Первая ярославская летняя школа по дискретной и вычислительной геометрии


https://doi.org/10.18255/1818-1015-2012-4-168-173

Полный текст:


Аннотация

Обобщены результаты работы первой ярославской летней школы по дискретной и вычислительной геометрии и обозначены перспективы будущей работы.

Об авторах

Николай Долбилин
P.G. Demidov Yaroslavl State University
Россия
Steklov Mathematical Institute, the member of International Delaunay Laboratory “Discrete and Computational Geometry” in P.G. Demidov Yaroslavl State University


Г. Эдельсбруннер
IST Austria (Institute of Science and Technology Austria); P.G. Demidov Yaroslavl State University
Австрия

Klosterneuburg, Austria;

the head of International Delaunay Laboratory “Discrete and Computational Geometry” in P.G. Demidov Yaroslavl State University



Александр Иванов
Moscow State University, P.G. Demidov Yaroslavl State University
Россия
the member of International Delaunay Laboratory “Discrete and Computational Geometry” in P.G. Demidov Yaroslavl State University


Олег Мусин
University of Texas in Brownsville; P.G. Demidov Yaroslavl State University
Соединённые Штаты Америки
the member of International Delaunay Laboratory “Discrete and Computational Geometry” in P.G. Demidov Yaroslavl State University


Список литературы

1. Edelsbrunner H. Geometry and Topology for Mesh Generation. Cambridge Univ. Press, Cambridge, England, 2001.

2. Matveev S. V. Lectures on Algebraic Topology. European Math. Soc., Zuerich, Switzerland, 2006.

3. Edelsbrunner H., Harer J. Computational Topology: An Introduction. Amer. Math. Soc., Providence, Rhode Island, 2010.

4. Dolbilin N. P. Properties of Faces of Parallelohedra // Proc. Steklov Inst. Math. 2009. 266. P. 105–119.

5. Delone B. N. Geometry of positive quadratic forms // Uspekhi Matem. Nauk. 1937. No 3. P. 16–62 [in Russian].

6. Alexandrov A. D. Convex Polyhedra. Berlin, Heidelberg, New York, Springer, 2005 [Translation from: Moscow, GTTL, 1950].

7. Matveev S. V. Algorithmic Topology and Classification of 3-manifolds. Springer ACM-monographs, 2003; Moscow, MTsMNO, 2007.

8. Matveev S. V. Roots and decompositions of topological 3D objects // Uspekhi matem. Nauk. 2012. 67: 3(405). P. 63—114 [in Russian, English Translation: Russian Math. Surveys, to appear].

9. Ivanov A. O. and Tuzhilin A. A. Branching Solutions to One-Dimensional Variational Problems World Scientific, Singapore, 2000.

10. Ivanov A. O., Tuzhilin A. A. Extreme Networks Theory. Moscow–Izhevsk, Inst. Komp. Issl., 2003 [in Russian].

11. Ivanov A. O., Tuzhilin A. A. One-dimensional Gromov minimal filling, arXiv:1101.0106v2 [math.MG] (http://arxiv.org), Matem. Sbornik. 2012. 203. P. 65–118.

12. Pak I. Lectures on Discrete and Polyhedral Geometry: Manuscript (http://www.math.ucla.edu/~pak/book.htm).

13. Kaplan H., Matouˇsek J., Sharir M. Simple proofs of classical theorems in discrete geometry via the Guth–Katz polynomial partitioning technique // Discrete Comput. Geom. 2012. 48. P. 499–517.

14. Kettner L., Mehlhorn K., Pion S., Schirra S., Yap C. Classroom examples of robustness problems in geometric computations // Computational Geometry: Theory and Applications. 2008. 40. P. 61–78.

15. Mehlhorn K., Yap C. Robust Geometric Computation: Manuscript (http://cs.nyu.edu/yap/book/egc/).

16. Liotta G., Preparata F. P., Tamassia R. Robust proximity queries: An illustration of degree-driven algorithmic design // SIAM Journal on Computing. 1999. 28. P. 864–889.

17. Burnikel C., Funke S., Seel M. Exact geometric computation using cascading // International Journal of Computational Geometry and Applications. 2001. 11. P. 245–266.

18. Funke S., Klein C., Mehlhorn K., Schmitt S. Controlled perturbation for Delaunay triangulations // Symposium on Discrete Algorithms. 2005. P. 1047–1056.

19. Halperin D., Leiserowitz E. Controlled perturbation for arrangements of circles // Symposium on Computational Geometry. 2003. P. 264–273.

20. Mehlhorn K., Osbild R., Sagraloff M. A general approach to the analysis of controlled perturbation algorithms // Computational Geometry: Theory and Applications. 2011. 44. P. 507–528.

21. Br¨onimann H., Burnikel C., Pion S. Interval arithmetic yields efficient dynamic filters for computational geometry // Discrete Applied Mathematics. 2001. 109. P. 25–47.

22. Devillers O., Pion S. Efficient exact geometric predicates for Delaunay triangulations // 5th Workshop on Algorithm Engineering and Experiments (ALENEX), 2003.

23. Kerber M. Geometric Algorithms for Algebraic Curves and Surfaces, PhD Thesis, Saarland University, 2009 (http://www.mpi-inf.mpg.de/~mkerber/kerber_diss.pdf).


Дополнительные файлы

Для цитирования: Долбилин Н., Эдельсбруннер Г., Иванов А., Мусин О. Первая ярославская летняя школа по дискретной и вычислительной геометрии. Моделирование и анализ информационных систем. 2012;19(4):168-173. https://doi.org/10.18255/1818-1015-2012-4-168-173

For citation: Dolbilin N., Edelsbrunner H., Ivanov A., Musin O. The First Yaroslavl Summer School on Discrete and Computational Geometry. Modeling and Analysis of Information Systems. 2012;19(4):168-173. (In Russ.) https://doi.org/10.18255/1818-1015-2012-4-168-173

Просмотров: 182

Обратные ссылки

  • Обратные ссылки не определены.


Creative Commons License
Контент доступен под лицензией Creative Commons Attribution 4.0 License.


ISSN 1818-1015 (Print)
ISSN 2313-5417 (Online)