#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Nayatani (1995) Colour Appearance Model
=======================================
Defines *Nayatani (1995)* colour appearance model objects:
- :class:`Nayatani95_Specification`
- :func:`XYZ_to_Nayatani95`
See Also
--------
`Nayatani (1995) Colour Appearance Model IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/appearance/nayatani95.ipynb>`_ # noqa
References
----------
.. [1] **Mark D. Fairchild**, *Color Appearance Models, 3nd Edition*,
The Wiley-IS&T Series in Imaging Science and Technology,
published June 2013, ASIN: B00DAYO8E2,
Locations 4810-5085.
.. [2] **Y. Nayatani, H. Sobagaki & K. H. T. Yano**,
*Lightness dependency of chroma scales of a nonlinear color-appearance
model and its latest formulation*,
*Color Research & Application, Volume 20, Issue 3, pages 156–167,
June 1995*,
DOI: https://doi.org/10.1002/col.5080200305
"""
from __future__ import division, unicode_literals
import math
import numpy as np
from collections import namedtuple
from colour.models import XYZ_to_xy
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2014 - Colour Developers'
__license__ = 'GPL V3.0 - http://www.gnu.org/licenses/'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = ['NAYATANI95_XYZ_TO_RGB_MATRIX',
'Nayatani95_ReferenceSpecification',
'Nayatani95_Specification',
'XYZ_to_Nayatani95',
'illuminance_to_luminance',
'intermediate_values',
'XYZ_to_RGB_Nayatani95',
'beta_1',
'beta_2',
'chromatic_adaptation_exponential_factors',
'scaling_coefficient',
'achromatic_response',
'tritanopic_response',
'protanopic_response',
'brightness_correlate',
'ideal_white_brightness_correlate',
'achromatic_lightness_correlate',
'normalised_achromatic_lightness_correlate',
'hue_angle',
'saturation_components',
'saturation_correlate',
'chroma_components',
'chroma_correlate',
'colourfulness_components',
'colourfulness_correlate',
'chromatic_strength_function', ]
NAYATANI95_XYZ_TO_RGB_MATRIX = np.array(
[[0.40024, 0.70760, -0.08081],
[-0.22630, 1.16532, 0.04570],
[0.00000, 0.00000, 0.91822]])
"""
*Nayatani (1995)* colour appearance model *CIE XYZ* colourspace to cone
responses matrix.
NAYATANI95_XYZ_TO_RGB_MATRIX : array_like, (3, 3)
"""
[docs]class Nayatani95_ReferenceSpecification(
namedtuple(
'Nayatani95_ReferenceSpecification',
('Lstar_P', 'C', 'theta', 'S', 'B_r', 'M', 'H', 'H_C', 'Lstar_N'))):
"""
Defines the *Nayatani (1995)* colour appearance model reference
specification.
This specification has field names consistent with **Mark D. Fairchild**
reference.
Parameters
----------
Lstar_P : numeric
Correlate of *achromatic Lightness* :math:`L_p^\star`.
C : numeric
Correlate of *chroma* :math:`C`.
theta : numeric
*Hue* angle :math:`\\theta` in degrees.
S : numeric
Correlate of *saturation* :math:`S`.
B_r : numeric
Correlate of *brightness* :math:`B_r`.
M : numeric
Correlate of *colourfulness* :math:`M`.
H : numeric
*Hue* :math:`h` quadrature :math:`H`.
H_C : numeric
*Hue* :math:`h` composition :math:`H_C`.
Lstar_N : numeric
Correlate of *normalised achromatic Lightness* :math:`L_n^\star`.
"""
[docs]class Nayatani95_Specification(
namedtuple('Nayatani95_Specification',
('Lstar_P', 'C', 'h', 's', 'Q', 'M', 'H', 'HC', 'Lstar_N'))):
"""
Defines the *Nayatani (1995)* colour appearance model specification.
This specification has field names consistent with the remaining colour
appearance models in :mod:`colour.appearance` but diverge from
**Mark D. Fairchild** reference.
Parameters
----------
Lstar_P : numeric
Correlate of *achromatic Lightness* :math:`L_p^\star`.
C : numeric
Correlate of *chroma* :math:`C`.
h : numeric
*Hue* angle :math:`\\theta` in degrees.
s : numeric
Correlate of *saturation* :math:`S`.
Q : numeric
Correlate of *brightness* :math:`B_r`.
M : numeric
Correlate of *colourfulness* :math:`M`.
H : numeric
*Hue* :math:`h` quadrature :math:`H`.
HC : numeric
*Hue* :math:`h` composition :math:`H_C`.
Lstar_N : numeric
Correlate of *normalised achromatic Lightness* :math:`L_n^\star`.
"""
[docs]def XYZ_to_Nayatani95(XYZ,
XYZ_n,
Y_o,
E_o,
E_or,
n=1):
"""
Computes the *Nayatani (1995)* colour appearance model correlates.
Parameters
----------
XYZ : array_like, (3,)
*CIE XYZ* colourspace matrix of test sample / stimulus in domain
[0, 100].
XYZ_n : array_like, (3,)
*CIE XYZ* colourspace matrix of reference white in domain [0, 100].
Y_o : numeric
Luminance factor :math:`Y_o` of achromatic background as percentage in
domain [0.18,]
E_o : numeric
Illuminance :math:`E_o` of the viewing field in lux.
E_or : numeric
Normalising illuminance :math:`E_{or}` in lux usually in domain
[1000, 3000]
n : numeric, optional
Noise term used in the non linear chromatic adaptation model.
Returns
-------
Nayatani95_Specification
*Nayatani (1995)* colour appearance model specification.
Warning
-------
The input domain of that definition is non standard!
Notes
-----
- Input *CIE XYZ* colourspace matrix is in domain [0, 100].
- Input *CIE XYZ_n* colourspace matrix is in domain [0, 100].
Raises
------
ValueError
If Luminance factor :math:`Y_o` is not greater or equal than 18%.
Examples
--------
>>> XYZ = np.array([19.01, 20, 21.78])
>>> XYZ_n = np.array([95.05, 100, 108.88])
>>> Y_o = 20.0
>>> E_o = 5000.0
>>> E_or = 1000.0
>>> XYZ_to_Nayatani95(XYZ, XYZ_n, Y_o, E_o, E_or) # doctest: +ELLIPSIS
Nayatani95_Specification(Lstar_P=49.9998829..., C=0.0133550..., h=257.5232268..., s=0.0133550..., Q=62.6266734..., M=0.0167262..., H=None, HC=None, Lstar_N=50.0039154...)
"""
if np.any(Y_o < 0.18):
raise ValueError(
'Luminance factor "Y_o" of achromatic background must '
'be greater or equal than 18%!')
X, Y, Z = np.ravel(XYZ)
# Computing adapting luminance :math:`L_o` and normalising luminance
# :math:`L_{or}` in in :math:`cd/m^2`.
L_o = illuminance_to_luminance(E_o, Y_o)
L_or = illuminance_to_luminance(E_or, Y_o)
# Computing :math:`\xi`, :math:`\eta`, :math:`\zeta` values.
xi, eta, zeta = x_e_z = intermediate_values(XYZ_n)
# Computing adapting field cone responses.
RGB_o = ((Y_o * E_o) / (100 * np.pi)) * x_e_z
# Computing stimulus cone responses.
R, G, B = RGB = XYZ_to_RGB_Nayatani95(np.array([X, Y, Z]))
# Computing exponential factors of the chromatic adaptation.
bRGB_o = chromatic_adaptation_exponential_factors(RGB_o)
bL_or = beta_1(L_or)
# Computing scaling coefficients :math:`e(R)` and :math:`e(G)`
eR = scaling_coefficient(R, xi)
eG = scaling_coefficient(G, eta)
# Computing opponent colour dimensions.
# Computing achromatic response :math:`Q`:
Q_response = achromatic_response(RGB, bRGB_o, x_e_z,
bL_or, eR, eG, n)
# Computing tritanopic response :math:`t`:
t_response = tritanopic_response(RGB, bRGB_o, x_e_z, n)
# Computing protanopic response :math:`p`:
p_response = protanopic_response(RGB, bRGB_o, x_e_z, n)
# -------------------------------------------------------------------------
# Computing the correlate of *brightness* :math:`B_r`.
# -------------------------------------------------------------------------
B_r = brightness_correlate(bRGB_o, bL_or, Q_response)
# Computing *brightness* :math:`B_{rw}` of ideal white.
brightness_ideal_white = ideal_white_brightness_correlate(bRGB_o,
x_e_z,
bL_or,
n)
# -------------------------------------------------------------------------
# Computing the correlate of achromatic *Lightness* :math:`L_p^\star`.
# -------------------------------------------------------------------------
Lstar_P = (
achromatic_lightness_correlate(Q_response))
# -------------------------------------------------------------------------
# Computing the correlate of normalised achromatic *Lightness*
# :math:`L_n^\star`.
# -------------------------------------------------------------------------
Lstar_N = (
normalised_achromatic_lightness_correlate(B_r,
brightness_ideal_white))
# -------------------------------------------------------------------------
# Computing the *hue* angle :math:`\\theta`.
# -------------------------------------------------------------------------
theta = hue_angle(p_response, t_response)
# TODO: Implement hue quadrature & composition computation.
# -------------------------------------------------------------------------
# Computing the correlate of *saturation* :math:`S`.
# -------------------------------------------------------------------------
S_RG, S_YB = saturation_components(theta, bL_or,
t_response,
p_response)
S = saturation_correlate(S_RG, S_YB)
# -------------------------------------------------------------------------
# Computing the correlate of *chroma* :math:`C`.
# -------------------------------------------------------------------------
C_RG, C_YB = chroma_components(Lstar_P, S_RG, S_YB)
C = chroma_correlate(Lstar_P, S)
# -------------------------------------------------------------------------
# Computing the correlate of *colourfulness* :math:`M`.
# -------------------------------------------------------------------------
# TODO: Investigate components usage.
M_RG, M_YB = colourfulness_components(C_RG, C_YB,
brightness_ideal_white)
M = colourfulness_correlate(C, brightness_ideal_white)
return Nayatani95_Specification(Lstar_P,
C,
theta,
S,
B_r,
M,
None,
None,
Lstar_N)
[docs]def illuminance_to_luminance(E, Y_f):
"""
Converts given *illuminance* :math:`E` value in lux to *luminance* in
:math:`cd/m^2`.
Parameters
----------
E : numeric
*Illuminance* :math:`E` in lux.
Y_f : numeric
*Luminance* factor :math:`Y_f` in :math:`cd/m^2`.
Returns
-------
numeric
*Luminance* :math:`Y` in :math:`cd/m^2`.
Examples
--------
>>> illuminance_to_luminance(5000.0, 20.0) # doctest: +ELLIPSIS
318.3098861...
"""
return Y_f * E / (100 * np.pi)
[docs]def XYZ_to_RGB_Nayatani95(XYZ):
"""
Converts from *CIE XYZ* colourspace to cone responses.
Parameters
----------
XYZ : array_like, (3,)
*CIE XYZ* colourspace matrix.
Returns
-------
ndarray, (3,)
Cone responses.
Examples
--------
>>> XYZ = np.array([19.01, 20, 21.78])
>>> XYZ_to_RGB_Nayatani95(XYZ) # doctest: +ELLIPSIS
array([ 20.000520..., 19.999783..., 19.998831...])
"""
return NAYATANI95_XYZ_TO_RGB_MATRIX.dot(XYZ)
[docs]def beta_1(x):
"""
Computes the exponent :math:`\\beta_1` for the middle and long-wavelength
sensitive cones.
Parameters
----------
x: numeric
Middle and long-wavelength sensitive cone response.
Returns
-------
numeric
Exponent :math:`\\beta_1`.
Examples
--------
>>> beta_1(318.323316315) # doctest: +ELLIPSIS
4.6106222...
"""
return (6.469 + 6.362 * (x ** 0.4495)) / (6.469 + (x ** 0.4495))
[docs]def beta_2(x):
"""
Computes the exponent :math:`\\beta_2` for the short-wavelength sensitive
cones.
Parameters
----------
x: numeric
Short-wavelength sensitive cone response.
Returns
-------
numeric
Exponent :math:`\\beta_2`.
Examples
--------
>>> beta_2(318.323316315) # doctest: +ELLIPSIS
4.6522416...
"""
return 0.7844 * (8.414 + 8.091 * (x ** 0.5128)) / (8.414 + (x ** 0.5128))
[docs]def chromatic_adaptation_exponential_factors(RGB_o):
"""
Returns the chromatic adaptation exponential factors :math:`\\beta_1(R_o)`,
`math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)` of given cone responses.
Parameters
----------
RGB_o: ndarray, (3,)
Cone responses.
Returns
-------
ndarray, (3,)
Chromatic adaptation exponential factors :math:`\\beta_1(R_o)`,
`math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)`.
Examples
--------
>>> RGB_o = np.array([318.32331631, 318.30352317, 318.23283482])
>>> chromatic_adaptation_exponential_factors(RGB_o) # doctest: +ELLIPSIS
array([ 4.6106222..., 4.6105892..., 4.6520698...])
"""
R_o, G_o, B_o = np.ravel(RGB_o)
bR_o = beta_1(R_o)
bG_o = beta_1(G_o)
bB_o = beta_2(B_o)
return np.array([bR_o, bG_o, bB_o])
[docs]def scaling_coefficient(x, y):
"""
Returns the scaling coefficient :math:`e(R)` or :math:`e(G)`.
Parameters
----------
x: numeric
Cone response.
y: numeric
Intermediate value.
Returns
-------
numeric
Scaling coefficient :math:`e(R)` or :math:`e(G)`.
Examples
--------
>>> x = 20.000520600000002
>>> y = 1.000042192
>>> scaling_coefficient(x, y)
1
"""
return 1.758 if x >= (20 * y) else 1
[docs]def achromatic_response(RGB, bRGB_o, x_e_z, bL_or, eR, eG, n=1):
"""
Returns the achromatic response :math:`Q` from given stimulus cone
responses.
Parameters
----------
RGB: ndarray, (3,)
Stimulus cone responses.
bRGB_o: ndarray, (3,)
Chromatic adaptation exponential factors :math:`\\beta_1(R_o)`,
`math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)`.
x_e_z: ndarray, (3,)
Intermediate values :math:`\\xi`, :math:`\eta`, :math:`\zeta`.
bL_or: numeric
Normalising chromatic adaptation exponential factor
:math:`\\beta_1(B_or)`.
eR: numeric
Scaling coefficient :math:`e(R)`.
eG: numeric
Scaling coefficient :math:`e(G)`.
n : numeric, optional
Noise term used in the non linear chromatic adaptation model.
Returns
-------
numeric
Achromatic response :math:`Q`.
Examples
--------
>>> RGB = np.array([20.0005206, 19.999783, 19.9988316])
>>> bRGB_o = np.array([4.61062223, 4.61058926, 4.65206986])
>>> x_e_z = np.array([1.00004219, 0.99998001, 0.99975794])
>>> bL_or = 3.6810214956040888
>>> eR = 1.0
>>> eG = 1.758
>>> n = 1.0
>>> achromatic_response(RGB, bRGB_o, x_e_z, bL_or, eR, eG, n) # noqa # doctest: +ELLIPSIS
-0.0001169...
"""
R, G, B = RGB
bR_o, bG_o, bB_o = bRGB_o
xi, eta, zeta = x_e_z
Q = (2 / 3) * bR_o * eR * np.log10((R + n) / (20 * xi + n))
Q += (1 / 3) * bG_o * eG * np.log10((G + n) / (20 * eta + n))
Q *= 41.69 / bL_or
return Q
[docs]def tritanopic_response(RGB, bRGB_o, x_e_z, n):
"""
Returns the tritanopic response :math:`t` from given stimulus cone
responses.
Parameters
----------
RGB: ndarray, (3,)
Stimulus cone responses.
bRGB_o: ndarray, (3,)
Chromatic adaptation exponential factors :math:`\\beta_1(R_o)`,
`math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)`.
x_e_z: ndarray, (3,)
Intermediate values :math:`\\xi`, :math:`\eta`, :math:`\zeta`.
n : numeric, optional
Noise term used in the non linear chromatic adaptation model.
Returns
-------
numeric
Tritanopic response :math:`t`.
Examples
--------
>>> RGB = np.array([20.0005206, 19.999783, 19.9988316])
>>> bRGB_o = np.array([4.61062223, 4.61058926, 4.65206986])
>>> x_e_z = np.array([1.00004219, 0.99998001, 0.99975794])
>>> n = 1.0
>>> tritanopic_response(RGB, bRGB_o, x_e_z, n) # doctest: +ELLIPSIS
-1.7703650...e-05
"""
R, G, B = RGB
bR_o, bG_o, bB_o = bRGB_o
xi, eta, zeta = x_e_z
t = (1 / 1) * bR_o * np.log10((R + n) / (20 * xi + n))
t += - (12 / 11) * bG_o * np.log10((G + n) / (20 * eta + n))
t += (1 / 11) * bB_o * np.log10((B + n) / (20 * zeta + n))
return t
[docs]def protanopic_response(RGB, bRGB_o, x_e_z, n):
"""
Returns the protanopic response :math:`p` from given stimulus cone
responses.
Parameters
----------
RGB: ndarray, (3,)
Stimulus cone responses.
bRGB_o: ndarray, (3,)
Chromatic adaptation exponential factors :math:`\\beta_1(R_o)`,
`math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)`.
x_e_z: ndarray, (3,)
Intermediate values :math:`\\xi`, :math:`\eta`, :math:`\zeta`.
n : numeric, optional
Noise term used in the non linear chromatic adaptation model.
Returns
-------
numeric
Protanopic response :math:`p`.
Examples
--------
>>> RGB = np.array([20.0005206, 19.999783, 19.9988316])
>>> bRGB_o = np.array([4.61062223, 4.61058926, 4.65206986])
>>> x_e_z = np.array([1.00004219, 0.99998001, 0.99975794])
>>> n = 1.0
>>> protanopic_response(RGB, bRGB_o, x_e_z, n) # doctest: +ELLIPSIS
-8.0021426...e-05
"""
R, G, B = RGB
bR_o, bG_o, bB_o = bRGB_o
xi, eta, zeta = x_e_z
p = (1 / 9) * bR_o * np.log10((R + n) / (20 * xi + n))
p += (1 / 9) * bG_o * np.log10((G + n) / (20 * eta + n))
p += - (2 / 9) * bB_o * np.log10((B + n) / (20 * zeta + n))
return p
[docs]def brightness_correlate(bRGB_o, bL_or, Q):
"""
Returns the *brightness* correlate :math:`B_r`.
Parameters
----------
bRGB_o: ndarray, (3,)
Chromatic adaptation exponential factors :math:`\\beta_1(R_o)`,
`math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)`.
bL_or: numeric
Normalising chromatic adaptation exponential factor
:math:`\\beta_1(B_or)`.
Q : numeric
Achromatic response :math:`Q`.
Returns
-------
numeric
*Brightness* correlate :math:`B_r`.
Examples
--------
>>> bRGB_o = np.array([4.61062223, 4.61058926, 4.65206986])
>>> bL_or = 3.6810214956040888
>>> Q = -0.000117024294955
>>> brightness_correlate(bRGB_o, bL_or, Q) # doctest: +ELLIPSIS
62.6266734...
"""
bR_o, bG_o, bB_o = bRGB_o
B_r = (50 / bL_or) * ((2 / 3) * bR_o + (1 / 3) * bG_o) + Q
return B_r
[docs]def ideal_white_brightness_correlate(bRGB_o, x_e_z, bL_or, n):
"""
Returns the ideal white *brightness* correlate :math:`B_{rw}`.
Parameters
----------
bRGB_o: ndarray, (3,)
Chromatic adaptation exponential factors :math:`\\beta_1(R_o)`,
`math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)`.
x_e_z: ndarray, (3,)
Intermediate values :math:`\\xi`, :math:`\eta`, :math:`\zeta`.
bL_or: numeric
Normalising chromatic adaptation exponential factor
:math:`\\beta_1(B_or)`.
n : numeric, optional
Noise term used in the non linear chromatic adaptation model.
Returns
-------
numeric
Ideal white *brightness* correlate :math:`B_{rw}`.
Examples
--------
>>> bRGB_o = np.array([4.61062223, 4.61058926, 4.65206986])
>>> x_e_z = np.array([1.00004219, 0.99998001, 0.99975794])
>>> bL_or = 3.6810214956040888
>>> n = 1.0
>>> ideal_white_brightness_correlate(bRGB_o, x_e_z, bL_or, n) # noqa # doctest: +ELLIPSIS
125.2435392...
"""
bR_o, bG_o, bB_o = bRGB_o
xi, eta, zeta = x_e_z
B_rw = (2 / 3) * bR_o * 1.758 * np.log10((100 * xi + n) / (20 * xi + n))
B_rw += (1 / 3) * bG_o * 1.758 * np.log10((100 * eta + n) / (20 * eta + n))
B_rw *= 41.69 / bL_or
B_rw += (50 / bL_or) * (2 / 3) * bR_o
B_rw += (50 / bL_or) * (1 / 3) * bG_o
return B_rw
[docs]def achromatic_lightness_correlate(Q):
"""
Returns the *achromatic Lightness* correlate :math:`L_p^\star`.
Parameters
----------
Q : numeric
Achromatic response :math:`Q`.
Returns
-------
numeric
*Achromatic Lightness* correlate :math:`L_p^\star`.
Examples
--------
>>> Q = -0.000117024294955
>>> achromatic_lightness_correlate(Q) # doctest: +ELLIPSIS
49.9998829...
"""
return Q + 50
[docs]def normalised_achromatic_lightness_correlate(B_r, B_rw):
"""
Returns the *normalised achromatic Lightness* correlate :math:`L_n^\star`.
Parameters
----------
B_r : numeric
*Brightness* correlate :math:`B_r`.
B_rw : numeric
Ideal white *brightness* correlate :math:`B_{rw}`.
Returns
-------
numeric
*Normalised achromatic Lightness* correlate :math:`L_n^\star`.
Examples
--------
>>> B_r = 62.626673467230766
>>> B_rw = 125.24353925846037
>>> normalised_achromatic_lightness_correlate(B_r, B_rw) # noqa # doctest: +ELLIPSIS
50.0039154...
"""
return 100 * (B_r / B_rw)
[docs]def hue_angle(p, t):
"""
Returns the *hue* angle :math:`h` in degrees.
Parameters
----------
p : numeric
Protanopic response :math:`p`.
t : numeric
Tritanopic response :math:`t`.
Returns
-------
numeric
*Hue* angle :math:`h` in degrees.
Examples
--------
>>> p = -8.002142682085493e-05
>>> t = -1.7703650668990973e-05
>>> hue_angle(p, t) # doctest: +ELLIPSIS
257.5250300...
"""
h_L = math.degrees(np.arctan2(p, t)) % 360
return h_L
[docs]def chromatic_strength_function(theta):
"""
Defines the chromatic strength function :math:`E_s(\\theta)` used to
correct saturation scale as function of hue angle :math:`\\theta`.
Parameters
----------
theta : numeric
Hue angle :math:`\\theta`
Returns
-------
numeric
Corrected saturation scale.
Examples
--------
>>> chromatic_strength_function(4.49462820973) # doctest: +ELLIPSIS
1.2267869...
"""
E_s = 0.9394
E_s += - 0.2478 * np.sin(1 * theta)
E_s += - 0.0743 * np.sin(2 * theta)
E_s += + 0.0666 * np.sin(3 * theta)
E_s += - 0.0186 * np.sin(4 * theta)
E_s += - 0.0055 * np.cos(1 * theta)
E_s += - 0.0521 * np.cos(2 * theta)
E_s += - 0.0573 * np.cos(3 * theta)
E_s += - 0.0061 * np.cos(4 * theta)
return E_s
[docs]def saturation_components(h, bL_or, t, p):
"""
Returns the *saturation* components :math:`S_{RG}` and :math:`S_{YB}`.
Parameters
----------
h: numeric
Correlate of *hue* :math:`h` in degrees.
bL_or: numeric
Normalising chromatic adaptation exponential factor
:math:`\\beta_1(B_or)`.
t : numeric
Tritanopic response :math:`t`.
p : numeric
Protanopic response :math:`p`.
Returns
-------
numeric
*Saturation* components :math:`S_{RG}` and :math:`S_{YB}`.
Examples
--------
>>> h = 257.52322689806243
>>> bL_or = 3.6810214956040888
>>> t = -1.7706764677181658e-05
>>> p = -8.0023561356363753e-05
>>> saturation_components(h, bL_or, t, p) # doctest: +ELLIPSIS
(-0.0028852..., -0.0130396...)
"""
E_s = chromatic_strength_function(math.radians(h))
S_RG = (488.93 / bL_or) * E_s * t
S_YB = (488.93 / bL_or) * E_s * p
return S_RG, S_YB
[docs]def saturation_correlate(S_RG, S_YB):
"""
Returns the correlate of *saturation* :math:`S`.
Parameters
----------
S_RG : numeric
*Saturation* component :math:`S_{RG}`.
S_YB : numeric
*Saturation* component :math:`S_{YB}`.
Returns
-------
numeric
Correlate of *saturation* :math:`S`.
Examples
--------
>>> S_RG = -0.0028852716381965863
>>> S_YB = -0.013039632941332499
>>> saturation_correlate(S_RG, S_YB) # doctest: +ELLIPSIS
0.0133550...
"""
S = np.sqrt((S_RG ** 2) + (S_YB ** 2))
return S
[docs]def chroma_components(Lstar_P, S_RG, S_YB):
"""
Returns the *chroma* components :math:`C_{RG}` and :math:`C_{YB}`.
Parameters
----------
Lstar_P : numeric
*Achromatic Lightness* correlate :math:`L_p^\star`.
S_RG : numeric
*Saturation* component :math:`S_{RG}`.
S_YB : numeric
*Saturation* component :math:`S_{YB}`.
Returns
-------
numeric
*Chroma* components :math:`C_{RG}` and :math:`C_{YB}`.
Examples
--------
>>> Lstar_P = 49.99988297570504
>>> S_RG = -0.0028852716381965863
>>> S_YB = -0.013039632941332499
>>> chroma_components(Lstar_P, S_RG, S_YB) # doctest: +ELLIPSIS
(-0.0028852..., -0.0130396...)
"""
C_RG = ((Lstar_P / 50) ** 0.7) * S_RG
C_YB = ((Lstar_P / 50) ** 0.7) * S_YB
return C_RG, C_YB
[docs]def chroma_correlate(Lstar_P, S):
"""
Returns the correlate of *chroma* :math:`C`.
Parameters
----------
Lstar_P : numeric
*Achromatic Lightness* correlate :math:`L_p^\star`.
S : numeric
Correlate of *saturation* :math:`S`.
Returns
-------
numeric
Correlate of *chroma* :math:`C`.
Examples
--------
>>> Lstar_P = 49.99988297570504
>>> S = 0.013355029751777615
>>> chroma_correlate(Lstar_P, S) # doctest: +ELLIPSIS
0.0133550...
"""
C = ((Lstar_P / 50) ** 0.7) * S
return C
[docs]def colourfulness_components(C_RG, C_YB, B_rw):
"""
Returns the *colourfulness* components :math:`M_{RG}` and :math:`M_{YB}`.
Parameters
----------
C_RG : numeric
*Chroma* component :math:`C_{RG}`.
C_YB : numeric
*Chroma* component :math:`C_{YB}`.
B_rw : numeric
Ideal white *brightness* correlate :math:`B_{rw}`.
Returns
-------
numeric
*Colourfulness* components :math:`M_{RG}` and :math:`M_{YB}`.
Examples
--------
>>> C_RG = -0.0028852716381965863
>>> C_YB = -0.013039632941332499
>>> B_rw = 125.24353925846037
>>> colourfulness_components(C_RG, C_YB, B_rw) # doctest: +ELLIPSIS
(-0.0036136..., -0.0163312...)
"""
M_RG = C_RG * B_rw / 100
M_YB = C_YB * B_rw / 100
return M_RG, M_YB
[docs]def colourfulness_correlate(C, B_rw):
"""
Returns the correlate of *colourfulness* :math:`M`.
Parameters
----------
C : numeric
Correlate of *chroma* :math:`C`.
B_rw : numeric
Ideal white *brightness* correlate :math:`B_{rw}`.
Returns
-------
numeric
Correlate of *colourfulness* :math:`M`.
Examples
--------
>>> C = 0.013355007871688761
>>> B_rw = 125.24353925846037
>>> colourfulness_correlate(C, B_rw) # doctest: +ELLIPSIS
0.0167262...
"""
M = C * B_rw / 100
return M
Colour 0.3