The reach, metric distortion, geodesic convexity and the variation of tangent spaces
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Publication:2324602
DOI10.1007/s41468-019-00029-8zbMath1431.53043OpenAlexW2771985859WikidataQ90840561 ScholiaQ90840561MaRDI QIDQ2324602
Jean-Daniel Boissonnat, André Lieutier, M. H. M. J. Wintraecken
Publication date: 11 September 2019
Published in: Journal of Applied and Computational Topology (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s41468-019-00029-8
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Cites Work
- Unnamed Item
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- Triangulating smooth submanifolds with light scaffolding
- Geometry-driven collapses for converting a Čech complex into a triangulation of a nicely triangulable shape
- Surface reconstruction by Voronoi filtering
- Finding the homology of submanifolds with high confidence from random samples
- Morse theory on Hilbert manifolds
- On \(C^1\)-complexes
- THE STABILITY OF DELAUNAY TRIANGULATIONS
- Curvature Measures
- CRITICAL POINTS OF DISTANCE TO AN ε-SAMPLING OF A SURFACE AND FLOW-COMPLEX-BASED SURFACE RECONSTRUCTION
- Local criteria for triangulation of manifolds
- Curve and Surface Reconstruction
- Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
- Natural neighbor coordinates of points on a surface