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Show 4 In the early days of computer graphiCS. Wire-frame representations us1ng vertices and edges were used 'Nh1ch is a natural extens1on of two-d1mens1onal representations. But. in a three-dimensional world. w1re-trame representation 1s ambiguous and is not appropriate for accurate representation . This amb1gu1ty 1s due to the fact that wire-frame modelling does not define surfaces. Therefore. there have been some attempts to represent objects by sets of surfaces . wh1ch has been termed surface modelling . In spite of this improvement. this was still not appropriate for sol ids. since surface modelling could represent 1mposs1ble solids. and was limited m that it could not define the tnside ot solids . Then solid modelling began . The following list shows some of the main representations for solids : * Explicit. This 1s where solids are expressed by the formula F(x,y,z) >=0. Here. F(x,y.z) defines the boundary. Since most solids cannot be represented by one formula. it is difficult to cover many solids by this representation . * Boundary Representation (8-rep). This is where solids are represented by a closed set of surfaces as the boundary. It is the most widely-used method because it is a natural extension of surface modelling, and it can model any solid. Usually, only planar surfaces are used to approximate solids; recently however. free-form surfaces have also been used for more sophisticated modelling. * Sweep. Sweep represents the object generated by moving a twodimensional object along a three-dimensional curve. Although its domain is not so wide as to be a major representation method. it is a natural way to represent objects and is used widely as an input method of solid modelling. * Constructive Solid Geometry (CSG). CSG is the method used to construct three-dimensional ob1ects by combining primttives with set operations. Set operations are usually expressed by three operators (INTERSECT. UNION. and DIFFERENCE). The domain of CSG totally depends on the number of primitives. It has a very wide domain even when it has few simple primitives. Since there 1s no actual limitation on the primitives. the object of any other representation can be a primitive. In this sense. CSG is a higher-level representation than others. Representations have some attributes such as completeness. uniqu eness. |
