Quality Multi-domain Meshing for Volumetric Data

Procedia Engineering, 2016

The Dual Contouring algorithm (DC) is a grid-based process used to generate surface meshes from volumetric data. The advantage of DC is that it can reproduce sharp features by inserting vertices anywhere inside the grid cube, as opposed to the Marching Cubes (MC) algorithm that can insert vertices only on the grid edges. However, DC is unable to guarantee 2-manifold and watertight meshes due to the fact that it produces only one vertex for each grid cube. We present a modified Dual Contouring algorithm that is capable of overcoming this limitation. Our method decomposes an ambiguous grid cube into a maximum of twelve tetrahedral cells; we introduce novel polygon generation rules that produce 2-manifold and watertight surface meshes. We have applied our proposed method on realistic data, and a comparison of the results of our proposed method with results from traditional DC shows the effectiveness of our method.

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.

International Journal for Numerical Methods in Engineering, 2017

The paper describes the main features of an automatic and three-dimensional Cartesian mesher specifically designed for compressible inviscid/viscous flow solvers based on an immersed boundary technique. The development of a meshing tool able of carrying out non-isotropic cell refinements is a very tiresome task. The major difficulty is to imagine, at the pre-design phase, a light but flexible data management, which minimizes the memory and CPUs resources. In particular, the embedded geometry has to be detected by means of a fast and robust tagging procedure. Cells in proximity of the wall have to be refined in a proper way to adequately solve large flow gradients. Smooth variation of mesh density between differently refined zones has to be guaranteed in order to increase the flow solver robustness. A procedure to obtain accurate data on the geometry surfaces should be foresee. Here a robust algorithm is developed to reconstruct a surface triangulation starting from the intersection points among volume cells and the geometry surfaces. The paper attempts to address all the above issues in order to help the readers in designing their own tools and suggesting them a way forward.

2007

Finite Element methods (FEM) usually require a mesh to describe the geometric domain on which the computations are occuring. These meshes must have several properties: 1) they must approximate the geometrical domain accurately, 2) they must have good numerical properties, and 3) they must be small enough so that the computations take a reasonable amount of time. These goals are somewhat contradictory and in many cases such as biomedical images -and particularly in the case of the head -, even though the geometric domains can effectively be extracted, eg from Magnetic Resonance Images (MRI), the generation of such meshes is quite difficult.

This paper presents a method for constructing consistent non-manifold meshes of multi-labeled volu- metric datasets. This approach is dieren t to traditional surface reconstruction algorithms which often only support extracting 2-manifold surfaces based on a binary voxel classication. However, in some { especially medical { applications, multi-labeled datasets, where up to eight dieren tly labeled voxels can be adjacent, are subject to visualization resulting in non-manifold meshes. In addition to an ecien t surface reconstruction method, a constrained geometric lter is developed which can be applied to these non-manifold meshes without producing ridges at mesh junctions.

Proceedings of the 16th International Meshing Roundtable, 2008

This paper describes an approach to construct unstructured tetrahedral and hexahedral meshes for a domain with multiple materials. In earlier works, we developed an octreebased isocontouring method to construct unstructured 3D meshes for a single-material domain. Based on this methodology, we introduce the notion of material change edge and use it to identify the interface between two or several materials. We then mesh each material region with conforming boundaries. Two kinds of surfaces, the boundary surface and the interface between two different material regions, are distinguished and meshed. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for hexahedral mesh construction. Finally the edge-contraction and smoothing method is used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimization techniques is used for hexahedral mesh quality improvement. The shrink set is defined automatically as the boundary of each material region. Several application results in different research fields are shown.

Advances in Engineering Software, 2002

Many physical phenomena in science and engineering can be modeled by partial differential equations and solved by means of the finite element method. Such a method uses as computational spatial support a mesh of the domain where the equations are formulated. The 'mesh quality' is a key-point for the accuracy of the numerical simulation. One can show that this quality is related to the shape and the size of the mesh elements. In the case where the element sizes are not specified in advance, a quality mesh is a regular mesh (whose elements are almost equilateral). This problem is a particular case of a more general mesh generation problem whose purpose is to construct meshes conforming to a prespecified isotropic size field associated with the computational domain. Such meshes can be seen as 'unit meshes' (whose elements are of unit size) in an appropriate non-Euclidean metric. In this case, a quality mesh of the domain is a unit mesh as regular as possible. In this paper, we are concerned with the generation of such a mesh and we propose a method to achieve this goal. First, the boundary of the domain is meshed using an indirect scheme via parametric domains and then the mesh of the three-dimensional (3D) domain is generated. In both cases, an empty mesh is first constructed, then enriched by field points, and finally optimized. The field points are defined following an algebraic or an advancing-front approach and are connected using a generalized Delaunay type method. To show the overall meshing process, we give an example of a 3D domain encountered in a classical computational fluid dynamics problem. q

2005

This paper describes an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging data. The extracted tetrahedral and hexahedral meshes are extensively used in the finite element method (FEM). A top-down octree subdivision coupled with a dual contouring method is used to rapidly extract adaptive 3D finite element meshes with correct topology from volumetric imaging data. The edge contraction and smoothing methods are used to improve mesh quality. The main contribution is extending the dual contouring method to crack-free interval volume 3D meshing with boundary feature sensitive adaptation. Compared to other tetrahedral extraction methods from imaging data, our method generates adaptive and quality 3D meshes without introducing any hanging nodes. The algorithm has been successfully applied to constructing quality meshes for finite element calculations. 2005 Elsevier B.V. All rights reserved.

Computer Methods in Applied Mechanics and Engineering, 2006

This paper describes an algorithm to extract adaptive and quality quadrilateral/hexahedral meshes directly from volumetric data. First, a bottom-up surface topology preserving octree-based algorithm is applied to select a starting octree level. Then the dual contouring method is used to extract a preliminary uniform quad/hex mesh, which is decomposed into finer quads/hexes adaptively without introducing any hanging nodes. The positions of all boundary vertices are recalculated to approximate the boundary surface more accurately. Mesh adaptivity can be controlled by a feature sensitive error function, the regions that users are interested in, or finite element calculation results. Finally, a relaxation based technique is deployed to improve mesh quality. Several demonstration examples are provided from a wide variety of application domains. Some extracted meshes have been extensively used in finite element simulations.

SIAM Journal on Scientific …, 2005

Parameterization of unstructured surface meshes is of fundamental importance in many applications of Digital Geometry Processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner.