Source code for colour.appearance.nayatani95

# -*- coding: utf-8 -*-
"""
Nayatani (1995) Colour Appearance Model
=======================================

Defines *Nayatani (1995)* colour appearance model objects:

-   :class:`colour.Nayatani95_Specification`
-   :func:`colour.XYZ_to_Nayatani95`

References
----------
-   :cite:`Fairchild2013ba` : Fairchild, M. D. (2013). The Nayatani et al.
    Model. In Color Appearance Models (3rd ed., pp. 4810-5085). Wiley.
    ISBN:B00DAYO8E2
-   :cite:`Nayatani1995a` : Nayatani, Y., Sobagaki, H., & Yano, K. H. T.
    (1995). Lightness dependency of chroma scales of a nonlinear
    color-appearance model and its latest formulation. Color Research &
    Application, 20(3), 156-167. doi:10.1002/col.5080200305
"""

from __future__ import division, unicode_literals

import numpy as np
from collections import namedtuple

from colour.algebra import spow
from colour.adaptation.cie1994 import (CIE1994_XYZ_TO_RGB_MATRIX, beta_1,
                                       exponential_factors,
                                       intermediate_values)
from colour.models import XYZ_to_xy
from colour.utilities import (as_float_array, dot_vector, from_range_degrees,
                              to_domain_100, tsplit, tstack)

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2020 - 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__ = [
    'NAYATANI95_XYZ_TO_RGB_MATRIX', 'Nayatani95_ReferenceSpecification',
    'Nayatani95_Specification', 'XYZ_to_Nayatani95',
    'illuminance_to_luminance', 'XYZ_to_RGB_Nayatani95', '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 = CIE1994_XYZ_TO_RGB_MATRIX
"""
*Nayatani (1995)* colour appearance model *CIE XYZ* tristimulus values to cone
responses matrix.

NAYATANI95_XYZ_TO_RGB_MATRIX : array_like, (3, 3)
"""


class Nayatani95_ReferenceSpecification(
        namedtuple('Nayatani95_ReferenceSpecification',
                   ('L_star_P', 'C', 'theta', 'S', 'B_r', 'M', 'H', 'H_C',
                    'L_star_N'))):
    """
    Defines the *Nayatani (1995)* colour appearance model reference
    specification.

    This specification has field names consistent with *Fairchild (2013)*
    reference.

    Parameters
    ----------
    L_star_P : numeric or array_like
        Correlate of *achromatic Lightness* :math:`L_p^\\star`.
    C : numeric or array_like
        Correlate of *chroma* :math:`C`.
    theta : numeric or array_like
        *Hue* angle :math:`\\theta` in degrees.
    S : numeric or array_like
        Correlate of *saturation* :math:`S`.
    B_r : numeric or array_like
        Correlate of *brightness* :math:`B_r`.
    M : numeric or array_like
        Correlate of *colourfulness* :math:`M`.
    H : numeric or array_like
        *Hue* :math:`h` quadrature :math:`H`.
    H_C : numeric or array_like
        *Hue* :math:`h` composition :math:`H_C`.
    L_star_N : numeric or array_like
        Correlate of *normalised achromatic Lightness* :math:`L_n^\\star`.

    References
    ----------
    :cite:`Fairchild2013ba`, :cite:`Nayatani1995a`
    """


[docs]class Nayatani95_Specification( namedtuple( 'Nayatani95_Specification', ('L_star_P', 'C', 'h', 's', 'Q', 'M', 'H', 'HC', 'L_star_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 *Fairchild (2013)* reference. Parameters ---------- L_star_P : numeric or array_like Correlate of *achromatic Lightness* :math:`L_p^\\star`. C : numeric or array_like Correlate of *chroma* :math:`C`. h : numeric or array_like *Hue* angle :math:`\\theta` in degrees. s : numeric or array_like Correlate of *saturation* :math:`S`. Q : numeric or array_like Correlate of *brightness* :math:`B_r`. M : numeric or array_like Correlate of *colourfulness* :math:`M`. H : numeric or array_like *Hue* :math:`h` quadrature :math:`H`. HC : numeric or array_like *Hue* :math:`h` composition :math:`H_C`. L_star_N : numeric or array_like Correlate of *normalised achromatic Lightness* :math:`L_n^\\star`. Notes ----- - This specification is the one used in the current model implementation. References ---------- :cite:`Fairchild2013ba`, :cite:`Nayatani1995a` """
[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 *CIE XYZ* tristimulus values of test sample / stimulus. XYZ_n : array_like *CIE XYZ* tristimulus values of reference white. Y_o : numeric or array_like Luminance factor :math:`Y_o` of achromatic background as percentage normalised to domain [0.18, 1.0] in **'Reference'** domain-range scale. E_o : numeric or array_like Illuminance :math:`E_o` of the viewing field in lux. E_or : numeric or array_like Normalising illuminance :math:`E_{or}` in lux usually normalised to domain [1000, 3000]. n : numeric or array_like, optional Noise term used in the non linear chromatic adaptation model. Returns ------- Nayatani95_Specification *Nayatani (1995)* colour appearance model specification. Notes ----- +--------------------------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +================================+=======================+===============+ | ``XYZ`` | [0, 100] | [0, 1] | +--------------------------------+-----------------------+---------------+ | ``XYZ_n`` | [0, 100] | [0, 1] | +--------------------------------+-----------------------+---------------+ +--------------------------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +================================+=======================+===============+ | ``Nayatani95_Specification.h`` | [0, 360] | [0, 1] | +--------------------------------+-----------------------+---------------+ References ---------- :cite:`Fairchild2013ba`, :cite:`Nayatani1995a` Examples -------- >>> XYZ = np.array([19.01, 20.00, 21.78]) >>> XYZ_n = np.array([95.05, 100.00, 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(L_star_P=49.9998829..., C=0.0133550..., \ h=257.5232268..., s=0.0133550..., Q=62.6266734..., M=0.0167262..., H=None, \ HC=None, L_star_N=50.0039154...) """ XYZ = to_domain_100(XYZ) XYZ_n = to_domain_100(XYZ_n) Y_o = as_float_array(Y_o) E_o = as_float_array(E_o) E_or = as_float_array(E_or) # 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. xez = intermediate_values(XYZ_to_xy(XYZ_n / 100)) xi, eta, _zeta = tsplit(xez) # Computing adapting field cone responses. RGB_o = (( (Y_o[..., np.newaxis] * E_o[..., np.newaxis]) / (100 * np.pi)) * xez) # Computing stimulus cone responses. RGB = XYZ_to_RGB_Nayatani95(XYZ) R, G, _B = tsplit(RGB) # Computing exponential factors of the chromatic adaptation. bRGB_o = 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, xez, bL_or, eR, eG, n) # Computing tritanopic response :math:`t`: t_response = tritanopic_response(RGB, bRGB_o, xez, n) # Computing protanopic response :math:`p`: p_response = protanopic_response(RGB, bRGB_o, xez, 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, xez, bL_or, n) # Computing the correlate of achromatic *Lightness* :math:`L_p^\\star`. L_star_P = (achromatic_lightness_correlate(Q_response)) # Computing the correlate of normalised achromatic *Lightness* # :math:`L_n^\\star`. L_star_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 = tsplit( 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 = tsplit(chroma_components(L_star_P, S_RG, S_YB)) C = chroma_correlate(L_star_P, S) # Computing the correlate of *colourfulness* :math:`M`. # TODO: Investigate components usage. # M_RG, M_YB = tsplit(colourfulness_components(C_RG, C_YB, # brightness_ideal_white)) M = colourfulness_correlate(C, brightness_ideal_white) return Nayatani95_Specification(L_star_P, C, from_range_degrees(theta), S, B_r, M, None, None, L_star_N)
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 or array_like *Illuminance* :math:`E` in lux. Y_f : numeric or array_like *Luminance* factor :math:`Y_f` in :math:`cd/m^2`. Returns ------- numeric or ndarray *Luminance* :math:`Y` in :math:`cd/m^2`. Examples -------- >>> illuminance_to_luminance(5000.0, 20.0) # doctest: +ELLIPSIS 318.3098861... """ E = as_float_array(E) Y_f = as_float_array(Y_f) return Y_f * E / (100 * np.pi) def XYZ_to_RGB_Nayatani95(XYZ): """ Converts from *CIE XYZ* tristimulus values to cone responses. Parameters ---------- XYZ : array_like *CIE XYZ* tristimulus values. Returns ------- ndarray Cone responses. Examples -------- >>> XYZ = np.array([19.01, 20.00, 21.78]) >>> XYZ_to_RGB_Nayatani95(XYZ) # doctest: +ELLIPSIS array([ 20.0005206..., 19.999783 ..., 19.9988316...]) """ return dot_vector(NAYATANI95_XYZ_TO_RGB_MATRIX, XYZ) def scaling_coefficient(x, y): """ Returns the scaling coefficient :math:`e(R)` or :math:`e(G)`. Parameters ---------- x: numeric or array_like Cone response. y: numeric or array_like Intermediate value. Returns ------- numeric or ndarray Scaling coefficient :math:`e(R)` or :math:`e(G)`. Examples -------- >>> x = 20.000520600000002 >>> y = 1.000042192 >>> scaling_coefficient(x, y) array(1.0) """ x = as_float_array(x) y = as_float_array(y) return np.where(x >= (20 * y), 1.758, 1) def achromatic_response(RGB, bRGB_o, xez, bL_or, eR, eG, n=1): """ Returns the achromatic response :math:`Q` from given stimulus cone responses. Parameters ---------- RGB: ndarray Stimulus cone responses. bRGB_o: ndarray Chromatic adaptation exponential factors :math:`\\beta_1(R_o)`, :math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)`. xez: ndarray Intermediate values :math:`\\xi`, :math:`\\eta`, :math:`\\zeta`. bL_or: numeric or array_like Normalising chromatic adaptation exponential factor :math:`\\beta_1(B_or)`. eR: numeric or array_like Scaling coefficient :math:`e(R)`. eG: numeric or array_like Scaling coefficient :math:`e(G)`. n : numeric or array_like, optional Noise term used in the non linear chromatic adaptation model. Returns ------- numeric or ndarray Achromatic response :math:`Q`. Examples -------- >>> RGB = np.array([20.00052060, 19.99978300, 19.99883160]) >>> bRGB_o = np.array([4.61062223, 4.61058926, 4.65206986]) >>> xez = np.array([1.00004219, 0.99998001, 0.99975794]) >>> bL_or = 3.681021495604089 >>> eR = 1.0 >>> eG = 1.758 >>> n = 1.0 >>> achromatic_response(RGB, bRGB_o, xez, bL_or, eR, eG, n) ... # doctest: +ELLIPSIS -0.0001169... """ R, G, _B = tsplit(RGB) bR_o, bG_o, _bB_o = tsplit(bRGB_o) xi, eta, _zeta = tsplit(xez) bL_or = as_float_array(bL_or) eR = as_float_array(eR) eG = as_float_array(eG) 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 def tritanopic_response(RGB, bRGB_o, xez, n): """ Returns the tritanopic response :math:`t` from given stimulus cone responses. Parameters ---------- RGB: ndarray Stimulus cone responses. bRGB_o: ndarray Chromatic adaptation exponential factors :math:`\\beta_1(R_o)`, :math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)`. xez: ndarray Intermediate values :math:`\\xi`, :math:`\\eta`, :math:`\\zeta`. n : numeric or array_like, optional Noise term used in the non linear chromatic adaptation model. Returns ------- numeric or ndarray Tritanopic response :math:`t`. Examples -------- >>> RGB = np.array([20.00052060, 19.99978300, 19.99883160]) >>> bRGB_o = np.array([4.61062223, 4.61058926, 4.65206986]) >>> xez = np.array([1.00004219, 0.99998001, 0.99975794]) >>> n = 1.0 >>> tritanopic_response(RGB, bRGB_o, xez, n) # doctest: +ELLIPSIS -1.7703650...e-05 """ R, G, B = tsplit(RGB) bR_o, bG_o, bB_o = tsplit(bRGB_o) xi, eta, zeta = tsplit(xez) t = 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 def protanopic_response(RGB, bRGB_o, xez, n): """ Returns the protanopic response :math:`p` from given stimulus cone responses. Parameters ---------- RGB: ndarray Stimulus cone responses. bRGB_o: ndarray Chromatic adaptation exponential factors :math:`\\beta_1(R_o)`, :math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)`. xez: ndarray Intermediate values :math:`\\xi`, :math:`\\eta`, :math:`\\zeta`. n : numeric or array_like, optional Noise term used in the non linear chromatic adaptation model. Returns ------- numeric or ndarray Protanopic response :math:`p`. Examples -------- >>> RGB = np.array([20.00052060, 19.99978300, 19.99883160]) >>> bRGB_o = np.array([4.61062223, 4.61058926, 4.65206986]) >>> xez = np.array([1.00004219, 0.99998001, 0.99975794]) >>> n = 1.0 >>> protanopic_response(RGB, bRGB_o, xez, n) # doctest: +ELLIPSIS -8.0021426...e-05 """ R, G, B = tsplit(RGB) bR_o, bG_o, bB_o = tsplit(bRGB_o) xi, eta, zeta = tsplit(xez) 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 def brightness_correlate(bRGB_o, bL_or, Q): """ Returns the *brightness* correlate :math:`B_r`. Parameters ---------- bRGB_o: ndarray Chromatic adaptation exponential factors :math:`\\beta_1(R_o)`, :math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)`. bL_or: numeric or array_like Normalising chromatic adaptation exponential factor :math:`\\beta_1(B_or)`. Q : numeric or array_like Achromatic response :math:`Q`. Returns ------- numeric or ndarray *Brightness* correlate :math:`B_r`. Examples -------- >>> bRGB_o = np.array([4.61062223, 4.61058926, 4.65206986]) >>> bL_or = 3.681021495604089 >>> Q = -0.000117024294955 >>> brightness_correlate(bRGB_o, bL_or, Q) # doctest: +ELLIPSIS 62.6266734... """ bR_o, bG_o, _bB_o = tsplit(bRGB_o) bL_or = as_float_array(bL_or) Q = as_float_array(Q) B_r = (50 / bL_or) * ((2 / 3) * bR_o + (1 / 3) * bG_o) + Q return B_r def ideal_white_brightness_correlate(bRGB_o, xez, bL_or, n): """ Returns the ideal white *brightness* correlate :math:`B_{rw}`. Parameters ---------- bRGB_o: ndarray Chromatic adaptation exponential factors :math:`\\beta_1(R_o)`, :math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)`. xez: ndarray Intermediate values :math:`\\xi`, :math:`\\eta`, :math:`\\zeta`. bL_or: numeric or array_like Normalising chromatic adaptation exponential factor :math:`\\beta_1(B_or)`. n : numeric or array_like, optional Noise term used in the non linear chromatic adaptation model. Returns ------- numeric or ndarray Ideal white *brightness* correlate :math:`B_{rw}`. Examples -------- >>> bRGB_o = np.array([4.61062223, 4.61058926, 4.65206986]) >>> xez = np.array([1.00004219, 0.99998001, 0.99975794]) >>> bL_or = 3.681021495604089 >>> n = 1.0 >>> ideal_white_brightness_correlate(bRGB_o, xez, bL_or, n) ... # doctest: +ELLIPSIS 125.2435392... """ bR_o, bG_o, _bB_o = tsplit(bRGB_o) xi, eta, _zeta = tsplit(xez) bL_or = as_float_array(bL_or) 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 def achromatic_lightness_correlate(Q): """ Returns the *achromatic Lightness* correlate :math:`L_p^\\star`. Parameters ---------- Q : numeric or array_like Achromatic response :math:`Q`. Returns ------- numeric or ndarray *Achromatic Lightness* correlate :math:`L_p^\\star`. Examples -------- >>> Q = -0.000117024294955 >>> achromatic_lightness_correlate(Q) # doctest: +ELLIPSIS 49.9998829... """ Q = as_float_array(Q) return Q + 50 def normalised_achromatic_lightness_correlate(B_r, B_rw): """ Returns the *normalised achromatic Lightness* correlate :math:`L_n^\\star`. Parameters ---------- B_r : numeric or array_like *Brightness* correlate :math:`B_r`. B_rw : numeric or array_like Ideal white *brightness* correlate :math:`B_{rw}`. Returns ------- numeric or ndarray *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) ... # doctest: +ELLIPSIS 50.0039154... """ B_r = as_float_array(B_r) B_rw = as_float_array(B_rw) return 100 * (B_r / B_rw) def hue_angle(p, t): """ Returns the *hue* angle :math:`h` in degrees. Parameters ---------- p : numeric or array_like Protanopic response :math:`p`. t : numeric or array_like Tritanopic response :math:`t`. Returns ------- numeric or ndarray *Hue* angle :math:`h` in degrees. Examples -------- >>> p = -8.002142682085493e-05 >>> t = -0.000017703650669 >>> hue_angle(p, t) # doctest: +ELLIPSIS 257.5250300... """ p = as_float_array(p) t = as_float_array(t) h_L = np.degrees(np.arctan2(p, t)) % 360 return h_L 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` in degrees. Parameters ---------- theta : numeric or array_like Hue angle :math:`\\theta` in degrees. Returns ------- numeric or ndarray Corrected saturation scale. Examples -------- >>> h = 257.52322689806243 >>> chromatic_strength_function(h) # doctest: +ELLIPSIS 1.2267869... """ theta = np.radians(theta) 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 def saturation_components(h, bL_or, t, p): """ Returns the *saturation* components :math:`S_{RG}` and :math:`S_{YB}`. Parameters ---------- h: numeric or array_like Correlate of *hue* :math:`h` in degrees. bL_or: numeric or array_like Normalising chromatic adaptation exponential factor :math:`\\beta_1(B_or)`. t : numeric or array_like Tritanopic response :math:`t`. p : numeric or array_like Protanopic response :math:`p`. Returns ------- numeric or ndarray *Saturation* components :math:`S_{RG}` and :math:`S_{YB}`. Examples -------- >>> h = 257.52322689806243 >>> bL_or = 3.681021495604089 >>> t = -0.000017706764677 >>> p = -0.000080023561356 >>> saturation_components(h, bL_or, t, p) # doctest: +ELLIPSIS array([-0.0028852..., -0.0130396...]) """ h = as_float_array(h) bL_or = as_float_array(bL_or) t = as_float_array(t) p = as_float_array(p) E_s = chromatic_strength_function(h) S_RG = (488.93 / bL_or) * E_s * t S_YB = (488.93 / bL_or) * E_s * p return tstack([S_RG, S_YB]) def saturation_correlate(S_RG, S_YB): """ Returns the correlate of *saturation* :math:`S`. Parameters ---------- S_RG : numeric or array_like *Saturation* component :math:`S_{RG}`. S_YB : numeric or array_like *Saturation* component :math:`S_{YB}`. Returns ------- numeric or ndarray Correlate of *saturation* :math:`S`. Examples -------- >>> S_RG = -0.002885271638197 >>> S_YB = -0.013039632941332 >>> saturation_correlate(S_RG, S_YB) # doctest: +ELLIPSIS 0.0133550... """ S_RG = as_float_array(S_RG) S_YB = as_float_array(S_YB) S = np.hypot(S_RG, S_YB) return S def chroma_components(L_star_P, S_RG, S_YB): """ Returns the *chroma* components :math:`C_{RG}` and :math:`C_{YB}`. Parameters ---------- L_star_P : numeric or array_like *Achromatic Lightness* correlate :math:`L_p^\\star`. S_RG : numeric or array_like *Saturation* component :math:`S_{RG}`. S_YB : numeric or array_like *Saturation* component :math:`S_{YB}`. Returns ------- ndarray *Chroma* components :math:`C_{RG}` and :math:`C_{YB}`. Examples -------- >>> L_star_P = 49.99988297570504 >>> S_RG = -0.002885271638197 >>> S_YB = -0.013039632941332 >>> chroma_components(L_star_P, S_RG, S_YB) # doctest: +ELLIPSIS array([-0.00288527, -0.01303961]) """ L_star_P = as_float_array(L_star_P) S_RG = as_float_array(S_RG) S_YB = as_float_array(S_YB) C_RG = spow(L_star_P / 50, 0.7) * S_RG C_YB = spow(L_star_P / 50, 0.7) * S_YB return tstack([C_RG, C_YB]) def chroma_correlate(L_star_P, S): """ Returns the correlate of *chroma* :math:`C`. Parameters ---------- L_star_P : numeric or array_like *Achromatic Lightness* correlate :math:`L_p^\\star`. S : numeric or array_like Correlate of *saturation* :math:`S`. Returns ------- numeric or ndarray Correlate of *chroma* :math:`C`. Examples -------- >>> L_star_P = 49.99988297570504 >>> S = 0.013355029751778 >>> chroma_correlate(L_star_P, S) # doctest: +ELLIPSIS 0.0133550... """ L_star_P = as_float_array(L_star_P) S = as_float_array(S) C = spow(L_star_P / 50, 0.7) * S return C def colourfulness_components(C_RG, C_YB, B_rw): """ Returns the *colourfulness* components :math:`M_{RG}` and :math:`M_{YB}`. Parameters ---------- C_RG : numeric or array_like *Chroma* component :math:`C_{RG}`. C_YB : numeric or array_like *Chroma* component :math:`C_{YB}`. B_rw : numeric or array_like Ideal white *brightness* correlate :math:`B_{rw}`. Returns ------- numeric or ndarray *Colourfulness* components :math:`M_{RG}` and :math:`M_{YB}`. Examples -------- >>> C_RG = -0.002885271638197 >>> C_YB = -0.013039632941332 >>> B_rw = 125.24353925846037 >>> colourfulness_components(C_RG, C_YB, B_rw) # doctest: +ELLIPSIS (-0.0036136..., -0.0163312...) """ C_RG = as_float_array(C_RG) C_YB = as_float_array(C_YB) B_rw = as_float_array(B_rw) M_RG = C_RG * B_rw / 100 M_YB = C_YB * B_rw / 100 return M_RG, M_YB def colourfulness_correlate(C, B_rw): """ Returns the correlate of *colourfulness* :math:`M`. Parameters ---------- C : numeric or array_like Correlate of *chroma* :math:`C`. B_rw : numeric or array_like Ideal white *brightness* correlate :math:`B_{rw}`. Returns ------- numeric or ndarray Correlate of *colourfulness* :math:`M`. Examples -------- >>> C = 0.013355007871689 >>> B_rw = 125.24353925846037 >>> colourfulness_correlate(C, B_rw) # doctest: +ELLIPSIS 0.0167262... """ C = as_float_array(C) B_rw = as_float_array(B_rw) M = C * B_rw / 100 return M