The word “topology” is derived from the Greek word “τοπος,” which means “position” or “location.” A simplified and thus partial definition has often been used (Croom, 1989, page 2): “topology deals with geometric properties which are dependent only upon the relative positions of the components of figures and not upon such concepts as length, size, and magnitude.” Topology deals with those properties of an object that remain invariant under continuous transformations (specifically bending, stretching, and squeezing, but not breaking or tearing). Topological notions and methods have illuminated and clarified basic structural concepts in diverse branches of modern mathematics. However, the influence of topology extends to almost every other discipline that formerly was not considered amenable to mathematical handling. For example, topology supports design and representation of mechanical devices, communication and transportation networks, topographic maps, and planning and controlling of complex activities. In addition, aspects of topology are closely related to symbolic logic, which forms the foundation of artificial intelligence. In the same way that the Euclidean plane satisfies certain axioms or postulates, it can be shown that certain abstract spaces—where the relations of points to sets and continuity of functions are important—have definite properties that can be analyzed without examining these spaces individually. By approaching engineering design from this abstract point of view, it is possible to use topological methods to study collections of geometric objects or collections of entities that are of concern in design analysis or synthesis. These collections of objects and or entities can be treated as spaces, and the elements in them as points.

This paper describes an algorithm for surface reconstruction from a set of scattered three-dimensional points extracted from an image sequence. In this process, additional information (such as location of the viewpoints and the points visible from a particular viewpoint) is available and can be exploited for accurately recovering the shape of the objects portrayed in the images. Initially, the set of points is subjected to a Delaunay triangulation that fills the convex hull of the set of points with disjoint tetrahedra. The key idea of the shape recovery algorithm is to eliminate triangles that obstruct the visibility of points from certain viewpoints, whose locations are known from the image acquisition process. The major contribution of this paper is that we have been able to design an algorithm for surface reconstruction that handles a wide variety of shapes, as opposed to currently existing techniques.

In this article, an approach is presented for the representation and reasoning over qualitative spatial relations. A set-theoretic approach is used for representing the topology of objects and underlying space by retaining connectivity relationships between objects and space components in a structure, denoted, adjacency matrix. Spatial relations are represented by the intersection of components, and spatial reasoning is achieved by the application of general rules for the propagation of the intersection constraints between those components. The representation approach is general and can be adapted for different space resolutions and granularities of relations. The reasoning mechanism is simple and the spatial compositions are achieved in a finite definite number of steps, controlled by the complexity needed in the representation of objects and the granularity of the spatial relations required. The application of the method is presented over geometric structures that takes into account qualitative surface height information. It is also shown how directional relationships can be used in a hybrid approach for richer composition scenarios. The main advantage of this work is that it offers a unified platform for handling different relations in the qualitative space, which is a step toward developing general spatial reasoning engines for large spatial databases.

The ability of a CAD system to perceive a three-dimensional model depicted in a single freehand sketch presents the practical possibility of bringing numerous established analysis tools into the early stages of design to institute conceptual analysis. In this article we hypothesize that the key to enabling systems to reason and communicate about conceptual design is the language of sketching. We explore this approach, outline the basic algorithms required, and provide several examples of an implemented system.

This article is an attempt to improve the efficiency of procedures for compositional synthesis of design solutions using building blocks. These procedures have found use in a wide range of applications, and are one of the most substantial outcomes of research into automated synthesis of design solutions. Due to their combinatorial nature, these procedures are highly inefficient in solving problems, especially when the database of building blocks for synthesis or the problem size is large. Previous literature often focuses on improving only the algorithm part of a procedure, while it is both its algorithm and database which together determine the overall efficiency of the procedure. This article uses a case study to investigate and develop a set of rules for structuring and preprocessing a database of building blocks so as to improve the efficiency of synthesis of design solutions using this database.

A case-based design functionality is a natural and intuitive addition to a design tool that can augment human capabilities and help designers remember and retrieve appropriate cases. SEED-Config, a design environment for conceptual building design, was developed to incorporate a case-based reasoning functionality to provide designers with initial potential solutions. The case representation in SEED-Config is the BENT information model, which records design knowledge, supports the hierarchical decomposition of design cases, offers multiple views, and encapsulates the outcome of the design in addition to the problem specification and the design solution. The case library was implemented in an object-oriented database management system to accumulate cases automatically and to provide efficient query facilities. The case retrieval aspect of SEED-Config offers three different methods to find the most useful cases stored in the case library: task-based, lineage-based, and customized. Case retrieval responds to the exploratory nature of the design process and supports versatile case retrieval by providing multiple paths to each case. The case adaptation aspect, which adjusts the selected case to the new problem to provide a complete solution, uses an adaptation method called derivational replay. The case-based design capabilities are completely integrated within the design environment from which the cases originate.

Production systems have traditionally been used in engineering to aid the designer in generating designs in domains not significantly influenced by geometry. However, in geometric-based domains such as mechanical engineering, their popularity has been limited. This work proposes the use of shape grammars as the framework for engineering expert systems. Shape grammars are shown to have all the generation and analysis capabilities of traditional production systems, while being able to represent knowledge about both the functionality and the form of a product. Additionally, the parametric nature of shape grammars, their ability to deal with physical form rather than abstract elements, and their ability to recognize emergent shapes give them significant advantages over traditional production systems for geometry-based engineering design.