Meshing Volumes Bounded by Smooth Surfaces

Effective Computational Geometry for Curves and Surfaces, 2006

Proceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145), 2000

We present a novel method to extract iso-surfaces from distance volumes. It generates high quality semi-regular multiresolution meshes of arbitrary topology. Our technique proceeds in two stages. First, a very coarse mesh with guaranteed topology is extracted. Subsequently an iterative multi-scale force-based solver refines the initial mesh into a semi-regular mesh with geometrically adaptive sampling rate and good aspect ratio triangles. The coarse mesh extraction is performed using a new approach we call surface wavefront propagation. A set of discrete iso-distance ribbons are rapidly built and connected while respecting the topology of the iso-surface implied by the data. Subsequent multi-scale refinement is driven by a simple force-based solver designed to combine good iso-surface fit and high quality sampling through reparameterization. In contrast to the Marching Cubes technique our output meshes adapt gracefully to the iso-surface geometry, have a natural multiresolution structure and good aspect ratio triangles, as demonstrated with a number of examples.

Proceedings of the …, 2004

This paper presents an algorithm for sampling and triangulating a smooth surface Σ ⊂ R 3 where the triangulation is homeomorphic to Σ. The only assumption we make is that the input surface representation is amenable to certain types of computations, namely computations of the intersection points of a line with the surface, computations of the critical points of some height functions defined on the surface and its restriction to a plane, and computations of some silhouette points. The algorithm ensures bounded aspect ratio, size optimality, and smoothness of the output triangulation. Unlike previous algorithms, this algorithm does not need to compute the local feature size for generating the sample points which was a major bottleneck. Experiments show the usefulness of the algorithm in remeshing and meshing CAD surfaces that are piecewise smooth.

IMPACT of Computing in Science and Engineering, 1990

Devoted to mesh generation of 3D domains, this paper examines the different approaches actually in progress. A new method is introduced which can be seen as a variant of the Delaunay-Voronoi' tesselation coupled with a control of the given boundary used to define the domain under consideration. 0 1990 Academic PISS, hc.

IEEE Transactions on Magnetics, 1990

Devoted to the mesh generation of 3DD-domains, this paper briefly describes difleerent approaches actually in progress. A new method is introduced which can be seen as a variant of the Delaunay-Vomnoi's tessellation coupled with a control of the given boundary used to defined the domain to be meshed.

Proceedings of the International Conference on Biomedical Engineering and Informatics. International Conference on Biomedical Engineering and Informatics, 2010

Multi-domain meshing from volumetric data is of great importance in many fields like medicine, biology and geology. This paper proposes a new approach to produce a high quality mesh with separated multiple domains. A point cloud is generated from a preliminary mesh representing the boundary between different domains from the discrete volumetric representation used as input. A higher-order level-set method is employed to produce a quality sub-mesh from this point cloud and geometric flow is used as smoothing mechanism. A new approach to detect and curate intersections within an assembly of these 2-manifold sub-meshes by utilizing the intermediate volumetric representation is developed. The separation between sub-meshes can be controlled by the user using a gap threshold parameter. The resulting high quality multi-domain mesh is free from self- and inter-domain intersections and can be further utilized in finite element and boundary element computations. The proposed pipeline has been...

International Journal for Numerical Methods in Engineering, 1994

Fully automatic three-dimensional mesh generation is an essential and increasingly crucial requirement for finite element solution of partial derivative equations. The results of numerical simulation, more precisely the convergence and accuracy of numerical solutions, closely depends on the quality of the underlying mesh. This work introduces a fully automatic finite element mesh algorithm with simplexes (tetrahedra), adapted to complex geometries described by disctete data. This paper is divided in four sections: (a) brief introduction to discrete geometry is given, as well as the basic definition of the domain of interest; (b) description of the voxel approach to tetrahedronization. The tetrahedronization process uses a divide-and-conquer method, which provides small elements on the boundary of the domain of interest. Voxels of the domain are subdivided according to an automatic procedure, which preserves the topology. Specific rules were introduced which allow reducing the number of voxel configurations to be treated, and consequently the computation time; (c) presentation of results and performances of the mesh algorithms. The resulting algorithm demonstrates an n logn growth rate with respect to the number of elements; (d) optimization of the mesh generation process at hand of a 'finite-octree' type of explicit controlling space.

Journal of Computational Physics, 2014

A novel parametric surface meshing technique is presented. Its distinctive feature relies on successive approximations of the CAD geometry through a hierarchical process where geometric information is gathered incrementally. A detailed review of zero-and firstorder surface approximations and their impact on parametric surface meshing algorithms is performed. The proposed approach emphasizes the use of three-dimensional information in order to be as independent as possible of the parametrization to overcome limitations of meshing purely in the parametric plane. The presented technique includes semi-structured boundary-layer surface mesh generation which is a critical capability for accurate solutions to flows around geometries that have leading edge features. Numerous examples illustrate the method's robustness and ability to high-quality meshes for complex CAD geometries.

International Journal for Numerical Methods in Engineering, 2021

This paper presents a methodology aiming at easing considerably the generation of high-quality meshes for complex 3D domains. We show that the whole mesh generation process can be controlled with only five parameters to generate in one stroke quality meshes for arbitrary geometries. The main idea is to build a meshsize field h(x) taking local features of the geometry, such as curvatures, into account. Meshsize information is then propagated from the surfaces into the volume, ensuring that the magnitude of |∇h| is always controlled so as to obtain a smoothly graded mesh. As the meshsize field is stored in an independent octree data structure, the function h can be computed separately, and then plugged in into any mesh generator able to respect a prescribed meshsize field. The whole procedure is automatic, in the sense that minimal interaction with the user is required. Applications examples based on models taken from the very large ABC dataset, are then presented, all treated with the same generic set of parameter values, to demonstrate the efficiency and the universality of the technique.

International Journal For Numerical Methods in Biomedical Engineering, 2012

An overview of surface and volume mesh generation techniques for creating valid meshes to carry out biomedical flows is provided. The methods presented are designed for robust numerical modelling of biofluid flow through subject-specific geometries. The applications of interest are haemodynamics in blood vessels and air flow in upper human respiratory tract. The methods described are designed to minimize distortion to a given domain boundary. They are also designed to generate a triangular surface mesh first and then volume mesh (tetrahedrons) with high quality surface and volume elements. For blood flow applications, a simple procedure to generate a boundary layer mesh is also described. The methods described here are semiautomatic in nature because of the fact that the geometries are complex, and automation of the procedures may be possible if high quality scans are used. of a well-defined object and patient-specific geometry is in building the surface mesh. Because the surface is not analytically defined in subject-specific applications, alternative approaches to that of the standard geometries are required.