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[diderot] Diff of /branches/vis12/doc/report/basis.tex
 [diderot] / branches / vis12 / doc / report / basis.tex

# Diff of /branches/vis12/doc/report/basis.tex

trunk/doc/report/basis.tex revision 1116, Thu May 5 04:49:02 2011 UTC branches/vis12/doc/report/basis.tex revision 1951, Sat Jul 7 19:52:14 2012 UTC
# Line 35  Line 35
35      loads the named image file, which should be a Nrrd file.      loads the named image file, which should be a Nrrd file.
36      Note that this function may only be used in the global initialization part of a Diderot      Note that this function may only be used in the global initialization part of a Diderot
37      program.      program.
38      \PFNSPEC{lerp}{\sigma}{(\tensorTy{\sigma},\,\tensorTy{\sigma},\,\mkw{real})}{\tensorTy{\sigma}}
39        linear interpolationover the interval $[0,1]$:
40        \begin{displaymath}
41          \mathtt{lerp} (x, y, t) = x(1-t) + y
42        \end{displaymath}%
43      \PFNSPEC{lerp}{\sigma}{(\tensorTy{\sigma},\,\tensorTy{\sigma},\,\mkw{real},\,\mkw{real},\,\mkw{real})}{\tensorTy{\sigma}}
44        linear interpolation over the interval $[\mathit{lo},\mathit{hi}]$:
45        \begin{displaymath}
46          \mathtt{lerp} (x, y, \mathit{lo}, t, \mathit{hi}) =
47            \mathtt{lerp}\left({x, y, \frac{t - \mathit{lo}}{\mathit{hi} - \mathit{lo}}}\right)
48        \end{displaymath}%
49    \FNSPEC{max}{(\mkw{real},\,\mkw{real})}{\mkw{real}}    \FNSPEC{max}{(\mkw{real},\,\mkw{real})}{\mkw{real}}
50      returns the minimum of its two arguments.      returns the minimum of its two arguments.
51    \FNSPEC{min}{(\mkw{real},\,\mkw{real})}{\mkw{real}}    \FNSPEC{min}{(\mkw{real},\,\mkw{real})}{\mkw{real}}
52      returns the maximum of its two arguments.      returns the maximum of its two arguments.
53    \FNSPEC{modulate}{(\mkw{tensor}[d],\,\mkw{tensor}[d])}{\mkw{tensor}[d]}    \PFNSPEC{modulate}{d}{(\mkw{tensor}[d],\,\mkw{tensor}[d])}{\mkw{tensor}[d]}
54        component-wise multiplication of two vectors.
55      \PFNSPEC{normalize}{d}{\mkw{tensor}[d]}{\mkw{tensor}[d]}
56        normalize a vector to a unit vector.
57    \FNSPEC{pow}{(\mkw{real},\,\mkw{real})}{\mkw{real}}    \FNSPEC{pow}{(\mkw{real},\,\mkw{real})}{\mkw{real}}
58      returns the first argument raised to the power of the second argument.      returns the first argument raised to the power of the second argument.
59    \PFNSPEC{principleEvec}{d}{\mkw{tensor}[d,d]}{\mkw{tensor}[d]}    \PFNSPEC{principleEvec}{d}{\mkw{tensor}[d,d]}{\mkw{tensor}[d]}
# Line 61  Line 75
75      \multicolumn{2}{c}{\textbf{Specification}} & \textbf{Description} \\ \hline      \multicolumn{2}{c}{\textbf{Specification}} & \textbf{Description} \\ \hline
76      \texttt{bspln3} & \kw{kernel\#}\texttt{2} & cubic bspline reconstruction (does not interpolate) \\      \texttt{bspln3} & \kw{kernel\#}\texttt{2} & cubic bspline reconstruction (does not interpolate) \\
77      \texttt{bspln5} & \kw{kernel\#}\texttt{4} & quintic bspline reconstruction (does not interpolate) \\      \texttt{bspln5} & \kw{kernel\#}\texttt{4} & quintic bspline reconstruction (does not interpolate) \\
78        \texttt{c4hexic} & \kw{kernel\#}\texttt{4} &
79          This kernel is the unique, 6-sample support, hexic, $C^4$ kernel,
80          with 1st and 3rd derivatives zero at origin, which integrates
81          to unity on the interval $[-2,2]$, with 4th order accuracy
82          (errors start showing up on 4th order polynomials).
83          It does not interpolate, but it actually rings once. \\
84      \texttt{ctmr} & \kw{kernel\#}\texttt{1} & Catmull-Rom interpolation \\      \texttt{ctmr} & \kw{kernel\#}\texttt{1} & Catmull-Rom interpolation \\
85      \texttt{tent} & \kw{kernel\#}\texttt{0} & linear interpolation \\ \hline      \texttt{tent} & \kw{kernel\#}\texttt{0} & linear interpolation \\ \hline
86    \end{tabular}%    \end{tabular}%

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