Constructive solid geometry

Existing solid modelling methods are reviewed in order to know whether or not they satisfy the requirements previously discussed. Among several solid modelling methods [Chiyokura, 1985, for description], the Boundary Representation(BR) model, the Spatial Occupancy Enumeration(SOE) model and the Constructive Solid Geometry(CSG) model are selected for the review. 

Another misunderstanding involves application of constructive solid geometry (CSG). In early solid modeling, CSG was a leading model representation now it has been replaced by boundary representation. CSG is still important as one of the model construction methods for solids, but CSG modeling procedures generate boundary representation. 

The shape of a mechanical part can be divided into a well-defined set of solid primitives. A purposeful sequence of combination operations with the primitives can be applied to form the shape of the part. Constructive solid geometry (CSG) is based on this recognition. CSG was the traditional way of solid modeling. The construction method is also applied in advanced part modeling. While the traditional method applied CSG data structure, present modeling methods generate boundary representation. This difference often causes misunderstanding around CSG. 

Closed line primitives (Figure 7-36a) can be combined by union (Figure 7-36b), difference (Figure 7-36c), and intersection (Figure 7-36d) operations similarly to constructive solid geometry. 

FIGURE 19.50 Various object representation schemes (a) wire-frame, (b) constructive solid geometry, (c) spatial occupancy, (d) surface-boundary, (e) generalized-cone, (f) aspect graph. 

Plastics with their inherent complex geometries are typically better suited to boundary representation models. Also functions such as finite element modeling or numerical control tool paths require explicit surface definitions which are only available with boundary representations. With constructive solid geometry systems, surface information must be evaluated before it is user accessible. Wireframe models again may be used as the base and are easily transferred to a boundary representation system. Conversely a boundary representation model may be readily converted to a wireframe. Many current commercial systems combine the features of both constructive solid geometry and boundary representation. A project consisting of simple machineable shapes may be done faster in a constructive solid geometry mode while a sculptured surface model would be more easily created in a boundary representation mode. The separate models can... 

It was stated that there is a need to understand the contents of a CAD data base. However, the contents of a particular data base may only reflect, for example, the input of the user in creating a particular model. In the case of high level representation schemes, such as used in constructive solid geometry (CSG) modelers, this is a suitable method of transferring the information. This is not always the case, however, since many geometric model data bases contain purely geometric and other associated information. The point to be made here is that the neutral transfer mechanism must cater not only for high level representations, but also the very lowest level of data. A further point to be made is that the neutral file is not a copy of a particular data base. It contains all the relevant data in such a way that here is no loss of information. 

Two principal representations are supported, namely Boundary Representation (B-rep) and Constructive Solid Geometry (CSG). 

Primitives for constructive solid geometry 5.9.6.1 PLAN AR H ALFSPACE... 

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