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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	699	% polymorphic function
7 :	jhr	329	\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 :	jhr	327	\newcommand{\imageTy}[2]{\mkw{image}(#1)[#2]}
10 :			\newcommand{\kernelTy}[2]{\mkw{kernel\#}#2}
11 :			\newcommand{\fieldTy}[3]{\mkw{field\#}#1(#2)[#3]}
12 :	jhr	700	\newcommand{\tensorTy}[1]{\mkw{tensor}[#1]}
13 :			\newcommand{\seqTy}[2]{#1\mkw{\{}#2\mkw{\}}}
14 :	jhr	327
15 :	jhr	326	\section{Overloaded operators}
16 :
17 :			\section{Other operators}
18 :
19 :			\section{Functions}
20 :			\begin{description}
21 :	jhr	699	\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 :	jhr	700	\FNSPEC{CL}{\tensorTy{3,3}}{\mkw{real}}
26 :	jhr	327	\PFNSPEC{convolve}{d,k,\sigma}{(\imageTy{d}{\sigma},\,\kernelTy{k})}{\fieldTy{k}{d}{\sigma}}
27 :			\FNSPEC{cos}{\mkw{real}}{\mkw{real}}
28 :	jhr	699	returns the cosine of its argument (measured in radians).
29 :	jhr	700	\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 :	jhr	327	\PFNSPEC{inside}{k,d,\sigma}{(\fieldTy{k}{d}{\sigma},\,\mkw{tensor}[d])}{\mkw{bool}}
34 :			\PFNSPEC{load}{d,\sigma}{\mkw{string}}{\imageTy{d}{\sigma}}
35 :	jhr	329	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 :	jhr	327	\FNSPEC{max}{(\mkw{real},\,\mkw{real})}{\mkw{real}}
39 :	jhr	326	returns the minimum of its two arguments.
40 :	jhr	327	\FNSPEC{min}{(\mkw{real},\,\mkw{real})}{\mkw{real}}
41 :	jhr	326	returns the maximum of its two arguments.
42 :	jhr	327	\FNSPEC{modulate}{(\mkw{tensor}[d],\,\mkw{tensor}[d])}{\mkw{tensor}[d]}
43 :			\FNSPEC{pow}{(\mkw{real},\,\mkw{real})}{\mkw{real}}
44 :	jhr	326	returns the first argument raised to the power of the second argument.
45 :	jhr	327	\PFNSPEC{principleEvec}{d}{\mkw{tensor}[d,d]}{\mkw{tensor}[d]}
46 :			\FNSPEC{sin}{\mkw{real}}{\mkw{real}}
47 :	jhr	699	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 :	jhr	700	\PFNSPEC{trace}{d}{\tensorTy{d,d}}{\mkw{real}}
53 :			returns the \emph{trace} of a square matrix.
54 :	jhr	326	\end{description}%
55 :
56 :			\section{Kernels}
57 :			Diderot knows about a number of standard convolution kernels, which are described in the
58 :			following table:
59 :			\begin{center}
60 :			\begin{tabular}{r@{ \texttt{:} }lp{3.5in}}
61 :			\multicolumn{2}{c}{\textbf{Specification}} & \textbf{Description} \\ \hline
62 :			\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) \\
64 :	jhr	356	\texttt{ctmr} & \kw{kernel\#}\texttt{1} & Catmull-Rom interpolation \\
65 :	jhr	326	\texttt{tent} & \kw{kernel\#}\texttt{0} & linear interpolation \\ \hline
66 :			\end{tabular}%
67 :			\end{center}%

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