This paper describes a new formulation of solid modeling for treating parts derived from volumetric scans (computed tomography, magnetic resonance, etc.) along with parts from traditional computer-aided design operations. Recent advances in segmentation via level set methods produce voxel grids of signed distance values, and we interpolate the signed distance values using wavelets to produce an implicit or function-based representation called wavelet signed distance function representation that provides inherent support for data compression, multiscale modeling, and skeletal-based operations.

A mixed variational principle and derivation of two simple and efficient tetrahedral finite elements with rotational degrees of freedom (DOF) are presented. Each element has four nodes. Every node has six DOF, which include three translational and three rotational DOF. Each element is capable of providing six rigid-body modes. The rotational DOF are based on the displacement formulation, while the translational DOF are hinged on the hybrid strain Hellinger–Reissner functional. Explicit expressions for stiffness matrices are obtained. Element performance has been evaluated with benchmark problems, indicating that they have superior accuracy compared with other lower-order tetrahedral elements.

Geometric data interoperability is critical in industrial applications where geometric data are transferred (translated) among multiple modeling systems for data sharing and reuse. A big obstacle in data translation lies in that geometric data are usually imprecise and geometric algorithm precisions vary from system to system. In the absence of common formal principles, both industry and academia embraced ad hoc solutions, costing billions of dollars in lost time and productivity. This paper explains how the problem of interoperability, and data translation in particular, may be formulated and studied in terms of a recently developed theory of ε -solidity. Furthermore, a systematic classification of problems in data translation shows that in most cases ε -solids can be maintained without expensive and arbitrary geometric repairs.

The present article proposes a method to significantly improve the construction and updating of 3D geological models used for oil and gas exploration. We present a prototype of a “geological pilot” which enables monitoring the automatic building of a 3D model topologically and geologically consistent, on which geological links between objects can easily be visualized. This model can automatically be revised in case of changes in the geometric data or in the interpretation.

Voxel-based modeling techniques are known for their robustness and flexibility. However, they have three major shortcomings: (1) Memory intensive, since a large number of voxels are needed to represent high-resolution models (2) Computationally expensive, since a large number of voxels need to be visited (3) Computationally expensive isosurface extraction is needed to visualize the results. We describe techniques which alleviate these by taking advantage of self-similarity in the data making voxel-techniques practical and attractive. We describe algorithms for MEMS process emulation, isosurface extraction and visualization which utilize these techniques.

Surface reconstruction from unorganized sample points is an important problem in computer graphics, computer aided design, medical imaging and solid modeling. Recently a few algorithms have been developed that have theoretical guarantee of computing a topologically correct and geometrically close surface under certain condition on sampling density. Unfortunately, this sampling condition is not always met in practice due to noise, non-smoothness or simply due to inadequate sampling. This leads to undesired holes and other artifacts in the output surface. Certain CAD applications such as creating a prototype from a model boundary require a water-tight surface, i.e., no hole should be allowed in the surface. In this paper we describe a simple algorithm called Tight Cocone that works on an initial mesh generated by a popular surface reconstruction algorithm and fills up all holes to output a water-tight surface. In doing so, it does not introduce any extra points and produces a triangulated surface interpolating the input sample points. In support of our method we present experimental results with a number of difficult data sets.

Information on tolerances and attributes of mechanical parts and assemblies is crucial for many activities in a product’s life cycle. Tolerance design is a complex task because many factors (functional, technological and economical) should be considered. It is an iterative process, starting from a first tolerances assignment and ending with the definition of their optimal values. Once all tolerances have been assigned to each part of an assembly, tolerance analysis is performed. This stage aim is to evaluate if the combined effects of the assigned tolerances let the design requirements be met. Then, feasible and economical aspects are considered on the basis of both available processes and cost evaluations. The whole tolerance design stage is usually defined as tolerance synthesis. The focus of this work is the discussion of the algorithms to model the geometrical variations, of each part of an assembly, allowed by geometric tolerances. This involves the change of the boundary nominal representation of a part face on the basis of the assigned dimensional and geometric tolerances. At present, the developed algorithms are able to simulate flatness, location and orientation. The modified parts, generated by tolerance simulation, may be used to evaluate the overall assemblability and, then, to verify the assembly functional requirements.

New and efficient paradigms for web-based collaborative product design in a global economy will be driven by increased outsourcing, increased competition, and pressures to reduce product development time. We have developed a three-tier (client-server-database) architecture based collaborative shape design system, Computer Aided Distributed Design and Collaboration (CADDAC). CADDAC has a centralized geometry kernel and constraint solver. The server-side provides support for solid modeling, constraint solving operations, data management, and synchronization of clients. The client-side performs real-time creation, modification, and deletion of geometry over the network. In order to keep the clients thin, many computationally intensive operations are performed at the server. Only the graphics rendering pipeline operations are performed at the client-side. A key contribution of this work is a flexible architecture that decouples Application Data (Model), Controllers, Viewers, and Collaboration. This decoupling allows new feature development to be modular and easy to develop and manage.

The use of multiresolution control toward the editing of freeform curves and surfaces has already been recognized as a valuable modeling tool [1–3]. Similarly, in contemporary computer aided geometric design, the use of constraints to precisely prescribe freeform shape is considered an essential capability [4,5]. This paper presents a scheme that combines multiresolution control with linear constraints into one framework, allowing one to perform multiresolution manipulation of nonuniform B-spline curves, while specifying and satisfying various linear constraints on the curves. Positional, tangential, and orthogonality constraints are all linear and can be easily incorporated into a multiresolution freeform curve editing environment, as will be shown. Moreover, we also show that the symmetry as well as the area constraints can be reformulated as linear constraints and similarly incorporated. The presented framework is extendible and we also portray this same framework in the context of freeform surfaces.

This paper introduces topological constraints to robustly and comprehensively process interference calculation in solid modeling and feature modeling, and describes a method of symbolic notation of their expressions and algorithms to handle them. The interference calculation should be processed consistently against the contradictions in numerical values and should output the result model in the same form of representation as that in the input. To satisfy this, the topological constraints are relied on in the processing rather than numerical values, and represented symbolically and explicitly in the solid model, which is based on the Face-based representation using a table of sequences of face names around each face of the solid. The topological constraints represent degeneracy and connectedness among faces, edges and vertices, and are used against errors derived from the ambiguities caused in the numerical calculation as well as in the input data, while the errors are deliberately kept within a given tolerance. The constraints are also specified by a designer for representing his intention. When the intersection is regarded as degenerate at a point such as vertex-vertex coincidence, its topological constraint is represented by a cluster of multiple basic intersection points between edges and faces, and the name of the cluster is expressed with face names around the degenerate point. In the calculation for the set operation, the symbols of cluster names and non-cluster intersection points are used to make intersection line loops, to divide the faces of both solids along the intersection lines and to reconnect the divided ones to make the result solid. Examples are shown to demonstrate that the algorithms generate output solids even when they are subtly intersected.

This paper proposes a constructive representation scheme for heterogeneous objects (or FGMs). In particular, this scheme focuses on the construction of complicated heterogeneous objects, guaranteeing desired material continuities at all the interfaces. In order to create various types of heterogeneous primitives, we first describe methods for specifying material composition functions such as geometry-independent, geometry-dependent functions, and multiple sets of these functions. Constructive Material Composition (CMC) and corresponding heterogeneous Boolean Operators (e.g., material union, difference, intersection, and partition) are then proposed to illustrate how material continuities are dealt with. Finally, we will describe the model hierarchy and data structure for computer representation. Even though the constructive representation alone is sufficient for modeling heterogeneous objects, the proposed scheme pursues a hybrid representation between decomposition and construction. That is because hybrid representation can avoid unnecessary growth of binary trees.