Triangulating topological spaces
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
New techniques for topologically correct surface reconstruction
Proceedings of the conference on Visualization '00
A geometric convection approach of 3-D reconstruction
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics)
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
A Discrete Laplace–Beltrami Operator for Simplicial Surfaces
Discrete & Computational Geometry
Regular and non-regular point sets: Properties and reconstruction
Computational Geometry: Theory and Applications
Edge flips and deforming surface meshes
Proceedings of the twenty-seventh annual symposium on Computational geometry
Visible neighborhood graph of point clouds
Graphical Models
| Hi-index | 0.00 |
We undertake a study of the local properties of 2-Gabriel meshes: manifold triangle meshes each of whose faces has an open Euclidean diametric ball that contains no mesh vertices. We show that, under mild constraints on the dihedral angles, such meshes are Delaunay meshes: the open geodesic circumdisk of each face contains no mesh vertex. The analysis is done by means of the Delaunay edge flipping algorithm and it reveals the details of the distinction between these two mesh structures. In particular we observe that the obstructions which prohibit the existence of Gabriel meshes as homeomorphic representatives of smooth surfaces do not hinder the construction of Delaunay meshes.