"""
Hunt Colour Appearance Model
============================
Define the *Hunt* colour appearance model for predicting perceptual colour
attributes under varying viewing conditions.
- :class:`colour.appearance.InductionFactors_Hunt`
- :attr:`colour.VIEWING_CONDITIONS_HUNT`
- :class:`colour.CAM_Specification_Hunt`
- :func:`colour.XYZ_to_Hunt`
References
----------
- :cite:`Fairchild2013u` : Fairchild, M. D. (2013). The Hunt Model. In Color
Appearance Models (3rd ed., pp. 5094-5556). Wiley. ISBN:B00DAYO8E2
- :cite:`Hunt2004b` : Hunt, R. W. G. (2004). The Reproduction of Colour (6th
ed.). John Wiley & Sons, Ltd. doi:10.1002/0470024275
"""
from __future__ import annotations
import typing
from dataclasses import dataclass, field
import numpy as np
from colour.algebra import spow, vecmul
if typing.TYPE_CHECKING:
from colour.hints import ArrayLike, Domain100
from colour.hints import Annotated, NDArrayFloat, cast
from colour.utilities import (
CanonicalMapping,
MixinDataclassArithmetic,
MixinDataclassIterable,
array_namespace,
as_float,
as_float_array,
from_range_degrees,
to_domain_100,
tsplit,
tstack,
usage_warning,
xp_as_float_array,
xp_degrees,
xp_interp,
)
__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__ = [
"InductionFactors_Hunt",
"VIEWING_CONDITIONS_HUNT",
"HUE_DATA_FOR_HUE_QUADRATURE",
"MATRIX_XYZ_TO_HPE",
"MATRIX_HPE_TO_XYZ",
"CAM_ReferenceSpecification_Hunt",
"CAM_Specification_Hunt",
"XYZ_to_Hunt",
"luminance_level_adaptation_factor",
"XYZ_to_rgb",
]
@dataclass(frozen=True)
class InductionFactors_Hunt(MixinDataclassIterable):
"""
Define the *Hunt* colour appearance model induction factors.
Parameters
----------
N_c
Chromatic surround induction factor :math:`N_c`.
N_b
Brightness surround induction factor :math:`N_b`.
N_cb
Chromatic background induction factor :math:`N_{cb}`, approximated
using tristimulus values :math:`Y_w` and :math:`Y_b` of
respectively the reference white and the background if not specified.
N_bb
Brightness background induction factor :math:`N_{bb}`, approximated
using tristimulus values :math:`Y_w` and :math:`Y_b` of
respectively the reference white and the background if not
specified.
References
----------
:cite:`Fairchild2013u`, :cite:`Hunt2004b`
"""
N_c: float
N_b: float
N_cb: float | None = field(default_factory=lambda: None)
N_bb: float | None = field(default_factory=lambda: None)
VIEWING_CONDITIONS_HUNT: CanonicalMapping = CanonicalMapping(
{
"Small Areas, Uniform Background & Surrounds": InductionFactors_Hunt(1, 300),
"Normal Scenes": InductionFactors_Hunt(1, 75),
"Television & CRT, Dim Surrounds": InductionFactors_Hunt(1, 25),
"Large Transparencies On Light Boxes": InductionFactors_Hunt(0.7, 25),
"Projected Transparencies, Dark Surrounds": InductionFactors_Hunt(0.7, 10),
}
)
VIEWING_CONDITIONS_HUNT.__doc__ = """
Define the reference *Hunt* colour appearance model viewing conditions.
References
----------
:cite:`Fairchild2013u`, :cite:`Hunt2004b`
Aliases:
- 'small_uniform': 'Small Areas, Uniform Background & Surrounds'
- 'normal': 'Normal Scenes'
- 'tv_dim': 'Television & CRT, Dim Surrounds'
- 'light_boxes': 'Large Transparencies On Light Boxes'
- 'projected_dark': 'Projected Transparencies, Dark Surrounds'
"""
VIEWING_CONDITIONS_HUNT["small_uniform"] = VIEWING_CONDITIONS_HUNT[
"Small Areas, Uniform Background & Surrounds"
]
VIEWING_CONDITIONS_HUNT["normal"] = VIEWING_CONDITIONS_HUNT["Normal Scenes"]
VIEWING_CONDITIONS_HUNT["tv_dim"] = VIEWING_CONDITIONS_HUNT[
"Television & CRT, Dim Surrounds"
]
VIEWING_CONDITIONS_HUNT["light_boxes"] = VIEWING_CONDITIONS_HUNT[
"Large Transparencies On Light Boxes"
]
VIEWING_CONDITIONS_HUNT["projected_dark"] = VIEWING_CONDITIONS_HUNT[
"Projected Transparencies, Dark Surrounds"
]
HUE_DATA_FOR_HUE_QUADRATURE: dict = {
"h_s": np.array([20.14, 90.00, 164.25, 237.53]),
"e_s": np.array([0.8, 0.7, 1.0, 1.2]),
}
MATRIX_XYZ_TO_HPE: NDArrayFloat = np.array(
[
[0.38971, 0.68898, -0.07868],
[-0.22981, 1.18340, 0.04641],
[0.00000, 0.00000, 1.00000],
]
)
"""
*Hunt* colour appearance model *CIE XYZ* tristimulus values to
*Hunt-Pointer-Estevez* :math:`\\rho\\gamma\\beta` colourspace matrix.
"""
MATRIX_HPE_TO_XYZ: NDArrayFloat = np.linalg.inv(MATRIX_XYZ_TO_HPE)
"""
*Hunt* colour appearance model *Hunt-Pointer-Estevez*
:math:`\\rho\\gamma\\beta` colourspace to *CIE XYZ* tristimulus values matrix.
"""
@dataclass
class CAM_ReferenceSpecification_Hunt(MixinDataclassArithmetic):
"""
Define the *Hunt* colour appearance model reference specification.
This specification contains field names consistent with the *Fairchild
(2013)* reference.
Parameters
----------
J
Correlate of *Lightness* :math:`J`.
C_94
Correlate of *chroma* :math:`C_{94}`.
h_S
*Hue* angle :math:`h_S` in degrees.
s
Correlate of *saturation* :math:`s`.
Q
Correlate of *brightness* :math:`Q`.
M_94
Correlate of *colourfulness* :math:`M_{94}`.
H
*Hue* :math:`h` quadrature :math:`H`.
H_C
*Hue* :math:`h` composition :math:`H_C`.
References
----------
:cite:`Fairchild2013u`, :cite:`Hunt2004b`
"""
J: float | NDArrayFloat | None = field(default_factory=lambda: None)
C_94: float | NDArrayFloat | None = field(default_factory=lambda: None)
h_S: float | NDArrayFloat | None = field(default_factory=lambda: None)
s: float | NDArrayFloat | None = field(default_factory=lambda: None)
Q: float | NDArrayFloat | None = field(default_factory=lambda: None)
M_94: float | NDArrayFloat | None = field(default_factory=lambda: None)
H: float | NDArrayFloat | None = field(default_factory=lambda: None)
H_C: float | NDArrayFloat | None = field(default_factory=lambda: None)
[docs]
@dataclass
class CAM_Specification_Hunt(MixinDataclassArithmetic):
"""
Define the *Hunt* colour appearance model specification.
This specification provides a standardized interface for the *Hunt* model
with field names consistent across all colour appearance models in
:mod:`colour.appearance`. While the field names differ from the original
*Fairchild (2013)* reference notation, they map directly to the model's
perceptual correlates.
Parameters
----------
J
Correlate of *lightness* :math:`J`.
C
Correlate of *chroma* :math:`C_{94}`.
h
*Hue* angle :math:`h_s` in degrees.
s
Correlate of *saturation* :math:`s`.
Q
Correlate of *brightness* :math:`Q`.
M
Correlate of *colourfulness* :math:`M_{94}`.
H
*Hue* :math:`h` quadrature :math:`H`.
HC
*Hue* :math:`h` composition :math:`H_C`.
Notes
-----
- This specification is the one used in the current model
implementation.
References
----------
:cite:`Fairchild2013u`, :cite:`Hunt2004b`
"""
J: float | NDArrayFloat | None = field(default_factory=lambda: None)
C: float | NDArrayFloat | None = field(default_factory=lambda: None)
h: float | NDArrayFloat | None = field(default_factory=lambda: None)
s: float | NDArrayFloat | None = field(default_factory=lambda: None)
Q: float | NDArrayFloat | None = field(default_factory=lambda: None)
M: float | NDArrayFloat | None = field(default_factory=lambda: None)
H: float | NDArrayFloat | None = field(default_factory=lambda: None)
HC: float | NDArrayFloat | None = field(default_factory=lambda: None)
[docs]
def XYZ_to_Hunt(
XYZ: Domain100,
XYZ_w: Domain100,
XYZ_b: Domain100,
L_A: ArrayLike,
surround: InductionFactors_Hunt = VIEWING_CONDITIONS_HUNT["Normal Scenes"],
L_AS: ArrayLike | None = None,
CCT_w: ArrayLike | None = None,
XYZ_p: Annotated[ArrayLike | None, 100] = None,
p: ArrayLike | None = None,
S: ArrayLike | None = None,
S_w: ArrayLike | None = None,
helson_judd_effect: bool = False,
discount_illuminant: bool = True,
) -> Annotated[CAM_Specification_Hunt, 360]:
"""
Compute the *Hunt* colour appearance model correlates from the specified
*CIE XYZ* tristimulus values.
Parameters
----------
XYZ
*CIE XYZ* tristimulus values of test sample / stimulus.
XYZ_w
*CIE XYZ* tristimulus values of reference white.
XYZ_b
*CIE XYZ* tristimulus values of background.
L_A
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`.
surround
Surround viewing conditions induction factors.
L_AS
Scotopic luminance :math:`L_{AS}` of the illuminant,
approximated if not specified.
CCT_w
Correlated colour temperature :math:`T_{cp}` of the illuminant,
required to approximate :math:`L_{AS}` when not specified.
XYZ_p
*CIE XYZ* tristimulus values of proximal field, assumed to equal
background if not specified.
p
Simultaneous contrast / assimilation factor :math:`p` with value
normalised to domain [-1, 0] for simultaneous contrast and
normalised to domain [0, 1] for assimilation.
S
Scotopic response :math:`S` to the stimulus, approximated using
tristimulus value :math:`Y` of the stimulus if not specified.
S_w
Scotopic response :math:`S_w` for the reference white,
approximated using tristimulus value :math:`Y_w` of the
reference white if not specified.
helson_judd_effect
Whether to account for the *Helson-Judd* effect.
discount_illuminant
Whether to discount the illuminant.
Returns
-------
:class:`colour.CAM_Specification_Hunt`
*Hunt* colour appearance model specification.
Raises
------
ValueError
If an illegal argument combination is specified.
Notes
-----
+---------------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+=====================+=======================+===============+
| ``XYZ`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``XYZ_w`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``XYZ_b`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``XYZ_p`` | 100 | 1 |
+---------------------+-----------------------+---------------+
+---------------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+=====================+=======================+===============+
| ``specification.h`` | 360 | 1 |
+---------------------+-----------------------+---------------+
References
----------
:cite:`Fairchild2013u`, :cite:`Hunt2004b`
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> XYZ_b = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> surround = VIEWING_CONDITIONS_HUNT["Normal Scenes"]
>>> CCT_w = 6504
>>> XYZ_to_Hunt(XYZ, XYZ_w, XYZ_b, L_A, surround, CCT_w=CCT_w)
... # doctest: +ELLIPSIS
CAM_Specification_Hunt(J=np.float64(30.0462678...), C=np.float64(0.1210508...), \
h=np.float64(269.2737594...), s=np.float64(0.0199093...), Q=np.float64(22.2097654...), \
M=np.float64(0.1238964...), H=None, HC=None)
"""
XYZ = to_domain_100(XYZ)
XYZ_w = to_domain_100(XYZ_w)
XYZ_b = to_domain_100(XYZ_b)
xp = array_namespace(XYZ, XYZ_w, XYZ_b, L_A)
XYZ = xp_as_float_array(XYZ, xp=xp)
XYZ_w = xp_as_float_array(XYZ_w, xp=xp, like=XYZ)
L_A = xp_as_float_array(L_A, xp=xp, like=XYZ)
_X, Y, _Z = tsplit(XYZ)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
X_b, Y_b, _Z_b = tsplit(XYZ_b)
# Arguments handling.
if XYZ_p is not None:
X_p, Y_p, Z_p = tsplit(to_domain_100(XYZ_p))
else:
X_p = X_b
Y_p = Y_b
Z_p = Y_b
usage_warning(
'Unspecified proximal field "XYZ_p" argument, using '
'background "XYZ_b" as approximation!'
)
if surround.N_cb is None:
N_cb = 0.725 * spow(Y_w / Y_b, 0.2)
usage_warning(f'Unspecified "N_cb" argument, using approximation: "{N_cb}"')
else:
N_cb = surround.N_cb
if surround.N_bb is None:
N_bb = 0.725 * spow(Y_w / Y_b, 0.2)
usage_warning(f'Unspecified "N_bb" argument, using approximation: "{N_bb}"')
else:
N_bb = surround.N_bb
if L_AS is None and CCT_w is None:
error = (
'Either the scotopic luminance "L_AS" of the '
"illuminant or its correlated colour temperature "
'"CCT_w" must be specified!'
)
raise ValueError(error)
if L_AS is None and CCT_w is not None:
# Approximating scotopic luminance :math:`L_{AS}` from the correlated
# colour temperature :math:`T_{cp}` per *Hunt (2004)*, "The
# Reproduction of Colour", 6th ed., section on scotopic responses.
L_AS = 2.26 * L_A * spow((cast("NDArrayFloat", CCT_w) / 4000) - 0.4, 1 / 3)
usage_warning(
f'Unspecified "L_AS" argument, using approximation from "CCT": "{L_AS}"'
)
if (S is None and S_w is not None) or (S is not None and S_w is None):
error = (
'Either both stimulus scotopic response "S" and '
'reference white scotopic response "S_w" arguments '
"need to be specified or none of them!"
)
raise ValueError(error)
if S is None and S_w is None:
S_p = Y
S_w_p = Y_w
usage_warning(
f'Unspecified stimulus scotopic response "S" and reference white '
f'scotopic response "S_w" arguments, using approximation: '
f'"{S}", "{S_w}"'
)
else:
# Both ``S`` and ``S_w`` are non-*None* here: the mixed-*None* case
# raises at the ``ValueError`` guard above.
S_p = xp_as_float_array(cast("ArrayLike", S), xp=xp, like=XYZ)
S_w_p = xp_as_float_array(cast("ArrayLike", S_w), xp=xp, like=XYZ)
if p is None:
usage_warning(
'Unspecified simultaneous contrast / assimilation "p" '
"argument, model will not account for simultaneous chromatic "
"contrast!"
)
XYZ_p = xp_as_float_array(tstack([X_p, Y_p, Z_p]), xp=xp, like=XYZ)
# Computing luminance level adaptation factor :math:`F_L`.
k = 1 / (5 * L_A + 1)
k4 = k**4
F_L = 0.2 * k4 * (5 * L_A) + 0.1 * (1 - k4) ** 2 * spow(5 * L_A, 1 / 3)
# Computing chromatic adaptation common to the stimulus and reference
# white. Only the final cone-response step is computed twice; the
# adaptation factors :math:`h_{rgb}`, :math:`F_{rgb}`, :math:`D_{rgb}`
# and :math:`B_{rgb}` depend only on the white and the viewing
# conditions.
rgb = vecmul(MATRIX_XYZ_TO_HPE, XYZ)
rgb_w = vecmul(MATRIX_XYZ_TO_HPE, XYZ_w)
h_rgb = 3 * rgb_w / xp.sum(rgb_w, axis=-1)[..., None]
if not discount_illuminant:
L_A_p = spow(L_A, 1 / 3)
F_rgb = (1 + L_A_p + h_rgb) / (1 + L_A_p + (1 / h_rgb))
else:
F_rgb = xp.ones_like(h_rgb)
def _f_n(x: NDArrayFloat) -> NDArrayFloat:
x_p = spow(x, 0.73)
return 40 * (x_p / (x_p + 2))
if helson_judd_effect:
Y_b_Y_w = Y_b / Y_w
Y_b_Y_w_F_L = Y_b_Y_w * F_L
D_rgb = _f_n(Y_b_Y_w_F_L * F_rgb[..., 1]) - _f_n(Y_b_Y_w_F_L * F_rgb)
else:
D_rgb = xp.zeros_like(F_rgb)
B_rgb = 10**7 / (10**7 + 5 * L_A[..., None] * (rgb_w / 100))
# Proximal-/background-adjusted reference white ``rgb_w_adapted`` used as
# the adaptation denominator (*Fairchild (2013)* Eq. 12.23-12.28). ``rgb_w``
# itself stays unadjusted: only the adaptation reference is adjusted, not
# the white stimulus.
if XYZ_p is not None and p is not None:
p = xp_as_float_array(p, xp=xp, like=XYZ)
rgb_p = vecmul(MATRIX_XYZ_TO_HPE, XYZ_p)
rgb_b = vecmul(MATRIX_XYZ_TO_HPE, XYZ_b)
p_rgb = rgb_p / rgb_b
rgb_w_adapted = (
rgb_w
* (spow((1 - p) * p_rgb + (1 + p) / p_rgb, 0.5))
/ (spow((1 + p) * p_rgb + (1 - p) / p_rgb, 0.5))
)
else:
rgb_w_adapted = rgb_w
# Final cone-response step for the stimulus and the reference white,
# ``rgb_a = 1 + B_rgb * (f_n(F_L * F_rgb * rgb / rgb_w_adapted) + D_rgb)``.
F_L_F_rgb = F_L[..., None] * F_rgb
rgb_n = F_L_F_rgb * rgb / rgb_w_adapted
rgb_a = 1.0 + B_rgb * (_f_n(rgb_n) + D_rgb)
rgb_w_n = F_L_F_rgb * rgb_w / rgb_w_adapted
rgb_aw = 1.0 + B_rgb * (_f_n(rgb_w_n) + D_rgb)
# Computing the achromatic post-adaptation signals :math:`A_a` and
# :math:`A_{aw}` from the adapted cone responses.
r_a, g_a, b_a = tsplit(rgb_a)
A_a = 2 * r_a + g_a + (1 / 20) * b_a - 3.05 + 1
r_aw, g_aw, b_aw = tsplit(rgb_aw)
A_aw = 2 * r_aw + g_aw + (1 / 20) * b_aw - 3.05 + 1
# Computing the colour difference signals :math:`C_1`, :math:`C_2`,
# :math:`C_3` from the adapted cone responses for the stimulus and
# the reference white.
C_1 = r_a - g_a
C_2 = g_a - b_a
C_3 = b_a - r_a
C_1_w = r_aw - g_aw
C_2_w = g_aw - b_aw
C_3_w = b_aw - r_aw
# Computing the *hue* angle :math:`h` in degrees in
# :math:`[0, 360)`.
# TODO: Implement hue quadrature & composition computation.
h = xp_degrees(xp.atan2(0.5 * (C_2 - C_3) / 4.5, C_1 - (C_2 / 11))) % 360
# Computing the eccentricity factor :math:`e_s` from the hue
# quadrature table with linear extensions outside the
# :math:`[20.14, 237.53]` range.
h_s = xp_as_float_array(HUE_DATA_FOR_HUE_QUADRATURE["h_s"], xp=xp, like=h)
e_s_lut = xp_as_float_array(HUE_DATA_FOR_HUE_QUADRATURE["e_s"], xp=xp, like=h)
e_s = xp_interp(h, h_s, e_s_lut, xp=xp)
e_s = xp.where(h < 20.14, 0.856 - (h / 20.14) * 0.056, e_s)
e_s = xp.where(h > 237.53, 0.856 + 0.344 * (360 - h) / (360 - 237.53), e_s)
# Computing the low-luminance tritanopia factor :math:`F_t`.
F_t = L_A / (L_A + 0.1)
# Computing the yellowness-blueness :math:`M_{yb}` and
# redness-greenness :math:`M_{rg}` responses for the stimulus and
# the reference white.
N_c = surround.N_c
yb_factor = e_s * (10 / 13) * N_c * N_cb
M_yb = 100 * (0.5 * (C_2 - C_3) / 4.5) * yb_factor * F_t
M_rg = 100 * (C_1 - (C_2 / 11)) * yb_factor
M_yb_w = 100 * (0.5 * (C_2_w - C_3_w) / 4.5) * yb_factor * F_t
M_rg_w = 100 * (C_1_w - (C_2_w / 11)) * yb_factor
# Computing the overall chromatic response :math:`M`.
M = xp.hypot(M_yb, M_rg)
M_w = xp.hypot(M_yb_w, M_rg_w)
# Computing the correlate of *saturation* :math:`s`.
s = 50 * M / xp.sum(rgb_a, axis=-1)
# Computing achromatic signals :math:`A` and :math:`A_w` from the
# achromatic post-adaptation signals and the scotopic response,
# mediated by the scotopic luminance level adaptation factor
# :math:`F_{LS}` and cone bleach factor :math:`B_S`.
L_AS_226 = cast("NDArrayFloat", L_AS) / 2.26
j_sc = 0.00001 / ((5 * L_AS_226) + 0.00001)
F_LS = 3800 * (j_sc**2) * (5 * L_AS_226) + 0.2 * (spow(1 - (j_sc**2), 0.4)) * (
spow(5 * L_AS_226, 1 / 6)
)
S_S_w = S_p / S_w_p
B_S = 0.5 / (1 + 0.3 * spow((5 * L_AS_226) * S_S_w, 0.3)) + 0.5 / (
1 + 5 * (5 * L_AS_226)
)
A_S = (_f_n(F_LS * S_S_w) * 3.05 * B_S) + 0.3
A = N_bb * (A_a - 1 + A_S - 0.3 + spow(1 + (0.3**2), 0.5))
S_S_w_w = S_w_p / S_w_p
B_S_w = 0.5 / (1 + 0.3 * spow((5 * L_AS_226) * S_S_w_w, 0.3)) + 0.5 / (
1 + 5 * (5 * L_AS_226)
)
A_S_w = (_f_n(F_LS * S_S_w_w) * 3.05 * B_S_w) + 0.3
A_w = N_bb * (A_aw - 1 + A_S_w - 0.3 + spow(1 + (0.3**2), 0.5))
# Computing the correlate of *brightness* :math:`Q` for the
# stimulus and the reference white.
# TODO: Implement whiteness-blackness :math:`Q_{wb}` computation.
N_b = surround.N_b
N_1 = spow(7 * A_w, 0.5) / (5.33 * spow(N_b, 0.13))
N_2 = (7 * A_w * spow(N_b, 0.362)) / 200
Q = spow(7 * (A + (M / 100)), 0.6) * N_1 - N_2
brightness_w = spow(7 * (A_w + (M_w / 100)), 0.6) * N_1 - N_2
# Computing the correlate of *Lightness* :math:`J`.
Z = 1 + spow(Y_b / Y_w, 0.5)
J = 100 * spow(Q / brightness_w, Z)
# Computing the correlate of *chroma* :math:`C_{94}`.
Y_b_Y_w_ratio = Y_b / Y_w
C_94 = (
2.44
* spow(s, 0.69)
* spow(Q / brightness_w, Y_b_Y_w_ratio)
* (1.64 - spow(0.29, Y_b_Y_w_ratio))
)
# Computing the correlate of *colourfulness* :math:`M_{94}`.
M_94 = spow(F_L, 0.15) * C_94
return CAM_Specification_Hunt(
J=as_float(J),
C=as_float(C_94),
h=as_float(from_range_degrees(h)),
s=as_float(s),
Q=as_float(Q),
M=as_float(M_94),
H=None,
HC=None,
)
def luminance_level_adaptation_factor(
L_A: ArrayLike,
) -> NDArrayFloat:
"""
Compute the *luminance* level adaptation factor :math:`F_L`.
Parameters
----------
L_A
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`.
Returns
-------
:class:`numpy.ndarray`
*Luminance* level adaptation factor :math:`F_L`.
Examples
--------
>>> luminance_level_adaptation_factor(318.31) # doctest: +ELLIPSIS
np.float64(1.1675444...)
"""
L_A = as_float_array(L_A)
k = 1 / (5 * L_A + 1)
k4 = k**4
F_L = 0.2 * k4 * (5 * L_A) + 0.1 * (1 - k4) ** 2 * spow(5 * L_A, 1 / 3)
return as_float(F_L)
def XYZ_to_rgb(XYZ: ArrayLike) -> NDArrayFloat:
"""
Convert from *CIE XYZ* tristimulus values to *Hunt-Pointer-Estevez*
:math:`\\rho\\gamma\\beta` colourspace.
Parameters
----------
XYZ
*CIE XYZ* tristimulus values.
Returns
-------
:class:`numpy.ndarray`
*Hunt-Pointer-Estevez* :math:`\\rho\\gamma\\beta` colourspace values.
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_to_rgb(XYZ) # doctest: +ELLIPSIS
array([19.4743367..., 20.3101217..., 21.78 ])
"""
return vecmul(MATRIX_XYZ_TO_HPE, XYZ)
