From 33e20f3f11252dd8d023d82753a341a20e90aacb Mon Sep 17 00:00:00 2001
From: jthorn <jthorn@0f49ee68-0e4f-0410-9b9c-b2c123ded7ef>
Date: Wed, 19 Apr 2006 03:02:55 +0000
Subject: some small tidying * fix the title and one other place: this is thorn
 AEILocalInterp,   not thorn LocalInterp * switch to new-style latex cactus
 style * a few small wording clarifications & typo fixes * add a reference on
 the non-smoothness of interpolation errors

git-svn-id: http://svn.aei.mpg.de/numrel/AEIThorns/AEILocalInterp/trunk@32 0f49ee68-0e4f-0410-9b9c-b2c123ded7ef
---
 doc/documentation.tex | 31 +++++++++++++++++++------------
 1 file changed, 19 insertions(+), 12 deletions(-)

diff --git a/doc/documentation.tex b/doc/documentation.tex
index 856e63b..bd32575 100644
--- a/doc/documentation.tex
+++ b/doc/documentation.tex
@@ -74,7 +74,7 @@
 % (Automatically used from Cactus distribution, if you have a 
 %  thorn without the Cactus Flesh download this from the Cactus
 %  homepage at www.cactuscode.org)
-\usepackage{../../../../doc/ThornGuide/cactus}
+\usepackage{../../../../doc/latex/cactus}
 
 \begin{document}
 
@@ -84,7 +84,7 @@
 \author{Jonathan Thornburg, incorporating code from Thomas Radke} 
 
 % The title of the document (not necessarily the name of the Thorn)
-\title{Thorn Guide for the {\bf LocalInterp} Thorn}
+\title{Thorn Guide for the {\bf AEILocalInterp} Thorn}
 
 % the date your document was last changed, if your document is in CVS, 
 % please us:
@@ -223,12 +223,12 @@ algorithm:
 \begin{verbatim}
 for each interpolation point
 {
-choose an interpolation molecule position
-  somewhere near the interpolation point
+choose an interpolation molecule position somewhere near the interpolation point
+
         for each output array
         {
-        compute an interpolating polynomial which approximates
-          the input data at the molecule points
+        compute an interpolating polynomial
+          which approximates the input data at the molecule points
         output = polynomial(interpolation point)
         }
 }
@@ -256,8 +256,15 @@ something special is done the interpolating function isn't smooth,
 with $O(\Delta x^n)$ jump discontinuities each time the interpolating
 polynomial changes.  Correspondingly, the interpolation error is
 generically a ``bump function'' which is zero at each grid point
-and rises to a local maximum in each grid cell.  This is the case,
-for example, for tensor-product Lagrange polynomial interpolation.
+and rises to a local maximum in each grid cell.%%%
+\footnote{%%%
+	 For a further discussion of the non-smoothness of
+	 interpolation errors, see appendix~F of J. Thornburg,
+	 \textit{Physical Review D} \textbf{59(10)}, 104007.
+	 }%%%
+{}  This is the case, for example, for tensor-product Lagrange
+polynomial interpolation.%%%
+	 
 
 [For maximum-degree Lagrange polynomial interpolation, the
 interpolation error may not be zero at the grid points, and the
@@ -283,7 +290,7 @@ interpolant.
 
 \subsection{More Terminology}
 
-As given in the Function Reference section of the Cactus User's Guide,
+As described in the Function Reference section of the Cactus User's Guide,
 \verb|interp_coords|, \verb|input_arrays|, and \verb|output_arrays| are
 actually all pointers to arrays of \verb|void *| pointers, since we
 support a number of different Cactus data types.  Internally, the
@@ -332,7 +339,7 @@ space.  (For example, the molecule position might just be the \verb|(i,j,k)|
 coordinates of the molecule's center.)  We also introduce
 \defn{molecule coordinates} \verb|(mi,mj,jk)|, which are just
 \verb|(i,j,k)| coordinates relative to the molecule position.
-We use \verb|m| or as a generic molecule coordinate.  Thus
+We use \verb|m| as a generic molecule coordinate.  Thus
 (in notation which should be obvious) a generic molecule operation
 can be written
 \begin{equation}
@@ -1471,8 +1478,8 @@ worry -- the code is actually ok.%%%
 this same file; again don't worry, the code is ok.
 
 See the \verb|README| file in the source code directory
-\verb|LocalInterp/src/UniformCartesian/| for further details on the
-implementation.
+\verb|AEILocalInterp/src/| and in its subdirectories for further details
+on the implementation.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-- 
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