Gabriel meshes and Delaunay edge flips

Dyer, Ramsay; Zhang, Hao; Möller, Torsten B.

doi:10.1145/1629255.1629293

Cited by 7 publications

(8 citation statements)

References 12 publications

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“…As a direct consequence, the flatter the surface appears to be locally, the better is the guarantee of a good reconstruction. More generally, the theoretical guarantee of a good reconstruction can be founded on the following theorem demonstrated by Dyer et al in [29]: A Gabriel mesh is a Delaunay mesh. In other words, any mesh in which every triangle verifies the G2S criterion verifies also the 3D Delaunay one.…”

Section: Mesh-growing Methodsmentioning

confidence: 99%

A Fast Mesh-Growing Algorithm for Manifold Surface Reconstruction

Angelo¹,

Stefano²,

Giaccari³

2013

Computer-Aided Design and Applications

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In a previous paper these authors presented a new mesh-growing approach based on the Gabriel 2 -Simplex (G2S) criterion. If compared with the Cocone family and the Ball Pivoting methods, G2S demonstrated to be competitive in terms of tessellation rate, quality of the generated triangles and defectiveness produced when the surface to be reconstructed was locally flat. Nonetheless, its major limitation was that, in the presence of a mesh which was locally non -flat or which was not sufficiently sampled, the method was less robust and holes and non -manifold vertices were generated. In order to overcome these limitations, in this paper, the performance of the G2S meshgrowing method is fully improved in terms of robustness. The performances of the new version of the G2S approach (in the following Robust G2S) has been compared with that of the old one, and that of the Cocone family and the Ball Pivoting methods in the tessellation of some benchmark point clouds and artificially noised test cases. The results obtained show that the use of the Robust G2S is advantageous, as opposed to the other methods here considered, even in the case of noised point clouds. Unlike the other methods, the one which is proposed preserves manifoldness and geometric details of the point cloud to be meshed.

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Section: Mesh-growing Methodsmentioning

confidence: 99%

A Fast Mesh-Growing Algorithm for Manifold Surface Reconstruction

Angelo¹,

Stefano²,

Giaccari³

2013

Computer-Aided Design and Applications

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“…If the empty open ball need not necessarily have d(p, q) as its diameter, then the resulting graph is the DG. It has applications in surface reconstruction [24,25] and normal estimation [26].…”

Section: Related Workmentioning

confidence: 99%

Visible neighborhood graph of point clouds

Long

et al. 2012

Graphical Models

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“…In the end, we show that if a vertex p lies in the diametric ball of a triangle τ , then p is near the boundary of this ball. A previous work claims that edge flips can produce triangles with empty diametric balls [9], which unfortunately has a flaw [12]. Also, the sampling is required to be dense with respect to the minimum LFS.…”

Section: Main Ideas and Related Workmentioning

confidence: 99%

Edge flips and deforming surface meshes

Cheng

Jin

2011

Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry

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We study edge flips in a surface mesh and the maintenance of a deforming surface mesh. If the vertices are dense with respect to the local feature size and the triangles have angles at least a constant, we can flip edges in linear time such that all triangles have almost empty diametric balls. For a planar triangulation with a constant angle lower bound, we can flip it to the Delaunay triangulation in linear time. We combine edge flips and vertex insertions and deletions in an algorithm to maintain a deforming surface mesh, specified only by a dense sample of n points that move with the surface. Under a reasonable motion model, we can enforce bounded aspect ratios and a small approximation error throughout the deformation. The update takes O(n) time at each time step. Our surface mesh maintenance algorithm also gives a good performance in experiments.

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Gabriel meshes and Delaunay edge flips

Cited by 7 publications

References 12 publications

A Fast Mesh-Growing Algorithm for Manifold Surface Reconstruction

A Fast Mesh-Growing Algorithm for Manifold Surface Reconstruction

Visible neighborhood graph of point clouds

Edge flips and deforming surface meshes

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