"""
RED Log Encodings
=================
Define 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_v1`
- :func:`colour.models.log_decoding_Log3G10_v1`
- :func:`colour.models.log_encoding_Log3G10_v2`
- :func:`colour.models.log_decoding_Log3G10_v2`
- :func:`colour.models.log_encoding_Log3G10_v3`
- :func:`colour.models.log_decoding_Log3G10_v3`
- :attr:`colour.models.LOG3G10_ENCODING_METHODS`
- :func:`colour.models.log_encoding_Log3G10`
- :attr:`colour.models.LOG3G10_DECODING_METHODS`
- :func:`colour.models.log_decoding_Log3G10`
- :func:`colour.models.log_encoding_Log3G12`
- :func:`colour.models.log_decoding_Log3G12`
References
----------
- :cite:`Nattress2016a` : Nattress, G. (2016). Private Discussion with Shaw,
N.
- :cite:`REDDigitalCinema2017` : RED Digital Cinema. (2017). White Paper on
REDWideGamutRGB and Log3G10. Retrieved January 16, 2021, from
https://www.red.com/download/white-paper-on-redwidegamutrgb-and-log3g10
- :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 annotations
import numpy as np
from colour.hints import ArrayLike, Literal, NDArrayFloat
from colour.models.rgb.transfer_functions import (
log_decoding_Cineon,
log_encoding_Cineon,
)
from colour.utilities import (
CanonicalMapping,
as_float,
as_float_array,
from_range_1,
to_domain_1,
validate_method,
)
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "BSD-3-Clause - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"
__all__ = [
"log_encoding_REDLog",
"log_decoding_REDLog",
"log_encoding_REDLogFilm",
"log_decoding_REDLogFilm",
"log_encoding_Log3G10_v1",
"log_decoding_Log3G10_v1",
"log_encoding_Log3G10_v2",
"log_decoding_Log3G10_v2",
"log_encoding_Log3G10_v3",
"log_decoding_Log3G10_v3",
"LOG3G10_ENCODING_METHODS",
"log_encoding_Log3G10",
"LOG3G10_DECODING_METHODS",
"log_decoding_Log3G10",
"log_encoding_Log3G12",
"log_decoding_Log3G12",
]
[docs]
def log_encoding_REDLog(
x: ArrayLike,
black_offset: ArrayLike = 10 ** ((0 - 1023) / 511),
) -> NDArrayFloat:
"""
Define the *REDLog* log encoding curve / opto-electronic transfer
function.
Parameters
----------
x
Linear data :math:`x`.
black_offset
Black offset.
Returns
-------
:class:`numpy.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)
black_offset = as_float_array(black_offset)
y = (1023 + 511 * np.log10(x * (1 - black_offset) + black_offset)) / 1023
return as_float(from_range_1(y))
[docs]
def log_decoding_REDLog(
y: ArrayLike,
black_offset: ArrayLike = 10 ** ((0 - 1023) / 511),
) -> NDArrayFloat:
"""
Define the *REDLog* log decoding curve / electro-optical transfer
function.
Parameters
----------
y
Non-linear data :math:`y`.
black_offset
Black offset.
Returns
-------
:class:`numpy.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)
black_offset = as_float_array(black_offset)
x = ((10 ** ((1023 * y - 1023) / 511)) - black_offset) / (1 - black_offset)
return as_float(from_range_1(x))
[docs]
def log_encoding_REDLogFilm(
x: ArrayLike,
black_offset: ArrayLike = 10 ** ((95 - 685) / 300),
) -> NDArrayFloat:
"""
Define the *REDLogFilm* log encoding curve / opto-electronic transfer
function.
Parameters
----------
x
Linear data :math:`x`.
black_offset
Black offset.
Returns
-------
:class:`numpy.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: ArrayLike,
black_offset: ArrayLike = 10 ** ((95 - 685) / 300),
) -> NDArrayFloat:
"""
Define the *REDLogFilm* log decoding curve / electro-optical transfer
function.
Parameters
----------
y
Non-linear data :math:`y`.
black_offset
Black offset.
Returns
-------
:class:`numpy.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)
def log_encoding_Log3G10_v1(x: ArrayLike) -> NDArrayFloat:
"""
Define the *Log3G10* *v1* log encoding curve / opto-electronic transfer
function, the curve used in *REDCINE-X PRO Beta 42* and *Resolve 12.5.2*.
Parameters
----------
x
Linear data :math:`x`.
Returns
-------
:class:`numpy.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_Log3G10_v1(0.18) # doctest: +ELLIPSIS
0.3333336...
"""
x = to_domain_1(x)
y = np.sign(x) * 0.222497 * np.log10((np.abs(x) * 169.379333) + 1)
return as_float(from_range_1(y))
def log_decoding_Log3G10_v1(y: ArrayLike) -> NDArrayFloat:
"""
Define the *Log3G10* *v1* log decoding curve / electro-optical transfer
function, the curve used in *REDCINE-X PRO Beta 42* and *Resolve 12.5.2*.
Parameters
----------
y
Non-linear data :math:`y`.
Returns
-------
:class:`numpy.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_v1(1.0 / 3) # doctest: +ELLIPSIS
0.1799994...
"""
y = to_domain_1(y)
x = np.sign(y) * (10.0 ** (np.abs(y) / 0.222497) - 1) / 169.379333
return as_float(from_range_1(x))
def log_encoding_Log3G10_v2(x: ArrayLike) -> NDArrayFloat:
"""
Define the *Log3G10* *v2* log encoding curve / opto-electronic transfer
function, the current curve in *REDCINE-X PRO*.
Parameters
----------
x
Linear data :math:`x`.
Returns
-------
:class:`numpy.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_Log3G10_v2(0.0) # doctest: +ELLIPSIS
0.0915514...
"""
x = to_domain_1(x)
y = np.sign(x + 0.01) * 0.224282 * np.log10((np.abs(x + 0.01) * 155.975327) + 1)
return as_float(from_range_1(y))
def log_decoding_Log3G10_v2(y: ArrayLike) -> NDArrayFloat:
"""
Define the *Log3G10* *v2* log decoding curve / electro-optical transfer
function, the current curve in *REDCINE-X PRO*.
Parameters
----------
y
Non-linear data :math:`y`.
Returns
-------
:class:`numpy.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_v2(1.0) # doctest: +ELLIPSIS
184.3223476...
"""
y = to_domain_1(y)
x = (np.sign(y) * (10.0 ** (np.abs(y) / 0.224282) - 1) / 155.975327) - 0.01
return as_float(from_range_1(x))
def log_encoding_Log3G10_v3(x: ArrayLike) -> NDArrayFloat:
"""
Define the *Log3G10* *v3* log encoding curve / opto-electronic transfer
function, the curve described in the *RedLog3G10* Whitepaper.
Parameters
----------
x
Linear data :math:`x`.
Returns
-------
:class:`numpy.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:`REDDigitalCinema2017`
Examples
--------
>>> log_encoding_Log3G10_v3(0.0) # doctest: +ELLIPSIS
0.09155148...
"""
a = 0.224282
b = 155.975327
c = 0.01
g = 15.1927
x = to_domain_1(x)
x = x + c
y = np.where(x < 0.0, x * g, np.sign(x) * a * np.log10((np.abs(x) * b) + 1.0))
return as_float(from_range_1(y))
def log_decoding_Log3G10_v3(y: ArrayLike) -> NDArrayFloat:
"""
Define the *Log3G10* *v3* log decoding curve / electro-optical transfer
function, the curve described in the *RedLog3G10* whitepaper.
Parameters
----------
y
Non-linear data :math:`y`.
Returns
-------
:class:`numpy.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:`REDDigitalCinema2017`
Examples
--------
>>> log_decoding_Log3G10_v3(1.0) # doctest: +ELLIPSIS
184.32234764...
"""
a = 0.224282
b = 155.975327
c = 0.01
g = 15.1927
y = to_domain_1(y)
x = np.where(
y < 0.0,
(y / g) - c,
np.sign(y) * (10 ** (np.abs(y) / a) - 1.0) / b - c,
)
return as_float(from_range_1(x))
LOG3G10_ENCODING_METHODS: CanonicalMapping = CanonicalMapping(
{
"v1": log_encoding_Log3G10_v1,
"v2": log_encoding_Log3G10_v2,
"v3": log_encoding_Log3G10_v3,
}
)
LOG3G10_ENCODING_METHODS.__doc__ = """
Supported *Log3G10* log encoding curve / opto-electronic transfer function
methods.
References
----------
:cite:`Nattress2016a`, :cite:`REDDigitalCinema2017`
"""
[docs]
def log_encoding_Log3G10(
x: ArrayLike,
method: Literal["v1", "v2", "v3"] | str = "v3",
) -> NDArrayFloat:
"""
Define the *Log3G10* log encoding curve / opto-electronic transfer
function.
Parameters
----------
x
Linear data :math:`x`.
method
Computation method.
Returns
-------
:class:`numpy.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 *Log3G10* *v1* 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 the *Log3G10* *v2* log encoding curve in the release
version of the *RED SDK*.
- The intent of the *Log3G10* *v1* 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`, :cite:`REDDigitalCinema2017`
Examples
--------
>>> log_encoding_Log3G10(0.0) # doctest: +ELLIPSIS
0.09155148...
>>> log_encoding_Log3G10(0.18, method="v1") # doctest: +ELLIPSIS
0.3333336...
"""
method = validate_method(method, tuple(LOG3G10_ENCODING_METHODS))
return LOG3G10_ENCODING_METHODS[method](x)
LOG3G10_DECODING_METHODS = CanonicalMapping(
{
"v1": log_decoding_Log3G10_v1,
"v2": log_decoding_Log3G10_v2,
"v3": log_decoding_Log3G10_v3,
}
)
LOG3G10_DECODING_METHODS.__doc__ = """
Supported *Log3G10* log decoding curve / electro-optical transfer function
methods.
References
----------
:cite:`Nattress2016a`, :cite:`REDDigitalCinema2017`
"""
[docs]
def log_decoding_Log3G10(
y, method: Literal["v1", "v2", "v3"] | str = "v3"
) -> NDArrayFloat:
"""
Define the *Log3G10* log decoding curve / electro-optical transfer
function.
Parameters
----------
y
Non-linear data :math:`y`.
method
Computation method.
Returns
-------
:class:`numpy.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`, :cite:`REDDigitalCinema2017`
Examples
--------
>>> log_decoding_Log3G10(1.0) # doctest: +ELLIPSIS
184.3223476...
>>> log_decoding_Log3G10(1.0 / 3, method="v1") # doctest: +ELLIPSIS
0.1799994...
"""
method = validate_method(method, tuple(LOG3G10_DECODING_METHODS))
return LOG3G10_DECODING_METHODS[method](y)
[docs]
def log_encoding_Log3G12(x: ArrayLike) -> NDArrayFloat:
"""
Define the *Log3G12* log encoding curve / opto-electronic transfer
function.
Parameters
----------
x
Linear data :math:`x`.
Returns
-------
:class:`numpy.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`, :cite:`REDDigitalCinema2017`
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 as_float(from_range_1(y))
[docs]
def log_decoding_Log3G12(y: ArrayLike) -> NDArrayFloat:
"""
Define the *Log3G12* log decoding curve / electro-optical transfer
function.
Parameters
----------
y
Non-linear data :math:`y`.
Returns
-------
:class:`numpy.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`, :cite:`REDDigitalCinema2017`
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 as_float(from_range_1(x))