The main objective of traditional modeling systems has been the representation of the shape of an object accurately and reliably as a computer understandable information. These models cannot be directly used to drive applications such as manufacturing planning on CAM system or handling and assembling in robotics applications since some information required for these tasks is totally absent in such models. In the last few years two new design paradigms have emerged: feature-based design and constraint-based design which addressing aspects that allow or facilitate the integration between modeling and applications. In this work we review a paper which proposes a hybrid representation of Feature-Based models.
There are three dominant representations used for solid modeling: Constructive Solid Geometry (CSG), Boundary representation (Brep) and Spatial subdivision. These three models have served as a basis for the develop of several CAD systems but their use have been basically limited to drafting purposes since, in general, they have a lack of support of adequate means for dealing with functionality either at the level of representation or at the level of provide efficient mechanisms to extract and manipulate such a functionality from the geometric and topological representation they use internally.
The basic problem with traditional applications based on the representations before mentioned is that in detailing the object geometry in terms of low level entities the overall meaning of the object is hidden. In these models the main objective is the final shape, and the meaning of the shape, which may represent the functionality in the application context, is not maintained in the model. In addition in many applications contexts, a description of the nominal geometry is not sufficient and this description must be complemented with tolerances and other constraints.
The new design paradigms expose a need to reconsider solid representation at a different level of abstraction which will allow the develop of more intelligent design systems and will provide the link between design and application. Basically the new system modelers must be able to capture and use the design objectives related to function and manufacturability. In the past five years these paradigms of design are appearing in commercial practice and at present, considerable attention is been focused on its potential. Features are seen as an effective mean to provide a more abstract product model than geometry alone. In the new design methodologies we need to represent entire classes of solids, comprising a generic design. Solids in a class are built structurally in the same way, from possibly complex shape primitives, and are instantiated subject to constraints and dimensions that interrelate specific shape elements [5]. Important research issues must be done in order to define precisely classes of solids, representation of generic solids, and ways to edit such designs.
The paper we are dealing with was presented in Proceedings of the IFIP in Japan in 1991 by Bianca Falcidieno and Franca Giannini. Both have been related with several works about feature-based modeling [1, 2, 3 ,4], in which appropriated representation schemes of features have been explored in order to integrate features and constraints in modeling systems. The rest of this work is organized as follow. Section 2 presents a background about solid modeling systems in general. Section 3 present issues to be considered in feature-base modeling. Section 3 presents a brief discussion about the proposed modeling scheme. Section 4 presents the conclusions.
In this scheme solid are represented as a set-theoretic Boolean expression of primitive solid objects, of a simpler structure. Both the surface and the interior of the final solid are thereby implicitly defined. The traditional CSG primitives are block, sphere, cylinder, cone, and torus. A solid is then represented as an algebraic expression that uses rigid motions and regularized set operations. The traditional regularized operations are union, intersection, and difference. Each solid has a default coordinate system. Using a rigid transformation, the solid is positioned relative to a global coordinate system. A Boolean operation then combines the solids with respect to the common coordinate system. Extrusion, sweep along a straight line; and revolution, a sweep about an axis, have been used to obtain more general primitives.
In this scheme solids are represented in terms of individual surfaces, edges, and vertices. A distinction is drawn between the topological description in which the three primitive topological entities, faces, edges, and vertices, are explicitly represented together their mutual adjacency relation, and the geometric location and shape of these entities. Two major families of Brep appear in the literature. One family restricts the solid surfaces to oriented manifolds in which every edge is incident to two faces, and every vertex is the apex of a single cone of incident edges and faces. The second family allows oriented nonmanifolds in which edges are adjacent to an even number of faces
In this scheme solids are decomposed into cells each with a simple topological structure and often with a simple geometric structure. Two categories of spatial subdivision can be considered [5]: Boundary conforming, and boundary approximating
Feature is a concept which can be defined in terms of generic shape and engineering semantics. A feature is a physical constituent of a part which synthesized a particular meaning in some parts of the productive process [3]. Therefore, feature is a concept which relates form and function. The first one is depending on the model and the other on the application. One of traditional models' problems is the lack of a median level of information in the model between the very high level (volumetric primitives) and very low level (individual topological entities) which is precisely the level at which information is required by applications programs. The integration between the design process and the application programs require of this information level and features may therefore hold the key to the integration of geometric modeling systems and application programs.
Conceptually, either Brep or CSG modelers are capable of representing and manipulating features, but the common opinion is that this would be best done by utilizing both approaches [2]. As a consequence of that several researchers have proposed hybrid CSG-Boundary schemes for represent feature information in the framework of solid modeling. These hybrid representations can be CSG-based or Boundary-based depending on which model is considered to be the master model in their definition.
Different systems have been used for creating a form feature based design. Two approaches have been considered by researchers in order to obtain a feature based representation: design with features and feature extraction. More recently systems which use both approaches have been proposed.
[2] describes an approach (feature extraction) which allow the automatic extraction and representation of form features in the framework of solid modeling. That approach is based on a boundary representation of the solid model data which is restructured in a process of two steps. In a first step, a hybrid model defined as a hierarchy of boundary volumes is created. In the process of restructuring the boundary representation data, the geometric entities are classified and the relationships between adjacent entities is determined. The result is the explicit representation of so-called generic shape features, divided into two general classes, protrusions and depressions. In the second step, the hierarchical representation of the object with its shape features is reorganized into a context dependent representation by associating sets of shape features functionally related in the application context. This second process involves searching for patterns in the hierarchical hybrid model and refining the hierarchical representation by grouping sets of its components. This work was based on a method proposed by Kyprianou in his Ph.D. Dissertation at the University of Cambridge in 1980.
[1] defines the following issues that a feature-based model should be have:
The modeling scheme proposed in the paper we are dealing with addresses each of these issues. Its more important contributions are:
First they use a double description of a feature-based model: a primary representation in terms of generic form features, and a set of viewpoint dependent feature-based representations which are created by transformations that are viewpoint specific. In this way shape and feature can be handled more properly, the first one more general and the second one more particular.
Second they support a combination of the two approaches has been considered by researchers: design with feature, and feature extraction. The first approach allows the incorporation of high level abstractions such as functionality and design purpose. Given that features are strictly dependent on the context, the models produced are also context dependent hence they cannot be shared between different functional viewpoints. The second approach is closed related with primitive components of a solid model of the object, such as faces, and edges. The problem with this approach is that even though some systems have proved that is possible to recognize some features from the geometric model, it has not yet been proven that such methods work for all kind of features. The properly combination of both approaches in an integrated system allows the creation of a more general modeling system suitable to be used in different application context.
Third they introduce the concept of neutral description which is created taking into account geometric and topological arrangements of faces, edges and vertices, and is independent from the application context. This model is used as an input to modules called Converters. These converters allow the transformation of the neutral description model (application independent) into a model dependent of the application context. For N different applications, N(N-1) transformations (converters) are required, but by using the neutral description model only N converters are required. The neutral description is based on the so-called Shape Feature Object Graph (SFOG). This is a hybrid model (Boundary/Volumetric) that can be considered a neutral format description of a feature-based model, since it is a form feature oriented but independent from a specific application. The graph representation proposed presents several advantages: first it makes the topological and geometric relationships between features explicit. Second it maintains information about the surrounding volumes and feature neighbors which is required in the context of some applications.
Fourth they provide a flexible user interaction. Three ways of interaction are available to the user. One called Geometric Model Interaction allows the user to define a traditional boundary model of the object which is used for other module to create the before referred Neutral Model. The second way of interaction, called Design with Feature allows the user to directly create a feature-based model for a given context. A library of feature descriptions is used in order to create such a model. The third way of interaction, called Feature Definition Interface, allows user to construct feature descriptions from examples (i.e. feature instances on an existing geometric model). A dual feature description is generated for this last interface: one oriented to facilitate the process of feature recognition, and another one to facilitate its utilization in the modeling with feature.
Fifth The proposed model is modular. The different modules provide the required level of abstraction claimed in the new paradigms of design solid-model systems.
Binary spatial partition trees are recursive subdivisions of 3D-space. Each interior node of the tree separates space into two disjoint point sets. In the simplest case, the root denotes a separator plane. All the points bellow or on the plane are represented by one subtree, all the points above the plane are represented by the other subtree. The two point sets are recursively subdivided by half planes at the subtree nodes. The leaves of the tree represent cells that are labeled in or out. The planes are usually face planes of a polyhedron, and the union of all cells labeled in is the polyhedron modeled.
3 The architecture of the system proposed
4 Conclusions
The hybrid representation in both at the level of geometrical model (CSG or Brep) and at the level of strategy of feature implementation appear as the most important result from this work. The model so obtained is suitable to be use efficiently in different contexts. This is considered by the authors as the basis of the next generation feature-based models.
5 References