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Funkcionalno programiranje

Funkcionalno programiranje. Rad sa grafi čkim elementima - nastavak. Zadaci. Nacrtati prikazanu sliku. Napisati funkciju perimeter:: Shape->Float koja ra čuna obim oblika tipa Shape. Tip podataka Region. data Region = Shape Shape -- primitive shape

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Funkcionalno programiranje

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  1. Funkcionalno programiranje Rad sa grafičkim elementima - nastavak

  2. Zadaci • Nacrtati prikazanu sliku. • Napisati funkciju perimeter:: Shape->Float koja računa obim oblika tipa Shape.

  3. Tip podataka Region data Region = Shape Shape -- primitive shape | Translate Vector Region -- translated region | Scale Vector Region -- scaled region | Complement Region -- inverse of region | Region `Union` Region -- union of regions | Region `Intersect` Region -- intersection of regions | Empty deriving Show type Vector = (Float, Float)

  4. Funkcija contains • containsR :: Region -> Vertex -> Bool • containsS :: Shape -> Vertex -> Bool

  5. s1 t2 s2 t1 Contains: pravougaonik Rectangle s1 s2 `containsS` (x,y)= let t1 = s1/2 t2 = s2/2 in -t1<=x && x<=t1 && -t2<=y && y<=t2

  6. r2 r1 Contains: elipsa Ellipse r1 r2 `containsS` (x,y) = (x/r1)^2 + (y/r2)^2 <= 1

  7. Contains: poligon Za vektor čija je početna tačka a a krajnja b, tačkapleži levo od vektora kada: b = (bx,by) p = (px,py) isLeftOf :: Coordinate -> Ray -> Bool (px,py) `isLeftOf` ((ax,ay),(bx,by)) = let (s,t) = (px-ax, py-ay) (u,v) = (px-bx, py-by) in s*v >= t*u type Ray = (Coordinate, Coordinate) a = (ax,ay)

  8. Contains: poligon Tačkapje unutar (konveksnog) poligonaako je svakoj njegovoj stranici sa leve strane, pri čemu su stranice usmerene u smeru suprotnom od kazaljke na satu. p Polygon pts `containsS` p = let shiftpts = tail pts ++ [head pts] leftOfList = map isLeftOfp (zip pts shiftpts) isLeftOfp p' = isLeftOf p p' in and leftOfList

  9. Contains: pravougli trougao RtTriangle s1 s2 `containsS` p = Polygon [(0,0),(s1,0),(0,s2)] `containsS` p (0,s2) s2 (0,0) (s1,0) s1

  10. Zadatak • Koristeći definisanu funkciju containsS, definisati funkciju containsR :: Region -> Vertex -> Bool

  11. Primer • Regions.hs

  12. Tip podataka Picture data Picture = Region Color Region | Picture `Over` Picture | EmptyPic deriving Show

  13. G.Region • Tip podataka G.Regionje dvodimenzioni niz (bit-map) koji čuva binarnu vrednost za svaki od piksela

  14. Bitmap operatori • Postoje ugrađene funkcije za kombinovanje bitmap slika. Na primer, za uniju: = + • Ove funkcije su brze ali zahtevaju dosta prostora

  15. G.Region Interface • createRectangle :: Point -> Point -> IO G.Region • createEllipse :: Point -> Point -> IO G.Region • createPolygon :: [Point] -> IO G.Region • andRegion :: G.Region -> G.Region -> IO G.Region • orRegion :: G.Region -> G.Region -> IO G.Region • xorRegion :: G.Region -> G.Region -> IO G.Region • diffRegion :: G.Region -> G.Region -> IO G.Region • deleteRegion :: G.Region -> IO () • drawRegion :: G.Region -> Graphic Funkcije definisane u Graphics.SOEbiblioteci.

  16. Crtanje G.Region-a drawRegionInWindow :: Window -> Color -> Region -> IO ()drawRegionInWindow w c r = drawInWindow w (withColor c (drawRegion (regionToGRegion r)))

  17. Crtanje Picture-sa drawPic :: Window -> Picture -> IO ()drawPic w (Region c r) = drawRegionInWindow w c rdrawPic w (p1 `Over` p2) = do drawPic w p2 drawPic w p1drawPic w EmptyPic = return ()

  18. Region -> G.Region • Pokušajmo najpre sa manjim problemom: suzimo tipove Region i Shape: data Region = Shape Shape | Scale Vector Region data Shape = Rectangle x y data NewRegion = Rect Side Side -- abstracts G.Region

  19. Pojednostavljena verzija regToNReg :: Region -> NewRegion --------------------------------------------------- regToNReg (Shape (Rectangle sx sy)) = Rect sx sy --------------------------------------------------- regToNReg (Scale (x,y) r) = regToNReg (scaleReg (x,y) r) where scaleReg (x,y) (Shape (Rectangle sx sy)) = Shape (Rectangle (x*sx) (y*sy)) scaleReg (x,y) (Scale s r) = Scale s (scaleReg (x,y) r)

  20. Problem • Posmatrajmo (Scale (x1,y1) (Scale (x2,y2) (Scale (x3,y3) ... (Shape (Rectangle sx sy)) ... ))) • Ako je skaliranje n nivoa duboko, koliko će se puta izvršitiregToNRegnad čitavimRegiondrvetom?

  21. Sličan problem • Kod funkcijereverse:reverse [] = [] reverse (x:xs) = (reverse xs) ++ [x] where [] ++ zs = zs (y:ys) ++ zs = y : (ys ++ zs) • Uvođenjem parametra za akumulaciju:reverse xs = revhelp xs [] where revhelp [] zs = zs revhelp (x:xs) zs = revhelp xs (x:zs)

  22. Sa akumulirajućim faktorom regToNReg2 :: Region -> NewRegion regToNReg2 r = rToNR (1,1) r where rToNR :: (Float,Float) -> Region -> NewRegion rToNR (x1,y1) (Shape (Rectangle sx sy)) = Rect (x1*sx) (y1*sy) rToNR (x1,y1) (Scale (x2,y2) r) = rToNR (x1*x2,y1*y2) r

  23. Konačna verzija regToGReg1 :: Vector -> Vector -> Region -> G.Region regToGReg1 loc sca (Shape s) = shapeToGRegion loc sca s regToGReg1 (x,y) sca (Translate (u,v) r) = regToGReg1 (x+u, y+v) sca r regToGReg1 loc (x,y) (Scale (u,v) r) = regToGReg1 loc (x*u, y*v) r regToGReg1 loc sca Empty = createRectangle (0,0) (0,0) regToGReg1 loc sca (r1 `Union` r2) = let gr1 = regToGReg1 loc sca r1 gr2 = regToGReg1 loc sca r2 in orRegion gr1 gr2

  24. Apstrakcija primGReg loc sca r1 r2 op = let gr1 = regToGReg loc sca r1 gr2 = regToGReg loc sca r2 in op gr1 gr2 • Ovaj šablon će nam se javljati i kod unije i kod preseka pa je zato pogodno izdvojiti ga

  25. Konačna verzija sa izmenama regToGReg :: Vector -> Vector -> Region -> G.Region regToGReg (loc@(x,y)) (sca@(a,b)) shape = case shape of Shape s -> shapeToGRegion loc sca s Translate (u,v) r -> regToGReg (x+u, y+v) sca r Scale (u,v) r -> regToGReg loc (a*u, b*v) r Empty -> createRectangle (0,0) (0,0) r1 `Union` r2 -> primGReg loc sca r1 r2 orRegion r1 `Intersect` r2 -> primGReg loc sca r1 r2 andRegion Complement r -> primGReg loc sca winRect r diffRegion where winRect :: Region winRect = Shape (Rectangle (pixelToInch xWin) (pixelToInch yWin)) regionToGRegion :: Region -> G.Region regionToGRegion r = regToGReg (0,0) (1,1) r

  26. s1 S2/2 s2 s1/2 ( xWin2, yWin2) ( xWin, yWin ) Shape to G.Region: Rectangle shapeToGRegion :: Vector -> Vector -> Shape -> IO G.Region shapeToGRegion (lx,ly) (sx,sy) (Rectangle s1 s2) = createRectangle (trans(-s1/2,-s2/2)) (trans (s1/2,s2/2)) where trans (x,y) = ( xWin2 + inchToPixel (lx+x*sx), yWin2 - inchToPixel (ly+y*sy) )

  27. r2 r1 Ellipse shapeToGRegion1 (lx,ly) (sx,sy) (Ellipse r1 r2) = createEllipse (trans (-r1,-r2)) (trans ( r1, r2)) where trans (x,y) = ( xWin2 + inchToPixel (lx+x*sx), yWin2 - inchToPixel (ly+y*sy) )

  28. Polygon and RtTriangle shapeToGRegion1 (lx,ly) (sx,sy) (Polygon pts) = createPolygon (map trans pts) where trans (x,y) = ( xWin2 + inchToPixel (lx+x*sx), yWin2 - inchToPixel (ly+y*sy) ) ------------------------------------------------------------------shapeToGRegion1 (lx,ly) (sx,sy) (RtTriangle s1 s2) = createPolygon (map trans [(0,0),(s1,0),(0,s2)]) where trans (x,y) = ( xWin2 + inchToPixel (lx+x*sx), yWin2 - inchToPixel (ly+y*sy) )

  29. Konačna verzija shapeToGRegion (lx,ly) (sx,sy) s = case s of Rectangle s1 s -> createRectangle (trans (-s1/2,-s2/2)) (trans( s1/2, s2/2)) Ellipse r1 r2-> createEllipse (trans (-r1,-r2)) (trans ( r1, r2)) Polygon pts -> createPolygon (map trans pts) RtTriangle s1 s2 -> createPolygon (map trans [(0,0),(s1,0),(0,s2)]) where trans (x,y) = ( xWin2 + inchToPixel (lx+x*sx), yWin2 - inchToPixel (ly+y*sy) )

  30. Primer • picture.hs

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