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 Data.Maybe
import qualified Data.Vector.Unboxed as V
import qualified Geom2D.CubicBezier.Linear as Bezier
import Graphics.SvgTree
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 =
mapMaybe lineEnd lineSegments
where
lineSegments = [partialLine (fromIntegral n / fromIntegral nPoints) cmds | n <- [0 .. nPoints -1]]
lineEnd [] = Nothing
lineEnd [LineBezier pts] = Just (last pts)
lineEnd (_ : xs) = lineEnd xs
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