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).

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).

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).

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 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.

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