Remove dot points add waffles

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

diff --git a/chapters/Background_Bezier.tex b/chapters/Background_Bezier.tex
index 974f064..3652358 100644 (file)
--- a/chapters/Background_Bezier.tex
+++ b/chapters/Background_Bezier.tex
@@ -10,5 +10,5 @@ Figure \ref{bezier_3} shows a Bezier Curve defined by the points $\left\{(0,0),
 
 A straightforward algorithm for rendering Bezier's is to simply sample $P(t)$ for some number of 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, in ???? 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, 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. The cost of this modification is that the algorithm is no longer $O(n)$ but $O(n^2)$; although it is not explicitly stated by Goldman it seems clear that the modified algorithm is mainly of theoretical interest.
+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.