Date post: | 19-Dec-2015 |
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1
Outline
• What is polar form?
• B-Spline– Labeling, why (0,1,2), (1,2,3)… ?– Knot Vector, why (-2,-1,0,1,2,…) ?
• Derivation of B-Spline points– Maybe(!?)
2
What is Polar Form Labeling?
• The sequences of parameters applied at each level of pyramid for de Casteljau evaluation.
P0 P1 P2
1-u0 1-u0u0 u0
u11-u1u1
u0
Pnew = (u0, u1)
20
(0,0,0)
(1,1,1)(0,0,1)
(0,1,1)
(2,2,2)
(1,1,2)
(1,2,2)
(0,1,2)
(0,0,0)
(0,0,1)
(0,1,1)
(0,0,0)
(0,0,1)
(0,1,2)
(0,1,1)
(0,0,0)
(0,0,1)(1,1,1)
(0,1,2)
(0,1,1)
(0,0,0)
(0,0,1)(1,1,2)
(1,1,1)
(0,1,2)
(0,1,1)
(0,0,0)
(0,0,1) (1,2,2)
(1,1,2)
(1,1,1)
(0,1,2)
(0,1,1)
(0,0,0)
(0,0,1)
(2,2,2)
(1,2,2)
(1,1,2)
(1,1,1)
(0,1,2)
(0,1,1)
(0,0,0)
(0,0,1)
22
(2,2,2)
(1,2,2)
(1,1,2)
(1,1,1)
(0,1,2)
(0,1,1)
(0,0,0)
(0,0,1)
(3,3,3)
(2,3,3)
(2,2,3)
(1,2,3)
(-1,-1,-1)
(0,-1,-1)
(0,0,-1)
(1,0,-1)
23
(2,2,2)
(1,2,2)
(1,1,2)
(1,1,1)
(0,1,2)
(0,1,1)
(0,0,0)
(0,0,1)
(3,3,3)
(2,3,3)
(2,2,3)
(1,2,3)
(-1,-1,-1)
(0,-1,-1)
(0,0,-1)
(-1,0,1) (-2,-2,-2)
(-1,-1,-2)
(-1,-2,-2)
(-2,-1,0)