Complex bézier curves and the geometry of polynomials

Authors:
Rachid Ait-Haddou;Taishin Nomura
Affiliations:
The Center of Advanced Medical Engineering and Informatics, Osaka University, Japan;The Center of Advanced Medical Engineering and Informatics, Osaka University, Japan
Venue:
Proceedings of the 7th international conference on Curves and Surfaces
Year:
2010

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Abstract

In this paper, we study the shape of the control polygon of a complex Bézier curve over a complex interval. We show that the location of the complex roots of the polynomial dictates geometrical constraints on the shape of the control polygon. Along the work, new proofs and generalizations of the Walsh coincidence Theorem and the Grace Theorem are given. Applications of the geometry of the control polygon of complex polynomials to Bernstein type inequalities are discussed.