Computer Aided Engineering Design

COMPUTATIONS FOR GEOMETRIC DESIGN 291

(a) Intersect all edges in A with that of B and vice versa and split them into segments if they
intersect. Place all these edge segments keeping the order of vertices consistent with the
polygon representation (left side representing the interior) into two lists corresponding to
polygonsA and B, respectively. This is illustrated in Figure 9.19 (a).
(b) For all edges in list 1 (that of polygon A), classify them as in,on or out of polygon B. This may
be accomplished by doing a point membership classification of the mid-point of each edge
segment in polygon B. Do a similar classification of edges in list 2 with polygon A. The step
is illustrated in Figure 9.19 (b). The line code followed is thick solid for on, thin solid for in and
dashed for out.
(c) Collect the edges representing the closed region after a regularized Boolean operation as
following:

AB

(a) (b)

A B

A∪*B A∩*B

(c) (d)

A

B

(e) (f)

A – *B

Figure 9.19 Regularized Boolean operations on polygons A and B

A

B

A

B

Figure 9.18 Boolean interaction between polygons A and B