INTERFACE RealRect;

Rect is short for rectangle; the rectangles referred to must have their sides parallel to the coordinate axes. All coordinates are REALs.

Index: rectangles

IMPORT Axis, RealInterval, RealPoint, Rect;

NOTATION: By <w,e,n,s> we mean empty if w>=e or n>=s, (w,e,n,s) otherwise. By |w,e,n,s| we mean empty if w=e or n=s; otherwise the rectangle determined by the intervals |w,e| and |n,s| (see Interval.def).

LAWS: (1) Programs which assume or generate bad rectangles are illegal. (2) All empty rectangles are identified; programs which discriminate between different empty rectangles are illegal. (3) The operations in this module are undefined on bad rectangles.

TYPE T = RECORD west, east, north, south: REAL END;

TYPE Edge = {W, E, N, S};

TYPE Vertex = {NW, NE, SW, SE};

CONST Empty = T {0.0, -1.0, 0.0, -1.0};  (* An empty rectangle *)

EXCEPTION Error; (* Client error *)

PROCEDURE FromEdges (w, e, n, s: REAL): T RAISES {};

Returns the rectangle <w,e,n,s>

PROCEDURE FromAbsEdges (w, e, n, s: REAL): T RAISES {};

Returns the rectangle |w,e,n,s|

PROCEDURE Float(READONLY r: Rect.T): T;

The set of all REAL points (h,v) such that h >= r.west, h < r.east, v >= r.north, and v < r.south. Same as FromEdges(FLOAT(r.west), FLOAT(r.east) - epsilon, FLOAT(r.north), FLOAT(r.south) - epsilon)

PROCEDURE Floor(READONLY r: T): Rect.T;

Rounds all points in the rectangle down to integer coordinates, and returns enclosing integer rectangle.

PROCEDURE Round(READONLY r: T): Rect.T;

Rounds all points in the rectnagle to the nearest integer coords, and returns enclosing integer rectangle.

PROCEDURE FromPoint (READONLY p: RealPoint.T): T RAISES {};

Returns the rectangle whose only member is p

PROCEDURE FromCorners (READONLY p, q: RealPoint.T): T RAISES {};

Returns the rectangle |p.h,q.h,p.v,q.v|

PROCEDURE FromCorner (READONLY p: RealPoint.T; hor, ver: REAL): T RAISES {};

Returns the rectangle <p.h,p.v,p.h+hor,p.v+ver>

PROCEDURE FromSize (hor, ver: REAL): T RAISES {};

Returns the rectangle <0.0,0.0,hor,ver>

PROCEDURE Center (READONLY r: T; READONLY p: RealPoint.T): T RAISES {};

Return a rectangle congruent to r, with middle at p

PROCEDURE FromIntervals (READONLY hor, ver: RealInterval.T): T RAISES {};

Returns the rectangle <hor.lo, hor.hi, ver.lo, ver.hi>

PROCEDURE FromAxes (axis: Axis.T; READONLY n, m: RealInterval.T): T RAISES {};

If axis=Hor then FromIntervals(n,m), else FromIntervals(m,n)

PROCEDURE NorthWest (READONLY r: T): RealPoint.T RAISES {};

north-west point

PROCEDURE NorthEast (READONLY r: T): RealPoint.T RAISES {};

north-east point

PROCEDURE SouthWest (READONLY r: T): RealPoint.T RAISES {};

south-west point

PROCEDURE SouthEast (READONLY r: T): RealPoint.T RAISES {};

south-east point

PROCEDURE GetVertex (v: Vertex; READONLY r: T): RealPoint.T RAISES {};

the point corresponding to the vertex v of r; origin if r is empty

PROCEDURE HorSize (READONLY r: T): REAL RAISES {};

r.east - r.west

PROCEDURE VerSize (READONLY r: T): REAL RAISES {};

r.south - r.north

PROCEDURE Size (a: Axis.T; READONLY r: T): REAL RAISES {};

HorSize(r) if a=Hor; VerSize(r) if a=Ver

PROCEDURE DiagSizeSquare (READONLY r: T): REAL RAISES {};

HorSize(r)**2.0+VerSize(r)**2.0

PROCEDURE Middle (READONLY r: T): RealPoint.T RAISES {};

(floor((r.west+r.east)/2.0), floor((r.north+r.south)/2.0)); an unspecified point if empty

PROCEDURE PickEdge (READONLY r: T; READONLY p: RealPoint.T): Edge RAISES {};

Return the edge of r closest to p (one of them if not unique)

PROCEDURE PickVertex(READONLY r: T; READONLY p: RealPoint.T): Vertex RAISES {};

Return the vertex of r closest to p (one of them if not unique)

PROCEDURE Project (READONLY r: T;
                   READONLY p: RealPoint.T): RealPoint.T RAISES {Error};

Return the point in r that is closest to p. r must be non-empty

PROCEDURE Add (READONLY r: T; READONLY p: RealPoint.T): T RAISES {Error};

increment r.e and r.w by p.h; increment r.n and r.s by p.v

PROCEDURE Sub (READONLY r: T; READONLY p: RealPoint.T): T RAISES {Error};

decrement r.e and r.w by p.h; decrement r.n and r.s by p.v

PROCEDURE Move (READONLY r: T; READONLY p: RealPoint.T): T RAISES {Error};

increment r.e and r.w by p.h; increment r.n and r.s by p.v

PROCEDURE MoveH (READONLY r: T; h: REAL): T RAISES {Error};

increment r.e and r.w by h

PROCEDURE MoveV (READONLY r: T; v: REAL): T RAISES {Error};

increment r.n and r.s by v

PROCEDURE MoveHV (READONLY r: T; h, v: REAL): T RAISES {Error};

increment r.e and r.w by h, r.n and r.s by v

PROCEDURE Scale (READONLY r: T; factor: REAL): T RAISES {};

scale a rectangle by a fraction

PROCEDURE Inset (READONLY r: T; n: REAL): T RAISES {};

If r is emtpy return emtpy, else return <r.w+n,r.e-n,r.n+n,r.s-n>

PROCEDURE Change (READONLY r: T; dw, de, dn, ds: REAL): T RAISES {};

If r is empty return empty, else return <r.w+dw,r.e+de,r.n+dn,r.s+ds>

PROCEDURE MoveEdge (READONLY r: T; e: Edge; dn: REAL): T RAISES {};

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: RealPoint.T): T
  RAISES {};

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: REAL): T RAISES {};

If r is empty return empty, else change the interval of r determined by axis.

PROCEDURE Join (READONLY r, s: T): T RAISES {};

the least rectangle including the union of the points in r and s

PROCEDURE Meet (READONLY r, s: T): T RAISES {};

the largest rectangle included in the intersection of r and s

PROCEDURE Extend (READONLY r: T; READONLY p: RealPoint.T): T RAISES {};

Returns Join(r,FromPoint(p))

PROCEDURE Chop (hv: Axis.T; READONLY r: T; n: REAL; VAR (*out*) s, t: T)
  RAISES {};

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, by: T; VAR (*out*) f: Partition; dh, dv: REAL)
  RAISES {};

PROCEDURE Mod (READONLY p: RealPoint.T; READONLY r: T): RealPoint.T
  RAISES {Error};

Return the member of r whose distance from p in either coordinate is a multiple of the size of r in the corresponding coordinate. r must be non-empty

PROCEDURE Equal (READONLY r, s: T): BOOLEAN RAISES {};

Rectangle equality; all empty rectangles are equal

PROCEDURE IsEmpty (READONLY r: T): BOOLEAN RAISES {};

whether r is empty

PROCEDURE Member (READONLY p: RealPoint.T; READONLY r: T): BOOLEAN RAISES {};

whether a point is in a rectangle

PROCEDURE Overlap (READONLY r, s: T): BOOLEAN RAISES {};

whether two rectangles overlap

PROCEDURE Subset (READONLY r, s: T): BOOLEAN RAISES {};

wheter r is a subset of s

PROCEDURE GlobToLoc (READONLY r: T;
                     READONLY p: RealPoint.T): RealPoint.T RAISES {};

Transform p (in global coordinates) to the local coordinate system of r. Return RealPoint.Sub(p,NorthWest(r))

PROCEDURE LocToGlob (READONLY r: T;
                     READONLY p: RealPoint.T): RealPoint.T RAISES {};

Transform p (in the local coordinate system of r) to global coordinates. Returns RealPoint.Add(p,NorthWest(r))

PROCEDURE New (READONLY value: T): REF T;

Allocates and initializes a new heap value

PROCEDURE NewArray (size: CARDINAL;  READONLY value := Empty): REF ARRAY OF T;

Allocates a new array from the heap and initializes all its elements with the given value

PROCEDURE UntracedNew (READONLY value: T): UNTRACED REF T;

Allocates and initializes a new untraced value

PROCEDURE UntracedNewArray (size: CARDINAL;  READONLY value := Empty):
                                                       UNTRACED REF ARRAY OF T;

Allocates a new untraced array from the heap and initializes all its elements with the given value

PROCEDURE Compare (READONLY a, b: T): INTEGER;

== RETURN (-1 if Lt (a, b), 0 if Eq (a, b), +1 o. w.)

PROCEDURE Lt (READONLY a, b: T): BOOLEAN;

== RETURN lexicographic comparison of a, b by <w, e, n, s>

PROCEDURE Eq (READONLY a, b: T): BOOLEAN;

== RETURN (a = b)

PROCEDURE Hash (READONLY a: T): INTEGER;

== RETURN a suitable hash value

END RealRect.