INTERFACE RT2;

(* 
  Real oriented projective geometry in two dimensions.
  Created 93-04-18 by Marcos C. Carrard.
  Based on H3.pas by J. Stolfi.
  Last edited by stolfi *)
   
IMPORT R2, R3, R3x3;

TYPE
  Point = RECORD c: R3.T END;  (* c[0..2] are coords [w,x,y]. *)
  Line =  RECORD f: R3.T END;  (* f[0..2] are coeffs <W,X,Y>. *)
  Sign =  [-1..1];
  
PROCEDURE FromCartesian(READONLY c: R2.T): Point;
  (*
    Point on "hither" side of space (i.e, with positive weight) whose 
    Cartesian coordinates are "c". *)
    
PROCEDURE ToCartesian(READONLY p: Point): R2.T;
  (*
    Cartesian coordinates of point "p" (which must be finite). *)

PROCEDURE Test(READONLY p: Point; READONLY Q: Line): Sign; 
  (*
    Returns sign of point "p" relative to line "Q": 0 on the line,
    +1 in positive halfplane, -1 in negative halfplane.
    May give inconsistent results for points very close to the line. *)

PROCEDURE Join(READONLY p, q: Point): Line;
  (*
    Return the line through "p" and "q". *)

PROCEDURE Meet(READONLY P, Q: Line): Point;
  (*
    Return the point common to "P" and "Q". *)

PROCEDURE Dir(READONLY frm, tto: Point): R2.T;
  (*
    Direction (a unit-length vector) of point "tto" seen from point "frm".
    Works even if one of them is at infinity.  Does not work if both
    are at infinity, or coincident, or antipodal. *)
    
PROCEDURE Normal(READONLY P: Line): R2.T;
  (*
    The normal direction of line "P", on the hither side of T3, pointing into 
    "P"'s positive halfspace.  Assumes "P" is not the line at infinity. *)
    
(* PROJECTIVE MAPS *)

TYPE
  PMap =  RECORD dir: R3x3.T; inv: R3x3.T END;  
    (* 
      "dir" is the map's matrix, "inv" is its inverse. *)

PROCEDURE MapPoint(READONLY p: Point; READONLY m: PMap): Point;
  (*
    Applies projective map "m" to point "p". *)

PROCEDURE MapLine(READONLY P: Line; READONLY m: PMap): Line;
  (*
    Applies projective map "m" to line "P" *)

PROCEDURE CompMap(READONLY m, n: PMap): PMap;
  (* 
    Returns the composition of "m" and "n", applied in that order *)

END RT2.