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ParticleBased Anisotropic Surface Meshing
"... Figure 1: Anisotropic meshing results generated by our particlebased method. This paper introduces a particlebased 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 metricadapted mesh ..."
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Figure 1: Anisotropic meshing results generated by our particlebased method. This paper introduces a particlebased 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 metricadapted 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 quasiNewton algorithm. All the computations can be reexpressed 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 stateoftheart in anisotropic surface meshing on several examples, using the standard measurement criteria.
Lattice Cleaving: Conforming Tetrahedral Meshes of Multimaterial Domains with Bounded Quality
"... Summary. We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces highquality tetrahedral meshes with upper and lower bounds on ..."
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Summary. We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces highquality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, in order to reduce element counts in regions of homogeneity.
Dynamic Particle System for Mesh Extraction on the GPU
"... Extracting isosurfaces represented as high quality meshes from threedimensional scalar fields is needed for many important applications, particularly visualization and numerical simulations. One recent advance for extracting high quality meshes for isosurface computation is based on a dynamic part ..."
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Extracting isosurfaces represented as high quality meshes from threedimensional scalar fields is needed for many important applications, particularly visualization and numerical simulations. One recent advance for extracting high quality meshes for isosurface computation is based on a dynamic particle system. Unfortunately, this stateoftheart particle placement technique requires a significant amount of time to produce a satisfactory mesh. To address this issue, we study the parallelism property of the particle placement and make use of CUDA, a parallel programming technique on the GPU, to significantly improve the performance of particle placement. This paper describes the curvature dependent sampling method used to extract high quality meshes and describes its implementation using CUDA on the GPU.
GPU Surface Extraction using the Closest Point Embedding
"... Isosurface extraction is a fundamental technique used for both surface reconstruction and mesh generation. One method to extract wellformed isosurfaces is a particle system; unfortunately, particle systems can be slow. In this paper, we introduce an enhanced parallel particle system that uses the c ..."
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Isosurface extraction is a fundamental technique used for both surface reconstruction and mesh generation. One method to extract wellformed isosurfaces is a particle system; unfortunately, particle systems can be slow. In this paper, we introduce an enhanced parallel particle system that uses the closest point embedding as the surface representation to speedup the particle system for isosurface extraction. The closest point embedding is used in the Closest Point Method (CPM), a technique that uses a standard three dimensional numerical PDE solver on two dimensional embedded surfaces. To fully take advantage of the closest point embedding, it is coupled with a BarnesHut tree code on the GPU. This new technique produces wellformed, conformal unstructured triangular and tetrahedral meshes from labeled multimaterial volume datasets. Further, this new parallel implementation of the particle system is faster than any known methods for conformal multimaterial mesh extraction. The resulting speedups gained in this implementation can reduce the time from labeled data to mesh from hours to minutes and benefits users, such as bioengineers, who employ triangular and tetrahedral meshes.