mirror of
https://gitlab.com/sheaf/metabrush.git
synced 2024-11-23 15:34:06 +00:00
add root solving code, coalesce event handling
This commit is contained in:
sheaf
parent
d74d4fd5cc
commit
2bd6847e78
1
.gitignore
vendored
1
.gitignore
vendored
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@ -3,6 +3,7 @@ cabal.project.local
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assets/*.svg
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assets/*/
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refs/
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*.txt
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*.md
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@ -60,6 +60,7 @@ library
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, Math.Bezier.Stroke
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, Math.Bezier.Subdivision
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, Math.Module
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, Math.RealRoots
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, Math.Vector2D
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build-depends:
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23
app/Main.hs
23
app/Main.hs
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@ -61,11 +61,9 @@ import MetaBrush.Document
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, Stroke(..)
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)
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import MetaBrush.Event
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( handleKeyboardPressEvent, handleKeyboardReleaseEvent )
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( handleEvents )
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import MetaBrush.Render.Util
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( widgetAddClass, widgetAddClasses )
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import MetaBrush.UI.Coordinates
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( keepViewportCoordinatesUpdated )
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import MetaBrush.UI.FileBar
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( createFileBar )
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import MetaBrush.UI.InfoBar
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@ -140,6 +138,8 @@ main = do
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GTK.setWindowDecorated window False
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GTK.setWindowTitle window "MetaBrush"
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GTK.windowSetDefaultSize window 800 600
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GTK.widgetAddEvents window
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[ GDK.EventMaskKeyPressMask, GDK.EventMaskKeyReleaseMask ]
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let
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baseMinWidth, baseMinHeight :: Int32
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@ -244,13 +244,6 @@ main = do
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infoBarElements <- createInfoBar colours infoBar
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keepViewportCoordinatesUpdated
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activeDocumentTVar
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openDocumentsTVar
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pressedKeysTVar
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infoBarElements
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viewportDrawingArea
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---------------------------------------------------------
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-- File bar
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@ -261,6 +254,7 @@ main = do
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window
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title
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viewportDrawingArea
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infoBarElements
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fileBar
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---------------------------------------------------------
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@ -271,12 +265,9 @@ main = do
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---------------------------------------------------------
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-- Actions
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GTK.widgetAddEvents window
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[ GDK.EventMaskKeyPressMask, GDK.EventMaskKeyReleaseMask ]
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_ <- GTK.onWidgetKeyPressEvent window ( handleKeyboardPressEvent pressedKeysTVar )
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_ <- GTK.onWidgetKeyReleaseEvent window ( handleKeyboardReleaseEvent pressedKeysTVar )
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_ <- GTK.onWidgetDestroy window GTK.mainQuit
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handleEvents
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activeDocumentTVar openDocumentsTVar pressedKeysTVar
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window viewportDrawingArea infoBarElements
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---------------------------------------------------------
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-- GTK main loop
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@ -1,12 +1,33 @@
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{-# LANGUAGE BlockArguments #-}
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{-# LANGUAGE PatternSynonyms #-}
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{-# LANGUAGE BlockArguments #-}
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{-# LANGUAGE NamedFieldPuns #-}
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{-# LANGUAGE PatternSynonyms #-}
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{-# LANGUAGE RecordWildCards #-}
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{-# LANGUAGE TypeApplications #-}
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module MetaBrush.Event where
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-- base
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import Control.Monad
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( unless )
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import Data.Foldable
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( for_ )
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import Data.Word
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( Word32 )
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-- acts
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import Data.Act
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( Act
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( (•) )
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, Torsor
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( (-->) )
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)
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-- containers
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import Data.IntMap.Strict
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( IntMap )
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import qualified Data.IntMap.Strict as IntMap
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( insert, lookup )
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-- gi-gdk
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import qualified GI.Gdk as GDK
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@ -17,10 +38,147 @@ import qualified GI.Gtk as GTK
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import qualified Control.Concurrent.STM as STM
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( atomically )
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import qualified Control.Concurrent.STM.TVar as STM
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( TVar, readTVar, writeTVar )
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( TVar, readTVar, readTVarIO, writeTVar )
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-- MetaBrush
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import Math.Module
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( (*^) )
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import Math.Vector2D
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( Point2D(..), Vector2D(..) )
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import MetaBrush.Document
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( Document(..), currentDocument )
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import MetaBrush.UI.Coordinates
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( toViewportCoordinates )
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import MetaBrush.UI.InfoBar
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( InfoBar, InfoData(..), updateInfoBar )
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--------------------------------------------------------------------------------
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handleEvents :: STM.TVar ( Maybe Int ) -> STM.TVar ( IntMap Document ) -> STM.TVar [ Word32 ] -> GTK.Window -> GTK.DrawingArea -> InfoBar -> IO ()
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handleEvents activeDocumentTVar openDocumentsTVar pressedKeysTVar window viewportDrawingArea infoBar = do
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-- Mouse events
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_ <- GTK.onWidgetMotionNotifyEvent viewportDrawingArea
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( handleMotionEvent activeDocumentTVar openDocumentsTVar viewportDrawingArea infoBar )
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_ <- GTK.onWidgetScrollEvent viewportDrawingArea
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( handleScrollEvent activeDocumentTVar openDocumentsTVar pressedKeysTVar viewportDrawingArea infoBar )
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-- Keyboard events
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_ <- GTK.onWidgetKeyPressEvent window ( handleKeyboardPressEvent pressedKeysTVar )
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_ <- GTK.onWidgetKeyReleaseEvent window ( handleKeyboardReleaseEvent pressedKeysTVar )
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-- Window quit
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_ <- GTK.onWidgetDestroy window GTK.mainQuit
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pure ()
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--------------------------------------------------------------------------------
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-- Mouse events.
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handleMotionEvent :: STM.TVar ( Maybe Int ) -> STM.TVar ( IntMap Document ) -> GTK.DrawingArea -> InfoBar -> GDK.EventMotion -> IO Bool
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handleMotionEvent activeDocumentTVar openDocumentsTVar viewportDrawingArea infoBar eventMotion = do
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mbDoc <- currentDocument activeDocumentTVar openDocumentsTVar
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for_ mbDoc \ ( Document { .. } ) -> do
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----------------------------------------------------------
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-- Update mouse position in info bar on mouse move event.
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x <- GDK.getEventMotionX eventMotion
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y <- GDK.getEventMotionY eventMotion
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viewportWidth <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedWidth viewportDrawingArea
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viewportHeight <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedHeight viewportDrawingArea
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let
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toViewport :: Point2D Double -> Point2D Double
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toViewport = toViewportCoordinates zoomFactor ( viewportWidth, viewportHeight ) viewportCenter
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infoData :: InfoData
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infoData =
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InfoData
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{ zoom = zoomFactor
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, mousePos = toViewport ( Point2D x y )
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, topLeftPos = toViewport ( Point2D 0 0 )
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, botRightPos = toViewport ( Point2D viewportWidth viewportHeight )
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}
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updateInfoBar infoBar infoData
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pure False
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handleScrollEvent :: STM.TVar ( Maybe Int ) -> STM.TVar ( IntMap Document ) -> STM.TVar [ Word32 ] -> GTK.DrawingArea -> InfoBar -> GDK.EventScroll -> IO Bool
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handleScrollEvent activeDocumentTVar openDocumentsTVar pressedKeysTVar viewportDrawingArea infoBar scrollEvent = do
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dx <- GDK.getEventScrollDeltaX scrollEvent
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dy <- GDK.getEventScrollDeltaY scrollEvent
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x <- GDK.getEventScrollX scrollEvent
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y <- GDK.getEventScrollY scrollEvent
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viewportWidth <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedWidth viewportDrawingArea
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viewportHeight <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedHeight viewportDrawingArea
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unless ( dx == 0 && dy == 0 ) do
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mbActiveDoc <- STM.readTVarIO activeDocumentTVar
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for_ mbActiveDoc \ i -> do
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docs <- STM.readTVarIO openDocumentsTVar
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for_ ( IntMap.lookup i docs ) \ ( doc@( Document { viewportCenter = oldCenter, zoomFactor = oldZoomFactor } ) ) -> do
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pressedKeys <- STM.readTVarIO pressedKeysTVar
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let
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toViewport :: Point2D Double -> Point2D Double
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toViewport = toViewportCoordinates oldZoomFactor ( viewportWidth, viewportHeight ) oldCenter
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-- Mouse position in the coordinate system of the document (not the drawing area GTK coordinates)
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mousePos :: Point2D Double
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mousePos = toViewport ( Point2D x y )
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newDoc :: Document
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newDoc
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-- Zooming using 'Control'.
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| any ( \ key -> key == Control_L || key == Control_R ) pressedKeys
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= let
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newZoomFactor :: Double
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newZoomFactor
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| dy > 0
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= max 0.0078125 ( oldZoomFactor / sqrt 2 )
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| otherwise
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= min 256 ( oldZoomFactor * sqrt 2 )
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newCenter :: Point2D Double
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newCenter
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= ( 1 - oldZoomFactor / newZoomFactor ) *^ ( oldCenter --> mousePos :: Vector2D Double )
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• oldCenter
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in doc { zoomFactor = newZoomFactor, viewportCenter = newCenter }
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-- Vertical scrolling turned into horizontal scrolling using 'Shift'.
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| dx == 0 && any ( \ key -> key == Shift_L || key == Shift_R ) pressedKeys
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= let
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newCenter :: Point2D Double
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newCenter = ( ( 25 / oldZoomFactor ) *^ Vector2D ( Point2D dy 0 ) ) • oldCenter
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in doc { viewportCenter = newCenter }
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-- Vertical scrolling.
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| otherwise
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= let
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newCenter :: Point2D Double
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newCenter = ( ( 25 / oldZoomFactor ) *^ Vector2D ( Point2D dx dy ) ) • oldCenter
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in doc { viewportCenter = newCenter }
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docs' :: IntMap Document
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docs' = IntMap.insert i newDoc docs
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STM.atomically ( STM.writeTVar openDocumentsTVar docs' )
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GTK.widgetQueueDraw viewportDrawingArea
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let
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newZoomFactor :: Double
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newZoomFactor = zoomFactor newDoc
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newCenter :: Point2D Double
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newCenter = viewportCenter newDoc
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toNewViewport :: Point2D Double -> Point2D Double
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toNewViewport = toViewportCoordinates newZoomFactor ( viewportWidth, viewportHeight ) newCenter
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infoData :: InfoData
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infoData = InfoData
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{ zoom = zoomFactor newDoc
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, mousePos
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, topLeftPos = toNewViewport ( Point2D 0 0 )
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, botRightPos = toNewViewport ( Point2D viewportWidth viewportHeight )
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}
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updateInfoBar infoBar infoData
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pure False
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--------------------------------------------------------------------------------
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-- Keyboard events.
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handleKeyboardPressEvent, handleKeyboardReleaseEvent :: STM.TVar [ Word32 ] -> GDK.EventKey -> IO Bool
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handleKeyboardPressEvent pressedKeysTVar evt = do
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keyCode <- GDK.getEventKeyKeyval evt
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@ -37,6 +195,9 @@ handleKeyboardReleaseEvent pressedKeysTVar evt = do
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STM.writeTVar pressedKeysTVar ( filter ( /= keyCode ) pressedKeys )
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pure True
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--------------------
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-- GDK keycodes.
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pattern Escape :: Word32
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pattern Escape = 0xff1b
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pattern Delete :: Word32
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@ -1,21 +1,7 @@
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{-# LANGUAGE BlockArguments #-}
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{-# LANGUAGE NamedFieldPuns #-}
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{-# LANGUAGE PatternSynonyms #-}
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{-# LANGUAGE RecordWildCards #-}
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{-# LANGUAGE TypeApplications #-}
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module MetaBrush.UI.Coordinates
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( keepViewportCoordinatesUpdated )
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( toViewportCoordinates )
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where
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-- base
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import Control.Monad
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( unless, void )
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import Data.Foldable
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( for_ )
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import Data.Word
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( Word32 )
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-- acts
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import Data.Act
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( Act
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@ -24,169 +10,14 @@ import Data.Act
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( (-->) )
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)
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-- containers
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import Data.IntMap.Strict
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( IntMap )
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import qualified Data.IntMap.Strict as IntMap
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( insert, lookup )
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-- gi-gdk
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import qualified GI.Gdk as GDK
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-- gi-gtk
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import qualified GI.Gtk as GTK
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-- stm
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import qualified Control.Concurrent.STM as STM
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( atomically )
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import qualified Control.Concurrent.STM.TVar as STM
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( TVar, readTVarIO, writeTVar )
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-- MetaBrush
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import Math.Module
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( (*^) )
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import Math.Vector2D
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( Point2D(..), Vector2D(..) )
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import MetaBrush.Document
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( Document(..), currentDocument )
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import MetaBrush.Event
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( pattern Control_L, pattern Control_R
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, pattern Shift_L, pattern Shift_R
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)
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import MetaBrush.UI.InfoBar
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( InfoBar, InfoData(..), updateInfoBar )
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--------------------------------------------------------------------------------
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-- | Updates viewport coordinates on mouse motion / mouse scroll.
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--
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-- * On a scroll event, modifies the viewport coordinates as required.
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-- * On a scroll event or a mouse motion event, updates the info bar coordinate display.
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--
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-- TODO: also update on change of document.
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keepViewportCoordinatesUpdated
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:: STM.TVar ( Maybe Int )
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-> STM.TVar ( IntMap Document )
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-> STM.TVar [ Word32 ]
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-> InfoBar
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-> GTK.DrawingArea
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-> IO ()
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keepViewportCoordinatesUpdated
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activeDocumentTVar
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openDocumentsTVar
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pressedKeysTVar
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infoBar
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viewportDrawingArea = do
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-----------------------------------------------------------------
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-- Update mouse position on mouse move event.
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void $ GTK.onWidgetMotionNotifyEvent viewportDrawingArea \ eventMotion -> do
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mbDoc <- currentDocument activeDocumentTVar openDocumentsTVar
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infoData <- case mbDoc of
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Nothing ->
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pure $
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InfoData
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{ zoom = 1
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, mousePos = Point2D 0 0
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, topLeftPos = Point2D 0 0
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, botRightPos = Point2D 0 0
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}
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Just ( Document { .. } ) -> do
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x <- GDK.getEventMotionX eventMotion
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y <- GDK.getEventMotionY eventMotion
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viewportWidth <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedWidth viewportDrawingArea
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viewportHeight <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedHeight viewportDrawingArea
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let
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toViewport :: Point2D Double -> Point2D Double
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toViewport = toViewportCoordinates zoomFactor ( viewportWidth, viewportHeight ) viewportCenter
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pure $
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InfoData
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{ zoom = zoomFactor
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, mousePos = toViewport ( Point2D x y )
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, topLeftPos = toViewport ( Point2D 0 0 )
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, botRightPos = toViewport ( Point2D viewportWidth viewportHeight )
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}
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updateInfoBar infoBar infoData
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pure False
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-----------------------------------------------------------------
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-- Update coordinates on scroll event.
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void $ GTK.onWidgetScrollEvent viewportDrawingArea \ scrollEvent -> do
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dx <- GDK.getEventScrollDeltaX scrollEvent
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dy <- GDK.getEventScrollDeltaY scrollEvent
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x <- GDK.getEventScrollX scrollEvent
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y <- GDK.getEventScrollY scrollEvent
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viewportWidth <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedWidth viewportDrawingArea
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viewportHeight <- fromIntegral @_ @Double <$> GTK.widgetGetAllocatedHeight viewportDrawingArea
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unless ( dx == 0 && dy == 0 ) do
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mbActiveDoc <- STM.readTVarIO activeDocumentTVar
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for_ mbActiveDoc \ i -> do
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docs <- STM.readTVarIO openDocumentsTVar
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for_ ( IntMap.lookup i docs ) \ ( doc@( Document { viewportCenter = oldCenter, zoomFactor = oldZoomFactor } ) ) -> do
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pressedKeys <- STM.readTVarIO pressedKeysTVar
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let
|
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toViewport :: Point2D Double -> Point2D Double
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toViewport = toViewportCoordinates oldZoomFactor ( viewportWidth, viewportHeight ) oldCenter
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-- Mouse position in the coordinate system of the document (not the drawing area GTK coordinates)
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mousePos :: Point2D Double
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mousePos = toViewport ( Point2D x y )
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newDoc :: Document
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newDoc
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-- Zooming using 'Control'.
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||||
| any ( \ key -> key == Control_L || key == Control_R ) pressedKeys
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= let
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newZoomFactor :: Double
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newZoomFactor
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| dy > 0
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= max 0.0078125 ( oldZoomFactor / sqrt 2 )
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| otherwise
|
||||
= min 256 ( oldZoomFactor * sqrt 2 )
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newCenter :: Point2D Double
|
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newCenter
|
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= ( 1 - oldZoomFactor / newZoomFactor ) *^ ( oldCenter --> mousePos :: Vector2D Double )
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• oldCenter
|
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in doc { zoomFactor = newZoomFactor, viewportCenter = newCenter }
|
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-- Vertical scrolling turned into horizontal scrolling using 'Shift'.
|
||||
| dx == 0 && any ( \ key -> key == Shift_L || key == Shift_R ) pressedKeys
|
||||
= let
|
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newCenter :: Point2D Double
|
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newCenter = ( ( 25 / oldZoomFactor ) *^ Vector2D ( Point2D dy 0 ) ) • oldCenter
|
||||
in doc { viewportCenter = newCenter }
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-- Vertical scrolling.
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||||
| otherwise
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||||
= let
|
||||
newCenter :: Point2D Double
|
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newCenter = ( ( 25 / oldZoomFactor ) *^ Vector2D ( Point2D dx dy ) ) • oldCenter
|
||||
in doc { viewportCenter = newCenter }
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docs' :: IntMap Document
|
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docs' = IntMap.insert i newDoc docs
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STM.atomically ( STM.writeTVar openDocumentsTVar docs' )
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GTK.widgetQueueDraw viewportDrawingArea
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let
|
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newZoomFactor :: Double
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newZoomFactor = zoomFactor newDoc
|
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newCenter :: Point2D Double
|
||||
newCenter = viewportCenter newDoc
|
||||
toNewViewport :: Point2D Double -> Point2D Double
|
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toNewViewport = toViewportCoordinates newZoomFactor ( viewportWidth, viewportHeight ) newCenter
|
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infoData :: InfoData
|
||||
infoData = InfoData
|
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{ zoom = zoomFactor newDoc
|
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, mousePos
|
||||
, topLeftPos = toNewViewport ( Point2D 0 0 )
|
||||
, botRightPos = toNewViewport ( Point2D viewportWidth viewportHeight )
|
||||
}
|
||||
updateInfoBar infoBar infoData
|
||||
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||||
pure True
|
||||
|
||||
|
||||
toViewportCoordinates :: Double -> ( Double, Double ) -> Point2D Double -> Point2D Double -> Point2D Double
|
||||
toViewportCoordinates zoomFactor ( viewportWidth, viewportHeight ) viewportCenter ( Point2D x y )
|
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= ( recip zoomFactor *^ ( Point2D ( 0.5 * viewportWidth ) ( 0.5 * viewportHeight ) --> Point2D x y :: Vector2D Double ) )
|
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|
|
|
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|
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@ -3,6 +3,7 @@
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{-# 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"
|
||||
|
|
|
|||
|
|
@ -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 )
|
||||
|
|
|
|||
|
|
@ -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 )
|
||||
|
|
|
|||
|
|
@ -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
115
src/lib/Math/RealRoots.hs
Normal 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 )
|
||||
|
|
@ -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
|
||||
|
|
|
|||
Loading…
Reference in a new issue