Enrich math formulas by using the Sphinx math. That will allow
using those formulas on pdf documents as well.
Signed-off-by: Mauro Carvalho Chehab <mchehab@xxxxxxxxxxxxxxxx>
---
Documentation/conf.py | 9 +-
Documentation/media/uapi/v4l/pixfmt-007.rst | 175 ++++++++++++++++++----------
2 files changed, 115 insertions(+), 69 deletions(-)
diff --git a/Documentation/conf.py b/Documentation/conf.py
index 96b7aa66c89c..163782912df9 100644
--- a/Documentation/conf.py
+++ b/Documentation/conf.py
@@ -28,14 +28,7 @@ sys.path.insert(0, os.path.abspath('sphinx'))
# Add any Sphinx extension module names here, as strings. They can be
# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
# ones.
-extensions = ['kernel-doc', 'rstFlatTable', 'kernel_include']
-
-# Gracefully handle missing rst2pdf.
-try:
- import rst2pdf
- extensions += ['rst2pdf.pdfbuilder']
-except ImportError:
- pass
+extensions = ['sphinx.ext.imgmath', 'kernel-doc', 'rstFlatTable', 'kernel_include']
# Add any paths that contain templates here, relative to this directory.
templates_path = ['_templates']
diff --git a/Documentation/media/uapi/v4l/pixfmt-007.rst b/Documentation/media/uapi/v4l/pixfmt-007.rst
index 8c946b0c63a0..2ecace31b9f5 100644
--- a/Documentation/media/uapi/v4l/pixfmt-007.rst
+++ b/Documentation/media/uapi/v4l/pixfmt-007.rst
@@ -72,23 +72,29 @@ 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 = L' / 4.5 for -0.081 < L' < 0.081
+ L = -\left( \frac{L' - 0.099}{-1.099} \right) ^{\frac{1}{0.45}} \text{, for } L' \le -0.081
- L = ((L' + 0.099) / 1.099) :sup:`1/0.45` for L' ≥ 0.081
+ L = \frac{L'}{4.5} \text{, for } -0.081 < 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'
@@ -169,23 +175,29 @@ 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 = L' / 4.5 for -0.081 < L' < 0.081
+ L = -\left( \frac{L' - 0.099}{-1.099} \right)^\frac{1}{0.45} \text{, for } L' \le -0.081
- L = ((L' + 0.099) / 1.099) :sup:`1/0.45` for L' ≥ 0.081
+ L = \frac{L'}{4.5}\text{, for } -0.081 < 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'
@@ -210,22 +222,26 @@ 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::
- Cb = (224 / 256) * (-0.1146R' - 0.3854G' + 0.5B')
+ Y' = \frac{219}{256} * (0.2126R' + 0.7152G' + 0.0722B') + \frac{16}{256}
- Cr = (224 / 256) * (0.5R' - 0.4542G' - 0.0458B')
+ Cb = \frac{224}{256} * (-0.1146R' - 0.3854G' + 0.5B')
+
+ 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
@@ -298,24 +314,30 @@ 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' = 12.92L for -0.0031308 ≤ L ≤ 0.0031308
+ L' = -1.055(-L)^{\frac{1}{2.4} } + 0.055\text{, for }L < -0.0031308
- L' = 1.055L :sup:`1/2.4` - 0.055 for 0.0031308 < L ≤ 1
+ L' = 12.92L\text{, for }-0.0031308 \le L \le 0.0031308
+
+ 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'
@@ -395,15 +417,21 @@ 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'
@@ -479,19 +507,25 @@ 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' + 0.099) / 1.099) :sup:`1/0.45` for L' ≥ 0.081
+ L = 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_BT2020`` encoding:
+.. math::
+
Y' = 0.2627R' + 0.6780G' + 0.0593B'
Cb = -0.1396R' - 0.3604G' + 0.5B'
@@ -506,23 +540,20 @@ 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.
@@ -596,11 +627,15 @@ 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.
@@ -670,19 +705,25 @@ 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 = ((L' + 0.1115) / 1.1115) :sup:`1/0.45` for L' ≥ 0.0913
+ L = \frac{L'}{4}\text{, for } 0 \le 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'
@@ -762,19 +803,25 @@ 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 = ((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'
@@ -852,19 +899,25 @@ 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' = 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' + 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'
--
2.7.4
--
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