-Segments are the segments of a circle between a chord and the
-perimeter of the circle. This also isn't clear to me, but it appears that
-perhaps the distance from chord to circle perimeter, and circle radius is
-defined by dx and dy. Chord is always horizontal through the origin, then
-translated and then rotated (???).
-
-\subsection{Phantom Size}
-Also note that the overall dimensions of the phantom are increased by 1\%
-above the specified sizes to avoid clipping due to round-off errors.
-So, if the phantom is defined as
-a rectangle of size 0.1 by 0.1, the actual phantom has extent 0.101
-in each direction.
-
-\section{Scanner}\label{conceptscanner}\index{Concepts,Scanner}%
-\subsection{Sizes}
-Understanding the scanning geometry is the most complicated aspect
-of using \ctsim. For our real-world CT simulators, this is actually
-quite simple. The geometry is fixed by the manufacturer during
-the construction of the scanner and can not be changed.
-\ctsim, being a very flexible simulator,
-gives tremendous options is setting up the geometry for a scan.
-
-In general, the geometry for a scan all starts from the size of the
-phantom being scanned. This is because \ctsim\ allows for statistical
-comparisons between the original phantom image and it's reconstructions.
-Since CT scanners scan a circular area, the first important
-variable is the diameter of the circle surround the phantom, or the
-\emph{phantom diameter}. Remember, as mentioned above, the
-phantom dimensions are also padded by 1\%.
-
-The other important geometry variables for scanning objects are
-the \emph{view diameter}, \emph{scan diameter}, and \emph{focal length}.
-These variables are all input into \ctsim\ in terms of ratios rather than
-absolute values.
-
-\subsubsection{Phantom Diameter}
+Segments are complex. They are the portion of an circle between a
+chord and the perimeter of the circle. \texttt{dy} sets the
+radius of the circle. Segments start with the center of the chord
+located at \texttt{(0,0)} and the chord horizontal. The half-width
+of the chord is set by \texttt{dx}. The portion of an circle
+lying below the chord is then added. The imaginary center of this
+circle is located at \texttt{(0,-dy)}. The segment is then rotated
+by \texttt{r} and then translated by \texttt{(cx,cy)}.
+
+\subsubsection{sector}
+Sectors are the like a ``pie slice'' from a circle. The radius of
+the circle is set by \texttt{dy}. Sectors are defined similarly to
+segments. In this case, though, a chord is not drawn. Instead,
+the lines are drawn from the origin of the circle \texttt{(0,-dy)}
+to the points \texttt{(-dx,0)} and \texttt{(dx,0)}. The perimeter
+of the circle is then drawn between those two points and lies
+below the x-axis. The sector is then rotated and translated the
+same as a segment.
+
+\subsection{Phantom Size}\index{Phantom!Size}
+The overall dimensions of the phantom are increased by 1\% above the
+specified sizes to avoid clipping due to round-off errors from
+sampling the polygons of the phantom elements. So, if the phantom is
+defined as a rectangle of size 0.1 by 0.1, the phantom size is
+0.101 in each direction.
+
+\section{Scanner}\label{conceptscanner}\index{Scanner!Concepts}%
+Understanding the scanning geometry is the most complicated aspect of
+using \ctsim. For real-world CT simulators, this is actually quite
+simple. The geometry is fixed by the manufacturer during the
+construction of the scanner and can not be changed. \ctsim,
+being a very flexible simulator, gives tremendous options in
+setting up the geometry for a scan.
+
+\subsection{Dimensions}
+The geometry for a scan starts with the size of
+the phantom being scanned. This is because \ctsim\ allows for
+statistical comparisons between the original phantom image and
+it's reconstructions. Since CT scanners scan a circular area, the
+first important variable is the diameter of the circle surround
+the phantom, the \emph{phantom diameter}. Remember, as mentioned
+above, the phantom dimensions are padded by 1\%.
+
+The other important geometry variables for scanning phantoms are
+the \emph{view diameter}, \emph{scan diameter}, and \emph{focal
+length}. These variables are input into \ctsim\ in terms of
+ratios rather than absolute values.
+
+\subsubsection{Phantom Diameter}\index{Phantom!Diameter}
+The phantom diameter is automatically calculated by \ctsim\ from
+the phantom definition. The maximum of the phantom length and
+height is used to define the square that completely surrounds the
+phantom. Let \latexonly{$p_l$}\latexignore{\emph{Pl}} be the width
+and height of this square. The diameter of this boundary box,
+\latexonly{$p_d$,}\latexignore{\emph{Pd},} is given by the
+Pythagorean theorem and is
+\latexignore{\\\centerline{\emph{Pl x sqrt(2)}}\\}
+\latexonly{\begin{equation}p_d = p_l \sqrt{2}\end{equation}}
+CT scanners collect projections around a
+circle rather than a square. The diameter of this circle is
+the diameter of the boundary square \latexonly{$p_d$.}
+\latexignore{\emph{Pd}.}
+\latexonly{These relationships are diagrammed in figure~\ref{phantomgeomfig}.}