Contact Points Define The Inside Set

The first source of information is the set of contact points. These points are the result of a contact between a probe and the shape. A contact point is either a vertex of the bounding polygon or part of one of its edges. Now remember that the shape under investigation is known to be convex. It follows that any point within the convex hull of the contact points must be part of the shape. The convex hull is the smallest polygon enclosing the points in a set thus an additional vertex inside the convex hull would inevitably lead to a non convex boundary. As a result of this property, the convex hull defines the boundary of the inside set. The following diagram shows the convex hull and the inside set resulting from a series of 5 probes.

Classification of Points

Probe Paths Define the Outside Set