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Revision 1951 - (download) (as text) (annotate)
Sat Jul 7 19:52:14 2012 UTC (9 years, 6 months ago) by jhr
File size: 4294 byte(s)
  added documentation for c4hexic
%!TEX root = report.tex
\chapter{The Diderot Basis Environment}

% polymorphic function 
\newcommand{\PFNSPEC}[4]{\item[\normalfont{$\mathtt{#1} : (#2) #3 \rightarrow #4$}]\mbox{}\\}
\newcommand{\FNSPEC}[3]{\item[\normalfont{$\mathtt{#1} : #2 \rightarrow #3$}]\mbox{}\\}

\section{Overloaded operators}

\section{Other operators}

    returns the principal value of the arc tangent of $\frac{y}{x}$,
    using the signs of both arguments to determine the quadrant of the return
    returns the cosine of its argument (measured in radians).
  \PFNSPEC{dot}{d}{(\tensorTy{d},\, \tensorTy{d})}{\mkw{real}}
    returns the dot product of two vectors.
    loads the named image file, which should be a Nrrd file.
    Note that this function may only be used in the global initialization part of a Diderot
    linear interpolationover the interval $[0,1]$:
      \mathtt{lerp} (x, y, t) = x(1-t) + y
    linear interpolation over the interval $[\mathit{lo},\mathit{hi}]$:
      \mathtt{lerp} (x, y, \mathit{lo}, t, \mathit{hi}) =
        \mathtt{lerp}\left({x, y, \frac{t - \mathit{lo}}{\mathit{hi} - \mathit{lo}}}\right)
    returns the minimum of its two arguments.
    returns the maximum of its two arguments.
    component-wise multiplication of two vectors.
    normalize a vector to a unit vector.
    returns the first argument raised to the power of the second argument.
    returns the sine of its argument (measured in radians).
    returns the square root of its argument.
    returns the tangent of its argument (measured in radians).
    returns the \emph{trace} of a square matrix.

Diderot knows about a number of standard convolution kernels, which are described in the
following table:
  \begin{tabular}{r@{ \texttt{:} }lp{3.5in}}
    \multicolumn{2}{c}{\textbf{Specification}} & \textbf{Description} \\ \hline
    \texttt{bspln3} & \kw{kernel\#}\texttt{2} & cubic bspline reconstruction (does not interpolate) \\
    \texttt{bspln5} & \kw{kernel\#}\texttt{4} & quintic bspline reconstruction (does not interpolate) \\
    \texttt{c4hexic} & \kw{kernel\#}\texttt{4} &
      This kernel is the unique, 6-sample support, hexic, $C^4$ kernel,
      with 1st and 3rd derivatives zero at origin, which integrates
      to unity on the interval $[-2,2]$, with 4th order accuracy
      (errors start showing up on 4th order polynomials).
      It does not interpolate, but it actually rings once. \\
    \texttt{ctmr} & \kw{kernel\#}\texttt{1} & Catmull-Rom interpolation \\
    \texttt{tent} & \kw{kernel\#}\texttt{0} & linear interpolation \\ \hline

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