Isotropic Surface Remeshing

International audienceThis paper proposes a new method for isotropic remeshing of tri- angulated surface meshes. Given a triangulated surface mesh to be resampled and a user-specified density function defined over it, we first distribute the desired number of samples by generalizing error diffusion, commonly used in image halftoning, to work directly on mesh triangles and feature edges. We then use the resulting sam- pling as an initial configuration for building a weighted centroidal Voronoi tessellation in a conformal parameter space, where the specified density function is used for weighting. We finally create the mesh by lifting the corresponding constrained Delaunay trian- gulation from parameter space. A precise control over the sampling is obtained through a flexible design of the density function, the latter being possibly low-pass filtered to obtain a smoother grada- tion. We demonstrate the versatility of our approach through vari- ous remeshing examples

Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement

The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application. In this paper, we design an algorithm to address all three optimization goals simultaneously. The user specifies desired bounds on approximation error {\delta}, minimal interior angle {\theta} and maximum mesh complexity N (number of vertices). Since such a desired mesh might not even exist, our optimization framework treats only the approximation error bound {\delta} as a hard constraint and the other two criteria as optimization goals. More specifically, we iteratively perform carefully prioritized local operators, whenever they do not violate the approximation error bound and improve the mesh otherwise. In this way our optimization framework greedily searches for the coarsest mesh with minimal interior angle above {\theta} and approximation error bounded by {\delta}. Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that our approach delivers high-quality meshes with implicitly preserved features and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.Comment: 14 pages, 20 figures. Submitted to IEEE Transactions on Visualization and Computer Graphic

Gap Processing for Adaptive Maximal Poisson-Disk Sampling

In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or have their radius changed. We build on the concepts of the regular triangulation and the power diagram. Third, we will show how our analysis can make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201

Surface segmentation for improved remeshing

Many remeshing techniques sample the input surface in a meaningful way and then triangulate the samples to produce an output triangulated mesh. One class of methods samples in a parametrization of the surface. Another class samples directly on the surface. These latter methods must have sufficient density of samples to achieve outputs that are homeomorphic to the input. In many datasets samples must be very dense even in some nearly planar regions due to small local feature size. We present an isotropic remeshing algorithm called κCVT that achieves topological correctness while sampling sparsely in all flat regions, regardless of local feature size. This is accomplished by segmenting the surface, remeshing the segmented subsurfaces individually and then stitching them back together. We show that κCVT produces quality meshes using fewer triangles than other methods. The output quality meshes are both homeomorphic and geometrically close to the input surface.postprin

A mesh adaptivity scheme on the Landau-de Gennes functional minimization case in 3D, and its driving efficiency

This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics, studied on the case of a nonlinear finite element minimization scheme for the Landau-de Gennes free energy functional of nematic liquid crystals. Newton's iteration for tensor fields is employed with steepest descent method possibly stepping in. Aspects relating the driving of mesh adaptivity within the nonlinear scheme are considered. The algorithmic performance is found to depend on at least two factors: when to trigger each single mesh adaptation, and the precision of the correlated remeshing. Each factor is represented by a parameter, with its values possibly varying for every new mesh adaptation. We empirically show that the time of the overall algorithm convergence can vary considerably when different sequences of parameters are used, thus posing a question about optimality. The extensive testings and debugging done within this work on the simulation of systems of nematic colloids substantially contributed to the upgrade of an open source finite element-oriented programming language to its 3D meshing possibilities, as also to an outer 3D remeshing module

Numerical and physical modelling in forming

An overview will be presented of recent developments concerning the application\ud and development of computer codes for numerical simulation of forming processes. Special\ud attention will be paid to the mathematical modeling of the material deformation and friction,\ud and the effect of these models on the results of simulation

Improvements in FE-analysis of real-life sheet metal forming

An overview will be presented of recent developments concerning the application\ud and development of computer codes for numerical simulation of sheet metal forming\ud processes. In this paper attention is paid to some strategies which are followed to improve the\ud accuracy and to reduce the computation time of a finite element simulation. Special attention\ud will be paid to the mathematical modeling of the material deformation and friction, and the\ud effect of these models on the results of simulations. An equivalent drawbead model is\ud developed which avoids a drastic increase of computation time without significant loss of\ud accuracy. The real geometry of the drawbead is replaced by a line on the tool surface. When\ud an element of the sheet metal passes this drawbead line an additional drawbead restraining\ud force, lift force and a plastic strain are added to that element. A commonly used yield\ud criterion for anisotropic plastic deformation is the Hill yield criterion. This description is not\ud always sufficient to accurately describe the material behavior. This is due to the\ud determination of material parameters by uni-axial tests only. A new yield criterion is\ud proposed, which directly uses the experimental results at multi-axial stress states. The yield\ud criterion is based on the pure shear point, the uni-axial point, the plane strain point and the\ud equi-biaxial point

Relation between shear parameter and Reynolds number in statistically stationary turbulent shear flows

Studies of the relation between the shear parameter S^* and the Reynolds number Re are presented for a nearly homogeneous and statistically stationary turbulent shear flow. The parametric investigations are in line with a generalized perspective on the return to local isotropy in shear flows that was outlined recently [Schumacher, Sreenivasan and Yeung, Phys. Fluids, vol.15, 84 (2003)]. Therefore, two parameters, the constant shear rate S and the level of initial turbulent fluctuations as prescribed by an energy injection rate epsilon_{in}, are varied systematically. The investigations suggest that the shear parameter levels off for larger Reynolds numbers which is supported by dimensional arguments. It is found that the skewness of the transverse derivative shows a different decay behavior with respect to Reynolds number when the sequence of simulation runs follows different pathways across the two-parameter plane. The study can shed new light on different interpretations of the decay of odd order moments in high-Reynolds number experiments.Comment: 9 pages, 9 Postscript figure