# -*- coding: utf-8 -*-
"""
RED Log Encodings
=================
Defines the *RED* log encodings:
- :func:`colour.models.log_encoding_REDLog`
- :func:`colour.models.log_decoding_REDLog`
- :func:`colour.models.log_encoding_REDLogFilm`
- :func:`colour.models.log_decoding_REDLogFilm`
- :func:`colour.models.log_encoding_Log3G10`
- :func:`colour.models.log_decoding_Log3G10`
- :func:`colour.models.log_encoding_Log3G12`
- :func:`colour.models.log_decoding_Log3G12`
See Also
--------
`RGB Colourspaces Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/models/rgb.ipynb>`_
References
----------
- :cite:`Nattress2016a` : Nattress, G. (2016). Private Discussion with
Shaw, N.
- :cite:`SonyImageworks2012a` : Sony Imageworks. (2012). make.py. Retrieved
November 27, 2014, from https://github.com/imageworks/OpenColorIO-Configs/\
blob/master/nuke-default/make.py
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.models.rgb.transfer_functions import (log_encoding_Cineon,
log_decoding_Cineon)
from colour.utilities import from_range_1, to_domain_1
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2019 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = [
'log_encoding_REDLog', 'log_decoding_REDLog', 'log_encoding_REDLogFilm',
'log_decoding_REDLogFilm', 'log_encoding_Log3G10', 'log_decoding_Log3G10',
'log_encoding_Log3G12', 'log_decoding_Log3G12'
]
[docs]def log_encoding_REDLog(x, black_offset=10 ** ((0 - 1023) / 511)):
"""
Defines the *REDLog* log encoding curve / opto-electronic transfer
function.
Parameters
----------
x : numeric or array_like
Linear data :math:`x`.
black_offset : numeric or array_like
Black offset.
Returns
-------
numeric or ndarray
Non-linear data :math:`y`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``x`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``y`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`SonyImageworks2012a`
Examples
--------
>>> log_encoding_REDLog(0.18) # doctest: +ELLIPSIS
0.6376218...
"""
x = to_domain_1(x)
y = (1023 + 511 * np.log10(x * (1 - black_offset) + black_offset)) / 1023
return from_range_1(y)
[docs]def log_decoding_REDLog(y, black_offset=10 ** ((0 - 1023) / 511)):
"""
Defines the *REDLog* log decoding curve / electro-optical transfer
function.
Parameters
----------
y : numeric or array_like
Non-linear data :math:`y`.
black_offset : numeric or array_like
Black offset.
Returns
-------
numeric or ndarray
Linear data :math:`x`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``y`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``x`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`SonyImageworks2012a`
Examples
--------
>>> log_decoding_REDLog(0.637621845988175) # doctest: +ELLIPSIS
0.1...
"""
y = to_domain_1(y)
x = ((10 ** ((1023 * y - 1023) / 511)) - black_offset) / (1 - black_offset)
return from_range_1(x)
[docs]def log_encoding_REDLogFilm(x, black_offset=10 ** ((95 - 685) / 300)):
"""
Defines the *REDLogFilm* log encoding curve / opto-electronic transfer
function.
Parameters
----------
x : numeric or array_like
Linear data :math:`x`.
black_offset : numeric or array_like
Black offset.
Returns
-------
numeric or ndarray
Non-linear data :math:`y`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``x`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``y`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`SonyImageworks2012a`
Examples
--------
>>> log_encoding_REDLogFilm(0.18) # doctest: +ELLIPSIS
0.4573196...
"""
return log_encoding_Cineon(x, black_offset)
[docs]def log_decoding_REDLogFilm(y, black_offset=10 ** ((95 - 685) / 300)):
"""
Defines the *REDLogFilm* log decoding curve / electro-optical transfer
function.
Parameters
----------
y : numeric or array_like
Non-linear data :math:`y`.
black_offset : numeric or array_like
Black offset.
Returns
-------
numeric or ndarray
Linear data :math:`x`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``y`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``x`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`SonyImageworks2012a`
Examples
--------
>>> log_decoding_REDLogFilm(0.457319613085418) # doctest: +ELLIPSIS
0.1799999...
"""
return log_decoding_Cineon(y, black_offset)
[docs]def log_encoding_Log3G10(x, legacy_curve=False):
"""
Defines the *Log3G10* log encoding curve / opto-electronic transfer
function.
Parameters
----------
x : numeric or array_like
Linear data :math:`x`.
legacy_curve : bool, optional
Whether to use the v1 *Log3G10* log encoding curve. Default is *False*.
Returns
-------
numeric or ndarray
Non-linear data :math:`y`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``x`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``y`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
- The v1 *Log3G10* log encoding curve is the one used in *REDCINE-X beta
42*. *Resolve 12.5.2* also uses the v1 curve. *RED* is planning to use
v2 *Log3G10* log encoding curve in the release version of the
*RED SDK*.
Use the `legacy_curve=True` argument to switch to the v1 curve for
compatibility with the current (as of September 21, 2016) *RED SDK*.
- The intent of the v1 *Log3G10* log encoding curve is that zero maps to
zero, 0.18 maps to 1/3, and 10 stops above 0.18 maps to 1.0.
The name indicates this in a similar way to the naming conventions of
*Sony HyperGamma* curves.
The constants used in the functions do not in fact quite hit these
values, but rather than use corrected constants, the functions here
use the official *RED* values, in order to match the output of the
*RED SDK*.
For those interested, solving for constants which exactly hit 1/3
and 1.0 yields the following values::
B = 25 * (np.sqrt(4093.0) - 3) / 9
A = 1 / np.log10(B * 184.32 + 1)
where the function takes the form::
Log3G10(x) = A * np.log10(B * x + 1)
Similarly for *Log3G12*, the values which hit exactly 1/3 and 1.0
are::
B = 25 * (np.sqrt(16381.0) - 3) / 9
A = 1 / np.log10(B * 737.28 + 1)
References
----------
:cite:`Nattress2016a`
Examples
--------
>>> log_encoding_Log3G10(0.18, legacy_curve=True) # doctest: +ELLIPSIS
0.3333336...
>>> log_encoding_Log3G10(0.0) # doctest: +ELLIPSIS
0.0915514...
"""
x = to_domain_1(x)
if legacy_curve:
y = np.sign(x) * 0.222497 * np.log10((np.abs(x) * 169.379333) + 1)
else:
y = (np.sign(x + 0.01) * 0.224282 *
np.log10((np.abs(x + 0.01) * 155.975327) + 1))
return from_range_1(y)
[docs]def log_decoding_Log3G10(y, legacy_curve=False):
"""
Defines the *Log3G10* log decoding curve / electro-optical transfer
function.
Parameters
----------
y : numeric or array_like
Non-linear data :math:`y`.
legacy_curve : bool, optional
Whether to use the v1 *Log3G10* log encoding curve. Default is *False*.
Returns
-------
numeric or ndarray
Linear data :math:`x`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``y`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``x`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Nattress2016a`
Examples
--------
>>> log_decoding_Log3G10(1.0 / 3, legacy_curve=True) # doctest: +ELLIPSIS
0.1799994...
>>> log_decoding_Log3G10(1.0) # doctest: +ELLIPSIS
184.3223476...
"""
y = to_domain_1(y)
if legacy_curve:
x = (np.sign(y) * (10.0 ** (np.abs(y) / 0.222497) - 1) / 169.379333)
else:
x = (np.sign(y) * (10.0 **
(np.abs(y) / 0.224282) - 1) / 155.975327) - 0.01
return from_range_1(x)
[docs]def log_encoding_Log3G12(x):
"""
Defines the *Log3G12* log encoding curve / opto-electronic transfer
function.
Parameters
----------
x : numeric or array_like
Linear data :math:`x`.
Returns
-------
numeric or ndarray
Non-linear data :math:`y`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``x`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``y`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Nattress2016a`
Examples
--------
>>> log_encoding_Log3G12(0.18) # doctest: +ELLIPSIS
0.3333326...
"""
x = to_domain_1(x)
y = np.sign(x) * 0.184904 * np.log10((np.abs(x) * 347.189667) + 1)
return from_range_1(y)
[docs]def log_decoding_Log3G12(y):
"""
Defines the *Log3G12* log decoding curve / electro-optical transfer
function.
Parameters
----------
y : numeric or array_like
Non-linear data :math:`y`.
Returns
-------
numeric or ndarray
Linear data :math:`x`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``y`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``x`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Nattress2016a`
Examples
--------
>>> log_decoding_Log3G12(1.0 / 3) # doctest: +ELLIPSIS
0.1800015...
"""
y = to_domain_1(y)
x = np.sign(y) * (10.0 ** (np.abs(y) / 0.184904) - 1) / 347.189667
return from_range_1(x)