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

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revision 327, Wed Aug 18 18:32:34 2010 UTC revision 1116, Thu May 5 04:49:02 2011 UTC
# Line 3  Line 3 
3  \chapter{The Diderot Basis Environment}  \chapter{The Diderot Basis Environment}
4  \label{chap:basis}  \label{chap:basis}
5    
6    % polymorphic function
7    \newcommand{\PFNSPEC}[4]{\item[\normalfont{$\mathtt{#1} : (#2) #3 \rightarrow #4$}]\mbox{}\\}
8    \newcommand{\FNSPEC}[3]{\item[\normalfont{$\mathtt{#1} : #2 \rightarrow #3$}]\mbox{}\\}
9  \newcommand{\imageTy}[2]{\mkw{image}(#1)[#2]}  \newcommand{\imageTy}[2]{\mkw{image}(#1)[#2]}
10  \newcommand{\kernelTy}[2]{\mkw{kernel\#}#2}  \newcommand{\kernelTy}[2]{\mkw{kernel\#}#2}
11  \newcommand{\fieldTy}[3]{\mkw{field\#}#1(#2)[#3]}  \newcommand{\fieldTy}[3]{\mkw{field\#}#1(#2)[#3]}
12    \newcommand{\tensorTy}[1]{\mkw{tensor}[#1]}
13    \newcommand{\seqTy}[2]{#1\mkw{\{}#2\mkw{\}}}
14    
15  \section{Overloaded operators}  \section{Overloaded operators}
16    
17  \section{Other operators}  \section{Other operators}
18    
19  \section{Functions}  \section{Functions}
 \newcommand{\PFNSPEC}[4]{\item[\normalfont{$\mathtt{#1} : (#2) #3 \rightarrow #4$}]\mbox{}\\}  
 \newcommand{\FNSPEC}[3]{\item[\normalfont{$\mathtt{#1} : #2 \rightarrow #3$}]\mbox{}\\}  
20  \begin{description}  \begin{description}
21    \FNSPEC{CL}{\mkw{tensor}[3,3]}{\mkw{real}}    \FNSPEC{atan2}{(\mkw{real},\,\mkw{real})}{\mkw{real}}
22        returns the principal value of the arc tangent of $\frac{y}{x}$,
23        using the signs of both arguments to determine the quadrant of the return
24        value.
25      \FNSPEC{CL}{\tensorTy{3,3}}{\mkw{real}}
26    \PFNSPEC{convolve}{d,k,\sigma}{(\imageTy{d}{\sigma},\,\kernelTy{k})}{\fieldTy{k}{d}{\sigma}}    \PFNSPEC{convolve}{d,k,\sigma}{(\imageTy{d}{\sigma},\,\kernelTy{k})}{\fieldTy{k}{d}{\sigma}}
27    \FNSPEC{cos}{\mkw{real}}{\mkw{real}}    \FNSPEC{cos}{\mkw{real}}{\mkw{real}}
28      returns the cosine of its argument.      returns the cosine of its argument (measured in radians).
29    \PFNSPEC{dot}{d}{(\mkw{tensor}[d],\,\mkw{tensor}[d])}{\mkw{real}}    \PFNSPEC{dot}{d}{(\tensorTy{d},\, \tensorTy{d})}{\mkw{real}}
30        returns the dot product of two vectors.
31      \FNSPEC{evals}{\tensorTy{3,3}}{\seqTy{\mkw{vec3}}{3}}
32      \FNSPEC{evecs}{\tensorTy{3,3}}{\seqTy{\mkw{real}}{3}}
33    \PFNSPEC{inside}{k,d,\sigma}{(\fieldTy{k}{d}{\sigma},\,\mkw{tensor}[d])}{\mkw{bool}}    \PFNSPEC{inside}{k,d,\sigma}{(\fieldTy{k}{d}{\sigma},\,\mkw{tensor}[d])}{\mkw{bool}}
34    \PFNSPEC{load}{d,\sigma}{\mkw{string}}{\imageTy{d}{\sigma}}    \PFNSPEC{load}{d,\sigma}{\mkw{string}}{\imageTy{d}{\sigma}}
35        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
37        program.
38    \FNSPEC{max}{(\mkw{real},\,\mkw{real})}{\mkw{real}}    \FNSPEC{max}{(\mkw{real},\,\mkw{real})}{\mkw{real}}
39      returns the minimum of its two arguments.      returns the minimum of its two arguments.
40    \FNSPEC{min}{(\mkw{real},\,\mkw{real})}{\mkw{real}}    \FNSPEC{min}{(\mkw{real},\,\mkw{real})}{\mkw{real}}
# Line 31  Line 44 
44      returns the first argument raised to the power of the second argument.      returns the first argument raised to the power of the second argument.
45    \PFNSPEC{principleEvec}{d}{\mkw{tensor}[d,d]}{\mkw{tensor}[d]}    \PFNSPEC{principleEvec}{d}{\mkw{tensor}[d,d]}{\mkw{tensor}[d]}
46    \FNSPEC{sin}{\mkw{real}}{\mkw{real}}    \FNSPEC{sin}{\mkw{real}}{\mkw{real}}
47      returns the sine of its argument.      returns the sine of its argument (measured in radians).
48      \FNSPEC{sqrt}{\mkw{real}}{\mkw{real}}
49        returns the square root of its argument.
50      \FNSPEC{tan}{\mkw{real}}{\mkw{real}}
51        returns the tangent of its argument (measured in radians).
52      \PFNSPEC{trace}{d}{\tensorTy{d,d}}{\mkw{real}}
53        returns the \emph{trace} of a square matrix.
54  \end{description}%  \end{description}%
55    
56  \section{Kernels}  \section{Kernels}
# Line 42  Line 61 
61      \multicolumn{2}{c}{\textbf{Specification}} & \textbf{Description} \\ \hline      \multicolumn{2}{c}{\textbf{Specification}} & \textbf{Description} \\ \hline
62      \texttt{bspln3} & \kw{kernel\#}\texttt{2} & cubic bspline reconstruction (does not interpolate) \\      \texttt{bspln3} & \kw{kernel\#}\texttt{2} & cubic bspline reconstruction (does not interpolate) \\
63      \texttt{bspln5} & \kw{kernel\#}\texttt{4} & quintic bspline reconstruction (does not interpolate) \\      \texttt{bspln5} & \kw{kernel\#}\texttt{4} & quintic bspline reconstruction (does not interpolate) \\
64      \texttt{ctmr} & \kw{kernel\#}\texttt{2} & Catmull-Rom interpolation \\      \texttt{ctmr} & \kw{kernel\#}\texttt{1} & Catmull-Rom interpolation \\
65      \texttt{tent} & \kw{kernel\#}\texttt{0} & linear interpolation \\ \hline      \texttt{tent} & \kw{kernel\#}\texttt{0} & linear interpolation \\ \hline
66    \end{tabular}%    \end{tabular}%
67  \end{center}%  \end{center}%

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