.
This exercise shows how to perform cycle decomposition in two
dimensions, again using. Redra just as you did in Exercise
8, with points 0 and 8 added, and ia and ib labels.
a. In the two-dimensional area, use solid lines to connect adjacent segments
in the order that they occur in x. (Connect 0 to 1a and 7b to 8 with arcs
that are concave downward.)
b. Use broken lines to connect adjacent segments in the order that they occur
in y3. (Connect 0 to 1a and 7b to 8 with arcs that are concave upward)
c. Now remove all segments 1–7 (corresponding to our not connecting the
ia and ib vertices when i is the same). Decompose the composite set of
broken and solid lines into disjoint cycles. (Cycles will contain both solid
and broken lines.) Use the number of cycles to compute d(x, y3). Does
this agree with the result of Exercise 7c and the number of reversals used
to produce y3 in the simulation?