Three-pencil lattice on triangulations

Jaklič, Gašper; Kozak, Jernej; Knez, Marjetka; Vitrih, Vito; Žagar, Emil

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Title:	Three-pencil lattice on triangulations
Authors:	ID Jaklič, Gašper (Author) ID Kozak, Jernej (Author) ID Knez, Marjetka (Author) ID Vitrih, Vito (Author) ID Žagar, Emil (Author)
Files:	http://dx.doi.org/10.1007/s11075-007-9068-4
Language:	English
Work type:	Not categorized
Typology:	1.08 - Published Scientific Conference Contribution
Organization:	IAM - Andrej Marušič Institute
Abstract:	In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S 3 on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.
Keywords:	numerical analysis, lattice, barycentric coordinates, triangulations, interpolation
Year of publishing:	2007
Number of pages:	str. 49-60
Numbering:	Vol. 45, no. 1-4
PID:	20.500.12556/RUP-7724
ISSN:	1017-1398
UDC:	519.65
DOI:	10.1007/s11075-007-9068-4
COBISS.SI-ID:	14426457
Publication date in RUP:	03.04.2017
Views:	2701
Downloads:	88
Metadata:
:	JAKLIČ, Gašper, KOZAK, Jernej, KNEZ, Marjetka, VITRIH, Vito and ŽAGAR, Emil, 2007, Three-pencil lattice on triangulations. In : [online]. Published Scientific Conference Contribution. 2007. p. 49–60. [Accessed 5 April 2025]. Retrieved from: http://dx.doi.org/10.1007/s11075-007-9068-4 Copy citation

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Secondary language

Language:	Slovenian
Title:	Mreže treh šopov na triangulacijah
Abstract:	V članku so obravnavane mreže treh šopov. Eksplicitna reprezentacija mreže, zasnovana na baricentričnih koordinatah, nam omogoča konstruirati točke mreže na enostaven in numerično stabilen način. Še več, ta reprezentacija omogoča naravno razširitev na triangulacije. Konstrukcija je osnovana na delovanju grupe $S_3$ na točkah triangulacije. Dokazano je, da je število prostostnih stopenj enako številu točk triangulacije.
Keywords:	numerična analiza, mreža, baricentrične koordinate, triangulacije, interpolacija

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