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add backend implementation of curve dragging
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@ -69,7 +69,7 @@ import Control.Monad.Trans.State.Strict
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-- MetaBrush
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import qualified Math.Bezier.Cubic as Cubic
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( Bezier(..) )
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( Bezier(..), fromQuadratic )
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import Math.Bezier.Cubic.Fit
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( FitPoint(..), FitParameters )
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import qualified Math.Bezier.Quadratic as Quadratic
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@ -381,28 +381,9 @@ drawLine ( Colours { path, controlPoint } ) zoom p1 p2 = do
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Cairo.restore
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drawQuadraticBezier :: Colours -> Double -> Quadratic.Bezier ( Point2D Double ) -> Cairo.Render ()
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drawQuadraticBezier ( Colours { path } ) zoom
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( Quadratic.Bezier
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{ p0 = Point2D x0 y0
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, p1 = Point2D x1 y1
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, p2 = Point2D x2 y2
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}
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)
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= do
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Cairo.save
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Cairo.moveTo x0 y0
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Cairo.curveTo
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( ( 2 * x1 + x0 ) / 3 ) ( ( 2 * y1 + y0 ) / 3 )
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( ( 2 * x1 + x2 ) / 3 ) ( ( 2 * y1 + y2 ) / 3 )
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x2 y2
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Cairo.setLineWidth ( 6 / zoom )
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withRGBA path Cairo.setSourceRGBA
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Cairo.stroke
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Cairo.restore
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drawQuadraticBezier cols zoom bez =
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drawCubicBezier cols zoom
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( Cubic.fromQuadratic @( Vector2D Double ) bez )
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drawCubicBezier :: Colours -> Double -> Cubic.Bezier ( Point2D Double ) -> Cairo.Render ()
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drawCubicBezier ( Colours { path } ) zoom
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@ -5,6 +5,8 @@
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{-# LANGUAGE DerivingVia #-}
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{-# LANGUAGE FlexibleInstances #-}
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{-# LANGUAGE MultiParamTypeClasses #-}
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{-# LANGUAGE NamedFieldPuns #-}
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{-# LANGUAGE NegativeLiterals #-}
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{-# LANGUAGE RecordWildCards #-}
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{-# LANGUAGE ScopedTypeVariables #-}
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{-# LANGUAGE StandaloneDeriving #-}
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@ -13,10 +15,12 @@
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module Math.Bezier.Cubic
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( Bezier(..)
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, fromQuadratic
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, bezier, bezier', bezier''
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, curvature, squaredCurvature
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, subdivide
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, ddist, closestPoint
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, drag
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)
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where
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@ -55,7 +59,7 @@ import Data.Group.Generics
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-- MetaBrush
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import qualified Math.Bezier.Quadratic as Quadratic
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( Bezier(Bezier), bezier )
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( Bezier(..), bezier )
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import Math.Epsilon
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( epsilon )
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import Math.Module
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@ -82,7 +86,16 @@ data Bezier p
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deriving anyclass ( NFData, NFData1 )
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deriving via Ap Bezier p
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instance Act v p => Act v ( Bezier p )
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instance {-# OVERLAPPING #-} Act v p => Act v ( Bezier p )
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-- | Degree raising: convert a quadratic Bézier curve to a cubic Bézier curve.
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fromQuadratic :: forall v r p. ( Torsor v p, Module r v, Fractional r ) => Quadratic.Bezier p -> Bezier p
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fromQuadratic ( Quadratic.Bezier { p0 = q0, p1 = q1, p2 = q2 } ) = Bezier {..}
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where
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p0 = q0
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p1 = lerp @v (2/3) q0 q1
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p2 = lerp @v (1/3) q1 q2
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p3 = q2
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-- | Cubic Bézier curve.
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bezier :: forall v r p. ( Torsor v p, Module r v ) => Bezier p -> r -> p
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@ -91,7 +104,6 @@ bezier ( Bezier {..} ) t =
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( Quadratic.bezier @v ( Quadratic.Bezier p0 p1 p2 ) t )
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( Quadratic.bezier @v ( Quadratic.Bezier p1 p2 p3 ) t )
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-- | Derivative of cubic Bézier curve.
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bezier' :: forall v r p. ( Torsor v p, Module r v ) => Bezier p -> r -> v
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bezier' ( Bezier {..} ) t
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@ -181,3 +193,25 @@ closestPoint pts@( Bezier {..} ) c = pickClosest ( 0 :| 1 : roots ) -- todo: als
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p' = bezier @v pts t'
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nm' :: r
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nm' = squaredNorm ( c --> p' :: v )
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-- | Drag a cubic Bézier curve to pass through a given point.
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--
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-- Given a cubic Bézier curve, a time \( 0 < t < 1 \) and a point `q`,
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-- modifies the control points to make the curve pass through `q` at time `t`.
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--
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-- Affects the two control points depending on how far along the dragged point is.
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-- For instance, dragging near the middle moves both control points equally,
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-- while dragging near an endpoint will mostly affect the control point associated with that endpoint.
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drag :: forall v r p. ( Torsor v p, Module r v, Fractional r ) => Bezier p -> r -> p -> Bezier p
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drag ( Bezier {..} ) t q = Bezier { p0, p1 = p1', p2 = p2', p3 }
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where
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v0, v1, v2, v3, delta :: v
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v0 = q --> p0
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v1 = q --> p1
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v2 = q --> p2
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v3 = q --> p3
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delta = ( recip $ t * ( -3 + t * ( 9 + t * ( -12 + 6 * t ) ) ) )
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*^ bezier @v ( Bezier v0 v1 v2 v3 ) t
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p1', p2' :: p
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p1' = ( ( 1 - t ) *^ delta ) • p1
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p2' = ( t *^ delta ) • p2
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@ -17,6 +17,7 @@ module Math.Bezier.Quadratic
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, curvature, squaredCurvature
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, subdivide
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, ddist, closestPoint
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, interpolate
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)
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where
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@ -80,7 +81,7 @@ data Bezier p
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deriving anyclass ( NFData, NFData1 )
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deriving via Ap Bezier p
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instance Act v p => Act v ( Bezier p )
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instance {-# OVERLAPPING #-} Act v p => Act v ( Bezier p )
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-- | Quadratic Bézier curve.
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bezier :: forall v r p. ( Torsor v p, Module r v ) => Bezier p -> r -> p
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@ -160,3 +161,17 @@ closestPoint pts@( Bezier {..} ) c = pickClosest ( 0 :| 1 : roots )
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p' = bezier @v pts t'
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nm' :: r
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nm' = squaredNorm ( c --> p' :: v )
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-- | Interpolation of a quadratic Bézier control point, given path points and Bézier parameter.
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--
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-- That is, given points `p0`, `p2`, and `q`, and parameter \( 0 < t < 1 \),
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-- this function finds the unique control point `p1` such that
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-- the quadratic Bézier curve with parameters `p0`, `p1`, `p2` passes through
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-- the point `q` at time `t`.
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interpolate :: forall v r p. ( Torsor v p, Module r v, Fractional r ) => p -> p -> r -> p -> Bezier p
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interpolate p0 p2 t q = Bezier {..}
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where
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p1 :: p
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p1 = ( ( 0.5 * ( t - 1 ) / t ) *^ ( q --> p0 :: v )
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^+^ ( 0.5 * t / ( t - 1 ) ) *^ ( q --> p2 :: v )
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) • q
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