Complex Bézier curves and the geometry of polygons

Authors:
Rachid Ait-Haddou;Walter Herzog;Taishin Nomura
Affiliations:
The Center for Advanced Medical Engineering and Informatics, Osaka University, Osaka, Japan;Human Performance Laboratory, Faculty of Kinesiology, The University of Calgary, Calgary, Canada;The Center for Advanced Medical Engineering and Informatics, Osaka University, Osaka, Japan and Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka U ...
Venue:
Computer Aided Geometric Design
Year:
2010

Citing 2
Cited 2

Blossoms are polar forms

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Complex bézier curves and the geometry of polynomials

Proceedings of the 7th international conference on Curves and Surfaces
The Bernstein polynomial basis: A centennial retrospective

Computer Aided Geometric Design

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Abstract

In this paper, we associate to every planar polygon a complex polynomial, in which the blossom of the polynomial function captures the process in which linear transformations applied to the polygon lead to regular structures. In particular, we prove, in a purely algebraic way several well-known theorems on polygons such as the Napoleon-Barlotti Theorem, the Petr-Douglas-Neumann Theorem, and the Fundamental Decomposition Theorem of polygons to regular polygons.