### Abstract

Original language | English |
---|---|

Pages (from-to) | 69 |

Number of pages | 79 |

Journal | Beiträge zur Algebra und Geometrie |

Volume | 58 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 2017 |

### Keywords

### Fields of Expertise

- Information, Communication & Computing

### Cite this

**Polygons and iteratively regularizing affine transformations.** / Röschel, Otto.

Research output: Contribution to journal › Article › Research › peer-review

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TY - JOUR

T1 - Polygons and iteratively regularizing affine transformations

AU - Röschel, Otto

PY - 2017/3

Y1 - 2017/3

N2 - We start with a generic planar n-gon Q0 with veritices qj,0 (j=0,…,n−1) and fixed reals u,v,w∈R with u+v+w=1. We iteratively define n-gons Qk of generation k∈N with vertices qj,k (j=0,…,n−1) via qj,k:=u qj,k−1+v qj+1,k−1+w qj+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 βk such that the sums Δk of the squared distances between the vertices of βk(Qk) and the respective vertices of a given regular prototype polygon P form a null series for k⟶∞.

AB - We start with a generic planar n-gon Q0 with veritices qj,0 (j=0,…,n−1) and fixed reals u,v,w∈R with u+v+w=1. We iteratively define n-gons Qk of generation k∈N with vertices qj,k (j=0,…,n−1) via qj,k:=u qj,k−1+v qj+1,k−1+w qj+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 βk such that the sums Δk of the squared distances between the vertices of βk(Qk) and the respective vertices of a given regular prototype polygon P form a null series for k⟶∞.

KW - Affine Iterations; Affine Regularization; Regular n-gons

U2 - 10.1007/s13366-016-0313-7

DO - 10.1007/s13366-016-0313-7

M3 - Article

VL - 58

SP - 69

JO - Beiträge zur Algebra und Geometrie

JF - Beiträge zur Algebra und Geometrie

SN - 0138-4821

IS - 1

ER -