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Farey sum for curve subdivision
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sheaf
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@ -31,6 +31,7 @@ import Data.Functor
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import qualified Data.List.NonEmpty as NE
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import Data.Maybe
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( fromMaybe, isNothing, listToMaybe )
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import Data.Ratio
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import Data.Semigroup
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( Arg(..), Min(..) )
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import Data.Traversable
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@ -66,11 +67,13 @@ import Control.Monad.Trans.Except
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( Except )
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import qualified Control.Monad.Trans.Except as Except
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import Control.Monad.Trans.State.Strict
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( State )
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( State, StateT )
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import qualified Control.Monad.Trans.State.Strict as State
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import Control.Monad.Trans.Writer.CPS
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( Writer )
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import qualified Control.Monad.Trans.Writer.CPS as Writer
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import Control.Monad.Trans.Class
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( lift )
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-- brush-strokes
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import qualified Math.Bezier.Cubic as Cubic
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@ -132,6 +135,7 @@ subdivide c doc@( Document { documentMetadata, documentContent }) =
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mbPrevSubdivision <- State.get
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let ( curves', subdivs ) =
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Writer.runWriter $
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( `State.evalStateT` Nothing ) $
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bifoldSpline @Open
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( subdivideCurve ( V2 0 0 ) )
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( const $ pure Seq.Empty )
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@ -156,11 +160,17 @@ subdivide c doc@( Document { documentMetadata, documentContent }) =
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:: T ( ℝ 2 )
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-> PointData brushParams
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-> Curve Open ( CurveData RealWorld ) ( PointData brushParams )
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-> Writer [ ( Curve Open () (), Double ) ]
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-> StateT ( Maybe Rational )
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( Writer [ ( Curve Open () (), Double ) ] )
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( Seq ( Curve Open ( CurveData RealWorld ) ( PointData brushParams ) ) )
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subdivideCurve offset sp0 crv =
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subdivideCurve offset sp0 crv = do
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mbPrevCrvIx <- State.get
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let i = curveIndex ( curveData crv )
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i' = case mbPrevCrvIx of { Nothing -> i - 1
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; Just i0 -> fareySum i0 i }
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State.put ( Just i )
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case crv of
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LineTo ( NextPoint sp1 ) dat -> do
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LineTo ( NextPoint sp1 ) ( CurveData _ dat ) -> do
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let
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p0, p1, s :: ℝ 2
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t :: Double
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@ -171,16 +181,16 @@ subdivide c doc@( Document { documentMetadata, documentContent }) =
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sqDist = quadrance @( T ( ℝ 2 ) ) c ( offset • s )
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if t > 0 && t < 1 && sqDist * zoomFactor ^ ( 2 :: Int ) < 16
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then do
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Writer.tell [ ( stripData crv, t ) ]
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lift $ Writer.tell [ ( stripData crv, t ) ]
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let
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subdiv :: PointData brushParams
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subdiv = lerp @( DiffPointData ( T brushParams ) ) t sp0 sp1
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return $
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LineTo ( NextPoint subdiv ) ( invalidateCache dat )
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Seq.:<| LineTo ( NextPoint sp1 ) ( invalidateCache dat )
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LineTo ( NextPoint subdiv ) ( CurveData i' $ invalidateCache dat )
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Seq.:<| LineTo ( NextPoint sp1 ) ( CurveData i $ invalidateCache dat )
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Seq.:<| Seq.Empty
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else return $ Seq.singleton crv
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Bezier2To sp1 ( NextPoint sp2 ) dat -> do
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Bezier2To sp1 ( NextPoint sp2 ) ( CurveData _ dat ) -> do
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let
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p0, p1, p2 :: ℝ 2
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p0 = coords sp0
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@ -193,14 +203,14 @@ subdivide c doc@( Document { documentMetadata, documentContent }) =
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then
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case Quadratic.subdivide @( DiffPointData ( T brushParams ) ) ( Quadratic.Bezier sp0 sp1 sp2 ) t of
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( Quadratic.Bezier _ q1 subdiv, Quadratic.Bezier _ r1 _ ) -> do
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Writer.tell [ ( stripData crv, t ) ]
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lift $ Writer.tell [ ( stripData crv, t ) ]
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let
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bez_start, bez_end :: Curve Open ( CurveData RealWorld ) ( PointData brushParams )
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bez_start = Bezier2To q1 ( NextPoint subdiv ) ( invalidateCache dat )
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bez_end = Bezier2To r1 ( NextPoint sp2 ) ( invalidateCache dat )
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bez_start = Bezier2To q1 ( NextPoint subdiv ) ( CurveData i' $ invalidateCache dat )
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bez_end = Bezier2To r1 ( NextPoint sp2 ) ( CurveData i $ invalidateCache dat )
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return ( bez_start Seq.:<| bez_end Seq.:<| Seq.Empty )
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else return $ Seq.singleton crv
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Bezier3To sp1 sp2 ( NextPoint sp3 ) dat -> do
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Bezier3To sp1 sp2 ( NextPoint sp3 ) ( CurveData _ dat ) -> do
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let
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p0, p1, p2, p3 :: ℝ 2
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p0 = coords sp0
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@ -213,15 +223,21 @@ subdivide c doc@( Document { documentMetadata, documentContent }) =
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then do
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case Cubic.subdivide @( DiffPointData ( T brushParams ) ) ( Cubic.Bezier sp0 sp1 sp2 sp3 ) t of
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( Cubic.Bezier _ q1 q2 subdiv, Cubic.Bezier _ r1 r2 _ ) -> do
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Writer.tell [ ( stripData crv, t ) ]
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lift $ Writer.tell [ ( stripData crv, t ) ]
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let
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bez_start, bez_end :: Curve Open ( CurveData RealWorld ) ( PointData brushParams )
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bez_start = Bezier3To q1 q2 ( NextPoint subdiv ) ( invalidateCache dat )
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bez_end = Bezier3To r1 r2 ( NextPoint sp3 ) ( invalidateCache dat )
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bez_start = Bezier3To q1 q2 ( NextPoint subdiv ) ( CurveData i' $ invalidateCache dat )
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bez_end = Bezier3To r1 r2 ( NextPoint sp3 ) ( CurveData i $ invalidateCache dat )
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return ( bez_start Seq.:<| bez_end Seq.:<| Seq.Empty )
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else
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return $ Seq.singleton crv
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-- | Stroke subdivision is the key reason why we index curves with 'Rational'
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-- rather than 'Integer'.
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fareySum :: Rational -> Rational -> Rational
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fareySum a b = ( numerator a + numerator b )
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% ( denominator a + denominator b )
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--------------------------------------------------------------------------------
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-- Selection.
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