- 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
- Download Statistik1943
- Peer ReviewNein
- 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.
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