Home My Page Projects Code Snippets Project Openings diderot

# SCM Repository

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

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

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}

Legend:
 Removed from v.628 changed lines Added in v.629