"""
Robertson (1968) Correlated Colour Temperature
==============================================
Defines the *Robertson (1968)* correlated colour temperature :math:`T_{cp}`
computations objects:
- :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.
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. 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.
https://www.adobe.com/support/downloads/dng/dng_sdk.html
- :cite:`Wyszecki2000x` : Wyszecki, Gùˆnther, & Stiles, W. S. (2000). Table
1(3.11) Isotemperature Lines. In Color Science: Concepts and Methods,
Quantitative Data and Formulae (p. 228). Wiley. ISBN:978-0-471-39918-6
- :cite:`Wyszecki2000y` : Wyszecki, Gùˆnther, & 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:978-0-471-39918-6
"""
from __future__ import annotations
import numpy as np
from dataclasses import dataclass
from colour.hints import ArrayLike, Floating, List, NDArray, Tuple
from colour.utilities import as_float_array, tsplit
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "New BSD License - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"
__all__ = [
"DATA_ISOTEMPERATURE_LINES_ROBERTSON1968",
"ISOTemperatureLine_Specification_Robertson1968",
"ISOTEMPERATURE_LINES_ROBERTSON1968",
"uv_to_CCT_Robertson1968",
"CCT_to_uv_Robertson1968",
]
DATA_ISOTEMPERATURE_LINES_ROBERTSON1968: Tuple = (
(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 as a *tuple* as follows::
(
('Reciprocal Megakelvin', 'CIE 1960 Chromaticity Coordinate *u*',
'CIE 1960 Chromaticity Coordinate *v*', 'Slope'),
...,
('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`
"""
@dataclass
class ISOTemperatureLine_Specification_Robertson1968:
"""
Define the data for a *Roberston (1968)* iso-temperature line.
Parameters
----------
r
Temperature :math:`r` in reciprocal mega-kelvin degrees.
u
*u* chromaticity coordinate of the temperature :math:`r`.
v
*v* chromaticity coordinate of the temperature :math:`r`.
t
Slope of the *v* chromaticity coordinate.
"""
r: Floating
u: Floating
v: Floating
t: Floating
ISOTEMPERATURE_LINES_ROBERTSON1968: List = [
ISOTemperatureLine_Specification_Robertson1968(*x)
for x in DATA_ISOTEMPERATURE_LINES_ROBERTSON1968
]
def _uv_to_CCT_Robertson1968(uv: ArrayLike) -> NDArray:
"""
Return 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
*CIE UCS* colourspace *uv* chromaticity coordinates.
Returns
-------
:class:`numpy.ndarray`
Correlated colour temperature :math:`T_{cp}`, :math:`\\Delta_{uv}`.
"""
u, v = tsplit(uv)
last_dt = last_dv = last_du = 0
for i in range(1, 31):
wr_ruvt = ISOTEMPERATURE_LINES_ROBERTSON1968[i]
wr_ruvt_previous = ISOTEMPERATURE_LINES_ROBERTSON1968[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 uv_to_CCT_Robertson1968(uv: ArrayLike) -> NDArray:
"""
Return 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
*CIE UCS* colourspace *uv* chromaticity coordinates.
Returns
-------
:class:`numpy.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])
"""
uv = as_float_array(uv)
CCT_D_uv = [_uv_to_CCT_Robertson1968(a) for a in np.reshape(uv, (-1, 2))]
return np.reshape(as_float_array(CCT_D_uv), uv.shape)
def _CCT_to_uv_Robertson1968(CCT_D_uv: ArrayLike) -> NDArray:
"""
Return 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_D_uv
Correlated colour temperature :math:`T_{cp}`, :math:`\\Delta_{uv}`.
Returns
-------
:class:`numpy.ndarray`
*CIE UCS* colourspace *uv* chromaticity coordinates.
"""
CCT, D_uv = tsplit(CCT_D_uv)
r = 1.0e6 / CCT
u, v = np.nan, np.nan
for i in range(30):
wr_ruvt = ISOTEMPERATURE_LINES_ROBERTSON1968[i]
wr_ruvt_next = ISOTEMPERATURE_LINES_ROBERTSON1968[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
break
return np.array([u, v])
[docs]def CCT_to_uv_Robertson1968(CCT_D_uv: ArrayLike) -> NDArray:
"""
Return 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_D_uv
Correlated colour temperature :math:`T_{cp}`, :math:`\\Delta_{uv}`.
Returns
-------
:class:`numpy.ndarray`
*CIE UCS* colourspace *uv* chromaticity coordinates.
References
----------
:cite:`AdobeSystems2013a`, :cite:`Wyszecki2000y`
Examples
--------
>>> CCT_D_uv = np.array([6500.0081378199056, 0.008333331244225])
>>> CCT_to_uv_Robertson1968(CCT_D_uv) # doctest: +ELLIPSIS
array([ 0.1937413..., 0.3152210...])
"""
CCT_D_uv = as_float_array(CCT_D_uv)
uv = [_CCT_to_uv_Robertson1968(a) for a in np.reshape(CCT_D_uv, (-1, 2))]
return np.reshape(as_float_array(uv), CCT_D_uv.shape)