"""
Kang, Moon, Hong, Lee, Cho and Kim (2002) Correlated Colour Temperature
=======================================================================
Define the *Kang et al. (2002)* correlated colour temperature :math:`T_{cp}`
computation objects.
- :func:`colour.temperature.xy_to_CCT_Kang2002`: Compute correlated colour
temperature :math:`T_{cp}` from specified *CIE xy* chromaticity
coordinates using the *Kang, Moon, Hong, Lee, Cho and Kim (2002)* method.
- :func:`colour.temperature.CCT_to_xy_Kang2002`: Compute *CIE xy*
chromaticity coordinates from specified correlated colour temperature
:math:`T_{cp}` using the *Kang, Moon, Hong, Lee, Cho and Kim (2002)*
method.
References
----------
- :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.
"""
from __future__ import annotations
import typing
if typing.TYPE_CHECKING:
from colour.hints import ArrayLike, NDArrayFloat
from colour.temperature.common import (
CCT_INVERSION_GRID_SAMPLES,
solve_CCT_Newton,
x0_CCT_grid,
)
from colour.utilities import (
array_namespace,
as_float,
as_float_array,
optional,
tstack,
usage_warning,
xp_select,
)
__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__ = [
"xy_to_CCT_Kang2002",
"CCT_to_xy_Kang2002",
]
[docs]
def xy_to_CCT_Kang2002(
xy: ArrayLike, optimisation_kwargs: dict | None = None
) -> NDArrayFloat:
"""
Compute the correlated colour temperature :math:`T_{cp}` from the
specified *CIE xy* chromaticity coordinates using *Kang et al. (2002)*
method.
Parameters
----------
xy
*CIE xy* chromaticity coordinates.
optimisation_kwargs
Inversion parameters forwarded to
:func:`colour.temperature.x0_CCT_grid` and
:func:`colour.temperature.solve_CCT_Newton`. Accepted keys are
``samples`` (grid density for the initial guess, default
:attr:`colour.temperature.CCT_INVERSION_GRID_SAMPLES`),
``newton_iterations``, ``backtrack_iterations`` and ``tolerance``
(forwarded to :func:`solve_CCT_Newton`).
Returns
-------
:class:`numpy.ndarray`
Correlated colour temperature :math:`T_{cp}`.
Warnings
--------
The *Kang et al. (2002)* method does not provide an analytical inverse
transformation to compute the correlated colour temperature
:math:`T_{cp}` from the specified *CIE xy* chromaticity coordinates.
The current implementation relies on a damped *Gauss-Newton* iteration
seeded by nearest-neighbour lookup against a coarse grid sampled from
the analytical forward over the [1667, 25000] domain. The lookup keeps
the iteration in the correct basin near the domain edges where the
polynomial is non-monotonic if extrapolated.
References
----------
:cite:`Kang2002a`
Examples
--------
>>> xy_to_CCT_Kang2002([0.31342600, 0.32359597]) # doctest: +ELLIPSIS
np.float64(6504.389303...)
"""
optimisation_kwargs = dict(optional(optimisation_kwargs, {}))
xy = as_float_array(xy)
x0 = x0_CCT_grid(
CCT_to_xy_Kang2002,
xy,
(1667.0, 25000.0),
samples=optimisation_kwargs.pop("samples", CCT_INVERSION_GRID_SAMPLES),
)
return as_float(
solve_CCT_Newton(CCT_to_xy_Kang2002, xy, x0=x0, **optimisation_kwargs)
)
[docs]
def CCT_to_xy_Kang2002(CCT: ArrayLike) -> NDArrayFloat:
"""
Compute the *CIE xy* chromaticity coordinates from the specified
correlated colour temperature :math:`T_{cp}` using *Kang et al. (2002)*
method.
Parameters
----------
CCT
Correlated colour temperature :math:`T_{cp}`.
Returns
-------
:class:`numpy.ndarray`
*CIE 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)
xp = array_namespace(CCT)
if xp.any(xp.logical_or(CCT < 1667, CCT > 25000)):
usage_warning(
"Correlated colour temperature must be in domain "
"[1667, 25000], unpredictable results may occur!"
)
CCT_3 = CCT**3
CCT_2 = CCT**2
x = xp.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,
)
x_3 = x**3
x_2 = x**2
cnd_l = [CCT <= 2222, xp.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 = xp_select(cnd_l, [i, j, k], xp=xp)
return tstack([x, y])
