SVGPath-1.0.3: src/Graphics/SVG/ReadPath.hs
--------------------------------------------------------------------
-- |
-- Module : Graphics.SVG.ReadPath
-- Copyright : (c) 2011 Tillmann Vogt
-- License : BSD3
--
-- Maintainer: Tillmann Vogt <Tillmann.Vogt@rwth-aachen.de>
-- Stability : stable
-- Portability: portable
--
-- parsing the SVG path command, see <http://www.w3.org/TR/SVG/paths.html#PathData> :
module Graphics.SVG.ReadPath
( pathFromString,
PathCommand(..),
commandsToPoints,
ctp,
bSubCurve
)
where
import Text.ParserCombinators.Parsec hiding (spaces)
import Text.ParserCombinators.Parsec.Expr
import qualified Text.ParserCombinators.Parsec.Token as P
import Text.ParserCombinators.Parsec.Language( javaStyle )
import System.IO.Unsafe (unsafePerformIO)
type X = Float
type Y = Float
type F2 = (X,Y)
type Tup = (X,Y)
type X1 = X
type Y1 = Y
type X2 = X
type Y2 = Y
data PathCommand =
M_abs Tup | -- ^Establish a new current point (with absolute coords)
M_rel Tup | -- ^Establish a new current point (with coords relative to the current point)
Z | -- ^Close current subpath by drawing a straight line from current point to current subpath's initial point
L_abs Tup | -- ^A line from the current point to Tup which becomes the new current point
L_rel Tup |
H_abs X | -- ^A horizontal line from the current point (cpx, cpy) to (x, cpy)
H_rel X |
V_abs Y | -- ^A vertical line from the current point (cpx, cpy) to (cpx, y)
V_rel Y |
C_abs (X1,Y1,X2,Y2,X,Y) | -- ^Draws a cubic Bézier curve from the current point to (x,y) using (x1,y1) as the
-- ^control point at the beginning of the curve and (x2,y2) as the control point at the end of the curve.
C_rel (X1,Y1,X2,Y2,X,Y) |
S_abs (X2,Y2,X,Y) | -- ^Draws a cubic Bézier curve from the current point to (x,y). The first control point is
-- assumed to be the reflection of the second control point on the previous command relative to the current point.
-- (If there is no previous command or if the previous command was not an C, c, S or s, assume the first control
-- point is coincident with the current point.) (x2,y2) is the second control point (i.e., the control point at
-- the end of the curve).
S_rel (X2,Y2,X,Y) |
Q_abs (X1,Y1,X,Y) | -- ^A quadr. Bézier curve from the curr. point to (x,y) using (x1,y1) as the control point
Q_rel (X1,Y1,X,Y) | -- ^Nearly the same as cubic, but with one point less
T_abs Tup | -- ^T_Abs = Shorthand/smooth quadratic Bezier curveto
T_rel Tup |
A_abs | -- ^A = Elliptic arc (not used)
A_rel
deriving Show
-- | convert a SVG path string into a list of commands
pathFromString :: String -> IO [PathCommand]
pathFromString str
= do{ case (parse path "" str) of
Left err -> do{ putStr "parse error at "
; print err
; return []
}
Right x -> return x
}
spaces = skipMany space
path :: Parser [PathCommand]
path = do{ whiteSpace
; l <- many1 pathElement
; eof
; return (concat l)
}
pathElement :: Parser [PathCommand]
pathElement = do{ whiteSpace;
do{ symbol "M"; l <- many1 tupel2; return (map (\x-> M_abs x) l) } <|>
do{ symbol "m"; l <- many1 tupel2; return (map (\x-> M_rel x) l) } <|>
do{ symbol "z"; return [Z]; } <|>
do{ symbol "Z"; return [Z]; } <|>
do{ symbol "L"; l <- many1 tupel2; return (map (\x-> L_abs x) l) } <|>
do{ symbol "l"; l <- many1 tupel2; return (map (\x-> L_rel x) l) } <|>
do{ symbol "H"; l <- many1 myfloat; return (map (\x-> H_abs (realToFrac x)) l) } <|>
do{ symbol "h"; l <- many1 myfloat; return (map (\x-> H_rel (realToFrac x)) l) } <|>
do{ symbol "V"; l <- many1 myfloat; return (map (\x-> V_abs (realToFrac x)) l) } <|>
do{ symbol "v"; l <- many1 myfloat; return (map (\x-> V_rel (realToFrac x)) l) } <|>
do{ symbol "C"; l <- many1 tupel6; return (map (\x-> C_abs x) l) } <|>
do{ symbol "c"; l <- many1 tupel6; return (map (\x-> C_rel x) l) } <|>
do{ symbol "S"; l <- many1 tupel4; return (map (\x-> S_abs x) l) } <|>
do{ symbol "s"; l <- many1 tupel4; return (map (\x-> S_rel x) l) } <|>
do{ symbol "Q"; l <- many1 tupel4; return (map (\x-> Q_abs x) l) } <|>
do{ symbol "q"; l <- many1 tupel4; return (map (\x-> Q_rel x) l) } <|>
do{ symbol "T"; l <- many1 tupel2; return (map (\x-> T_abs x) l) } <|>
do{ symbol "t"; l <- many1 tupel2; return (map (\x-> T_rel x) l) } <|>
do{ symbol "A"; l <- many1 tupel2; return (map (\x-> A_abs) l) } <|> -- not used
do{ symbol "a"; l <- many1 tupel2; return (map (\x-> A_rel) l) } -- not used
}
tupel2 :: Parser (X,Y)
tupel2 = do{ x <- myfloat; spaces; y <- myfloat; spaces;
; return (realToFrac x, realToFrac y)
}
tupel4 :: Parser (X,Y,X,Y)
tupel4 = do{ x1 <- myfloat; spaces; y1 <- myfloat; spaces; x <- myfloat; spaces; y <- myfloat; spaces;
; return (realToFrac x1, realToFrac y1, realToFrac x, realToFrac y)
}
tupel6 :: Parser (X,Y,X,Y,X,Y)
tupel6 = do{ x1 <- myfloat; spaces; y1 <- myfloat; spaces;
x2 <- myfloat; spaces; y2 <- myfloat; spaces; x <- myfloat; spaces; y <- myfloat; spaces;
; return (realToFrac x1, realToFrac y1, realToFrac x2, realToFrac y2, realToFrac x, realToFrac y)
}
myfloat = try (do{ symbol "-"; n <- float; return (negate n) }) <|>
try float <|> -- 0 is not recognized as a float, so recognize it as an integer and then convert it to float
do { i<-integer; return(fromIntegral i) }
lexer = P.makeTokenParser oDef
oDef = javaStyle
whiteSpace = P.whiteSpace lexer
symbol = P.symbol lexer
integer = P.integer lexer
float = P.float lexer
-------------------------------------------
-- | convert path-commands to outline points
commandsToPoints :: [PathCommand] -> F2 -> [[F2]]
commandsToPoints commands (dx, dy) | length result == 0 = []
| otherwise = result
where result = ctp commands [(0,0)] (0,0) False 255 (dx,dy)
ctp :: [PathCommand] -> [F2] -> F2 -> Bool -> Int -> F2 -> [[F2]]
ctp [] _ _ _ _ _ = []
ctp (c:commands) points lastContr useTex n (dx, dy) -- dx, dy is the size of a pixel, used for rasterisation
| (length nextPoints) == 0 = [tail $ tail points] ++ -- one outline completed
( ctp commands [] (contr c) useTex nminus (dx,dy) )
| otherwise = ctp commands (points ++ (tail nextPoints)) (contr c) useTex nminus (dx,dy)
where nminus = if n>0 then n-1 else 0
nextPoints = (go c)
contr ( C_abs (x1,y1,x2,y2,x,y) ) = ( (x+x-x2)/dx, (y+y-y2)/dy ) -- control point of bezier curve
contr ( C_rel (x1,y1,x2,y2,x,y) ) = (x0+(x+x-x2)/dx, y0+(y+y-y2)/dy )
contr ( S_abs (x2,y2,x,y) ) = ( (x+x-x2)/dx, (y+y-y2)/dy )
contr ( S_rel (x2,y2,x,y) ) = (x0+(x+x-x2)/dx, y0+(y+y-y2)/dy )
contr ( Q_abs (x1,y1,x,y) ) = ( (x+x-x1)/dx, (y+y-y1)/dy )
contr ( Q_rel (x1,y1,x,y) ) = (x0+(x+x-x1)/dx, y0+(y+y-y1)/dy )
contr ( T_abs (x,y) ) = ( (x+x)/dx-cx, (y+y)/dy - cy )
contr ( T_rel (x,y) ) = ( 2*(x0+x/dx)-cx, 2*(y0+y/dy)-cy ) -- absolute coordinates
contr ( L_abs (x,y) ) = ( x/dx, y/dy)
contr ( L_rel (x,y) ) = (x0 + x/dx, y0 + y/dy)
contr ( M_abs (x,y) ) = ( x/dx, y/dy)
contr ( M_rel (x,y) ) = (x0 + x/dx, y0 + y/dy)
contr ( H_abs x ) = ( x/dx, y0 )
contr ( H_rel x ) = (x0 + x/dx, y0 )
contr ( V_abs y ) = (x0, y/dy )
contr ( V_rel y ) = (x0, y0 + y/dy )
go ( L_abs (x,y) ) = bsub [(x0,y0), (x/dx, y/dy)]
go ( L_rel (x,y) ) = bsub [(x0,y0), (x0 + x/dx, y0 + y/dy)]
go ( M_abs (x,y) ) = [(0, 0), (x/dx, y/dy)]
go ( M_rel (x,y) ) = [(0, 0), (x0 + x/dx, y0 + y/dy)]
go ( H_abs x) = bsub [(x0,y0), (x/dx, y0)]
go ( H_rel x) = bsub [(x0,y0), (x0 + x/dx, y0)]
go ( V_abs y) = bsub [(x0,y0), (x0, y/dy)]
go ( V_rel y) = bsub [(x0,y0), (x0, y0 + y/dy)]
go ( C_abs (x1,y1,x2,y2,x,y) ) = bsub [(x0, y0), (x1/dx, y1/dy), (x2/dx, y2/dy), (x/dx, y/dy)]
go ( C_rel (x1,y1,x2,y2,x,y) ) = bsub [(x0, y0), (x0+x1/dx, y0+y1/dy), (x0+x2/dx,y0+y2/dy), (x0+x/dx,y0+y/dy)]
go ( S_abs ( x2,y2,x,y) ) = bsub [(x0, y0), (cx, cy), (x2/dx, y2/dy), (x/dx, y/dy) ]
go ( S_rel ( x2,y2,x,y) ) = bsub [(x0, y0), (cx, cy), (x0 + x2/dx, y0 + y2/dy), (x0 + x/dx, y0 + y/dy)]
go ( Q_abs (x1,y1,x,y) ) = bsub [(x0, y0), (x1/dx, y1/dy), (x/dx, y/dy)]
go ( Q_rel (x1,y1,x,y) ) = bsub [(x0, y0), (x0 + x1/dx, y0 + y1/dy), (x0 + x/dx, y0 + y/dy)]
go ( T_abs (x,y) ) = bsub [(x0,y0), (cx, cy), (x/dx, y/dy) ]
go ( T_rel (x,y) ) = bsub [(x0,y0), (cx, cy), (x0 + x/dx, y0 + y/dy)]
go ( Z ) = []
x0 = fst (last points)
y0 = snd (last points)
cx = (fst lastContr) -- last control point is always in absolute coordinates
cy = (snd lastContr)
bsub xs = bSubCurve useTex (dx,dy) xs
-----------------
-- bezier-curves
-----------------
linearInterp t ((x0,y0), (x1,y1)) = ( (1-t)*x0 + t*x1, (1-t)*y0 + t*y1)
tuplesOfTwo (bi:bj:[]) = [(bi,bj)]
tuplesOfTwo (bi:bj:bs) = (bi,bj) : tuplesOfTwo (bj:bs)
eval t bs = map (linearInterp t) (tuplesOfTwo bs)
deCas2 t (bi:[]) = [bi]
deCas2 t bs = [head bs] ++ (deCas2 t e) ++ [last bs]
where e = eval t bs
-- | bSubcurve uses bezier subdivision. (inspired by Hersch, Font Rasterization: the State of the Art (freely available))
-- It divides an arc into two arcs recursively until the arc is either completely
-- between two vertical raster lines or completely between two horizontal raster lines or the line is at most 1 pixel long.
-- This function computes outline points (tex==False) as well as border points for rasterisation (tex==True) by using
-- an x-, y-resoultion raster. dx, dy is the width and height of a pixel of this raster.
bSubCurve :: Bool -> (X,Y) -> [F2] -> [F2]
bSubCurve useTex (dx,dy) bs | ((abs (p1x-p0x)) < dx && (abs (p1y-p0y)) < dy && (not useTex)) || -- line that is at most one pixel long
((dx == 0 || dy == 0) && (not useTex)) ||
((abs (p1x-p0x)) < 1 && (abs (p1y-p0y)) < 1 && useTex) ||
((abs (p1x-p0x)) < 1 && p0x_int == p1x_int && useTex) || -- vertical line
((abs (p1y-p0y)) < 1 && p0y_int == p1y_int && useTex) -- horizontal line
= [ (p0x, p0y), (p1x, p1y) ]
| otherwise = firstArc ++ (tail secondArc) -- subdivide
where firstArc = bSubCurve useTex (dx,dy) (take l twoArcs)
secondArc = bSubCurve useTex (dx,dy) (drop (l-1) twoArcs)
twoArcs = deCas2 0.5 bs
l = (length twoArcs) `div` 2 + 1
(p0x, p0y) = head bs
(p1x, p1y) = last bs
(p0x_int, p0y_int) | p0y < p1y = (truncate p0x, truncate p0y)
| otherwise = (truncate p1x, truncate p1y)
(p1x_int, p1y_int) | p0y < p1y = (truncate p1x, truncate p1y)
| otherwise = (truncate p0x, truncate p0y)