# -*- coding: utf-8 -*-
"""
ITU-R BT.2020
=============
Defines *ITU-R BT.2020* opto-electrical transfer function (OETF / OECF) and
electro-optical transfer function (EOTF / EOCF):
- :func:`colour.models.oetf_BT2020`
- :func:`colour.models.eotf_BT2020`
See Also
--------
`RGB Colourspaces Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/models/rgb.ipynb>`_
References
----------
- :cite:`InternationalTelecommunicationUnion2015h` : International
Telecommunication Union. (2015). Recommendation ITU-R BT.2020 - Parameter
values for ultra-high definition television systems for production and
international programme exchange. Retrieved from
https://www.itu.int/dms_pubrec/itu-r/rec/bt/\
R-REC-BT.2020-2-201510-I!!PDF-E.pdf
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.algebra import spow
from colour.utilities import (Structure, as_float, domain_range_scale,
from_range_1, to_domain_1)
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2019 - Colour Developers'
__license__ = 'New BSD License - https://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = [
'BT2020_CONSTANTS', 'BT2020_CONSTANTS_PRECISE', 'oetf_BT2020',
'eotf_BT2020'
]
BT2020_CONSTANTS = Structure(
alpha=lambda x: 1.0993 if x else 1.099,
beta=lambda x: 0.0181 if x else 0.018)
"""
*BT.2020* colourspace constants.
BT2020_CONSTANTS : Structure
"""
BT2020_CONSTANTS_PRECISE = Structure(
alpha=lambda x: 1.09929682680944, beta=lambda x: 0.018053968510807)
"""
*BT.2020* colourspace constants at double precision to connect the two curve
segments smoothly.
References
----------
:cite:`InternationalTelecommunicationUnion2015h`
BT2020_CONSTANTS_PRECISE : Structure
"""
[docs]def oetf_BT2020(E, is_12_bits_system=False, constants=BT2020_CONSTANTS):
"""
Defines *Recommendation ITU-R BT.2020* opto-electrical transfer function
(OETF / OECF).
Parameters
----------
E : numeric or array_like
Voltage :math:`E` normalised by the reference white level and
proportional to the implicit light intensity that would be detected
with a reference camera colour channel R, G, B.
is_12_bits_system : bool, optional
*BT.709* *alpha* and *beta* constants are used if system is not 12-bit.
constants : Structure, optional
*Recommendation ITU-R BT.2020* constants.
Returns
-------
numeric or ndarray
Resulting non-linear signal :math:`E'`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`InternationalTelecommunicationUnion2015h`
Examples
--------
>>> oetf_BT2020(0.18) # doctest: +ELLIPSIS
0.4090077...
"""
E = to_domain_1(E)
a = constants.alpha(is_12_bits_system)
b = constants.beta(is_12_bits_system)
E_p = np.where(E < b, E * 4.5, a * spow(E, 0.45) - (a - 1))
return as_float(from_range_1(E_p))
[docs]def eotf_BT2020(E_p, is_12_bits_system=False, constants=BT2020_CONSTANTS):
"""
Defines *Recommendation ITU-R BT.2020* electro-optical transfer function
(EOTF / EOCF).
Parameters
----------
E_p : numeric or array_like
Non-linear signal :math:`E'`.
is_12_bits_system : bool, optional
*BT.709* *alpha* and *beta* constants are used if system is not 12-bit.
constants : Structure, optional
*Recommendation ITU-R BT.2020* constants.
Returns
-------
numeric or ndarray
Resulting voltage :math:`E`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`InternationalTelecommunicationUnion2015h`
Examples
--------
>>> eotf_BT2020(0.705515089922121) # doctest: +ELLIPSIS
0.4999999...
"""
E_p = to_domain_1(E_p)
a = constants.alpha(is_12_bits_system)
b = constants.beta(is_12_bits_system)
with domain_range_scale('ignore'):
E = np.where(
E_p < oetf_BT2020(b),
E_p / 4.5,
spow((E_p + (a - 1)) / a, 1 / 0.45),
)
return as_float(from_range_1(E))