Literally not finished

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

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@@ -13,7 +13,7 @@ Bresenham's Line Algorithm was developed in 1965 with the motivation of controll
 
 In Figure \ref{rasterising-line} a) and b) we illustrate the rasterisation of a line width a single pixel width. The path followed by Bresenham's algorithm is shown. It can be seen that the pixels which are more than half filled by the line are set by the algorithm. This causes a jagged effect called aliasing which is particularly noticable on low resolution displays. From a signal processing point of view this can be understood as due to the sampling of a continuous signal on a discrete grid\cite{wu1991anefficient}.
 
-Figure \ref{rasterising-line} c) shows an (idealised) antialiased rendering of the line. The pixel intensity has been set to the average of the line and background colours over that pixel. Such an ideal implementation would be impractically computationally expensive on real devices\cite{elias2000graphics}. In 1991 Wu introduced an algorithm for drawing anti-aliased lines which, while equivelant in results to existing algorithms by Fujimoto and Iwata, set the state of the art in performance\cite{wu1991anefficient}\footnote{Techniques for anti-aliasing primitives other than straight lines, including the anti-aliasing of images in a raster format shown at different scales (such as Figure \ref{}) are discussed in some detail in Chapter 4 of ``Computer Graphics'' \cite{computergraphics2}}.
+Figure \ref{rasterising-line} c) shows an (idealised) antialiased rendering of the line. The pixel intensity has been set to the average of the line and background colours over that pixel. Such an ideal implementation would be impractically computationally expensive on real devices\cite{elias2000graphics}. In 1991 Wu introduced an algorithm for drawing anti-aliased lines which, while equivelant in results to existing algorithms by Fujimoto and Iwata, set the state of the art in performance\cite{wu1991anefficient}\footnote{Techniques for anti-aliasing primitives other than straight lines are discussed in some detail in Chapter 4 of ``Computer Graphics'' \cite{computergraphics2}}.
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