TY - GEN
T1 - Complex Bézier curves and the geometry of polynomials
AU - Ait-Haddou, Rachid
AU - Nomura, Taishin
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Bernstein type inequalities
KW - Complex Bézier curves
KW - Grace Theorem
KW - Walsh coincidence Theorem
KW - complex de Casteljau algorithm
KW - polar derivative
UR - https://www.scopus.com/pages/publications/84855674681
U2 - 10.1007/978-3-642-27413-8_3
DO - 10.1007/978-3-642-27413-8_3
M3 - Conference contribution
AN - SCOPUS:84855674681
SN - 9783642274121
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 43
EP - 65
BT - Curves and Surfaces - 7th International Conference, Curves and Surfaces 2010, Revised Selected Papers
ER -