Cyber-Physical Systems

242 Cyber-Physical Systems: From Theory to Practice

algorithm does not start the new segment with the initial condition x

i

−  ≤ y

i

≤ x

i

+ , where y

i

is

the value of the left endpoint of the new segment. Instead, a smaller range on y

i

is set to guarantee the

connectivity of two consecutive segments. Specifically, to decide the range of y

i

, the last nonempty

polygon intersection in the previous point is used.

Suppose points x

1

, ..., x

j−1

are checked but have not been compressed yet, that is, poly(1, 2) ∩

···∩poly(1, j −1) = ∅. The exact intersection of the parallelograms is kept. The intersection is used

to confine the range of y

j

. Apparently, as the