an:05869128
Zbl 1217.68233
Ait-Haddou, Rachid; Herzog, Walter; Nomura, Taishin
Complex B??zier curves and the geometry of polygons
EN
Comput. Aided Geom. Des. 27, No. 7, 525-537 (2010).
00274321
2010
j
68U07 30C10 65D17
B??zier curve; polar forms; geometry of polygons; discrete Fourier transform; Napoleon-Barlotti theorem; Petr-Douglas-Neumann theorem
Summary: 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.