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Commit b7ff94df authored by Mauro Carvalho Chehab's avatar Mauro Carvalho Chehab
Browse files

[media] pixfmt-007.rst: use Sphinx math:: expressions 



Enrich math formulas by using the Sphinx math. That will allow
using those formulas on pdf documents as well.

Signed-off-by: default avatarMauro Carvalho Chehab <mchehab@s-opensource.com>
parent 43c78e11

Documentation/media/uapi/v4l/pixfmt-007.rst

+114 −61
Original line number Diff line number Diff line
@@ -74,23 +74,29 @@ SMPTE C set, so this colorspace is sometimes called SMPTE C as well. 
The transfer function defined for SMPTE 170M is the same as the one

defined in Rec. 709.



    L' = -1.099(-L) :sup:`0.45` + 0.099 for L ≤ -0.018

.. math::



    L' = 4.5L for -0.018 < L < 0.018

    L' = -1.099(-L)^{0.45} + 0.099 \text{, for } L \le-0.018



    L' = 1.099L :sup:`0.45` - 0.099 for L ≥ 0.018

    L' = 4.5L \text{, for } -0.018 < L < 0.018



    L' = 1.099L^{0.45} - 0.099 \text{, for } L \ge 0.018



Inverse Transfer function:



    L = -((L' - 0.099) / -1.099) :sup:`1/0.45` for L' ≤ -0.081

.. math::



    L = -\left( \frac{L' - 0.099}{-1.099} \right) ^{\frac{1}{0.45}} \text{, for } L' \le -0.081



    L = L' / 4.5 for -0.081 < L' < 0.081

    L = \frac{L'}{4.5} \text{, for } -0.081 < L' < 0.081



    L = ((L' + 0.099) / 1.099) :sup:`1/0.45` for L' ≥ 0.081

    L = \left(\frac{L' + 0.099}{1.099}\right)^{\frac{1}{0.45} } \text{, for } L' \ge 0.081



The luminance (Y') and color difference (Cb and Cr) are obtained with

the following ``V4L2_YCBCR_ENC_601`` encoding:



.. math::



    Y' = 0.299R' + 0.587G' + 0.114B'



    Cb = -0.169R' - 0.331G' + 0.5B'
@@ -173,23 +179,29 @@ The full name of this standard is Rec. ITU-R BT.709-5. 
Transfer function. Normally L is in the range [0…1], but for the

extended gamut xvYCC encoding values outside that range are allowed.



    L' = -1.099(-L) :sup:`0.45` + 0.099 for L ≤ -0.018

.. math::



    L' = 4.5L for -0.018 < L < 0.018

    L' = -1.099(-L)^{0.45} + 0.099 \text{, for } L \le -0.018



    L' = 1.099L :sup:`0.45` - 0.099 for L ≥ 0.018

    L' = 4.5L \text{, for } -0.018 < L < 0.018



    L' = 1.099L^{0.45} - 0.099 \text{, for } L \ge 0.018



Inverse Transfer function:



    L = -((L' - 0.099) / -1.099) :sup:`1/0.45` for L' ≤ -0.081

.. math::



    L = -\left( \frac{L' - 0.099}{-1.099} \right)^\frac{1}{0.45} \text{, for } L' \le -0.081



    L = L' / 4.5 for -0.081 < L' < 0.081

    L = \frac{L'}{4.5}\text{, for } -0.081 < L' < 0.081



    L = ((L' + 0.099) / 1.099) :sup:`1/0.45` for L' ≥ 0.081

    L = \left(\frac{L' + 0.099}{1.099}\right)^{\frac{1}{0.45} } \text{, for } L' \ge 0.081



The luminance (Y') and color difference (Cb and Cr) are obtained with

the following ``V4L2_YCBCR_ENC_709`` encoding:



.. math::



    Y' = 0.2126R' + 0.7152G' + 0.0722B'



    Cb = -0.1146R' - 0.3854G' + 0.5B'
@@ -214,22 +226,26 @@ similar to the Rec. 709 encoding, but it allows for R', G' and B' values 
that are outside the range [0…1]. The resulting Y', Cb and Cr values are

scaled and offset:



    Y' = (219 / 256) * (0.2126R' + 0.7152G' + 0.0722B') + (16 / 256)

.. math::



    Y' = \frac{219}{256} * (0.2126R' + 0.7152G' + 0.0722B') + \frac{16}{256}



    Cb = (224 / 256) * (-0.1146R' - 0.3854G' + 0.5B')

    Cb = \frac{224}{256} * (-0.1146R' - 0.3854G' + 0.5B')



    Cr = (224 / 256) * (0.5R' - 0.4542G' - 0.0458B')

    Cr = \frac{224}{256} * (0.5R' - 0.4542G' - 0.0458B')



The xvYCC 601 encoding (``V4L2_YCBCR_ENC_XV601``, :ref:`xvycc`) is

similar to the BT.601 encoding, but it allows for R', G' and B' values

that are outside the range [0…1]. The resulting Y', Cb and Cr values are

scaled and offset:



    Y' = (219 / 256) * (0.299R' + 0.587G' + 0.114B') + (16 / 256)

.. math::



    Cb = (224 / 256) * (-0.169R' - 0.331G' + 0.5B')

    Y' = \frac{219}{256} * (0.299R' + 0.587G' + 0.114B') + \frac{16}{256}



    Cr = (224 / 256) * (0.5R' - 0.419G' - 0.081B')

    Cb = \frac{224}{256} * (-0.169R' - 0.331G' + 0.5B')



    Cr = \frac{224}{256} * (0.5R' - 0.419G' - 0.081B')



Y' is clamped to the range [0…1] and Cb and Cr are clamped to the range

[-0.5…0.5]. The non-standard xvYCC 709 or xvYCC 601 encodings can be
@@ -304,24 +320,30 @@ These chromaticities are identical to the Rec. 709 colorspace. 
Transfer function. Note that negative values for L are only used by the

Y'CbCr conversion.



    L' = -1.055(-L) :sup:`1/2.4` + 0.055 for L < -0.0031308

.. math::



    L' = -1.055(-L)^{\frac{1}{2.4} } + 0.055\text{, for }L < -0.0031308



    L' = 12.92L for -0.0031308 ≤ L ≤ 0.0031308

    L' = 12.92L\text{, for }-0.0031308 \le L \le 0.0031308



    L' = 1.055L :sup:`1/2.4` - 0.055 for 0.0031308 < L ≤ 1

    L' = 1.055L ^{\frac{1}{2.4} } - 0.055\text{, for }0.0031308 < L \le 1



Inverse Transfer function:



    L = -((-L' + 0.055) / 1.055) :sup:`2.4` for L' < -0.04045

.. math::



    L = L' / 12.92 for -0.04045 ≤ L' ≤ 0.04045

    L = -((-L' + 0.055) / 1.055) ^{2.4}\text{, for }L' < -0.04045



    L = ((L' + 0.055) / 1.055) :sup:`2.4` for L' > 0.04045

    L = L' / 12.92\text{, for }-0.04045 \le L' \le 0.04045



    L = ((L' + 0.055) / 1.055) ^{2.4}\text{, for }L' > 0.04045



The luminance (Y') and color difference (Cb and Cr) are obtained with

the following ``V4L2_YCBCR_ENC_SYCC`` encoding as defined by

:ref:`sycc`:



.. math::



    Y' = 0.2990R' + 0.5870G' + 0.1140B'



    Cb = -0.1687R' - 0.3313G' + 0.5B'
@@ -403,15 +425,21 @@ are: 


Transfer function:



    L' = L :sup:`1/2.19921875`

.. math::



    L' = L ^{\frac{1}{2.19921875}}



Inverse Transfer function:



    L = L' :sup:`2.19921875`

.. math::



    L = L'^{(2.19921875)}



The luminance (Y') and color difference (Cb and Cr) are obtained with

the following ``V4L2_YCBCR_ENC_601`` encoding:



.. math::



    Y' = 0.299R' + 0.587G' + 0.114B'



    Cb = -0.169R' - 0.331G' + 0.5B'
@@ -489,19 +517,25 @@ of the primary colors and the white reference are: 


Transfer function (same as Rec. 709):



    L' = 4.5L for 0 ≤ L < 0.018

.. math::



    L' = 1.099L :sup:`0.45` - 0.099 for 0.018 ≤ L ≤ 1

    L' = 4.5L\text{, for }0 \le L < 0.018



    L' = 1.099L ^{0.45} - 0.099\text{, for } 0.018 \le L \le 1



Inverse Transfer function:



    L = L' / 4.5 for L' < 0.081

.. math::



    L = L' / 4.5\text{, for } L' < 0.081



    L = ((L' + 0.099) / 1.099) :sup:`1/0.45` for L' ≥ 0.081

    L = \left( \frac{L' + 0.099}{1.099}\right) ^{\frac{1}{0.45} }\text{, for } L' \ge 0.081



The luminance (Y') and color difference (Cb and Cr) are obtained with

the following ``V4L2_YCBCR_ENC_BT2020`` encoding:



.. math::



    Y' = 0.2627R' + 0.6780G' + 0.0593B'



    Cb = -0.1396R' - 0.3604G' + 0.5B'
@@ -516,23 +550,20 @@ There is also an alternate constant luminance R'G'B' to Yc'CbcCrc 


Luma:



    Yc' = (0.2627R + 0.6780G + 0.0593B)'



B' - Yc' ≤ 0:



    Cbc = (B' - Yc') / 1.9404



B' - Yc' > 0:



    Cbc = (B' - Yc') / 1.5816



R' - Yc' ≤ 0:



    Crc = (R' - Y') / 1.7184



R' - Yc' > 0:



    Crc = (R' - Y') / 0.9936

.. math::

    :nowrap:



    \begin{align*}

    Yc' = (0.2627R + 0.6780G + 0.0593B)'& \\

    B' - Yc' \le 0:& \\

        &Cbc = (B' - Yc') / 1.9404 \\

    B' - Yc' > 0: & \\

        &Cbc = (B' - Yc') / 1.5816 \\

    R' - Yc' \le 0:& \\

        &Crc = (R' - Y') / 1.7184 \\

    R' - Yc' > 0:& \\

        &Crc = (R' - Y') / 0.9936

    \end{align*}



Yc' is clamped to the range [0…1] and Cbc and Crc are clamped to the

range [-0.5…0.5]. The Yc'CbcCrc quantization is limited range.
@@ -610,11 +641,15 @@ is ``V4L2_XFER_FUNC_DCI_P3``. The default Y'CbCr encoding is 


Transfer function:



    L' = L :sup:`1/2.6`

.. math::



    L' = L^{\frac{1}{2.6}}



Inverse Transfer function:



    L = L' :sup:`2.6`

.. math::



    L = L'^{(2.6)}



Y'CbCr encoding is not specified. V4L2 defaults to Rec. 709.
@@ -686,19 +721,25 @@ These chromaticities are identical to the SMPTE 170M colorspace. 


Transfer function:



    L' = 4L for 0 ≤ L < 0.0228

.. math::



    L' = 1.1115L :sup:`0.45` - 0.1115 for 0.0228 ≤ L ≤ 1

    L' = 4L\text{, for } 0 \le L < 0.0228



    L' = 1.1115L ^{0.45} - 0.1115\text{, for } 0.0228 \le L \le 1



Inverse Transfer function:



    L = L' / 4 for 0 ≤ L' < 0.0913

.. math::



    L = \frac{L'}{4}\text{, for } 0 \le L' < 0.0913



    L = ((L' + 0.1115) / 1.1115) :sup:`1/0.45` for L' ≥ 0.0913

    L = \left( \frac{L' + 0.1115}{1.1115}\right) ^{\frac{1}{0.45} }\text{, for } L' \ge 0.0913



The luminance (Y') and color difference (Cb and Cr) are obtained with

the following ``V4L2_YCBCR_ENC_SMPTE240M`` encoding:



.. math::



    Y' = 0.2122R' + 0.7013G' + 0.0865B'



    Cb = -0.1161R' - 0.3839G' + 0.5B'
@@ -782,19 +823,25 @@ reference are: 
The transfer function was never properly defined for NTSC 1953. The Rec.

709 transfer function is recommended in the literature:



    L' = 4.5L for 0 ≤ L < 0.018

.. math::



    L' = 1.099L :sup:`0.45` - 0.099 for 0.018 ≤ L ≤ 1

    L' = 4.5L\text{, for } 0 \le L < 0.018



    L' = 1.099L ^{0.45} - 0.099\text{, for } 0.018 \le L \le 1



Inverse Transfer function:



    L = L' / 4.5 for L' < 0.081

.. math::



    L = \frac{L'}{4.5} \text{, for } L' < 0.081



    L = ((L' + 0.099) / 1.099) :sup:`1/0.45` for L' ≥ 0.081

    L = \left( \frac{L' + 0.099}{1.099}\right) ^{\frac{1}{0.45} }\text{, for } L' \ge 0.081



The luminance (Y') and color difference (Cb and Cr) are obtained with

the following ``V4L2_YCBCR_ENC_601`` encoding:



.. math::



    Y' = 0.299R' + 0.587G' + 0.114B'



    Cb = -0.169R' - 0.331G' + 0.5B'
@@ -874,19 +921,25 @@ are: 
The transfer function was never properly defined for this colorspace.

The Rec. 709 transfer function is recommended in the literature:



    L' = 4.5L for 0 ≤ L < 0.018

.. math::



    L' = 4.5L\text{, for } 0 \le L < 0.018



    L' = 1.099L :sup:`0.45` - 0.099 for 0.018 ≤ L ≤ 1

    L' = 1.099L ^{0.45} - 0.099\text{, for } 0.018 \le L \le 1



Inverse Transfer function:



    L = L' / 4.5 for L' < 0.081

.. math::



    L = ((L' + 0.099) / 1.099) :sup:`1/0.45` for L' ≥ 0.081

    L = \frac{L'}{4.5} \text{, for } L' < 0.081



    L = \left(\frac{L' + 0.099}{1.099} \right) ^{\frac{1}{0.45} }\text{, for } L' \ge 0.081



The luminance (Y') and color difference (Cb and Cr) are obtained with

the following ``V4L2_YCBCR_ENC_601`` encoding:



.. math::



    Y' = 0.299R' + 0.587G' + 0.114B'



    Cb = -0.169R' - 0.331G' + 0.5B'