"""
ITU-R BT.2020
=============
Defines the *ITU-R BT.2020* opto-electrical transfer function (OETF) and
electro-optical transfer function (EOTF):
- :func:`colour.models.eotf_inverse_BT2020`
- :func:`colour.models.eotf_BT2020`
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 (pp. 1-8).
https://www.itu.int/dms_pubrec/itu-r/rec/bt/\
R-REC-BT.2020-2-201510-I!!PDF-E.pdf
"""
from __future__ import annotations
import numpy as np
from colour.algebra import spow
from colour.hints import Boolean, FloatingOrArrayLike, FloatingOrNDArray
from colour.utilities import (
Structure,
as_float,
domain_range_scale,
from_range_1,
to_domain_1,
)
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 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__ = [
"CONSTANTS_BT2020",
"CONSTANTS_BT2020_PRECISE",
"eotf_inverse_BT2020",
"eotf_BT2020",
]
CONSTANTS_BT2020: Structure = 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."""
CONSTANTS_BT2020_PRECISE: Structure = 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`
"""
[docs]def eotf_inverse_BT2020(
E: FloatingOrArrayLike,
is_12_bits_system: Boolean = False,
constants: Structure = CONSTANTS_BT2020,
) -> FloatingOrNDArray:
"""
Define *Recommendation ITU-R BT.2020* inverse electro-optical transfer
function (EOTF).
Parameters
----------
E
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
*BT.709* *alpha* and *beta* constants are used if system is not 12-bit.
constants
*Recommendation ITU-R BT.2020* constants.
Returns
-------
:class:`numpy.floating` or :class:`numpy.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
--------
>>> eotf_inverse_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: FloatingOrArrayLike,
is_12_bits_system: Boolean = False,
constants: Structure = CONSTANTS_BT2020,
) -> FloatingOrNDArray:
"""
Define *Recommendation ITU-R BT.2020* electro-optical transfer function
(EOTF).
Parameters
----------
E_p
Non-linear signal :math:`E'`.
is_12_bits_system
*BT.709* *alpha* and *beta* constants are used if system is not 12-bit.
constants
*Recommendation ITU-R BT.2020* constants.
Returns
-------
:class:`numpy.floating` or :class:`numpy.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 < eotf_inverse_BT2020(b),
E_p / 4.5,
spow((E_p + (a - 1)) / a, 1 / 0.45),
)
return as_float(from_range_1(E))