mirror of
https://gitlab.com/sheaf/metabrush.git
synced 2024-11-23 23:44:07 +00:00
update render & select for new brush manipulation
This commit is contained in:
sheaf
parent
15d50f8d76
commit
5ff935b4b2
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@ -53,7 +53,7 @@
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color: rgb(184,80,80);
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}
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.brush {
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color: rgb(235,118,219);
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color: rgb(106,63,222);
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}
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.brushStroke {
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color: rgba(235,118,219,0.66);
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@ -5,7 +5,7 @@ constraints:
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allow-newer:
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waargonaut:*,
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*:haskell-gi-base, *:haskell-gi,
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*:haskell-gi-base, *:haskell-gi
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-- various fixes for 'hmatrix'
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source-repository-package
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@ -3,8 +3,7 @@
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On Windows, we need to install an up-to-date MinGW/MSYS2 toolchain,
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together with the packages required by the `haskell-gi` libraries (for `GTK`),
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as well as the `hmatrix` library.
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the `hmatrix` library, as well as `flint` and `msolve`.
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With an `MSYS2` installation, the following environment variables will need to be set (with `MSYS2` installed at `C:\msys64`):
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@ -16,9 +15,22 @@ With an `MSYS2` installation, the following environment variables will need to b
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Then we install some necessary packages using the following command:
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```bash
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pacman -S -q --noconfirm mingw64/mingw-w64-x86_64-pkg-config mingw64/mingw-w64-x86_64-gobject-introspection mingw64/mingw-w64-x86_64-gtksourceview3 mingw64/mingw-w64-x86_64-openblas
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pacman -S -q --noconfirm mingw64/mingw-w64-x86_64-pkg-config mingw64/mingw-w64-x86_64-gobject-introspection mingw64/mingw-w64-x86_64-openblas
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```
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Next, `flint`, which `msolve` depends on.
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Build `flint` by downloading it and running the configure script. On Windows (MINGW64):
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```bash
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./configure ABI=64 --build=${MINGW_CHOST} --prefix=${MINGW_PREFIX} --enable-static --disable-shared --with-gmp=${MINGW_PREFIX} --with-mpfr=${MINGW_PREFIX}
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make && make install
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```
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`flint` needs `gmp`, `mpfr`, but these should already be present.
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For `msolve`, the default installation directions (`./autogen.sh`, `./configure`, `make && make install`) seem to work (without having to set any additional options), as of `msolve` version `0.1.3`.
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## Possible errors
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### pkg-config could not be found
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@ -103,7 +103,7 @@ import Math.Bezier.Spline
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import Math.Bezier.Stroke
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( CachedStroke(..), invalidateCache )
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import Math.Module
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( Module((*^)) )
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( Module((*^)), quadrance )
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import Math.Vector2D
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( Point2D(..), Vector2D(..) )
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import MetaBrush.Context
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@ -722,7 +722,13 @@ data MouseClickType
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| DoubleClick
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deriving stock Show
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data MouseClick = MouseClick !ActionOrigin !MouseClickType !Word32 !( Point2D Double )
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data MouseClick =
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MouseClick
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{ clickOrigin :: !ActionOrigin
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, clickType :: !MouseClickType
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, clickButton :: !Word32
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, clickCoords :: !( Point2D Double )
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}
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deriving stock Show
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instance HandleAction MouseClick where
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@ -744,9 +750,6 @@ instance HandleAction MouseClick where
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pos = toViewport mouseClickCoords
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STM.writeTVar mousePosTVar ( Just pos )
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mode <- STM.readTVar modeTVar
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case mode of
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BrushMode -> pure Don'tModifyDoc -- TODO: brush parameter modification UI
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_ ->
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case actionOrigin of
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ViewportOrigin -> case ty of
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@ -766,7 +769,8 @@ instance HandleAction MouseClick where
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case selectionMode modifiers of
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-- Drag move: not holding shift or alt, click has selected something.
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New
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| Just ( dragMove, newDoc ) <- dragMoveSelect pos doc
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| PathMode <- mode
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, Just ( dragMove, newDoc ) <- dragMoveSelect pos doc
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-> do
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STM.writeTVar mouseHoldTVar ( Just $ DragMoveHold pos dragMove )
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case dragMove of
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@ -782,7 +786,7 @@ instance HandleAction MouseClick where
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pure Don'tModifyDoc
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-- Pen tool: start or continue a drawing operation.
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Pen -> do
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Pen | PathMode <- mode -> do
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mbPartialPath <- STM.readTVar partialPathTVar
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STM.writeTVar mouseHoldTVar ( Just $ DrawHold pos )
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case mbPartialPath of
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@ -811,6 +815,8 @@ instance HandleAction MouseClick where
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STM.writeTVar partialPathTVar ( Just $ pp { firstPoint = False } )
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pure Don'tModifyDoc
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_ -> pure Don'tModifyDoc
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DoubleClick -> do
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tool <- STM.readTVar toolTVar
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modifs <- STM.readTVar modifiersTVar
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@ -940,9 +946,6 @@ instance HandleAction MouseRelease where
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_ -> do
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tool <- STM.readTVar toolTVar
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mode <- STM.readTVar modeTVar
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case mode of
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BrushMode -> pure Don'tModifyDoc -- TODO: brush parameter modification UI
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_ ->
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case tool of
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Selection -> do
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@ -951,8 +954,9 @@ instance HandleAction MouseRelease where
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selMode = selectionMode modifiers
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case mbHoldPos of
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Just hold
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| DragMoveHold { holdStartPos = pos0, dragAction } <- hold
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, pos0 /= pos
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| PathMode <- mode
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, DragMoveHold { holdStartPos = pos0, dragAction } <- hold
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, quadrance @( Vector2D Double ) pos0 pos * zoomFactor ^ ( 2 :: Int ) >= 16
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-> let
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alternateMode :: Bool
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alternateMode = any ( \case { Alt _ -> True; _ -> False } ) modifiers
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@ -960,10 +964,13 @@ instance HandleAction MouseRelease where
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Just upd -> pure $ UpdateDoc ( UpdateDocumentTo upd )
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Nothing -> pure Don'tModifyDoc
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| SelectionHold pos0 <- hold
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, quadrance @( Vector2D Double ) pos0 pos * zoomFactor ^ ( 2 :: Int ) >= 16
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-> pure ( UpdateDoc . UpdateDocumentTo . TrivialChange $ selectRectangle selMode pos0 pos doc )
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_ -> pure ( UpdateDoc . UpdateDocumentTo . TrivialChange $ selectAt selMode pos doc )
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Pen -> do
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Pen
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| PathMode <- mode
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-> do
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mbPartialPath <- STM.readTVar partialPathTVar
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case mbPartialPath of
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-- Normal pen mode mouse click should have created an anchor.
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@ -1046,6 +1053,8 @@ instance HandleAction MouseRelease where
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changeText = "Continue stroke"
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pure ( UpdateDoc . UpdateDocumentTo $ HistoryChange {..} )
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_ -> pure Don'tModifyDoc
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-- Other mouse buttons: ignored (for the moment at least).
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_ -> pure ()
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@ -116,7 +116,13 @@ data ActionOrigin
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data MouseClickType
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= SingleClick
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| DoubleClick
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data MouseClick = MouseClick !ActionOrigin !MouseClickType !Word32 !( Point2D Double )
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data MouseClick =
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MouseClick
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{ clickOrigin :: !ActionOrigin
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, clickType :: !MouseClickType
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, clickButton :: !Word32
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, clickCoords :: !( Point2D Double )
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}
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instance HandleAction MouseClick
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data MouseRelease = MouseRelease !Word32 !( Point2D Double )
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@ -177,8 +177,7 @@ selectAt selMode c doc@( Document { zoomFactor } ) =
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. ( KnownSplineType clo )
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=> StrokeSpline clo brushParams -> State Bool ( StrokeSpline clo brushParams )
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updateSpline oldSpline =
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bitraverseSpline
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( const pure )
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traverse
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( updateSplinePoint strokeVisible )
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oldSpline
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@ -159,6 +159,11 @@ compositeRenders = sequenceA_
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toAll :: Cairo.Render () -> Compose Renders Cairo.Render ()
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toAll action = Compose ( pure action )
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data RenderMode
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= RenderingPath
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| RenderingBrush
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deriving stock ( Show, Eq )
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--------------------------------------------------------------------------------
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blankRender :: Colours -> Cairo.Render ()
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@ -251,7 +256,7 @@ getDocumentRender
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Cairo.scale zoomFactor zoomFactor
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Cairo.translate ( -cx ) ( -cy )
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for_ strokesRenderData
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( compositeRenders . getCompose . renderStroke cols mbHoverContext mode debug zoomFactor )
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( compositeRenders . getCompose . renderStroke cols mbHoverContext mode RenderingPath debug zoomFactor )
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renderSelectionRect
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Cairo.restore
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@ -327,16 +332,16 @@ strokeRenderData fitParams
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= Nothing
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renderStroke
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:: Colours -> Maybe HoverContext -> Mode -> Bool -> Double
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:: Colours -> Maybe HoverContext -> Mode -> RenderMode -> Bool -> Double
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-> StrokeRenderData
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-> Compose Renders Cairo.Render ()
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renderStroke cols@( Colours { brush } ) mbHoverContext mode debug zoom = \case
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renderStroke cols@( Colours { brush } ) mbHoverContext mode rdrMode debug zoom = \case
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StrokeRenderData { strokeDataSpline } ->
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renderStrokeSpline cols mode mbHoverContext zoom ( const ( pure () ) ) strokeDataSpline
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renderStrokeSpline cols mode rdrMode mbHoverContext zoom ( const ( pure () ) ) strokeDataSpline
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StrokeWithOutlineRenderData strokeDataSpline strokeOutlineData strokeBrushFunction ->
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renderStrokeSpline cols mode mbHoverContext zoom
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renderStrokeSpline cols mode rdrMode mbHoverContext zoom
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( when ( mode == BrushMode )
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. renderBrushShape ( cols { path = brush } ) mbHoverContext ( 1.5 * zoom ) strokeBrushFunction
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. renderBrushShape ( cols { path = brush } ) mbHoverContext ( 2 * zoom ) strokeBrushFunction
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)
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strokeDataSpline
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*> Compose blank { renderStrokes = drawOutline cols debug zoom strokeOutlineData }
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@ -348,17 +353,21 @@ renderStroke cols@( Colours { brush } ) mbHoverContext mode debug zoom = \case
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renderStrokeSpline
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:: forall clo crvData pointData
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. ( Show pointData, KnownSplineType clo )
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=> Colours -> Mode -> Maybe HoverContext -> Double
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=> Colours -> Mode -> RenderMode -> Maybe HoverContext -> Double
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-> ( PointData pointData -> Compose Renders Cairo.Render () )
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-> Spline clo crvData ( PointData pointData )
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-> Compose Renders Cairo.Render ()
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renderStrokeSpline cols mode mbHover zoom renderSubcontent spline =
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renderStrokeSpline cols mode rdrMode mbHover zoom renderSubcontent spline =
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bifoldSpline ( renderSplineCurve ( splineStart spline ) ) renderSplinePoint spline
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where
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renderSplinePoint :: PointData pointData -> Compose Renders Cairo.Render ()
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renderSplinePoint sp0
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= Compose blank { renderPPts = when ( mode == PathMode ) $ drawPoint cols mbHover zoom PathPoint sp0 }
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= Compose blank
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{ renderPPts =
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when ( rdrMode == RenderingPath ) do
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drawPoint cols mbHover zoom PathPoint sp0
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}
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*> renderSubcontent sp0
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renderSplineCurve
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:: forall clo'
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@ -366,8 +375,7 @@ renderStrokeSpline cols mode mbHover zoom renderSubcontent spline =
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=> PointData pointData -> PointData pointData -> Curve clo' crvData ( PointData pointData ) -> Compose Renders Cairo.Render ()
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renderSplineCurve start p0 ( LineTo np1 _ )
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= Compose blank
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{ renderPPts =
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when ( mode == PathMode ) $
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{ renderPPts = when ( rdrMode == RenderingPath ) do
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for_ np1 \ p1 ->
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drawPoint cols mbHover zoom PathPoint p1
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, renderPath =
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@ -378,36 +386,39 @@ renderStrokeSpline cols mode mbHover zoom renderSubcontent spline =
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renderSplineCurve start p0 ( Bezier2To p1 np2 _ )
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= Compose blank
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{ renderCLines
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= when ( mode == PathMode ) do
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= when ( rdrMode == RenderingPath ) do
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drawLine cols zoom ControlPoint p0 p1
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drawLine cols zoom ControlPoint p1 ( fromNextPoint start np2 )
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, renderCPts
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= when ( mode == PathMode ) $ drawPoint cols mbHover zoom ControlPoint p1
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= when ( rdrMode == RenderingPath ) do
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drawPoint cols mbHover zoom ControlPoint p1
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, renderPPts
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= when ( mode == PathMode ) $
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= when ( rdrMode == RenderingPath ) do
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for_ np2 \ p2 ->
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drawPoint cols mbHover zoom PathPoint p2
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, renderPath
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= unless ( mode == MetaMode ) $ drawQuadraticBezier cols zoom ( coords <$> Quadratic.Bezier { p0, p1, p2 = fromNextPoint start np2 } )
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= unless ( mode == MetaMode ) do
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drawQuadraticBezier cols zoom ( coords <$> Quadratic.Bezier { p0, p1, p2 = fromNextPoint start np2 } )
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}
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*> renderSubcontent p1
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*> for_ np2 \ p2 -> renderSubcontent p2
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renderSplineCurve start p0 ( Bezier3To p1 p2 np3 _ )
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= Compose blank
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{ renderCLines
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= when ( mode == PathMode ) do
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= when ( rdrMode == RenderingPath ) do
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drawLine cols zoom ControlPoint p0 p1
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drawLine cols zoom ControlPoint p2 ( fromNextPoint start np3 )
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, renderCPts
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= when ( mode == PathMode ) do
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= when ( rdrMode == RenderingPath ) do
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drawPoint cols mbHover zoom ControlPoint p1
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drawPoint cols mbHover zoom ControlPoint p2
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, renderPPts
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= when ( mode == PathMode ) $
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= when ( rdrMode == RenderingPath ) do
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for_ np3 \ p3 ->
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drawPoint cols mbHover zoom PathPoint p3
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, renderPath
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= unless ( mode == MetaMode ) $ drawCubicBezier cols zoom ( coords <$> Cubic.Bezier { p0, p1, p2, p3 = fromNextPoint start np3 } )
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= unless ( mode == MetaMode ) do
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drawCubicBezier cols zoom ( coords <$> Cubic.Bezier { p0, p1, p2, p3 = fromNextPoint start np3 } )
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}
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*> renderSubcontent p1
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*> renderSubcontent p2
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@ -430,9 +441,8 @@ renderBrushShape cols mbHoverContext zoom brushFn pt =
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toAll do
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Cairo.save
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Cairo.translate x y
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*> renderStrokeSpline cols PathMode mbHoverContext' zoom ( const $ pure () )
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*> renderStrokeSpline cols BrushMode RenderingBrush mbHoverContext' zoom ( const $ pure () )
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( fmap ( \ p -> PointData p Normal () ) brushPts )
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*> Compose blank { renderPPts = drawCross cols zoom }
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*> toAll Cairo.restore
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drawPoint :: Colours -> Maybe HoverContext -> Double -> PointType -> PointData brushData -> Cairo.Render ()
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@ -659,6 +669,7 @@ drawSelectionRectangle ( Colours {..} ) zoom ( Point2D x0 y0 ) ( Point2D x1 y1 )
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Cairo.restore
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{-
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drawCross :: Colours -> Double -> Cairo.Render ()
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drawCross ( Colours {..} ) zoom = do
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Cairo.save
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@ -677,7 +688,7 @@ drawCross ( Colours {..} ) zoom = do
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Cairo.stroke
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Cairo.restore
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-}
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hsl2rgb :: Double -> Double -> Double -> ( Double, Double, Double )
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hsl2rgb h s l = case hc2rgb h c of
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|
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@ -1,3 +1,7 @@
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{-# LANGUAGE DataKinds #-}
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{-# LANGUAGE DerivingStrategies #-}
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{-# LANGUAGE NamedFieldPuns #-}
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{-# LANGUAGE PartialTypeSignatures #-}
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{-# LANGUAGE ScopedTypeVariables #-}
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{-# LANGUAGE TypeApplications #-}
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@ -29,6 +33,163 @@ import Math.Vector2D
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--------------------------------------------------------------------------------
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{-
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data StrokePolynomialData
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= StrokePolynomialData
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{ envelope :: !Poly
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, envelope' :: !Poly
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, tangent :: !( Poly, Poly )
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, type1Cusps :: [ ( Double, Double ) ]
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, type2Cusps :: [ ( Double, Double ) ]
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}
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deriving stock Show
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validRoot :: Sized 2 ( Complex Double ) -> Maybe ( Double, Double )
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validRoot r
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| any isNaN [a,b,c,d]
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|| any isInfinite [a,b,c,d]
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|| any ( not . nearZero ) [b,d]
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|| any ( < 0 ) [ a, c ]
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|| any ( > 1 ) [ a, c ]
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= Nothing
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| otherwise
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= Just ( a, c )
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where
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a, b, c, d :: Double
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a :+ b = r %!! 0
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c :+ d = r %!! 1
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{-
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:seti -XNegativeLiterals -XFlexibleInstances -XRebindableSyntax
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:m Math.Vector2D Math.Bezier.Envelope
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import qualified Math.Bezier.Cubic as Cubic
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import Prelude hiding ( fromInteger )
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import AlgebraicPrelude ( fromInteger )
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:{
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let
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path :: Cubic.Bezier ( Point2D AlgebraicPrelude.Rational )
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path = Cubic.Bezier
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(Point2D p0_x p0_y) (Point2D p1_x p1_y) (Point2D p2_x p2_y) (Point2D p3_x p3_y)
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brush :: Cubic.Bezier ( Cubic.Bezier ( Point2D AlgebraicPrelude.Rational ) )
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brush = Cubic.Bezier
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( Cubic.Bezier (Point2D b00_x b00_y) (Point2D b01_x b01_y) (Point2D b02_x b02_y) (Point2D b03_x b03_y) )
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( Cubic.Bezier (Point2D b10_x b10_y) (Point2D b11_x b11_y) (Point2D b12_x b12_y) (Point2D b13_x b13_y) )
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( Cubic.Bezier (Point2D b20_x b20_y) (Point2D b21_x b21_y) (Point2D b22_x b22_y) (Point2D b23_x b23_y) )
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( Cubic.Bezier (Point2D b30_x b30_y) (Point2D b31_x b31_y) (Point2D b32_x b32_y) (Point2D b33_x b33_y) )
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:}
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:{
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let
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path :: Cubic.Bezier ( Point2D AlgebraicPrelude.Rational )
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path = Cubic.Bezier
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(Point2D 0.5 0.5) (Point2D 0.5 4) (Point2D 1 4) (Point2D 6 2)
|
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brush :: Cubic.Bezier ( Cubic.Bezier ( Point2D AlgebraicPrelude.Rational ) )
|
||||
brush = Cubic.Bezier
|
||||
( Cubic.Bezier (Point2D 0 -0.5) (Point2D 1 1 ) (Point2D -1 1 ) (Point2D 0 -0.5) )
|
||||
( Cubic.Bezier (Point2D 0.5 -0.5) (Point2D 5 1 ) (Point2D -5 1 ) (Point2D 0 -0.5) )
|
||||
( Cubic.Bezier (Point2D 0 -0.5) (Point2D 1 1 ) (Point2D -1 1 ) (Point2D 0 -0.5) )
|
||||
( Cubic.Bezier (Point2D 1 -0.2) (Point2D -3 -0.8) (Point2D -1 -0.2) (Point2D 1 -0.2) )
|
||||
:}
|
||||
|
||||
strokePolynomialData33 path brush
|
||||
|
||||
-}
|
||||
|
||||
-- c(t,u) = p(t) + b(t,u) = ( x(t,u), y(t,u) )
|
||||
strokePolynomialData33
|
||||
:: Cubic.Bezier ( Point2D CA.Rational )
|
||||
-> Cubic.Bezier ( Cubic.Bezier ( Point2D CA.Rational ) )
|
||||
-> StrokePolynomialData
|
||||
strokePolynomialData33 ( Cubic.Bezier (Point2D p0_x p0_y) (Point2D p1_x p1_y) (Point2D p2_x p2_y) (Point2D p3_x p3_y) )
|
||||
( Cubic.Bezier
|
||||
( Cubic.Bezier (Point2D b00_x b00_y) (Point2D b01_x b01_y) (Point2D b02_x b02_y) (Point2D b03_x b03_y) )
|
||||
( Cubic.Bezier (Point2D b10_x b10_y) (Point2D b11_x b11_y) (Point2D b12_x b12_y) (Point2D b13_x b13_y) )
|
||||
( Cubic.Bezier (Point2D b20_x b20_y) (Point2D b21_x b21_y) (Point2D b22_x b22_y) (Point2D b23_x b23_y) )
|
||||
( Cubic.Bezier (Point2D b30_x b30_y) (Point2D b31_x b31_y) (Point2D b32_x b32_y) (Point2D b33_x b33_y) )
|
||||
) = StrokePolynomialData
|
||||
{ envelope
|
||||
, envelope' = pepu
|
||||
, tangent = ( dxdt, dydt )
|
||||
, type1Cusps = trace ( show "grobner = " <> show grobner ) [] --mapMaybe validRoot $ unsafePerformIO . evalRandIO $ CA.solveM ( CA.toIdeal [ envelope, pepu ] )
|
||||
, type2Cusps = [] --mapMaybe validRoot $ unsafePerformIO . evalRandIO $ CA.solveM ( CA.toIdeal [ dxdt, dydt ] )
|
||||
}
|
||||
where
|
||||
|
||||
grobner = CA.f4 ( CA.toIdeal [ envelope, dxdt, dydt ] )
|
||||
|
||||
-- Computation of ∂c/∂t: partial derivatives ∂x/∂t and ∂y/∂t.
|
||||
|
||||
t, u :: Poly
|
||||
t = CA.fromMonomial $ ( CA.varMonom ( Data.Type.Natural.sNat @2 ) 0 )
|
||||
u = CA.fromMonomial $ ( CA.varMonom ( Data.Type.Natural.sNat @2 ) 1 )
|
||||
|
||||
bez3Pol :: Poly -> Poly -> Poly -> Poly -> Poly -> Poly
|
||||
bez3Pol v a0 a1 a2 a3
|
||||
= a0 * ( 1 - v ) ^ ( 3 :: Int )
|
||||
+ 3 * a1 * v * ( 1 - v ) ^ ( 2 :: Int )
|
||||
+ 3 * a2 * ( 1 - v ) * v ^ ( 2 :: Int )
|
||||
+ a3 * v ^ ( 3 :: Int )
|
||||
|
||||
bez3'Pol :: Poly -> Poly -> Poly -> Poly -> Poly -> Poly
|
||||
bez3'Pol v a0 a1 a2 a3
|
||||
= 3 *
|
||||
( a1 - a0
|
||||
+ 2 * ( a0 + a2 - 2 * a1 ) * v
|
||||
+ ( a3 - 3 * a2 + 3 * a1 - a0 ) * v ^ ( 2 :: Int )
|
||||
)
|
||||
|
||||
f0_x, f1_x, f2_x, f3_x, f0_y, f1_y, f2_y, f3_y :: Poly
|
||||
f0_x = bez3'Pol t ( CA.injectCoeff b00_x ) ( CA.injectCoeff b10_x ) ( CA.injectCoeff b20_x ) ( CA.injectCoeff b30_x )
|
||||
f1_x = bez3'Pol t ( CA.injectCoeff b01_x ) ( CA.injectCoeff b11_x ) ( CA.injectCoeff b21_x ) ( CA.injectCoeff b31_x )
|
||||
f2_x = bez3'Pol t ( CA.injectCoeff b02_x ) ( CA.injectCoeff b12_x ) ( CA.injectCoeff b22_x ) ( CA.injectCoeff b32_x )
|
||||
f3_x = bez3'Pol t ( CA.injectCoeff b03_x ) ( CA.injectCoeff b13_x ) ( CA.injectCoeff b23_x ) ( CA.injectCoeff b33_x )
|
||||
f0_y = bez3'Pol t ( CA.injectCoeff b00_y ) ( CA.injectCoeff b10_y ) ( CA.injectCoeff b20_y ) ( CA.injectCoeff b30_y )
|
||||
f1_y = bez3'Pol t ( CA.injectCoeff b01_y ) ( CA.injectCoeff b11_y ) ( CA.injectCoeff b21_y ) ( CA.injectCoeff b31_y )
|
||||
f2_y = bez3'Pol t ( CA.injectCoeff b02_y ) ( CA.injectCoeff b12_y ) ( CA.injectCoeff b22_y ) ( CA.injectCoeff b32_y )
|
||||
f3_y = bez3'Pol t ( CA.injectCoeff b03_y ) ( CA.injectCoeff b13_y ) ( CA.injectCoeff b23_y ) ( CA.injectCoeff b33_y )
|
||||
|
||||
pxpt, pypt :: Poly
|
||||
pxpt = trace "pxpt = " . traceShowId $ bez3'Pol t ( CA.injectCoeff p0_x ) ( CA.injectCoeff p1_x ) ( CA.injectCoeff p2_x ) ( CA.injectCoeff p3_x ) + bez3Pol u f0_x f1_x f2_x f3_x
|
||||
pypt = trace "pypt = " . traceShowId $ bez3'Pol t ( CA.injectCoeff p0_y ) ( CA.injectCoeff p1_y ) ( CA.injectCoeff p2_y ) ( CA.injectCoeff p3_y ) + bez3Pol u f0_y f1_y f2_y f3_y
|
||||
|
||||
-- Computation of ∂c/∂u: partial derivatives ∂x/∂u and ∂y/∂u.
|
||||
|
||||
g0_x, g1_x, g2_x, g3_x, g0_y, g1_y, g2_y, g3_y :: Poly
|
||||
g0_x = bez3Pol t ( CA.injectCoeff b00_x ) ( CA.injectCoeff b10_x ) ( CA.injectCoeff b20_x ) ( CA.injectCoeff b30_x )
|
||||
g1_x = bez3Pol t ( CA.injectCoeff b01_x ) ( CA.injectCoeff b11_x ) ( CA.injectCoeff b21_x ) ( CA.injectCoeff b31_x )
|
||||
g2_x = bez3Pol t ( CA.injectCoeff b02_x ) ( CA.injectCoeff b12_x ) ( CA.injectCoeff b22_x ) ( CA.injectCoeff b32_x )
|
||||
g3_x = bez3Pol t ( CA.injectCoeff b03_x ) ( CA.injectCoeff b13_x ) ( CA.injectCoeff b23_x ) ( CA.injectCoeff b33_x )
|
||||
g0_y = bez3Pol t ( CA.injectCoeff b00_y ) ( CA.injectCoeff b10_y ) ( CA.injectCoeff b20_y ) ( CA.injectCoeff b30_y )
|
||||
g1_y = bez3Pol t ( CA.injectCoeff b01_y ) ( CA.injectCoeff b11_y ) ( CA.injectCoeff b21_y ) ( CA.injectCoeff b31_y )
|
||||
g2_y = bez3Pol t ( CA.injectCoeff b02_y ) ( CA.injectCoeff b12_y ) ( CA.injectCoeff b22_y ) ( CA.injectCoeff b32_y )
|
||||
g3_y = bez3Pol t ( CA.injectCoeff b03_y ) ( CA.injectCoeff b13_y ) ( CA.injectCoeff b23_y ) ( CA.injectCoeff b33_y )
|
||||
|
||||
pxpu, pypu :: Poly
|
||||
pxpu = bez3'Pol u g0_x g1_x g2_x g3_x
|
||||
pypu = bez3'Pol u g0_y g1_y g2_y g3_y
|
||||
|
||||
-- Envelope equation.
|
||||
envelope :: Poly
|
||||
envelope = pxpt * pypu - pypt * pxpu
|
||||
|
||||
-- Computation of total derivative dc/dt = ( dx/dt, dy/dt ).
|
||||
-- Rather, we are clearing denominators:
|
||||
-- dc/dt = ∂c/∂t + ∂c/∂u ∂u/dt
|
||||
-- ∂u/∂t = - ( ∂ envelope / ∂ t ) / ( ∂ envelope / ∂ u )
|
||||
--
|
||||
-- So we compute instead:
|
||||
-- ( ∂ envelope / ∂ u ) dc/dt = ( ∂ envelope / ∂ u ) ∂c/∂t - ( ∂ envelope / ∂ t ) ∂c/∂u.
|
||||
|
||||
pepu, pept :: Poly
|
||||
pept = CA.diff 0 envelope
|
||||
pepu = CA.diff 1 envelope
|
||||
|
||||
dxdt, dydt :: Poly
|
||||
dxdt = pxpt * pepu - pxpu * pept
|
||||
dydt = pypt * pepu - pypu * pept
|
||||
|
||||
-}
|
||||
-- | Find the roots of the envelope equation for a family of cubic Bézier curves
|
||||
-- varying along a cubic Bézier path.
|
||||
--
|
||||
|
|
|
|||
|
|
@ -483,7 +483,7 @@ outlineFunctions ptParams brushFn sp0 crv =
|
|||
-> ( brush3, Cubic.bezier @( Vector2D Double ) bez, Cubic.bezier' bez )
|
||||
fwd, bwd :: Double -> ( Point2D Double, Vector2D Double )
|
||||
fwd t
|
||||
= ( offset ( withTangent ( fwd' t ) ( brush t ) ) • f t
|
||||
= ( off t --offset ( withTangent ( fwd' t ) ( brush t ) ) • f t
|
||||
, fwd' t
|
||||
)
|
||||
where
|
||||
|
|
@ -502,7 +502,7 @@ outlineFunctions ptParams brushFn sp0 crv =
|
|||
| otherwise
|
||||
= offTgt u
|
||||
bwd t
|
||||
= ( offset ( withTangent ( (-1) *^ bwd' s ) ( brush s ) ) • f s
|
||||
= ( off s --offset ( withTangent ( (-1) *^ bwd' s ) ( brush s ) ) • f s
|
||||
, bwd' s
|
||||
)
|
||||
where
|
||||
|
|
|
|||
Loading…
Reference in a new issue