MODULE Triangle;

(* Procedures and predicates for 
   triangles. *)

IMPORT Math, R2, Geometry, PS, Angle;

PROC Draw(a, b, c) IS 
  IF 
    PS.MoveTo(a); 
    PS.LineTo(b); 
    PS.LineTo(c); 
    PS.Close() 
  FI 
END;

UI PointTool(Draw);

(* Add the closed triangle on the 
   vertices "a", "b", and "c" to 
   the current path. *)

FUNC p = OutCenter(a, b, c) IS 
  (b, p) CONG (p, a) AND 
  (a, p) CONG (p, c) 
END;

UI PointTool(OutCenter);

(* "p" is the center of the circle 
   circumscribing the triangle 
   "abc". *)

FUNC p = InCenter(a, b, c) IS 
  Angle.OnBisector(p, a, b, c) AND 
  Angle.OnBisector(p, b, a, c) 
END;

UI PointTool(InCenter);

(* "p" is the center of the circle 
   inscribed in the triangle "abc". 
*)

FUNC res = Area(a, b, c) IS 
  (E ab = R2.Minus(b, a),
     ac = R2.Minus(c, a), 
     det = R2.Det(ab, ac) :: 
    res = Math.Abs(det) / 2) 
END;

(* "res" is the area of the 
   triangle "abc". *)