Webby DOM stuff

[ipdf/sam.git] / chapters / Background.tex

diff --git a/chapters/Background.tex b/chapters/Background.tex
index bc3b089..8a85ce0 100644 (file)
--- a/chapters/Background.tex
+++ b/chapters/Background.tex
@@ -30,8 +30,7 @@ Splines are continuous curves formed from piecewise polynomial segments. A polyn
 
 A straight line is simply a polynomial of $0$th degree. Splines may be rasterised by sampling of $y(x)$ at a number of points $x_i$ and rendering straight lines between  $(x_i, y_i)$ and $(x_{i+1}, y_{i+1})$ as discussed in Section \ref{Straight Lines}. More direct algorithms for drawing splines based upon Brasenham and Wu's algorithms also exist\cite{citationneeded}.
 
 
 A straight line is simply a polynomial of $0$th degree. Splines may be rasterised by sampling of $y(x)$ at a number of points $x_i$ and rendering straight lines between  $(x_i, y_i)$ and $(x_{i+1}, y_{i+1})$ as discussed in Section \ref{Straight Lines}. More direct algorithms for drawing splines based upon Brasenham and Wu's algorithms also exist\cite{citationneeded}.
 

-There are many different ways to define a spline. One approach is to specify ``knots'' on the spline and solve for the cooefficients to generate a cubic spline ($n = 3$) passing through the points. Alternatively, special polynomials may be defined using ``control'' points which themselves are not part of the curve; these are convenient for graphical based editors. For example, drawing bezier curves with the mouse is the primary method of constructing paths in the Inkscape SVG editor\cite{inkscape}.
-
+There are many different ways to define a spline. One approach is to specify ``knots'' on the spline and solve for the cooefficients to generate a cubic spline ($n = 3$) passing through the points. Alternatively, special polynomials may be defined using ``control'' points which themselves are not part of the curve; these are convenient for graphical based editors. Bezier splines are the most straight forward way to define a curve in the standards considered in Section \ref{Document Representations}

 \subsubsection{Bezier Curves}
 \input{chapters/Background_Bezier}
 
 \subsubsection{Bezier Curves}
 \input{chapters/Background_Bezier}
 


@@ -55,7 +54,7 @@ Traditionally, vector graphics have been rasterized by the CPU before being sent
 
 \rephrase{2. Here are the ways documents are structured ... we got here eventually}
 
 
 \rephrase{2. Here are the ways documents are structured ... we got here eventually}
 

-\section{Document Representations}
+\section{Document Representations}\label{Document Representations}

 
 The representation of information, particularly for scientific purposes, has changed dramatically over the last few decades. For example, Brassel's 1979 paper referenced earlier has been produced on a mechanical type writer. Although the paper discusses an algorithm for shading on computer displays, the figures illustrating this algorithm have not been generated by a computer, but drawn by Brassel's assistant\cite{brassel1979analgorithm}. In contrast, modern papers such as Barnes et. al's recent paper on embedding 3d images in PDF documents\cite{barnes2013embeddding} can themselves be an interactive proof of concept.
 
 
 The representation of information, particularly for scientific purposes, has changed dramatically over the last few decades. For example, Brassel's 1979 paper referenced earlier has been produced on a mechanical type writer. Although the paper discusses an algorithm for shading on computer displays, the figures illustrating this algorithm have not been generated by a computer, but drawn by Brassel's assistant\cite{brassel1979analgorithm}. In contrast, modern papers such as Barnes et. al's recent paper on embedding 3d images in PDF documents\cite{barnes2013embeddding} can themselves be an interactive proof of concept.
 


@@ -88,6 +87,7 @@ Hayes' 2012 article ``Pixels or Perish'' discusses the recent history and curren
        \item Solves security issues, more efficient
 \end{itemize}
 
        \item Solves security issues, more efficient
 \end{itemize}
 

+\pagebreak

 \subsection{Document Object Model}\label{Document Object Model}
 \input{chapters/Background_DOM}
 
 \subsection{Document Object Model}\label{Document Object Model}
 \input{chapters/Background_DOM}
 


@@ -107,7 +107,7 @@ The document and the code that produces it are one and the same.
 
 \section{Precision in Modern Document Formats}
 
 
 \section{Precision in Modern Document Formats}
 

-We briefly summarise the requirements of standard document formats in regards to the precision of number representations:
+We briefly summarise the requirements of the standards discussed so far in regards to the precision of mathematical operations:

 \begin{itemize}
        \item {\bf PostScript} predates the IEEE-754 standard and originally specified a floating point representation with ? bits of exponent and ? bits of mantissa. Version ? of the PostScript standard changed to specify IEEE-754 binary32 ``single precision'' floats.
        \item {\bf PDF} has also specified IEEE-754 binary32 since version ?. Importantly, the standard states that this is a \emph{maximum} precision; documents created with higher precision would not be viewable in Adobe Reader.
 \begin{itemize}
        \item {\bf PostScript} predates the IEEE-754 standard and originally specified a floating point representation with ? bits of exponent and ? bits of mantissa. Version ? of the PostScript standard changed to specify IEEE-754 binary32 ``single precision'' floats.
        \item {\bf PDF} has also specified IEEE-754 binary32 since version ?. Importantly, the standard states that this is a \emph{maximum} precision; documents created with higher precision would not be viewable in Adobe Reader.