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1 :	jhr	326	%!TEX root = report.tex
2 :			%
3 :			\chapter{The Diderot Basis Environment}
4 :			\label{chap:basis}
5 :
6 :	jhr	329	\newcommand{\PFNSPEC}[4]{\item[\normalfont{$\mathtt{#1} : (#2) #3 \rightarrow #4$}]\mbox{}\\}
7 :			\newcommand{\FNSPEC}[3]{\item[\normalfont{$\mathtt{#1} : #2 \rightarrow #3$}]\mbox{}\\}
8 :	jhr	327	\newcommand{\imageTy}[2]{\mkw{image}(#1)[#2]}
9 :			\newcommand{\kernelTy}[2]{\mkw{kernel\#}#2}
10 :			\newcommand{\fieldTy}[3]{\mkw{field\#}#1(#2)[#3]}
11 :
12 :	jhr	326	\section{Overloaded operators}
13 :
14 :			\section{Other operators}
15 :
16 :			\section{Functions}
17 :			\begin{description}
18 :	jhr	327	\FNSPEC{CL}{\mkw{tensor}[3,3]}{\mkw{real}}
19 :			\PFNSPEC{convolve}{d,k,\sigma}{(\imageTy{d}{\sigma},\,\kernelTy{k})}{\fieldTy{k}{d}{\sigma}}
20 :			\FNSPEC{cos}{\mkw{real}}{\mkw{real}}
21 :	jhr	326	returns the cosine of its argument.
22 :	jhr	327	\PFNSPEC{dot}{d}{(\mkw{tensor}[d],\,\mkw{tensor}[d])}{\mkw{real}}
23 :			\PFNSPEC{inside}{k,d,\sigma}{(\fieldTy{k}{d}{\sigma},\,\mkw{tensor}[d])}{\mkw{bool}}
24 :			\PFNSPEC{load}{d,\sigma}{\mkw{string}}{\imageTy{d}{\sigma}}
25 :	jhr	329	loads the named image file, which should be a Nrrd file.
26 :			Note that this function may only be used in the global initialization part of a Diderot
27 :			program.
28 :	jhr	327	\FNSPEC{max}{(\mkw{real},\,\mkw{real})}{\mkw{real}}
29 :	jhr	326	returns the minimum of its two arguments.
30 :	jhr	327	\FNSPEC{min}{(\mkw{real},\,\mkw{real})}{\mkw{real}}
31 :	jhr	326	returns the maximum of its two arguments.
32 :	jhr	327	\FNSPEC{modulate}{(\mkw{tensor}[d],\,\mkw{tensor}[d])}{\mkw{tensor}[d]}
33 :			\FNSPEC{pow}{(\mkw{real},\,\mkw{real})}{\mkw{real}}
34 :	jhr	326	returns the first argument raised to the power of the second argument.
35 :	jhr	327	\PFNSPEC{principleEvec}{d}{\mkw{tensor}[d,d]}{\mkw{tensor}[d]}
36 :			\FNSPEC{sin}{\mkw{real}}{\mkw{real}}
37 :	jhr	326	returns the sine of its argument.
38 :			\end{description}%
39 :
40 :			\section{Kernels}
41 :			Diderot knows about a number of standard convolution kernels, which are described in the
42 :			following table:
43 :			\begin{center}
44 :			\begin{tabular}{r@{ \texttt{:} }lp{3.5in}}
45 :			\multicolumn{2}{c}{\textbf{Specification}} & \textbf{Description} \\ \hline
46 :			\texttt{bspln3} & \kw{kernel\#}\texttt{2} & cubic bspline reconstruction (does not interpolate) \\
47 :			\texttt{bspln5} & \kw{kernel\#}\texttt{4} & quintic bspline reconstruction (does not interpolate) \\
48 :			\texttt{ctmr} & \kw{kernel\#}\texttt{2} & Catmull-Rom interpolation \\
49 :			\texttt{tent} & \kw{kernel\#}\texttt{0} & linear interpolation \\ \hline
50 :			\end{tabular}%
51 :			\end{center}%

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