(* --------------------------------------------------- 
     Por odem do Stolfi, nao usaremos Union-Find   
     na manipulacao das esquinas de uma borda   
PROCEDURE BorderOf(self: Corner) : Border =
  BEGIN
    WITH
      b = self.border,      (* "b" = border's record refered by "self"         *)
      c = b.borderDesc(),   (* "c" = corner descriptor of the border of "self" *)
      d = c.border          (* "d" = border's record refered by "c"            *) 
    DO
      IF d # b THEN     
      (* border's records refered by "self" and by "c" are different;
         so, update the field "border" of "self" to refer to "d"
         directly -- heuristic path compression *)
         b.removeCorner(self);
         d.insertCorner(self);
      END;
      RETURN d
    END 
  END BorderOf;
---------------------------------------------------  *)


(* --------------------------------------------------- 
     Por odem do Stolfi, nao usaremos Union-Find   
     na manipulacao das esquinas de uma borda   

PROCEDURE AreInSameBorder(self: Corner; c : Corner) : BOOLEAN =
  BEGIN
    WITH 
      cbd = c.borderOf().borderDesc(),
      csbd = c.sym().borderOf().borderDesc(),
      sbd = self.borderOf().borderDesc()
    DO 
      RETURN sbd = cbd OR sbd = csbd
    END
  END AreInSameBorder;
---------------------------------------------------  *)