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Unformatted text preview: s ( u ) consisting of segments s ( u ) and s 1 ( u ) at u = 1 , u = 2 , u = 5 , and u = 7 in order to draw s ( n ) and the respective Bezier polygons over the interval [0 , 9]. ( 10 points ) 7.3. For distinct points P , P 1 , . . . , P n , the Bezier curve of order n ( n = 0 , 1 , 2 , . . . ) can be recur-sively deﬁned by B ( t, P ) := P B n ( t, P , . . . , P n ) := (1-t ) · B n-1 ( t, P , . . . , P n-1 ) + t · B n-1 ( t, P 1 , . . . , P n ) ( n > 0) where 0 ≤ t ≤ 1. Show that for any non-negative integer n , the Bezier curve of order n is given by the equation B n ( t, P , . . . , P n ) = n X k =0 ± n k ² t k (1-t ) n-k · P k ( 7 points ) Due: 26.03.10, at 3 pm (in the mailbox labeled Linsen in the entrance hall of Res.I )...
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- Spring '10
- Numerical Analysis, Polynomial interpolation, Prof. Dr. Lars Linsen, Dr. Lars Linsen