1. In practice, testing each point in a polygon to determine whether it is inside or outside the polygon is extremely inefficient. Describe the general strategies that you might pursue to avoid point-by-point testing.

2. Devise a test to determine whether a two-dimensional polygon is simple.

3. In Section 2.4, we saw that in computer graphics we can specify polygons using lists of vertices.Why might it be better to define polygons by their edges? Hint: Consider how you might represent a mesh efficiently.

4. Devise a test for the convexity of a two-dimensional polygon.