Design the classes' interaction: aggregation or duplication?

I have the two separate classes:

class RecTarget : public Target /* Abstract class */
{ /* The Points are located in a form of Rectangle */

  std::set<Point> Set;
  /* I've chosen the std::set to easy searching, 
   * "is the hit to Target is success?"
   */

  /* ... */
};

class Moves
{ std::map< Point*, std::list<WayToGetTheHit> > hmoves;
  /* This class monitors and saves the moves to hit
   * for each Point of Target.
   */
   Target* target; /* Aggregation? */
   /* ... */
};

What is the best design way? Must I use an aggregation for correct handle the situation (Point* pointers to target->Set->Point), or must I duplicate all of the Points in this class instead of links to existing Points in Target? Or something else???

Thank you, in advance.