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  • Autor
    • Roeschel, Otto
  • TitelPolygons and iteratively regularizing affine transformations
  • Datei
  • DOI10.1007/s13366-016-0313-7
  • Persistent Identifier
  • Erschienen inBeiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
  • Band58
  • Erscheinungsjahr2017
  • Heft1
  • Seiten69-79
  • ISSN2191-0383
  • ZugriffsrechteCC-BY
  • Download Statistik371
  • Peer ReviewJa
  • AbstractWe start with a generic planar n-gon \(Q_0\) with veritices \(q_{j,0}(j=0, \dots, n-1)\) and fixed reals \(u, v, w \in \mathbb{R} \) with \(u + v + w = 1\). We iteratively define n-gons \(Q_k\) of generation \(k \in \mathbb{N}\) with vertices \(q_{j,k} (j = 0, \dots, n-1)\) via \(q_{j,k} := u\ q_{j,k-1} + v\ q_{j+1,k-1} + w\ q_{j+2,k-1}\). We are able to show that this affine iteration process for general input data generally regularizes the polygons in the following sense: There is a series of affine mappings \(\beta_k\) such that the sums \(\Delta_k\) of the squared distances between the vertices of \(\beta_k(Q_k)\) and the respective vertices of a given regular prototype polygon P form a null series for \(k \longrightarrow \infty\).