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Convex subdivision of a Bézier curve

✍ Scribed by Rachid Ait-Haddou; Walter Herzog

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
202 KB
Volume
19
Category
Article
ISSN
0167-8396

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✦ Synopsis

Using the Walsh coincidence theorem, we show in this paper that the shape of the control polygon of a Bézier curve is closely related to the location of the complex roots of the corresponding polynomial. This explains why a convex polynomial over an interval does not necessarily produce a convex control polygon with respect to the same interval. Furthermore, our findings lead to an interesting algorithm of subdividing a Bézier curve into segments with convex control polygons.

📜 SIMILAR VOLUMES

Subdivision of the Bézier curve
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Any segment between two points on a BCzier curve is itself a Bezier curve whose BCzier polygon is expressed explicitly in terms of the sides of the BCzier polygon associated with the original curve.

A subdivision algorithm for generalized
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## In this paper, subdivision methods for rectangular Be ´zier A rectangular Be ´zier surface of degree n ϫ m can be surfaces are generalized to subdivide a rectangular Be ´zier surface patch of degree n ؋ m into two rectangular Be ´zier sur-represented by face patches of degree n ؋ (m ؉ n), while