Restricted delaunay triangulations and normal cycle

By David Cohen-Steiner, J. Morvan. SCG '03, 2003

582 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/9760afc87e1d81506cebcc11e5089ae10cb167ef

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Leonidas J. Guibas
2. M. Ovsjanikov
3. Hao Zhang
4. Bruno Lévy
5. Evangelos Kalogerakis
6. Pierre Alliez
7. Daniel Cohen-Or
8. David Cohen-Steiner

In Computer Graphics and Computer-Aided Design

1. Leonidas J. Guibas
2. Bruno Lévy
3. Hao Zhang
4. M. Ovsjanikov
5. Pierre Alliez
6. David Cohen-Steiner
7. Evangelos Kalogerakis
8. Mathieu Desbrun

Citations in the corpus

• Estimating differential quantities using polynomial fitting of osculating jets (2003, background): “Based upon the normal cycle and restricted Delaunay triangulations, an estimate for the second fundamental form of a surface is developed in ( Cohen-Steiner and Morvan, 2003 ).”
• Anisotropic Laplace-Beltrami Operators for Shape Analysis (2014, unknown): “In order to express numerically the anisotropic tensor D, we computed at each vertex of the mesh the principal curvatures and corresponding directions using the method described in [7] as implemented in [17], and then averaged over each triangle to obtain a constant operator.”
• Mesh Segmentation via Spectral Embedding and Contour Analysis (2007, methodology): “To capture local surface geometry, we define for edge e = ( i , j ) where κ i and κ j , computed as in [CSM03], are the minimal principal curvatures at vertices i and j , ~ z is the normalized average of the principal curvature directions for κ i and κ j , ~ e is the (normalized) direction of e ,…”
• Surface Matching via Currents (2005, background): “Given the recent active developments in exterior calculus [22] and current based approaches to curvature estimation [23], we expect the representations to become more sophisticated (perhaps incorporating second order geometric information), and that discretization will continue to get better.”
• Voronoi-Based Curvature and Feature Estimation from Point Clouds (2011, methodology): “Cohen-Steiner and Morvan [CSM03] used the normal cycle from geometric measure theory in order to de(cid:28)ne a closed-form second fundamental measure of a mesh.”
• Approximate Symmetry Detection in Partial 3D Meshes (2014, methodology): “For the computation of principal curvatures, we use the method of normal cycles proposed in [CSM03].”
• Extracting lines of curvature from noisy point clouds (2009, background): “(4) Check if the current flow line is crossing into a new datapoint Voronoi cell by intersecting one of the separating hyperplanes of the current cell.”