36 AutoCAD and Its Applications—Advanced Copyright Goodheart-Willcox Co., Inc. group are called Boolean operations. George Boole (1815–1864) was an English math- ematician who developed a system of mathematical logic where all variables have the value of either one or zero. Boole’s two-value logic, or binary algebra, is the basis for the mathematical calculations used by computers and, with respect to modeling, for those required in the construction of composite solids. NOTE NOTE Boolean operations used to create composite solids can also be used on meshes that have been converted to solids. See Chapter 9 for a complete discussion of meshes. Joining Two or More Solid Objects The UNION command is used to combine solid objects, Figure 2-19. The solids do not need to touch or intersect to form a union. Therefore, accurately locate the prim- itives when drawing them. After selecting the objects to join, press [Enter] and the action is completed. In the examples shown in Figure 2-19B, notice that lines, or edges, are shown at the new intersection points of the joined objects. This is an indication that the features are one object, not separate objects. Subtracting Solids The SUBTRACT command allows you to remove the volume of one or more solids from another solid. Several examples are shown in Figure 2-20. The fi rst object selected in the subtraction operation is the object from which volume is to be subtracted. The next object is the object to be subtracted from the fi rst. The completed object will be a new solid. If the result is the opposite of what you intended, you may have selected the objects in the wrong order. Just undo the operation and try again. Creating New Solids from the Intersection of Solids When solid objects intersect, the overlap forms a common volume, a space that both objects share. This shared space is called an intersection. An intersection (common volume) can be made into a composite solid using the INTERSECT command. Figure 2-21 shows several examples. A solid is formed from the common volume. The original objects are removed. UNION Ribbon Home Solid Editing Solid Boolean Solid, Union Type UNION UNI SUBTRACT Ribbon Home Solid Editing Solid Boolean Solid, Subtract Type SUBTRACT SU INTERSECT Ribbon Home Solid Editing Solid Boolean Solid, Intersect Type INTERSECT IN A B Figure 2-19. A—The solid primitives shown here have areas of intersection and overlap. B—Composite solids after using the UNION command. Notice the lines displayed where the previous objects intersected.