Boundary Representation Models Research Articles

Reverse engineering of geometric models—an introduction

In many areas of industry, it is desirable to create geometric models of existing objects for which no such model is available. This paper reviews the process of reverse engineering of shapes. After identifying the purpose of reverse engineering and the main application areas, the most important algorithmic steps are outlined and various reconstruction strategies are presented. Pros and cons of various data acquisition techniques are described with related problems of boundary representation model construction. Specific issues addressed include characterization of geometric models and related surface representations, segmentation and surface fitting for simple and free-form shapes, multiple view combination and creating consistent and accurate B-rep models. The limitations of currently known solutions are also described, and we point out areas in which further work is required before reverse engineering of shape becomes a practical, widely-available engineering tool.

An approach to And the minimum wall thickness of a part from its B-Rep model

Recently, concurrent engineering (CE) has become one of the major conceptual approaches in reducing product developing time. Design for manufacturing (DFM) and design for assembly (DFA) are two of the major areas in CE. Several researchers have integrated a CAD/CAM system and a knowledge-based system to implement DFA and DFM concepts. However, the incompatibility of the data representation methods between CAD/CAM and knowledge-based systems is the major issue in this integration method. In this paper, an approach is proposed to find the minimum wall thickness of a part from its boundary representation (B-Rep) model. These data can then be directly utilized by a knowledge-based system to analyse the manufacturability of thin wall parts such as injection moulded or diecast parts.

Extracting Topological Relationships from Wire-Frame CAD Model

This paper presents an algorithm for extracting topological relationships from a wire-frame computer-aided design (CAD) model of a given concrete floor. The algorithm consists of three stages. The first stage processes the wire-frame CAD data to differentiate between the interior and the exterior of a given floor configuration and to identify obstacles. The second stage employs the plane sweep paradigm to obtain all interior beam to beam intersection points. The third stage partitions the interior of the given floor into rectangular slabs (face entities). Information regarding the location and dimensions of concrete columns are also obtained using a range-searching technique and is stored along with the partitioning information. Plane sweeps are performed in two principal directions to extract adjacency relationships among the partitioning rectangles. The adjacency relationships are stored in a graph, called the rectangle adjacency graph (RAG), similar to the face adjacency graph (FAG) commonly used in boundary representation (B-Rep) models. The RAG can be used as a complete information model for computer-aided generation of: (1) A construction process plan; and (2) a detailed path plan for computer numerically controlled (CNC) concrete placement. The algorithm is applicable to concrete floors designed using one- and two-way slab theories that guarantee orthogonal polygon shaped floor boundaries and interior obstacles.

Integrity Verification of Topology-based Shape Representation Model Data (A Basic Theory).

Constraint conditions of previously reported mathematical data models, geometric cell complex chains (basic models), are theoretically defined as a basis for verifying the integrity of topology-based shape representation model data. These constraint conditions are mainly classified into three conditions, called cell conditions, complex conditions and chain conditions. Constraint conditions of mathematical shape models, so-called well-formedness conditions, can be derived from these constraint conditions and shape model transformation of these mathematical data models. Methods for applying constraint conditions of these mathematical data models to the integrity verification of the topology-based non-manifold shape representation model data and so-called solid boundary representation model data are described.

Quantifying differences between computer models of orebody shapes

Abstract Several different methods have been used for the representation of orebody shapes in computer systems including serial-slice, gridded seam, regular block, mathematical functions, solid geometry, and boundary representation models. The accuracy and precison of such models are affected by factors such as errors associated with the original data used, natural variations, errors in data capture and processing, etc. In order to asses the relative importance of such factors it is necessary to quantify differences in accuracy and precision between different model structures. To meet this objective a new technique which relies on statistical study of a series of sample lines, intersecting two or more different orebody models, is proposed. Application of this technique on orebody models at the Neves-Corvo copper-tin deposits in southern Portugal suggested that in certain circumstances regular block models can give very poor estimates of the total volume of materials of different geological types. In addition it was shown quantitatively that shape interpretations close to the plane of drill-sections are better, in terms of accuracy and precision, than interpretations for zones falling between the drill-section planes.

都市空間の３次元表現手法（ディジタル都市空間モデル）の開発

Conventional two dimensional (2D) maps and DEM's are insufficient to represent geographic information in urban space comprising high-rise buildings and underground structures. There is a pressing need for a model of three dimensional (3D) representation of urban space, that is, a Digital Urban Space Model (DUSM) . However existing solid modelling techniques cannot be directly applied to the 3D representation due to several problems such as the inefficiency in building and updating 3D spatial database. Based on the boundary representation (BR) model, the authors propose a Surface Representation (SR) model which can greatly improve the efficiency in building and updating 3D spatial database. Through an example of the 3D representation of urban space, it is demonstrated that the SR model can be successfully applied.

Formal specification of topological subdivisions using hypermaps

In a way, the ideas of Lienhardt about boundary-representation models are extended, interpreted and rewritten. He has shown that the topology of graphical objects can easily be described by mathematical concepts of map and generalized map. The map specification problems are emphasized, to take into account topology and, to some extent, geometry. Indications are also given about implementation. A technique of algebraic specification is used to define a universe of graphical objects and operations based on the maps and their extensions. First, a unifying concept of hypermap is specified, for which different levels of operations are given. In the next step, this notion is specialized to retrieve the maps and the generalized maps with their own operations. The fundamental properties of the model of boundary representation are defined, and then obtained from the formal specification. It is shown that the notion of hypermap helps to precisely define the morphology of the objects, i.e. geometrical embedding and photometry, which can be attached to elements of hypermaps. The case of surfaces is specially considered. The question of implementation is also considered. From an algebraic specificatio, numerous concrete representations can be developed. Two different representations are demonstrated: a rapid prototyping in OBJ3 and an efficient pointer realization in C.

Utilization of Topological Representation in Mechanical Design : An Attempt

This work is a preliminary investigation carried out in an attempt to develop a software system which detects the possible sources of degradation in the original design of machines and structures and provides alternatives to improve their integrities in terms of strength by noting their geometrical distinctions. The computer stores their topological data using a boundary representation model. The system detects the distinctive geometrical features and reasons based on them whether they might be triggers for degradation or not by referring to the attributes attached to each geometrical feature. The fundamental validity of the approach is verified on a personal computer using Prolog. What should be stressed as the originality of this paper is that although the design models cannot be modified without numerical data in the conventional strength-related designs, they can be improved or better alternatives can be suggested as long as their topological data are available in our system.

Boolean operations between solids and surfaces by octrees: models and algorithm

In integrating surfaces and solids, the realisation of Boolean operations is an important problem. To solve this problem, a model based on extended octrees to present sculptured surfaces composed of biquadratic patches is reviewed. Thus a model is available to represent both solids and free-form surfaces. Moreover, it has been demonstrated that the extended octrees model is suitable for Boolean operations between solids and, hence, it can also be appropriate for Boolean operations between solids and surfaces. The paper discusses algorithms that convert sculptured surfaces to the extended octrees model and also algorithms that perform the intersection between two surfaces in this model and do Boolean operations between solids and surfaces. Finally, a boundary representation model is presented for representing the results of this operation, which will be mixed objects, as is an algorithm to pass from the extended octrees model to this boundary representation model.

Generation of Topological Boundary Representations from Octree Encoding

By generating a sequence of Euler operations, the algorithms presented here make it possible to convert octree models to a variety of boundary representation models.