COMPUTATIONAL GEOMETRY, COMP 163, HOMEWORK 1
– Due: Tuesday, September 29 (in class, or by email)
Assume general position.
1. Given a set S of n points, and a point x not in S, describe how to
determine if x is inside the convex hull of S, without computing the
entire hull.
2. Given a simple n-gon P , and a point x not on the boundary of P , find
a ray from x that intersects the boundary of P as few times as possible,
in O(n log n) time.
3. Given a point set S, a quadrangle is a polygon formed by 4 vertices of
S, such that its interior contains no other points from S.
To quadrangulate S means to partition the area enclosed by the convex
hull of S into disjoint quadrangles.
Prove that S can be quadrangulated if the number of points on the
convex hull of S is even and greater than 3.