Generalizing the advancing front method to composite surfaces in the context of meshing constraints topology

Being able to automatically mesh composite geometry is an important issue in the context of CAD–FEA integration. In some specific contexts of this integration, such as using virtual topology or meshing constraints topology (MCT), it is even a key requirement. In this paper, we present a new approach to automatic mesh generation over composite geometry. The proposed mesh generation approach is based on a generalization of the advancing front method (AFM) over curved surfaces. The adaptation of the AFM to composite faces (composed of multiple boundary representation (B-Rep) faces) involves the computation of complex paths along these B-Rep faces, on which progression of the advancing front is based. Each mesh segment or mesh triangle generated through this progression on composite geometry is likely to lie on multiple B-Rep faces and consequently, it is likely to be associated with a composite definition across multiple parametric spaces. Collision tests between new front segments and existing mesh elements also require specific and significant adaptations of the AFM, since a given front segment is also likely to lie on multiple B-Rep faces. This new mesh generation approach is presented in the context of MCT, which requires being able to handle composite geometry along with non-manifold boundary configurations, such as edges and vertices lying in the interior domain of B-Rep faces.     

Automatic unstructured all-hexahedral mesh generation from B-Reps for non-manifold CAD assemblies

This paper describes an automatic and robust approach to convert non-manifold CAD assemblies into unstructured all-hexahedral meshes conformal to the given B-Reps (boundary-representations) and with sharp feature preservation. In previous works, we developed an octree-based isocontouring method to construct unstructured hexahedral meshes for arbitrary non-manifold and manifold domains. However, sharp feature preservation still remains a challenge, especially for non-manifold CAD assemblies. In this paper, boundary features such as NURBS (non-uniform rational B-Splines) curves and surface patches are first extracted from the given B-Reps. Features shared by multiple components are identified and distinguished. To preserve these non-manifold features, one given surface patch may need to be split into several small ones. An octree-based algorithm is then carried out to create an unstructured all-hexahedral base mesh, detecting and preserving all the sharp features via a curve and surface parametrization. Two sets of local refinement templates are provided for adaptive mesh generation, along with a novel 2-refinement implementation. Vertices in the base mesh are categorized into four groups based on the given non-manifold topology, and each group is relocated using various methods with all sharp features preserved. After this stage, a novel two-step pillowing technique is developed for such complicated non-manifold domains to eliminate triangle-shaped quadrilateral elements along the curves and “doublets”, handling non-manifold and manifold features in different ways. Finally, a combination of smoothing and optimization is used to further improve the mesh quality. Our algorithm is automatic and robust for non-manifold and manifold domains. We have applied our algorithm to several complicated CAD assemblies.     

Boolean operations on multi-region solids for mesh generation

An algorithm for Boolean operations on non-manifold models is proposed to allow the treatment of solids with multiple regions (internal interfaces) and degenerate portions (shells and wires), in the context of mesh generation. In a solid modeler, one of the most powerful tools to create three-dimensional objects with any level of geometric complexity is the Boolean set operators. They are intuitive and popular ways to combine solids, based on the operations applied to point sets. To assure that the resulting objects have the same dimension as the original objects, without loose or dangling parts, a regularization process is usually applied after a Boolean operation. In practice, the regularization is performed classifying the topological elements and removing internal or lower-dimensional structures. However, in many engineering applications, the adopted geometric model may contain idealized internal parts, as in the case of multi-region models, or lower-dimensional parts, as in the case of solids that contain dangling slabs that are represented as zero-thickness surfaces or wireframes in the model. Therefore, the aim of this work is the development of a generic algorithm that allows the application of the Boolean set operations in a geometric modeling environment applied to finite and boundary element mesh generation. This environment adopts a non-manifold boundary representation that considers an undefined number of topological entities (group concept), and works with objects of different dimensions and with objects not necessarily plane or polyhedral (parametric curved surfaces). Numerical examples are presented to illustrate the proposed methodology.     

Generation of Tetrahedral Meshes with Multiple Elements through Thin Sections

Finite element simulations in domains with strong gradients across thin sections typically require meshes with multiple elements through these sections to accurately capture the solution. Most of the published techniques for isotropic mesh generation are not suited for the creation of such meshes in general, arbitrarily complex, non-manifold domains. In this paper, an automatic method is described for identification of thin sections of a domain and anisotropic refinement of an initial mesh to introduce a user-requested number of elements through the thin sections. The method uses local mesh modification operations to effect the refinement and subsequent realignment of edges along the thickness direction and perpendicular to it. Results are presented for a number of general models to illustrate the capability of the mesh generator.     

GeoTran-HC: Geometric transformation of highly coupled variable topology multi-body problems

Manipulating geometry to prepare a CAD design model for mesh generation is an important step in the finite element analysis (FEA) process. However, complex problems such as electronic chip packages often consist of hundreds or even thousands of sub-features with varying materials, complex geometrical shapes and changeable connectivity configurations. We define a subclass of such problems, termed highly coupled variable topology multi-body (HCVTMB) problems, where configuration and relative geometric sizes cause meshing changes in one body to propagate throughout much of the model. Today creating FEA models for HCVTMB problems typically requires manual geometrical manipulation which is labour-intensive and error-prone.In this paper we introduce an automated geometric transformation method-GeoTran-HC-within the context of a knowledge-based modeling method for CAD-FEA integration. Through five steps-geometry extraction, cell decomposition, associativity maintenance, feature recognition and associativity recovery-this transformation method automatically decomposes an HCVTMB analytical model into a meshable model. It also manages mesh quality and attribution of non-geometrical information such as material properties and boundary conditions.A plastic ball grid array chip package thermo-mechanical case study demonstrates the efficacy of GeoTran-HC within the context of our knowledge-based FEA modelling method. This and similar studies show reductions in total FEA modeling time from days/hours (using traditional methods) to hours/minutes (using the presented method), as well as enhanced modularity and reusability.     

An automatic 3D mesh generation method for domains with multiple materials

This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a single material (homogeneous) domain with manifold boundary. In this paper, we introduce the notion of a material change edge and use it to identify the interface between two or several different materials. A novel method to calculate the minimizer point for a cell shared by more than two materials is provided, which forms a non-manifold node on the boundary. We then mesh all the material regions simultaneously and automatically while conforming to their boundaries directly from volumetric data. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for proper hexahedral mesh construction. Finally, edge-contraction and smoothing methods are 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 of pillowing schemes is defined automatically as the boundary of each material region. Several application results of our multi-material mesh generation method are also provided.     

A multi-resolution topological representation for non-manifold meshes

We address the problem of representing and processing 3D objects, described through simplicial meshes, which consist of parts of mixed dimensions, and with a non-manifold topology, at different levels of detail. First, we describe a multi-resolution model, that we call a non-manifold multi-tessellation (NMT), and we consider the selective refinement query, which is at the heart of several analysis operations on multi-resolution meshes. Next, we focus on a specific instance of a NMT, generated by simplifying simplicial meshes based on vertex-pair contraction, and we describe a compact data structure for encoding such a model. We also propose a new data structure for two-dimensional simplicial meshes, capable of representing both connectivity and adjacency information with a small memory overhead, which is used to describe the mesh extracted from an NMT through selective refinement. Finally, we present algorithms to efficiently perform updates on such a data structure.     

Computer diagnosis system for thermal analysis by BEM aided with simple CAD

With the aid of the supercomputer we have performed three-dimensional simulations in practical cpu time. At the same time, though, huge amounts of output data must be treated automatically by post processors, so that only necessary information will be extracted and changes of models, mesh subdivisions, or boundary conditions will be taken into account. This type of information processing cannot be attained by conventional postprocessors, and a new concept of postprocessing and system must be developed in the sense of computer-aided engineering or computer diagnosis. We present a computer tomographic system COMTOS-BEM based on three-dimensional boundary element analysis; it houses its own geometric modeling and automatic mesh generation. Furthermore, it supports design feedback reactions to change modeling or meshing, make recalculations, and renew boundary conditions. In this paper, we state the basic concept of the proposed computer diagnosis system and present the necessary geometric modeling and processing and boundary element formulations. Some numerical examples illustrate the validity and effectiveness of our system in practice.     

各向同性三角形重新网格化方法综述

三维网格模型的重新网格化是计算机图形学中的重要内容,是许多几何应用的关键组成部分。近年来迅速发展的三维处理技术,如有限元模拟、计算机动画、三维打印等,对网格质量的要求不断提升,促进了三维网格模型重新网格化的持续发展,由此产生了许多新的重新网格化技术。首先介绍了三角形网格质量评估的标准,然后概述了各向同性重新网格化的最新进展,并详细研究和比较了各种重新网格化算法的优缺点,最后对未来的研究提出了新的问题与方向。     

数值流形方法物理覆盖的自动生成

数值流形方法物理覆盖的自动生成在工程应用中具有重要意义同时也是一项困难的工程.它主要包括两个难点,一是几何模型的建立相当耗时耗力;二是数学网格和物理网格的自动生成,从而生成物理覆盖.通过设计AutoCAD软件与数值流形方法程序的集成接口解决了建立高效准确的工程模型的难点问题;通过生成规则等边三角形数学网格系统,并利用由裂隙或块体边界彤成的物理网格对数学网格系统进行再剖分形成物理覆盖.将以上工作一体化就实现了物理覆盖的自动生成.仿真结果表明:可以有效提高数值流形方法程序的效率和准确性.     

Field modeling with sampled distances

Traditional mesh-based approaches to the modeling and analysis of physical fields within geometric models require some form of topological reconstruction and conversion in the mesh generation process. Such manipulations tend to be tedious and error-prone manual processes that are not easily automated. We show that most field problems may be solved directly by using approximate distance fields computed from designed or sampled geometric data, thus avoiding many of the difficult reconstruction and meshing problems. With distances we can model fields that satisfy boundary conditions while approximating the governing differential equations to arbitrary precision. Because the method is based on sampling, it provides natural control for multi-resolution both in geometric detail of the domain and in accuracy of the computed physical field. We demonstrate the field modeling capability with several heat transfer applications, including a typical transient problem and a ‘scan and solve’ approach to the simulation of a physical field in a real-world artifact.     

Feature-based modeling for automatic mesh generation

Automatic meshing algorithms for finite element analysis are based on a computer understanding of the geometry of the part to be discretized. Current mesh generators understand the part as either a boundary representation, an octree, or a point set. A higher-level understanding of the part can be achieved by associating engineering significance and engineering data, such as loading and boundary conditions, with generic shapes in the part. This technique, called feature-based modeling, is a popular approach to integrating computer-aided design (CAD) and computer-aided manufacturing through the use of machinable shapes in the CAD model. It would seem that feature-based design also could aid in the finite element mesh generation process by making engineering information explicit in the model.This paper describes an approach to feature-based mesh generation. The feature representation of a fully functioning feature-based system that does automatic process planning and inspection was extended to include finite element mesh generation. This approach is based on a single feature representation that can be used for design, finite element analysis, process planning, and inspection of prismatic parts. The paper describes several advantages that features provide to the meshing process, such as improved point sets and a convenient method of simplifying the geometry of the model. Also discussed are possible extensions to features to enhance the finite element meshing process.     

Fun sheet matching: towards automatic block decomposition for hexahedral meshes

Depending upon the numerical approximation method that may be implemented, hexahedral meshes are frequently preferred to tetrahedral meshes. Because of the layered structure of hexahedral meshes, the automatic generation of hexahedral meshes for arbitrary geometries is still an open problem. This layered structure usually requires topological modifications to propagate globally, thus preventing the general development of meshing algorithms such as Delaunay??s algorithm for tetrahedral meshes or the advancing-front algorithm based on local decisions. To automatically produce an acceptable hexahedral mesh, we claim that both global geometric and global topological information must be taken into account in the mesh generation process. In this work, we propose a theoretical classification of the layers or sheets participating in the geometry capture procedure. These sheets are called fundamental, or fun-sheets for short, and make the connection between the global layered structure of hexahedral meshes and the geometric surfaces that are captured during the meshing process. Moreover, we propose a first generation algorithm based on fun-sheets to deal with 3D geometries having 3- and 4-valent vertices.     

Integration of CAD and boundary element analysis through subdivision methods

Subdivision methods have been mainly used in computer graphics. This paper extends their applications to mechanical design and boundary element analysis (BEA), and fulfills the seamless integration of CAD and BEA in the model and representation.Traditionally, geometric design and BEA are treated as separate modules requiring different representations and models, which include continuous parametric models and discrete models. Due to the incompatibility of the involved representations and models, the post-processing in geometric design or the pre-processing in BEA is essential. The transition from geometric design to BEA requires substantial effort and errors are inevitably introduced during the transition. In this paper, a framework of realizing the integration of CAD and BEA was first presented based on subdivision methods. A common model or a unified representation for geometric design and BEA was created with subdivision surfaces. For general 3D structures, automatic mesh generation for geometric design and BEA was fulfilled through subdivision methods. The seamless integration improves the accuracy of numerical analysis and shortens the cycle of geometric design and BEA.     

Constructing 3-D object models using multiple simulated 2.5-D sketches

Many applications involve the construction of 3-D object models from which images, often requiring a high degree of realism, are later produced. Constructing such models frequently involves considerable human intervention, even in cases where a physical model or the actual object to be modelled exists. This paper describes an approach to the automatic construction of 3-D object models using images of scenes. This method employs a representation of the visible surfaces in a scene called the 2.5-D sketch and a model construction process is described that utilizes multiple simulated 2.5-D sketches.     

A unified subdivision approach for multi-dimensional non-manifold modeling

This paper presents a new unified subdivision scheme that is defined over a k-simplicial complex in n-D space with k≤3. We first present a series of definitions to facilitate topological inquiries during the subdivision process. The scheme is derived from the double (k+1)-directional box splines over k-simplicial domains. Thus, it guarantees a certain level of smoothness in the limit on a regular mesh. The subdivision rules are modified by spatial averaging to guarantee C¹ smoothness near extraordinary cases. Within a single framework, we combine the subdivision rules that can produce 1-, 2-, and 3-manifolds in arbitrary n-D space. Possible solutions for non-manifold regions between the manifolds with different dimensions are suggested as a form of selective subdivision rules according to user preference. We briefly describe the subdivision matrix analysis to ensure a reasonable smoothness across extraordinary topologies, and empirical results support our assumption. In addition, through modifications, we show that the scheme can easily represent objects with singularities, such as cusps, creases, or corners. We further develop local adaptive refinement rules that can achieve level-of-detail control for hierarchical modeling. Our implementation is based on the topological properties of a simplicial domain. Therefore, it is flexible and extendable. We also develop a solid modeling system founded on our subdivision schemes to show potential benefits of our work in industrial design, geometric processing, and other applications.     

Automatic mesh generation and transformation for topology optimization methods

This paper presents automatic tools aimed at the generation and adaptation of unstructured tetrahedral meshes in the context of composite or heterogeneous geometry. These tools are primarily intended for applications in the domain of topology optimization methods but the approach introduced presents great potential in a wider context. Indeed, various fields of application can be foreseen for which meshing heterogeneous geometry is required, such as finite element simulations (in the case of heterogeneous materials and assemblies, for example), animation and visualization (medical imaging, for example). Using B-Rep concepts as well as specific adaptations of advancing front mesh generation algorithms, the mesh generation approach presented guarantees, in a simple and natural way, mesh continuity and conformity across interior boundaries when trying to mesh a composite domain. When applied in the context of topology optimization methods, this approach guarantees that design and non-design sub-domains are meshed so that finite elements are tagged as design and non-design elements and so that continuity and conformity are guaranteed at the interface between design and non-design sub-domains. The paper also presents how mesh transformation and mesh smoothing tools can be successfully used when trying to derive a functional shape from raw topology optimization results.     

Interactive 3-D indoor modeler for virtualizing service fields

This paper describes an interactive 3-D indoor modeler that effectively creates photo-realistic 3-D indoor models from multiple photographs. This modeler supports the creation of 3-D models from photographs by implementing interaction techniques that use geometric constraints estimated from photographs and visualization techniques that help to easily understand shapes of 3-D models. We evaluated the availability and usability by applying the modeler to model service fields where actual workers provide services and an experience-based exhibit. Our results confirmed that the modeler enables the creation of large-scale indoor environments such as hot-spring inns and event sites at a relatively modest cost. We also confirmed that school children could learn modeling operations and create 3-D models from a photograph for approximately 20 min because of the easy operations. In addition, we describe additional functions that increase the effectiveness of 3-D modeling based on knowledge from service-field modeling. We present applications for behavior analysis of service workers and for 3-D indoor navigation using augmented virtuality (AV)-based visualization realized by photo-realistic 3-D models.     

Enhanced medial-axis-based block-structured meshing in 2-D

New techniques are presented for using the medial axis to generate decompositions on which high quality block-structured meshes with well-placed mesh singularities can be generated. Established medial-axis-based meshing algorithms are effective for some geometries, but in general, they do not produce the most favourable decompositions, particularly when there are geometric concavities. This new approach uses both the topological and geometric information in the medial axis to establish a valid and effective arrangement of mesh singularities for any 2-D surface. It deals with concavities effectively and finds solutions that are most appropriate to the geometric shapes. Resulting meshes are shown for a number of example models.