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2014 | 12 | 12 | 1796-1810
Tytuł artykułu

Properties of triangulations obtained by the longest-edge bisection

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The Longest-Edge (LE) bisection of a triangle is obtained by joining the midpoint of its longest edge with the opposite vertex. Here two properties of the longest-edge bisection scheme for triangles are proved. For any triangle, the number of distinct triangles (up to similarity) generated by longest-edge bisection is finite. In addition, if LE-bisection is iteratively applied to an initial triangle, then minimum angle of the resulting triangles is greater or equal than a half of the minimum angle of the initial angle. The novelty of the proofs is the use of an hyperbolic metric in a shape space for triangles.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
12
Strony
1796-1810
Opis fizyczny
Daty
wydano
2014-12-01
online
2014-07-20
Twórcy
autor
Bibliografia
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  • [17] Perdomo F., Plaza A., A new proof of the degeneracy property of the longest-edge n-section refinement scheme for triangular meshes, Appl. Math. & Compt., 2012, 219, 2342–2344 http://dx.doi.org/10.1016/j.amc.2012.08.029
  • [18] Perdomo F., Plaza A., Proving the non-degeneracy of the longest-edge trisection by a space of triangular shapes with hyperbolic metric, Appl. Math. & Compt., 2013, 221, 424–432 http://dx.doi.org/10.1016/j.amc.2013.06.075
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0448-4
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