# -*- coding: utf-8 -*-
"""
Correlated Colour Temperature :math:`T_{cp}`
============================================
Defines correlated colour temperature :math:`T_{cp}` computations objects:
- :func:`colour.temperature.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:`colour.temperature.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:`colour.temperature.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:`colour.temperature.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.
- :attr:`colour.UV_TO_CCT_METHODS`: Supported *CIE UCS* colourspace *uv*
chromaticity coordinates to correlated colour temperature :math:`T_{cp}`
computation methods.
- :func:`colour.uv_to_CCT`: Correlated colour temperature :math:`T_{cp}` and
:math:`\\Delta_{uv}` computation from given *CIE UCS* colourspace *uv*
chromaticity coordinates using given method.
- :attr:`colour.CCT_TO_UV_METHODS`: Supported correlated colour temperature
:math:`T_{cp}` to *CIE UCS* colourspace *uv* chromaticity coordinates
computation methods.
- :func:`colour.CCT_to_uv`: *CIE UCS* colourspace *uv* chromaticity
coordinates computation from given correlated colour temperature
:math:`T_{cp}` using given method.
- :func:`colour.temperature.CCT_to_uv_Krystek1985`: *CIE UCS* colourspace
*uv* chromaticity coordinates computation of given correlated colour
temperature :math:`T_{cp}` using *Krystek (1985)* method.
- :func:`colour.temperature.xy_to_CCT_McCamy1992`: Correlated colour
temperature :math:`T_{cp}` computation of given *CIE XYZ* tristimulus
values *xy* chromaticity coordinates using *McCamy (1992)* method.
- :func:`colour.temperature.xy_to_CCT_Hernandez1999`: Correlated colour
temperature :math:`T_{cp}` computation of given *CIE XYZ* tristimulus
values *xy* chromaticity coordinates using
*Hernandez-Andres, Lee and Romero (1999)* method.
- :func:`colour.temperature.CCT_to_xy_Kang2002`: *CIE XYZ* tristimulus
values *xy* chromaticity coordinates computation of given correlated colour
temperature :math:`T_{cp}` using
*Kang, Moon, Hong, Lee, Cho and Kim (2002)* method.
- :func:`colour.temperature.CCT_to_xy_CIE_D`: *CIE XYZ* tristimulus values
*xy* chromaticity coordinates computation of *CIE Illuminant D Series* from
given correlated colour temperature :math:`T_{cp}` of that
*CIE Illuminant D Series*.
- :attr:`colour.XY_TO_CCT_METHODS`: Supported *CIE XYZ* tristimulus values
*xy* chromaticity coordinates to correlated colour temperature
:math:`T_{cp}` computation methods.
- :func:`colour.xy_to_CCT`: Correlated colour temperature :math:`T_{cp}`
computation from given *CIE XYZ* tristimulus values *xy* chromaticity
coordinates using given method.
- :attr:`colour.CCT_TO_XY_METHODS`: Supported correlated colour temperature
:math:`T_{cp}` to *CIE XYZ* tristimulus values *xy* chromaticity
coordinates computation methods.
- :func:`colour.CCT_to_xy`: *CIE XYZ* tristimulus values *xy* chromaticity
coordinates computation from given correlated colour temperature
:math:`T_{cp}` using given method.
See Also
--------
`Colour Temperature & Correlated Colour Temperature Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/temperature/cct.ipynb>`_
References
----------
- :cite:`AdobeSystems2013` : 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
- :cite:`AdobeSystems2013a` : 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
- :cite:`Hernandez-Andres1999a` : Hernandez-Andres, 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. doi:10.1364/AO.38.005703
- :cite:`Kang2002a` : 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 Physical Society, 41(6), 865-871.
Retrieved from http://cat.inist.fr/?aModele=afficheN&cpsidt=14448733
- :cite:`Krystek1985b` : Krystek, M. (1985). An algorithm to calculate
correlated colour temperature. Color Research & Application, 10(1),
38-40. doi:10.1002/col.5080100109
- :cite:`Ohno2014a` : Ohno, Y. (2014). Practical Use and Calculation of CCT
and Duv. LEUKOS, 10(1), 47-55. doi:10.1080/15502724.2014.839020
- :cite:`Wikipedia2001` : Wikipedia. (2001). Approximation. Retrieved June
28, 2014, from http://en.wikipedia.org/wiki/Color_temperature#Approximation
- :cite:`Wikipedia2001a` : Wikipedia. (2001). Color temperature. Retrieved
June 28, 2014, from http://en.wikipedia.org/wiki/Color_temperature
- :cite:`Wyszecki2000x` : 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
- :cite:`Wyszecki2000y` : 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
- :cite:`Wyszecki2000z` : 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
"""
from __future__ import division, unicode_literals
import numpy as np
from collections import namedtuple
from colour.colorimetry import (
ASTME30815_PRACTISE_SHAPE, STANDARD_OBSERVERS_CMFS,
daylight_locus_function, sd_blackbody, sd_to_XYZ)
from colour.models import UCS_to_uv, XYZ_to_UCS
from colour.utilities import (CaseInsensitiveMapping, as_float_array, as_float,
filter_kwargs, runtime_warning, tsplit, tstack,
usage_warning)
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2019 - 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', 'CCT_to_uv_Krystek1985', '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
----------
:cite:`Wyszecki2000x`
"""
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
]
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 = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
>>> uv = np.array([0.1978, 0.3122])
>>> pprint(planckian_table(uv, cmfs, 1000, 1010, 10))
... # doctest: +ELLIPSIS
[PlanckianTable_Tuvdi(Ti=1000.0, \
ui=0.4479628..., vi=0.3546296..., di=0.2537355...),
PlanckianTable_Tuvdi(Ti=1001.1111111..., \
ui=0.4477030..., vi=0.3546521..., di=0.2534831...),
PlanckianTable_Tuvdi(Ti=1002.2222222..., \
ui=0.4474434..., vi=0.3546746..., di=0.2532310...),
PlanckianTable_Tuvdi(Ti=1003.3333333..., \
ui=0.4471842..., vi=0.3546970..., di=0.2529792...),
PlanckianTable_Tuvdi(Ti=1004.4444444..., \
ui=0.4469252..., vi=0.3547194..., di=0.2527277...),
PlanckianTable_Tuvdi(Ti=1005.5555555..., \
ui=0.4466666..., vi=0.3547417..., di=0.2524765...),
PlanckianTable_Tuvdi(Ti=1006.6666666..., \
ui=0.4464083..., vi=0.3547640..., di=0.2522256...),
PlanckianTable_Tuvdi(Ti=1007.7777777..., \
ui=0.4461502..., vi=0.3547862..., di=0.2519751...),
PlanckianTable_Tuvdi(Ti=1008.8888888..., \
ui=0.4458925..., vi=0.3548084..., di=0.2517248...),
PlanckianTable_Tuvdi(Ti=1010.0, \
ui=0.4456351..., vi=0.3548306..., di=0.2514749...)]
"""
ux, vx = uv
cmfs = cmfs.copy().trim(ASTME30815_PRACTISE_SHAPE)
shape = cmfs.shape
table = []
for Ti in np.linspace(start, end, count):
sd = sd_blackbody(Ti, shape)
XYZ = sd_to_XYZ(sd, cmfs)
XYZ /= np.max(XYZ)
UVW = XYZ_to_UCS(XYZ)
ui, vi = UCS_to_uv(UVW)
di = np.hypot(ux - ui, vx - vi)
table.append(PLANCKIAN_TABLE_TUVD(Ti, ui, vi, di))
return table
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 = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
>>> uv = np.array([0.1978, 0.3122])
>>> table = planckian_table(uv, 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['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
-------
ndarray
Correlated colour temperature :math:`T_{cp}`, :math:`\\Delta_{uv}`.
References
----------
:cite:`Ohno2014a`
Examples
--------
>>> from colour import STANDARD_OBSERVERS_CMFS
>>> cmfs = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
>>> uv = np.array([0.1978, 0.3122])
>>> uv_to_CCT_Ohno2013(uv, cmfs) # doctest: +ELLIPSIS
array([ 6.5074738...e+03, 3.2233461...e-03])
"""
# Ensuring we do at least one iteration to initialise variables.
iterations = max(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:
runtime_warning(
('Minimal distance index is on lowest planckian table bound, '
'unpredictable results may occur!'))
index += 1
elif index == len(table) - 1:
runtime_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.hypot(uin - uip, vin - vip) # noqa
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 np.abs(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 np.array([T, D_uv])
[docs]def CCT_to_uv_Ohno2013(
CCT,
D_uv=0,
cmfs=STANDARD_OBSERVERS_CMFS['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
-------
ndarray
*CIE UCS* colourspace *uv* chromaticity coordinates.
References
----------
:cite:`Ohno2014a`
Examples
--------
>>> from colour import STANDARD_OBSERVERS_CMFS
>>> cmfs = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
>>> CCT = 6507.4342201047066
>>> D_uv = 0.003223690901513
>>> CCT_to_uv_Ohno2013(CCT, D_uv, cmfs) # doctest: +ELLIPSIS
array([ 0.1977999..., 0.3122004...])
"""
cmfs = cmfs.copy().trim(ASTME30815_PRACTISE_SHAPE)
shape = cmfs.shape
delta = 0.01
sd = sd_blackbody(CCT, shape)
XYZ = sd_to_XYZ(sd, cmfs)
XYZ *= 1 / np.max(XYZ)
UVW = XYZ_to_UCS(XYZ)
u0, v0 = UCS_to_uv(UVW)
if D_uv == 0:
return np.array([u0, v0])
else:
sd = sd_blackbody(CCT + delta, shape)
XYZ = sd_to_XYZ(sd, 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.hypot(du, dv))
v = v0 + D_uv * (du / np.hypot(du, dv))
return np.array([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
-------
ndarray
Correlated colour temperature :math:`T_{cp}`, :math:`\\Delta_{uv}`.
References
----------
:cite:`AdobeSystems2013`, :cite:`Wyszecki2000y`
Examples
--------
>>> uv = np.array([0.193741375998230, 0.315221043940594])
>>> uv_to_CCT_Robertson1968(uv) # doctest: +ELLIPSIS
array([ 6.5000162...e+03, 8.3333289...e-03])
"""
u, v = uv
last_dt = last_dv = last_du = 0
for i in range(1, 31):
wr_ruvt = ROBERTSON_ISOTEMPERATURE_LINES[i]
wr_ruvt_previous = ROBERTSON_ISOTEMPERATURE_LINES[i - 1]
du = 1
dv = wr_ruvt.t
length = np.hypot(1, 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:
dt = 0
dt = -dt
f = 0 if i == 1 else 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.hypot(du, dv)
du /= length
dv /= length
D_uv = uu * du + vv * dv
break
last_dt = dt
last_du = du
last_dv = dv
return np.array([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
-------
ndarray
*CIE UCS* colourspace *uv* chromaticity coordinates.
References
----------
:cite:`AdobeSystems2013a`, :cite:`Wyszecki2000y`
Examples
--------
>>> CCT = 6500.0081378199056
>>> D_uv = 0.008333331244225
>>> CCT_to_uv_Robertson1968(CCT, D_uv) # doctest: +ELLIPSIS
array([ 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.hypot(1, vv1)
length2 = np.hypot(1, 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 np.array([u, v])
[docs]def CCT_to_uv_Krystek1985(CCT):
"""
Returns the *CIE UCS* colourspace *uv* chromaticity coordinates from given
correlated colour temperature :math:`T_{cp}` using *Krystek (1985)* method.
Parameters
----------
CCT : numeric
Correlated colour temperature :math:`T_{cp}`.
Returns
-------
ndarray
*CIE UCS* colourspace *uv* chromaticity coordinates.
Notes
-----
- *Krystek (1985)* method computations are valid for correlated colour
temperature :math:`T_{cp}` normalised to domain [1000, 15000].
References
----------
:cite:`Krystek1985b`
Examples
--------
>>> CCT_to_uv_Krystek1985(6504.38938305) # doctest: +ELLIPSIS
array([ 0.1837669..., 0.3093443...])
"""
T = as_float_array(CCT)
u = ((0.860117757 + 1.54118254 * 10e-4 * T + 1.28641212 * 10e-7 * T ** 2) /
(1 + 8.42420235 * 10e-4 * T + 7.08145163 * 10e-7 * T ** 2))
v = ((0.317398726 + 4.22806245 * 10e-5 * T + 4.20481691 * 10e-8 * T ** 2) /
(1 - 2.89741816 * 10e-5 * T + 1.61456053 * 10e-7 * T ** 2))
return tstack([u, v])
UV_TO_CCT_METHODS = CaseInsensitiveMapping({
'Ohno 2013': uv_to_CCT_Ohno2013,
'Robertson 1968': uv_to_CCT_Robertson1968
})
UV_TO_CCT_METHODS.__doc__ = """
Supported *CIE UCS* colourspace *uv* chromaticity coordinates to correlated
colour temperature :math:`T_{cp}` computation methods.
References
----------
:cite:`AdobeSystems2013`, :cite:`AdobeSystems2013a`, :cite:`Ohno2014a`,
:cite:`Wyszecki2000y`
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.
Other Parameters
----------------
cmfs : XYZ_ColourMatchingFunctions, optional
{:func:`colour.temperature.uv_to_CCT_Ohno2013`},
Standard observer colour matching functions.
start : numeric, optional
{:func:`colour.temperature.uv_to_CCT_Ohno2013`},
Temperature range start in kelvins.
end : numeric, optional
{:func:`colour.temperature.uv_to_CCT_Ohno2013`},
Temperature range end in kelvins.
count : int, optional
{:func:`colour.temperature.uv_to_CCT_Ohno2013`},
Temperatures count in the planckian tables.
iterations : int, optional
{:func:`colour.temperature.uv_to_CCT_Ohno2013`},
Number of planckian tables to generate.
Returns
-------
ndarray
Correlated colour temperature :math:`T_{cp}`, :math:`\\Delta_{uv}`.
References
----------
:cite:`AdobeSystems2013`, :cite:`AdobeSystems2013a`, :cite:`Ohno2014a`,
:cite:`Wyszecki2000y`
Examples
--------
>>> from colour import STANDARD_OBSERVERS_CMFS
>>> cmfs = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
>>> uv = np.array([0.1978, 0.3122])
>>> uv_to_CCT(uv, cmfs=cmfs) # doctest: +ELLIPSIS
array([ 6.5074738...e+03, 3.2233461...e-03])
"""
function = UV_TO_CCT_METHODS[method]
return function(uv, **filter_kwargs(function, **kwargs))
CCT_TO_UV_METHODS = CaseInsensitiveMapping({
'Ohno 2013': CCT_to_uv_Ohno2013,
'Robertson 1968': CCT_to_uv_Robertson1968,
'Krystek 1985': CCT_to_uv_Krystek1985
})
CCT_TO_UV_METHODS.__doc__ = """
Supported correlated colour temperature :math:`T_{cp}` to *CIE UCS* colourspace
*uv* chromaticity coordinates computation methods.
References
----------
:cite:`AdobeSystems2013`, :cite:`AdobeSystems2013a`, :cite:`Krystek1985b`,
:cite:`Ohno2014a`, :cite:`Wyszecki2000y`
CCT_TO_UV_METHODS : CaseInsensitiveMapping
**{'Ohno 2013', 'Robertson 1968', 'Krystek 1985}**
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, method='Ohno 2013', **kwargs):
"""
Returns the *CIE UCS* colourspace *uv* 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
**{'Ohno 2013', 'Robertson 1968', 'Krystek 1985}**,
Computation method.
Other Parameters
----------------
D_uv : numeric
{:func:`CCT_to_uv_Ohno2013, CCT_to_uv_Robertson1968`},
:math:`\\Delta_{uv}`.
cmfs : XYZ_ColourMatchingFunctions, optional
{:func:`colour.temperature.CCT_to_uv_Ohno2013`},
Standard observer colour matching functions.
Returns
-------
ndarray
*CIE UCS* colourspace *uv* chromaticity coordinates.
References
----------
:cite:`AdobeSystems2013`, :cite:`AdobeSystems2013a`, :cite:`Krystek1985b`,
:cite:`Ohno2014a`, :cite:`Wyszecki2000y`
Examples
--------
>>> from colour import STANDARD_OBSERVERS_CMFS
>>> cmfs = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
>>> CCT = 6507.47380460
>>> D_uv = 0.00322335
>>> CCT_to_uv(CCT, D_uv=D_uv, cmfs=cmfs) # doctest: +ELLIPSIS
array([ 0.1977999..., 0.3121999...])
"""
function = CCT_TO_UV_METHODS[method]
return function(CCT, **filter_kwargs(function, **kwargs))
def xy_to_CCT_McCamy1992(xy):
"""
Returns the correlated colour temperature :math:`T_{cp}` from given
*CIE XYZ* tristimulus values *xy* chromaticity coordinates using
*McCamy (1992)* method.
Parameters
----------
xy : array_like
*xy* chromaticity coordinates.
Returns
-------
numeric or ndarray
Correlated colour temperature :math:`T_{cp}`.
References
----------
:cite:`Wikipedia2001`
Examples
--------
>>> xy = np.array([0.31270, 0.32900])
>>> xy_to_CCT_McCamy1992(xy) # doctest: +ELLIPSIS
6505.0805913...
"""
x, y = tsplit(xy)
n = (x - 0.3320) / (y - 0.1858)
CCT = -449 * n ** 3 + 3525 * 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* tristimulus values *xy* chromaticity coordinates using
*Hernandez-Andres et al. (1999)* method.
Parameters
----------
xy : array_like
*xy* chromaticity coordinates.
Returns
-------
numeric
Correlated colour temperature :math:`T_{cp}`.
References
----------
:cite:`Hernandez-Andres1999a`
Examples
--------
>>> xy = np.array([0.31270, 0.32900])
>>> xy_to_CCT_Hernandez1999(xy) # doctest: +ELLIPSIS
6500.7420431...
"""
x, y = tsplit(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))
n = np.where(CCT > 50000, (x - 0.3356) / (y - 0.1691), n)
CCT = np.where(
CCT > 50000,
36284.48953 + 0.00228 * np.exp(-n / 0.07861) +
5.4535e-36 * np.exp(-n / 0.01543),
CCT,
)
return as_float(CCT)
[docs]def CCT_to_xy_Kang2002(CCT):
"""
Returns the *CIE XYZ* tristimulus values *xy* chromaticity coordinates from
given correlated colour temperature :math:`T_{cp}` using
*Kang et al. (2002)* method.
Parameters
----------
CCT : numeric or array_like
Correlated colour temperature :math:`T_{cp}`.
Returns
-------
ndarray
*xy* chromaticity coordinates.
Raises
------
ValueError
If the correlated colour temperature is not in appropriate domain.
References
----------
:cite:`Kang2002a`
Examples
--------
>>> CCT_to_xy_Kang2002(6504.38938305) # doctest: +ELLIPSIS
array([ 0.313426 ..., 0.3235959...])
"""
CCT = as_float_array(CCT)
if np.any(CCT[np.asarray(np.logical_or(CCT < 1667, CCT > 25000))]):
usage_warning(('Correlated colour temperature must be in domain '
'[1667, 25000], unpredictable results may occur!'))
x = np.where(
CCT <= 4000,
-0.2661239 * 10 ** 9 / CCT ** 3 - 0.2343589 * 10 ** 6 / CCT ** 2 +
0.8776956 * 10 ** 3 / CCT + 0.179910,
-3.0258469 * 10 ** 9 / CCT ** 3 + 2.1070379 * 10 ** 6 / CCT ** 2 +
0.2226347 * 10 ** 3 / CCT + 0.24039,
)
cnd_l = [CCT <= 2222, np.logical_and(CCT > 2222, CCT <= 4000), CCT > 4000]
i = -1.1063814 * x ** 3 - 1.34811020 * x ** 2 + 2.18555832 * x - 0.20219683
j = -0.9549476 * x ** 3 - 1.37418593 * x ** 2 + 2.09137015 * x - 0.16748867
k = 3.0817580 * x ** 3 - 5.8733867 * x ** 2 + 3.75112997 * x - 0.37001483
y = np.select(cnd_l, [i, j, k])
xy = tstack([x, y])
return xy
[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 or array_like
Correlated colour temperature :math:`T_{cp}`.
Returns
-------
ndarray
*xy* chromaticity coordinates.
Raises
------
ValueError
If the correlated colour temperature is not in appropriate domain.
References
----------
:cite:`Wyszecki2000z`
Examples
--------
>>> CCT_to_xy_CIE_D(6504.38938305) # doctest: +ELLIPSIS
array([ 0.3127077..., 0.3291128...])
"""
CCT = as_float_array(CCT)
if np.any(CCT[np.asarray(np.logical_or(CCT < 4000, CCT > 25000))]):
usage_warning(('Correlated colour temperature must be in domain '
'[4000, 25000], unpredictable results may occur!'))
x = np.where(
CCT <= 7000,
-4.607 * 10 ** 9 / CCT ** 3 + 2.9678 * 10 ** 6 / CCT ** 2 +
0.09911 * 10 ** 3 / CCT + 0.244063,
-2.0064 * 10 ** 9 / CCT ** 3 + 1.9018 * 10 ** 6 / CCT ** 2 +
0.24748 * 10 ** 3 / CCT + 0.23704,
)
y = daylight_locus_function(x)
xy = tstack([x, y])
return xy
XY_TO_CCT_METHODS = CaseInsensitiveMapping({
'McCamy 1992': xy_to_CCT_McCamy1992,
'Hernandez 1999': xy_to_CCT_Hernandez1999
})
XY_TO_CCT_METHODS.__doc__ = """
Supported *CIE XYZ* tristimulus values *xy* chromaticity coordinates to
correlated colour temperature :math:`T_{cp}` computation methods.
References
----------
:cite:`Hernandez-Andres1999a`, :cite:`Wikipedia2001`, :cite:`Wikipedia2001a`
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'):
"""
Returns the correlated colour temperature :math:`T_{cp}` from given
*CIE XYZ* tristimulus values *xy* chromaticity coordinates using given
method.
Parameters
----------
xy : array_like
*xy* chromaticity coordinates.
method : unicode, optional
**{'McCamy 1992', 'Hernandez 1999'}**,
Computation method.
Returns
-------
numeric or ndarray
Correlated colour temperature :math:`T_{cp}`.
References
----------
:cite:`Hernandez-Andres1999a`, :cite:`Wikipedia2001`,
:cite:`Wikipedia2001a`
"""
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
})
CCT_TO_XY_METHODS.__doc__ = """
Supported correlated colour temperature :math:`T_{cp}` to *CIE XYZ* tristimulus
values *xy* chromaticity coordinates computation methods.
References
----------
:cite:`Kang2002a`, :cite:`Wikipedia2001a`, :cite:`Wyszecki2000z`
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* tristimulus values *xy* chromaticity coordinates from
given correlated colour temperature :math:`T_{cp}` using given method.
Parameters
----------
CCT : numeric or array_like
Correlated colour temperature :math:`T_{cp}`.
method : unicode, optional
**{'Kang 2002', 'CIE Illuminant D Series'}**,
Computation method.
Returns
-------
ndarray
*xy* chromaticity coordinates.
References
----------
:cite:`Kang2002a`, :cite:`Wikipedia2001a`, :cite:`Wyszecki2000z`
"""
return CCT_TO_XY_METHODS.get(method)(CCT)