Mesh generation from X-ray computed tomography (CT) images of mechanical parts is an important consideration in industrial application, and boundary surface meshes in multimaterial parts can be extracted by generating segmented meshes from segmented images. In this paper, the authors outline a new approach for achieving segmented mesh generation. The image is first subjected to centroidal Voronoi tessellation and Delaunay tessellation steered by a density map to create a triangular mesh while maintaining discontinuities between materials. Given an input domain and a number of initial sites, the energy function is minimized automatically by iteratively updating the Voronoi tessellation and relocating sites to produce optimized domain discretization and form the mesh. Thus, the mesh in question is effectively and quickly segmented into different parts via this new graph cut method. The proposed approach is considered more efficient because there are fewer triangles than pixels, which reduces computation time and memory usage.

This work presents a methodology for adaptive generation of 3D finite element meshes using geometric modeling with multiregions and parametric surfaces, considering a geometric model described by curves, surfaces, and volumes. This methodology is applied in the simulation of stress analysis of solid structures using a displacement-based finite element method and may be extended to other types of 3D finite element simulation. The adaptive strategy is based on an independent and hierarchical refinement of curves, surfaces, and volumes. From an initial model, new sizes of elements obtained from a discretization error analysis and from geometric restrictions are stored in a global background structure, a recursive spatial composition represented by an octree. Based on this background structure, the model's curves are initially refined using a binary partition algorithm. Curve discretization is then used as input for the refinement of adjacent surfaces. Surface discretization also employs the background octree-based refinement, which is coupled to an advancing front technique in the surface's parametric space to generate an unstructured triangulated mesh. Surface meshes are finally used as input for the refinement of adjacent volumetric domains, which also uses an advancing front technique but in 3D space. In all stages of the adaptive strategy, the refinement of curves, surface meshes, and solid meshes is based on estimated discretization errors associated with the mesh of the previous step in the adaptive process. In addition, curve and surface refinement takes curvature information into account. Numerical examples of simulation of engineering problems are presented in order to validate the methodology proposed in this work.

This paper presents the current issues and trends in meshing and geometric processing, core tasks in the preparation stage of computational engineering analyses. In product development, computational simulation of product functionality and manufacturing process have contributed significantly toward improving the quality of a product, shortening the time-to-market and reducing the cost of the product and manufacturing process. The computational simulation can predict various physical behaviors of a target object or system, including its structural, thermal, fluid, dynamic, and electro-magnetic behaviors. In industry, the computer-aided engineering (CAE) software packages have been the driving force behind the ever-increasing usage of computational engineering analyses. While these tools have been improved continuously since their inception in the early 1960s, the demand for more complex computational simulation has grown significantly in recent years, creating some major shortfalls in the capability of current CAE tools. This paper first discusses the current trends of computational engineering analyses and then focuses on two areas of such shortfalls: meshing and geometric processing, critical tasks required in the preparation stage of engineering analyses that use common numerical methods such as the finite element method and the boundary element method.

In this paper, a traction superimposition method for simulating the deformation of multicomponent elastic models with different interfacial mesh densities is introduced. By applying linear interpolation method, the displacement data can be transferred between nonconforming interfaces. With the application of energy conservation principle, a relationship between the forces on different surfaces is constructed. By considering the displacement compatibility conditions together with force equilibrium conditions over the common interfaces, a relation between different components of a system is established. However, this interpolation method is only applicable to object components with the same or similar mesh densities. For models with different mesh densities between neighboring components, abnormities arise in the deformation. The causes of these abnormities are parsed by experiments and theoretical analysis. To eliminate the abnormal deformation, a traction superimposition method is proposed to enforce the force constraints on the interfaces. Experimental results are provided to verify this approach.

To achieve effective 3D shape retrieval, there is a crucial need for efficient shape matching methods. This paper introduces a new method for 3D shape matching, which uses a simplified octree representation of 3D mesh models. The simplified octree representation was developed to improve time and space efficiency over prior representations. The proposed method also stores octree information in extensible markup language format, rather than in a new proprietary data file type, to facilitate comparing models over the Internet.

This paper presents an infrastructure that integrates a haptic interface into a mainstream computer-aided design (CAD) system. A haptic interface, by providing force feedback in human-computer interaction, can improve the working efficiency of CAD/computer-aided manufacturing (CAM) systems in a unique way. The full potential of the haptic technology is best realized when it is integrated effectively into the product development environment and process. For large manufacturing companies this means integration into a commercial CAD system ( Stewart, et al., 1997, “Direct Integration of Haptic User Interface in CAD Systems,” ASME Dyn. Syst. Control Div., 61, pp. 93–99 ). Mainstream CAD systems typically use constructive solid geometry (CSG) and boundary representation (B-Rep) format as their native format, while internally they automatically maintain triangulated meshes for graphics display and for numerical evaluation tasks such as surface-surface intersection. In this paper, we propose to render a point-based haptic force feedback by leveraging built-in functions of the CAD systems. The burden of collision detection and haptic rendering computation is alleviated by using bounding spheres and an OpenGL feedback buffer. The major contribution of this paper is that we developed a sound structure and methodology for haptic interaction with native CAD models inside mainstream CAD systems. We did so by analyzing CAD application models and by examining haptic rendering algorithms. The technique enables the user to directly touch and manipulate native 3D CAD models in mainstream CAD systems with force/touch feedback. It lays the foundation for future tasks such as direct CAD model modification, dynamic simulation, and virtual assembly with the aid of a haptic interface. Hence, by integrating a haptic interface directly with mainstream CAD systems, the powerful built-in functions of CAD systems can be leveraged and enhanced to realize more agile 3D CAD design and evaluation.

This paper presents an approach to automatically recover mesh surfaces with sharp edges for solids from their binary volumetric discretizations (i.e., voxel models). Our method consists of three steps. The topology singularity is first eliminated on the binary grids so that a topology correct mesh M 0 can be easily constructed. After that, the shape of M 0 is refined, and its connectivity is iteratively optimized into M n . The shape refinement is governed by the duplex distance fields derived from the input binary volume model. However, the refined mesh surface lacks sharp edges. Therefore, we employ an error-controlled variational shape approximation algorithm to segment M n into nearly planar patches and then recover sharp edges by applying a novel segmentation-enhanced bilateral filter to the surface. Using the technique presented in this paper, smooth regions and sharp edges can be automatically recovered from raw binary volume models without scalar field or Hermite data Compared to other related surface recovering methods on binary volume, our algorithm needs less heuristic coefficients.

This paper addresses the problem of fitting flattenable mesh surfaces in R 3 onto piecewise linear boundary curves, where a flattenable mesh surface inherits the isometric mapping to a planar region in R 2 . The developable surface in differential geometry shows the nice property. However, it is difficult to fit developable surfaces to a boundary with complex shape. The technique presented in this paper can model a piecewise linear flattenable surface that interpolates the given boundary curve and approximates the cross-tangent normal vectors on the boundary. At first, an optimal planar polygonal region is computed from the given boundary curve B ∊ R 3 , triangulated into a planar mesh surface, and warped into a mesh surface in R 3 , satisfying the continuities defined on B . Then, the fitted mesh surface is further optimized into a flattenable Laplacian (FL) mesh, which preserves the positional continuity and minimizes the variation of cross-tangential normals. Assembled set of such FL mesh patches can be employed to model complex products fabricated from sheets without stretching.

Recently, 3D model construction from 2D images using an uncalibrated camera has attracted significant attention in the research community. Most of the algorithms for 3D model construction suffer from problems such as inefficiency, irregular construction, and necessity of camera calibration. In this paper, a novel algorithm is presented that uses the silhouette images obtained from the object to construct the 3D model. To carry out the 3D modeling, multiple views of the object are taken from different angles. Then using a silhouette based technique, new silhouettes are constructed and feature points are derived from them. These feature points are then used to construct the triangular meshes, which in turn construct the whole surface of the 3D model. The noise in the silhouette images is dealt with a probabilistic framework. In addition, a faster technique is presented to reduce the time and space complexity of this algorithm making it feasible for most commercial applications. The algorithm has been successfully tested on several objects. The experimental results and comparison with a voxelization technique over several sequences shows the superiority and the effectiveness of our technique.

We consider the problem of representing and manipulating nonmanifold objects of any dimension and at multiple resolutions. We present a modeling scheme based on (1) a multiresolution representation, called the vertex-based nonmanifold multitessellation , (2) a compact and dimension-independent data structure, called the Simplified Incidence Graph (SIG) , and (3) an atomic mesh update operator, called vertex-pair contraction/vertex expansion . We propose efficient algorithms for performing the vertex-pair contraction on a simplicial mesh encoded as a SIG, and an effective representation for encoding this multiresolution model based on a compact encoding of vertex-pair contractions and vertex expansions.

This paper introduces a high- and low-resolution data integration method for scanning systems. The high-resolution data captured by a touch probe on a CMM, in the form of geometric features, and the low-resolution laser scanned model, in the form of triangulated mesh, are sent to a CAD software. The two model types are first integrated into a unique coordinate system and then unified into a precise CAD model. Depending on the part complexity, some or all of the modelling process can be done automatically. This data fusion method enhances the flexibility of scanning while maintaining the accuracy of the results.

Volumetric models of 3D objects have recently been introduced into the reverse engineering (RE) process. Grid-based methods are considered as the major technique for reconstructing surfaces from these volumetric models. This is mainly due to the efficiency and simplicity of these methods. However, these grid-based methods suffer from a number of inherent drawbacks, resulting from the fact that the imposed Cartesian grid in general is not well adapted to the surface, neither in size nor in orientation. In order to overcome the above obstacles a new iso-surface extraction method is proposed for volumetric models. The main idea is first to construct a geometrical field that is induced by the object’s shape. This geometrical field represents the natural directions and a grid cell size for each point in the domain. Then, the imposed volumetric grid is deformed by the produced geometrical field toward the object’s shape. The iso-surface meshes can be extracted from the resulting adaptive grid by any conventional grid-based contouring technique. The proposed method provides better approximation of the unknown surface and exhibits anisotropy, which is present inherently in the surface. Moreover, since the produced meshes are quad-dominant, Catmull-Clark subdivision surfaces are directly constructed from these meshes.

State-of-the-art numerical analyses require mesh representation with a data structure that provides topological information. Due to the increasing size of the meshes currently used for simulating complex behaviors with finite elements or boundary elements (e.g., adaptive and/or coupled analyses), several researchers have proposed the use of reduced mesh representations. In a reduced representation, only a few types of the defined topological entities are explicitly represented; all the others are implicit and retrieved “on-the-fly,” as required. Despite being very effective in reducing the memory space needed to represent large models, reduced representations face the challenge of ensuring the consistency of all implicit entities when the mesh undergoes modifications. As implicit entities are usually described by references to explicit ones, modifying the mesh may change the way implicit entities (which are not directly modified) are represented, e.g., the referenced explicit entities may no longer exist. We propose a new and effective strategy to treat implicit entities in reduced representations, which is capable of handling transient nonmanifold configurations. Our strategy allows, from the application point of view, explicit and implicit entities to be interchangeably handled in a uniform and transparent way. As a result, the application can list, access, attach properties to, and hold references to implicit entities, and the underlying data structure ensures that all such information remains valid even if the mesh is modified. The validity of the proposed approach is demonstrated by running a set of computational experiments on different models subjected to dynamic remeshing operations.

An accurate three-dimensional (3D) mesh of biological models is fundamental for analysis and treatment simulations. Generally noninvasive magnetic resonance image (MRI) data are taken as the input for the simulation. The topologic relationship of anatomy is extracted from MR images through segmentation processes. To accelerate the biological modeling phase, template surface and volume meshes are generated based on MR images and∕or anatomical atlases (e.g., brain atlas, etc.). The boundary surfaces are extracted from segmented regions on the image slices, which are used as the input for 3D volume mesh generation. An intuitive graphic user interface was developed for biomedical applications. It integrated MRI data manipulation with surface mesh and volume mesh generators. Image volume and mesh geometries are registered in the MRI working space. As the core component of the system, a robust 3D mesh generation approach is presented. It is capable of describing irregular geometries exhibiting concave and convex surfaces. It uses deltahedral building blocks for volume mesh generation and creates high-quality, regular-shaped tetrahedral mesh elements. The approach supports multiple levels of localized refinement without reducing the overall mesh quality. The validity of this new mesh generation strategy and implementation is demonstrated via the medical applications in brain vasculature modeling, multimodality imaging for breast cancer detection, and numerous anatomically accurate models presented. Multiple material boundaries are preserved in each mesh with fidelity.

This paper presents a generalization of a data analysis technique called a singular spectrum analysis (SSA). The original SSA is a tool for analyzing one-dimensional data such as time series, whereas the generalization presented in this paper is suitable for multidimensional data such as three-dimensional polygonal meshes. The basic idea is to generalize the autocorrelation matrix so as to represent mutual relations of multidimensional data flexibly. Two applications of the proposed generalization are also shown briefly.

This paper describes recently developed procedures for local conformal refinement and coarsening of all-hexahedral unstructured meshes. Both refinement and coarsening procedures take advantage of properties found in the dual or “twist planes” of the mesh. A twist plane manifests itself as a conformal layer or sheet of hex elements within the global mesh. We suggest coarsening techniques that will identify and remove sheets to satisfy local mesh density criteria while not seriously degrading element quality after deletion. A two-dimensional local coarsening algorithm is introduced. We also explain local hexahedral refinement procedures that involve both the placement of new sheets, either between existing hex layers or within an individual layer. Hex elements earmarked for refinement may be defined to be as small as a single node or as large as a major group of existing elements. Combining both refinement and coarsening techniques allows for significant control over the density and quality of the resulting modified mesh.

The process of finite element analysis that deals with large deformation often produces distorted elements in the later stages of the analysis. These distorted elements lead to analysis problems, such as inaccurate solutions, slow convergence, and premature termination of the analysis. This paper proposes a new mesh generation algorithm to mesh the input part for pure Lagrangian analysis, where our goal is to improve the shape quality of the elements along the analysis process to reduce the number of inverted elements at the later stage, and to decrease the possibility of premature termination of the analysis. One pre-analysis is required to collect geometric and stress information in the analysis. The proposed method then uses the deformed-shape boundary known from the pre-analysis, finds the optimal node locations, considers the stress information to control the mesh sizes, as well as control the mesh directionality, generates meshes on the deformed boundary, and finally, maps the elements back to the undeformed boundary using inverse bilinear mapping. The proposed method has been tested on two forging example problems. The results indicate that the method can improve the shape quality of the elements at the later stage of the analysis, and consequently extend the life of the analysis, thereby reducing the chance of premature analysis termination.

This article presents a technique for the adaptive refinement of tetrahedral meshes. What makes this method new is that no neighbor information is required for the refined mesh to be compatible everywhere. Refinement consists of inserting new vertices at edge midpoints until some tolerance (geometric or otherwise) is met. For a tetrahedron, the six edges present 2 6 = 64 possible subdivision combinations. The challenge is to triangulate the new vertices (i.e., the original vertices plus some subset of the edge midpoints) in a way that neighboring tetrahedra always generate the same triangles on their shared boundary. A geometric solution based on edge lengths was developed previously, but did not account for geometric degeneracies (edges of equal length). This article provides a solution that works in all cases, while remaining entirely communication-free.

A common operation in clothing and shoe design is to design a folding pattern over a narrow strip and then superimpose it with a smooth surface; the shape of the folding pattern is controlled by the boundary curve of the strip. Previous research results studying folds focused mostly on cloth modeling or in animations, which are driven more by visual realism, but allow large elastic deformations and usually completely ignore or avoid the surface developability issue. In reality, most materials used in garment and shoe industry are inextensible and uncompressible and hence any feasible folded surface must be developable, since it eventually needs to be flattened to its two-dimensional pattern for manufacturing. Borrowing the classical boundary triangulation concept from descriptive geometry, this paper describes a computer-based method that automatically generates a specialized boundary triangulation approximation of a developable surface that interpolates a given strip. The development is achieved by geometrically simulating the folding process of the sheet as it would occur when rolled from one end of the strip to the other. Ample test examples are presented to validate the feasibility of the proposed method.

In this paper, we propose a new triangular finite element mesh generation scheme from various kinds of triangular meshes using the multiresolution technique. The proposed scheme consists of two methods: a mesh quality improvement method and a mesh property control method. The basic strategy of these methods is a combination of the mesh subdivision and simplification. Given mesh is first subdivided to obtain enough degree of freedom for a property change, then by simplification using edge collapse for the resulting mesh to change the mesh properties, we can easily improve and control the mesh properties required for finite element analysis.