| Title:
|
O triangulacích bez tupých úhlů (Czech) |
| Title:
|
On the triangulation without obtuse angles (English) |
| Author:
|
Brandts, Jan |
| Author:
|
Korotov, Sergej |
| Author:
|
Křížek, Michal |
| Language:
|
Czech |
| Journal:
|
Pokroky matematiky, fyziky a astronomie |
| ISSN:
|
0032-2423 |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
193-207 |
| . |
| Category:
|
math |
| . |
| Keyword:
|
triangulation |
| Keyword:
|
simplexes with orthogonal corners |
| Keyword:
|
non-obtuse triangles |
| MSC:
|
65D18 |
| MSC:
|
65N55 |
| idZBL:
|
Zbl 1265.65033 |
| . |
| Date available:
|
2010-12-11T21:06:17Z |
| Last updated:
|
2015-11-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141271 |
| . |
| Reference:
|
[1] Aristote: Du ciel.Text établi et traduit par Paul Moraux, Les Belles Lettres, Paris 1965. |
| Reference:
|
[2] Axelsson, O., Blaheta, R.: Two simple derivations of universal bounds for the C. B. S. inequality constant.Appl. Math. 49 (2004), 57–72. MR 2032148, 10.1023/B:APOM.0000024520.06175.8b |
| Reference:
|
[3] Bern, M., Chew, P., Eppstein, D., Ruppert, J.: Dihedral bounds for mesh generation in high dimensions.Proc. 6th AMC-SIAM Sympos. on Discrete Algorithms 1995, 189–196. Zbl 0849.68116, MR 1321850 |
| Reference:
|
[4] Blaheta, R.: Nested tetrahedral grids and strengthened CBS inequality.Numer. Linear Alg. Appl. 10 (2003), 619–637. MR 2030627, 10.1002/nla.340 |
| Reference:
|
[5] Bliss, A., Su, F. E.: Lower bounds for simplicial covers and triangulations of cubes.Discrete Comput. Geom. 33 (2005), 669–686. Zbl 1078.52013, MR 2132296, 10.1007/s00454-004-1128-0 |
| Reference:
|
[6] Brandts, J., Korotov, S., Křížek, M.: On the right triangle and its higher dimensional generalizations.Nieuwe Wiskrant 24e (2004), No. 2, 12–16. |
| Reference:
|
[7] Brandts, J., Křížek, M.: Gradient superconvergence on uniform simplicial partitions of polytopes.IMA J. Numer. Anal. 23 (2003), 489–505. Zbl 1042.65081, MR 1987941, 10.1093/imanum/23.3.489 |
| Reference:
|
[8] Cassidy, C., Lord, G.: A square acutely triangulated.J. Recreational Math. 13 (1980), 263–268. MR 0625260 |
| Reference:
|
[9] Coxeter, H. S. M.: Trisecting an orthoscheme.Computers Math. Applic. 17 (1989), 59–71. Zbl 0706.51019, MR 0994189, 10.1016/0898-1221(89)90148-X |
| Reference:
|
[10] Delaunay, B.: Sur la sphère vide.Izd. Akad. Nauk SSSR, Otdel. Mat. Estestv. Nauk 7 (1934), 793–800. Zbl 0010.41101 |
| Reference:
|
[11] Eppstein, D., Sullivan, J. M., Üngör, A.: Tiling space and slabs with acute tetrahedra.Comput. Geom. 27 (2004), 237–255. Zbl 1054.65020, MR 2039173, 10.1016/j.comgeo.2003.11.003 |
| Reference:
|
[12] Frank, F. C., Kasper, J. S.: Complex alloy structures regarded as sphere packings, Parts I and II.Acta Crystall. 11 (1958), 184–190; 12 (1959), 483–499. |
| Reference:
|
[13] Fiedler, M.: Geometrie simplexu v $E_n$.Časopis Pěst. Mat. XII (1954), 297–320. |
| Reference:
|
[14] Fiedler, M.: Aggregation in graphs.Coll. Math. Soc. J. Bolyai 18 (1976), 315–330. MR 0519274 |
| Reference:
|
[15] Fiedler, M.: Matice a grafy v euklidovské geometrii.DIMATIA MFF UK, Praha 2001. |
| Reference:
|
[16] Freudenthal, H.: Simplizialzerlegungen von beschränkter Flachheit.Ann. Math. Sci. Engrg. 43 (1942), 580–582. Zbl 0060.40701, MR 0007105, 10.2307/1968813 |
| Reference:
|
[17] Gardner, M.: Mathematical games.Scient. Amer. 202 (1960), 172–186. 10.1038/scientificamerican0360-172 |
| Reference:
|
[18] Gerver, J. L.: The dissection of a polygon into nearly equilateral triangles.Geom. Dedicata 16 (1984), 93–106. Zbl 0547.05026, MR 0757798, 10.1007/BF00147425 |
| Reference:
|
[19] Goldberg, M.: Three infinite families of tetrahedral space-fillers.J. Comb. Theory (A) 16 (1974), 348–354. Zbl 0286.52008, MR 0343156, 10.1016/0097-3165(74)90058-2 |
| Reference:
|
[20] Hadwiger, H.: Vorlesungen über Inhalt, Oberfläche und Isoperimetrie.Die Grundlehren der Math. Wissenschaften 93. Springer-Verlag, Berlin 1957. Zbl 0078.35703, MR 0102775 |
| Reference:
|
[21] Haiman, M.: A simple and relatively efficient triangulation of the $N$-cube.Discrete Comput. Geom. 6 (1991), 287–289. Zbl 0727.68044, MR 1098809, 10.1007/BF02574690 |
| Reference:
|
[22] Hughes, R. B., Anderson, M. R.: Simplexity of the cube.Discrete Math. 158 (1996), 99–150. Zbl 0862.52005, MR 1411113, 10.1016/0012-365X(95)00075-8 |
| Reference:
|
[23] Charsischwili, A. B.: Orthogonale Simplexe im vierdimensionalen Raum.Mitt. Akad. Wiss. der Georgischen SSR 88 (1982), 33–36. |
| Reference:
|
[24] Kaiser, H.: Zum Problem der Zerlegbarkeit von Simplexen in Orthoscheme.Studia Sci. Math. Hungarica 21 (1986), 227–242. Zbl 0561.52011, MR 0898861 |
| Reference:
|
[25] Katrnoška, F.: Genetické algebry.PMFA 50 (2005), 62–74. |
| Reference:
|
[26] Korotov, S., Křížek, M.: Acute type refinements of tetrahedral partitions of polyhedral domains.SIAM J. Numer. Anal. 39 (2001), 724–733. Zbl 1069.65017, MR 1860255, 10.1137/S003614290037040X |
| Reference:
|
[27] Korotov, S., Křížek, M.: Global and local refinement techniques yielding nonobtuse tetrahedral partitions.Comput. Math. Appl. 50 (2005), 1105–1113. Zbl 1086.65116, MR 2167747, 10.1016/j.camwa.2005.08.012 |
| Reference:
|
[28] Korotov, S., Křížek, M., Neittaanmäki, P.: Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle.Math. Comp. 70 (2001), 107–119. Zbl 1001.65125, MR 1803125, 10.1090/S0025-5718-00-01270-9 |
| Reference:
|
[29] Křížek, M.: Superconvergence phenomena on three-dimensional meshes.Internat. J. Numer. Anal. Model. 2 (2005), 43–56. Zbl 1071.65139, MR 2112657 |
| Reference:
|
[30] Křížek, M.: There is no face-to-face partition of $R^5$ into acute simplices.Submitted in 2005, 1–9. |
| Reference:
|
[31] Křížek, M., Šolc, J.: Acute versus nonobtuse tetrahedralizations.In: Conjugate Gradient Algorithms and Finite Element Methods, Springer-Verlag, Berlin 2004, 161–170. Zbl 1069.65133, MR 2082560 |
| Reference:
|
[32] Kuhn, H. W.: Some combinatorial lemmas in topology.IBM J. Res. Develop. 45 (1960), 518–524. Zbl 0109.15603, MR 0124038, 10.1147/rd.45.0518 |
| Reference:
|
[33] Lenhard, H. C.: Zerlegung von Tetraedern in Orthogonaltetraeder.Elem. Math. 15 (1960), 106–107. MR 0116226 |
| Reference:
|
[34] Lindgren, H.: Geometric dissections.Van Nostrand, Princeton, New Jersey 1964. |
| Reference:
|
[35] Lyusternik, L. A.: Convex figures and polyhedra.Dover Publications, Inc., New York 1963; Moscow 1956. Zbl 0113.16201, MR 0161219 |
| Reference:
|
[36] Manheimer, W., Federico, J. P. et al.: Dissecting an obtuse triangle into acute triangles.Amer. Math. Monthly 67 (1960), 923. |
| Reference:
|
[37] Møller, J.: Lectures on random Voronoi tessellations.Springer, New York 1994. MR 1295245 |
| Reference:
|
[38] Okabe, A., Boots, B., Sugihara, K.: Spatial tessellations. Concepts and applications of Voronoi diagrams.John Wiley & Sons, New York 1992. Zbl 0877.52010, MR 1210959 |
| Reference:
|
[39] Penrose, R.: Pentaplexity: a class of nonperiodic tilings of the plane.Math. Intelligencer 2 (1979/80), 32–37. MR 0558670, 10.1007/BF03024384 |
| Reference:
|
[40] Rajan, V. T.: Optimality of the Delaunay triangulation in $R^d$.Discrete Comput. Geom. 12 (1994), 189–202. MR 1283887, 10.1007/BF02574375 |
| Reference:
|
[41] Schläfli, L.: Theorie der vielfachen Kontinuität (aus dem Jahre 1852).Aufträge der Denkschriften-Kommission der Schweizer naturforschender Gesellschaft, Zurcher & Furre 1901. In: Gesammelte mathematische Abhandlungen, Birkhäuser, Basel 1950. |
| Reference:
|
[42] Stillwell, J.: Stodvacetistěn v $R^4$.PMFA 46 (2001), 265–280. |
| Reference:
|
[43] Struik, D. J.: Het probleem “De impletione loci”.Nieuf Archief voor Wiskunde, 2nd series, 15 (1925), 121–134. |
| Reference:
|
[44] Stoyan, D., Kendall, W. S., Mecke, J.: Stochastic geometry and its applications.John Wiley & Sons, New York 1985, 1995. MR 0895588 |
| Reference:
|
[45] Tschirpke, K.: On the dissection of simplices into orthoschemes.Geom. Dedicata 46 (1993), 313–329. Zbl 0780.52016, MR 1220122, 10.1007/BF01263622 |
| Reference:
|
[46] Tschirpke, K.: Orthoschemzerlegungen fünfdimensionaler Simplexe in Räumen konstanter Krümmung.Dissertation, Univ. Jena 1993. MR 1220122 |
| Reference:
|
[47] Tschirpke, K.: The dissection of five-dimensional simplices into orthoschemes.Beiträge zur Algebra und Geometrie 35 (1994), 1–11. Zbl 0806.52012, MR 1287191 |
| Reference:
|
[48] Voronoï, G.: Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Recherches sur les parallélloedres primitifs.J. Reine Angew. Math. 134 (1908), 198–287. |
| Reference:
|
[49] Zhu, Q., Lin, Q., Liu, L.: Monte Carlo finite element method.Sborník semináře Programy a algoritmy numerické matematiky, MÚ AV ČR, Praha 1996, 210–217. |
| Reference:
|
[50] Zlámal, M.: Finite element solution of the fundamental equations of semiconductor devices, Parts I and II.Math. Comp. 49 (1986), 27–43; Appl. Math. 46 (2001), 251–294. 10.2307/2008212 |
| Reference:
|
[51] : .www.ics.uci.edu/~eppstein/junkyard/all.html |
| . |
