Source code for colour.temperature.cct

#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
Correlated Colour Temperature :math:`T_{cp}`
============================================

Defines correlated colour temperature :math:`T_{cp}` computations objects:

-   :func:`uv_to_CCT_Ohno2013`: Correlated colour temperature :math:`T_{cp}`
    and :math:`\Delta_{uv}` computation of given *CIE UCS* colourspace *uv*
    chromaticity coordinates using *Ohno (2013)* method.
-   :func:`CCT_to_uv_Ohno2013`: *CIE UCS* colourspace *uv* chromaticity
    coordinates computation of given correlated colour temperature
    :math:`T_{cp}`, :math:`\Delta_{uv}` using *Ohno (2013)* method.
-   :func:`uv_to_CCT_Robertson1968`: Correlated colour temperature
    :math:`T_{cp}` and :math:`\Delta_{uv}` computation of given *CIE UCS*
    colourspace *uv* chromaticity coordinates using *Robertson (1968)* method.
-   :func:`CCT_to_uv_Robertson1968`: *CIE UCS* colourspace *uv* chromaticity
    coordinates computation of given correlated colour temperature
    :math:`T_{cp}` and :math:`\Delta_{uv}` using *Robertson (1968)* method.
-   :func:`CCT_to_uv_Krystek1985`: *CIE UCS* colourspace *uv* chromaticity
    coordinates computation of given correlated colour temperature
    :math:`T_{cp}` using *Krystek (1985)* method.
-   :func:`xy_to_CCT_McCamy1992`: Correlated colour temperature :math:`T_{cp}`
    computation of given *CIE XYZ* tristimulus values *xy* chromaticity
    coordinates using *McCamy (1992)* method.
-   :func:`xy_to_CCT_Hernandez1999`: Correlated colour temperature
    :math:`T_{cp}` computation of given *CIE XYZ* tristimulus values *xy*
    chromaticity coordinates using *Hernandez-Andres, Lee and Romero (1999)*
    method.
-   :func:`CCT_to_xy_Kang2002`: *CIE XYZ* tristimulus values *xy* chromaticity
    coordinates computation of given correlated colour temperature
    :math:`T_{cp}` using *Kang, Moon, Hong, Lee, Cho and Kim (2002)* method.
-   :func:`CCT_to_xy_CIE_D`: *CIE XYZ* tristimulus values *xy* chromaticity
    coordinates computation of *CIE Illuminant D Series* from given correlated
    colour temperature :math:`T_{cp}` of that *CIE Illuminant D Series*.

See Also
--------
`Colour Temperature & Correlated Colour Temperature Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/temperature/cct.ipynb>`_

References
----------
.. [1]  Wikipedia. (n.d.). Color temperature. Retrieved June 28, 2014, from
        http://en.wikipedia.org/wiki/Color_temperature
"""

from __future__ import division, unicode_literals

import numpy as np
from collections import namedtuple

from colour.colorimetry import (
    ASTME30815_PRACTISE_SHAPE,
    STANDARD_OBSERVERS_CMFS,
    blackbody_spd,
    spectral_to_XYZ)
from colour.models import UCS_to_uv, XYZ_to_UCS
from colour.utilities import (
    CaseInsensitiveMapping,
    as_numeric,
    filter_kwargs,
    tsplit,
    tstack,
    warning)

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2017 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'

__all__ = ['PLANCKIAN_TABLE_TUVD',
           'CCT_MINIMAL',
           'CCT_MAXIMAL',
           'CCT_SAMPLES',
           'CCT_CALCULATION_ITERATIONS',
           'ROBERTSON_ISOTEMPERATURE_LINES_DATA',
           'ROBERTSON_ISOTEMPERATURE_LINES_RUVT',
           'ROBERTSON_ISOTEMPERATURE_LINES',
           'planckian_table',
           'planckian_table_minimal_distance_index',
           'uv_to_CCT_Ohno2013',
           'CCT_to_uv_Ohno2013',
           'uv_to_CCT_Robertson1968',
           'CCT_to_uv_Robertson1968',
           'CCT_to_uv_Krystek1985',
           'UV_TO_CCT_METHODS',
           'uv_to_CCT',
           'CCT_TO_UV_METHODS',
           'CCT_to_uv',
           'xy_to_CCT_McCamy1992',
           'xy_to_CCT_Hernandez1999',
           'CCT_to_xy_Kang2002',
           'CCT_to_xy_CIE_D',
           'XY_TO_CCT_METHODS',
           'xy_to_CCT',
           'CCT_TO_XY_METHODS',
           'CCT_to_xy']

PLANCKIAN_TABLE_TUVD = namedtuple('PlanckianTable_Tuvdi',
                                  ('Ti', 'ui', 'vi', 'di'))

CCT_MINIMAL = 1000
CCT_MAXIMAL = 100000
CCT_SAMPLES = 10
CCT_CALCULATION_ITERATIONS = 6

ROBERTSON_ISOTEMPERATURE_LINES_DATA = (
    (0, 0.18006, 0.26352, -0.24341),
    (10, 0.18066, 0.26589, -0.25479),
    (20, 0.18133, 0.26846, -0.26876),
    (30, 0.18208, 0.27119, -0.28539),
    (40, 0.18293, 0.27407, -0.30470),
    (50, 0.18388, 0.27709, -0.32675),
    (60, 0.18494, 0.28021, -0.35156),
    (70, 0.18611, 0.28342, -0.37915),
    (80, 0.18740, 0.28668, -0.40955),
    (90, 0.18880, 0.28997, -0.44278),
    (100, 0.19032, 0.29326, -0.47888),
    (125, 0.19462, 0.30141, -0.58204),
    (150, 0.19962, 0.30921, -0.70471),
    (175, 0.20525, 0.31647, -0.84901),
    (200, 0.21142, 0.32312, -1.0182),
    (225, 0.21807, 0.32909, -1.2168),
    (250, 0.22511, 0.33439, -1.4512),
    (275, 0.23247, 0.33904, -1.7298),
    (300, 0.24010, 0.34308, -2.0637),
    (325, 0.24792, 0.34655, -2.4681),  # 0.24702 ---> 0.24792 Bruce Lindbloom
    (350, 0.25591, 0.34951, -2.9641),
    (375, 0.26400, 0.35200, -3.5814),
    (400, 0.27218, 0.35407, -4.3633),
    (425, 0.28039, 0.35577, -5.3762),
    (450, 0.28863, 0.35714, -6.7262),
    (475, 0.29685, 0.35823, -8.5955),
    (500, 0.30505, 0.35907, -11.324),
    (525, 0.31320, 0.35968, -15.628),
    (550, 0.32129, 0.36011, -23.325),
    (575, 0.32931, 0.36038, -40.770),
    (600, 0.33724, 0.36051, -116.45))
"""
*Robertson (1968)* iso-temperature lines.

ROBERTSON_ISOTEMPERATURE_LINES_DATA : tuple
    (Reciprocal Megakelvin,
    CIE 1960 Chromaticity Coordinate *u*,
    CIE 1960 Chromaticity Coordinate *v*,
    Slope)

Notes
-----
-   A correction has been done by Lindbloom for *325* Megakelvin
    temperature: 0.24702 ---> 0.24792

References
----------
.. [2]  Wyszecki, G., & Stiles, W. S. (2000). Table 1(3.11) Isotemperature
        Lines. In Color Science: Concepts and Methods, Quantitative Data and
        Formulae (p. 228). Wiley. ISBN:978-0471399186
"""

ROBERTSON_ISOTEMPERATURE_LINES_RUVT = namedtuple(
    'WyszeckiRobertson_ruvt', ('r', 'u', 'v', 't'))

ROBERTSON_ISOTEMPERATURE_LINES = [
    ROBERTSON_ISOTEMPERATURE_LINES_RUVT(*x)
    for x in ROBERTSON_ISOTEMPERATURE_LINES_DATA]


[docs]def planckian_table(uv, cmfs, start, end, count): """ Returns a planckian table from given *CIE UCS* colourspace *uv* chromaticity coordinates, colour matching functions and temperature range using *Ohno (2013)* method. Parameters ---------- uv : array_like *uv* chromaticity coordinates. cmfs : XYZ_ColourMatchingFunctions Standard observer colour matching functions. start : numeric Temperature range start in kelvins. end : numeric Temperature range end in kelvins. count : int Temperatures count in the planckian table. Returns ------- list Planckian table. Examples -------- >>> from colour import STANDARD_OBSERVERS_CMFS >>> from pprint import pprint >>> cmfs = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer'] >>> uv = np.array([0.1978, 0.3122]) >>> pprint(planckian_table( # doctest: +ELLIPSIS ... uv, cmfs, 1000, 1010, 10)) [PlanckianTable_Tuvdi(Ti=1000.0, \ ui=0.4479628..., vi=0.3546296..., di=0.2537355...), PlanckianTable_Tuvdi(Ti=1001.1111111..., \ ui=0.4477030..., vi=0.3546521..., di=0.2534831...), PlanckianTable_Tuvdi(Ti=1002.2222222..., \ ui=0.4474434..., vi=0.3546746..., di=0.2532310...), PlanckianTable_Tuvdi(Ti=1003.3333333..., \ ui=0.4471842..., vi=0.3546970..., di=0.2529792...), PlanckianTable_Tuvdi(Ti=1004.4444444..., \ ui=0.4469252..., vi=0.3547194..., di=0.2527277...), PlanckianTable_Tuvdi(Ti=1005.5555555..., \ ui=0.4466666..., vi=0.3547417..., di=0.2524765...), PlanckianTable_Tuvdi(Ti=1006.6666666..., \ ui=0.4464083..., vi=0.3547640..., di=0.2522256...), PlanckianTable_Tuvdi(Ti=1007.7777777..., \ ui=0.4461502..., vi=0.3547862..., di=0.2519751...), PlanckianTable_Tuvdi(Ti=1008.8888888..., \ ui=0.4458925..., vi=0.3548084..., di=0.2517248...), PlanckianTable_Tuvdi(Ti=1010.0, \ ui=0.4456351..., vi=0.3548306..., di=0.2514749...)] """ ux, vx = uv cmfs = cmfs.clone().trim_wavelengths(ASTME30815_PRACTISE_SHAPE) shape = cmfs.shape table = [] for Ti in np.linspace(start, end, count): spd = blackbody_spd(Ti, shape) XYZ = spectral_to_XYZ(spd, cmfs) XYZ /= np.max(XYZ) UVW = XYZ_to_UCS(XYZ) ui, vi = UCS_to_uv(UVW) di = np.hypot(ux - ui, vx - vi) table.append(PLANCKIAN_TABLE_TUVD(Ti, ui, vi, di)) return table
[docs]def planckian_table_minimal_distance_index(planckian_table_): """ Returns the shortest distance index in given planckian table using *Ohno (2013)* method. Parameters ---------- planckian_table_ : list Planckian table. Returns ------- int Shortest distance index. Examples -------- >>> from colour import STANDARD_OBSERVERS_CMFS >>> cmfs = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer'] >>> uv = np.array([0.1978, 0.3122]) >>> table = planckian_table(uv, cmfs, 1000, 1010, 10) >>> planckian_table_minimal_distance_index(table) 9 """ distances = [x.di for x in planckian_table_] return distances.index(min(distances))
[docs]def uv_to_CCT_Ohno2013( uv, cmfs=STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer'], start=CCT_MINIMAL, end=CCT_MAXIMAL, count=CCT_SAMPLES, iterations=CCT_CALCULATION_ITERATIONS): """ Returns the correlated colour temperature :math:`T_{cp}` and :math:`\Delta_{uv}` from given *CIE UCS* colourspace *uv* chromaticity coordinates, colour matching functions and temperature range using *Ohno (2013)* method. The iterations parameter defines the calculations precision: The higher its value, the more planckian tables will be generated through cascade expansion in order to converge to the exact solution. Parameters ---------- uv : array_like *CIE UCS* colourspace *uv* chromaticity coordinates. cmfs : XYZ_ColourMatchingFunctions, optional Standard observer colour matching functions. start : numeric, optional Temperature range start in kelvins. end : numeric, optional Temperature range end in kelvins. count : int, optional Temperatures count in the planckian tables. iterations : int, optional Number of planckian tables to generate. Returns ------- ndarray Correlated colour temperature :math:`T_{cp}`, :math:`\Delta_{uv}`. References ---------- .. [3] Ohno, Y. (2014). Practical Use and Calculation of CCT and Duv. LEUKOS, 10(1), 47–55. doi:10.1080/15502724.2014.839020 Examples -------- >>> from colour import STANDARD_OBSERVERS_CMFS >>> cmfs = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer'] >>> uv = np.array([0.1978, 0.3122]) >>> uv_to_CCT_Ohno2013(uv, cmfs) # doctest: +ELLIPSIS array([ 6.5075128...e+03, 3.2233587...e-03]) """ # Ensuring we do at least one iteration to initialise variables. iterations = max(iterations, 1) # Planckian table creation through cascade expansion. for _i in range(iterations): table = planckian_table(uv, cmfs, start, end, count) index = planckian_table_minimal_distance_index(table) if index == 0: warning( ('Minimal distance index is on lowest planckian table bound, ' 'unpredictable results may occur!')) index += 1 elif index == len(table) - 1: warning( ('Minimal distance index is on highest planckian table bound, ' 'unpredictable results may occur!')) index -= 1 start = table[index - 1].Ti end = table[index + 1].Ti _ux, vx = uv Tuvdip, Tuvdi, Tuvdin = (table[index - 1], table[index], table[index + 1]) Tip, uip, vip, dip = Tuvdip.Ti, Tuvdip.ui, Tuvdip.vi, Tuvdip.di Ti, di = Tuvdi.Ti, Tuvdi.di Tin, uin, vin, din = Tuvdin.Ti, Tuvdin.ui, Tuvdin.vi, Tuvdin.di # Triangular solution. l = np.hypot(uin - uip, vin - vip) x = (dip ** 2 - din ** 2 + l ** 2) / (2 * l) T = Tip + (Tin - Tip) * (x / l) vtx = vip + (vin - vip) * (x / l) sign = 1 if vx - vtx >= 0 else -1 D_uv = (dip ** 2 - x ** 2) ** (1 / 2) * sign # Parabolic solution. if D_uv < 0.002: X = (Tin - Ti) * (Tip - Tin) * (Ti - Tip) a = (Tip * (din - di) + Ti * (dip - din) + Tin * (di - dip)) * X ** -1 b = (-(Tip ** 2 * (din - di) + Ti ** 2 * (dip - din) + Tin ** 2 * (di - dip)) * X ** -1) c = (-(dip * (Tin - Ti) * Ti * Tin + di * (Tip - Tin) * Tip * Tin + din * (Ti - Tip) * Tip * Ti) * X ** -1) T = -b / (2 * a) D_uv = sign * (a * T ** 2 + b * T + c) return np.array([T, D_uv])
[docs]def CCT_to_uv_Ohno2013( CCT, D_uv=0, cmfs=STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']): """ Returns the *CIE UCS* colourspace *uv* chromaticity coordinates from given correlated colour temperature :math:`T_{cp}`, :math:`\Delta_{uv}` and colour matching functions using *Ohno (2013)* method. Parameters ---------- CCT : numeric Correlated colour temperature :math:`T_{cp}`. D_uv : numeric, optional :math:`\Delta_{uv}`. cmfs : XYZ_ColourMatchingFunctions, optional Standard observer colour matching functions. Returns ------- ndarray *CIE UCS* colourspace *uv* chromaticity coordinates. References ---------- .. [4] Ohno, Y. (2014). Practical Use and Calculation of CCT and Duv. LEUKOS, 10(1), 47–55. doi:10.1080/15502724.2014.839020 Examples -------- >>> from colour import STANDARD_OBSERVERS_CMFS >>> cmfs = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer'] >>> CCT = 6507.4342201047066 >>> D_uv = 0.003223690901513 >>> CCT_to_uv_Ohno2013(CCT, D_uv, cmfs) # doctest: +ELLIPSIS array([ 0.1977999..., 0.3122004...]) """ cmfs = cmfs.clone().trim_wavelengths(ASTME30815_PRACTISE_SHAPE) shape = cmfs.shape delta = 0.01 spd = blackbody_spd(CCT, shape) XYZ = spectral_to_XYZ(spd, cmfs) XYZ *= 1 / np.max(XYZ) UVW = XYZ_to_UCS(XYZ) u0, v0 = UCS_to_uv(UVW) if D_uv == 0: return np.array([u0, v0]) else: spd = blackbody_spd(CCT + delta, shape) XYZ = spectral_to_XYZ(spd, cmfs) XYZ *= 1 / np.max(XYZ) UVW = XYZ_to_UCS(XYZ) u1, v1 = UCS_to_uv(UVW) du = u0 - u1 dv = v0 - v1 u = u0 - D_uv * (dv / np.hypot(du, dv)) v = v0 + D_uv * (du / np.hypot(du, dv)) return np.array([u, v])
[docs]def uv_to_CCT_Robertson1968(uv): """ Returns the correlated colour temperature :math:`T_{cp}` and :math:`\Delta_{uv}` from given *CIE UCS* colourspace *uv* chromaticity coordinates using *Roberston (1968)* method. Parameters ---------- uv : array_like *CIE UCS* colourspace *uv* chromaticity coordinates. Returns ------- ndarray Correlated colour temperature :math:`T_{cp}`, :math:`\Delta_{uv}`. References ---------- .. [5] Wyszecki, G., & Stiles, W. S. (2000). DISTRIBUTION TEMPERATURE, COLOR TEMPERATURE, AND CORRELATED COLOR TEMPERATURE. In Color Science: Concepts and Methods, Quantitative Data and Formulae (pp. 224–229). Wiley. ISBN:978-0471399186 .. [6] Adobe Systems. (2013). Adobe DNG Software Development Kit (SDK) - 1.3.0.0 - dng_sdk_1_3/dng_sdk/source/dng_temperature.cpp:: dng_temperature::Set_xy_coord. Retrieved from https://www.adobe.com/support/downloads/dng/dng_sdk.html Examples -------- >>> uv = np.array([0.193741375998230, 0.315221043940594]) >>> uv_to_CCT_Robertson1968(uv) # doctest: +ELLIPSIS array([ 6.5000162...e+03, 8.3333289...e-03]) """ u, v = uv last_dt = last_dv = last_du = 0 for i in range(1, 31): wr_ruvt = ROBERTSON_ISOTEMPERATURE_LINES[i] wr_ruvt_previous = ROBERTSON_ISOTEMPERATURE_LINES[i - 1] du = 1 dv = wr_ruvt.t length = np.hypot(1, dv) du /= length dv /= length uu = u - wr_ruvt.u vv = v - wr_ruvt.v dt = -uu * dv + vv * du if dt <= 0 or i == 30: if dt > 0: dt = 0 dt = -dt f = 0 if i == 1 else dt / (last_dt + dt) T = 1.0e6 / (wr_ruvt_previous.r * f + wr_ruvt.r * (1 - f)) uu = u - (wr_ruvt_previous.u * f + wr_ruvt.u * (1 - f)) vv = v - (wr_ruvt_previous.v * f + wr_ruvt.v * (1 - f)) du = du * (1 - f) + last_du * f dv = dv * (1 - f) + last_dv * f length = np.hypot(du, dv) du /= length dv /= length D_uv = uu * du + vv * dv break last_dt = dt last_du = du last_dv = dv return np.array([T, -D_uv])
[docs]def CCT_to_uv_Robertson1968(CCT, D_uv=0): """ Returns the *CIE UCS* colourspace *uv* chromaticity coordinates from given correlated colour temperature :math:`T_{cp}` and :math:`\Delta_{uv}` using *Roberston (1968)* method. Parameters ---------- CCT : numeric Correlated colour temperature :math:`T_{cp}`. D_uv : numeric :math:`\Delta_{uv}`. Returns ------- ndarray *CIE UCS* colourspace *uv* chromaticity coordinates. References ---------- .. [7] Wyszecki, G., & Stiles, W. S. (2000). DISTRIBUTION TEMPERATURE, COLOR TEMPERATURE, AND CORRELATED COLOR TEMPERATURE. In Color Science: Concepts and Methods, Quantitative Data and Formulae (pp. 224–229). Wiley. ISBN:978-0471399186 .. [8] Adobe Systems. (2013). Adobe DNG Software Development Kit (SDK) - 1.3.0.0 - dng_sdk_1_3/dng_sdk/source/dng_temperature.cpp:: dng_temperature::xy_coord. Retrieved from https://www.adobe.com/support/downloads/dng/dng_sdk.html Examples -------- >>> CCT = 6500.0081378199056 >>> D_uv = 0.008333331244225 >>> CCT_to_uv_Robertson1968(CCT, D_uv) # doctest: +ELLIPSIS array([ 0.1937413..., 0.3152210...]) """ r = 1.0e6 / CCT for i in range(30): wr_ruvt = ROBERTSON_ISOTEMPERATURE_LINES[i] wr_ruvt_next = ROBERTSON_ISOTEMPERATURE_LINES[i + 1] if r < wr_ruvt_next.r or i == 29: f = (wr_ruvt_next.r - r) / (wr_ruvt_next.r - wr_ruvt.r) u = wr_ruvt.u * f + wr_ruvt_next.u * (1 - f) v = wr_ruvt.v * f + wr_ruvt_next.v * (1 - f) uu1 = uu2 = 1.0 vv1, vv2 = wr_ruvt.t, wr_ruvt_next.t length1 = np.hypot(1, vv1) length2 = np.hypot(1, vv2) uu1 /= length1 vv1 /= length1 uu2 /= length2 vv2 /= length2 uu3 = uu1 * f + uu2 * (1 - f) vv3 = vv1 * f + vv2 * (1 - f) len3 = np.sqrt(uu3 * uu3 + vv3 * vv3) uu3 /= len3 vv3 /= len3 u += uu3 * -D_uv v += vv3 * -D_uv return np.array([u, v])
[docs]def CCT_to_uv_Krystek1985(CCT): """ Returns the *CIE UCS* colourspace *uv* chromaticity coordinates from given correlated colour temperature :math:`T_{cp}` using *Krystek (1985)* method. Parameters ---------- CCT : numeric Correlated colour temperature :math:`T_{cp}`. Returns ------- ndarray *CIE UCS* colourspace *uv* chromaticity coordinates. Notes ----- - *Krystek (1985)* method computations are valid for correlated colour temperature :math:`T_{cp}` in domain [1000, 15000]. References ---------- .. [9] Krystek, M. (1985). An algorithm to calculate correlated colour temperature. Color Research & Application, 10(1), 38–40. doi:10.1002/col.5080100109 Examples -------- >>> CCT_to_uv_Krystek1985(6504.38938305) # doctest: +ELLIPSIS array([ 0.1837669..., 0.3093443...]) """ T = np.asarray(CCT) u = ((0.860117757 + 1.54118254 * 10e-4 * T + 1.28641212 * 10e-7 * T ** 2) / (1 + 8.42420235 * 10e-4 * T + 7.08145163 * 10e-7 * T ** 2)) v = ((0.317398726 + 4.22806245 * 10e-5 * T + 4.20481691 * 10e-8 * T ** 2) / (1 - 2.89741816 * 10e-5 * T + 1.61456053 * 10e-7 * T ** 2)) return tstack((u, v))
UV_TO_CCT_METHODS = CaseInsensitiveMapping( {'Ohno 2013': uv_to_CCT_Ohno2013, 'Robertson 1968': uv_to_CCT_Robertson1968}) """ Supported *CIE UCS* colourspace *uv* chromaticity coordinates to correlated colour temperature :math:`T_{cp}` computation methods. UV_TO_CCT_METHODS : CaseInsensitiveMapping **{'Ohno 2013', 'Robertson 1968'}** Aliases: - 'ohno2013': 'Ohno 2013' - 'robertson1968': 'Robertson 1968' """ UV_TO_CCT_METHODS['ohno2013'] = UV_TO_CCT_METHODS['Ohno 2013'] UV_TO_CCT_METHODS['robertson1968'] = UV_TO_CCT_METHODS['Robertson 1968']
[docs]def uv_to_CCT(uv, method='Ohno 2013', **kwargs): """ Returns the correlated colour temperature :math:`T_{cp}` and :math:`\Delta_{uv}` from given *CIE UCS* colourspace *uv* chromaticity coordinates using given method. Parameters ---------- uv : array_like *CIE UCS* colourspace *uv* chromaticity coordinates. method : unicode, optional **{'Ohno 2013', 'Robertson 1968'}**, Computation method. Other Parameters ---------------- cmfs : XYZ_ColourMatchingFunctions, optional {:func:`uv_to_CCT_Ohno2013`}, Standard observer colour matching functions. start : numeric, optional {:func:`uv_to_CCT_Ohno2013`}, Temperature range start in kelvins. end : numeric, optional {:func:`uv_to_CCT_Ohno2013`}, Temperature range end in kelvins. count : int, optional {:func:`uv_to_CCT_Ohno2013`}, Temperatures count in the planckian tables. iterations : int, optional {:func:`uv_to_CCT_Ohno2013`}, Number of planckian tables to generate. Returns ------- ndarray Correlated colour temperature :math:`T_{cp}`, :math:`\Delta_{uv}`. Examples -------- >>> from colour import STANDARD_OBSERVERS_CMFS >>> cmfs = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer'] >>> uv = np.array([0.1978, 0.3122]) >>> uv_to_CCT(uv, cmfs=cmfs) # doctest: +ELLIPSIS array([ 6.5075128...e+03, 3.2233587...e-03]) """ function = UV_TO_CCT_METHODS[method] filter_kwargs(function, **kwargs) return function(uv, **kwargs)
CCT_TO_UV_METHODS = CaseInsensitiveMapping( {'Ohno 2013': CCT_to_uv_Ohno2013, 'Robertson 1968': CCT_to_uv_Robertson1968, 'Krystek 1985': CCT_to_uv_Krystek1985}) """ Supported correlated colour temperature :math:`T_{cp}` to *CIE UCS* colourspace *uv* chromaticity coordinates computation methods. CCT_TO_UV_METHODS : CaseInsensitiveMapping **{'Ohno 2013', 'Robertson 1968', 'Krystek 1985}** Aliases: - 'ohno2013': 'Ohno 2013' - 'robertson1968': 'Robertson 1968' """ CCT_TO_UV_METHODS['ohno2013'] = CCT_TO_UV_METHODS['Ohno 2013'] CCT_TO_UV_METHODS['robertson1968'] = CCT_TO_UV_METHODS['Robertson 1968']
[docs]def CCT_to_uv(CCT, method='Ohno 2013', **kwargs): """ Returns the *CIE UCS* colourspace *uv* chromaticity coordinates from given correlated colour temperature :math:`T_{cp}` using given method. Parameters ---------- CCT : numeric Correlated colour temperature :math:`T_{cp}`. method : unicode, optional **{'Ohno 2013', 'Robertson 1968', 'Krystek 1985}**, Computation method. Other Parameters ---------------- D_uv : numeric {:func:`CCT_to_uv_Ohno2013, CCT_to_uv_Robertson1968`}, :math:`\Delta_{uv}`. cmfs : XYZ_ColourMatchingFunctions, optional {:func:`CCT_to_uv_Ohno2013`}, Standard observer colour matching functions. Returns ------- ndarray *CIE UCS* colourspace *uv* chromaticity coordinates. Examples -------- >>> from colour import STANDARD_OBSERVERS_CMFS >>> cmfs = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer'] >>> CCT = 6507.4342201047066 >>> D_uv = 0.003223690901513 >>> CCT_to_uv(CCT, D_uv=D_uv, cmfs=cmfs) # doctest: +ELLIPSIS array([ 0.1977999..., 0.3122004...]) """ function = CCT_TO_UV_METHODS[method] filter_kwargs(function, **kwargs) return function(CCT, **kwargs)
[docs]def xy_to_CCT_McCamy1992(xy): """ Returns the correlated colour temperature :math:`T_{cp}` from given *CIE XYZ* tristimulus values *xy* chromaticity coordinates using *McCamy (1992)* method. Parameters ---------- xy : array_like *xy* chromaticity coordinates. Returns ------- numeric or ndarray Correlated colour temperature :math:`T_{cp}`. References ---------- .. [10] Wikipedia. (n.d.). Approximation. Retrieved June 28, 2014, from http://en.wikipedia.org/wiki/Color_temperature#Approximation Examples -------- >>> xy = np.array([0.31270, 0.32900]) >>> xy_to_CCT_McCamy1992(xy) # doctest: +ELLIPSIS 6505.0805913... """ x, y = tsplit(xy) n = (x - 0.3320) / (y - 0.1858) CCT = -449 * n ** 3 + 3525 * n ** 2 - 6823.3 * n + 5520.33 return CCT
[docs]def xy_to_CCT_Hernandez1999(xy): """ Returns the correlated colour temperature :math:`T_{cp}` from given *CIE XYZ* tristimulus values *xy* chromaticity coordinates using Hernandez-Andres et al. (1999) method. Parameters ---------- xy : array_like *xy* chromaticity coordinates. Returns ------- numeric Correlated colour temperature :math:`T_{cp}`. References ---------- .. [11] Hernández-Andrés, J., Lee, R. L., & Romero, J. (1999). Calculating correlated color temperatures across the entire gamut of daylight and skylight chromaticities. Applied Optics, 38(27), 5703–5709. doi:10.1364/AO.38.005703 Examples -------- >>> xy = np.array([0.31270, 0.32900]) >>> xy_to_CCT_Hernandez1999(xy) # doctest: +ELLIPSIS 6500.7420431... """ x, y = tsplit(xy) n = (x - 0.3366) / (y - 0.1735) CCT = (-949.86315 + 6253.80338 * np.exp(-n / 0.92159) + 28.70599 * np.exp(-n / 0.20039) + 0.00004 * np.exp(-n / 0.07125)) n = np.where(CCT > 50000, (x - 0.3356) / (y - 0.1691), n) CCT = np.where(CCT > 50000, 36284.48953 + 0.00228 * np.exp(-n / 0.07861) + 5.4535e-36 * np.exp(-n / 0.01543), CCT) return as_numeric(CCT)
[docs]def CCT_to_xy_Kang2002(CCT): """ Returns the *CIE XYZ* tristimulus values *xy* chromaticity coordinates from given correlated colour temperature :math:`T_{cp}` using Kang et al. (2002) method. Parameters ---------- CCT : numeric or array_like Correlated colour temperature :math:`T_{cp}`. Returns ------- ndarray *xy* chromaticity coordinates. Raises ------ ValueError If the correlated colour temperature is not in appropriate domain. References ---------- .. [12] 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 …, 41(6), 865–871. Retrieved from http://cat.inist.fr/?aModele=afficheN&cpsidt=14448733 Examples -------- >>> CCT_to_xy_Kang2002(6504.38938305) # doctest: +ELLIPSIS array([ 0.313426..., 0.3235959...]) """ CCT = np.asarray(CCT) if np.any(CCT[np.asarray(np.logical_or(CCT < 1667, CCT > 25000))]): warning(('Correlated colour temperature must be in domain ' '[1667, 25000], unpredictable results may occur!')) x = np.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) y = np.select([CCT <= 2222, np.logical_and(CCT > 2222, CCT <= 4000), CCT > 4000], [-1.1063814 * x ** 3 - 1.34811020 * x ** 2 + 2.18555832 * x - 0.20219683, -0.9549476 * x ** 3 - 1.37418593 * x ** 2 + 2.09137015 * x - 0.16748867, 3.0817580 * x ** 3 - 5.8733867 * x ** 2 + 3.75112997 * x - 0.37001483]) xy = tstack((x, y)) return xy
[docs]def CCT_to_xy_CIE_D(CCT): """ Converts from the correlated colour temperature :math:`T_{cp}` of a *CIE Illuminant D Series* to the chromaticity of that *CIE Illuminant D Series* illuminant. Parameters ---------- CCT : numeric or array_like Correlated colour temperature :math:`T_{cp}`. Returns ------- ndarray *xy* chromaticity coordinates. Raises ------ ValueError If the correlated colour temperature is not in appropriate domain. References ---------- .. [13] Wyszecki, G., & Stiles, W. S. (2000). CIE Method of Calculating D-Illuminants. In Color Science: Concepts and Methods, Quantitative Data and Formulae (pp. 145–146). Wiley. ISBN:978-0471399186 Examples -------- >>> CCT_to_xy_CIE_D(6504.38938305) # doctest: +ELLIPSIS array([ 0.3127077..., 0.3291128...]) """ CCT = np.asarray(CCT) if np.any(CCT[np.asarray(np.logical_or(CCT < 4000, CCT > 25000))]): warning(('Correlated colour temperature must be in domain ' '[4000, 25000], unpredictable results may occur!')) x = np.where(CCT <= 7000, -4.607 * 10 ** 9 / CCT ** 3 + 2.9678 * 10 ** 6 / CCT ** 2 + 0.09911 * 10 ** 3 / CCT + 0.244063, -2.0064 * 10 ** 9 / CCT ** 3 + 1.9018 * 10 ** 6 / CCT ** 2 + 0.24748 * 10 ** 3 / CCT + 0.23704) y = -3 * x ** 2 + 2.87 * x - 0.275 xy = tstack((x, y)) return xy
XY_TO_CCT_METHODS = CaseInsensitiveMapping( {'McCamy 1992': xy_to_CCT_McCamy1992, 'Hernandez 1999': xy_to_CCT_Hernandez1999}) """ Supported *CIE XYZ* tristimulus values *xy* chromaticity coordinates to correlated colour temperature :math:`T_{cp}` computation methods. XY_TO_CCT_METHODS : CaseInsensitiveMapping **{'McCamy 1992', 'Hernandez 1999'}** Aliases: - 'mccamy1992': 'McCamy 1992' - 'hernandez1999': 'Hernandez 1999' """ XY_TO_CCT_METHODS['mccamy1992'] = XY_TO_CCT_METHODS['McCamy 1992'] XY_TO_CCT_METHODS['hernandez1999'] = XY_TO_CCT_METHODS['Hernandez 1999']
[docs]def xy_to_CCT(xy, method='McCamy 1992'): """ Returns the correlated colour temperature :math:`T_{cp}` from given *CIE XYZ* tristimulus values *xy* chromaticity coordinates using given method. Parameters ---------- xy : array_like *xy* chromaticity coordinates. method : unicode, optional **{'McCamy 1992', 'Hernandez 1999'}**, Computation method. Returns ------- numeric or ndarray Correlated colour temperature :math:`T_{cp}`. """ return XY_TO_CCT_METHODS.get(method)(xy)
CCT_TO_XY_METHODS = CaseInsensitiveMapping( {'Kang 2002': CCT_to_xy_Kang2002, 'CIE Illuminant D Series': CCT_to_xy_CIE_D}) """ Supported correlated colour temperature :math:`T_{cp}` to *CIE XYZ* tristimulus values *xy* chromaticity coordinates computation methods. CCT_TO_XY_METHODS : CaseInsensitiveMapping **{'Kang 2002', 'CIE Illuminant D Series'}** Aliases: - 'kang2002': 'Kang 2002' - 'cie_d': 'Hernandez 1999' """ CCT_TO_XY_METHODS['kang2002'] = CCT_TO_XY_METHODS['Kang 2002'] CCT_TO_XY_METHODS['cie_d'] = CCT_TO_XY_METHODS['CIE Illuminant D Series']
[docs]def CCT_to_xy(CCT, method='Kang 2002'): """ Returns the *CIE XYZ* tristimulus values *xy* chromaticity coordinates from given correlated colour temperature :math:`T_{cp}` using given method. Parameters ---------- CCT : numeric or array_like Correlated colour temperature :math:`T_{cp}`. method : unicode, optional **{'Kang 2002', 'CIE Illuminant D Series'}**, Computation method. Returns ------- ndarray *xy* chromaticity coordinates. """ return CCT_TO_XY_METHODS.get(method)(CCT)