Literally not finished

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

diff --git a/chapters/Background_Bezier.tex b/chapters/Background_Bezier.tex
deleted file mode 100644 (file)
index 9f24b17..0000000
--- a/chapters/Background_Bezier.tex
+++ /dev/null
@@ -1,14 +0,0 @@
-Cubic and Quadratic Bezier Splines are used to define curved paths in the PostScript\cite{plrm}, PDF\cite{pdfref17} and SVG\cite{svg2011-1.1} standards which we will discuss in Section \ref{Document Representations}.  Cubic Beziers are also used to define vector fonts for rendering text\cite{knuth1983metafont} (See Section \ref{Fonts}).
-
-A Bezier Curve of degree $n$ is defined by $n$ ``control points'' $\left\{P_0, ... P_n\right\}$. 
-Points $P(t) = (x(t), y(t))$ along the curve are defined by:
-\begin{align}
-       P(t) &= \displaystyle\sum_{j=0}^{n} B_j^n(t) P_j
-\end{align}
-Where $t \epsilon [0,1]$ is a control parameter. $P(0) = P_0$ and $P(1) = P_n$.
-
-A straightforward algorithm for rendering Bezier's is to simply sample $P(t)$ for suffiently many values of $t$ and connect the resulting points with straight lines using Bresenham or Wu's algorithm (See Section \ref{Straight Lines}). Whilst the performance of this algorithm is linear, De Casteljau derived a more efficient means of sub dividing beziers into line segments.
-
-Recently, Goldman presented an argument that Bezier's could be considered as fractal in nature, because the De Casteljau algorithm could be modified to be expressed as an iterated function system\cite{goldman_thefractal}.
-
-