module Reanimate.Svg.LineCommand
( CmdM
, LineCommand(..)
, lineLength
, toLineCommands
, lineToPath
, lineToPoints
, partialSvg
) where
import Control.Lens ((%~), (&), (.~))
import Control.Monad.Fix
import Control.Monad.State
import Data.Functor
import qualified Data.Vector.Unboxed as V
import qualified Geom2D.CubicBezier.Linear as Bezier
import Graphics.SvgTree hiding (height, line, path, use, width)
import Linear.Metric
import Linear.V2 hiding (angle)
import Linear.Vector
type CmdM a = State RPoint a
data LineCommand
= LineMove RPoint
| LineBezier [RPoint]
| LineEnd RPoint
deriving (Show)
lineToPath :: [LineCommand] -> [PathCommand]
lineToPath = map worker
where
worker (LineMove p) = MoveTo OriginAbsolute [p]
worker (LineBezier [a,b,c]) = CurveTo OriginAbsolute [(a,b,c)]
worker (LineBezier [a,b]) = QuadraticBezier OriginAbsolute [(a,b)]
worker (LineBezier [a]) = LineTo OriginAbsolute [a]
worker LineBezier{} = error "Reanimate.Svg.lineToPath: invalid bezier curve"
worker LineEnd{} = EndPath
lineToPoints :: Int -> [LineCommand] -> [RPoint]
lineToPoints nPoints cmds =
map lineEnd lineSegments
where
lineSegments = [ partialLine (fromIntegral n/ fromIntegral nPoints) cmds | n <- [0 .. nPoints-1] ]
lineEnd [LineBezier pts] = last pts
lineEnd (_:xs) = lineEnd xs
lineEnd _ = error "invalid line"
partialLine :: Double -> [LineCommand] -> [LineCommand]
partialLine alpha cmds = evalState (worker 0 cmds) zero
where
worker _d [] = pure []
worker d (cmd:xs) = do
from <- get
len <- lineLength cmd
let frac = (targetLen-d) / len
if len == 0 || frac >= 1
then (cmd:) <$> worker (d+len) xs
else pure [adjustLineLength frac from cmd]
totalLen = evalState (sum <$> mapM lineLength cmds) zero
targetLen = totalLen * alpha
adjustLineLength :: Double -> RPoint -> LineCommand -> LineCommand
adjustLineLength alpha from cmd =
case cmd of
LineBezier points -> LineBezier $ drop 1 $ partialBezierPoints (from:points) 0 alpha
LineMove p -> LineMove p
LineEnd p -> LineBezier [lerp alpha p from]
lineLength :: LineCommand -> CmdM Double
lineLength cmd =
case cmd of
LineMove to -> 0 <$ put to
LineBezier [dst] -> gets (distance dst) <* put dst
LineBezier lst -> do
from <- get
let bezier = rpointsToBezier (from:lst)
tol = 0.0001
put (last lst)
pure $ Bezier.arcLength bezier 1 tol
LineEnd to -> gets (distance to) <* put to
rpointsToBezier :: [RPoint] -> Bezier.CubicBezier Double
rpointsToBezier lst =
case lst of
[a,b] -> Bezier.CubicBezier a a b b
[a,b,c] -> Bezier.quadToCubic (Bezier.QuadBezier a b c)
[a,b,c,d] -> Bezier.CubicBezier a b c d
_ -> error $ "rpointsToBezier: Invalid list of points: " ++ show lst
toLineCommands :: [PathCommand] -> [LineCommand]
toLineCommands ps = evalState (worker zero Nothing ps) zero
where
worker _startPos _mbPrevControlPt [] = pure []
worker startPos mbPrevControlPt (cmd:cmds) = do
lcmds <- toLineCommand startPos mbPrevControlPt cmd
let startPos' =
case lcmds of
[LineMove pos] -> pos
_ -> startPos
(lcmds++) <$> worker startPos' (cmdToControlPoint $ last lcmds) cmds
cmdToControlPoint :: LineCommand -> Maybe RPoint
cmdToControlPoint (LineBezier points) = Just (last (init points))
cmdToControlPoint _ = Nothing
mkStraightLine :: RPoint -> LineCommand
mkStraightLine p = LineBezier [p]
toLineCommand :: RPoint -> Maybe RPoint -> PathCommand -> CmdM [LineCommand]
toLineCommand startPos mbPrevControlPt cmd =
case cmd of
MoveTo OriginAbsolute [] -> pure []
MoveTo OriginAbsolute lst -> put (last lst) *> gets (pure.LineMove)
MoveTo OriginRelative lst -> modify (+ sum lst) *> gets (pure.LineMove)
LineTo OriginAbsolute lst -> forM lst (\to -> put to $> mkStraightLine to)
LineTo OriginRelative lst -> forM lst (\to -> modify (+to) *> gets mkStraightLine)
HorizontalTo OriginAbsolute lst ->
forM lst $ \x -> modify (_x .~ x) *> gets mkStraightLine
HorizontalTo OriginRelative lst ->
forM lst $ \x -> modify (_x %~ (+x)) *> gets mkStraightLine
VerticalTo OriginAbsolute lst ->
forM lst $ \y -> modify (_y .~ y) *> gets mkStraightLine
VerticalTo OriginRelative lst ->
forM lst $ \y -> modify (_y %~ (+y)) *> gets mkStraightLine
CurveTo OriginAbsolute quads ->
forM quads $ \(a,b,c) -> put c $> LineBezier [a,b,c]
CurveTo OriginRelative quads ->
forM quads $ \(a,b,c) -> do
from <- get <* modify (+c)
pure $ LineBezier $ map (+from) [a,b,c]
SmoothCurveTo o lst -> mfix $ \result -> do
let ctrl = mbPrevControlPt : map cmdToControlPoint result
forM (zip lst ctrl) $ \((c2,to), mbControl) -> do
from <- get <* adjustPosition o to
let c1 = maybe (makeAbsolute o from c2) (mirrorPoint from) mbControl
pure $ LineBezier [c1,makeAbsolute o from c2,makeAbsolute o from to]
QuadraticBezier OriginAbsolute pairs ->
forM pairs $ \(a,b) -> put b $> LineBezier [a,b]
QuadraticBezier OriginRelative pairs ->
forM pairs $ \(a,b) -> do
from <- get <* modify (+b)
pure $ LineBezier $ map (+from) [a,b]
SmoothQuadraticBezierCurveTo o lst -> mfix $ \result -> do
let ctrl = mbPrevControlPt : map cmdToControlPoint result
forM (zip lst ctrl) $ \(to, mbControl) -> do
from <- get <* adjustPosition o to
let c1 = maybe from (mirrorPoint from) mbControl
pure $ LineBezier [c1,makeAbsolute o from to]
EllipticalArc o points -> concat <$>
forM points (\(rotX, rotY, angle, largeArc, sweepFlag, to) -> do
from <- get <* adjustPosition o to
return $ convertSvgArc from rotX rotY angle largeArc sweepFlag (makeAbsolute o from to))
EndPath -> put startPos $> [LineEnd startPos]
where
mirrorPoint c p = c*2-p
adjustPosition OriginRelative p = modify (+p)
adjustPosition OriginAbsolute p = put p
makeAbsolute OriginAbsolute _from p = p
makeAbsolute OriginRelative from p = from+p
calculateVectorAngle :: Double -> Double -> Double -> Double -> Double
calculateVectorAngle ux uy vx vy
| tb >= ta
= tb - ta
| otherwise
= pi * 2 - (ta - tb)
where
ta = atan2 uy ux
tb = atan2 vy vx
convertSvgArc :: RPoint -> Coord -> Coord -> Coord -> Bool -> Bool -> RPoint -> [LineCommand]
convertSvgArc (V2 x0 y0) radiusX radiusY angle largeArcFlag sweepFlag (V2 x y)
| x0 == x && y0 == y
= []
| radiusX == 0.0 && radiusY == 0.0
= [LineBezier [V2 x y]]
| otherwise
= calcSegments x0 y0 theta1' segments'
where
sinPhi = sin (angle * pi/180)
cosPhi = cos (angle * pi/180)
x1dash = cosPhi * (x0 - x) / 2.0 + sinPhi * (y0 - y) / 2.0
y1dash = -sinPhi * (x0 - x) / 2.0 + cosPhi * (y0 - y) / 2.0
numerator = radiusX * radiusX * radiusY * radiusY - radiusX * radiusX * y1dash * y1dash - radiusY * radiusY * x1dash * x1dash
s = sqrt(1.0 - numerator / (radiusX * radiusX * radiusY * radiusY))
rx = if (numerator < 0.0) then (radiusX * s) else radiusX
ry = if (numerator < 0.0) then (radiusY * s) else radiusY
root = if (numerator < 0.0)
then (0.0)
else ((if ((largeArcFlag && sweepFlag) || (not largeArcFlag && not sweepFlag)) then (-1.0) else 1.0) *
sqrt(numerator / (radiusX * radiusX * y1dash * y1dash + radiusY * radiusY * x1dash * x1dash)))
cxdash = root * rx * y1dash / ry
cydash = -root * ry * x1dash / rx
cx = cosPhi * cxdash - sinPhi * cydash + (x0 + x) / 2.0
cy = sinPhi * cxdash + cosPhi * cydash + (y0 + y) / 2.0
theta1' = calculateVectorAngle 1.0 0.0 ((x1dash - cxdash) / rx) ((y1dash - cydash) / ry)
dtheta' = calculateVectorAngle ((x1dash - cxdash) / rx) ((y1dash - cydash) / ry) ((-x1dash - cxdash) / rx) ((-y1dash - cydash) / ry)
dtheta = if (not sweepFlag && dtheta' > 0)
then (dtheta' - 2 * pi)
else (if (sweepFlag && dtheta' < 0) then dtheta' + 2 * pi else dtheta')
segments' = ceiling (abs (dtheta / (pi / 2.0)))
delta = dtheta / fromInteger segments'
t = 8.0 / 3.0 * sin(delta / 4.0) * sin(delta / 4.0) / sin(delta / 2.0)
calcSegments startX startY theta1 segments
| segments == 0
= []
| otherwise
= LineBezier [ V2 (startX + dx1) (startY + dy1)
, V2 (endpointX + dxe) (endpointY + dye)
, V2 endpointX endpointY ] : calcSegments endpointX endpointY theta2 (segments - 1)
where
cosTheta1 = cos theta1
sinTheta1 = sin theta1
theta2 = theta1 + delta
cosTheta2 = cos theta2
sinTheta2 = sin theta2
endpointX = cosPhi * rx * cosTheta2 - sinPhi * ry * sinTheta2 + cx
endpointY = sinPhi * rx * cosTheta2 + cosPhi * ry * sinTheta2 + cy
dx1 = t * (-cosPhi * rx * sinTheta1 - sinPhi * ry * cosTheta1)
dy1 = t * (-sinPhi * rx * sinTheta1 + cosPhi * ry * cosTheta1)
dxe = t * (cosPhi * rx * sinTheta2 + sinPhi * ry * cosTheta2)
dye = t * (sinPhi * rx * sinTheta2 - cosPhi * ry * cosTheta2)
partialBezierPoints :: [RPoint] -> Double -> Double -> [RPoint]
partialBezierPoints ps a b =
let c1 = Bezier.AnyBezier (V.fromList ps)
Bezier.AnyBezier os = Bezier.bezierSubsegment c1 a b
in V.toList os
partialSvg :: Double
-> Tree
-> Tree
partialSvg alpha | alpha >= 1 = id
partialSvg alpha = mapTree worker
where
worker (PathTree path) =
PathTree $ path & pathDefinition %~ lineToPath . partialLine alpha . toLineCommands
worker t = t