"""
Helmholtz—Kohlrausch Effect
===========================
Defines the following methods for estimating Helmholtz-Kohlrausch effect (HKE):
- :attr:`colour.HKE_NAYATANI1997_METHODS`: Nayatani HKE computation methods,
choice between variable achromatic colour ('VAC') and variable chromatic
colour ('VCC').
- :func:`colour.HelmholtzKohlrausch_effect_object_Nayatani1997`:
*Nayatani (1997)* HKE estimation for object colours.
- :func:`colour.HelmholtzKohlrausch_effect_luminous_Nayatani1997`:
*Nayatani (1997)* HKE estimation for luminous colours.
- :func:`colour.appearance.coefficient_q_Nayatani1997`:
Calculates :math:`WI` coefficient for *Nayatani 1997* HKE estimation.
- :func:`colour.appearance.coefficient_K_Br_Nayatani1997`:
Calculates :math:`K_{Br}` coefficient for *Nayatani 1997* HKE estimation.
References
----------
- :cite:`Nayatani1997` : Nayatani, Y. (1997). Simple estimation methods for
the Helmholtz—Kohlrausch effect. Color Research & Application, 22(6),
385-401. doi:10.1002/(SICI)1520-6378(199712)22:6<385::AID-COL6>3.0.CO;2-R
"""
from __future__ import annotations
import numpy as np
from colour.algebra import spow
from colour.hints import (
ArrayLike,
FloatingOrArrayLike,
FloatingOrNDArray,
Literal,
Union,
)
from colour.utilities import (
CaseInsensitiveMapping,
as_float_array,
tsplit,
validate_method,
)
__author__ = "Ilia Sibiryakov"
__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__ = [
"HKE_NAYATANI1997_METHODS",
"HelmholtzKohlrausch_effect_object_Nayatani1997",
"HelmholtzKohlrausch_effect_luminous_Nayatani1997",
"coefficient_q_Nayatani1997",
"coefficient_K_Br_Nayatani1997",
]
HKE_NAYATANI1997_METHODS = CaseInsensitiveMapping(
{
"VAC": -0.1340,
"VCC": -0.8660,
}
)
HKE_NAYATANI1997_METHODS.__doc__ = """
*Nayatani (1997)* *HKE* computation methods, choice between variable achromatic
colour ('VAC') and variable chromatic colour ('VCC')
References
----------
:cite:`Nayatani1997`
"""
[docs]def HelmholtzKohlrausch_effect_object_Nayatani1997(
uv: ArrayLike,
uv_c: ArrayLike,
L_a: FloatingOrArrayLike,
method: Union[Literal["VAC", "VCC"], str] = "VCC",
) -> FloatingOrNDArray:
"""
Return the *HKE* value for object colours using *Nayatani (1997)* method.
Parameters
----------
uv
*CIE uv* chromaticity coordinates of samples.
uv_c
*CIE uv* chromaticity coordinates of reference white.
L_a
Adapting luminance in :math:`cd/m^2`.
method
Which estimation method to use, *VCC* or *VAC*.
Returns
-------
:class:`numpy.floating` or :class:`numpy.ndarray`
Luminance factor (:math:`\\Gamma`) value(s) computed with Nayatani
object colour estimation method.
References
----------
:cite:`Nayatani1997`
Examples
--------
>>> import colour
>>> white = colour.xy_to_Luv_uv(colour.temperature.CCT_to_xy_CIE_D(6504))
>>> colours = colour.XYZ_to_xy(
... [colour.wavelength_to_XYZ(430 + i * 50) for i in range(5)])
>>> L_adapting = 65
>>> HelmholtzKohlrausch_effect_object_Nayatani1997( # doctest: +ELLIPSIS
... colour.xy_to_Luv_uv(colours), white, L_adapting)
array([ 2.2468383..., 1.4619799..., 1.1801658..., 0.9031318..., \
1.7999376...])
"""
u, v = tsplit(uv)
u_c, v_c = tsplit(uv_c)
method = validate_method(method, HKE_NAYATANI1997_METHODS)
K_Br = coefficient_K_Br_Nayatani1997(L_a)
q = coefficient_q_Nayatani1997(np.arctan2(v - v_c, u - u_c))
S_uv = 13 * np.sqrt((u - u_c) ** 2 + (v - v_c) ** 2)
return 1 + (HKE_NAYATANI1997_METHODS[method] * q + 0.0872 * K_Br) * S_uv
[docs]def HelmholtzKohlrausch_effect_luminous_Nayatani1997(
uv: ArrayLike,
uv_c: ArrayLike,
L_a: FloatingOrArrayLike,
method: Union[Literal["VAC", "VCC"], str] = "VCC",
) -> FloatingOrNDArray:
"""
Return the *HKE* factor for luminous colours using *Nayatani (1997)* method.
Parameters
----------
uv
*CIE uv* chromaticity coordinates of samples.
uv_c
*CIE uv* chromaticity coordinates of reference white.
L_a
Adapting luminance in :math:`cd/m^2`.
method
Which estimation method to use, *VCC* or *VAC*.
Returns
-------
:class:`numpy.floating` or :class:`numpy.ndarray`
Luminance factor (:math:`\\Gamma`) value(s) computed with Nayatani
luminous colour estimation method.
References
----------
:cite:`Nayatani1997`
Examples
--------
>>> import colour
>>> white = colour.xy_to_Luv_uv(colour.temperature.CCT_to_xy_CIE_D(6504))
>>> colours = colour.XYZ_to_xy(
... [colour.wavelength_to_XYZ(430 + i * 50) for i in range(5)])
>>> L_adapting = 65
>>> HelmholtzKohlrausch_effect_luminous_Nayatani1997( # doctest: +ELLIPSIS
... colour.xy_to_Luv_uv(colours), white, L_adapting)
array([ 7.4460471..., 2.4767159..., 1.4723422..., 0.7938695..., \
4.1828629...])
"""
return (
0.4462
* (
HelmholtzKohlrausch_effect_object_Nayatani1997(
uv, uv_c, L_a, method
)
+ 0.3086
)
** 3
)
[docs]def coefficient_q_Nayatani1997(
theta: FloatingOrArrayLike,
) -> FloatingOrNDArray:
"""
Return the :math:`q(\\theta)` coefficient for *Nayatani (1997)* *HKE*
computations.
The hue angle :math:`\\theta` can be computed as follows:
:math:`tan^{-1}\\cfrac{v' - v'_c}{u' - u'_c}`
where :math:`u'` and :math:`v'` are the CIE 1976 chromaticity coordinates
of the test chromatic light and :math:`u'_c` and :math:`v'_c` are the CIE
1976 chromaticity coordinates of the reference white light.
Parameters
----------
theta
Hue angle (:math:`\\theta`) in radians.
Returns
-------
:class:`numpy.floating` or :class:`numpy.ndarray`
:math:`q` coefficient for *Nayatani (1997)* *HKE* methods.
References
----------
:cite:`Nayatani1997`
Examples
--------
This recreates *FIG. A-1*.
>>> import matplotlib.pyplot as plt
>>> angles = [(np.pi * 2 / 100 * i) for i in range(100)]
>>> q_values = coefficient_q_Nayatani1997(angles)
>>> plt.plot(np.array(angles), q_values / (np.pi * 2) * 180)
... # doctest: +ELLIPSIS
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.show() # doctest: +SKIP
"""
theta = as_float_array(theta)
theta_2, theta_3, theta_4 = 2 * theta, 3 * theta, 4 * theta
return (
-0.01585
- 0.03017 * np.cos(theta)
- 0.04556 * np.cos(theta_2)
- 0.02667 * np.cos(theta_3)
- 0.00295 * np.cos(theta_4)
+ 0.14592 * np.sin(theta)
+ 0.05084 * np.sin(theta_2)
- 0.01900 * np.sin(theta_3)
- 0.00764 * np.sin(theta_4)
)
[docs]def coefficient_K_Br_Nayatani1997(
L_a: FloatingOrArrayLike,
) -> FloatingOrNDArray:
"""
Return the :math:`K_{Br}` coefficient for *Nayatani (1997)* *HKE*
computations.
Parameters
----------
L_a
Adapting luminance in :math:`cd/m^2`.
Returns
-------
:class:`numpy.floating` or :class:`numpy.ndarray`
:math:`K_{Br}` coefficient for *Nayatani (1997)* *HKE* methods.
Notes
-----
- The :math:`K_{Br}` coefficient is normalised to unity around
:math:`63.66cd/m^2`.
References
----------
:cite:`Nayatani1997`
Examples
--------
>>> L_a_values = [10 + i * 20 for i in range(5)]
>>> coefficient_K_Br_Nayatani1997(L_a_values) # doctest: +ELLIPSIS
array([ 0.7134481..., 0.8781172..., 0.9606248..., 1.0156689..., \
1.0567008...])
>>> coefficient_K_Br_Nayatani1997(63.66) # doctest: +ELLIPSIS
1.0001284...
"""
L_a_4495 = spow(L_a, 0.4495)
return 0.2717 * (6.469 + 6.362 * L_a_4495) / (6.469 + L_a_4495)