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# Geometry for Modeling and Design

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## 4.16 Solid Primitives

Many 3D objects can be visualized, sketched, and modeled in a CAD system by combining simple 3D shapes or primitives. They are the building blocks for many solid objects. You should become familiar with these common shapes and their geometry. The same primitives that are useful when sketching objects are also used to create 3D models of those objects.

A common set of primitive solids used to build more complex objects is shown in Figure 4.57. Which of these objects are polyhedra? Which are bounded by single-curved surfaces? Which are bounded by double-curved surfaces? How many vertices do you see on the cone? How many on the wedge? How many edges do you see on the box? Familiarity with the appearance of these primitive shapes when shown in orthographic views can help you in interpreting drawings and in recognizing features that make up objects. Figure 4.58 shows the primitives in two orthographic views. Review the orthographic views and match each to the isometric of the same primitive shown in Figure 4.57.

Look around and identify some solid primitives that make up the shapes you see. The ability to identify the primitive shapes can help you model features of the objects using a CAD system (see Figure 4.59). Also, knowing how primitive shapes appear in orthographic views can help you sketch these features correctly and read drawings that others have created.

### Making Complex Shapes with Boolean Operations

Boolean operations, common to most 3D modelers, allow you to join, subtract, and intersect solids. Boolean operations are named for the English mathematician George Boole, who developed them to describe how sets can be combined. Applied to solid modeling, Boolean operations describe how volumes can be combined to create new solids.

The three Boolean operations, defined in Table 4.1, are

• Difference (subtract)

• Intersection

#### Table 4.1 Boolean Operations

Figure 4.61 illustrates the result of the Boolean operations on three pairs of solid models. Look at some everyday objects around you and make a list of the primitive solid shapes and Boolean operations needed to make them.

Figure 4.62 shows a bookend and a list of the primitives available in the CAD system used to create it, along with the Boolean operations used to make the part.