Colinear Contact Points Define Edges or Edge Segments

Consider three colinear contact points p1, p2, p3 as shown in the diagram below. As explained before, these three points are part of the bounding polygon. By definition of a convex polygon, these three point must be part of a single edge or edge segment of the bounding polygon. Moreover, the infinite line described by the three points automatically discards points on its exterior side into the outside set. As we will see in later sections this property allows us to verify our hypothesis about the shape of the polygon. This diagram illustrates this observation. 

Probe Paths Define the Outside Set

Summary