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

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revision 1115, Thu May 5 04:42:18 2011 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{}\\}  \newcommand{\PFNSPEC}[4]{\item[\normalfont{$\mathtt{#1} : (#2) #3 \rightarrow #4$}]\mbox{}\\}
8  \newcommand{\FNSPEC}[3]{\item[\normalfont{$\mathtt{#1} : #2 \rightarrow #3$}]\mbox{}\\}  \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    
# Line 15  Line 18 
18    
19  \section{Functions}  \section{Functions}
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.      loads the named image file, which should be a Nrrd file.
# Line 34  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}

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