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(* band.sml * * COPYRIGHT (c) 1994 by AT&T Bell Laboratories * * Code for band data structure. * * A band is a list non-continguous rectangles listed from left * to right (increasing x) that all have the same upper and lower * y coordinates. Regions (see region-sig.sml and region.sml) * are essentially ordered lists of bands. * * *) signature BAND = sig structure G : GEOMETRY datatype rect_overlap = RectangleOut | RectangleIn | RectanglePart datatype band = BAND of { y1 : int, (* top y value *) y2 : int, (* bottom y value *) xs : (int * int) list (* list of (left,right) values *) } (* Return y1(y2) of band *) val y1Of : band -> int val y2Of : band -> int (* Return number of intervals. Always > 0 *) val sizeOf : band -> int (* concat list of rectangles of band on accumlator list * The leftmost rectangle in the band will be the head of * the resulting list. *) val rectsOfBand : band * G.rect list -> G.rect list (* True if point is in band *) val inBand : band * G.point -> bool (* Return left and right extent of band *) val bandExtent : band -> (int * int) (* Compares argument interval with x intervals of band *) val rectInBand : band * int * int -> rect_overlap (* Returns true if any two x intervals of the bands intersect *) val overlap : band * band -> bool (* Translate band by given vector *) val offsetBand : G.point -> band -> band (* Translate band horizontally(vertically) *) val xOffsetBand : int -> band -> band val yOffsetBand : int -> band -> band (* Coalesce lower band below upper band. * Return SOME of new band if successful. * Assumes y values are compatible. *) val coalesce : {lower : band, upper : band} -> band option (* Create a new band that is the union(intersection,difference) * of the two argument bands. The integer return value is * the number of intervals in the band. * The integer arguments provide the upper * and lower y coordinates for the resulting band. The operation * only involves the x intervals; it is assumed that y overlap * has already been checked. *) val union : band * band * int * int -> (band * int) val intersect : band * band * int * int -> (band * int) val subtract : band * band * int * int -> (band * int) (* Return a new band that has the same x intervals as the * argument band, but with the new upper and lower y values. *) val squeeze : band * int * int -> (band * int) end structure Band : BAND = struct structure G = Geometry datatype rect_overlap = RectangleOut | RectangleIn | RectanglePart (* It might be worthwhile to maintain the length of xs in the band *) datatype band = BAND of { y1 : int, y2 : int, xs : (int * int) list } fun isIn (x : int) (x1,x2) = x1 <= x andalso x < x2 fun xoff (x : int) (x1,x2) = (x1+x,x2+x) fun ontop ([],l,n) = (l,n) | ontop (a::t,l,n) = ontop(t,a::l,n+1) fun mkr (y1,y2) = let val ht = y2 - y1 in fn ((x1,x2),l) => ((G.RECT{x=x1,y=y1,wid=x2 - x1,ht = ht})::l) end fun rectsOfBand (BAND{xs,y1,y2},l) = foldr (mkr (y1,y2)) l xs fun squeeze (BAND{xs,...},top,bot) = (BAND{xs=xs,y1=top,y2=bot},length xs) fun y1Of (BAND{y1,...}) = y1 fun y2Of (BAND{y2,...}) = y2 fun sizeOf (BAND{xs,...}) = length xs fun inBand (BAND{y1,y2,xs},G.PT{x=px,y=py}) = y1 <= py andalso py < y2 andalso List.exists (isIn px) xs fun bandExtent (BAND{xs = xs as ((x1,_)::_),...}) = let fun right ([(l,r)]) = r | right (_::t) = right t | right _ = raise LibBase.Impossible "Band.bandExtent.right" in (x1,right xs) end | bandExtent _ = raise LibBase.Impossible "Band.bandExtent" fun rectInBand (BAND{y1,y2,xs},x1,x2) = let fun rib [] = RectangleOut | rib ((l,r)::rest) = if r <= x1 then rib rest else if x2 <= l then RectangleOut else if l <= x1 andalso x2 <= r then RectangleIn else RectanglePart in rib xs end (* Only check overlap of x intervals *) fun overlap (BAND{xs,...},BAND{xs=xs',...}) = let fun loop([],_) = false | loop(_,[]) = false | loop(x as ((x1,x2)::xs),x' as ((x1',x2')::xs')) = if x2 <= x1' then loop(xs,x') else if x2' <= x1 then loop(x,xs') else true in loop (xs,xs') end fun xOffsetBand dx (BAND{y1,y2,xs}) = BAND{y1=y1,y2=y2, xs = map (xoff dx) xs} fun yOffsetBand dy (BAND{y1,y2,xs}) = BAND{y1=y1+dy,y2=y2+dy, xs = xs} fun offsetBand (G.PT{x=dx,y=dy}) (BAND{y1,y2,xs}) = BAND{y1=y1+dy,y2=y2+dy, xs = map (xoff dx) xs} (* coalesces two bands into one, if possible. * assume y1 of lower band = y2 of upper band * Check that each contain same horizontal intervals. * If so, combine and return SOME of resulting band. * Else return NONE. *) fun coalesce {lower = BAND{y2,xs,...}, upper = BAND{y1=y1',xs=xs',...}} = if xs = xs' then SOME(BAND{y1=y1',y2=y2,xs=xs}) else NONE fun union (BAND{xs,...},BAND{xs=xs',...},top,bot) = let val h = hd xs val h' = hd xs' fun finalmerge([],ci,xs) = ontop(xs,[ci],1) | finalmerge((i as (l,r))::t ,i' as (l',r'),xs) = if r' < l then ontop(xs,i'::i::t,2 + length t) else if r <= r' then finalmerge(t,i',xs) else ontop(xs,(l',r)::t,1 + length t) fun loop ([],[],ci,xs) = ontop(xs,[ci],1) | loop (x,[],ci,xs) = finalmerge(x,ci,xs) | loop ([],x,ci,xs) = finalmerge(x,ci,xs) | loop (x as ((i as (x1,x2))::t),x' as ((i' as (x1',x2'))::t'),ci,xs) = if x1 < x1' then merge(t,x',i,ci,xs) else merge(x,t',i',ci,xs) and merge(t,t',i as (l,r),i' as (l',r'),xs) = if r' < l then loop(t,t',i,i'::xs) else if r <= r' then loop(t,t',i',xs) else loop(t,t',(l',r),xs) val (xs'',n) = if #1 h < #1 h' then loop(tl xs,xs',h,[]) else loop(xs,tl xs',h',[]) in (BAND{y1=top,y2=bot,xs= xs''},n) end fun intersect (BAND{xs,...},BAND{xs=xs',...},top,bot) = let fun loop ([],_,xs) = ontop(xs,[],0) | loop (_,[],xs) = ontop(xs,[],0) | loop (x as ((x1,x2)::t),x' as ((x1',x2')::t'),xs) = let val l = Int.max(x1,x1') val r = Int.min(x2,x2') val xs' = if l < r then (l,r)::xs else xs in if x2 < x2' then loop(t,x',xs') else if x2 > x2' then loop(x,t',xs') else loop(t,t',xs') end in case loop(xs,xs',[]) of (xs'',n) => (BAND{y1=top,y2=bot,xs= xs''},n) end fun subtract (BAND{xs,...},BAND{xs=xs',...},top,bot) = let fun loop ([],_,xs) = ontop(xs,[],0) | loop (x,[],xs) = ontop(xs,x,length x) | loop (x as ((x1,x2)::t),x' as ((x1',x2')::t'),xs) = if x2' <= x1 then loop(x,t',xs) else if x2 <= x1' then loop(t,x',(x1,x2)::xs) else if x1' <= x1 then if x2' < x2 then loop((x2',x2)::t,t',xs) else if x2' = x2 then loop(t,t',xs) else loop(t,x',xs) else if x2' < x2 then loop((x2',x2)::t,t',(x1,x1')::xs) else if x2' = x2 then loop(t,t',(x1,x1')::xs) else loop(t,x',(x1,x1')::xs) in case loop(xs,xs',[]) of (xs'',n) => (BAND{y1=top,y2=bot,xs=xs''},n) end end

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