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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 3, Pages 499–520 (Mi zvmmf9673)  

This article is cited in 7 scientific papers (total in 7 papers)

Generation of three-dimensional delaunay meshes from weakly structured and inconsistent data

V. A. Garanzha, L. N. Kudryavtseva

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia

Abstract: A method is proposed for the generation of three-dimensional tetrahedral meshes from incomplete, weakly structured, and inconsistent data describing a geometric model. The method is based on the construction of a piecewise smooth scalar function defining the body so that its boundary is the zero isosurface of the function. Such implicit description of three-dimensional domains can be defined analytically or can be constructed from a cloud of points, a set of cross sections, or a “soup” of individual vertices, edges, and faces. By applying Boolean operations over domains, simple primitives can be combined with reconstruction results to produce complex geometric models without resorting to specialized software. Sharp edges and conical vertices on the domain boundary are reproduced automatically without using special algorithms. Refs. 42. Figs. 25.

Key words: tetrahedral meshes, Delaunay triangulation, surface reconstruction, radial basis functions, variational method.

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:3, 427–447

Bibliographic databases:

UDC: 519.634
Received: 16.06.2011

Citation: V. A. Garanzha, L. N. Kudryavtseva, “Generation of three-dimensional delaunay meshes from weakly structured and inconsistent data”, Zh. Vychisl. Mat. Mat. Fiz., 52:3 (2012), 499–520; Comput. Math. Math. Phys., 52:3 (2012), 427–447

Citation in format AMSBIB
\by V.~A.~Garanzha, L.~N.~Kudryavtseva
\paper Generation of three-dimensional delaunay meshes from weakly structured and inconsistent data
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2012
\vol 52
\issue 3
\pages 499--520
\jour Comput. Math. Math. Phys.
\yr 2012
\vol 52
\issue 3
\pages 427--447

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Kofanov, V. D. Liseikin, “Grid construction for discretely defined configurations”, Comput. Math. Math. Phys., 53:6 (2013), 759–765  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. A. S. Bolkhovitinov, “Dostizhenie sopostavimosti morfometricheskikh i modelnykh gistogeneticheskikh-morfogeneticheskikh dannykh s pomoschyu testovykh funktsii globalnoi optimizatsii”, Morfologiya, 7:2 (2013), 5–19  elib
    3. A. I. Belokrys-Fedotov, V. A. Garanzha, L. N. Kudryavtseva, “Generation of Delaunay meshes in implicit domains with edge sharpening”, Comput. Math. Math. Phys., 56:11 (2016), 1901–1918  mathnet  crossref  crossref  isi  elib
    4. Yu. G. Evtushenko, M. A. Posypkin, L. A. Rybak, A. V. Turkin, “Finding sets of solutions to systems of nonlinear inequalities”, Comput. Math. Math. Phys., 57:8 (2017), 1241–1247  mathnet  crossref  crossref  isi  elib
    5. A. I. Belokrys-Fedotov, V. A. Garanzha, L. N. Kudryavtseva, “Delaunay meshing of implicit domains with boundary edge sharpening and sliver elimination”, Math. Comput. Simul., 147:SI (2018), 2–26  crossref  mathscinet  isi  scopus
    6. Yu. Evtushenko, M. Posypkin, L. Rybak, A. Turkin, “Approximating a solution set of nonlinear inequalities”, J. Glob. Optim., 71:1, SI (2018), 129–145  crossref  mathscinet  zmath  isi  scopus
    7. M. V. Yakobovskii, S. K. Grigorev, “Algoritm garantirovannoi generatsii tetraedralnoi setki proektsionnym metodom”, Preprinty IPM im. M. V. Keldysha, 2018, 109, 18 pp.  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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