Hauptmenü
• Autor
• Lang, Johann
• Mick, Sybille
• Röschel, Otto
• TitelRegularizing transformations of polygons
• Datei
• DOI10.1007/s00022-017-0373-3
• Persistent Identifier
• Erschienen inJournal of Geometry
• Band108
• Erscheinungsjahr2017
• Heft2
• Seiten791-801
• ISSN1420-8997
• Zugriffsrechte
• AbstractWe start with a generic n-gon $$Q_0$$ with vertices $$q_{j,0}(j = 0, \ldots , n-1)$$ in the d-dimensional Euclidean space $$\mathbb{E}^d$$. Additionally, $$m+1$$ real numbers $$u_0, \ldots, u_m \in \mathbb{R} (m < n)$$ with $$\sum^m_{\mu=0} u_\mu = 1$$ are given. From these initial data we iteratively define generations of n-gons $$Q_k$$ in $$\mathbb{E}^d$$ for $$k \in \mathbb{N}$$ with vertices $$q_{j,k} := \sum^m_{\mu=0} u_\mu q_{j+\mu,k-1}$$. We can show that this affine iteration generally regularizes in an affine sense.