Convert equations in figures to MathJax

AOMediaCodec · Aug 22, 2023 · 7ac62ed · 7ac62ed
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diff --git a/footer.include b/footer.include
@@ -163,4 +163,17 @@
 
 })();
 </script>
+<script>
+MathJax = {
+  loader: {
+     load: ['[tex]/tagFormat']
+  },
+  tex: {
+    packages: {'[+]': ['tagFormat']},
+    tags: "all"
+  },
+};
+</script>
+<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
+<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3.0.1/es5/tex-mml-chtml.js"></script>
 </html>
diff --git a/images/3.1.2ch Down-mix Matrix for 5.1.2ch.png b/images/3.1.2ch Down-mix Matrix for 5.1.2ch.png
diff --git a/images/3.1.2ch Down-mix Matrix for 5.1.4ch.png b/images/3.1.2ch Down-mix Matrix for 5.1.4ch.png
diff --git a/images/3.1.2ch Down-mix Matrix for 7.1.2ch.png b/images/3.1.2ch Down-mix Matrix for 7.1.2ch.png
diff --git a/images/3.1.2ch Down-mix Matrix for 7.1.4ch.png b/images/3.1.2ch Down-mix Matrix for 7.1.4ch.png
diff --git a/images/Example of Transformation Matrix with 4 CGs.png b/images/Example of Transformation Matrix with 4 CGs.png
diff --git a/index.bs b/index.bs
@@ -2390,19 +2390,149 @@ This specification RECOMMENDs dynamic down-mixing matrices generated by the down
 
 This section provides RECOMMENDED static down-mix matrices to render to 3.1.2ch from 5.1.2ch, 5.1.4ch, 7.1.2ch, and 7.1.4ch.
 
-<center><img src="images/3.1.2ch Down-mix Matrix for 5.1.2ch.png" style="width:80%; height:auto;"></center>
-<center><figcaption>3.1.2ch Down-mix matrix for 5.1.2ch</figcaption></center>
-
-<center><img src="images/3.1.2ch Down-mix Matrix for 5.1.4ch.png" style="width:80%; height:auto;"></center>
-<center><figcaption>3.1.2ch Down-mix matrix for 5.1.4ch</figcaption></center>
-
-<center><img src="images/3.1.2ch Down-mix Matrix for 7.1.2ch.png" style="width:100%; height:auto;"></center>
-<center><figcaption>3.1.2ch Down-mix matrix for 7.1.2ch</figcaption></center>
-
-<center><img src="images/3.1.2ch Down-mix Matrix for 7.1.4ch.png" style="width:100%; height:auto;"></center>
-<center><figcaption>3.1.2ch Down-mix matrix for 7.1.4ch</figcaption></center>
-
-In the matrices above, p1 = 0.707. Implementations MAY use a limiter defined in [[#processing-post-limiter]] to preserve the energy of audio signals instead of using normalization factors.
+In all the matrices below, \(p = 0.707\). Implementations MAY use a limiter defined in [[#processing-post-limiter]] to preserve the energy of audio signals instead of using normalization factors.
+
+The 3.1.2ch down-mix matrix for 5.1.2ch is:
+
+\[
+\begin{bmatrix}
+	\text{L3} \\
+	\text{C} \\
+	\text{R3} \\
+	\text{Ltf3} \\
+	\text{Rtf3} \\
+	\text{LFE}
+\end{bmatrix}
+=
+\begin{bmatrix}
+	1 & 0 & 0 & p & 0 & 0 & 0 & 0 \\
+	0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 1 & 0 & p & 0 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
+	0 & 0 & 0 & 0 & 0 & 0 & 0 & 1
+\end{bmatrix}
+\ast
+\begin{bmatrix}
+	\text{L5} \\
+	\text{C} \\
+	\text{R5} \\
+	\text{Ls} \\
+	\text{Rs} \\
+	\text{Ltf2} \\
+	\text{Rtf2} \\
+	\text{LFE}
+\end{bmatrix}.
+\]
+
+The 3.1.2ch down-mix matrix for 5.1.4ch is:
+
+\[
+\begin{bmatrix}
+	\text{L3} \\
+	\text{C} \\
+	\text{R3} \\
+	\text{Ltf3} \\
+	\text{Rtf3} \\
+	\text{LFE}
+\end{bmatrix}
+=
+\begin{bmatrix}
+	1 & 0 & 0 & p & 0 & 0 & 0 & 0 & 0 & 0 \\
+	0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 1 & 0 & p & 0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 & 1 & 0 & p & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & p & 0 \\
+	0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1
+\end{bmatrix}
+\ast
+\begin{bmatrix}
+	\text{L5} \\
+	\text{C} \\
+	\text{R5} \\
+	\text{Ls} \\
+	\text{Rs} \\
+	\text{Ltf4} \\
+	\text{Rtf4} \\
+	\text{Ltb} \\
+	\text{Rtb} \\
+	\text{LFE}
+\end{bmatrix}.
+\]
+
+The 3.1.2ch down-mix matrix for 7.1.2ch is:
+
+\[
+\begin{bmatrix}
+	\text{L3} \\
+	\text{C} \\
+	\text{R3} \\
+	\text{Ltf3} \\
+	\text{Rtf3} \\
+	\text{LFE}
+\end{bmatrix}
+=
+\frac{2}{1 + 2 \ast p}
+\ast
+\begin{bmatrix}
+	1 & 0 & 0 & p & 0 & p & 0 & 0 & 0 & 0 \\
+	0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 1 & 0 & p & 0 & p & 0 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
+	0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1
+\end{bmatrix}
+\ast
+\begin{bmatrix}
+	\text{L7} \\
+	\text{C} \\
+	\text{R7} \\
+	\text{Lss} \\
+	\text{Rss} \\
+	\text{Lrs} \\
+	\text{Rrs} \\
+	\text{Ltf2} \\
+	\text{Rtf2} \\
+	\text{LFE}
+\end{bmatrix}.
+\]
+
+The 3.1.2ch down-mix matrix for 7.1.4ch is:
+
+\[
+\begin{bmatrix}
+	\text{L3} \\
+	\text{C} \\
+	\text{R3} \\
+	\text{Ltf3} \\
+	\text{Rtf3} \\
+	\text{LFE}
+\end{bmatrix}
+=
+\frac{2}{1 + 2 \ast p}
+\ast
+\begin{bmatrix}
+	1 & 0 & 0 & p & 0 & p & 0 & 0 & 0 & 0 & 0 & 0 \\
+	0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 1 & 0 & p & 0 & p & 0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & p & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & p & 0 \\
+	0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1
+\end{bmatrix}
+\ast
+\begin{bmatrix}
+	\text{L7} \\
+	\text{C} \\
+	\text{R7} \\
+	\text{Lss} \\
+	\text{Rss} \\
+	\text{Lrs} \\
+	\text{Rrs} \\
+	\text{Ltf2} \\
+	\text{Rtf2} \\
+	\text{LFE}
+\end{bmatrix}.
+\]
 
 
 # IAMF Generation Process (Informative) # {#iamfgeneration}
@@ -2841,8 +2971,93 @@ For a given channel-based input audio and the list of CLs ({CL #i: i = 1, 2, ...
 		- If Ti-1 = 0, the top channels of the [=down-mixed audio=] for CL #i are contained in this [=Channel Group=] #i.
 		- If Ti-1 = 2, the Ltf and Rtf channels of the [=down-mixed audio=] for CL #i are contained in this [=Channel Group=] #i.
 
-The figure below shows one example of a transformation matrix with 4 CGs (2ch/3.1.2ch/5.1.2ch/7.1.4ch).
-
-<center><img src="images/Example of Transformation Matrix with 4 CGs.png" style="width:100%; height:auto;"></center>
-<center><figcaption>Example of Transformation Matrix with 4 CGs</figcaption></center>
-
+An example of a transformation matrix with 4 CGs (2ch/3.1.2ch/5.1.2ch/7.1.4ch) is given below:
+
+\[
+	\begin{array}{c}
+	\text{BCG} \enspace \left\{ \vphantom{
+	    \begin{bmatrix}
+		\text{L2} \\
+		\text{R2}
+	    \end{bmatrix}
+	} \right. \\
+	\vphantom{
+	    \rule{1.5cm}{0.4pt} \\
+	} \\
+	\text{DCG 1} \enspace \left\{ \vphantom{
+	  \begin{bmatrix}
+	      \text{C} \\
+	      \text{Ltf3} \\
+	      \text{Rtf3} \\
+	      \text{LFE}
+	  \end{bmatrix}
+	} \right. \\
+	\vphantom{
+	    \rule{1.5cm}{0.4pt} \\
+	} \\
+	\text{DCG 2} \enspace \left\{ \vphantom{
+	  \begin{bmatrix}
+	      \text{L5} \\
+	      \text{R5} \\
+	  \end{bmatrix}
+	} \right. \\
+	\vphantom{
+	    \rule{1.5cm}{0.4pt} \\
+	} \\
+	\text{DCG 3} \enspace \left\{ \vphantom{
+		\begin{bmatrix}
+		\text{Lss7} \\
+		\text{Rss7} \\
+		\text{Ltf} \\
+		\text{Rtf}
+		\end{bmatrix}
+	} \right. \\
+	\end{array}
+	\begin{bmatrix}
+		\text{L2} \\
+		\text{R2} \\
+		\rule{1.5cm}{0.4pt} \\
+		\text{C} \\
+		\text{Ltf3} \\
+		\text{Rtf3} \\
+		\text{LFE} \\
+		\rule{1.5cm}{0.4pt} \\
+		\text{L5} \\
+		\text{R5} \\
+		\rule{1.5cm}{0.4pt} \\
+		\text{Lss7} \\
+		\text{Rss7} \\
+		\text{Ltf} \\
+		\text{Rtf}
+	\end{bmatrix}
+	=
+	\begin{bmatrix}
+		1 & p_2 & 0 & \delta(k) \ast \alpha(k) & 0 & \delta(k) \ast \beta(k) & 0 & 0 & 0 & 0 & 0 & 0 \\
+		0 & p_2 & 1 & 0 & \delta(k) \ast \alpha(k) & 0 & \delta(k) \ast \beta(k) & 0 & 0 & 0 & 0 & 0 \\
+		0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+		0 & 0 & 0 & w(k) \ast \delta(k) \ast \alpha(k) & 0 & w(k) \ast \delta(k) \ast \beta(k) & 0 & 1 & 0 & \gamma(k) & 0 & 0 \\
+		0 & 0 & 0 & 0 & w(k) \ast \delta(k) \ast \alpha(k) & 0 & w(k) \ast \delta(k) \ast \beta(k) & 0 & 1 & 0 & \gamma(k) & 0 \\
+		0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
+		1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+		0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+		0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+		0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+		0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
+		0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0
+	\end{bmatrix}
+	\ast
+	\begin{bmatrix}
+		\text{L} \\
+		\text{C} \\
+		\text{R} \\
+		\text{Lss} \\
+		\text{Rss} \\
+		\text{Lrs} \\
+		\text{Rrs} \\
+		\text{Ltf} \\
+		\text{Rtf} \\
+		\text{Ltb} \\
+		\text{Rtb} \\
+		\text{LFE}
+	\end{bmatrix}.
+\]