add root solving code, coalesce event handling

This commit is contained in:
sheaf 2020-08-12 22:43:47 +02:00
parent d74d4fd5cc
commit 2bd6847e78
11 changed files with 421 additions and 199 deletions

1
.gitignore vendored
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@ -3,6 +3,7 @@ cabal.project.local
assets/*.svg
assets/*/
refs/
*.txt
*.md

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@ -60,6 +60,7 @@ library
, Math.Bezier.Stroke
, Math.Bezier.Subdivision
, Math.Module
, Math.RealRoots
, Math.Vector2D
build-depends:

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@ -61,11 +61,9 @@ import MetaBrush.Document
, Stroke(..)
)
import MetaBrush.Event
( handleKeyboardPressEvent, handleKeyboardReleaseEvent )
( handleEvents )
import MetaBrush.Render.Util
( widgetAddClass, widgetAddClasses )
import MetaBrush.UI.Coordinates
( keepViewportCoordinatesUpdated )
import MetaBrush.UI.FileBar
( createFileBar )
import MetaBrush.UI.InfoBar
@ -140,6 +138,8 @@ main = do
GTK.setWindowDecorated window False
GTK.setWindowTitle window "MetaBrush"
GTK.windowSetDefaultSize window 800 600
GTK.widgetAddEvents window
[ GDK.EventMaskKeyPressMask, GDK.EventMaskKeyReleaseMask ]
let
baseMinWidth, baseMinHeight :: Int32
@ -244,13 +244,6 @@ main = do
infoBarElements <- createInfoBar colours infoBar
keepViewportCoordinatesUpdated
activeDocumentTVar
openDocumentsTVar
pressedKeysTVar
infoBarElements
viewportDrawingArea
---------------------------------------------------------
-- File bar
@ -261,6 +254,7 @@ main = do
window
title
viewportDrawingArea
infoBarElements
fileBar
---------------------------------------------------------
@ -271,12 +265,9 @@ main = do
---------------------------------------------------------
-- Actions
GTK.widgetAddEvents window
[ GDK.EventMaskKeyPressMask, GDK.EventMaskKeyReleaseMask ]
_ <- GTK.onWidgetKeyPressEvent window ( handleKeyboardPressEvent pressedKeysTVar )
_ <- GTK.onWidgetKeyReleaseEvent window ( handleKeyboardReleaseEvent pressedKeysTVar )
_ <- GTK.onWidgetDestroy window GTK.mainQuit
handleEvents
activeDocumentTVar openDocumentsTVar pressedKeysTVar
window viewportDrawingArea infoBarElements
---------------------------------------------------------
-- GTK main loop

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@ -1,12 +1,33 @@
{-# LANGUAGE BlockArguments #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE BlockArguments #-}
{-# LANGUAGE NamedFieldPuns #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE RecordWildCards #-}
{-# LANGUAGE TypeApplications #-}
module MetaBrush.Event where
-- base
import Control.Monad
( unless )
import Data.Foldable
( for_ )
import Data.Word
( Word32 )
-- acts
import Data.Act
( Act
( () )
, Torsor
( (-->) )
)
-- containers
import Data.IntMap.Strict
( IntMap )
import qualified Data.IntMap.Strict as IntMap
( insert, lookup )
-- gi-gdk
import qualified GI.Gdk as GDK
@ -17,10 +38,147 @@ import qualified GI.Gtk as GTK
import qualified Control.Concurrent.STM as STM
( atomically )
import qualified Control.Concurrent.STM.TVar as STM
( TVar, readTVar, writeTVar )
( TVar, readTVar, readTVarIO, writeTVar )
-- MetaBrush
import Math.Module
( (*^) )
import Math.Vector2D
( Point2D(..), Vector2D(..) )
import MetaBrush.Document
( Document(..), currentDocument )
import MetaBrush.UI.Coordinates
( toViewportCoordinates )
import MetaBrush.UI.InfoBar
( InfoBar, InfoData(..), updateInfoBar )
--------------------------------------------------------------------------------
handleEvents :: STM.TVar ( Maybe Int ) -> STM.TVar ( IntMap Document ) -> STM.TVar [ Word32 ] -> GTK.Window -> GTK.DrawingArea -> InfoBar -> IO ()
handleEvents activeDocumentTVar openDocumentsTVar pressedKeysTVar window viewportDrawingArea infoBar = do
-- Mouse events
_ <- GTK.onWidgetMotionNotifyEvent viewportDrawingArea
( handleMotionEvent activeDocumentTVar openDocumentsTVar viewportDrawingArea infoBar )
_ <- GTK.onWidgetScrollEvent viewportDrawingArea
( handleScrollEvent activeDocumentTVar openDocumentsTVar pressedKeysTVar viewportDrawingArea infoBar )
-- Keyboard events
_ <- GTK.onWidgetKeyPressEvent window ( handleKeyboardPressEvent pressedKeysTVar )
_ <- GTK.onWidgetKeyReleaseEvent window ( handleKeyboardReleaseEvent pressedKeysTVar )
-- Window quit
_ <- GTK.onWidgetDestroy window GTK.mainQuit
pure ()
--------------------------------------------------------------------------------
-- Mouse events.
handleMotionEvent :: STM.TVar ( Maybe Int ) -> STM.TVar ( IntMap Document ) -> GTK.DrawingArea -> InfoBar -> GDK.EventMotion -> IO Bool
handleMotionEvent activeDocumentTVar openDocumentsTVar viewportDrawingArea infoBar eventMotion = do
mbDoc <- currentDocument activeDocumentTVar openDocumentsTVar
for_ mbDoc \ ( Document { .. } ) -> do
----------------------------------------------------------
-- Update mouse position in info bar on mouse move event.
x <- GDK.getEventMotionX eventMotion
y <- GDK.getEventMotionY eventMotion
viewportWidth <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedWidth viewportDrawingArea
viewportHeight <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedHeight viewportDrawingArea
let
toViewport :: Point2D Double -> Point2D Double
toViewport = toViewportCoordinates zoomFactor ( viewportWidth, viewportHeight ) viewportCenter
infoData :: InfoData
infoData =
InfoData
{ zoom = zoomFactor
, mousePos = toViewport ( Point2D x y )
, topLeftPos = toViewport ( Point2D 0 0 )
, botRightPos = toViewport ( Point2D viewportWidth viewportHeight )
}
updateInfoBar infoBar infoData
pure False
handleScrollEvent :: STM.TVar ( Maybe Int ) -> STM.TVar ( IntMap Document ) -> STM.TVar [ Word32 ] -> GTK.DrawingArea -> InfoBar -> GDK.EventScroll -> IO Bool
handleScrollEvent activeDocumentTVar openDocumentsTVar pressedKeysTVar viewportDrawingArea infoBar scrollEvent = do
dx <- GDK.getEventScrollDeltaX scrollEvent
dy <- GDK.getEventScrollDeltaY scrollEvent
x <- GDK.getEventScrollX scrollEvent
y <- GDK.getEventScrollY scrollEvent
viewportWidth <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedWidth viewportDrawingArea
viewportHeight <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedHeight viewportDrawingArea
unless ( dx == 0 && dy == 0 ) do
mbActiveDoc <- STM.readTVarIO activeDocumentTVar
for_ mbActiveDoc \ i -> do
docs <- STM.readTVarIO openDocumentsTVar
for_ ( IntMap.lookup i docs ) \ ( doc@( Document { viewportCenter = oldCenter, zoomFactor = oldZoomFactor } ) ) -> do
pressedKeys <- STM.readTVarIO pressedKeysTVar
let
toViewport :: Point2D Double -> Point2D Double
toViewport = toViewportCoordinates oldZoomFactor ( viewportWidth, viewportHeight ) oldCenter
-- Mouse position in the coordinate system of the document (not the drawing area GTK coordinates)
mousePos :: Point2D Double
mousePos = toViewport ( Point2D x y )
newDoc :: Document
newDoc
-- Zooming using 'Control'.
| any ( \ key -> key == Control_L || key == Control_R ) pressedKeys
= let
newZoomFactor :: Double
newZoomFactor
| dy > 0
= max 0.0078125 ( oldZoomFactor / sqrt 2 )
| otherwise
= min 256 ( oldZoomFactor * sqrt 2 )
newCenter :: Point2D Double
newCenter
= ( 1 - oldZoomFactor / newZoomFactor ) *^ ( oldCenter --> mousePos :: Vector2D Double )
oldCenter
in doc { zoomFactor = newZoomFactor, viewportCenter = newCenter }
-- Vertical scrolling turned into horizontal scrolling using 'Shift'.
| dx == 0 && any ( \ key -> key == Shift_L || key == Shift_R ) pressedKeys
= let
newCenter :: Point2D Double
newCenter = ( ( 25 / oldZoomFactor ) *^ Vector2D ( Point2D dy 0 ) ) oldCenter
in doc { viewportCenter = newCenter }
-- Vertical scrolling.
| otherwise
= let
newCenter :: Point2D Double
newCenter = ( ( 25 / oldZoomFactor ) *^ Vector2D ( Point2D dx dy ) ) oldCenter
in doc { viewportCenter = newCenter }
docs' :: IntMap Document
docs' = IntMap.insert i newDoc docs
STM.atomically ( STM.writeTVar openDocumentsTVar docs' )
GTK.widgetQueueDraw viewportDrawingArea
let
newZoomFactor :: Double
newZoomFactor = zoomFactor newDoc
newCenter :: Point2D Double
newCenter = viewportCenter newDoc
toNewViewport :: Point2D Double -> Point2D Double
toNewViewport = toViewportCoordinates newZoomFactor ( viewportWidth, viewportHeight ) newCenter
infoData :: InfoData
infoData = InfoData
{ zoom = zoomFactor newDoc
, mousePos
, topLeftPos = toNewViewport ( Point2D 0 0 )
, botRightPos = toNewViewport ( Point2D viewportWidth viewportHeight )
}
updateInfoBar infoBar infoData
pure False
--------------------------------------------------------------------------------
-- Keyboard events.
handleKeyboardPressEvent, handleKeyboardReleaseEvent :: STM.TVar [ Word32 ] -> GDK.EventKey -> IO Bool
handleKeyboardPressEvent pressedKeysTVar evt = do
keyCode <- GDK.getEventKeyKeyval evt
@ -37,6 +195,9 @@ handleKeyboardReleaseEvent pressedKeysTVar evt = do
STM.writeTVar pressedKeysTVar ( filter ( /= keyCode ) pressedKeys )
pure True
--------------------
-- GDK keycodes.
pattern Escape :: Word32
pattern Escape = 0xff1b
pattern Delete :: Word32

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@ -1,21 +1,7 @@
{-# LANGUAGE BlockArguments #-}
{-# LANGUAGE NamedFieldPuns #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE RecordWildCards #-}
{-# LANGUAGE TypeApplications #-}
module MetaBrush.UI.Coordinates
( keepViewportCoordinatesUpdated )
( toViewportCoordinates )
where
-- base
import Control.Monad
( unless, void )
import Data.Foldable
( for_ )
import Data.Word
( Word32 )
-- acts
import Data.Act
( Act
@ -24,169 +10,14 @@ import Data.Act
( (-->) )
)
-- containers
import Data.IntMap.Strict
( IntMap )
import qualified Data.IntMap.Strict as IntMap
( insert, lookup )
-- gi-gdk
import qualified GI.Gdk as GDK
-- gi-gtk
import qualified GI.Gtk as GTK
-- stm
import qualified Control.Concurrent.STM as STM
( atomically )
import qualified Control.Concurrent.STM.TVar as STM
( TVar, readTVarIO, writeTVar )
-- MetaBrush
import Math.Module
( (*^) )
import Math.Vector2D
( Point2D(..), Vector2D(..) )
import MetaBrush.Document
( Document(..), currentDocument )
import MetaBrush.Event
( pattern Control_L, pattern Control_R
, pattern Shift_L, pattern Shift_R
)
import MetaBrush.UI.InfoBar
( InfoBar, InfoData(..), updateInfoBar )
--------------------------------------------------------------------------------
-- | Updates viewport coordinates on mouse motion / mouse scroll.
--
-- * On a scroll event, modifies the viewport coordinates as required.
-- * On a scroll event or a mouse motion event, updates the info bar coordinate display.
--
-- TODO: also update on change of document.
keepViewportCoordinatesUpdated
:: STM.TVar ( Maybe Int )
-> STM.TVar ( IntMap Document )
-> STM.TVar [ Word32 ]
-> InfoBar
-> GTK.DrawingArea
-> IO ()
keepViewportCoordinatesUpdated
activeDocumentTVar
openDocumentsTVar
pressedKeysTVar
infoBar
viewportDrawingArea = do
-----------------------------------------------------------------
-- Update mouse position on mouse move event.
void $ GTK.onWidgetMotionNotifyEvent viewportDrawingArea \ eventMotion -> do
mbDoc <- currentDocument activeDocumentTVar openDocumentsTVar
infoData <- case mbDoc of
Nothing ->
pure $
InfoData
{ zoom = 1
, mousePos = Point2D 0 0
, topLeftPos = Point2D 0 0
, botRightPos = Point2D 0 0
}
Just ( Document { .. } ) -> do
x <- GDK.getEventMotionX eventMotion
y <- GDK.getEventMotionY eventMotion
viewportWidth <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedWidth viewportDrawingArea
viewportHeight <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedHeight viewportDrawingArea
let
toViewport :: Point2D Double -> Point2D Double
toViewport = toViewportCoordinates zoomFactor ( viewportWidth, viewportHeight ) viewportCenter
pure $
InfoData
{ zoom = zoomFactor
, mousePos = toViewport ( Point2D x y )
, topLeftPos = toViewport ( Point2D 0 0 )
, botRightPos = toViewport ( Point2D viewportWidth viewportHeight )
}
updateInfoBar infoBar infoData
pure False
-----------------------------------------------------------------
-- Update coordinates on scroll event.
void $ GTK.onWidgetScrollEvent viewportDrawingArea \ scrollEvent -> do
dx <- GDK.getEventScrollDeltaX scrollEvent
dy <- GDK.getEventScrollDeltaY scrollEvent
x <- GDK.getEventScrollX scrollEvent
y <- GDK.getEventScrollY scrollEvent
viewportWidth <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedWidth viewportDrawingArea
viewportHeight <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedHeight viewportDrawingArea
unless ( dx == 0 && dy == 0 ) do
mbActiveDoc <- STM.readTVarIO activeDocumentTVar
for_ mbActiveDoc \ i -> do
docs <- STM.readTVarIO openDocumentsTVar
for_ ( IntMap.lookup i docs ) \ ( doc@( Document { viewportCenter = oldCenter, zoomFactor = oldZoomFactor } ) ) -> do
pressedKeys <- STM.readTVarIO pressedKeysTVar
let
toViewport :: Point2D Double -> Point2D Double
toViewport = toViewportCoordinates oldZoomFactor ( viewportWidth, viewportHeight ) oldCenter
-- Mouse position in the coordinate system of the document (not the drawing area GTK coordinates)
mousePos :: Point2D Double
mousePos = toViewport ( Point2D x y )
newDoc :: Document
newDoc
-- Zooming using 'Control'.
| any ( \ key -> key == Control_L || key == Control_R ) pressedKeys
= let
newZoomFactor :: Double
newZoomFactor
| dy > 0
= max 0.0078125 ( oldZoomFactor / sqrt 2 )
| otherwise
= min 256 ( oldZoomFactor * sqrt 2 )
newCenter :: Point2D Double
newCenter
= ( 1 - oldZoomFactor / newZoomFactor ) *^ ( oldCenter --> mousePos :: Vector2D Double )
oldCenter
in doc { zoomFactor = newZoomFactor, viewportCenter = newCenter }
-- Vertical scrolling turned into horizontal scrolling using 'Shift'.
| dx == 0 && any ( \ key -> key == Shift_L || key == Shift_R ) pressedKeys
= let
newCenter :: Point2D Double
newCenter = ( ( 25 / oldZoomFactor ) *^ Vector2D ( Point2D dy 0 ) ) oldCenter
in doc { viewportCenter = newCenter }
-- Vertical scrolling.
| otherwise
= let
newCenter :: Point2D Double
newCenter = ( ( 25 / oldZoomFactor ) *^ Vector2D ( Point2D dx dy ) ) oldCenter
in doc { viewportCenter = newCenter }
docs' :: IntMap Document
docs' = IntMap.insert i newDoc docs
STM.atomically ( STM.writeTVar openDocumentsTVar docs' )
GTK.widgetQueueDraw viewportDrawingArea
let
newZoomFactor :: Double
newZoomFactor = zoomFactor newDoc
newCenter :: Point2D Double
newCenter = viewportCenter newDoc
toNewViewport :: Point2D Double -> Point2D Double
toNewViewport = toViewportCoordinates newZoomFactor ( viewportWidth, viewportHeight ) newCenter
infoData :: InfoData
infoData = InfoData
{ zoom = zoomFactor newDoc
, mousePos
, topLeftPos = toNewViewport ( Point2D 0 0 )
, botRightPos = toNewViewport ( Point2D viewportWidth viewportHeight )
}
updateInfoBar infoBar infoData
pure True
toViewportCoordinates :: Double -> ( Double, Double ) -> Point2D Double -> Point2D Double -> Point2D Double
toViewportCoordinates zoomFactor ( viewportWidth, viewportHeight ) viewportCenter ( Point2D x y )
= ( recip zoomFactor *^ ( Point2D ( 0.5 * viewportWidth ) ( 0.5 * viewportHeight ) --> Point2D x y :: Vector2D Double ) )

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@ -3,6 +3,7 @@
{-# LANGUAGE GADTs #-}
{-# LANGUAGE NamedFieldPuns #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE RecordWildCards #-}
{-# LANGUAGE TypeApplications #-}
module MetaBrush.UI.FileBar
@ -35,23 +36,32 @@ import Data.Text
( Text )
-- MetaBrush
import Math.Vector2D
( Point2D(..) )
import MetaBrush.Document
( Document(..) )
import MetaBrush.Render.Util
( widgetAddClass, widgetAddClasses )
import MetaBrush.UI.Coordinates
( toViewportCoordinates )
import MetaBrush.UI.InfoBar
( InfoBar, InfoData(..), updateInfoBar )
--------------------------------------------------------------------------------
-- | Add the file bar: tabs allowing selection of the active document.
--
-- Updates the active document when buttons are clicked.
createFileBar
:: STM.TVar ( Maybe Int )
-> STM.TVar ( IntMap Document )
-> GTK.Window
-> GTK.Label
-> GTK.DrawingArea
-> InfoBar
-> GTK.ScrolledWindow
-> IO ( IntMap GTK.RadioButton )
createFileBar activeDocumentTVar openDocumentsTVar window title viewportArea fileBar = do
createFileBar activeDocumentTVar openDocumentsTVar window title viewportArea infoBar fileBar = do
widgetAddClass fileBar "fileBar"
@ -64,9 +74,9 @@ createFileBar activeDocumentTVar openDocumentsTVar window title viewportArea fil
-- TODO: currently using static list of documents.
-- Need to dynamically update this widget as the user opens/closes documents.
documents <- STM.readTVarIO openDocumentsTVar
fileButtons <- ( `IntMap.traverseWithKey` documents ) \ i ( Document { displayName, unsavedChanges } ) -> do
fileButtons <- ( `IntMap.traverseWithKey` documents ) \ i ( Document { displayName = currDisplayName } ) -> do
-- File tab elements.
pgButton <- GTK.radioButtonNewWithLabelFromWidget ( Just fileBarPhantomRadioButton ) displayName
pgButton <- GTK.radioButtonNewWithLabelFromWidget ( Just fileBarPhantomRadioButton ) currDisplayName
GTK.toggleButtonSetMode pgButton False -- don't display radio indicator
closeFileButton <- GTK.buttonNewWithLabel "x"
@ -95,7 +105,7 @@ createFileBar activeDocumentTVar openDocumentsTVar window title viewportArea fil
Nothing -> do
GTK.labelSetText title "MetaBrush"
GTK.setWindowTitle window "MetaBrush"
Just ( Document { displayName, unsavedChanges } ) -> do
Just ( Document { .. } ) -> do
let
titleText :: Text
titleText
@ -105,6 +115,20 @@ createFileBar activeDocumentTVar openDocumentsTVar window title viewportArea fil
= displayName <> " MetaBrush"
GTK.labelSetText title titleText
GTK.setWindowTitle window titleText
viewportWidth <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedWidth viewportArea
viewportHeight <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedHeight viewportArea
let
toViewport :: Point2D Double -> Point2D Double
toViewport = toViewportCoordinates zoomFactor ( viewportWidth, viewportHeight ) viewportCenter
infoData :: InfoData
infoData =
InfoData
{ zoom = zoomFactor
, mousePos = Point2D 0 0
, topLeftPos = toViewport ( Point2D 0 0 )
, botRightPos = toViewport ( Point2D viewportWidth viewportHeight )
}
updateInfoBar infoBar infoData
else do
GTK.widgetSetStateFlags tab ( filter ( /= GTK.StateFlagsActive ) flags ) True
GTK.labelSetText title "MetaBrush"

View file

@ -13,10 +13,13 @@ module Math.Bezier.Cubic
( Bezier(..)
, bezier, bezier'
, subdivide
, closestPoint
)
where
-- base
import Data.List.NonEmpty
( NonEmpty(..) )
import GHC.Generics
( Generic )
@ -27,12 +30,15 @@ import Data.Act
)
-- MetaBrush
import qualified Math.Bezier.Quadratic as Quadratic
( Bezier(Bezier), bezier )
import Math.Module
( Module (..)
, lerp
, Inner(..), squaredNorm
)
import qualified Math.Bezier.Quadratic as Quadratic
( Bezier(Bezier), bezier )
import Math.RealRoots
( realRoots )
--------------------------------------------------------------------------------
@ -74,3 +80,41 @@ subdivide ( Bezier { .. } ) t = ( Bezier p0 q1 q2 pt, Bezier pt r1 r2 p3 )
q2 = lerp @v t q1 s
r1 = lerp @v t s r2
pt = lerp @v t q2 r1
-- | Finds the closest point to a given point on a cubic Bézier curve.
closestPoint :: forall v r p. ( Torsor v p, Inner r v, RealFloat r ) => Bezier p -> p -> ( r, p )
closestPoint pts@( Bezier { .. } ) c = pickClosest ( 0 :| 1 : roots )
where
roots :: [ r ]
roots = filter ( \ r -> r > 0 && r < 1 ) ( realRoots [ a0, a1, a2, a3, a4, a5 ] )
v, v', v'', v''' :: v
v = c --> p0
v' = p0 --> p1
v'' = p1 --> p0 ^+^ p1 --> p2
v''' = p0 --> p3 ^+^ 3 *^ ( p2 --> p1 )
a0, a1, a2, a3, a4, a5 :: r
a0 = v ^.^ v'
a1 = 3 * squaredNorm v' + 2 * v ^.^ v''
a2 = 9 * v' ^.^ v'' + 3 * v ^.^ v'''
a3 = 6 * squaredNorm v'' + 4 * v' ^.^ v'''
a4 = 5 * v'' ^.^ v'''
a5 = squaredNorm v'''
pickClosest :: NonEmpty r -> ( r, p )
pickClosest ( s :| ss ) = go s q nm0 ss
where
q :: p
q = bezier @v pts s
nm0 :: r
nm0 = squaredNorm ( c --> q :: v )
go t p _ [] = ( t, p )
go t p nm ( t' : ts )
| nm' < nm = go t' p' nm' ts
| otherwise = go t p nm ts
where
p' :: p
p' = bezier @v pts t'
nm' :: r
nm' = squaredNorm ( c --> p' :: v )

View file

@ -13,10 +13,13 @@ module Math.Bezier.Quadratic
( Bezier(..)
, bezier, bezier'
, subdivide
, closestPoint
)
where
-- base
import Data.List.NonEmpty
( NonEmpty(..) )
import GHC.Generics
( Generic )
@ -30,7 +33,10 @@ import Data.Act
import Math.Module
( Module (..)
, lerp
, Inner(..), squaredNorm
)
import Math.RealRoots
( realRoots )
--------------------------------------------------------------------------------
@ -61,3 +67,38 @@ subdivide ( Bezier { .. } ) t = ( Bezier p0 q1 pt, Bezier pt r1 p2 )
q1 = lerp @v t p0 p1
r1 = lerp @v t p1 p2
pt = lerp @v t q1 r1
-- | Finds the closest point to a given point on a quadratic Bézier curve.
closestPoint :: forall v r p. ( Torsor v p, Inner r v, RealFloat r ) => Bezier p -> p -> ( r, p )
closestPoint pts@( Bezier { .. } ) c = pickClosest ( 0 :| 1 : roots )
where
roots :: [ r ]
roots = filter ( \ r -> r > 0 && r < 1 ) ( realRoots [ a0, a1, a2, a3 ] )
v, v', v'' :: v
v = c --> p0
v' = p0 --> p1
v'' = p1 --> p0 ^+^ p1 --> p2
a0, a1, a2, a3 :: r
a0 = v ^.^ v'
a1 = v ^.^ v'' + 2 * squaredNorm v'
a2 = 3 * ( v' ^.^ v'' )
a3 = squaredNorm v''
pickClosest :: NonEmpty r -> ( r, p )
pickClosest ( s :| ss ) = go s q nm0 ss
where
q :: p
q = bezier @v pts s
nm0 :: r
nm0 = squaredNorm ( c --> q :: v )
go t p _ [] = ( t, p )
go t p nm ( t' : ts )
| nm' < nm = go t' p' nm' ts
| otherwise = go t p nm ts
where
p' :: p
p' = bezier @v pts t'
nm' :: r
nm' = squaredNorm ( c --> p' :: v )

View file

@ -4,8 +4,8 @@
{-# LANGUAGE ScopedTypeVariables #-}
module Math.Module
( Module(..)
, lerp
( Module(..), lerp
, Inner(..), squaredNorm
)
where
@ -20,7 +20,7 @@ import Data.Act
--------------------------------------------------------------------------------
infixl 6 ^+^, ^-^
infix 8 ^*, *^
infix 9 ^*, *^
class Num r => Module r m | m -> r where
@ -37,3 +37,12 @@ class Num r => Module r m | m -> r where
lerp :: forall v r p. ( Module r v, Torsor v p ) => r -> p -> p -> p
lerp t p0 p1 = ( t *^ ( p0 --> p1 :: v ) ) p0
infixl 8 ^.^
class Module r m => Inner r m where
(^.^) :: m -> m -> r
-- | Squared norm of a vector, computed using the inner product.
squaredNorm :: Inner r m => m -> r
squaredNorm v = v ^.^ v

115
src/lib/Math/RealRoots.hs Normal file
View file

@ -0,0 +1,115 @@
{-# LANGUAGE ScopedTypeVariables #-}
module Math.RealRoots
( realRoots )
where
-- base
import Data.Complex
( Complex(..), magnitude )
import Data.List.NonEmpty
( NonEmpty(..), toList )
import Data.Maybe
( mapMaybe )
--------------------------------------------------------------------------------
-- | Find real roots of a polynomial.
realRoots :: forall r. RealFloat r => [ r ] -> [ r ]
realRoots p = mapMaybe isReal ( roots eps 10000 ( map (:+ 0) p ) )
where
isReal :: Complex r -> Maybe r
isReal ( a :+ b )
| abs b < eps = Just a
| otherwise = Nothing
eps :: r
eps = encodeFloat 1 ( 5 - floatDigits ( 0 :: r ) )
-- | Compute all roots of a polynomial using Laguerre's method and (forward) deflation.
--
-- Polynomial coefficients are given in order of ascending degree (e.g. constant coefficient first).
--
-- N.B. The forward deflation process is only guaranteed to be numerically stable
-- if Laguerre's method finds roots in increasing order of magnitude.
roots :: forall a. RealFloat a => a -> Int -> [ Complex a ] -> [ Complex a ]
roots eps maxIters p = go p []
where
go :: [ Complex a ] -> [ Complex a ] -> [ Complex a ]
go q rs
| length q <= 2 = r : rs
| otherwise = go ( deflate r q ) ( r : rs )
where
r :: Complex a
r = laguerre eps maxIters q 0
-- Start the iteration at 0 for best chance of numerical stability.
-- | Deflate a polynomial: factor out a root of the polynomial.
--
-- The polynomial must have degree at least 2.
deflate :: forall a. Num a => a -> [ a ] -> [ a ]
deflate r ( _ : c : cs ) = toList $ go ( c :| cs )
where
go :: NonEmpty a -> NonEmpty a
go ( a :| [] ) = a :| []
go ( a :| a' : as ) = case go ( a' :| as ) of
( b' :| bs ) -> ( a + r * b' ) :| ( b' : bs )
deflate _ _ = error "deflate: polynomial of degree < 2"
-- | Laguerre's method.
laguerre
:: forall a. RealFloat a
=> a -- ^ error tolerance
-> Int -- ^ max number of iterations
-> [ Complex a ] -- ^ polynomial
-> Complex a -- ^ initial point
-> Complex a
laguerre eps maxIters p x0 = go maxIters x0
where
p', p'' :: [ Complex a ]
p' = derivative p
p'' = derivative p'
go :: Int -> Complex a -> Complex a
go iterationsLeft x
| iterationsLeft <= 0 = x
| magnitude ( x' - x ) < eps = x'
| otherwise = go ( iterationsLeft - 1 ) x'
where
x' :: Complex a
x' = laguerreStep eps p p' p'' x
-- | Take a single step in Laguerre's method.
laguerreStep
:: forall a. RealFloat a
=> a -- ^ error tolerance
-> [ Complex a ] -- ^ polynomial
-> [ Complex a ] -- ^ first derivative of polynomial
-> [ Complex a ] -- ^ second derivative of polynomial
-> Complex a -- ^ initial point
-> Complex a
laguerreStep eps p p' p'' x
| magnitude px < eps = x
| otherwise = x - n / denom
where
n = fromIntegral ( length p )
px = eval p x
p'x = eval p' x
p''x = eval p'' x
g = p'x / px
g² = g * g
h = g² - p''x / px
delta = sqrt $ ( n - 1 ) * ( n * h - g² )
gp = g + delta
gm = g - delta
denom
| magnitude gm > magnitude gp
= gm
| otherwise
= gp
-- | Evaluate a polynomial.
eval :: Num a => [ a ] -> a -> a
eval as x = foldr ( \ a b -> a + x * b ) 0 as
-- | Derivative of a polynomial.
derivative :: Num a => [ a ] -> [ a ]
derivative as = zipWith ( \ i a -> fromIntegral i * a ) [ ( 1 :: Int ) .. ] ( tail as )

View file

@ -32,7 +32,7 @@ import Data.Group.Generics
-- MetaBrush
import Math.Module
( Module (..) )
( Module(..), Inner(..) )
--------------------------------------------------------------------------------
@ -52,3 +52,7 @@ instance Num a => Module a ( Vector2D a ) where
c *^ p = fmap ( c * ) p
p ^* c = fmap ( * c ) p
instance Num a => Inner a ( Vector2D a ) where
( Vector2D ( Point2D x1 y1 ) ) ^.^ ( Vector2D ( Point2D x2 y2 ) )
= x1 * x2 + y1 * y2