Geodesic
Regular triangulations and Steiner points
Algebra i analiz, Tome 16 (2004) no. 4, pp. 88-113.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{AA_2004_16_4_a4,
     author = {M. Yu. Zvagel'skii and A. V. Proskurnikov and Yu. R. Romanovskii},
     title = {Regular triangulations and {Steiner} points},
     journal = {Algebra i analiz},
     pages = {88--113},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2004_16_4_a4/}
}
TY  - JOUR
AU  - M. Yu. Zvagel'skii
AU  - A. V. Proskurnikov
AU  - Yu. R. Romanovskii
TI  - Regular triangulations and Steiner points
JO  - Algebra i analiz
PY  - 2004
SP  - 88
EP  - 113
VL  - 16
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2004_16_4_a4/
LA  - ru
ID  - AA_2004_16_4_a4
ER  - 
%0 Journal Article
%A M. Yu. Zvagel'skii
%A A. V. Proskurnikov
%A Yu. R. Romanovskii
%T Regular triangulations and Steiner points
%J Algebra i analiz
%D 2004
%P 88-113
%V 16
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2004_16_4_a4/
%G ru
%F AA_2004_16_4_a4
M. Yu. Zvagel'skii; A. V. Proskurnikov; Yu. R. Romanovskii. Regular triangulations and Steiner points. Algebra i analiz, Tome 16 (2004) no. 4, pp. 88-113. http://geodesic.mathdoc.fr/item/AA_2004_16_4_a4/

[1] Gelfand I. M., Zelevinskii A. V., Kapranov M. M., “Diskriminanty mnogochlenov ot mnogikh peremennykh i triangulyatsii mnogogrannikov Nyutona”, Algebra i analiz, 2:3 (1990), 1–62 | MR

[2] Billera L. J., Filliman P., Sturmfels B., “Constructions and complexity of secondary polytopes”, Adv. Math., 83 (1990), 155–179 | DOI | MR | Zbl

[3] Proskurnikov A. V., Romanovskii Yu. P., “O regulyarnykh triangulyatsiyakh nevypuklykh mnogogrannikov”, Uspekhi mat. nauk, 57:4(346) (2002), 185–186 | MR | Zbl

[4] Ruppert J., Seidel R., “On the difficulty of triangulating three-dimensional nonconvex polyhedra”, Discrete Comput. Geom., 7 (1992), 227–253 | DOI | MR | Zbl

[5] Shewchuk J. R., A condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations, Proceedings of the 14th Annual Symposium on Computational Geometry, 1998, 76–85 | Zbl

[6] Shewchuk J. R., Updating and constructing constrained Delaunay and constrained regular triangulations by flips, Proceedings of the 19th Annual Symposium on Computational Geometry, 2003, 181–190

[7] Delone B. H., “Sur la sphère vide”, Izv. AN SSSR. VII ser. Otdel. mat. i estestv. nauk, 1934, no. 6, 793–800 | Zbl

[8] Edelsbrunner H., Shah N. R., “Incremental topological flipping works for regular triangulations”, Algorithmica, 15 (1996), 223–241 | DOI | MR | Zbl

[9] Cheng Siu-Wing, Dey T. K., Edelsbrunner H., Facello M. A., Teng Shang-Hua, “Sliver exudation”, J. ACM, 47 (2000), 883–904 | DOI | MR

[10] Aurenhammer F., “Power diagrams: properties, algorithms and applications”, SIAM J. Comput., 16:1 (1987), 78–96 | DOI | MR | Zbl

[11] Ziegler G. M., Lectures on polytopes, Grad. Texts in Math., 152, Springer-Verlag, New York, 1995 | MR | Zbl

[12] Khachiyan L. G., “Polinomialnyi algoritm v lineinom programmirovanii”, Dokl. AN SSSR, 244:5 (1979), 1093–1096 | MR | Zbl

[13] Preparata F., Sheimos M., Vychislitelnaya geometriya: Vvedenie, Mir, M., 1989 | MR | Zbl

[14] Schonhardt E., “Über die Zerlegung von Dreieckspolyedern in Tetraeder”, Math. Ann., 98 (1928), 309–312 | DOI | MR

[15] Rambau J., On a generalization of Schönhardt's polyhedron, MSRI Preprint no. 2003-13, 2003

[16] Huber B., Rambau J., Santos F., “The Caley trick, lifting subdivisions, and the Bohne–Dress theorem on zonotopal tilings”, J. Eur. Math. Soc., 2 (2000), 179–198 | DOI | MR | Zbl