Add documentation for aspath and azpath

doc/colvars-refman-main.tex

@@ -2968,7 +2968,7 @@
 \item %
   \key
     {fittingAtoms}{%
-    \texttt{gspath} and \texttt{gspath}}{%
+    \texttt{gspath} and \texttt{gzpath}}{%
     The atoms that are used for alignment}{%
     Group of atoms}{%
 		Before calculating $\mathbf{v}_1$, $\mathbf{v}_2$, $\mathbf{v}_3$ and $\mathbf{v}_4$, the current frame need to be aligned to the corresponding reference frames. This option specifies which atoms are used to do alignment.
@@ -3297,6 +3297,98 @@
 All distances are calculated every \texttt{freq} timesteps to update the list of nearby images.
 }\fi
 
+\cvsubsubsec{\texttt{aspath}: progress along a path defined in atomic Cartesian coordinate space.}{sec:cvc_aspath}
+\labelkey{colvar|aspath}
+
+This CV computes a special case of Eq. \ref{eq:apath_s}, where $x_j$ is the
+$j$-th atomic position, $x_{i,j}$ is the $j$-th atomic position of the $i$-th
+reference frame. The subtraction $x_j - x_{i,j}$ is actually calculated as
+$\mathbf{x}_j - R_i\mathbf{x}_{i,j}$, where $\mathrm{R}_i$ is a 3x3 rotation
+matrix that minimizes the RMSD between the current atomic positions of
+simulation and the $i$-th reference frame. Bold $\mathbf{x}_j$ is used since
+an atomic position is a vector.
+
+\ifdefined\cvvmdornamd{
+For NAMD and VMD users, this component can be regarded as an improved C++
+implementation of the PCV progress component of the Tcl-scripted version
+(see \ref{sec:apath_scripted}).
+}\fi
+
+\begin{cvcoptions}
+\item %
+  \key
+    {atoms}{%
+    \texttt{aspath} and \texttt{azpath}}{%
+    Group of atoms}{%
+    Block \texttt{atoms \{...\}}}{%
+    Defines the atoms whose coordinates make up the value of the component.}
+
+\item %
+  \key
+    {refPositionsCol}{%
+    \texttt{aspath} and \texttt{azpath}}{%
+    PDB column containing atom flags}{%
+    \texttt{O}, \texttt{B}, \texttt{X}, \texttt{Y}, or \texttt{Z}}{%
+    If \texttt{refPositionsFileN} is a PDB file that contains all the atoms in the topology, this option may be provided to set which PDB field is used to flag the reference coordinates for \texttt{atoms}.}
+
+\item %
+  \key
+    {refPositionsFileN}{%
+    \texttt{aspath} and \texttt{azpath}}{%
+    File containing the reference positions for fitting}{%
+    UNIX filename}{%
+		The path is defined by multiple \texttt{refPositionsFile}s which are similiar to \texttt{refPositionsFile} in the \texttt{rmsd} CV. If your path consists of $10$ nodes, you can list the coordinate file (in PDB or XYZ format) from \texttt{refPositionsFile1} to \texttt{refPositionsFile10}.
+    }
+
+\item %
+  \key
+    {fittingAtoms}{%
+    \texttt{aspath} and \texttt{azpath}}{%
+    The atoms that are used for alignment}{%
+    Group of atoms}{%
+		Before calculating $\mathbf{v}_1$, $\mathbf{v}_2$, $\mathbf{v}_3$ and $\mathbf{v}_4$, the current frame need to be aligned to the corresponding reference frames. This option specifies which atoms are used to do alignment.
+    }
+
+\end{cvcoptions}
+
+\cvsubsubsec{\texttt{azpath}: distance from a path defined in atomic Cartesian coordinate space.}{sec:cvc_azpath}
+\labelkey{colvar|azpath}
+
+Similar to \refkey{aspath}{colvar|aspath}, this CV computes a special case of Eq.
+\ref{eq:apath_z}, and shares the same options as \refkey{aspath}{colvar|aspath}.
+
+The usage of \texttt{azpath} and \texttt{aspath} is illustrated below:
+
+\begin{cvexampleinput}
+colvar \{\\
+\-~~\# Progress along the path\\
+\-~~name as\\
+\-~~\# The path is defined by 5 reference frames (from string-00.pdb to string-04.pdb)\\
+\-~~\# Use atomic coordinate from atoms 1, 2 and 3 to compute the path\\
+\-~~aspath \{\\
+\-~~~~atoms \{atomnumbers \{ 1 2 3 \}\}\\
+\-~~~~refPositionsFile1 string-00.pdb\\
+\-~~~~refPositionsFile2 string-01.pdb\\
+\-~~~~refPositionsFile3 string-02.pdb\\
+\-~~~~refPositionsFile4 string-03.pdb\\
+\-~~~~refPositionsFile5 string-04.pdb\\
+\-~~\}\\
+\}\\
+\noindent\ttfamily colvar \{\\
+\-~~\# Distance from the path\\
+\-~~name az\\
+\-~~\# The path is defined by 5 reference frames (from string-00.pdb to string-04.pdb)\\
+\-~~\# Use atomic coordinate from atoms 1, 2 and 3 to compute the path\\
+\-~~azpath \{\\
+\-~~~~atoms \{atomnumbers \{ 1 2 3 \}\}\\
+\-~~~~refPositionsFile1 string-00.pdb\\
+\-~~~~refPositionsFile2 string-01.pdb\\
+\-~~~~refPositionsFile3 string-02.pdb\\
+\-~~~~refPositionsFile4 string-03.pdb\\
+\-~~~~refPositionsFile5 string-04.pdb\\
+\-~~\}\\
+\}
+\end{cvexampleinput}
 
 \cvsubsec{Dense neural network in CV space (MLCV)}{sec:cvc_neuralNetwork}
 \labelkey{colvar|NeuralNetwork}