**6.5 CAD solid modelling – Middle end**

The mathematics used in the solid model ensures the reality of constructive geometric entity modelled. The solid model performs mathematical methods to validate real possibility of the existence of the modelled geometry. Because of this geometric validation, among other factors, a CAD solid model is great limitations to the modelling of complex shapes, such as, for example, a computer mouse, the panel of a car, bottle packaging, among others objects. There are difficulties in parts of issues surface in the tangent of specific points and ensuring continuity. To work with geometries with these characteristics, a CAD modeller surfaces may be more appropriate.

A CAD solid model should possess the following characteristics:


CAD systems have advanced graphical tools to detect such discontinuities in a surface. Figure 25b illustrates a surface with discontinuities. The CAD system identifies the discrete regions through hazards. The parallel strips and gently represent regions consistent with good degree of continuity. The discrete regions are illustrated by the tracks with abrupt changes (Figure 25c). This may occur for mathematical limitations and / or the method used to construct the surface. The surface of Figure 25 (b and c) is a surface Fillet, calculated

(a) Product (b) Discontinuous surface (c) Abrupt changes in gray bands

The abrupt changes of the bands indicate regions with continuity compromised. However, after identifying these regions and/or surfaces, CAD systems are still not able to help troubleshoot the problem. The reasons that caused specific discontinuities are not presented. Thus, the user must develop empirical ability to solve or minimize the problem. In the case illustrated in Figure 25, the surface of agreement (Fillet) was calculated by the software with a large number of longitudinal and lateral, creating the problem of continuity observed. Performing a work setting "manual" to delete longitudinal and lateral, it was observed an

The mathematics used in the solid model ensures the reality of constructive geometric entity modelled. The solid model performs mathematical methods to validate real possibility of the existence of the modelled geometry. Because of this geometric validation, among other factors, a CAD solid model is great limitations to the modelling of complex shapes, such as, for example, a computer mouse, the panel of a car, bottle packaging, among others objects. There are difficulties in parts of issues surface in the tangent of specific points and ensuring continuity. To work with geometries with these characteristics, a CAD modeller surfaces

Fig. 25. Surface emphasized the problem of discontinuity

A CAD solid model should possess the following characteristics:

Generation of simple objects (compared to the models of surfaces).

improvement in continuity of surface.

**6.5 CAD solid modelling – Middle end** 

Geometry unambiguous and real.

Suitable for engineering geometry.

may be more appropriate.

automatically by the software.

Different computational techniques for solid modelling. The internal representation of a solid object is commonly used to classify the modeller. The internal representation is how the software stores the model. This is different from the external representation, which presents the model on the computer screen. Two techniques of internal representation are: a) B-Rep (Boundary Representation). This representation employs models described by boundaries, proposed by Ian Braid, Cambridge University. b) CSG (Constructive Solid Geometry). This method was proposed by Voelcker and Requicha the University of Rochester.

Both methods were applied in commercial systems in the late 70's. Other methods of representation of solids were developed, such as octree, quadtree, cell breakdown, among others. However, the methods of representation of solids used in most current CAD systems are the CSG (Constructive Solid Geometry) and B-Rep (Boundary Representation).

In this method, solid objects are built with a combination of simple solid primitives such as cylinders, cubes, cones, spheres, etc. Through Boolean operations (George Boole, 1815-1864, developed the Boolean algebra) addition, subtraction and intersection between solid objects in case of CAD software. When an object is constructed with a CSG modeller, the system saves a history of creation (creating topographic tree), which includes all solid primitives with their size and positioning, and information about all the Boolean operations used to construct the object.
