Variational Anisotropic Surface Meshing with Voronoi Parallel Linear Enumeration

Lévy, Bruno; Bonneel, Nicolas

doi:10.1007/978-3-642-33573-0_21

Cited by 58 publications

(88 citation statements)

References 40 publications

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“…Given the set of n points v i d i 1 n, the Voronoi diagram V is the collection of subsets V i where each subset can be defined by the following [12]:…”

Section: Interior Distance Voronoi Diagrammentioning

confidence: 99%

Shape conforming volumetric interpolation with interior distances

Fryazinov

Sanchez

Pasko

2015

Computers & Graphics

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Source based heterogeneous modelling is a powerful way of defining gradient materials within a volume. The current solutions do not take into account the topology of the object and can provide counter intuitive results for complex objects. This paper presents a method to interpolate material properties and attributes based on the accessibility of the points in respect to the material features defined by the user. Our method requires the non overlapping source features with constant material to interpolate gradient materials, by using Voronoi diagrams on interior distances. It leads to intuitive material properties across the shape regardless of its topology or complexity. We show how the shape conformal field is defined inside the volume and can be extended outside the volume to create a valid operator for a heterogeneous modelling system dealing with scalar fields. The presented method is computationally e cient and has several applications, such as material property interpolation and shape aware procedural micro structures.Keywords: Heterogeneous modelling, material interpolation, shape conformal, interior distance, procedural texturing

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“…Given the set of n points v i d i 1 n, the Voronoi diagram V is the collection of subsets V i where each subset can be defined by the following [12]:…”

Section: Interior Distance Voronoi Diagrammentioning

confidence: 99%

Shape conforming volumetric interpolation with interior distances

Fryazinov

Sanchez

Pasko

2015

Computers & Graphics

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“…Uniformly meshing surfaces embedded in higher dimensional space has also been studied in the literature [Cañas and Gortler 2006;Kovacs et al 2010;Lévy and Bonneel 2012]. The work of Lévy and Bonneel [2012] is most related to ours, since both can be considered as using the framework of energy optimization in a higher dimensional embedding space.…”

Section: Surface Meshing In Higher Dimensional Spacementioning

confidence: 99%

“…The work of Lévy and Bonneel [2012] is most related to ours, since both can be considered as using the framework of energy optimization in a higher dimensional embedding space. They extended the computation of CVT to a 6D space in order to achieve a curvature-adaptation.…”

Section: Surface Meshing In Higher Dimensional Spacementioning

confidence: 99%

“…They extended the computation of CVT to a 6D space in order to achieve a curvature-adaptation. In particular, the anisotropic meshing on a 3D surface is transformed to an isotropic one on the surface embedded in 6D space, which can be efficiently computed by CVT equipped with Voronoi Parallel Linear Enumeration [Lévy and Bonneel 2012]. However, it does not provide users with the flexibility to control the anisotropy via an input metric tensor field.…”

Section: Surface Meshing In Higher Dimensional Spacementioning

confidence: 99%

“…Our particle-based optimization framework can be easily extended to handle the 6D embedding case as suggested by Lévy and Bonneel [2012]. The basic idea of Lévy and Bonneel's approach is to use the embedding ϕ : Ω → R 6 defined by:…”

Section: Extension To 6d Surfacesmentioning

confidence: 99%

See 2 more Smart Citations

Particle-based anisotropic surface meshing

Zhong¹,

Guo²,

Wang

et al. 2013

ACM Trans. Graph.

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This paper introduces a particle-based approach for anisotropic surface meshing. Given an input polygonal mesh endowed with a Riemannian metric and a specified number of vertices, the method generates a metric-adapted mesh. The main idea consists of mapping the anisotropic space into a higher dimensional isotropic one, called "embedding space". The vertices of the mesh are generated by uniformly sampling the surface in this higher dimensional embedding space, and the sampling is further regularized by optimizing an energy function with a quasi-Newton algorithm. All the computations can be re-expressed in terms of the dot product in the embedding space, and the Jacobian matrices of the mappings that connect different spaces. This transform makes it unnecessary to explicitly represent the coordinates in the embedding space, and also provides all necessary expressions of energy and forces for efficient computations. Through energy optimization, it naturally leads to the desired anisotropic particle distributions in the original space. The triangles are then generated by computing the Restricted Anisotropic Voronoi Diagram and its dual Delaunay triangulation. We compare our results qualitatively and quantitatively with the state-of-the-art in anisotropic surface meshing on several examples, using the standard measurement criteria. *

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Quadrangular Mesh Generation Using Centroidal Voronoi Tessellation on Voxelized Surface

Soni

Bhowmick

2018

Lecture Notes in Computer Science

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Variational Anisotropic Surface Meshing with Voronoi Parallel Linear Enumeration

Cited by 58 publications

References 40 publications

Shape conforming volumetric interpolation with interior distances

Shape conforming volumetric interpolation with interior distances

Particle-based anisotropic surface meshing

Quadrangular Mesh Generation Using Centroidal Voronoi Tessellation on Voxelized Surface

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