INTERFACE RT3;

(* 
  Oriented projective geometry in three dimensions.
  Created 93-04-18 by Marcos C. Carrard.
  Based on H3.pas by J. Stolfi.
  Last edited by stolfi *)
   
IMPORT R3, R4, R4x4;

TYPE
  Point = RECORD c: R4.T END;  (* c[0..3] are coords [w,x,y,z]. *)
  Plane = RECORD f: R4.T END;  (* f[0..3] are coeffs <W,X,Y,Z>. *)
  Sign =  [-1..1];
  
PROCEDURE FromCartesian(READONLY c: R3.T): Point;
  (*
    Point on "hither" side of space (i.e, with positive weight) whose 
    Cartesian coordinates are "c". *)
    
PROCEDURE ToCartesian(READONLY p: Point): R3.T;
  (*
    Cartesian coordinates of point "p" (which must be finite). *)

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

PROCEDURE Join(READONLY p, q, r: Point): Plane;
  (*
    Return the plane through "p", "q", and "r". *)

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

PROCEDURE Dir(READONLY frm, tto: Point): R3.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: Plane): R3.T;
  (*
    The normal direction of plane "P", on the hither side of T3, pointing into 
    "P"'s positive halfspace.  Assumes "P" is not the plane at infinity. *)
    
(* PROJECTIVE MAPS *)

TYPE
  PMap =  RECORD dir: R4x4.T; inv: R4x4.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 MapPlane(READONLY P: Plane; READONLY m: PMap): Plane;
  (*
    Applies projective map "m" to plane "P" *)

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

PROCEDURE PerspMap(READONLY obs, foc, upp: Point): PMap;
  (* 
    Computes a perspective transformation with given viewing parameters.
      obs => the scenesys coords of imagesys (0,0,d) (observer)
      foc => the scenesys coords of imagesys (0,0,0) (image focus)
      up  => the scenesys coords of some point with imagesys X = 0 (up reference). *)

END RT3.