Curvature-adapted Remeshing of CAD Surfaces

A common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of Levy \ub4 and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples

A curvature-adapted anisotropic surface remeshing method

We present a new method for remeshing surfaces that respect the intrinsic anisotropy of the surfaces. In particular, we use the normal informations of the surfaces, and embed the surfaces into a higher dimensional space (here we use 6d). This allow us to form an isotropic mesh optimization problem in this embedded space. Starting from an initial mesh of a surface, we optimize the mesh by improving the mesh quality measured in the embedded space. The mesh is optimized by combining common local modifications operations, i.e., edge flip, edge contraction, vertex smoothing, and vertex insertion. All operations are applied directly on the 3d surface mesh. This method results a curvature-adapted mesh of the surface. This method can be easily adapted to mesh multi-patches surfaces, i.e., containing corner singularities and sharp features. We present examples of remeshed surfaces from implicit functions and CAD models

Discrete curvature approximations and segmentation of polyhedral surfaces

The segmentation of digitized data to divide a free form surface into patches is one of the key steps required to perform a reverse engineering process of an object. To this end, discrete curvature approximations are introduced as the basis of a segmentation process that lead to a decomposition of digitized data into areas that will help the construction of parametric surface patches. The approach proposed relies on the use of a polyhedral representation of the object built from the digitized data input. Then, it is shown how noise reduction, edge swapping techniques and adapted remeshing schemes can participate to different preparation phases to provide a geometry that highlights useful characteristics for the segmentation process. The segmentation process is performed with various approximations of discrete curvatures evaluated on the polyhedron produced during the preparation phases. The segmentation process proposed involves two phases: the identification of characteristic polygonal lines and the identification of polyhedral areas useful for a patch construction process. Discrete curvature criteria are adapted to each phase and the concept of invariant evaluation of curvatures is introduced to generate criteria that are constant over equivalent meshes. A description of the segmentation procedure is provided together with examples of results for free form object surfaces

Geometry Modeling for Unstructured Mesh Adaptation

The quantification and control of discretization error is critical to obtaining reliable simulation results. Adaptive mesh techniques have the potential to automate discretization error control, but have made limited impact on production analysis workflow. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic mesh adaptation mechanics. However, the poor integration of initial mesh generation and adaptive mesh mechanics to typical sources of geometry has hindered adoption of adaptive mesh techniques, where these geometries are often created in Mechanical Computer- Aided Design (MCAD) systems. The difficulty of this coupling is compounded by two factors: the inherent complexity of the model (e.g., large range of scales, bodies in proximity, details not required for analysis) and unintended geometry construction artifacts (e.g., translation, uneven parameterization, degeneracy, self-intersection, sliver faces, gaps, large tolerances be- tween topological elements, local high curvature to enforce continuity). Manual preparation of geometry is commonly employed to enable fixed-grid and adaptive-grid workflows by reducing the severity and negative impacts of these construction artifacts, but manual process interaction inhibits workflow automation. Techniques to permit the use of complex geometry models and reduce the impact of geometry construction artifacts on unstructured grid workflows are models from the AIAA Sonic Boom and High Lift Prediction are shown to demonstrate the utility of the current approach

Merging enriched Finite Element triangle meshes for fast prototyping of alternate solutions in the context of industrial maintenance

A new approach to the merging of Finite Element (FE) triangle meshes is proposed. Not only it takes into account the geometric aspects, but it also considers the way the semantic information possibly associated to the groups of entities (nodes, faces) can be maintained. Such high level modification capabilities are of major importance in all the engineering activities requiring fast modifications of meshes without going back to the CAD model. This is especially true in the context of industrial maintenance where the engineers often have to solve critical problems in very short time. Indeed, in this case, the product is already designed, the CAD models are not necessarily available and the FE models might be tuned. Thus, the product behaviour has to be studied and improved during its exploitation while prototyping directly several alternate solutions. Such a framework also finds interest in the preliminary design phases where alternative solutions have to be simulated. The algorithm first removes the intersecting faces in an n-ring neighbourhood so that the filling of the created holes produces triangles whose sizes smoothly evolve according to the possibly heterogeneous sizes of the surrounding triagles. The holefilling algorithm is driven by an aspect ratio factor which ensures that the produced triangulation fits well the FE requirements. It is also constrained by the boundaries of the groups of entities gathering together the simulation semantic. The filled areas are then deformed to blend smoothly with the surroundings meshes

an anisoptropic surface remeshing strategy combining higher dimensional embedding with radial basis functions

Abstract Many applications heavily rely on piecewise triangular meshes to describe complex surface geometries. High-quality meshes significantly improve numerical simulations. In practice, however, one often has to deal with several challenges. Some regions in the initial mesh may be overrefined, others too coarse. Additionally, the triangles may be too thin or not properly oriented. We present a novel mesh adaptation procedure which greatly improves the problematic input mesh and overcomes all of these drawbacks. By coupling surface reconstruction via radial basis functions with the higher dimensional embedding surface remeshing technique, we can automatically generate anisotropic meshes. Moreover, we are not only able to fill or coarsen certain mesh regions but also align the triangles according to the curvature of the reconstructed surface. This yields an acceptable trade-off between computational complexity and accuracy

Surface remeshing by local hermite diffuse interpolation

International audienceWe propose a method to build a three-dimensional adapted surface mesh with respect to a mesh size map driven by surface curvature. The data needed to optimize the mesh have been reduced to an initial mesh. The building of a local geometrical model but continuous over the whole domain is based on a local Hermite diffuse interpolation calculated from the nodes of the initial mesh and from the normal vectors to the surface. The optimization procedures involve extracting from the surface mesh sets of triangles sharing the same node or the same edge and then remeshing the outer contour to a higher criterion (size or shape). These procedures may be used in order to refine or coarsen the mesh but also in a final step to enhance the shape quality of the elements. Examples demonstrate the ability of the method to create adapted meshes of complex surfaces while meeting high-quality standards and a good respect of the geometrical surface

A novel surface remeshing scheme via higher dimensional embedding and radial basis functions

Many applications heavily rely on piecewise triangular meshes to describe complex surface geometries. High-quality meshes significantly improve numerical simulations. In practice, however, one often has to deal with several challenges. Some regions in the initial mesh may be overrefined, others too coarse. Additionally, the triangles may be too thin or not properly oriented. We present a novel mesh adaptation procedure which greatly improves the problematic input mesh and overcomes all of these drawbacks. By coupling surface reconstruction via radial basis functions with the higher dimensional embedding surface remeshing technique, we can automatically generate anisotropic meshes. Moreover, we are not only able to fill or coarsen certain mesh regions but also align the triangles according to the curvature of the reconstructed surface. This yields an acceptable trade-off between computational complexity and accuracy

Automatic surface mesh generation for discrete models: A complete and automatic pipeline based on reparameterization

Triangulations are an ubiquitous input for the finite element community. However, most raw triangulations obtained by imaging techniques are unsuitable as-is for finite element analysis. In this paper, we give a robust pipeline for handling those triangulations, based on the computation of a one-to-one parametrization for automatically selected patches of input triangles, which makes each patch amenable to remeshing by standard finite element meshing algorithms. Using only geometrical arguments, we prove that a discrete parametrization of a patch is one-to-one if (and only if) its image in the parameter space is such that all parametric triangles have a positive area. We then derive a non-standard linear discretization scheme based on mean value coordinates to compute such one-to-one parametrizations, and show that the scheme does not discretize a Laplacian on a structured mesh. The proposed pipeline is implemented in the open source mesh generator Gmsh, where the creation of suitable patches is based on triangulation topology and parametrization quality, combined with feature edge detection. Several examples illustrate the robustness of the resulting implementation.Comment: Images have lower quality in order to meet arxiv requirement