(******************************************************************************
 ** SIDE.sml
 ** sml
 **
 ** Franklin Chen and Guy Blelloch 
 ** The SIDE signature
 ******************************************************************************)

(* This signature defines a three valued logic to deal with regions of
  space.  The values of Side.t are in (inside), on (on the boundary) and
  out (outside).  Many of the functions in other signatures return one
  of these values (e.g. Halfspace.pointIn). *)

signature SIDE =
    sig

	datatype t = In | On | Out

        val == : t * t -> bool
        val != : t * t -> bool
        val toString : t -> string

	(* Converts LESS to In, EQUAL to On, and GREATER to Out *)
        val fromOrder : order -> t
        val toOrder : t -> order

	(* In if both inputs are In, On if one input is On and the
	 the other is On or In, and Out otherwise *)
	val intersection : t * t -> t

	(* In if either input is In, On if one input is On and the
	 the other is On or Out, and Out otherwise *)
	val union : t * t -> t

	(* In to Out, Out to In, and On to On *)
	val complement : t -> t

	(* True if both inputs are In, both inputs are Out, or 
       	 either input is On *)
	val sameSide : t * t -> bool

    end