Abstract:
We define the Delaunay triangulation for surfaces and prove an analog of the G. Voronoi empty sphere theorem. We also prove the convergence theorem for gradients of piecewise linear approximations constructed on the Delaunay triangulation for functions differentiable on smooth surfaces.
Keywords:
simplex, triangulation, approximation of gradient.
Citation:
V. A. Klyachin, A. A. Shirokii, “The Delaunay triangulation for multidimensional surfaces and its approximative properties”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 1, 31–39; Russian Math. (Iz. VUZ), 56:1 (2012), 27–34
This publication is cited in the following 18 articles:
V. A. Klyachin, “Otsenki kusochno-lineinoi approksimatsii proizvodnykh funktsii klassov Soboleva”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 49 (2024), 78–89
Vladislav Kuzmin, “Calculation of 3D Shape of a Hyperelastic Body for Nonlinear Elasticity Models Using the Newton Method”, Mathematical Physics and Computer Simulation, 27:2 (2024), 80
V. A. Klyachin, V. V. Kuzmin, E. V. Khizhnyakova, “Metod triangulyatsii dlya priblizhennogo resheniya variatsionnykh zadach nelineinoi teorii uprugosti”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 45 (2023), 54–72
A. A. Klyachin, “Otsenka pogreshnosti vychisleniya funktsionala, soderzhaschego proizvodnye vtorogo poryadka, na treugolnoi setke”, Sib. elektron. matem. izv., 16 (2019), 1856–1867
R. Sh. Khasyanov, “Ermitova interpolyatsiya na simplekse”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 18:3 (2018), 316–327
V. A. Klyachin, “Approximation of the gradient of a function on the basis of a special
class of triangulations”, Izv. Math., 82:6 (2018), 1136–1147
A. A. Klyachin, “Postroenie treugolnoi setki dlya oblastei, ogranichennykh zamknutymi prostymi krivymi”, Matematicheskaya fizika i kompyuternoe modelirovanie, 21:3 (2018), 31–38
A. V. Boluchevskaya, V. A. Klyachin, M. E. Sapraliev, “Otsenki radiusa prosveta konechnogo mnozhestva edinichnogo shara v Rn”, Matematicheskaya fizika i kompyuternoe modelirovanie, 20:3 (2017), 6–17
V. A. Klyachin, “Modified Delaunay empty sphere condition in the problem of approximation of the gradient”, Izv. Math., 80:3 (2016), 549–556
A. Yu. Igumnov, “Metrizatsiya prostranstva semeistv tochek v Rn i smezhnye voprosy”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 6(37), 40–54
Liuyang Fang, Jie Chen, 2016 15th International Symposium on Parallel and Distributed Computing (ISPDC), 2016, 70
V. A. Klyachin, D. V. Shurkaeva, “Koeffitsient izoperimetrichnosti simpleksa v zadache approksimatsii proizvodnykh”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 15:2 (2015), 151–160
V. A. Klyachin, E. G. Grigoreva, “Chislennoe issledovanie ustoichivosti ravnovesnykh poverkhnostei s ispolzovaniem paketa NumPy”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 2(27), 17–30
V. A. Klyachin, “Ekstremalnye svoistva triangulyatsii, osnovannoi na uslovii pustogo vypuklogo mnozhestva”, Sib. elektron. matem. izv., 12 (2015), 991–997
A. A. Klyachin, A. Yu. Belenikina, “Triangulyatsiya prostranstvennykh elementarnykh oblastei”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 4(29), 6–12
V. A. Klyachin, “Optimizatsiya postroeniya raschetnoi setki dlya resheniya zadachi lokalnogo kriovozdeistviya s ispolzovaniem mnogomernogo geometricheskogo kheshirovaniya na osnove paketa NumPy”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 14:3 (2014), 355–362
Peng Jiao Sun, Xiao Man Wang, Bo Huang, “The Design of Weldment Model Based on Improved Delaunay Triangulation Algorithm”, AMM, 411-414 (2013), 1414
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