#!/usr/bin/env python
# -*- 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:`oetf_BT2020`
- :func:`eotf_BT2020`
See Also
--------
`RGB Colourspaces Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/models/rgb.ipynb>`_
References
----------
.. [1] International Telecommunication Union. (2015). Recommendation
ITU-R BT.2020 - Parameter values for ultra-high definition television
systems for production and international programme exchange (Vol. 1).
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.utilities import Structure, as_numeric
__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__ = ['BT2020_CONSTANTS', '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
"""
[docs]def oetf_BT2020(E, is_12_bits_system=False):
"""
Defines *Recommendation ITU-R BT.2020* opto-electrical transfer function
(OETF / OECF).
Parameters
----------
E : numeric or array_like
Voltage :math:`E` normalized 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
*BT.709* *alpha* and *beta* constants are used if system is not 12-bit.
Returns
-------
numeric or ndarray
Resulting non-linear signal :math:`E'`.
Examples
--------
>>> oetf_BT2020(0.18) # doctest: +ELLIPSIS
0.4090077...
"""
E = np.asarray(E)
a = BT2020_CONSTANTS.alpha(is_12_bits_system)
b = BT2020_CONSTANTS.beta(is_12_bits_system)
return as_numeric(np.where(E < b, E * 4.5, a * (E ** 0.45) - (a - 1)))
[docs]def eotf_BT2020(E_p, is_12_bits_system=False):
"""
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
*BT.709* *alpha* and *beta* constants are used if system is not 12-bit.
Returns
-------
numeric or ndarray
Resulting voltage :math:`E`.
Examples
--------
>>> eotf_BT2020(0.705515089922121) # doctest: +ELLIPSIS
0.4999999...
"""
E_p = np.asarray(E_p)
a = BT2020_CONSTANTS.alpha(is_12_bits_system)
b = BT2020_CONSTANTS.beta(is_12_bits_system)
return as_numeric(
np.where(E_p < oetf_BT2020(b), E_p / 4.5, ((E_p + (a - 1)) / a) ** (
1 / 0.45)))