Merge branch 'master' of github.com:sfstoolbox/sfs-documentation

* 'master' of github.com:sfstoolbox/sfs-documentation:
  Adjust figure numbers
  Add dipole png preview
  Fixed a typo
  figure for monochromatic 3D dipole source
  replace old equation labelling for 3D Dipole Source
  add formulas for 3D dipole source

02_theory_of_sound_field_synthesis/02_theory_of_sound_field_synthesis.tex

@@ -15,6 +15,7 @@
 {\PATH/\CHAPTWO/fig2_10/}%
 {\PATH/\CHAPTWO/fig2_11/}%
 {\PATH/\CHAPTWO/fig2_12/}%
+{\PATH/\CHAPTWO/fig2_13/}%
 }
 
 
@@ -723,6 +724,53 @@ \section{Model-Based Rendering}
 for $|k_x|<|\omegac|$ and with $(x_\text{s},y_\text{s})$ describing the position
 of the point source.
 
+%----%----%----%----%----%----%----%----%----%----%----%----%----%----%----%----
+\paragraph{3D Dipole Source}
+\label{sec:dipole_source_3D}
+%
+The source model for a three dimensional dipole source is given by the
+directional derivative of the three dimensional Green's function with respect to
+\(\ns\) defining the orientation of the dipole source.
+%
+\begin{equation}
+  \begin{aligned}
+  S(\x,\omega) &= A(\omega) 
+  \left\langle
+    \nabla_{\xs} \left( \frac{1}{4\PI} \frac{\E^{-\I\omegac|\x-\xs|}}{|\x-\xs|}
+    \right), \ns
+  \right\rangle \\
+  &=
+    A(\omega)
+    \frac{1}{4\PI} 
+    \left( \frac{1}{|\x-\xs|} + \I \omegac \right)
+    \frac{\langle \x-\xs, \ns \rangle}{|\x-\xs|^2}
+    \E^{-\I\omegac|\x-\xs|}
+  \qp
+  \end{aligned}
+  \eqlabel{S:dps}
+\end{equation}
+%
+\begin{marginfigure}
+  \centering
+  \ft
+  \input{fig2_06/sound_field_dipole_source}
+  \caption{Sound pressure for a monochromatic 3D dipole source
+    ~(\ref{eq:S:dps}) placed at $(0,0,0)$. Parameters: $f =
+    800$\,Hz.
+    \reproduce{\GITHUB/fig2_06}}
+\end{marginfigure}
+%
+Transformed to the temporal domain this becomes
+%
+\begin{equation}
+  s(\x,t) = a(t) *
+  \left( \frac{1}{|\x-\xs|} + \IFT{ \frac{\I\omega}{c} } \right)
+  *
+  \frac{\langle \x-\xs, \ns \rangle}{4\PI |\x-\xs|^2}
+  \deltafunc{t - \frac{|\x-\xs|}{c}} .
+  \eqlabel{s:dps}
+\end{equation}
+%
 
 %----%----%----%----%----%----%----%----%----%----%----%----%----%----%----%----
 \paragraph{Line Source}
@@ -740,11 +788,11 @@ \section{Model-Based Rendering}
 \begin{marginfigure}
     \centering
     \ft
-    \input{fig2_06/sound_field_line_source}
+    \input{fig2_07/sound_field_line_source}
     \caption{Sound pressure for a monochromatic line
     source~(\ref{eq:S:ls}) placed at $(0,0,0)$. Parameters: $f =
         800$\,Hz.
-        \reproduce{\GITHUB/fig2_06}}
+        \reproduce{\GITHUB/fig2_07}}
 \end{marginfigure}
 %
 Applying the large argument approximation of the Hankel
@@ -833,11 +881,11 @@ \subsection{Near-Field Compensated Higher Order Ambisonics and Spectral Division
 \begin{marginfigure}
     \centering
     \ft
-    \input{fig2_07/sound_field_nfchoa_pw}
+    \input{fig2_08/sound_field_nfchoa_pw}
     \caption{Sound pressure of a monochromatic plane wave synthesized with
         \twohalfD \ac{NFC-HOA}~(\ref{eq:D:hoa:pw:2.5D}). Parameters: $\n_k = (0,-1,0)$,
         $\xref = (0,0,0)$, $f = 1$\,kHz.
-        \reproduce{\GITHUB/fig2_07}}
+        \reproduce{\GITHUB/fig2_08}}
 \end{marginfigure}
 %
 For a circular secondary source distribution with radius $R_0$ the circular
@@ -924,11 +972,11 @@ \subsection{Near-Field Compensated Higher Order Ambisonics and Spectral Division
 \begin{marginfigure}
     \centering
     \ft
-    \input{fig2_08/sound_field_nfchoa_ps}
+    \input{fig2_09/sound_field_nfchoa_ps}
     \caption{Sound pressure for a monochromatic point source synthesized by
         \twohalfD \ac{NFC-HOA}~\eqref{eq:D:hoa:ps:2.5D}. Parameters: $\xs =
         (0,2.5,0)$\,m, $\xref = (0,0,0)$, $f = 1$\,kHz.
-        \reproduce{\GITHUB/fig2_08}}
+        \reproduce{\GITHUB/fig2_09}}
 \end{marginfigure}
 %
 For a circular secondary source distribution with radius $R_0$ and point source
@@ -1060,11 +1108,11 @@ \subsection{Wave Field Synthesis}
 \begin{marginfigure}[-0.5cm]
     \centering
     \ft
-    \input{fig2_09/sound_field_wfs_pw}
+    \input{fig2_10/sound_field_wfs_pw}
     \caption{Sound pressure for a monochromatic plane wave synthesized by
     \twohalfD \ac{WFS}~(\ref{eq:D:wfs:pw:2.5D}). Parameters: $\n_k = (0,-1,0)$, $\xref
         = (0,0,0)$, $f = 1$\,kHz.
-        \reproduce{\GITHUB/fig2_09}}
+        \reproduce{\GITHUB/fig2_10}}
 \end{marginfigure}
 %
 Transfered to the temporal domain via an inverse Fourier
@@ -1124,11 +1172,11 @@ \subsection{Wave Field Synthesis}
 \begin{marginfigure}
     \centering
     \ft
-    \input{fig2_10/sound_field_wfs_ps}
+    \input{fig2_11/sound_field_wfs_ps}
     \caption{Sound pressure for a monochromatic point source synthesized by
         \twohalfD \ac{WFS}~(\ref{eq:D:wfs:ps:2.5D}). Parameters: $\xs = (0,2.5,0)$\,m,
         $\xref = (0,0,0)$, $f = 1$\,kHz.
-        \reproduce{\GITHUB/fig2_10}}
+        \reproduce{\GITHUB/fig2_11}}
 \end{marginfigure}
 %
 \begin{multline}
@@ -1235,11 +1283,11 @@ \subsection{Wave Field Synthesis}
 \begin{marginfigure}
     \centering
     \ft
-    \input{fig2_11/sound_field_wfs_ls}
+    \input{fig2_12/sound_field_wfs_ls}
     \caption{Sound pressure for a monochromatic line source synthesized by
         \twohalfD \ac{WFS}~\eqref{eq:D:wfs:ls:2.5D}. Parameters: $\xs = (0,2.5,0)$\,m,
         $\xref = (0,0,0)$, $f = 1$\,kHz.
-        \reproduce{\GITHUB/fig2_11}}
+        \reproduce{\GITHUB/fig2_12}}
 \end{marginfigure}
 %
 Applying $\H{1}{2}(\zeta) \approx -\sqrt{\frac{2}{\PI \I\zeta}} \E^{-\I\zeta}$ for $z\gg1$ after
@@ -1288,11 +1336,11 @@ \subsection{Wave Field Synthesis}
 \begin{marginfigure}
     \centering
     \ft
-    \input{fig2_12/sound_field_wfs_fs}
+    \input{fig2_13/sound_field_wfs_fs}
     \caption{Sound pressure of a mono-frequent focused source synthesized with
         \twohalfD \ac{WFS}~(\ref{eq:D:wfs:fs:2.5D}). Parameters: $\xs = (0,0.5,0)$\,m,
         $\n_\text{s} = (0,-1,0)$, $\xref = (0,0,0)$, $f = 1$\,kHz.
-        \reproduce{\GITHUB/fig2_12}}
+        \reproduce{\GITHUB/fig2_13}}
     \label{fig:wfs_focused_source}
 \end{marginfigure}
 %

02_theory_of_sound_field_synthesis/fig2_06/README.md

@@ -1,7 +1,7 @@
 ![Fig 2.6](fig2_06.png)
 
 **Figure 2.6**: Sound pressure for a
-monochromatic line source (2.39)
+monochromatic dipole source (2.39)
 placed at (0,0,0). Parameters:
 f = 800 Hz.