Computer Aided Geometric Design Class Exercise 13 l

Computer Aided Geometric Design Class Exercise #13 l Advanced Topics - Blossoming 1

The Blossom of a Bezier Curve l 2

The Blossom of a Bezier Curve l 3

The Blossom of a Bezier Curve l 4

Q. 1 l 5

Solution l 6

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Q. 2 Prove that the blossom of a Bezier curve is: Symmetric l Multi-Affine. l 12

Solution We show the symmetry for two variables. The general case follows from the same arguments. Consider: 13

Solution l 14

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Solution From the symmetry – it suffices to show that the blossom is affine with respect to the first variable. The proof is by induction using the de. Casteljau recursion rule! 18

Blossoms as Polar Forms l 19

Blossoms as Polar Forms l 20

Blossoms as Polar Forms l 21

Blossoms as Polar Forms l 22

Q. 3 l 23

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Solution 25