ABSTRACT
Boolean operations are named after George Boole, an English mathematician who described logical operations in terms of mathematical symbols. A Boolean operation typically affects two objects at any one time, and is the basis of the binary systems that underlie most of computing. Boolean operations are absolutely fundamental in CAD, and allow the creation of complex forms and compositions by their successive application to objects that may initially be quite simple. Several of the later case studies illustrate just how important they are in generating form (e.g. chapter 20). Learning how to think in terms of applying successive Boolean operations to generate a particular form is essential for CAD users. The Boolean operations that can be performed between the 2-D objects A and B are as follows:
Add (sometimes referred to as Union) joins objects A and B together.
Add combines overlapping objects (polygons) and deletes line segments in the overlapping region. In terms of the CAD system, the first object (polygon) selected is the altered object (polygon) that remains after the operation. The second object (polygon) is deleted.
Subtract subtracts the second selected object (a 2-D polygon in this example) from the first.
Subtraction (A–B) subtracts object B from A
Subtraction (B–A) subtracts object A from B (illustrated opposite)
Intersect leaves the difference between objects A and B. Intersection deletes all but the overlapping portions of the two objects (polygons). The first object (polygon) selected is the altered object (polygon) that remains after the operation. The second object (polygon) is deleted.
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