index 974f064..3652358 100644 (file)
@@ -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$and connect the resulting points with straight lines using Bresenham or Wu's algorithm (See Section \ref{Straight Lines}). Whilst the performance of this algorithm is linear, in ???? De Casteljau derived a more efficient means of sub dividing beziers into line segments. A straightforward algorithm for rendering Bezier's is to simply sample$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.

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