Copyright (C) 1992, Digital Equipment Corporation
All rights reserved.
See the file COPYRIGHT for a full description.
Last modified on Tue May 17 21:13:45 PDT 1994 by mhb
modified on Tue Jun 16 16:46:22 PDT 1992 by muller
MODULE RealRect;
IMPORT Interval, RealPoint, Axis, RealInterval, Rect;
<* FATAL Error, RealInterval.Error *>
TYPE
RefT = REF T;
PtrT = UNTRACED REF T;
RefArrayT = REF ARRAY OF T;
PtrArrayT = UNTRACED REF ARRAY OF T;
PROCEDURE FromEdges (w, e, n, s: REAL): T RAISES {} =
VAR r: T;
BEGIN
IF (w >= e) OR (n >= s) THEN RETURN Empty; END;
r.west := w;
r.east := e;
r.north := n;
r.south := s;
RETURN r;
END FromEdges;
PROCEDURE FromAbsEdges (w, e, n, s: REAL): T RAISES {} =
VAR r: T;
BEGIN
IF (w = e) OR (n = s) THEN RETURN Empty; END;
IF (w < e) THEN
r.west := w;
r.east := e;
ELSE
r.west := e;
r.east := w;
END;
IF (n < s) THEN
r.north := n;
r.south := s;
ELSE
r.north := s;
r.south := n;
END;
RETURN r;
END FromAbsEdges;
PROCEDURE Float(READONLY r: Rect.T): T =
VAR s: T;
BEGIN
IF Rect.IsEmpty(r) THEN RETURN Empty END;
s.west := RealInterval.Float(Interval.T{r.west, r.east}).lo;
s.east := RealInterval.Float(Interval.T{r.west, r.east}).hi;
s.north := RealInterval.Float(Interval.T{r.north, r.south}).lo;
s.south := RealInterval.Float(Interval.T{r.north, r.south}).hi;
RETURN s
END Float;
PROCEDURE Floor(READONLY r: T): Rect.T =
VAR s: Rect.T;
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RETURN Rect.Empty END;
s.west := RealInterval.Floor(RealInterval.T{r.west, r.east}).lo;
s.east := RealInterval.Floor(RealInterval.T{r.west, r.east}).hi;
s.north := RealInterval.Floor(RealInterval.T{r.north, r.south}).lo;
s.south := RealInterval.Floor(RealInterval.T{r.north, r.south}).hi;
RETURN s
END Floor;
PROCEDURE Round(READONLY r: T): Rect.T =
VAR s: Rect.T;
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RETURN Rect.Empty END;
s.west := RealInterval.Round(RealInterval.T{r.west, r.east}).lo;
s.east := RealInterval.Round(RealInterval.T{r.west, r.east}).hi;
s.north := RealInterval.Round(RealInterval.T{r.north, r.south}).lo;
s.south := RealInterval.Round(RealInterval.T{r.north, r.south}).hi;
RETURN s
END Round;
PROCEDURE FromPoint (READONLY p: RealPoint.T): T RAISES {} =
BEGIN
RETURN FromEdges (p.h, p.h, p.v, p.v);
END FromPoint;
PROCEDURE FromCorners (READONLY p, q: RealPoint.T): T RAISES {} =
BEGIN
RETURN FromAbsEdges (p.h, q.h, p.v, q.v);
END FromCorners;
PROCEDURE FromCorner (READONLY p: RealPoint.T;
hor, ver: REAL): T RAISES {} =
VAR r: T;
BEGIN
IF (hor < 0.0) OR (ver < 0.0) THEN RETURN Empty; END;
r.west := p.h;
r.east := p.h + hor;
r.north := p.v;
r.south := p.v + ver;
RETURN r;
END FromCorner;
PROCEDURE FromSize (hor, ver: REAL): T RAISES {} =
VAR r: T;
BEGIN
IF (hor < 0.0) OR (ver < 0.0) THEN RETURN Empty; END;
r.west := 0.0;
r.east := hor;
r.north := 0.0;
r.south := ver;
RETURN r;
END FromSize;
PROCEDURE Center (READONLY r: T; READONLY p: RealPoint.T): T RAISES {} =
VAR res: T; h, v: REAL;
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RETURN Empty END;
h := p.h - ((r.west + r.east)/2.0);
v := p.v - ((r.north + r.south)/2.0);
res.west := r.west + h;
res.east := r.east + h;
res.north := r.north + v;
res.south := r.south + v;
RETURN res
END Center;
PROCEDURE FromIntervals (READONLY hor, ver: RealInterval.T): T RAISES {} =
VAR r: T;
BEGIN
IF (hor.lo > hor.hi) OR (ver.lo > ver.hi) THEN RETURN Empty; END;
r.west := hor.lo;
r.east := hor.hi;
r.north := ver.lo;
r.south := ver.hi;
RETURN r;
END FromIntervals;
PROCEDURE FromAxes (axis: Axis.T; READONLY n, m: RealInterval.T): T RAISES {} =
VAR r: T;
BEGIN
IF (n.lo > n.hi) OR (m.lo > m.hi) THEN RETURN Empty END;
IF (axis = Axis.T.Hor) THEN
r.west := n.lo;
r.east := n.hi;
r.north := m.lo;
r.south := m.hi;
ELSE
r.west := m.lo;
r.east := m.hi;
r.north := n.lo;
r.south := n.hi;
END;
RETURN r
END FromAxes;
PROCEDURE NorthWest (READONLY r: T): RealPoint.T RAISES {} =
VAR p: RealPoint.T;
BEGIN
p.h := r.west;
p.v := r.north;
RETURN p;
END NorthWest;
PROCEDURE NorthEast (READONLY r: T): RealPoint.T RAISES {} =
VAR p: RealPoint.T;
BEGIN
p.h := r.east;
p.v := r.north;
RETURN p;
END NorthEast;
PROCEDURE SouthWest (READONLY r: T): RealPoint.T RAISES {} =
VAR p: RealPoint.T;
BEGIN
p.h := r.west;
p.v := r.south;
RETURN p;
END SouthWest;
PROCEDURE SouthEast (READONLY r: T): RealPoint.T RAISES {} =
VAR p: RealPoint.T;
BEGIN
p.h := r.east;
p.v := r.south;
RETURN p;
END SouthEast;
PROCEDURE GetVertex (v: Vertex; READONLY r: T): RealPoint.T RAISES {} =
BEGIN
IF (r.west >= r.east)(* OR (r.north>=r.south) *) THEN
RETURN RealPoint.Origin;
END;
CASE v OF
| Vertex.NW => RETURN NorthWest (r);
| Vertex.NE => RETURN NorthEast (r);
| Vertex.SW => RETURN SouthWest (r);
| Vertex.SE => RETURN SouthEast (r);
END;
END GetVertex;
PROCEDURE HorSize (READONLY r: T): REAL RAISES {} =
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RETURN 0.0 END;
RETURN r.east - r.west;
END HorSize;
PROCEDURE VerSize (READONLY r: T): REAL RAISES {} =
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RETURN 0.0;
ELSE RETURN r.south - r.north END
END VerSize;
PROCEDURE Size (a: Axis.T; READONLY r: T): REAL RAISES {} =
BEGIN
CASE a OF
| Axis.T.Hor => RETURN HorSize (r);
| Axis.T.Ver => RETURN VerSize (r);
END;
END Size;
PROCEDURE DiagSizeSquare (READONLY r: T): REAL RAISES {} =
VAR hor, ver: REAL;
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RETURN 0.0 END;
hor := HorSize (r);
ver := VerSize (r);
RETURN hor * hor + ver * ver;
END DiagSizeSquare;
PROCEDURE Middle (READONLY r: T): RealPoint.T RAISES {} =
VAR p: RealPoint.T;
BEGIN
IF (r.west > r.east)(* OR (r.north > r.south) *) THEN
RETURN RealPoint.Origin;
END;
p.h := (r.west + r.east)/2.0;
p.v := (r.north + r.south)/2.0;
RETURN p;
END Middle;
PROCEDURE PickEdge (READONLY r: T; READONLY p: RealPoint.T): Edge RAISES {} =
VAR mid, se, q: RealPoint.T; a, b: REAL;
BEGIN
mid := Middle (r);
se := RealPoint.Sub (SouthEast (r), mid);
q := RealPoint.Sub (p, mid);
a := se.v * q.h;
b := se.h * q.v;
IF a >= b THEN
IF -a >= b THEN RETURN Edge.N ELSE RETURN Edge.E END;
ELSE
IF -a >= b THEN RETURN Edge.W ELSE RETURN Edge.S END;
END;
END PickEdge;
PROCEDURE PickVertex (READONLY r: T;
READONLY p: RealPoint.T): Vertex RAISES {} =
VAR q: RealPoint.T;
BEGIN
q := RealPoint.Sub (p, Middle (r));
IF q.h > 0.0 THEN
IF q.v > 0.0 THEN RETURN Vertex.SE ELSE RETURN Vertex.NE END;
ELSE
IF q.v > 0.0 THEN RETURN Vertex.SW ELSE RETURN Vertex.NW END;
END;
END PickVertex;
PROCEDURE Project (READONLY r: T; READONLY p: RealPoint.T): RealPoint.T RAISES {} =
VAR res: RealPoint.T;
BEGIN
<* ASSERT r.east > r.west *>
IF (r.west > r.east) OR (r.north > r.south) THEN RAISE Error END;
res.h := MAX (MIN (p.h, r.east), r.west);
res.v := MAX (MIN (p.v, r.south), r.north);
RETURN res
END Project;
PROCEDURE Add (READONLY r: T; READONLY p: RealPoint.T): T RAISES {Error} =
VAR s: T;
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RAISE Error END;
s.west := r.west + p.h;
s.east := r.east + p.h;
s.north := r.north + p.v;
s.south := r.south + p.v;
RETURN s;
END Add;
PROCEDURE Sub (READONLY r: T; READONLY p: RealPoint.T): T RAISES {Error} =
VAR s: T;
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RAISE Error END;
s.west := r.west - p.h;
s.east := r.east - p.h;
s.north := r.north - p.v;
s.south := r.south - p.v;
RETURN s;
END Sub;
PROCEDURE Move (READONLY r: T; READONLY p: RealPoint.T): T RAISES {Error} =
VAR s: T;
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RAISE Error END;
s.west := r.west + p.h;
s.east := r.east + p.h;
s.north := r.north + p.v;
s.south := r.south + p.v;
RETURN s;
END Move;
PROCEDURE MoveH (READONLY r: T; h: REAL): T RAISES {Error} =
VAR s: T;
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RAISE Error END;
s.west := r.west + h;
s.east := r.east + h;
s.north := r.north;
s.south := r.south;
RETURN s;
END MoveH;
PROCEDURE MoveV (READONLY r: T; v: REAL): T RAISES {Error} =
VAR s: T;
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RAISE Error END;
s.west := r.west;
s.east := r.east;
s.north := r.north + v;
s.south := r.south + v;
RETURN s;
END MoveV;
PROCEDURE MoveHV (READONLY r: T; h: REAL; v: REAL): T RAISES {Error} =
VAR s: T;
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RAISE Error END;
s.west := r.west + h;
s.east := r.east + h;
s.north := r.north + v;
s.south := r.south + v;
RETURN s;
END MoveHV;
PROCEDURE Scale(READONLY r: T; factor: REAL): T RAISES {} =
VAR s: T;
BEGIN
IF (r.west > r.east) OR (r.north > r.south)
OR (factor = 0.0) THEN
RETURN Empty
END;
IF factor > 0.0 THEN
s.north := r.north * factor;
s.south := r.south * factor;
s.west := r.west * factor;
s.east := r.east * factor;
ELSE
s.south := r.north * factor;
s.north := r.south * factor;
s.east := r.west * factor;
s.west := r.east * factor;
END;
RETURN s
END Scale;
PROCEDURE Inset (READONLY r: T; n: REAL): T RAISES {} =
VAR s: T;
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RETURN Empty; END;
s.west := r.west + n;
s.east := r.east - n;
s.north := r.north + n;
s.south := r.south - n;
RETURN s;
END Inset;
PROCEDURE Change (READONLY r: T; dw, de, dn, ds: REAL): T RAISES {} =
VAR s: T;
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RETURN Empty; END;
s.west := r.west + dw;
s.east := r.east + de;
s.north := r.north + dn;
s.south := r.south + ds;
RETURN s;
END Change;
PROCEDURE MoveEdge (READONLY r: T; e: Edge; dn: REAL): T RAISES {} =
VAR s: T;
BEGIN
s := r;
CASE e OF
| Edge.W => s.west := r.west + dn;
| Edge.E => s.east := r.east + dn;
| Edge.N => s.north := r.north + dn;
| Edge.S => s.south := r.south + dn;
END;
IF (s.west > s.east) OR (s.north > s.south) THEN RETURN Empty; END;
RETURN s;
END MoveEdge;
PROCEDURE MoveVertex (READONLY r: T; v: Vertex; READONLY dp: RealPoint.T): T
RAISES {} =
VAR s: T;
BEGIN
s := r;
CASE v OF
| Vertex.NW => s.west := r.west + dp.h; s.north := r.north + dp.v;
| Vertex.NE => s.east := r.east + dp.h; s.north := r.north + dp.v;
| Vertex.SW => s.west := r.west + dp.h; s.south := r.south + dp.v;
| Vertex.SE => s.east := r.east + dp.h; s.south := r.south + dp.v;
END;
IF (s.west > s.east) OR (s.north > s.south) THEN RETURN Empty; END;
RETURN s;
END MoveVertex;
PROCEDURE Stretch (READONLY r: T; axis: Axis.T; lo, hi: REAL): T RAISES {} =
VAR res: T;
BEGIN
IF (r.west > r.east)(* OR (r.north > r.south) *) THEN RETURN Empty; END;
IF axis = Axis.T.Hor THEN
res.north := r.north;
res.south := r.south;
res.west := lo;
res.east := hi
ELSE
res.north := lo;
res.south := hi;
res.west := r.west;
res.east := r.east
END;
RETURN res
END Stretch;
PROCEDURE Join (READONLY r, s: T): T RAISES {} =
VAR t: T;
BEGIN
IF (r.west > r.east)(* OR (r.north> r.south) *) THEN RETURN s; END;
IF (s.west > s.east)(* OR (s.north> s.south) *) THEN RETURN r; END;
t.west := MIN (r.west, s.west);
t.east := MAX (r.east, s.east);
t.north := MIN (r.north, s.north);
t.south := MAX (r.south, s.south);
RETURN t;
END Join;
PROCEDURE Meet (READONLY r, s: T): T RAISES {} =
VAR t: T;
BEGIN
t.west := MAX (r.west, s.west);
t.east := MIN (r.east, s.east);
IF t.west > t.east THEN RETURN Empty END;
t.north := MAX (r.north, s.north);
t.south := MIN (r.south, s.south);
IF t.north > t.south THEN RETURN Empty; END;
RETURN t;
END Meet;
PROCEDURE Extend (READONLY r: T; READONLY p: RealPoint.T): T RAISES {} =
BEGIN
RETURN Join (r, FromPoint (p));
END Extend;
PROCEDURE Chop (hv: Axis.T; READONLY r: T; n: REAL; VAR s, t: T) RAISES {} =
VAR
si, ti: RealInterval.T;
BEGIN
s := r;
t := r;
IF hv = Axis.T.Hor THEN
RealInterval.Chop(
RealInterval.T{r.west, r.east},
n,
si,
ti
);
s.west := si.lo; s.east := si.hi;
t.west := ti.lo; t.east := ti.hi;
IF s.east < s.west THEN s := Empty END;
IF t.east < t.west THEN t := Empty END;
ELSE
RealInterval.Chop(
RealInterval.T{r.north, r.south},
n,
si,
ti
);
s.north := si.lo; s.south := si.hi;
t.north := ti.lo; t.south := ti.hi;
IF s.south < s.north THEN s := Empty END;
IF t.south < t.north THEN t := Empty END;
END
END Chop;
This is what it really means:
PROCEDURE Factor(READONLY r, by: T; VAR f: Partition; dh, dv: INTEGER)
RAISES {}; VAR northIndex, westIndex: INTEGER; mid, temp: T; BEGIN IF dh >
0 THEN westIndex := 3 ELSE westIndex := 1 END; IF dv > 0 THEN northIndex
:= 4 ELSE northIndex := 0 END; Chop(Axis.Ver, r, by.north, f[northIndex],
temp); Chop(Axis.Ver, temp, by.south, mid, f[4 - northIndex]);
Chop(Axis.Hor, mid, by.west, f[westIndex], temp); Chop(Axis.Hor, temp,
by.east, f[2], f[4 - westIndex]); END Factor;
PROCEDURE Factor (READONLY r, by: T;
VAR f: Partition; dh, dv: REAL) RAISES {} =
VAR ix: INTEGER;
rw, re, rn, rs, bw, be, bn, bs: REAL;
BEGIN
WITH z = by DO
bw := z.west;
be := z.east;
bn := z.north;
bs := z.south
END;
WITH z = r DO
rw := z.west;
re := z.east;
rn := z.north;
rs := z.south
END;
IF (bw > be) OR (bn > bs)
OR (rw > re) OR (rn > rs)
OR (be < rw) OR (bw > re) OR (bs < rn) OR (bn > rs) THEN
(* Disjoint: *)
f[0] := Empty;
f[1] := Empty;
f[2] := r;
f[3] := Empty;
f[4] := Empty;
RETURN
END;
(* The rectangles have non-empty intersection *)
(* Chop parts above and below b, leave rest in rn, rs, rw, re: *)
IF dv > 0.0 THEN ix := 4 ELSE ix := 0 END;
IF rn < bn THEN
WITH z = f[ix] DO
z.west := rw; z.east := re; z.north := rn;
(* z.south := RealExtra.PRED(bn) *)
z.south := bn
END;
rn := bn;
ELSE
f[ix] := Empty;
END;
IF rs > bs THEN
WITH z = f[4 - ix] DO
z.west := rw; z.east := re;
(* z.north := RealExtra.SUCC(bs); *)
z.north := bs;
z.south := rs
END;
rs := bs
ELSE
f[4 - ix] := Empty
END;
(* Chop parts to the left and right of b: *)
IF dh > 0.0 THEN ix := 3 ELSE ix := 1 END;
IF rw < bw THEN
WITH z = f[ix] DO
z.north := rn; z.south := rs; z.west := rw;
(* z.east := RealExtra.PRED(bw) *)
z.east := bw
END;
rw := bw;
ELSE
f[ix] := Empty
END;
IF re > be THEN
WITH z = f[4 - ix] DO
z.north := rn; z.south := rs;
(* z.west := RealExtra.SUCC(be); *)
z.west := be;
z.east := re
END;
re := be;
ELSE
f[4 - ix] := Empty
END;
WITH z = f[2] DO
z.north := rn; z.south := rs; z.west := rw; z.east := re
END;
END Factor;
PROCEDURE Mod (READONLY p: RealPoint.T; READONLY r: T): RealPoint.T
RAISES {Error} =
VAR q: RealPoint.T;
BEGIN
IF (r.west > r.east) OR (r.north > r.south) THEN RAISE Error END;
q.h := RealInterval.Mod(p.h, RealInterval.T{r.west, r.west});
q.v := RealInterval.Mod(p.v, RealInterval.T{r.north, r.south});
RETURN q
END Mod;
PROCEDURE Equal (READONLY r, s: T): BOOLEAN RAISES {} =
BEGIN
RETURN
((r.west = s.west) AND (r.east = s.east) AND (r.north = s.north)
AND (r.south = s.south))
OR (((r.west > r.east) OR (r.north > r.south) )
AND ((s.west > s.east) OR (s.north > s.south) ))
END Equal;
PROCEDURE IsEmpty (READONLY r: T): BOOLEAN RAISES {} =
BEGIN
RETURN (r.west > r.east) OR (r.north > r.south);
END IsEmpty;
PROCEDURE Member (READONLY p: RealPoint.T; READONLY r: T): BOOLEAN RAISES {} =
BEGIN
RETURN (r.west <= p.h) AND (p.h <= r.east) AND (r.north <= p.v)
AND (p.v <= r.south);
END Member;
PROCEDURE Overlap (READONLY r, s: T): BOOLEAN RAISES {} =
BEGIN
RETURN (MAX (r.west, s.west) <= MIN (r.east, s.east))
AND (MAX (r.north, s.north) <= MIN (r.south, s.south));
END Overlap;
PROCEDURE Subset (READONLY r, s: T): BOOLEAN RAISES {} =
BEGIN
RETURN (r.west > r.east)
OR ((r.west >= s.west) AND (r.east <= s.east) AND (r.north >= s.north)
AND (r.south <= s.south));
END Subset;
PROCEDURE GlobToLoc (READONLY r: T;
READONLY p: RealPoint.T): RealPoint.T RAISES {} =
VAR q: RealPoint.T;
BEGIN
q.h := p.h - r.west;
q.v := p.v - r.north;
RETURN q;
END GlobToLoc;
PROCEDURE LocToGlob (READONLY r: T;
READONLY p: RealPoint.T): RealPoint.T RAISES {} =
VAR q: RealPoint.T;
BEGIN
q.h := p.h + r.west;
q.v := p.v + r.north;
RETURN q;
END LocToGlob;
PROCEDURE New (READONLY value: T): RefT =
VAR r: RefT;
BEGIN
r := NEW (RefT);
r^ := value;
RETURN r;
END New;
PROCEDURE NewArray
(size: CARDINAL; READONLY value: T(* := Empty*)): RefArrayT =
VAR arr: RefArrayT; i: CARDINAL;
BEGIN
arr := NEW (RefArrayT, size);
(* Assumes the allocator initializes to Empty automatically: *)
(*IF value # Empty THEN *)
FOR z := 0 TO size - 1 DO i := z; arr[i] := value END;
(*END;*)
RETURN arr
END NewArray;
PROCEDURE UntracedNew (READONLY value: T): PtrT =
VAR r: PtrT;
BEGIN
r := NEW (PtrT);
r^ := value;
RETURN r;
END UntracedNew;
PROCEDURE UntracedNewArray
(size: CARDINAL; READONLY value: T(* := Empty*)): PtrArrayT =
VAR arr: PtrArrayT; i: CARDINAL;
BEGIN
arr := NEW (PtrArrayT, size);
(* Assumes the allocator initializes to Empty automatically: *)
(*IF value # Empty THEN *)
FOR z := 0 TO size - 1 DO i := z; arr[i] := value END;
(*END; *)
RETURN arr
END UntracedNewArray;
PROCEDURE Compare (READONLY a, b: T): INTEGER =
BEGIN
IF (a.west < b.west) THEN RETURN -1 END;
IF (a.west > b.west) THEN RETURN +1 END;
IF (a.east < b.east) THEN RETURN -1 END;
IF (a.east > b.east) THEN RETURN +1 END;
IF (a.north < b.north) THEN RETURN -1 END;
IF (a.north > b.north) THEN RETURN +1 END;
IF (a.south < b.south) THEN RETURN -1 END;
IF (a.south > b.south) THEN RETURN +1 END;
RETURN 0;
END Compare;
PROCEDURE Lt (READONLY a, b: T): BOOLEAN =
BEGIN
IF (a.west < b.west) THEN RETURN TRUE END;
IF (a.west > b.west) THEN RETURN FALSE END;
IF (a.east < b.east) THEN RETURN TRUE END;
IF (a.east > b.east) THEN RETURN FALSE END;
IF (a.north < b.north) THEN RETURN TRUE END;
IF (a.north > b.north) THEN RETURN FALSE END;
IF (a.south < b.south) THEN RETURN TRUE END;
IF (a.south > b.south) THEN RETURN FALSE END;
RETURN FALSE;
END Lt;
PROCEDURE Eq (READONLY a, b: T): BOOLEAN =
BEGIN
RETURN Equal (a, b);
END Eq;
PROCEDURE Hash (READONLY a: T): INTEGER =
BEGIN
RETURN ROUND(100.0 * a.north * a.south);
END Hash;
BEGIN
END RealRect.