2.2 Solid Modellers

A solid model
Fig.3 A solid model

Solid models (Fig. 3) work by defining the space occupied by the component. They therefore provide real three-dimensional representations. The practical advantages of using them include the provision of complete physical properties (mass, volume, centre of gravity, moments of inertia, radii of gyration etc.), as well as the ability to generate section views, add full visual physical properties, and detect interference between adjacent components.

Conceptually, solid models are more elegant than surface models, as they deal with complete physical representations rather than just the shells of objects. It is impossible to produce a nonsense solid model, e.g. with objects of zero thickness. They are also more intuitive, as they deal with shapes rather than a series of surfaces, and this has been an attraction not only in archaeology but also in other fields dealing with structure, such as architecture and quantity surveying (Lauden Crosley 1988, 120; Atkin et al. 1987, 34).

The principal disadvantage is that such models are computationally very expensive, in both storage and processing requirements (MacFarlane 1995, 2). Also, solid modellers have tended to have had very unfriendly user interfaces, since they were intended more for calculations than visual design (Chapman 1990, 83; Wood & Chapman 1992, 144), and because of computational problems with a graphical interface for solid modellers (Burridge et al. 1989, 550).

They are also less robust than surface models. This is largely because of the problems of implementing an abstract machine to carry out substratum operations such as vector-computations.and incidence tests. The introduction of floating point arithmetic makes the machine non-robust, while the use of exact arithmetic is unacceptably inefficient when dealing with curved boundaries. The 'robustness problem' is only overcome with heuristics and user workarounds discovered through trial and error (Hoffmann & Rossignac 1996, 6).

Types of Solid Model

There are three dominant solid representation schemata which are currently used in modelling: constructive solid geometry (CSG), boundary representations (b-rep), and spatial-subdivision (Hoffmann & Rossignac 1996, 3).

Constructive Solid Geometry

CSG modellers work with objects made up of primitive geometric solids (e.g. sphere, box, cone) combined with a series of Boolean operations (they are thus sometimes referred to as 'set-theoretic'). They are intuitively the most simple to grasp. Although they are computationally more difficult to manage than other schemata, they have greater numerical stability (Woodward 1986, 90).

Boundary Representation

B-rep models represent solids with boundary faces; unlike surface models, b-rep software holds information about the inside of faces as well as the outside. B-rep models achieve topological consistency, although they do not ensure geometrical consistency (e.g. it is possible for a concavity in an object to protrude through the opposite side of the polyhedron) (Woodward 1986, 85). Some solid modellers which appear to be CSG modellers in fact use a CSG-based interface for a b-rep modeller.

Spatial Subdivision

spatial-subdivision models decompose the solid into cells, each with a simple topological structure and also often a simple geometric structure. They can be divided into boundary conforming and boundary approximating schemata (Hoffmann & Rossignac 1996, 5). Mesh representations, which are a boundary conforming method, are commonly used in the finite element analysis of CSG and b-rep models.

The Origins of Solid Modelling

Solid modellers were developed as part of Computer Aided Engineering (CAE). CAE was developed, like CAD, to design objects, with the added ability of testing the physical qualities of those objects.

The objective of solid modelling is to represent, manipulate, and reason about, the three-dimensional shape of solid physical objects, by computer. Such representations should be unambiguous.

(Hoffman & Rossignac 1996, abstract). The requirement to represent the object visually is one which has developed only in the last decade, as it is not one given by Woodward (1986, 84). All that was required was that the object can be mathematically expressed and manipulated. Even today the visual output of solid modellers is incidental to much, though not all, CAE work, and is solely for the human operators' benefit.


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Last updated: Thu May 1 1997