@inproceedings{e6a992d1f5d64ac6b6c81c97507a1ffe,

title = "Complex B{\'e}zier curves and the geometry of polynomials",

abstract = "In this paper, we study the shape of the control polygon of a complex B{\'e}zier 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.",

keywords = "Bernstein type inequalities, Complex B{\'e}zier curves, Grace Theorem, Walsh coincidence Theorem, complex de Casteljau algorithm, polar derivative",

author = "Rachid Ait-Haddou and Taishin Nomura",

year = "2012",

month = jan,

day = "16",

doi = "10.1007/978-3-642-27413-8_3",

language = "English (US)",

isbn = "9783642274121",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "43--65",

booktitle = "Curves and Surfaces - 7th International Conference, Curves and Surfaces 2010, Revised Selected Papers",

note = "7th International Conference on Curves and Surfaces, Curves and Surfaces 2010 ; Conference date: 24-06-2010 Through 30-06-2010",

}