"""
Robertson (1968) Correlated Colour Temperature
==============================================
Define the *Robertson (1968)* correlated colour temperature :math:`T_{cp}`
computation objects.
- :func:`colour.temperature.mired_to_CCT`: Convert micro reciprocal
degrees to correlated colour temperature :math:`T_{cp}`.
- :func:`colour.temperature.CCT_to_mired`: Convert correlated colour
temperature :math:`T_{cp}` to micro reciprocal degrees.
- :func:`colour.temperature.uv_to_CCT_Robertson1968`: Compute correlated
colour temperature :math:`T_{cp}` and :math:`\\Delta_{uv}` from
specified *CIE UCS* colourspace *uv* chromaticity coordinates using
the *Robertson (1968)* method.
- :func:`colour.temperature.CCT_to_uv_Robertson1968`: Compute *CIE UCS*
colourspace *uv* chromaticity coordinates from specified correlated
colour temperature :math:`T_{cp}` and :math:`\\Delta_{uv}` using the
*Robertson (1968)* method.
References
----------
- :cite:`Wyszecki2000x` : Wyszecki, Günther, & 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, Günther, & 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 typing
from dataclasses import dataclass
import numpy as np
from colour.algebra import sdiv, sdiv_mode
if typing.TYPE_CHECKING:
from colour.hints import ArrayLike, NDArrayFloat
from colour.utilities import as_float_array, tsplit
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "BSD-3-Clause - 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",
"mired_to_CCT",
"CCT_to_mired",
"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 a data structure for a *Robertson (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: float
u: float
v: float
t: float
ISOTEMPERATURE_LINES_ROBERTSON1968: list = [
ISOTemperatureLine_Specification_Robertson1968(*x)
for x in DATA_ISOTEMPERATURE_LINES_ROBERTSON1968
]
[docs]
def mired_to_CCT(mired: ArrayLike) -> NDArrayFloat:
"""
Convert specified micro reciprocal degree (mired) to correlated colour
temperature :math:`T_{cp}`.
Parameters
----------
mired
Micro reciprocal degree.
Returns
-------
:class:`numpy.ndarray`
Correlated colour temperature :math:`T_{cp}`.
Examples
--------
>>> CCT_to_mired(153.84615384615384) # doctest: +ELLIPSIS
np.float64(6500.0)
"""
mired = as_float_array(mired)
with sdiv_mode():
return sdiv(1.0e6, mired)
[docs]
def CCT_to_mired(CCT: ArrayLike) -> NDArrayFloat:
"""
Convert specified correlated colour temperature :math:`T_{cp}` to micro
reciprocal degree (mired).
Parameters
----------
CCT
Correlated colour temperature :math:`T_{cp}`.
Returns
-------
:class:`numpy.ndarray`
Micro reciprocal degree.
Examples
--------
>>> CCT_to_mired(6500) # doctest: +ELLIPSIS
np.float64(153.8461538...)
"""
CCT = as_float_array(CCT)
with sdiv_mode():
return sdiv(1.0e6, CCT)
[docs]
def uv_to_CCT_Robertson1968(uv: ArrayLike) -> NDArrayFloat:
"""
Compute the correlated colour temperature :math:`T_{cp}` and
:math:`\\Delta_{uv}` from the specified *CIE UCS* colourspace *uv*
chromaticity coordinates using *Robertson (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:`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)
shape = uv.shape
uv = uv.reshape(-1, 2)
r_itl, u_itl, v_itl, t_itl = tsplit(
np.array(DATA_ISOTEMPERATURE_LINES_ROBERTSON1968)
)
# Normalized direction vectors
length = np.hypot(1.0, t_itl)
du_itl = 1.0 / length
dv_itl = t_itl / length
# Vectorized computation for all UV pairs at once
u, v = tsplit(uv)
u = u[:, np.newaxis] # Shape (N, 1)
v = v[:, np.newaxis] # Shape (N, 1)
# Compute distances for all UV pairs against all isotemperature lines
# Broadcasting: (N, 1) - (30,) = (N, 30)
uu = u - u_itl[1:] # Shape (N, 30)
vv = v - v_itl[1:] # Shape (N, 30)
dt = -uu * dv_itl[1:] + vv * du_itl[1:] # Shape (N, 30)
# Find the first crossing point for each UV pair
mask = dt <= 0
i = np.where(np.any(mask, axis=1), np.argmax(mask, axis=1) + 1, 30)
# Interpolation factor
idx = np.arange(len(i))
dt_current = -np.minimum(dt[idx, i - 1], 0.0)
dt_previous = dt[idx, i - 2]
f = np.where(
i == 1, 0.0, np.where(i > 1, dt_current / (dt_previous + dt_current), 0.0)
)
# Interpolate temperature
T = mired_to_CCT(r_itl[i - 1] * f + r_itl[i] * (1 - f))
# Interpolate uv position
u_i = u_itl[i - 1] * f + u_itl[i] * (1 - f)
v_i = v_itl[i - 1] * f + v_itl[i] * (1 - f)
# Interpolate direction vectors
du_i = du_itl[i] * (1 - f) + du_itl[i - 1] * f
dv_i = dv_itl[i] * (1 - f) + dv_itl[i - 1] * f
# Normalize interpolated direction
length_i = np.hypot(du_i, dv_i)
du_i /= length_i
dv_i /= length_i
# Calculate D_uv
uu = u.ravel() - u_i
vv = v.ravel() - v_i
D_uv = uu * du_i + vv * dv_i
result = np.stack([T, -D_uv], axis=-1)
return result.reshape(shape)
[docs]
def CCT_to_uv_Robertson1968(CCT_D_uv: ArrayLike) -> NDArrayFloat:
"""
Return the *CIE UCS* colourspace *uv* chromaticity coordinates from the
specified correlated colour temperature :math:`T_{cp}` and
:math:`\\Delta_{uv}` using *Robertson (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:`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)
shape = CCT_D_uv.shape
CCT_D_uv = CCT_D_uv.reshape(-1, 2)
r_itl, u_itl, v_itl, t_itl = tsplit(
np.array(DATA_ISOTEMPERATURE_LINES_ROBERTSON1968)
)
# Precompute normalized direction vectors
length = np.hypot(1.0, t_itl)
du_itl = 1.0 / length
dv_itl = t_itl / length
# Vectorized computation for all CCT/D_uv pairs at once
CCT, D_uv = tsplit(CCT_D_uv)
r = CCT_to_mired(CCT)
# Find the isotemperature range containing r for all values
mask = r[:, np.newaxis] < r_itl[1:]
i = np.where(np.any(mask, axis=1), np.argmax(mask, axis=1), 29)
# Interpolation factor
f = (r_itl[i + 1] - r) / (r_itl[i + 1] - r_itl[i])
# Interpolate uv position on Planckian locus
u = u_itl[i] * f + u_itl[i + 1] * (1 - f)
v = v_itl[i] * f + v_itl[i + 1] * (1 - f)
# Interpolate direction vectors
du_i = du_itl[i] * f + du_itl[i + 1] * (1 - f)
dv_i = dv_itl[i] * f + dv_itl[i + 1] * (1 - f)
# Normalize interpolated direction
length_i = np.hypot(du_i, dv_i)
du_i /= length_i
dv_i /= length_i
# Offset by D_uv along the isotherm
u += du_i * -D_uv
v += dv_i * -D_uv
result = np.stack([u, v], axis=-1)
return result.reshape(shape)
