Algorithms for investigating optimality of cone triangulation for a polyhedron
Apstrakt
The problem of finding minimal triangulation of a given polyhedra (dividing polyhedra into tetrahedra) is very actual now. It is known that cone triangulation for a polyhedron provides the smallest number of tetrahedra, or close to it. In earlier investigations when this triangulation was the optimal one, it was shown that conditions for vertices to be of the order five, six or for separated vertices of order four was only the necessary ones. It was shown that then if it exists the "separating circle" of order less then six, for two vertices of order six, cone triangulation is not the minimal one. Here, test algorithms will be given, for the case when the given polyhedron has separating circle of order five or less.
Ključne reči:
triangulation of polyhedra / minimal triangulation / graph algorithms / abstract data type of graphIzvor:
Kragujevac Journal of Mathematics, 2007, 30, 327-342Izdavač:
- Univerzitet u Kragujevcu - Prirodno-matematički fakultet, Kragujevac
Institucija/grupa
Fakultet organizacionih naukaTY - JOUR AU - Stojanović, Milica AU - Vučković, Milica PY - 2007 UR - https://rfos.fon.bg.ac.rs/handle/123456789/414 AB - The problem of finding minimal triangulation of a given polyhedra (dividing polyhedra into tetrahedra) is very actual now. It is known that cone triangulation for a polyhedron provides the smallest number of tetrahedra, or close to it. In earlier investigations when this triangulation was the optimal one, it was shown that conditions for vertices to be of the order five, six or for separated vertices of order four was only the necessary ones. It was shown that then if it exists the "separating circle" of order less then six, for two vertices of order six, cone triangulation is not the minimal one. Here, test algorithms will be given, for the case when the given polyhedron has separating circle of order five or less. PB - Univerzitet u Kragujevcu - Prirodno-matematički fakultet, Kragujevac T2 - Kragujevac Journal of Mathematics T1 - Algorithms for investigating optimality of cone triangulation for a polyhedron EP - 342 IS - 30 SP - 327 UR - conv_526 ER -
@article{ author = "Stojanović, Milica and Vučković, Milica", year = "2007", abstract = "The problem of finding minimal triangulation of a given polyhedra (dividing polyhedra into tetrahedra) is very actual now. It is known that cone triangulation for a polyhedron provides the smallest number of tetrahedra, or close to it. In earlier investigations when this triangulation was the optimal one, it was shown that conditions for vertices to be of the order five, six or for separated vertices of order four was only the necessary ones. It was shown that then if it exists the "separating circle" of order less then six, for two vertices of order six, cone triangulation is not the minimal one. Here, test algorithms will be given, for the case when the given polyhedron has separating circle of order five or less.", publisher = "Univerzitet u Kragujevcu - Prirodno-matematički fakultet, Kragujevac", journal = "Kragujevac Journal of Mathematics", title = "Algorithms for investigating optimality of cone triangulation for a polyhedron", pages = "342-327", number = "30", url = "conv_526" }
Stojanović, M.,& Vučković, M.. (2007). Algorithms for investigating optimality of cone triangulation for a polyhedron. in Kragujevac Journal of Mathematics Univerzitet u Kragujevcu - Prirodno-matematički fakultet, Kragujevac.(30), 327-342. conv_526
Stojanović M, Vučković M. Algorithms for investigating optimality of cone triangulation for a polyhedron. in Kragujevac Journal of Mathematics. 2007;(30):327-342. conv_526 .
Stojanović, Milica, Vučković, Milica, "Algorithms for investigating optimality of cone triangulation for a polyhedron" in Kragujevac Journal of Mathematics, no. 30 (2007):327-342, conv_526 .