The outer CCB of a face of an arrangement is NOT necessarily a simple polygon. Consider the CASE where there are "inner antennas"; imagine a face represented by a simple polygon and a vertex v on the outer CCB of the face. Now connect a COMPONENT that starts and ENDS at v and lies in the interior of the face (one edge incident at v suffices).

MIND that if you are using an inexact number TYPE you might get a non-simple polygon even if the outer CCB represents one due to numerical errors.

The outer CCB of a face of an arrangement is NOT necessarily a simple polygon. Consider the case where there are "inner antennas"; imagine a face represented by a simple polygon and a vertex v on the outer CCB of the face. Now connect a component that starts and ends at v and lies in the interior of the face (one edge incident at v suffices).

Mind that if you are using an inexact number type you might get a non-simple polygon even if the outer CCB represents one due to numerical errors.