Zobrazeno 1 - 10
of 210
pro vyhledávání: '"Jean-Daniel Boissonnat"'
We quantise Whitney’s construction to prove the existence of a triangulation for any$$C^2$$C2manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::75e227bc171f8a4a67a04d5a702a9298
https://inria.hal.science/hal-01950149v2/document
https://inria.hal.science/hal-01950149v2/document
Publikováno v:
SIAM Journal on Computing
SIAM Journal on Computing, 2023, 52, pp.452-486. ⟨10.1137/21m1412918⟩
SIAM Journal on Computing, 2023, 52, pp.452-486. ⟨10.1137/21m1412918⟩
International audience; Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. submanifolds of $\mathbb{R}^d$ defined as the zero set of a multivariate multivalued smooth function $f: \mathbb{R}^d\rightarrow \
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dc8d35e8b9f3dd0091304293e898ff1c
https://hal.science/hal-04083489/document
https://hal.science/hal-04083489/document
Publikováno v:
Journal of Applied and Computational Topology
Journal of Applied and Computational Topology, 2023, ⟨10.1007/s41468-023-00116-x⟩
Journal of Applied and Computational Topology, 2023, ⟨10.1007/s41468-023-00116-x⟩
International audience; Kleinjohann [1] and Bangert [2] extended the reach rch(S) from subsets S of Euclidean space to the reach rch M (S) of subsets S of Riemannian manifolds M, where M is smooth (we'll assume at least C^3). Bangert showed that sets
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6cb3a8ad807ab6c3a9ea7c65c4dccee5
https://hal.science/hal-04083524/document
https://hal.science/hal-04083524/document
Publikováno v:
Journal of Topology and Analysis
Journal of Topology and Analysis, 2021, pp.1-29. ⟨10.1142/S1793525321500291⟩
Journal of Topology and Analysis, 2021, pp.1-29. ⟨10.1142/S1793525321500291⟩
In this paper, we introduce a fast and memory efficient approach to compute the Persistent Homology (PH) of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the input sequence by using strong collapses, as introduced
Publikováno v:
Journal of Applied and Computational Topology
Journal of Applied and Computational Topology, 2021, 5, pp.671-691. ⟨10.1007/s41468-021-00079-x⟩
Journal of Applied and Computational Topology, Springer, 2021, 5, pp.671-691. ⟨10.1007/s41468-021-00079-x⟩
SoCG 2020-36th International Symposium on Computational Geometry
SoCG 2020-36th International Symposium on Computational Geometry, Jun 2020, Zurich, Switzerland. ⟨10.4230/LIPIcs.SoCG.2020.10⟩
Journal of Applied and Computational Topology, 2021, 5, pp.671-691. ⟨10.1007/s41468-021-00079-x⟩
Journal of Applied and Computational Topology, Springer, 2021, 5, pp.671-691. ⟨10.1007/s41468-021-00079-x⟩
SoCG 2020-36th International Symposium on Computational Geometry
SoCG 2020-36th International Symposium on Computational Geometry, Jun 2020, Zurich, Switzerland. ⟨10.4230/LIPIcs.SoCG.2020.10⟩
Given a set P of n points and a constant k, we are interested in computing the persistent homology of the Cech filtration of P for the k-distance, and investigate the effectiveness of dimensionality reduction for this problem, answering an open quest
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::39597ec06b22ff4c98d7b1c5ef11d047
https://hal-amu.archives-ouvertes.fr/hal-03412594/file/DimReducTDA.pdf
https://hal-amu.archives-ouvertes.fr/hal-03412594/file/DimReducTDA.pdf
Publikováno v:
Foundations of Computational Mathematics
Foundations of Computational Mathematics, 2021, 22, pp.967-1012. ⟨10.1007/s10208-021-09520-0⟩
SoCG 2020-36th International Symposium on Computational Geometry
SoCG 2020-36th International Symposium on Computational Geometry, Jun 2020, Zurich, Switzerland. ⟨10.4230/LIPIcs.SoCG.2020.20⟩
Foundations of Computational Mathematics, 2021, 22, pp.967-1012. ⟨10.1007/s10208-021-09520-0⟩
SoCG 2020-36th International Symposium on Computational Geometry
SoCG 2020-36th International Symposium on Computational Geometry, Jun 2020, Zurich, Switzerland. ⟨10.4230/LIPIcs.SoCG.2020.20⟩
Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f: ℝ^d → ℝ^(d-n). A natural (and efficient) way to approximate
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ebdd6bfb299f5a9f14bda7557ec982aa
https://inria.hal.science/hal-03760378/file/approx-isoman-focm.pdf
https://inria.hal.science/hal-03760378/file/approx-isoman-focm.pdf
Autor:
Jean-Daniel Boissonnat
Enseignement Cours et seminaires – Geometrie algorithmique : donnees, modeles, programmes Introduction Le monde numerique n’est maintenant plus limite au texte, au son et aux images, et les representations numeriques de formes tridimensionnelles
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0ca4830b1e4bc2f8c895c240d849d7c5
http://journals.openedition.org/annuaire-cdf/14474
http://journals.openedition.org/annuaire-cdf/14474
Publikováno v:
Discrete and Computational Geometry
Discrete and Computational Geometry, 2022, ⟨10.1007/s00454-022-00431-7⟩
Discrete and Computational Geometry, 2022, ⟨10.1007/s00454-022-00431-7⟩
We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex $${\mathscr {A}}$$ A , and a map H from the underlying space of $${\mathscr {A}}$$ A to M, our criteria are presented in local coordinate cha
Publikováno v:
Discrete and Computational Geometry
Discrete and Computational Geometry, Springer Verlag, 2017, ⟨10.1145/336154.336221⟩
Discrete and Computational Geometry, 2017, ⟨10.1145/336154.336221⟩
Discrete & computational geometry, 59(1), 226-237. SPRINGER
Discrete and Computational Geometry, Springer Verlag, 2017, ⟨10.1145/336154.336221⟩
Discrete and Computational Geometry, 2017, ⟨10.1145/336154.336221⟩
Discrete & computational geometry, 59(1), 226-237. SPRINGER
Delaunay has shown that the Delaunay complex of a finite set of points $P$ of Euclidean space $\mathbb{R}^m$ triangulates the convex hull of $P$, provided that $P$ satisfies a mild genericity property. Voronoi diagrams and Delaunay complexes can be d
Publikováno v:
ESA 2019-27th Annual European Symposium on Algorithms
ESA 2019-27th Annual European Symposium on Algorithms, Sep 2019, Munich, Germany. ⟨10.4230/LIPIcs.ESA.2019.22⟩
Discrete & Computational Geometry
Discrete and Computational Geometry
Discrete and Computational Geometry, Springer Verlag, 2020, 64, pp.33. ⟨10.1007/s00454-020-00235-7⟩
[Research Report] INRIA. 2019
Discrete and Computational Geometry, 2020, 64, pp.33. ⟨10.1007/s00454-020-00235-7⟩
ESA 2019-27th Annual European Symposium on Algorithms, Sep 2019, Munich, Germany. ⟨10.4230/LIPIcs.ESA.2019.22⟩
Discrete & Computational Geometry
Discrete and Computational Geometry
Discrete and Computational Geometry, Springer Verlag, 2020, 64, pp.33. ⟨10.1007/s00454-020-00235-7⟩
[Research Report] INRIA. 2019
Discrete and Computational Geometry, 2020, 64, pp.33. ⟨10.1007/s00454-020-00235-7⟩
Randomized incremental construction (RIC) is one of the most important paradigms for building geometric data structures. Clarkson and Shor developed a general theory that led to numerous algorithms which are both simple and efficient in theory and in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b81efecf3aaf06a8d1ff8d33b1a899e8
https://hal.inria.fr/hal-02185566/document
https://hal.inria.fr/hal-02185566/document