Solid Representation Research Articles

Geometric modelling based on simplicial chains

In this work we present a mathematical formulation for geometric modelling which may be applied in spaces of any dimension. The model can be seen as an example of a graphic object algebra [see Torres, J. C. and Clares, B., Graphics objects: a mathematical abstract model for computer graphics. Computer Graphics Forum, 1993, 12(5), 311–328 and Feito, F. R. and Torres, J. C., Boundary representation of polyhedral heterogenous solids in the context of a graphics objects algebra. The Visual Computer, 1997, 13(2), 64–77]. It is based on the concept of simplicial chain which is considered a particular case of the polyhedral chains presented by Whitney ( Geometric Integration Theory, Princeton University Press, Princeton, NJ, 1957). From the algebraic operations with simplicial chains we can obtain any element of the general polyhedral solids (manifold and non-manifold). Similarly, from the defined operations with chains, we can obtain the usual operations of geometric modelling (union, intersection and difference). So, the model can be considered a new scheme of representation of solids based on simplician chains. One of its uses is to obtain the usual operations of geometric modelling by means of operations with simplices (triangles, tetrahedra, etc) which are simple elements.

Fetal biomodelling.

A study has been performed to determine if a stereolithographic (SL) biomodel of a fetal face could be created from 3 dimensional (3D) ultrasound (US). 3D ultrasound images were acquired by Diasonics Gateway 2D Array ultrasound systems (Diasonics Ultrasound, San Jose, CA, USA) using an electromagnetic localizer (Tomtec Free Hand Scanning Device, Tomtec Imaging Systems, Middle Cove, Australia). 3D volumetric reconstruction of the fetal face was performed and the data was prepared to guide the construction of an exact solid biomodel by stereolithography (SLA 250 3D Systems, Valencia, CA, USA). A faithful solid representation of the fetal face was produced within 12 hours of the US scan. The fetal biomodel seemed to improve the display of the 3D data. The user-friendly nature of biomodelling may have clinical utility for fetal morphological assessment and as an aid when counselling parents.

Discrete elements model for evaluating impact and impulsive response of reinforced concrete plates and shells subjected to impulsive loading

The application of a discrete element representation of solids to the analysis of reinforced concrete plates and shells is discussed. Yielding of steel as well as fracture of concrete are duly accounted for by means of constitutive criteria that quantifies coupling between both effects. Comparison with experimental results show excellent correlation.

Requirements for a solid modeler coupled to finite-element mesh generators

This paper presents the necessary requirements for a multi-representational solid modeler combining constructive solid geometry (CSG) and boundary representation (B-rep) to be coupled to a 3D automatic finite-element mesh generator in electromagnetic problems. A modeler architecture and the functional specifications of the modules are defined. Implementation details, including object oriented data structures and class definitions are described.

RSVP: a geometric toolkit for controlled repair of solid models

The paper presents a system and the associated algorithms for repairing the boundary representation of CAD models. Two types of errors are considered: topological errors, i.e., aggregate errors, like zero volume parts, duplicate or missing parts, inconsistent surface orientation, etc., and geometric errors, i.e., numerical imprecision errors, like cracks or overlaps of geometry. The output of our system describes a set of clean and consistent two-manifolds (possibly with boundaries) with derived adjacencies. Such solid representation enables the application of a variety of rendering and analysis algorithms, e.g., finite element analysis, radiosity computation, model simplification, and solid free form fabrication. The algorithms described were originally designed to correct errors in polygonal B-Reps. We also present an extension for spline surfaces. Central to our system is a procedure for inferring local adjacencies of edges. The geometric representation of topologically adjacent edges are merged to evolve a set of two-manifolds. Aggregate errors are discovered during the merging step. Unfortunately, there are many ambiguous situations where errors admit more than one valid solution. Our system proposes an object repairing process based on a set of user tunable heuristics. The system also allows the user to override the algorithm's decisions in a repair visualization step. In essence, this visualization step presents an organized and intuitive way for the user to explore the space of valid solutions and to select the correct one.

The virtual engineer: 21st Century product development

Before you spend any money on physical prototypes, learn how a systems engineering can help you bring new products to market faster and at less cost! The Virtual Engineer explains how a company can incorporate advanced processes into their existing systems, intergrating the product development, manufacturing, marketing and costing functions. Howard Crabb, the pioneer of the visual engineering concept, draws on his 30 years of experience as a manager of Technical Computing at Ford Motor Company. There he intergrated solids modeling with traditional CAD to produce a solid representation of a design, opening up the potential for leapfrogging the competition. He explains in clear and effective language: Steps required to reinvent the current new product development process How change benefits the organization, in terms of reduced cycle time, reduced engineering changes, reduced number of physical prototypes and improved product quality Developments in the semiconductor industry and their impact on the desktop computing environment and Best practices of existing firms

Boundary Representation-Based Feature Recognition

This paper introduces an ongoing research which is aimed at the development of an intelligent form feature extraction system from Computer Aided Design (CAD) database, a high level data structure form useful for Computer Aided Manufacturing (CAM) such as Automated Process Planning System (APPS). Part description in CAD models is the form of basic geometry and topology that is unsuitable for direct application in APPS. Furthermore, CAD software does not incorporate sufficient manufacturing specific data to be used in APPS. Therefore, feature recognition systems will provide the capabilities for bridging the gap between the CAD database and the CAM database. A solid boundary representation (B-rep) model of the part is used to describe the part. This paper concentrates on the recognition of machinable features of either depression or protrusion types to be used in Automated Process Planning System. Logical procedures were developed to recognise these features which consists of both simple and intersecting features.

Boundary representation of polyhedral heterogeneous solids in the context of a graphic object algebra

Boundary representation of polyhedral heterogeneous solids in the context of a graphic object algebra

A robot vision VLSI processor for the rectangular solid representation of three-dimensional objects

A compact rectangular solid representation of three-dimensional (3-D) objects is proposed for motion planning of intelligent robots. A VLSI-oriented algorithm that transforms the discrete point representation of a 3-D object to a rectangular solid representation is considered. A new architecture is proposed to perform matching operations between a rectangular solid and discrete points in parallel. Performance evaluation shows that the VLSI processor that implements the algorithm is 25,000 times faster than a RAM-based architecture. © 1997 Scripta Technica, Inc. Syst Comp Jpn, 28(3): 54–61, 1997

Robot Vision VLSI Processor for the Rectangular Solid Representation of 3-Dimensional Objects

A compact rectangular solid representation of the 3-dimensional (3-D) objects is proposed for motion planning of intelligent robots. A VLSI-oriented algorithm is considered by which the discrete point representation of a 3-D object is transformed to the rectangular solid representation. A new architecture is proposed to perform matching operations between a rectangular solid and discrete points in parallel. The performance evaluation shows that the designed VLSI processor is 25,000 times faster than the RAM-based architecture.

Function Representation of Solids Reconstructed from Scattered Surface Points and Contours

AbstractThis paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality f(x,y,z) ≥ 0. The volume spline is based on use of the Green's function for interpolation of scalar function values of a chosen “carrier” solid. Our algorithm is capable of generating highly concave and branching objects automatically. The particular case where the surface is reconstructed from cross‐sections is discussed too. Potential applications of this algorithm are in tomography, image processing, animation and CAD for bodies with complex surfaces.

Computation of 3D skeletons using a generalized Delaunay triangulation technique

The skeletal representation of 3D solids based on the medial axis transform has many applications in engineering. However, these applications are seldom realized, owing to the lack of viable computational techniques for generating skeletons. Such a computational technique, based on a notion of the generalized Voronoi diagram of a set of mixed-dimensional entities, is presented. It is shown that the generalized Voronoi diagram of a set of specific mixed dimensional set derived from the set of boundary entities of a polyhedron is, in fact, the exact skeleton of the polyhedron. Rather than the generalized Voronoi diagram being directly computed, its dual, an abstract Delaunay triangulation, is computed, from which the skeleton can be derived. An approach based on the Voronoi diagram of a well chosen representative point set on the boundary is also discussed as a special case; it is shown that the limitations of this approach are overcome by the generalization developed. Overall, it is argued that this generalization of the Voronoi diagram and the notion of the abstract generalized Delaunay triangulation are useful, and that they provide a viable approach to the computation of skeletons. Finally, details of the implementation, results, and an evaluation are presented.

Use of graph grammars for the description of mechanical parts

A solid representation formalism is defined on the basis of the parsable family of IE-graphs. edNLC-type graph grammars are used for the dynamic building and manipulation of such representations. The other two syntactic pattern recognition schemes, namely programmed edNLC grammars and a syntax-directed scheme translating graph languages, are introduced for reasoning over structural descriptions and an automatic modification of a modelling process. Multiaspect taxonomies defined for features allow one to solve problems of constructing unique and unambiguous descriptions of modelled solids.

Incremental feature generation and modification during design evolution

The concept of feature was introduced because of need to integrate the design and the manufacturing activities. Therefore, the generation of features usually occurs after design completion. However, in recent product development approaches such as concurrent engineering (CE), features need to be generated during design evolution. This paper presents an incremental feature generation (IFG) and feature modification (FM) approach applicable during design evolution, defined by constructive solid geometry (CSG) and boundary representation (B-rep). In IFG, a classified boundary component, obtained from boundary evaluation, is defined as a protrusion or depression (P/D) according to Boolean operation and convexity analysis. The existing features are then updated in accordance with feature interactions in the FM. The FM involves feature existence analysis and modification procedures. The modification procedures are; 1) decide whether the remaining part of an existing feature is valid for a feature definition, 2) update it as a new feature and 3) define the feature relationship. In the IFG approach, the geometry of the current design step is automatically isolated by Boolean operation and defined as a protrusion or depression (P/D) without convexity calculation of topological entities such as edges or face sets. The above procedures are performed through tracing Boolean operations and convexity checking of an intersection edge loop generated during design evolution.

Real functions for representation of rigid solids

A range of values of a real function fnof; : E d → R can be used to implicitly define a subset of Euclidean space E d . Such “implicit functions” have many uses in geometric and solid modeling. This paper focuses on the properties and construction of real functions for the representation of rigid solids (compact, semi-analytic, and regular subsets of E d ). We review some known facts about real functions defining compact semi-analytic sets, and their applications. The theory of R-functions developed in (Rvachev, 1982) provides means for constructing real function representations of solids described by the standard (non-regularized) set operations. But solids are not closed under the standard set operations, and such real function representations are rarely available in modern solid modeling systems. More generally, assuring that a real function fnof; represents a regular set may be difficult. Until now, the regularity has either been assumed, or treated in an ad hoc fashion. We show that topological and extremal properties of real functions can be used to test for regularity, and discuss procedures for constructing real functions with desired properties for arbitrary solids.

Constructive shell representations for freeform surfaces and solids

We usually model freeform surfaces (mathematically, 2D r-sets embedded in 3D Euclidean space E/sup 3/) as a finite union of patches represented in the traditional parametric or the recently developed algebraic forms. The article introduces a new representation scheme for freeform surfaces called constructive shell representation (CSR), that draws on recent research on algebraic patches. CSRs of surfaces that constitute boundaries of solids are very useful for solid modeling. They represent thick shells derived from freeform surfaces and provide a means to compute exact CSG representations of freeform solids. >

Perceptual impulsions and unfamiliar solids: Evidence from a drawing task

Previous work (Dziurawiec & Deregowski, 1992) has shown that children's distorted drawings of animal models may be explained by the child's tendency to depict typical contours, the outlines of the surfaces which undergo pronounced change. The present paper investigates whether the typical contours notion can be extended to purely geometric solids. Results from a drawing task by children aged nine and eleven years, using unfamiliar models of varying complexity, indicate that the tendency to draw in perspective increases with the increase in figure complexity for both age groups, but younger children show a greater reliance on typical contours than older children. Recasting the data from previous drawing experiments (Bartel, 1928/1958; Cox, 1986) further confirms the utility of the typical contours approach. Finally, the advantages of such an approach over that of canonicity (cf. Palmer, Rosch & Chase, 1981) for the representation of solids are elaborated.

Non-invasive bone biopsy: a new method to analyse and display the three-dimensional structure of trabecular bone

Three-dimensional (3D) structure is one of the main factors influencing the mechanical behaviour of cancellous bone. To analyse the trabecular bone structure nondestructively the authors used a peripheral QCT system and applied a special thin-slice technique to create high-resolution volumetric data sets serving as a basis for something they would like to call noninvasive bone biopsy. In order to obtain binary data sets, the mineralized bone in the CT volume was separated from bone marrow and muscle tissue with the help of a sophisticated 3D segmentation algorithm based on the analysis of directional derivatives, which are computed from a locally approximated fit function of the original CT volume. Binary volumes including either a solid representation of trabecular plates and rods or a topological representation of the cancellous bone architecture were acquired. Such volumes can be processed nondestructively and, even more important, repetitively. By using a surface reconstruction algorithm based on interpolating triangulation it was possible to visualize the 3D surface of the trabecular bone structure. The results showed that surface representation and visualization in combination with a multiple thin-slice measuring technique are valuable tools in studying 3D bone architecture. In the future, the noninvasive bone biopsies will be evaluated by means of 3D mechanical analysis incorporating finite element modelling and direct morphological investigations of the cancellous bone architecture for a better prediction of bone strength as an index for fracture risk or osteoporosis.

Feature model-based grasp formulation

Abstract The most flexible means of transferring components between machines within a work cell is provided by robotic manipulation. This implicitly requires that a stable grasp of each component can be determined. The CAD representation of the part may be used for this purpose. A conventional search over the solid model representation of the part for the optimal grasp can be computationally expensive, especially when non-planar surfaces are present. In this paper, we present a logical evaluation of the solid feature model of the component, that finds an acceptable grasp with little computational effort. While the procedure does not guarantee that a grasp will be found, its efficiency and success for the majority of components more than justify its use before an exhaustive search is conducted. The technique is illustrated by means of an example.

Point representation versus solid representation of limb mass and its effect on the moment at a joint

Biomechanical models which assess spinal stresses require estimation of moments at various body articulations. One such moment is the moment due to a body segment mass at the segment's proximal joint. Traditionally, this moment is calculated by multiplying the body segment mass, assumed to be concentrated at the body segment's center of mass (point representation), by the distance of the center of mass from the proximal joint. This technical note describes a study undertaken to test the hypothesis that volumetric representation of a body segment's mass, which more accurately represents the distribution of the body segment's mass, would lead to a different moment at the proximal joint than the moment provided by the point representation of the body segment's mass. The hypothesis was tested on the forearm and moment at the elbow joint was calculated by both the point representation as well as the volumetric representation. No significant difference was found between the two values, thus indicating that traditional simplification to calculate such moments (point representation) is reasonable.