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1.2 THE BASIC TYPES OF SOLID MODELS

Requicha [1992] asserts that there are three fundamental methods for representing solid objects: Decomposition, Boundaries, and Construction. Decomposition uses representations which attempt to divide space in some discrete manner. These approaches include thin 2 dimensional slices, voxels, ray casting, oct-trees, and binary space partition trees. Boundary methods use the faces, edges, and vertices of the object. Various data structures differentiate much of the work in this field. Requicha [1992] also states that additional information is required with the boundaries to establish solid properties. Finally, Constructive approaches build up the data representation from other geometries. The most popular constructive techniques are the CSG (Constructive Solids Geometry) and Sweeping methods.

There are clear differentiations between each of the three main solid modelling approaches. The Constructive methods are well defined volumes, whereas the other methods are subject to spatial resolution, volume location and data abstraction problems. For example the CSG method is described by Requicha as “rooted, directed, acyclic, binary graphs, where the internal nodes correspond to Boolean operations or rigid-body transformations and where leaves are primitive bounded solids or half spaces. CSG representations are concise, always valid in the r-set modeling domain, and easily parameterized and edited.”

Higher level methods for representing solids have also been examined in recent research. One particular method often cited is feature modelling. In this approach the part is described with features. The features are treated as solids, and operated upon as solids [ElMaraghy, 1991]. In addition to problems mentioned in the last chapter, a problem it causes for Solid Modeling is that when features overlap there is no method for determining priority [Requicha, 1992]. For example, if a fillet overlaps a hole, does the fillet cover the hole, or is it removed?

The CSG representation has been chosen for this thesis because it is both abstract and unambiguous. This makes it well suited to serve as the basis for this reasoning system. More specifically the representation will be done with the CSG expressions in Boolean form.