Convex subdivision of a Bézier curve

Rachid Ait-Haddou; Walter Herzog

doi:10.1016/S0167-8396(02)00161-9

Convex subdivision of a Bézier curve

Rachid Ait-Haddou^*, Walter Herzog

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	663-671
Number of pages	9
Journal	Computer Aided Geometric Design
Volume	19
Issue number	8
DOIs	https://doi.org/10.1016/S0167-8396(02)00161-9
State	Published - Oct 2002
Externally published	Yes

ASJC Scopus subject areas

Aerospace Engineering
Automotive Engineering
Modeling and Simulation
Computer Graphics and Computer-Aided Design

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10.1016/S0167-8396(02)00161-9

Cite this

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abstract = "Using the Walsh coincidence theorem, we show in this paper that the shape of the control polygon of a B{\'e}zier 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 B{\'e}zier curve into segments with convex control polygons.",

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AU - Herzog, Walter

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AB - 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.

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Convex subdivision of a Bézier curve

Abstract

ASJC Scopus subject areas

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