DIFFERENTIAL TOPOLOGY AND GEOMETRY OF SMOOTH EMBEDDED SURFACES: SELECTED TOPICS

DOI10.1142/S0218195905001816zbMath1083.68134OpenAlexW2124552073WikidataQ115245929 ScholiaQ115245929MaRDI QIDQ5709138

Frédéric Cazals, Marc Pouget

Publication date: 29 November 2005

Published in: International Journal of Computational Geometry & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218195905001816

zbMATH Keywords

ridgefoliationdifferential geometryisotopymedial axisline of curvaturesmooth embedded surfaceumbilits

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Singularities of vector fields, topological aspects (58K45) Surfaces in Euclidean and related spaces (53A05) Research exposition (monographs, survey articles) pertaining to computer science (68-02)

Related Items (8)

Subdivision surface fitting to a dense mesh using ridges and umbilics ⋮ Shock-conforming mesh generation for aerodynamic analyses at supersonic regimes ⋮ Computing lines of curvature for implicit surfaces ⋮ Numerical simulation of multiple 3D fracture propagation using arbitrary meshes ⋮ Numerical analysis of differential operators on raw point clouds ⋮ Ridge extraction of a smooth 2-manifold surface based on vector field ⋮ The implicit structure of ridges of a smooth parametric surface ⋮ Fast, robust, and faithful methods for detecting crest lines on meshes

Cites Work

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• Computational topology: Ambient isotopic approximation of 2-manifolds.
• Surface reconstruction by Voronoi filtering
• Continuous skeleton computation by Voronoi diagram
• Natural neighbor coordinates of points on a surface

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