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Diff of /branches/pure-cfg/doc/probe/paper.tex

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revision 628, Wed Mar 16 15:56:29 2011 UTC revision 629, Wed Mar 16 23:14:00 2011 UTC
# Line 57  Line 57 
57  \maketitle  \maketitle
58  \thispagestyle{empty}  \thispagestyle{empty}
59    
 \bibliographystyle{../common/alpha}  
 \bibliography{../common/strings-short,../common/manticore}  
   
60  \section{Introduction}  \section{Introduction}
61    
62  This note describes the code needed to implement a probe of a field operation.  This note describes the code needed to implement a probe of a field operation.
# Line 85  Line 82 
82  \begin{eqnarray*}  \begin{eqnarray*}
83    \left[\begin{array}{c} x \\ 1 \end{array}\right] & = & \matM^{-1} \left[\begin{array}{c} p \\ 1 \end{array}\right] \qquad \text{\textit{transform to image space}} \\    \left[\begin{array}{c} x \\ 1 \end{array}\right] & = & \matM^{-1} \left[\begin{array}{c} p \\ 1 \end{array}\right] \qquad \text{\textit{transform to image space}} \\
84    n  & = & \FLOOR{x} \qquad \text{\textit{integer part of position}} \\    n  & = & \FLOOR{x} \qquad \text{\textit{integer part of position}} \\
85    f  & = & x - f \qquad \text{\textit{fractional part of position}} \\    f  & = & x - n \qquad \text{\textit{fractional part of position}} \\
86    F\mkw{@}p & = & \sum_{i=1-s}^s {V(n+i) h(f - i)}    F\mkw{@}p & = & \sum_{i=1-s}^s {V(n+i) h(f - i)}
87  \end{eqnarray*}%  \end{eqnarray*}%
88  Note that the coordinate system of the convolution filter is flipped (negated) from the coordinate system  Note that the coordinate system of the convolution filter is flipped (negated) from the coordinate system
# Line 100  Line 97 
97  \end{displaymath}%  \end{displaymath}%
98  Thus, we can rewrite the probe computation as  Thus, we can rewrite the probe computation as
99  \begin{displaymath}  \begin{displaymath}
100    F\mkw{@}x = \sum_{i=1-s}^{s} {V(n+i) h_{s-i}(i - f)}    F\mkw{@}x = \sum_{i=1-s}^{s} {V(n+i) h_{s-i}(f - i)}
101  \end{displaymath}%  \end{displaymath}%
102  \figref{fig:1d-probe} illustrates the situation for a kernel $h$ with support $s = 2$,  \figref{fig:1d-probe} illustrates the situation for a kernel $h$ with support $s = 2$,
103  and \figref{fig:1d-probe-code} gives the C code for the probe operation, assuming that  and \figref{fig:1d-probe-code} gives the C code for the probe operation, assuming that
# Line 447  Line 444 
444  \label{fig:3d-deriv-probe-code-c}  \label{fig:3d-deriv-probe-code-c}
445  \end{figure}  \end{figure}
446    
447    
448    \bibliographystyle{../common/alpha}
449    \bibliography{../common/strings-short,../common/manticore}
450    
451  \end{document}  \end{document}

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