Algorithms for triangulating polyhedra into a small number of tetrahedra
Abstract
Two algorithms for triangulating polyhedra, which give the number of tetrahedra depending linearly on the number of vertices, are discussed. Since the smallest possible number of tetrahedra necessary to triangulate given polyhedra is of interest, for the first–"Greedy peeling" algorithm, we give a better estimation of the greatest number of tetrahedra (3n - 20 instead of 3n - 11), while for the second one–"cone triangulation", we discuss cases when it is possible to improve it in such a way as to obtain a smaller number of tetrahedra.
Keywords:
triangulation of polyhedra / minimal triangulationSource:
Matematički vesnik, 2005, 57, 1-2, 1-9Publisher:
- Društvo matematičara Srbije, Beograd
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Institution/Community
Fakultet organizacionih naukaTY - JOUR AU - Stojanović, Milica PY - 2005 UR - https://rfos.fon.bg.ac.rs/handle/123456789/307 AB - Two algorithms for triangulating polyhedra, which give the number of tetrahedra depending linearly on the number of vertices, are discussed. Since the smallest possible number of tetrahedra necessary to triangulate given polyhedra is of interest, for the first–"Greedy peeling" algorithm, we give a better estimation of the greatest number of tetrahedra (3n - 20 instead of 3n - 11), while for the second one–"cone triangulation", we discuss cases when it is possible to improve it in such a way as to obtain a smaller number of tetrahedra. PB - Društvo matematičara Srbije, Beograd T2 - Matematički vesnik T1 - Algorithms for triangulating polyhedra into a small number of tetrahedra EP - 9 IS - 1-2 SP - 1 VL - 57 UR - conv_6 ER -
@article{ author = "Stojanović, Milica", year = "2005", abstract = "Two algorithms for triangulating polyhedra, which give the number of tetrahedra depending linearly on the number of vertices, are discussed. Since the smallest possible number of tetrahedra necessary to triangulate given polyhedra is of interest, for the first–"Greedy peeling" algorithm, we give a better estimation of the greatest number of tetrahedra (3n - 20 instead of 3n - 11), while for the second one–"cone triangulation", we discuss cases when it is possible to improve it in such a way as to obtain a smaller number of tetrahedra.", publisher = "Društvo matematičara Srbije, Beograd", journal = "Matematički vesnik", title = "Algorithms for triangulating polyhedra into a small number of tetrahedra", pages = "9-1", number = "1-2", volume = "57", url = "conv_6" }
Stojanović, M.. (2005). Algorithms for triangulating polyhedra into a small number of tetrahedra. in Matematički vesnik Društvo matematičara Srbije, Beograd., 57(1-2), 1-9. conv_6
Stojanović M. Algorithms for triangulating polyhedra into a small number of tetrahedra. in Matematički vesnik. 2005;57(1-2):1-9. conv_6 .
Stojanović, Milica, "Algorithms for triangulating polyhedra into a small number of tetrahedra" in Matematički vesnik, 57, no. 1-2 (2005):1-9, conv_6 .