Copyright (C) 1994, Digital Equipment Corp.
A Rect.T is a set of points lying in a rectangle with its sides
parallel to the coordinate axes. The directions of the screen are
named after the compass points, with north at the top. A rectangle
rect contains a point pt if
pt.h is in [rect.west .. rect.east - 1] AND
pt.v is in [rect.north .. rect.south - 1]
We impose the restriction that if a rectangle contains no points,
then it must be equal as a record to Rect.Empty.
INTERFACE Rect;
IMPORT Axis, Interval, Point;
TYPE T = RECORD west, east, north, south: INTEGER END;
TYPE Edge = {W, E, N, S};
TYPE Vertex = {NW, NE, SW, SE};
CONST Empty = T {0,0,0,0}; (* An empty rectangle *)
CONST Full = T {FIRST(INTEGER), LAST(INTEGER), FIRST(INTEGER), LAST(INTEGER)};
(* The biggest possible rectangle *)
--- Initialization ---
PROCEDURE FromEdges(w, e, n, s: INTEGER): T;
If w >= e or n >= s return Empty, else return T{w,e,n,s}.
PROCEDURE FromAbsEdges(h1, h2, v1, v2: INTEGER): T;
Return
FromEdges(MIN(h1,h2), MAX(h1,h2),
MIN(v1,v2), MAX(v1,v2))
PROCEDURE FromPoint(READONLY p: Point.T): T;
Return the rectangle whose only element is p.
PROCEDURE FromCorners(READONLY p, q: Point.T): T;
Return FromAbsEdges(p.h,q.h,p.v,q.v).
PROCEDURE FromCorner(
READONLY p: Point.T;
hor, ver: CARDINAL): T;
Return FromEdges(p.h, p.h+hor, p.v, p.v+ver).
PROCEDURE FromSize(hor, ver: CARDINAL): T;
Return FromCorner(Point.Origin,hor,ver).
PROCEDURE Center(READONLY r: T; READONLY p: Point.T): T;
If r is empty then return Empty else return a rectangle s
such that Congruent(r, s) and Middle(s)=p.
PROCEDURE FromIntervals
(READONLY hor, ver: Interval.T): T;
Return FromEdges(hor.lo,hor.hi,ver.lo,ver.hi).
PROCEDURE FromAxes (axis: Axis.T; READONLY n, m: Interval.T): T;
If axis=Hor then FromIntervals(n,m), else FromIntervals(m,n)
--- Selection ---
PROCEDURE NorthWest(READONLY r: T): Point.T;
Return Point.T{r.west,r.north}.
PROCEDURE NorthEast(READONLY r: T): Point.T;
Return Point.T{r.east,r.north}.
PROCEDURE SouthWest(READONLY r: T): Point.T;
Return Point.T{r.west,r.south}.
PROCEDURE SouthEast(READONLY r: T): Point.T;
Return Point.T{r.east,r.south}.
PROCEDURE GetVertex (v: Vertex; READONLY r: T): Point.T;
the point corresponding to the vertex v of r; origin if r is empty
PROCEDURE HorSize(READONLY r: T): CARDINAL;
Return r.east - r.west.
PROCEDURE VerSize(READONLY r: T): CARDINAL;
Return r.south - r.north.
PROCEDURE Size (a: Axis.T; READONLY r: T): CARDINAL;
HorSize(r) if a=Hor; VerSize(r) if a=Ver
PROCEDURE DiagSizeSquare (READONLY r: T): CARDINAL;
HorSize(r)**2+VerSize(r)**2
PROCEDURE Middle(READONLY r: T): Point.T;
Return Point.T{r.west+r.east DIV 2, r.north+r.south DIV 2}.
PROCEDURE PickEdge (READONLY r: T; READONLY p: Point.T): Edge;
Return the edge of r closest to p (one of them if not unique)
PROCEDURE PickVertex (READONLY r: T; READONLY p: Point.T): Vertex;
Return the vertex of r closest to p (one of them if not unique)
PROCEDURE Project(READONLY r: T;
READONLY p: Point.T): Point.T;
Return the element of r that is closest to p. This is a
checked runtime error if r is empty.
--- Transformation ---
PROCEDURE Add(READONLY r: T; READONLY p: Point.T): T;
Return
FromEdges(r.west+p.h, r.east+p.h,
r.north+p.v,r.south+p.v)
PROCEDURE Sub(READONLY r: T; READONLY p: Point.T): T;
Return Add(r, Point.Minus(p)).
PROCEDURE Move (READONLY r: T; READONLY p: Point.T): T;
increment r.e and r.w by p.h; increment r.n and r.s by p.v
PROCEDURE MoveH (READONLY r: T; h: INTEGER): T;
increment r.e and r.w by h
PROCEDURE MoveV (READONLY r: T; v: INTEGER): T;
increment r.n and r.s by v
PROCEDURE MoveHV (READONLY r: T; h, v: INTEGER): T;
increment r.e and r.w by h, r.n and r.s by v
PROCEDURE Scale (READONLY r: T; num, den: INTEGER): T;
scale a rectangle by a fraction
PROCEDURE Change
(READONLY r: T; dw,de,dn,ds: INTEGER): T;
If r is empty return Empty, else return the rectangle
FromEdges(r.west+dw, r.east+de, r.north+dn, r.south+ds).
PROCEDURE Inset(READONLY r: T; n: INTEGER): T;
Return Change(r, n, -n, n, -n).
PROCEDURE Transpose(READONLY r: T; ax := Axis.T.Ver): T;
If r is empty or if ax = Axis.Hor, then return
r, else return T{r.north, r.south, r.west, r.east}.
PROCEDURE MoveEdge (READONLY r: T; e: Edge; dn: INTEGER): T;
If r is empty return empty, else move the edge e of r by dn in the positive
direction of the axis perpendicular to it
PROCEDURE MoveVertex (READONLY r: T; v: Vertex; READONLY dp: Point.T): T
;
If r is empty return empty, else move the vertex v of r by dp in the
northwest-southeast direction
PROCEDURE Stretch (READONLY r: T; axis: Axis.T; lo, hi: INTEGER): T;
If r is empty return empty, else change the interval of r determined by
axis.
PROCEDURE Join(READONLY r, s: T): T;
Return the smallest rectangle containing both r and s.
PROCEDURE Meet(READONLY r, s: T): T;
Return the largest rectangle contained in both r and s.
PROCEDURE Extend (READONLY r: T; READONLY p: Point.T): T;
Returns Join(r,FromPoint(p))
PROCEDURE Chop (hv: Axis.T; READONLY r: T; n: INTEGER; VAR (*out*) s, t: T)
;
Chop a rectangle in two. If hv=Ver, s and t become the top and bottom parts
of r resp. If hv=Hor, s and t become the left and right parts of r resp.
TYPE Partition = ARRAY [0..4] OF T;
PROCEDURE Factor(
READONLY r, s: T;
VAR (*out*) f: Partition;
dh, dv: INTEGER) ;
Partition r into 5 pieces f[0]..f[4] where f[2] = Meet(r,s),
and the other rectangles in f partition the set difference r-s.
The order of f is such that if i<j then f[i] translated by
any positive multiple of (dh,dv) doesn't intersect f[j]. (Only
the signs of dh and dv affect the order, not their magnitude.)
PROCEDURE Mod(READONLY p: Point.T;
READONLY r: T): Point.T;
Return the element of r whose distance from p in each axis is a
multiple of the size of r in that axis. This is a checked runtime
error if r is empty.
--- Test ---
PROCEDURE Equal (READONLY r, s: T): BOOLEAN;
Rectangle equality; all empty rectangles are equal
PROCEDURE IsEmpty(READONLY r: T): BOOLEAN;
Return whether r is empty.
PROCEDURE Member(READONLY p: Point.T;
READONLY r: T): BOOLEAN;
Return whether p is in r.
PROCEDURE Overlap(READONLY r, s: T): BOOLEAN;
Return whether r and s have any element in common.
PROCEDURE Subset(READONLY r, s: T): BOOLEAN;
Return whether r is contained in s.
PROCEDURE Congruent(READONLY r, s: T): BOOLEAN;
Return whether r and s are congruent, that is,
whether they have the same height and width.
--- Coordinate Transformation ---
PROCEDURE GlobToLoc (READONLY r: T; READONLY p: Point.T): Point.T;
Transform p (in global coordinates) to the local coordinate system of r.
Return Point.Sub(p,NorthWest(r))
PROCEDURE LocToGlob (READONLY r: T; READONLY p: Point.T): Point.T;
Transform p (in the local coordinate system of r) to global coordinates.
Returns Point.Add(p,NorthWest(r))
--- Standard type operations ---
PROCEDURE Compare (READONLY a, b: T): INTEGER;
== lexicographic comparison of a, b by <w, e, n, s>
PROCEDURE Hash (READONLY a: T): INTEGER;
== RETURN a suitable hash value
END Rect.