = CaseInsensitiveMapping(
{'McCamy 1992': xy_to_CCT_McCamy1992,
'Hernandez 1999': xy_to_CCT_Hernandez1999})
"""
Supported *CIE XYZ* colourspace *xy* chromaticity coordinates to correlated
colour temperature :math:`T_{cp}` computation methods.
XY_TO_CCT_METHODS : CaseInsensitiveMapping
{'McCamy 1992', 'Hernandez 1999'}
Aliases:
- 'mccamy1992': 'McCamy 1992'
- 'hernandez1999': 'Hernandez 1999'
"""
XY_TO_CCT_METHODS['mccamy1992'] = XY_TO_CCT_METHODS['McCamy 1992']
XY_TO_CCT_METHODS['hernandez1999'] = XY_TO_CCT_METHODS['Hernandez 1999']
[docs]def xy_to_CCT(xy, method='McCamy 1992', **kwargs):
"""
Returns the correlated colour temperature :math:`T_{cp}` from given
*CIE XYZ* colourspace *xy* chromaticity coordinates using given method.
Parameters
----------
xy : array_like
*xy* chromaticity coordinates.
method : unicode, optional
{'McCamy 1992', 'Hernandez 1999'}
Computation method.
\*\*kwargs : \*\*
Keywords arguments.
Returns
-------
numeric
Correlated colour temperature :math:`T_{cp}`.
"""
return XY_TO_CCT_METHODS.get(method)(xy)
CCT_TO_XY_METHODS = CaseInsensitiveMapping(
{'Kang 2002': CCT_to_xy_Kang2002,
'CIE Illuminant D Series': CCT_to_xy_CIE_D})
"""
Supported correlated colour temperature :math:`T_{cp}` to *CIE XYZ* colourspace
*xy* chromaticity coordinates computation methods.
CCT_TO_XY_METHODS : CaseInsensitiveMapping
{'Kang 2002', 'CIE Illuminant D Series'}
Aliases:
- 'kang2002': 'Kang 2002'
- 'cie_d': 'Hernandez 1999'
"""
CCT_TO_XY_METHODS['kang2002'] = CCT_TO_XY_METHODS['Kang 2002']
CCT_TO_XY_METHODS['cie_d'] = CCT_TO_XY_METHODS['CIE Illuminant D Series']
[docs]def CCT_to_xy(CCT, method='Kang 2002'):
"""
Returns the *CIE XYZ* colourspace *xy* chromaticity coordinates from given
correlated colour temperature :math:`T_{cp}` using given method.
Parameters
----------
CCT : numeric
Correlated colour temperature :math:`T_{cp}`.
method : unicode, optional
{'Kang 2002', 'CIE Illuminant D Series'}
Computation method.
Returns
-------
tuple
*xy* chromaticity coordinates.
"""
return CCT_TO_XY_METHODS.get(method)(CCT)
Colour 0.3