1. (de Berg et al. ex. 6.14): Suppose we wish to do point location on
   the surface of the earth. How would you define a spherical
   subdivision--a subdivision of the surface of a sphere? Give a point
   location structure for such a subdivision.

2. (de Berg et al. ex. 6.12): Use a plane sweep argument to prove that
   the trapezoidal map of n line segments in general position (no two
   sharing an endpoint, no two endpoints having the same x coordinate)
   has at most 3n+1 trapezoids. That is, imagine a vertical line
   sweeping the plane from left to right, stopping at all endpoints of
   segments. Count the number of trapezoids that are encountered by the
   sweep line. Your analysis should have separate cases for two kinds of
   events: the sweep line crossing the left and right endpoints of
   segments.