X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fsam.git;a=blobdiff_plain;f=chapters%2FBackground_Spline.tex;h=d54ef10f596405b0dec5c7658ee9dc2b27fe6f54;hp=7e2bf4a09c3f8570baa8f2d20e7a2c7fcc452dff;hb=0d7e6aa4d2966020240ea5b5f2a824502f271eaa;hpb=1e1740165abac91f4f620ef8223a30e37e7124ab

diff --git a/chapters/Background_Spline.tex b/chapters/Background_Spline.tex
index 7e2bf4a..d54ef10 100644
--- a/chapters/Background_Spline.tex
+++ b/chapters/Background_Spline.tex
@@ -32,7 +32,7 @@ De Casteljau's algorithm of 1959 is often used for approximating B{\'e}ziers\cit
 \end{align}
 
 
-In much of the literature it is taken as trivial that it is only necessary to specify the control points of a B{\'e}zier in order to be able to render it at any level of detail\cite{knuth1983metafont, computergraphics2}. Recently, Goldman presented an argument that B{\'e}zier's could be considered as fractal in nature, because the De Casteljau algorithm may be modified to be expressed the polynomial $P(t)$ as the result of iterated function system\cite{goldman_thefractal}. If this argument is correct, any primitive that can be described soley in terms of B{\'e}zier Curves may also be considered as fractal in nature. Ideally all these primitives may be rendered at any level of detail or ``zoom'' desired; however, computation of the pixel locations of the curve will be subject to the precision limits of the numerical representation which is used; we discuss these issues in Section \ref{Num}.
+In much of the literature it is taken as trivial that it is only necessary to specify the control points of a B{\'e}zier in order to be able to render it at any level of detail\cite{knuth1983metafont, computergraphics2}. Recently, Goldman presented an argument that B{\'e}zier's could be considered as fractal in nature, because the De Casteljau algorithm may be modified to be expressed the polynomial $P(t)$ as the result of iterated function system\cite{goldman_thefractal}. If this argument is correct, any primitive that can be described soley in terms of B{\'e}zier Curves may also be considered as fractal in nature. Ideally all these primitives may be rendered at any level of detail or ``zoom'' desired; however, computation of the pixel locations of the curve will be subject to the precision limits of the numerical representation which is used; we discuss these issues in Section \ref{Number Representations}.
 
 
 \begin{figure}[H]