AMS 345/CSE 355 (Spring, 2009)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Set # 2
Due at the beginning of class on Wednesday, February 18, 2009.
Recommended Reading: O’Rourke, Chapter 1 (sections 1.3–1.6) and Chapter 2 (sections 2.1–2.2).
Reminder:
In all of the exercises, be sure to give at least a brief explanation or justification
for each claim that you make.
(1).
[20 points] (Based on
O’Rourke, problem 3, section 1.3.9, page 24.
) A simple polygon
P
is
specified by a list of vertices,
v
0
,v
1
,...,v
n
.
While we generally assume that the list is given in
counterclockwise (ccw) orientation, in practice the list is often given in either orientation (cw or
ccw). Using the proof of Lemma 1.2.1 (
Every polygon must have at least one strictly convex vertex
)
to guide your thought process, give an efficient algorithm to test the orientation of the sequence
v
0
,v
1
,...,v
n
of vertices of a simple polygon: Your algorithm should determine if the orientation is
cw or ccw. What is the efficiency (running time in terms of bigOh notation, as a function of
n
)?
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 Spring '08
 Mitchell,J
 Computer program, Line segment, Diagonal

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