X-Git-Url: https://git.ucc.asn.au/?a=blobdiff_plain;f=chapters%2FBackground_Bezier.tex;h=2d49de986d4b2ad2b658da65864d78e63f8bed27;hb=747a93660e5c5784f9f76b6c4f2a60bb92f7bdf3;hp=3652358d48a85f38780fbc4cd7d5c965c93aaed3;hpb=fb42dc0335ed47cbfdd9176a1cfdd37cab487ddd;p=ipdf%2Fsam.git diff --git a/chapters/Background_Bezier.tex b/chapters/Background_Bezier.tex index 3652358..2d49de9 100644 --- a/chapters/Background_Bezier.tex +++ b/chapters/Background_Bezier.tex @@ -7,6 +7,7 @@ Points $P(t)$ along the curve are defined by: From this definition it should be apparent $P(t)$ for a Bezier Curve of degree $0$ maps to a single point, whilst $P(t)$ for a Bezier of degree $1$ is a straight line between $P_0$ and $P_1$. $P(t)$ always begins at $P_0$ for $t = 0$ and ends at $P_n$ when $t = 1$. Figure \ref{bezier_3} shows a Bezier Curve defined by the points $\left\{(0,0), (1,0), (1,1)\right\}$. +Figure \ref{SVG} shows a more complex spline defined by Bezier curves. 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.