Webby DOM stuff

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

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+Cubic beziers form all curves in the PostScript\cite{plrm}, PDF\cite{pdfref17} and SVG\cite{svg2011-1.1} standards which we will discuss in Section \ref{Document Representations}. One of the shapes in Figure \ref{SVG} is a region defined by a cubic bezier spline. Beziers are also used to construct vector fonts for rendering text in these standards.
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 A Bezier Curve of degree $n$ is defined by $n$ ``control points'' $\left\{P_0, ... P_n\right\}$. 
 Points $P(t)$ along the curve are defined by:
 \begin{align}
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 Recently, Goldman presented an argument that Bezier's could be considered as fractal in nature, a fractal being the fixed point of an iterated function system\cite{goldman_thefractal}. Goldman's proof depends upon a modification to the De Casteljau Subdivision algorithm which expresses the subdivisions as an iterated function system.
 
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