Mathijs Wintraecken

45
Documents

Présentation

I work on computational geometry and topology. My three main interests are:

  1. triangulations/meshes,
  2. sets of positive reach and the medial axis, and the symmetry set,
  3. topological data analysis and persistent homology, and in particular the topological complexity of vineyards.

Domaines de recherche

Informatique [cs]

Publications

Publications

Image document

The medial axis of any closed bounded set is locally Lipschitz stable with respect to the Hausdorff distance under ambient diffeomorphisms

Hana Dal Poz Kouřimská , André Lieutier , Mathijs Wintraecken
Journal of Applied and Computational Topology, 2025, 9 (3), pp.20. ⟨10.1007/s41468-025-00216-w⟩
Article dans une revue hal-05225764 v1
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Burning or Collapsing the Medial Axis is Unstable

Erin Wolf Chambers , Christopher Fillmore , Elizabeth Stephenson , Mathijs Wintraecken
Article dans une revue hal-05225734 v1
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Brillouin Zones of Integer Lattices and Their Perturbations

Herbert Edelsbrunner , Alexey Garber , Mohadese Ghafari , Teresa Heiss , Morteza Saghafian et al.
SIAM Journal on Discrete Mathematics, 2024, 38 (2), pp.1784-1807. ⟨10.1137/22M1489071⟩
Article dans une revue hal-04628684 v1
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Local Criteria for Triangulating General Manifolds

Jean-Daniel Boissonnat , Ramsay Dyer , Arijit Ghosh , Mathijs Wintraecken
Discrete and Computational Geometry, 2023, 69, pp.156-191. ⟨10.1007/s00454-022-00431-7⟩
Article dans une revue hal-03794702 v1
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The reach of subsets of manifolds

Jean-Daniel Boissonnat , Mathijs Wintraecken
Journal of Applied and Computational Topology, 2023, ⟨10.1007/s41468-023-00116-x⟩
Article dans une revue hal-04083524 v1
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Tracing Isomanifolds in R^d in Time Polynomial in d using Coxeter–Freudenthal–Kuhn Triangulations

Jean-Daniel Boissonnat , Siargey Kachanovich , Mathijs Wintraecken
SIAM Journal on Computing, 2023, 52, pp.452 - 486. ⟨10.1137/21m1412918⟩
Article dans une revue hal-04083489 v1
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Local Conditions for Triangulating Submanifolds of Euclidean Space

Jean-Daniel Boissonnat , Ramsay Dyer , Arijit Ghosh , Andre Lieutier , Mathijs Wintraecken
Discrete and Computational Geometry, 2021, 66 (2), pp.666-686. ⟨10.1007/s00454-020-00233-9⟩
Article dans une revue hal-03372073 v1
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The Topological Correctness of PL Approximations of Isomanifolds

Jean-Daniel Boissonnat , Mathijs Wintraecken
Foundations of Computational Mathematics, 2021, 22, pp.967 - 1012. ⟨10.1007/s10208-021-09520-0⟩
Article dans une revue hal-03760378 v1
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Triangulating submanifolds: An elementary and quantified version of Whitney’s method

Jean-Daniel Boissonnat , Siargey Kachanovich , Mathijs Wintraecken
Discrete and Computational Geometry, 2020, ⟨10.1007/s00454-020-00250-8⟩
Article dans une revue hal-03109814 v1
Image document

Anisotropic triangulations via discrete Riemannian Voronoi diagrams

Jean-Daniel Boissonnat , Maël Rouxel-Labbé , Mathijs Wintraecken
SIAM Journal on Computing, 2019
Article dans une revue hal-02419460 v1
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The reach, metric distortion, geodesic convexity and the variation of tangent spaces

Jean-Daniel Boissonnat , André Lieutier , Mathijs Wintraecken
Journal of Applied and Computational Topology, 2019, ⟨10.1007/s41468-019-00029-8⟩
Article dans une revue hal-02266258 v1

The Topology of the Cosmic Web in Terms of Persistent Betti Numbers

Pratyush Pranav , Herbert Edelsbrunner , Rien van de Weygaert , Gert Vegter , Michael Kerber et al.
Monthly Notices of the Royal Astronomical Society, 2017, 465 (4), pp.4281-4310. ⟨10.1093/mnras/stw2862⟩
Article dans une revue hal-01554114 v1
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Tight Bounds for the Learning of Homotopy à la Niyogi, Smale, and Weinberger for Subsets of Euclidean Spaces and of Riemannian Manifolds

Dominique Attali , Hana Dal Poz Kouřimská , Christopher Fillmore , Ishika Ghosh , André Lieutier et al.
SoCG 2024 - 40th International Symposium on Computational Geometry, Jun 2024, Athènes, Greece. ⟨10.4230/LIPIcs.SoCG.2024.11⟩
Communication dans un congrès hal-04628805 v1
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The Ultimate Frontier: An Optimality Construction for Homotopy Inference (Media Exposition)

Dominique Attali , Hana Dal Poz Kouřimská , Christopher Fillmore , Ishika Ghosh , André Lieutier et al.
SoCG 2024 - 40th International Symposium on Computational Geometry, Jun 2024, Athènes, Greece. pp.87:1-87:6, ⟨10.4230/LIPIcs.SoCG.2024.87⟩
Communication dans un congrès hal-04628855 v1
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The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms

Hana Dal Poz Kouřimská , André Lieutier , Mathijs Wintraecken
SoCG 2024 - 40th International Symposium on Computational Geometry, Jun 2024, Athens, Greece. ⟨10.4230/LIPIcs.SoCG.2024.69⟩
Communication dans un congrès hal-04628829 v1
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Hausdorff and Gromov-Hausdorff Stable Subsets of the Medial Axis

André Lieutier , Mathijs Wintraecken
STOC 2023 - 55th Annual ACM Symposium on Theory of Computing, ACM, Jun 2023, Orlando (Florida), United States. pp.1768-1776, ⟨10.1145/3564246.3585113⟩
Communication dans un congrès hal-04095824 v1
Image document

Tracing isomanifolds in R^d in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations

Jean-Daniel Boissonnat , Siargey Kachanovich , Mathijs Wintraecken
SoCG 2021 - 37th Symposium on Computational Geometry, Jun 2021, Buffalo, United States. ⟨10.4230/LIPICS.SOCG.2021.17⟩
Communication dans un congrès hal-03006663 v3
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The Topological Correctness of PL-Approximations of Isomanifolds

Jean-Daniel Boissonnat , Mathijs Wintraecken
SoCG 2020 - 36th International Symposium on Computational Geometry, Jun 2020, Zurich, Switzerland. ⟨10.4230/LIPIcs.SoCG.2020.20⟩
Communication dans un congrès hal-02873794 v1
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Local Criteria for Triangulation of Manifolds

Jean-Daniel Boissonnat , Ramsay Dyer , Arijit Ghosh , Mathijs Wintraecken
International Symposium on Computational Geometry, Jun 2018, Budapest, Hungary. ⟨10.4230/LIPIcs.SoCG.2018.9⟩
Communication dans un congrès hal-01801616 v1
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The reach, metric distortion, geodesic convexity and the variation of tangent spaces

Jean-Daniel Boissonnat , André Lieutier , Mathijs Wintraecken
SoCG 2018 - 34th International Symposium on Computational Geometry, Jun 2018, Budapest, Hungary. pp.1-14, ⟨10.4230/LIPIcs.SoCG.2018⟩
Communication dans un congrès hal-01801667 v1
Image document

Anisotropic triangulations via discrete Riemannian Voronoi diagrams

Jean-Daniel Boissonnat , Mael Rouxel-Labbé , Mathijs Wintraecken
Symposium on Computational Geometry SoCG 2017, Jul 2017, Brisbane, Australia. ⟨10.4230/LIPIcs.SoCG.2017.19⟩
Communication dans un congrès hal-01507111 v1
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Supplementary material: The ultimate frontier: An optimality construction for homotopy inference

Dominique Attali , Hana Dal Poz Kouřimská , Christopher Fillmore , Ishika Ghosh , André Lieutier et al.
2024
Pré-publication, Document de travail hal-04501285 v1
Image document

Tight Bounds for the Learning of Homotopy à la Niyogi, Smale, and Weinberger for Subsets of Euclidean Spaces and of Riemannian Manifolds

Dominique Attali , Hana Dal Poz Kouřimská , Christopher Fillmore , Ishika Ghosh , André Lieutier et al.
2024
Pré-publication, Document de travail hal-03721463 v2
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Manifolds of positive reach, differentiability, tangent variation, and attaining the reach

André Lieutier , Mathijs Wintraecken
2024
Pré-publication, Document de travail hal-04816588 v1
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A free lunch: manifolds of positive reach can be smoothed without decreasing the reach

Hana Dal Poz Kouřimská , André Lieutier , Mathijs Wintraecken
2024
Pré-publication, Document de travail hal-04816535 v1
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Quasi-optimal interpolation of gradients and vector-fields on protected Delaunay meshes in $\mathbb{R}^d$

David Williams , Mathijs Wintraecken
2024
Pré-publication, Document de travail hal-04822711 v1
Image document

The medial axis of closed bounded sets is Lipschitz stable with respect to the Hausdorff distance under ambient diffeomorphisms

Hana Dal Poz Kouřimská , André Lieutier , Mathijs Wintraecken
2023
Pré-publication, Document de travail hal-04297370 v1
Image document

Simplicial subdivision of simplices of arbitrary dimension in a space of constant non-zero curvature with bounded quality

Jean-Daniel Boissonnat , Florestan Brunck , Hana Dal Poz Kouřimská , Arijit Ghosh , Mathijs Wintraecken
2023
Pré-publication, Document de travail hal-04297480 v1
Image document

Triangulating submanifolds: An elementary and quantified version of Whitney's method

Jean-Daniel Boissonnat , Siargey Kachanovich , Mathijs Wintraecken
2023
Pré-publication, Document de travail hal-01950149 v2
Image document

Hausdorff and Gromov-Hausdorff stable subsets of the medial axis

André Lieutier , Mathijs Wintraecken
2023
Pré-publication, Document de travail hal-04083167 v1
Image document

Burning or collapsing the medial axis is unstable

Erin Wolf Chambers , Christopher Fillmore , Elizabeth Stephenson , Mathijs Wintraecken
2023
Pré-publication, Document de travail hal-04297424 v1
Image document

The topological correctness of PL-approximations of isomanifolds

Jean-Daniel Boissonnat , Mathijs Wintraecken
2020
Pré-publication, Document de travail hal-02386193 v3
Image document

Tracing Isomanifolds of Fixed Dimension in Polynomial Time

Jean-Daniel Boissonnat , Siargey Kachanovich , Mathijs Wintraecken
2020
Pré-publication, Document de travail hal-02889048 v2
Image document

A compact data structure for high dimensional Coxeter-Freudenthal-Kuhn triangulations

Jean-Daniel Boissonnat , Siargey Kachanovich , Mathijs Wintraecken
2020
Pré-publication, Document de travail hal-03006608 v1
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Sampling and Meshing Submanifolds in High Dimension

Jean-Daniel Boissonnat , Siargey Kachanovich , Mathijs Wintraecken
2019
Pré-publication, Document de travail hal-02386169 v2
Image document

Local conditions for triangulating submanifolds of Euclidean space

Jean-Daniel Boissonnat , Ramsay Dyer , Arijit Ghosh , André Lieutier , Mathijs Wintraecken
2019
Pré-publication, Document de travail hal-02267620 v1
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Local criteria for triangulation of manifolds *

Jean-Daniel Boissonnat , Ramsay Dyer , Arijit Ghosh , Mathijs Wintraecken
2017
Pré-publication, Document de travail hal-01661230 v1
Image document

The reach, metric distortion, geodesic convexity and the variation of tangent spaces

Jean-Daniel Boissonnat , André Lieutier , Mathijs Wintraecken
2017
Pré-publication, Document de travail hal-01661227 v1
Image document

Coxeter triangulations have good quality

Aruni Choudhary , Siargey Kachanovich , Mathijs Wintraecken
2017
Pré-publication, Document de travail hal-01667404 v1
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Triangulating stratified manifolds I: a reach comparison theorem

Jean-Daniel Boissonnat , Mathijs Wintraecken
2017
Pré-publication, Document de travail hal-01661233 v1
Image document

Anisotropic triangulations via discrete Riemannian Voronoi diagrams

Jean-Daniel Boissonnat , Mael Rouxel-Labbé , Mathijs Wintraecken
[Research Report] RR-9056, Inria Sophia Antipolis. 2017
Rapport (rapport de recherche) hal-01507273 v1
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Discretized Riemannian Delaunay Triangulations

Mael Rouxel-Labbé , Mathijs Wintraecken , Jean-Daniel Boissonnat
[Research Report] RR-9103, INRIA Sophia Antipolis - Méditerranée. 2017, pp.51
Rapport (rapport de recherche) hal-01612924 v1