The Delaunay Triangulation for Multidimensional Surfaces and its Approximative Properties

被引：10

作者：

Klyachin, V. A. ^{[1
]}

Shirokii, A. A. ^{[1
]}

机构：

[1] Volgograd State Univ, Univ Pr 100, Volgograd 400062, Russia

来源：

RUSSIAN MATHEMATICS | 2012年 / 56卷 / 01期

关键词：

simplex; triangulation; approximation of gradient;

D O I：

10.3103/S1066369X12010045

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define the Delaunay triangulation for surfaces and prove an analog of the G. Voronoi empty sphere theorem. We also prove a convergence theorem for gradients of piecewise linear approximations constructed on the Delaunay triangulation for functions differentiable on smooth surfaces.

引用

页码：27 / 34

页数：8

共 12 条

[1]

[Боровиков С.Н. Borovikov S.N.], 2006, [Математическое моделирование, Mathematical Models and Computer Simulations, Matematicheskoe modelirovanie], V18, P37

[2]

Delaunay B. P., 2006, ZAP SEMIN SVERKHMEDL, P147

[3] AN ACYCLICITY THEOREM FOR CELL COMPLEXES IN D-DIMENSION [J].

EDELSBRUNNER, H .

COMBINATORICA, 1990, 10 (03) :251-260

[4]

Garanzha V. A., 2010, ZH VYCHISL MATEM IMA, V50, P71

[5]

Gelbaum B. R., 1964, COUNTEREXAMPLES ANAL

[6]

Klyachin VA, 2008, VESTN TOMSK GOS U-MA, P48

[7]

Klyachin V. A., 2010, SIB ZH IND MAT, VXIII, P69

[8]

Korotov S., 2010, P NUMGR 2010, P41

[9]

Pushkina I. G., 2000, MAT MODEL, V12, P97

[10] OPTIMALITY OF THE DELAUNAY TRIANGULATION IN RD [J].

RAJAN, VT .

DISCRETE & COMPUTATIONAL GEOMETRY, 1994, 12 (02) :189-202

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