dynamic-plot-0.4.2.0: Graphics/Dynamic/Plot/R2.hs
-- |
-- Module : Graphics.Dynamic.Plot.R2
-- Copyright : (c) Justus Sagemüller 2013-2019
-- License : GPL v3
--
-- Maintainer : (@) jsag $ hvl.no
-- Stability : experimental
-- Portability : requires GHC>6 extensions
{-# LANGUAGE NoMonomorphismRestriction #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE RecordWildCards #-}
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UnicodeSyntax #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE LiberalTypeSynonyms #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE CPP #-}
module Graphics.Dynamic.Plot.R2 (
-- * Display
-- ** Static
plotPrerender
-- ** Interactive
, plotWindow, plotWindow'
-- * Plottable objects
-- ** Class
, Plottable(..)
-- ** Simple function plots
, fnPlot, paramPlot
, continFnPlot
, tracePlot
, lineSegPlot
, linregressionPlot
, colourPaintPlot
, PlainGraphicsR2
, shapePlot
, diagramPlot
-- ** Multiple objects in one plot
, plotMultiple
-- ** Computation in progress
, plotLatest
-- * Plot-object attributes
-- ** Colour
, tint, autoTint
-- ** Legend captions
, legendName
, plotLegendPrerender
-- ** Animation
, plotDelay, freezeAnim, startFrozen
-- * Viewport
-- ** View selection
, xInterval, yInterval, forceXRange, forceYRange
, unitAspect
-- ** Interactive content
-- $interactiveExplanation
-- *** Mouse
, MousePressed (..), MousePress(..), MouseClicks(..)
, clickThrough, withDraggablePoints, mouseInteractive
, MouseEvent, clickLocation, releaseLocation
-- *** Displayed range
, ViewXCenter(..), ViewYCenter(..), ViewWidth(..), ViewHeight(..)
-- *** Resolution
, ViewXResolution(..), ViewYResolution(..)
-- * Auxiliary plot objects
, dynamicAxes, noDynamicAxes, xAxisLabel, yAxisLabel
-- * Types
-- ** The plot type
, DynamicPlottable
, tweakPrerendered
-- ** Viewport choice
, ViewportConfig
-- *** Resolution
, xResV, yResV
-- *** Background
, setSolidBackground
-- *** Output scaling
, prerenderScaling
, PrerenderScaling(..)
, LegendDisplayConfig
, legendPrerenderSize
-- *** General
, graphicsPostprocessing
) where
import Graphics.Dynamic.Plot.Colour
import Graphics.Dynamic.Plot.Internal.Types
import Graphics.Text.Annotation
import qualified Prelude
import Diagrams.Prelude ((^&), (&), _x, _y)
import qualified Diagrams.Prelude as Dia
import qualified Diagrams.TwoD.Size as Dia
import qualified Diagrams.TwoD.Types as DiaTypes
import Diagrams.TwoD.Types (V2(V2))
import Diagrams.BoundingBox (BoundingBox)
import qualified Diagrams.BoundingBox as DiaBB
import qualified Diagrams.Backend.Cairo as Cairo
import qualified Diagrams.Backend.Cairo.Text as CairoTxt
import qualified Data.Colour as DCol
import qualified Data.Colour.SRGB as DCol (toSRGB24, RGB(..))
import qualified Data.Colour.Names as DCol
import qualified Codec.Picture as JPix
import qualified Codec.Picture.Types as JPix
import Graphics.Image.Resample (refiningScaleX2Bilinear)
import qualified Diagrams.Backend.Gtk as BGTK
import qualified Graphics.UI.Gtk as GTK
import Graphics.UI.Gtk ( AttrOp((:=)) )
import qualified Graphics.UI.Gtk.Gdk.EventM as Event
import qualified System.Glib.Signals (on)
import Control.Monad.Trans (liftIO, lift)
import Control.Monad.Trans.State (evalState, get, put)
import Control.Monad.ST
import Control.Applicative ((<|>))
import Data.STRef
import qualified Control.Category.Hask as Hask
import Control.Category.Constrained.Prelude hiding ((^))
import Control.Arrow.Constrained
import Control.Monad.Constrained
import Control.Lens hiding ((...), (<.>))
import Control.Lens.TH(makeLenses)
import Control.Concurrent (runInBoundThread, threadDelay, ThreadId, forkIO, killThread)
import Control.Concurrent.MVar
import Control.DeepSeq
import Control.Exception (evaluate)
import Data.List (foldl', sort, sortBy, partition, zip4)
import qualified Data.List.NonEmpty as NE
import Data.List.NonEmpty (NonEmpty (..))
import qualified Data.Vector as Arr
import Data.Maybe
import Data.Semigroup
import Data.Default
import Data.Foldable (fold, foldMap, minimumBy)
import qualified Data.Foldable as Hask
import Data.Function (on)
import Data.Ord (comparing)
import Data.VectorSpace
import Math.LinearMap.Category
import Data.Basis
import Data.AffineSpace
import Data.Manifold.PseudoAffine
#if MIN_VERSION_manifolds(0,6,0)
import Data.Manifold.WithBoundary
#endif
import Data.Function.Differentiable
import Data.Manifold.Types
import Data.Manifold.Shade
import Data.Manifold.TreeCover
import Data.Manifold.Web
import Data.Manifold.Riemannian (Geodesic, pointsBarycenter)
import qualified Data.Map.Lazy as Map
import qualified Data.Colour.Manifold as CSp
import qualified Data.Colour.Manifold.Internal as CSp
import qualified Data.Random as Random
import qualified System.Random as Random
import qualified Data.Random.Manifold
import Data.IORef
import System.IO
import System.Exit
import System.Process
import Data.Time
data Plot = Plot {
_plotAnnotations :: [Annotation]
, _getPlot :: PlainGraphicsR2
}
makeLenses ''Plot
data RangeRequest r
= OtherDimDependantRange (Maybe (Interval r) -> Maybe (Interval r))
| MustBeThisRange (Interval r)
type GraphWindowSpec = GraphWindowSpecR2
type AxisLabel = (ℝ², String)
data Interactions x = Interactions {
_mouseClicksCompleted :: [MouseEvent x]
, _currentDragEndpoints :: Maybe (MouseEvent x)
}
deriving (Eq)
instance Semigroup (Interactions x) where
Interactions cca cda<>Interactions ccb cdb = Interactions (cca<>ccb) (cda<|>cdb)
instance Monoid (Interactions x) where
mempty = Interactions [] Nothing
mappend = (<>)
data DynamicPlottable' m = DynamicPlottable {
_relevantRange_x, _relevantRange_y :: RangeRequest R
, _viewportConstraint :: GraphWindowSpec -> GraphWindowSpec
, _inherentColours :: [PColour]
, _occlusiveness :: Double
-- ^ How surface-occupying the plot is.
-- Use positive values for opaque 2D plots that would tend to obscure
-- other objects, negative values for sparse/small point plots.
-- The z-order will be chosen accordingly.
, _axesNecessity :: Necessity
, _frameDelay :: NominalDiffTime
, _legendEntries :: [LegendEntry]
, _axisLabelRequests :: [AxisLabel]
, _futurePlots :: Interactions (ℝ,ℝ) -> Maybe (DynamicPlottable' m)
, _dynamicPlotWithAxisLabels :: [AxisLabel] -> GraphWindowSpec -> m Plot
}
makeLenses ''DynamicPlottable'
dynamicPlot :: Setter' (DynamicPlottable' m) (GraphWindowSpec -> m Plot)
dynamicPlot = dynamicPlotWithAxisLabels . mapped
sustained :: Hask.Functor m
=> Setter' (DynamicPlottable' m) a -> Setter' (DynamicPlottable' m) a
sustained q = sets $ \f p -> p & q %~ f
& futurePlots %~ fmap (fmap $ sustained q %~ f)
allDynamicPlot :: Hask.Functor m => Setter' (DynamicPlottable' m)
(GraphWindowSpec -> m Plot)
allDynamicPlot = sustained dynamicPlot
type DynamicPlottable = DynamicPlottable' Random.RVar
type AnnotPlot = (Plot, ([LegendEntry],[AxisLabel]))
data ObjInPlot = ObjInPlot {
_lastStableView :: IORef (Maybe (GraphWindowSpec, AnnotPlot))
, _newPlotView :: MVar (GraphWindowSpec, AnnotPlot)
, _mouseEventsForObj :: MVar (Interactions (ℝ,ℝ))
, _plotObjColour :: Maybe AColour
, _originalPlotObject :: DynamicPlottable
}
makeLenses ''ObjInPlot
newtype PlainGraphics = PlainGraphics { getPlainGraphics :: PlainGraphicsR2 }
deriving (Semigroup, Monoid)
-- | Class for types that can be plotted in some canonical, “obvious”
-- way. If you want to display something and don't know about any specific caveats,
-- try just using 'plot'!
class Plottable p where
plot :: p -> DynamicPlottable
instance Plottable DynamicPlottable where
plot = id
instance Plottable (R -> R) where
plot f = continFnPlot $ realToFrac . f . realToFrac
-- {-# RULES "plot/R->R" plot = fnPlot #-}
instance (Plottable p) => Plottable [p] where
plot = foldMap plot
instance (Plottable p) => Plottable (Option p) where
plot = foldMap plot
instance (Plottable p) => Plottable (Maybe p) where
plot = foldMap plot
instance Plottable PlainGraphics where
plot (PlainGraphics d) = case DiaBB.getCorners bb of
Just (c1, c2) -> let (rlx,rly) = ( c1^._x ... c2^._x
, c1^._y ... c2^._y ) in def
& relevantRange_x .~ atLeastInterval rlx
& relevantRange_y .~ atLeastInterval rly
& inherentColours .~ [TrueColour DCol.grey]
& axesNecessity .~ -1
& dynamicPlot .~ pure.plot
Nothing -> mempty
where bb = DiaBB.boundingBox d
plot _ = mkPlot d
-- | Use a generic diagram within a plot.
--
-- Like with the various specialised function plotters, this will get automatically
-- tinted to be distinguishable from other plot objects in the same window.
-- Use 'diagramPlot' instead, if you want to view the diagram as-is.
shapePlot :: PlainGraphicsR2 -> DynamicPlottable
shapePlot d = diagramPlot d
& inherentColours .~ []
& axesNecessity .~ 0
-- | Plot a generic 'Dia.Diagram'.
diagramPlot :: PlainGraphicsR2 -> DynamicPlottable
diagramPlot d = plot $ PlainGraphics d
metricFromLength :: ∀ s . RealFrac' s => s -> Norm s
metricFromLength l | l>0 = case closedScalarWitness :: ClosedScalarWitness s of
ClosedScalarWitness -> spanNorm [1 / l]
instance Plottable (R-->R) where
plot f = def & relevantRange_y .~ OtherDimDependantRange yRangef
& autoTint
& axesNecessity .~ 1
& dynamicPlot .~ pure.plot
where yRangef Nothing = Nothing
yRangef (Just (Interval l r))
= case intervalImages
100
( const . metricFromLength $ (r-l)/16 , const $ metricFromLength 0.0001 )
( alg (\x -> ( point l?<x?<point r ?-> (f$~x) ))) of
([],[]) -> Nothing
(liv,riv) -> pure . foldr1 (<>) . map (uncurry Interval . snd)
$ take 4 liv ++ take 4 riv
plot gs@(GraphWindowSpecR2{..}) = curves `deepseq`
mkPlot (foldMap trace curves)
where curves :: [[P2]]
curves = map (map $ convℝ² . snd) . gatherSides
$ discretisePathSegs
10000
( const . metricFromLength
$ (rBound-lBound)/fromIntegral xResolution
, coerceMetric $ resolutionFunction gs )
((id&&&f)
. alg (\x -> ( point lBound?<x?<point rBound ?-> x )))
trace (p:q:ps) = simpleLine p q <> trace (q:ps)
trace _ = mempty
gatherSides = uncurry (++) . (take 50 *** take 50)
convℝ² = Dia.p2
c = realToFrac
instance Plottable (R-->(R,R)) where
plot f = def & relevantRange_y .~ mempty
& autoTint
& axesNecessity .~ 1
& dynamicPlot .~ pure.plot
where plot gs@(GraphWindowSpecR2{..}) = curves `deepseq`
mkPlot (foldMap trace curves)
where curves :: [[P2]]
curves = map (map $ convℝ² . snd) . gatherSides
$ discretisePathSegs
1000
( const . metricFromLength $ 1/100
, coerceMetric $ resolutionFunction gs )
f
trace (p:q:ps) = simpleLine p q <> trace (q:ps)
trace _ = mempty
gatherSides = uncurry (++) . (take 50 *** take 50)
convℝ² = Dia.p2
c = realToFrac
resolutionFunction :: GraphWindowSpecR2 -> RieMetric ℝ²
resolutionFunction GraphWindowSpecR2{..} = resoFunc
where w = rBound - lBound; h = tBound - bBound
ε = spanNorm [(recip δx^&0), (0^&recip δy)]
δx = w / fromIntegral xResolution
δy = h / fromIntegral yResolution
resoFunc (DiaTypes.V2 x y)
| x >= lBound, x <= rBound, y >= bBound, y <= tBound = ε
| otherwise = spanNorm [(recip qx^&0), (0^&recip qy)]
where qx | x < lBound = lBound - x
| x > rBound = x - rBound
| otherwise = δx * qy/δy
qy | y < bBound = bBound - y
| y > tBound = y - tBound
| otherwise = δy * qx/δx
instance Plottable (R-.^>R) where
plot rPCM@(RecursivePCM gPFit gDetails gFitDevs (PCMRange x₀ wsp) gSplN ())
= def
& relevantRange_x .~ atLeastInterval (Interval x₀ xr)
& relevantRange_y .~ otherDimDependence (rPCMLinFitRange rPCM)
& autoTint
& axesNecessity .~ 1
& dynamicPlot .~ plot
where
xr = wsp * fromIntegral gSplN
plot (GraphWindowSpecR2{..}) = pure . mkPlot . trace
$ flattenPCM_resoCut bb δx rPCM
where
trace dPath = fold [ trMBound [ p & _y +~ s*δ
| (p, DevBoxes _ δ) <- dPath ]
| s <- [-1, 1] ]
<> trStRange dPath
trStRange ((p,DevBoxes σp' δp) : qd@(q,DevBoxes σq' δq) : ps)
= (let η = (σp/δp + σq/δq)/2
in Dia.opacity (1-η)
(Dia.strokeLocLoop (Dia.fromVertices
[_y+~σq $ q, _y+~σp $ p, _y-~σp $ p, _y-~σq $ q
,_y+~σq $ q ]))
<> Dia.opacity (η^2)
(Dia.strokeLocLoop (Dia.fromVertices
[_y+~δq $ q, _y+~δp $ p, _y-~δp $ p, _y-~δq $ q
,_y+~δq $ q ]))
) <> trStRange (qd:ps)
where [σp,σq] = map (|$|1) [σp', σq']
trStRange _ = mempty
trMBound l = Dia.fromVertices l & Dia.dashingO [2,2] 0
w = rBound - lBound; h = tBound - bBound
δx = w * 3/fromIntegral xResolution
bb = Interval lBound rBound
-*| Interval (bBound - h) (tBound + h) -- Heuristic \"buffering\",
-- to account for the missing ability of 'flattenPCM_resoCut' to
-- take deviations from quadratic-fit into account.
instance Plottable (RecursiveSamples Int P2 (DevBoxes P2)) where
plot rPCM@(RecursivePCM gPFit gDetails gFitDevs (PCMRange t₀ τsp) gSplN ())
= def
& relevantRange_x .~ atLeastInterval xRange
& relevantRange_y .~ atLeastInterval yRange
& autoTint
& axesNecessity .~ 1
& dynamicPlot .~ plot
where plot (GraphWindowSpecR2{..}) = pure . mkPlot
. foldMap trStRange
$ flattenPCM_P2_resoCut bbView [(1/δxl)^&0, 0^&(1/δyl)] rPCM
where trStRange (Left appr) = trSR $ map calcNormDev appr
where trSR ((pl,pr) : qd@(ql,qr) : ps)
= Dia.opacity 0.3
(Dia.strokeLocLoop (Dia.fromVertices
[ ql, pl, pr, qr, ql ]
)) <> trSR (qd:ps)
trSR _ = mempty
calcNormDev ((p,v), DevBoxes σ _) = (p .+^ d, p .-^ d)
where d = let v' = turnLeft v in v' ^* (σ|$|v')
trStRange (Right pts) = (`foldMap`pts)
$ \(p, DevBoxes dv _)
-> let δxm = dv |$| 1^&0
δym = dv |$| 0^&1
in if δxm > δx && δym > δy
then simpleLine (_x +~ δxm $ p) (_x -~ δxm $ p)
<> simpleLine (_y +~ δym $ p) (_y -~ δym $ p)
else (Dia.rect (max δx $ δxm*2) (max δy $ δym*2)
& Dia.moveTo p)
w = rBound - lBound; h = tBound - bBound
δxl = 6 * δx; δyl = 6 * δy
δx = w/fromIntegral xResolution; δy = h/fromIntegral yResolution
bbView = Interval lBound rBound -*| Interval bBound tBound
bb = rPCM_R2_boundingBox rPCM
(xRange,yRange) = xyRanges bb
instance Plottable (Int -.^> P2) where
plot = plot . fmap (\() -> DevBoxes mempty zeroV :: DevBoxes P2)
-- | Plot a sequence of points @(x,y)@. The appearance of the plot will be automatically
-- chosen to match resolution and point density: at low densities, each point will simply
-- get displayed on its own. When the density goes so high you couldn't distinguish
-- individual points anyway, we switch to a “trace view”, approximating
-- the probability density function around a “local mean path”, which is
-- rather more insightful (and much less obstructive/clunky) than a simple cloud of
-- independent points.
--
-- In principle, this should be able to handle vast amounts of data
-- (so you can, say, directly plot an audio file); at the moment the implementation
-- isn't efficient enough and will get slow for more than some 100000 data points.
tracePlot :: [(Double, Double)] -> DynamicPlottable
tracePlot = plot . recursiveSamples . map ((,()) . Dia.p2)
-- | Simply connect the points by straight line segments, in the given order.
-- Beware that this will always slow down the performance when the list is large;
-- there is no Éc;statistic optimisationÉd; as in 'tracePlot'.
lineSegPlot :: [(Double, Double)] -> DynamicPlottable
lineSegPlot ps'
| null ps = mempty & autoTint
| otherwise = def
& relevantRange_x .~ atLeastInterval'
( getOption $ foldMap (pure . spInterval . fst) (concat ps) )
& relevantRange_y .~ atLeastInterval'
( getOption $ foldMap (pure . spInterval . snd) (concat ps) )
& autoTint
& axesNecessity .~ 1
& dynamicPlot .~ pure . plot
where plot (GraphWindowSpecR2{..}) = mkPlot (foldMap trace ps)
where trace (p:q:ps) = simpleLine (Dia.p2 p) (Dia.p2 q) <> trace (q:ps)
trace _ = mempty
ps = filter ((>1) . length) $ safeSeg ps'
safeSeg [] = [[]]
safeSeg ((x,y):l) | x==x && not (isInfinite x) && y==y && not (isInfinite y)
= case safeSeg l of { h:r -> ((x,y):h):r }
| otherwise = [] : safeSeg l
flattenPCM_resoCut :: R2Box -> R -> (R-.^>R) -> [(P2, DevBoxes R)]
flattenPCM_resoCut bb δx = case DiaBB.getCorners bb of
Nothing -> const []
Just cs -> ($[]) . go' cs
where go' cs@(lCorn,rCorn) = go where
go rPCM@(RecursivePCM pFit details fitDevs (PCMRange x₁ wsp) splN ())
| DiaBB.isEmptyBox $ DiaBB.intersection bb sqRange
= id
| w > δx, Left (Pair s1 s2) <- details
= go s1 . go s2
| otherwise
= ((xm ^& constCoeff pFit, fitDevs) :)
where xr = x₁ + w
xm = x₁ + w / 2
w = wsp * fromIntegral splN
sqRange = xRange -*| rPCMLinFitRange rPCM xRange_norm'd
xRange = x₁ ... xr
xRange_norm'd = max (-1) ((lCorn^._x - xm)/w)
... min 1 ((rCorn^._x - xm)/w)
flattenPCM_P2_resoCut :: R2Box -> [DualVector R2]
-> (RecursiveSamples x P2 t)
-> [ Either [((P2, R2), DevBoxes P2)]
[(P2, t)] ]
flattenPCM_P2_resoCut bb δs = case DiaBB.getCorners bb of
Nothing -> const []
Just cs -> ($[]) . go' cs
where go' cs@(lCorn,rCorn) = go where
go rPCM@(RecursivePCM (LinFitParams pm pa) details fitDevs@(DevBoxes dev _) _ _ ())
| DiaBB.isEmptyBox $ DiaBB.intersection bb (rPCM_R2_boundingBox rPCM)
= \case l@(Left [] : _) -> l
l -> Left [] : l
| sum (normSq dev<$>δs) > 1/4 || (sum $ ((^2).(pa<.>^)) <$> δs) > 3
, Left (Pair s1 s2) <- details
= go s1 . go s2
| Right pts <- details = (Right (Arr.toList pts) :)
| otherwise
= \case
(Left h : r) -> Left (((pm, dir), fitDevs) : h) : r
r -> Left [((pm, dir), fitDevs)] : r
where dir = case magnitude pa of 0 -> zeroV; m -> pa ^/ m
turnLeft :: R2 -> R2
turnLeft (DiaTypes.V2 x y) = DiaTypes.V2 (-y) x
rPCMPlot :: [R] -> DynamicPlottable
rPCMPlot = plot . recursivePCM (PCMRange (0 :: Double) 1)
instance Plottable (Shade P2) where
plot shade = def
& relevantRange_x .~ atLeastInterval xRange
& relevantRange_y .~ atLeastInterval yRange
& autoTint
& axesNecessity .~ 1
& dynamicPlot .~ plot
where plot _ = pure . mkPlot $ foldMap axLine eigVs
where axLine eigV = simpleLine (ctr .-~^ eigV) (ctr .+~^ eigV)
(xRange,yRange) = shadeExtends shade
ctr = shade^.shadeCtr
eigVs = normSpanningSystem $ shade^.shadeExpanse
instance Plottable (Shade ℝ²) where
plot (Shade v e) = plot (Shade (Dia.P v) e :: Shade P2)
instance Plottable (Shade (R,R)) where
plot sh = plot (coerceShade sh :: Shade R2)
instance Plottable (Shade' (R,R)) where
plot shade = def
& autoTint
& axesNecessity .~ 1
& dynamicPlot .~ plot
where plot wSpec = pure . mkPlot $ Dia.circle 1
& Dia.scaleX w₁ & Dia.scaleY w₂
& Dia.rotate ϑ
& Dia.opacity 0.2
& Dia.moveTo ctr
where [w₁,w₂] = recip . sqrt
. max (recip $ 100 * max ((wSpec^.windowDiameter)^2) ctrDistance)
. fst <$> [ev₁, ev₂]
ctrDistance = distanceSq (shade^.shadeCtr) (wSpec^.windowCenter)
ctr = Dia.p2 $ shade^.shadeCtr
Norm expanr = shade^.shadeNarrowness
[ev₁@(_,(e₁x,e₁y)),ev₂] = case eigen $ arr expanr of
(e₁:e₂:_) -> [e₁,e₂]
[e@(_,(vx,vy))] -> [e, (0,(-vx,vy))]
[] -> [(0,(1,0)), (0,(0,1))]
ϑ = atan2 e₁y e₁x Dia.@@ Dia.rad
instance Plottable (ConvexSet ℝ²) where
plot EmptyConvex = mempty
plot (ConvexSet hull intersects)
= plot (ConvexSet (coerceShade hull) (coerceShade<$>intersects) :: ConvexSet (ℝ,ℝ))
instance Plottable (ConvexSet (R,R)) where
plot EmptyConvex = mempty
plot (ConvexSet hull intersects)
= plot [ plot intersects
& tweakPrerendered (Dia.opacity
(1 / fromIntegral (length intersects)) )
, plot hull
& tweakPrerendered ( Dia.lwO 3
>>> Dia.opacity 1
>>> Dia.fcA (Dia.withOpacity Dia.grey 0.01) ) ]
instance Plottable (Shade' ℝ²) where
plot sh = plot (coerceShade sh :: Shade' (ℝ,ℝ))
instance Plottable (Shade' P2) where
plot (Shade' (Dia.P v) e) = plot (Shade' v e :: Shade' ℝ²)
instance Plottable (Shaded ℝ ℝ) where
plot tr | length trivs' >= 2
= def & relevantRange_x .~ atLeastInterval (Interval xmin xmax)
& relevantRange_y .~ atLeastInterval (Interval ymin ymax)
& autoTint
& axesNecessity .~ 1
& dynamicPlot .~ plot
where plot grWS@(GraphWindowSpecR2{..}) = pure . mkPlot $
foldMap parallelogram trivs
<> (foldMap (singlePointFor grWS) leafPoints
-- & Dia.dashingO [2,3] 0
& Dia.opacity 0.4 )
where parallelogram ((x,δx), ((y,δy), j))
= lLoop [ (x+δx)^&(y+δy+jδx), (x-δx)^&(y+δy-jδx)
, (x-δx)^&(y-δy-jδx), (x+δx)^&(y-δy+jδx) ]
& Dia.strokeLocLoop
& Dia.opacity 0.3
where jδx = j $ δx
trivs' = sortBy (comparing fst) $ stiAsIntervalMapping tr
trivs = NE.fromList $ ccδs trivs'
where ccδs [(x, yq), (x', yq')] = [((x,δx),yq), ((x',δx),yq')]
where δx = (x' - x)/2
ccδs [(x, yq), (x', yq'), (x'', yq'')]
= [((x,δx),yq), ((x',δx),yq'), ((x'',δx),yq'')]
where δx = (x'' - x)/4
ccδs ((x, yq) : xyqs@((x', yq') : (x'', _) : _))
= ((x,δx),yq) : ((x',δx),yq') : tail (ccδs xyqs)
where δx = (x'' - x)/4
[xmin, ymin, xmax, ymax]
= [minimum, maximum]<*>[fst<$>allLeaves, snd<$>allLeaves]
lLoop ps@(p:_) = Dia.fromVertices $ ps++[p]
leafPoints = sortBy (comparing (^._x))
$ (\(x,y) -> y^&x) <$> allLeaves
allLeaves = onlyLeaves tr
plot _ = def
instance Plottable (PointsWeb ℝ (Shade' ℝ)) where
plot web | length locals >= 2
= def & relevantRange_x .~ atLeastInterval (Interval xmin xmax)
& relevantRange_y .~ atLeastInterval (Interval ymin ymax)
& autoTint
& axesNecessity .~ 1
& dynamicPlot .~ pure . plot
where plot grWS@(GraphWindowSpecR2{..}) = mkPlot $
foldMap parallelogram trivs
<> foldMap vbar divis
where parallelogram ((x,(δxl,δxr)), ((y,δy), j))
= lLoop [ (x+δxr)^&(y+δy+jδxr), (x-δxl)^&(y+δy-jδxl)
, (x-δxl)^&(y-δy-jδxl), (x+δxr)^&(y-δy+jδxr) ]
& Dia.strokeLocLoop
& Dia.opacity 0.3
where jδxl = j $ δxl
jδxr = j $ δxr
vbar (x,(δxl,δxr)) = Dia.fromVertices
[ (x-δxl)^&tBound, (x-δxl)^&bBound
, (x+δxr)^&bBound, (x+δxr)^&tBound ]
trivs :: [((ℝ, (Diff ℝ,Diff ℝ)), ((ℝ, Diff ℝ), LocalLinear ℝ ℝ))]
divis :: [(ℝ, (Diff ℝ,Diff ℝ))]
(trivs,divis) = concat***concat $ unzip (map mkTriv locals)
where mkTriv :: ((ℝ, Shade' ℝ), [(ℝ, Shade' ℝ)])
-> ( [((ℝ, (Diff ℝ,Diff ℝ)), ((ℝ, Diff ℝ), LocalLinear ℝ ℝ))]
, [(ℝ, (Diff ℝ,Diff ℝ))] )
mkTriv ((xc,Shade' yc yce), [(δxo, Shade' yo _)])
= case findNormalLength yce of
Just ry ->
( [ ( (xc, dirSort 0 δxo)
, ( (yc, ry)
, id ^* ((yo-yc)/δxo) ) ) ], [] )
Nothing ->
( [], [(xc, dirSort 0 δxo)] )
mkTriv ((xc,Shade' yc yce), [(δxl, Shade' yl _), (δxr, Shade' yr _)])
= case findNormalLength yce of
Just ry ->
( [ ( (xc, dirSort δxl δxr)
, ( (yc, ry)
, id ^* η ) ) ], [] )
Nothing ->
( [], [(xc, dirSort δxl δxr)] )
where δxg = (δxr - δxl)/2
η = (yr - yl)/(2*δxg)
mkTriv (p,lrs) = concat***concat $ unzip [mkTriv (p,[l,r]) | l<-ls, r<-rs]
where (ls,rs) = partition ((<0) . fst) lrs
dirSort δ₁ δ₂ | δ₁ < δ₂ = (-δ₁, δ₂)
| otherwise = (-δ₂, δ₁)
lLoop ps@(p:_) = Dia.fromVertices $ ps++[p]
[xmin, ymin, xmax, ymax]
= [minimum, maximum]<*>[fst.fst<$>locals, (^.shadeCtr).snd.fst<$>locals]
locals :: [((ℝ, Shade' ℝ), [(ℝ, Shade' ℝ)])]
locals = Hask.toList $ localFocusWeb web
plot _ = def
instance Plottable (PointsWeb ℝ² (CSp.Colour ℝ)) where
plot web = plot (coerceWebDomain web :: PointsWeb (ℝ,ℝ) (CSp.Colour ℝ))
instance Plottable (PointsWeb (ℝ,ℝ) (CSp.Colour ℝ)) where
plot = webbedSurfPlot $ pure . toRGBA
where toRGBA (Just c)
= JPix.promotePixel (CSp.quantiseColour c :: JPix.PixelRGB8)
toRGBA _ = JPix.PixelRGBA8 0 0 0 0
#if MIN_VERSION_manifolds(0,6,0)
instance Plottable (PointsWeb ℝ² (Shade CSp.ColourNeedle)) where
#else
instance Plottable (PointsWeb ℝ² (Shade (CSp.Colour ℝ))) where
#endif
plot web = plot (coerceWebDomain web :: PointsWeb (ℝ,ℝ) (Shade CSp.ColourNeedle))
#if MIN_VERSION_manifolds(0,6,0)
instance Plottable (PointsWeb (ℝ,ℝ) (Shade CSp.ColourNeedle)) where
#else
instance Plottable (PointsWeb (ℝ,ℝ) (Shade (CSp.Colour ℝ))) where
#endif
plot = webbedSurfPlot toRGBA
where toRGBA (Just c)
= JPix.promotePixel . (CSp.quantiseColour :: CSp.Colour ℝ -> JPix.PixelRGB8)
#if MIN_VERSION_manifolds(0,6,0)
. fromInterior
#endif
<$> Random.rvar c
toRGBA _ = return $ JPix.PixelRGBA8 0 0 0 0
instance Plottable (Cutplane (ℝ,ℝ)) where
plot (Cutplane (x₀,y₀) (Stiefel1 (dy,dx)))
= plot (Cutplane (V2 x₀ y₀) (Stiefel1 (V2 dy dx)))
instance Plottable (Cutplane ℝ²) where
plot (Cutplane (V2 x₀ y₀) (Stiefel1 (V2 dy dx)))
= def & autoTint
& axesNecessity .~ 1
& dynamicPlot .~ pure . plot
where plot grWS@(GraphWindowSpecR2{..}) = mkPlot $ simpleLine p q
where [p,q]
| abs (dy*(rBound-lBound)) > abs (dx*(tBound-bBound))
= [xf bBound ^& bBound, xf tBound ^& tBound]
| otherwise
= [lBound ^& yf lBound, rBound ^& yf rBound]
yf x = y₀ - dy/dx * (x-x₀)
xf y = x₀ - dx/dy * (y-y₀)
webbedSurfPlot :: Geodesic a
=> (Maybe a -> Random.RVar JPix.PixelRGBA8)
-> PointsWeb (ℝ,ℝ) a -> DynamicPlottable
webbedSurfPlot toRGBA web = def & dynamicPlot .~ plotWeb
& relevantRange_x .~ atLeastInterval (x₀...x₁)
& relevantRange_y .~ atLeastInterval (y₀...y₁)
& occlusiveness .~ 4
where plotWeb graSpec = do
pixRendered <- pixRender
pure . mkPlot $
(Dia.image $ Dia.DImage
(Dia.ImageRaster $ JPix.ImageRGBA8 pixRendered)
renderWidth renderHeight
placement)
cartesianed = sampleEntireWeb_2Dcartesian_lin web renderWidth renderHeight
renderWidth = 120 -- xResolution graSpec
renderHeight = 90 -- yResolution graSpec
x₀ = minimum (fst<$>pts)
x₁ = maximum (fst<$>pts)
y₀ = minimum (snd<$>pts)
y₁ = maximum (snd<$>pts)
pts = fst . fst <$> Hask.toList (localFocusWeb web)
xc = (x₀+x₁)/2
yc = (y₀+y₁)/2
wPix = (x₁ - x₀)/renderWidth
hPix = (y₁ - y₀)/renderHeight
placement = Dia.translation (xc^&yc) <> Dia.scalingX wPix <> Dia.scalingY hPix
pixRender = do
seed <- Random.mkStdGen <$> Random.stdUniform
return $ runST (do
randomGen <- newSTRef seed
cursorState <- newSTRef (0, reverse cartesianed)
JPix.withImage renderWidth renderHeight $ \_ix iy -> do
(iyPrev, (y, xvs) : yvs) <- readSTRef cursorState
vc <- if iy > iyPrev
then case yvs of
((y',(_x,vc):xvs') : yvs') -> do
writeSTRef cursorState (iy, (y', xvs') : yvs')
return vc
else case xvs of
((_x,vc) : xvs') -> do
writeSTRef cursorState (iy, (y, xvs') : yvs)
return vc
rg <- readSTRef randomGen
let (c, rg') = Random.sampleState (toRGBA vc) rg
writeSTRef randomGen rg'
return c
)
-- | Combine multiple objects in a single plot. Each will get an individual 'tint'
-- (if applicable). This is also the default behaviour of 'plotWindow'.
--
-- To plot a family objects all with the /same/ (but automatically-chosen) tint,
-- simply use 'plot' on the list, or combine them monoidally with '<>'.
plotMultiple :: Plottable x => [x] -> DynamicPlottable
plotMultiple = fold . chooseAutoTints . map plot
instance (Plottable x) => Plottable (Latest x) where
plot (Latest (ev₀ :| [])) = plot ev₀
plot (Latest (ev₀ :| ev₁:evs))
= plot ev₀ & futurePlots .~ (const . Just . plot . Latest $ ev₁:|evs)
-- | Lazily consume the list, always plotting the latest value available as they
-- arrive.
-- Useful for displaying results of expensive computations that iteratively improve
-- some result, but also for making simple animations (see 'plotDelay').
plotLatest :: Plottable x => [x] -> DynamicPlottable
plotLatest (x:xs) = plot $ Latest (x:|xs)
plotLatest l = plot l
instance Plottable (SimpleTree P2) where
plot (GenericTree Nothing) = plot ([] :: [SimpleTree P2])
plot (GenericTree (Just (ctr, root)))
= def
& relevantRange_x .~ atLeastInterval xRange
& relevantRange_y .~ atLeastInterval yRange
& autoTint
& axesNecessity .~ 1
& dynamicPlot .~ plot
where plot _ = pure . mkPlot $ go 4 ctr (treeBranches root)
where go w bctr = foldMap (\(c,GenericTree b)
-> autoDashLine w bctr c
<> go (w*0.6) c b )
(xRange, yRange) = let allPoints = gPts tree
(xmin,xmax) = (minimum&&&maximum) $ (^._x) <$> allPoints
(ymin,ymax) = (minimum&&&maximum) $ (^._y) <$> allPoints
in (xmin ... xmax, ymin ... ymax)
where gPts (GenericTree brchs) = foldr (\(c,b) r -> c : gPts b ++ r) [] brchs
tree = GenericTree [(ctr,root)]
instance Plottable (Trees P2) where
plot (GenericTree ts) = plot $ (GenericTree . Just) <$> ts
instance Plottable (Trees R2) where
plot = plot . fmap Dia.P
instance Plottable (SimpleTree (R,R)) where
plot = plot . fmap (\(x,y) -> DiaTypes.p2 (x,y))
instance Plottable (Trees (R,R)) where
plot (GenericTree ts) = plot $ (GenericTree . Just) <$> ts
instance Plottable (SimpleTree (R`WithAny`R)) where
plot = plot . fmap (\(WithAny y x) -> DiaTypes.p2 (x,y))
instance Plottable (Trees (R`WithAny`R)) where
plot (GenericTree ts) = plot $ (GenericTree . Just) <$> ts
pixelDim :: GraphWindowSpecR2 -> (R, R)
pixelDim grWS = ( graphWindowWidth grWS / fromIntegral (xResolution grWS)
, graphWindowHeight grWS / fromIntegral (yResolution grWS) )
singlePointFor :: GraphWindowSpecR2 -> P2 -> PlainGraphicsR2
singlePointFor spec = Dia.place circ
where (pxw,pxh) = pixelDim spec
circ = Dia.circle 1 & Dia.scaleX pxw & Dia.scaleY pxh
moveStepRel :: (R, R) -- ^ Relative translation @(Δx/w, Δy/h)@.
-> (R, R) -- ^ Relative zoom.
-> GraphWindowSpec -> GraphWindowSpec
moveStepRel (δx,δy) (ζx,ζy) (GraphWindowSpecR2 l r b t xRes yRes clSchm)
= GraphWindowSpecR2 l' r' b' t' xRes yRes clSchm
where qx = (r-l)/2 ; qy = (t-b)/2
mx'= l + qx*(1+δx) ; my'= b + qy*(1+δy)
qx'= zoomSafeGuard mx' $ qx/ζx; qy'= zoomSafeGuard my' $ qy/ζy
l' = mx' - qx' ; b' = my' - qy'
r' = mx' + qx' ; t' = my' + qy'
zoomSafeGuard m = max (1e-250 + abs m*1e-6) . min 1e+250
graphWindowWidth, graphWindowHeight :: GraphWindowSpec -> R
graphWindowWidth grWS = rBound grWS - lBound grWS
graphWindowHeight grWS = tBound grWS - bBound grWS
instance Semigroup Plot where
Plot a1 d1 <> Plot a2 d2 = Plot (a1<>a2) (d1<>d2)
instance Monoid Plot where
mempty = Plot mempty mempty
mappend = (<>)
mkPlot :: PlainGraphicsR2 -> Plot
mkPlot = Plot mempty
mkAnnotatedPlot :: [Annotation] -> PlainGraphicsR2 -> Plot
mkAnnotatedPlot ans = Plot ans
instance Semigroup DynamicPlottable where
DynamicPlottable rx₁ ry₁ vpc₁ tm₁ oc₁ ax₁ dl₁ le₁ al₁ fu₁ dp₁
<> DynamicPlottable rx₂ ry₂ vpc₂ tm₂ oc₂ ax₂ dl₂ le₂ al₂ fu₂ dp₂
= DynamicPlottable
(rx₁<>rx₂) (ry₁<>ry₂) (vpc₁.vpc₂) (tm₁++tm₂)
(oc₁+oc₂) (ax₁+ax₂) (max dl₁ dl₂)
(le₁++le₂) (al₁++al₂)
((<>)<$>fu₁<*>fu₂) (liftA2(liftA2(<>))<$>dp₁<*>dp₂)
instance Monoid DynamicPlottable where
mempty = DynamicPlottable
mempty -- don't request any range
mempty
id -- don't enforce anything about the viewport
[] -- no colours
0 -- neither obscures anything nor has details that could be obscured
0 -- don't need axis (but don't mind them either)
(1/20) -- 20 fps is at the moment the fastest enabled refresh rate anyway
[] -- no legend entries
[] -- no axis labels
mempty -- no time-evolution
(const . const $ pure mempty)
mappend = (<>)
instance Default DynamicPlottable where def = mempty
-- | Set the caption for this plot object that should appear in the
-- plot legend.
legendName :: String -> DynamicPlottable -> DynamicPlottable
legendName n obj = sustained legendEntries %~ (LegendEntry (PlainText n) colour mempty :)
$ obj
where colour = case obj^.inherentColours of
(c₀:_) -> Just c₀
_ -> Nothing
-- | Colour this plot object in a fixed shade.
tint :: DCol.Colour ℝ -> DynamicPlottable -> DynamicPlottable
tint col = sustained inherentColours .~ [TrueColour col]
>>> allDynamicPlot %~ fmap (fmap $ getPlot %~ Dia.lc col . Dia.fc col)
>>> sustained legendEntries %~ map
(plotObjRepresentativeColour ?~ TrueColour col)
-- | Allow the object to be automatically assigned a colour that's otherwise
-- unused in the plot. (This is the default for most plot objects.)
autoTint :: DynamicPlottable -> DynamicPlottable
autoTint = sustained inherentColours .~ []
-- | Assign each object an individual colour, if applicable.
chooseAutoTints :: [DynamicPlottable] -> [DynamicPlottable]
chooseAutoTints = go defaultColourSeq
where go (c:cs) (o:os)
| null $ o^.inherentColours
= (o & sustained inherentColours.~[SymbolicColour c]
& allDynamicPlot %~
(\plotF gwSpec ->
let ac = asAColourWith (colourScheme gwSpec) c
in fmap (getPlot %~ Dia.lcA ac . Dia.fcA ac) $ plotF gwSpec)
& sustained legendEntries %~ map
(plotObjRepresentativeColour ?~ SymbolicColour c)
) : go cs os
go cs (o:os) = o : go cs os
go _ [] = []
instance (Ord r) => Semigroup (RangeRequest r) where
MustBeThisRange r <> _ = MustBeThisRange r
_ <> MustBeThisRange r = MustBeThisRange r
OtherDimDependantRange r1 <> OtherDimDependantRange r2 = OtherDimDependantRange $ r1<>r2
instance (Ord r) => Monoid (RangeRequest r) where
mempty = OtherDimDependantRange $ const Nothing
mappend = (<>)
otherDimDependence :: (Interval r->Interval r) -> RangeRequest r
otherDimDependence = OtherDimDependantRange . fmap
atLeastInterval :: Interval r -> RangeRequest r
atLeastInterval = atLeastInterval' . pure
atLeastInterval' :: Maybe (Interval r) -> RangeRequest r
atLeastInterval' = OtherDimDependantRange . const
-- | Render a single view of a collection of plottable objects. This can be
-- used the same way as 'plotWindow', but does not open any GTK but gives
-- the result as-is.
--
-- If the objects contain animations, only the initial frame will be rendered.
plotPrerender :: ViewportConfig -> [DynamicPlottable] -> IO PlainGraphicsR2
plotPrerender vpc [] = plotPrerender vpc [dynamicAxes]
plotPrerender vpc plotObjs = do
renderd <- Random.runRVar ((getPlot%~Dia.lwO defLineWidth)
<$>(plotMultiple plotObjs' ^. dynamicPlotWithAxisLabels)
axLabels
viewport)
Random.StdRandom
annot <- renderAnnotationsForView viewport (renderd^.plotAnnotations)
return $ annot <> renderd^.getPlot
& case vpc^.prerenderScaling of
ValuespaceScaling ->
Dia.withEnvelope (Dia.rect w h
& Dia.alignTL
& Dia.moveTo (Dia.P $ V2 lBound tBound)
:: PlainGraphicsR2)
prs -> normaliseView viewport
>>> (vpc^.graphicsPostprocessing)
>>> Dia.withEnvelope (Dia.rect 2 2 :: PlainGraphicsR2)
>>> case prs of
NormalisedScaling -> id
OutputCoordsScaling -> Dia.translate (1 ^& (-1))
>>> Dia.scaleX (fromInt xResolution / 2)
>>> Dia.scaleY (fromInt yResolution / 2)
>>> case vpc^.plotBackground of
Nothing -> id
Just bgc -> Dia.bg bgc
where viewport@(GraphWindowSpecR2{..}) = autoDefaultView vpc plotObjs'
w = rBound - lBound; h = tBound - bBound
plotObjs' = plotObjs ++ if axesNeed>0
then [dynamicAxes]
else []
axLabels = concat $ _axisLabelRequests<$>plotObjs
axesNeed = sum $ _axesNecessity<$>plotObjs
-- | Render the legend (if any) belonging to a collection of plottable objects.
plotLegendPrerender :: LegendDisplayConfig -> [DynamicPlottable]
-> IO (Maybe PlainGraphicsR2)
plotLegendPrerender ldc [] = pure Nothing
plotLegendPrerender ldc l = prerenderLegend (TextTK defaultTxtStyle 10 1 0.2 0.2)
colourScheme ldc entries
where tintedl = chooseAutoTints l
entries = (^.legendEntries) =<< tintedl
GraphWindowSpecR2{..} = autoDefaultView def $ tintedl
-- | Plot some plot objects to a new interactive GTK window. Useful for a quick
-- preview of some unknown data or real-valued functions; things like selection
-- of reasonable view range and colourisation are automatically chosen.
--
-- Example:
--
-- <<images/examples/HelloWorld.gif>>
--
-- The individual objects you want to plot can be evaluated in multiple threads, so
-- a single hard calculatation won't freeze the responsitivity of the whole window.
-- Invoke e.g. from @ghci +RTS -N4@ to benefit from this.
--
-- ATTENTION: the window may sometimes freeze, especially when displaying
-- complicated functions with 'fnPlot` from ghci. This is apparently
-- a kind of deadlock problem with one of the C libraries that are invoked,
-- At the moment, we can recommend no better solution than to abort and restart ghci
-- (or what else you use – iHaskell kernel, process, ...) if this occurs.
plotWindow :: [DynamicPlottable] -> IO GraphWindowSpec
plotWindow = plotWindow' def
-- | Like 'plotWindow', but with explicit specification how the window is supposed
-- to show up. ('plotWindow' uses the default configuration, i.e. 'def'.)
plotWindow' :: ViewportConfig -> [DynamicPlottable] -> IO GraphWindowSpec
plotWindow' viewportConfig [] = plotWindow' viewportConfig [dynamicAxes]
plotWindow' viewportConfig givenPlotObjs = runInBoundThread $ do
let defColourScheme = defaultColourScheme
tintedPlotObjs = chooseAutoTints givenPlotObjs
viewState <- newIORef $ autoDefaultView viewportConfig tintedPlotObjs
viewTgt <- newIORef =<< readIORef viewState
let objAxisLabels = concat $ _axisLabelRequests<$>givenPlotObjs
viewTgtGlobal <- newMVar . (,objAxisLabels) =<< readIORef viewState
screenResolution <- newIORef (viewportConfig^.xResV, viewportConfig^.yResV)
let viewConstraint = flip (foldr _viewportConstraint) givenPlotObjs
let screenCoordsToData (sx,sy) = do
GraphWindowSpecR2{..} <- readIORef viewState
let snx = sx / fromIntegral xResolution
sny = sy / fromIntegral yResolution
return (lBound + snx*(rBound-lBound), tBound - sny*(tBound-bBound))
dgStore <- newIORef mempty
(plotObjs, cancelWorkers) :: ([ObjInPlot], IO ()) <- do
let assignPlObjPropties :: [DynamicPlottable] -> Necessity
-> IO [(ObjInPlot, ThreadId)]
assignPlObjPropties [] axesNeed
| axesNeed > 0 = assignPlObjPropties [tint Dia.grey dynamicAxes] (-1)
| otherwise = return []
assignPlObjPropties (o:os) axn = do
newDia <- newEmptyMVar
newMouseEvs <- newEmptyMVar
workerId <- forkIO $ objectPlotterThread o viewTgtGlobal newMouseEvs newDia
stableView <- newIORef Nothing
((ObjInPlot stableView newDia newMouseEvs cl o, workerId) :)
<$> assignPlObjPropties os (axn + o^.axesNecessity)
where cl | TrueColour c₀:_ <- o^.inherentColours
= Just $ Dia.opaque c₀
| SymbolicColour c₀:_ <- o^.inherentColours
= Just $ defColourScheme c₀
| otherwise = Nothing
(pObs, workerId) <- unzip <$> assignPlObjPropties tintedPlotObjs 0
return ( sortBy (comparing $ _occlusiveness . _originalPlotObject) pObs
, forM_ workerId killThread )
GTK.initGUI
window <- GTK.windowNew
mouseAnchor <- newIORef Nothing
mousePressedAt <- newIORef Nothing
refreshDraw <- do
drawA <- GTK.drawingAreaNew
GTK.onExpose drawA $ \_ -> do
(canvasX,canvasY) <- GTK.widgetGetSize drawA
modifyIORef viewTgt
$ \view -> viewConstraint $ view{ xResolution = fromIntegral canvasX
, yResolution = fromIntegral canvasY }
dia <- readIORef dgStore
let scaledDia = Dia.bg (case viewportConfig^.plotBackground of
Just bgc -> bgc
Nothing -> Dia.black)
. Dia.scaleX (fromInt canvasX / 2)
. Dia.scaleY (-fromInt canvasY / 2)
. Dia.translate (1 ^& (-1))
. Dia.withEnvelope (Dia.rect 2 2 :: PlainGraphicsR2)
. (viewportConfig^.graphicsPostprocessing)
$ dia
drawWindow <- GTK.widgetGetDrawWindow drawA
BGTK.renderToGtk drawWindow $ scaledDia
return True
GTK.on drawA GTK.buttonPressEvent . Event.tryEvent $ do
Event.eventButton >>= guard.(==defaultDragButton)
anchXY <- Event.eventCoordinates
liftIO . writeIORef mouseAnchor $ Just anchXY
GTK.on drawA GTK.buttonReleaseEvent . Event.tryEvent $ do
Event.eventButton >>= guard.(==defaultDragButton)
liftIO . writeIORef mouseAnchor $ Nothing
GTK.on drawA GTK.buttonPressEvent . Event.tryEvent $ do
Event.eventButton >>= guard.(==defaultEditButton)
(pressX,pressY) <- liftIO . screenCoordsToData =<< Event.eventCoordinates
liftIO . writeIORef mousePressedAt $ Just (pressX,pressY)
let event = MouseEvent (pressX^&pressY) (pressX^&pressY)
liftIO . forM_ plotObjs $ _mouseEventsForObj >>> \mevs -> do
tryTakeMVar mevs >>= \case
Nothing -> putMVar mevs $ Interactions [] (Just event)
Just (Interactions qe _)
-> putMVar mevs $ Interactions qe (Just event)
GTK.on drawA GTK.buttonReleaseEvent . Event.tryEvent $ do
Event.eventButton >>= guard.(==defaultEditButton)
(relX,relY) <- liftIO . screenCoordsToData =<< Event.eventCoordinates
liftIO (readIORef mousePressedAt) >>= \case
Just (pressX,pressY) -> liftIO $ do
let event = MouseEvent (pressX^&pressY) (relX^&relY)
forM_ plotObjs $ _mouseEventsForObj >>> \mevs -> do
tryTakeMVar mevs >>= \case
Nothing -> putMVar mevs $ Interactions [event] Nothing
Just (Interactions qe _)
-> putMVar mevs $ Interactions (event:qe) Nothing
Nothing -> mzero
liftIO . writeIORef mouseAnchor $ Nothing
GTK.on drawA GTK.motionNotifyEvent . Event.tryEvent $ do
liftIO (readIORef mouseAnchor) >>= \case
Just (oldX,oldY) -> do
(mvX,mvY) <- Event.eventCoordinates
(canvasX,canvasY) <- liftIO $ GTK.widgetGetSize drawA
let ηX = (oldX-mvX) / fromIntegral canvasX
ηY = (mvY-oldY) / fromIntegral canvasY
liftIO . modifyIORef viewTgt $ \view@GraphWindowSpecR2{..} ->
let w = rBound - lBound
h = tBound - bBound
in view{ lBound = lBound + w * ηX
, rBound = rBound + w * ηX
, tBound = tBound + h * ηY
, bBound = bBound + h * ηY
}
liftIO . modifyIORef mouseAnchor . fmap $ const (mvX,mvY)
Nothing -> liftIO (readIORef mousePressedAt) >>= \case
Just (pressX,pressY) -> do
(curX,curY) <- liftIO . screenCoordsToData =<< Event.eventCoordinates
let event = MouseEvent (pressX^&pressY) (curX^&curY)
liftIO . forM_ plotObjs $ _mouseEventsForObj >>> \mevs -> do
tryTakeMVar mevs >>= \case
Nothing -> putMVar mevs $ Interactions [] (Just event)
Just (Interactions qe _)
-> putMVar mevs $ Interactions qe (Just event)
Nothing -> mzero
GTK.widgetAddEvents drawA [GTK.ButtonMotionMask]
GTK.on drawA GTK.scrollEvent . Event.tryEvent $ do
(canvasX,canvasY) <- liftIO $ GTK.widgetGetSize drawA
(scrollX,scrollY) <- Event.eventCoordinates
let (rcX,rcY) = ( scrollX*2 / fromIntegral canvasX - 1
, 1 - scrollY*2 / fromIntegral canvasY )
scrollD <- Event.eventScrollDirection
liftIO . modifyIORef viewTgt $ \view@GraphWindowSpecR2{..} ->
let w = rBound - lBound
h = tBound - bBound
ηl = (rcX + 1)^2/4; ηr = (rcX - 1)^2/4
ηb = (rcY + 1)^2/4; ηt = (rcY - 1)^2/4
ηh = (1-ηt) * (1-ηb) + ηl + ηr
ηv = (1-ηl) * (1-ηr) + ηt + ηb
in case defaultScrollBehaviour scrollD of
ScrollZoomIn -> view{
lBound = lBound + w * ηl * ηh * scrollZoomStrength
, rBound = rBound - w * ηr * ηh * scrollZoomStrength
, tBound = tBound - h * ηt * ηv * scrollZoomStrength
, bBound = bBound + h * ηb * ηv * scrollZoomStrength
}
ScrollZoomOut -> view{
lBound = lBound - w * ηr * ηh * scrollZoomStrength
, rBound = rBound + w * ηl * ηh * scrollZoomStrength
, tBound = tBound + h * ηb * ηv * scrollZoomStrength
, bBound = bBound - h * ηt * ηv * scrollZoomStrength
}
GTK.set window [ GTK.windowTitle := "Plot"
, GTK.windowDefaultWidth := viewportConfig^.xResV
, GTK.windowDefaultHeight := viewportConfig^.yResV
, GTK.containerChild := drawA
]
GTK.widgetShowAll window
return $ GTK.widgetQueueDraw drawA
t₀ <- getCurrentTime
lastFrameTime <- newIORef t₀
let refreshScreen = do
currentView@(GraphWindowSpecR2{..}) <- readIORef viewState
let textTK txSiz asp = TextTK defaultTxtStyle txSiz asp 0.2 0.2
renderComp plotObj = do
plt <- tryTakeMVar (plotObj^.newPlotView) >>= \case
Nothing -> fmap snd <$> readIORef (plotObj^.lastStableView)
newDia -> do
writeIORef (plotObj^.lastStableView) newDia
return $ snd <$> newDia
case plt of
Nothing -> return mempty
Just (Plot{..}, objLegend) -> do
renderedAnnot
<- renderAnnotationsForView currentView _plotAnnotations
return (normaliseView currentView
$ renderedAnnot <> _getPlot, objLegend)
(thisPlots, thisLegends)
<- unzip . reverse <$> mapM renderComp (reverse plotObjs)
let thePlot = mconcat thisPlots
theLegend <- prerenderLegend (textTK 10 1) colourScheme
(LegendDisplayConfig Dia.absolute)
$ concat (fst<$>thisLegends)
writeIORef dgStore $ maybe mempty
(\l -> l & Dia.scaleX (0.1 / sqrt (fromIntegral xResolution))
& Dia.scaleY (0.1 / sqrt (fromIntegral yResolution))
& (`Dia.place`(0.75^&0.75)) ) theLegend
<> thePlot
refreshDraw
let mainLoop = do
t <- getCurrentTime
δt <- fmap (diffUTCTime t) $ readIORef lastFrameTime
writeIORef lastFrameTime t
do vt <- readIORef viewTgt
modifyMVar_ viewTgtGlobal $ return . first (const vt)
modifyIORef viewState $ \vo ->
let a%b = let η = min 1 $ 2 * realToFrac δt in η*a + (1-η)*b
in GraphWindowSpecR2 (lBound vt % lBound vo) (rBound vt % rBound vo)
(bBound vt % bBound vo) (tBound vt % tBound vo)
(xResolution vt) (yResolution vt)
defColourScheme
-- GTK.sleep 0.01
refreshScreen
-- GTK.pollEvents
return True
GTK.onDestroy window $ do
cancelWorkers
GTK.mainQuit
GTK.timeoutAdd mainLoop 50
GTK.mainGUI
readIORef viewState
objectPlotterThread :: DynamicPlottable
-> MVar (GraphWindowSpec, [AxisLabel])
-> MVar (Interactions (ℝ,ℝ))
-> MVar (GraphWindowSpec, AnnotPlot)
-> IO ()
objectPlotterThread pl₀ viewVar mouseVar diaVar = loop Nothing pl₀ where
loop lastMousePressed pl = do
tPrev <- getCurrentTime
(view, labels) <- readMVar viewVar
newMice <- tryTakeMVar mouseVar
let mice = case (newMice, lastMousePressed) of
(Just m, _) -> m
(Nothing, p) -> Interactions [] p
diagram <- evaluate . (getPlot %~ Dia.lwO defLineWidth) =<< Random.runRVar
((pl^.dynamicPlotWithAxisLabels) labels view)
Random.StdRandom
putMVar diaVar (view, (diagram, (pl^.legendEntries, pl^.axisLabelRequests)))
waitTill $ addUTCTime (pl^.frameDelay) tPrev
loop (_currentDragEndpoints mice) $ case pl^.futurePlots $ mice of
Just pl' -> pl'
Nothing -> pl
normaliseView :: GraphWindowSpecR2 -> PlainGraphicsR2 -> PlainGraphicsR2
normaliseView currentView@(GraphWindowSpecR2{..})
= (Dia.scaleX xUnZ :: PlainGraphicsR2->PlainGraphicsR2)
. Dia.scaleY yUnZ
. Dia.translate (Dia.r2(-x₀,-y₀))
where xUnZ = 1/w; yUnZ = 1/h
w = (rBound - lBound)/2; h = (tBound - bBound)/2
x₀ = lBound + w; y₀ = bBound + h
-- | Require that both coordinate axes are zoomed the same way, such that e.g.
-- the unit circle will appear as an actual circle.
unitAspect :: DynamicPlottable
unitAspect = def & viewportConstraint . mapped . windowDataAspect .~ 1
autoDefaultView :: ViewportConfig -> [DynamicPlottable] -> GraphWindowSpec
autoDefaultView vpConf graphs =
foldr _viewportConstraint
(GraphWindowSpecR2 l r b t
(vpConf^.xResV) (vpConf^.yResV) defaultColourScheme)
graphs
where (xRange, yRange) = foldMap (_relevantRange_x &&& _relevantRange_y) graphs
((l,r), (b,t)) = ( xRange `dependentOn` yRange
, yRange `dependentOn` xRange )
dependentOn :: RangeRequest R -> RangeRequest R -> (R,R)
MustBeThisRange (Interval a b) `dependentOn` _ = (a,b)
OtherDimDependantRange ξ `dependentOn` MustBeThisRange i
= addMargin . defRng . ξ $ pure i
OtherDimDependantRange ξ `dependentOn` OtherDimDependantRange υ
= addMargin . defRng . ξ . pure . defRng $ υ Nothing
defRng (Just (Interval a b)) | b>a
= Interval a b
defRng _ = Interval (-1) 1 -- ad-hoc hack to catch NaNs etc..
addMargin (Interval a b) = (a - q, b + q)
where q = (b - a) * (1/(vpConf^.plotContentZoomFactor) - 1)
renderAnnotationsForView :: GraphWindowSpecR2 -> [Annotation] -> IO PlainGraphicsR2
renderAnnotationsForView viewport@GraphWindowSpecR2{..}
= fmap mconcat . mapM (prerenderAnnotation antTK)
where antTK = DiagramTK { viewScope = viewport
, textTools = TextTK defaultTxtStyle txtSize aspect 0.2 0.2 }
txtSize = h * fontPts / fromIntegral yResolution
aspect = w * fromIntegral yResolution
/ (h * fromIntegral xResolution)
w = (rBound - lBound)/2; h = (tBound - bBound)/2
fontPts = 12
data ScrollAction = ScrollZoomIn | ScrollZoomOut
defaultScrollBehaviour :: Event.ScrollDirection -> ScrollAction
defaultScrollBehaviour Event.ScrollUp = ScrollZoomIn
defaultScrollBehaviour Event.ScrollDown = ScrollZoomOut
defaultDragButton :: Event.MouseButton
defaultDragButton = Event.MiddleButton
defaultEditButton :: Event.MouseButton
defaultEditButton = Event.LeftButton
scrollZoomStrength :: Double
scrollZoomStrength = 1/20
-- | Plot an (assumed continuous) function in the usual way.
-- Since this uses functions of actual 'Double' values, you have more liberty
-- of defining functions with range-pattern-matching etc., which is at the moment
-- not possible in the ':-->' category.
--
-- However, because 'Double' can't really prove properties of a mathematical
-- function, aliasing and similar problems are not taken into account. So it only works
-- accurately when the function is locally linear on pixel scales (what most
-- other plot programs just assume silently). In case of singularities, the
-- naïve thing is done (extend as far as possible; vertical line at sign change),
-- which again is common enough though not really right.
--
-- We'd like to recommend using 'fnPlot' whenever possible, which automatically adjusts
-- the resolution so the plot is guaranteed accurate (but it's not usable yet for
-- a lot of real applications).
continFnPlot :: (Double -> Double) -> DynamicPlottable
continFnPlot f = def
& relevantRange_y .~ otherDimDependence yRangef
& autoTint
& axesNecessity .~ 1
& dynamicPlot .~ pure . plot
where yRangef = onInterval $ \(l, r) -> ((!%0.1) &&& (!%0.9)) . sort . pruneOutlyers
$ map f [l, l + (r-l)/80 .. r]
plot (GraphWindowSpecR2{..}) = curve `deepseq` mkPlot (trace curve)
where δx = (rBound - lBound) * 2 / fromIntegral xResolution
curve = [ (x ^& f x) | x<-[lBound, lBound+δx .. rBound] ]
trace (p:q:ps) = (if not $ any (isNaN . (^._y)) [p, q]
then simpleLine p q else mempty
) <> trace (q:ps)
trace _ = mempty
pruneOutlyers = filter (not . isNaN)
l!%η = case length l of
ll | ll<2 -> error
"Function appears to yield NaN most of the time. Cannot be plotted."
| otherwise -> l !! floor (fromIntegral ll * η)
-- | Plot a function that assigns every point in view a colour value.
--
-- @
-- > plotWindow [colourPaintPlot $ \(x,y) -> case (x^2+y^2, atan2 y x) of (r,φ) -> guard (sin (7*φ-2*r) > r) >> Just (Dia.blend (tanh r) Dia.red Dia.green), unitAspect ]
-- @
--
-- <<images/examples/propeller.png>>
--
-- We try to evaluate that function no more often than necessary, but since it's a
-- plain function with no differentiability information there's only so much that can
-- be done; this requires a tradeoff between rasterisation fineness and performance.
-- It works well for simple, smooth functions, but may not be adequate for
-- functions with strong edges/transients, nor for expensive to compute functions.
colourPaintPlot :: ((Double,Double) -> Maybe (DCol.Colour Double)) -> DynamicPlottable
colourPaintPlot f = def & dynamicPlot .~ pure . plot
& axesNecessity .~ 0.5
where plot graSpec = mkPlot . Dia.image $ Dia.DImage
(Dia.ImageRaster $ JPix.ImageRGBA8 pixRendered)
renderWidth renderHeight
placement
where preSeekWidth = round $ fromIntegral (xResolution graSpec) / 12
preSeekHeight = round $ fromIntegral (yResolution graSpec) / 12
roughRenderWidth = fromIntegral preSeekWidth * 2 - 1
roughRenderHeight = fromIntegral preSeekHeight * 2 - 1
renderWidth, renderHeight :: Num n => n
renderWidth = fromIntegral roughRenderWidth * 2 - 1
renderHeight = fromIntegral roughRenderHeight * 2 - 1
x₀ = lBound graSpec
x₁ = rBound graSpec
y₀ = bBound graSpec
y₁ = tBound graSpec
xc = (x₀+x₁)/2
yc = (y₀+y₁)/2
wPix = (x₁ - x₀)/renderWidth
wRoughPix = (x₁+wPix - x₀)/fromIntegral roughRenderWidth
wPreSeekPix = (x₁+wRoughPix - x₀)/fromIntegral preSeekWidth
hPix = (y₁ - y₀)/renderHeight
hRoughPix = (y₁+hPix - y₀)/fromIntegral roughRenderHeight
hPreSeekPix = (y₁+hRoughPix - y₀)/fromIntegral preSeekHeight
placement
= Dia.translation (xc^&yc) <> Dia.scalingX wPix <> Dia.scalingY hPix
pixRendered = runST (do
hits <- newSTRef ([] :: [(Int,Int)])
rough² <- JPix.withImage preSeekWidth preSeekHeight
`id`\ix iy -> do
let x = x₀ + wPreSeekPix*fromIntegral ix
y = y₁ - hPreSeekPix*fromIntegral iy
case f (x,y) of
Just fxy -> do
modifySTRef hits ((ix,iy):)
pure `id` JPix.promotePixel
(CSp.quantiseColour fxy :: JPix.PixelRGB8)
Nothing ->
pure `id` JPix.PixelRGBA8 0 0 0 0
allHits <- readSTRef hits
let (intermediate, gradientHotSpots)
= refiningScaleX2Bilinear allHits
(\(ix,iy) -> case f ( x₀ + wRoughPix*fromIntegral ix
, y₁ - hRoughPix*fromIntegral iy ) of
Just fxy -> JPix.promotePixel
(CSp.quantiseColour fxy :: JPix.PixelRGB8)
Nothing -> JPix.PixelRGBA8 0 0 0 0 )
rough²
pure . fst . refiningScaleX2Bilinear gradientHotSpots
(\(ix,iy) -> case f ( x₀ + wPix*fromIntegral ix
, y₁ - hPix*fromIntegral iy ) of
Just fxy -> JPix.promotePixel
(CSp.quantiseColour fxy :: JPix.PixelRGB8)
Nothing -> JPix.PixelRGBA8 0 0 0 0 )
$ intermediate
)
type (-->) = RWDiffable ℝ
-- | Plot a continuous function in the usual way, taking arguments from the
-- x-Coordinate and results to the y one.
-- The signature looks more complicated than it is; think about it as requiring
-- a polymorphic 'Floating' function. Any simple expression like
-- @'fnPlot' (\\x -> sin x / cos (sqrt x))@ will work.
--
-- Under the hood this uses the category of region-wise differentiable functions,
-- 'RWDiffable', to prove that no details are omitted (like small high-frequency
-- bumps). Note that this can become difficult for contrived cases like @cos(1/sin x)@
-- – while such functions will never come out with aliasing artifacts, they also
-- may not come out quickly at all. (But for well-behaved functions, using the
-- differentiable category actually tends to be more effective, because the algorithm
-- immediately sees when it can describe an almost-linear region with only a few line
-- segments.)
--
-- This function is equivalent to using 'plot' on an 'RWDiffable' arrow.
fnPlot :: (∀ m . Object (RWDiffable ℝ) m
=> AgentVal (-->) m ℝ -> AgentVal (-->) m ℝ )
-> DynamicPlottable
fnPlot f = plot fd
where fd :: ℝ --> ℝ
fd = alg f
uncertainFnPlot :: ∀ m . (SimpleSpace m, Scalar m ~ ℝ)
=> (ℝ -> (m +> ℝ)) -> Shade' m -> DynamicPlottable
uncertainFnPlot = case linearManifoldWitness :: LinearManifoldWitness m of
LinearManifoldWitness
#if !MIN_VERSION_manifolds(0,6,0)
BoundarylessWitness
#endif
-> \mfun (Shade' mBest me)
-> plot $ continFnPlot (($ mBest) . mfun)
: [ tweakPrerendered (Dia.opacity 0.2)
$ continFnPlot (($ mBest^+^σ*^δm) . mfun)
| δm <- normSpanningSystem' me
, σ <- [-1,1] ]
linregressionPlot :: ∀ x m y . ( SimpleSpace m, Scalar m ~ ℝ, y ~ ℝ, x ~ ℝ )
=> (x -> (m +> y)) -> [(x, Shade' y)]
-> (Shade' m -> DynamicPlottable -> DynamicPlottable
-> DynamicPlottable)
-> DynamicPlottable
linregressionPlot = lrp (linearManifoldWitness, dualSpaceWitness)
where lrp :: (LinearManifoldWitness m, DualSpaceWitness m)
-> (x -> (m +> y)) -> [(x, Shade' y)]
-> (Shade' m -> DynamicPlottable -> DynamicPlottable
-> DynamicPlottable)
-> DynamicPlottable
lrp _ _ [] _ = mempty
lrp (LinearManifoldWitness
#if !MIN_VERSION_manifolds(0,6,0)
BoundarylessWitness
#endif
, DualSpaceWitness)
mfun dataPts resultHook = resultHook shm
(plot [ plot (Shade (x,y) (sumSubspaceNorms mempty $ dualNorm ey)
:: Shade (ℝ,ℝ))
| (x, Shade' y ey) <- dataPts ])
(uncertainFnPlot mfun shm)
where mBest = linearFit_bestModel regResult
regResult = linearRegression (mfun . (bcx.+~^))
[ (δx,(fromInterior y,ey))
| (x,Shade' y ey)<-dataPts
, let Just δx = x.-~.bcx ]
Just bcx = (pointsBarycenter . NE.fromList $ fst<$>dataPts)
shm :: Shade' m
shm = Shade' mBest $ linearFit_modelUncertainty regResult
-- | Plot a continuous, “parametric function”, i.e. mapping the real line to a path in ℝ².
paramPlot :: (∀ m . ( WithField ℝ PseudoAffine m, SimpleSpace (Needle m) )
=> AgentVal (-->) m ℝ -> (AgentVal (-->) m ℝ, AgentVal (-->) m ℝ) )
-> DynamicPlottable
paramPlot f = plot fd
where fd :: ℝ --> (ℝ,ℝ)
fd = alg1to2 f
scrutiniseDiffability :: (∀ m . ( WithField ℝ PseudoAffine m
, SimpleSpace (Needle m) )
=> AgentVal (-->) m ℝ -> AgentVal (-->) m ℝ )
-> DynamicPlottable
scrutiniseDiffability f = plot [{-plot fd, -}dframe 0.2, dframe 0.02]
where fd :: ℝ --> ℝ
fd = alg f
fscrut = analyseLocalBehaviour fd
dframe rfh = def
& autoTint
& dynamicPlot .~ pure . mkFrame
where mkFrame (GraphWindowSpecR2{..}) = case fscrut xm of
Just ((ym,y'm), δOδx²)
| Just δx <- δOδx² δy
-> δx `seq` let frame = mconcat
[ simpleLine ((xm-δx)^&(ym+yo-δx*y'm))
((xm+δx)^&(ym+yo+δx*y'm))
| yo <- [-δy, δy] ]
in mkPlot frame
| otherwise
-> y'm `seq` mkPlot
( autoDashLine 0.5 ((xm-δxdef)^&(ym-δxdef*y'm))
((xm+δxdef)^&(ym+δxdef*y'm)) )
_ -> mempty
where xm = (rBound + lBound) / 2
δxdef = (rBound - lBound) / 10
δy = rfh * (tBound - bBound)
continColourSurfaceFnPlot :: ((Double,Double) -> DCol.Colour Double) -> DynamicPlottable
continColourSurfaceFnPlot f = def
& axesNecessity .~ 1
& occlusiveness .~ 4
& dynamicPlot .~ plot
where plot (GraphWindowSpecR2{..}) = pure . mkPlot
$ Dia.place
( Dia.rasterDia cf (xResolution`div`4) (yResolution`div`4)
& Dia.scaleX wPix & Dia.scaleY hPix
) ( ((lBound+rBound-wPix)/2) ^& ((tBound+bBound+hPix)/2) )
where cf i j = f ( lBound + wPix * fromIntegral i, tBound - hPix * fromIntegral j )
`Dia.withOpacity` 0.2
w = rBound - lBound; h = tBound - bBound
wPix = w*4 / fromIntegral xResolution
hPix = h*4 / fromIntegral yResolution
data AxesStyle = DynamicAxesStyle
data DynamicAxes = DynamicAxes { yAxisClasses, xAxisClasses :: [AxisClass] }
data AxisClass = AxisClass { visibleAxes :: [Axis], axisStrength :: Double, decPrecision :: Int }
data Axis = Axis { axisPosition :: R }
crtDynamicAxes :: GraphWindowSpec -> DynamicAxes
crtDynamicAxes (GraphWindowSpecR2 {..}) = DynamicAxes yAxCls xAxCls
where [yAxCls, xAxCls] = zipWith3 directional
[lBound, bBound] [rBound, tBound] [xResolution, yResolution]
directional l u res = map lvl lvlSpecs
where span = u - l
upDecaSpan = 10**(ceil $ lg span)
pixelScale = span / (fromIntegral res * upDecaSpan)
baseDecaval = upDecaSpan * (flor $ l / upDecaSpan)
lvl (minSpc, strength)
= AxisClass [ Axis v | i<-[0 .. luDSdiv*2]
, let v=(baseDecaval + i*laSpc), v>l, v<u ]
strength
(floor $ lg laSpc)
where laSpc = upDecaSpan / luDSdiv
luDSdiv = ll . takeWhile (\d -> pixelScale * minSpc < 1/d )
. join $ iterate (map(*10)) [1, 2, 5]
ll [] = error $ "pixelScale = "++show pixelScale
++"; minSpc = "++show minSpc
ll l = last l
lvlSpecs = [ (80, 0.3), (18, 0.1) ]
-- | Coordinate axes with labels. For many plottable objects, these will be added
-- automatically, by default (unless inhibited with 'noDynamicAxes').
dynamicAxes :: DynamicPlottable
dynamicAxes = def
& axesNecessity .~ superfluent
& occlusiveness .~ 1
& dynamicPlotWithAxisLabels .~ \lbls -> pure . plot lbls
where plot poLabels gwSpec@(GraphWindowSpecR2{..}) = Plot (dirLabels++tickLabels) lines
where (DynamicAxes yAxCls xAxCls) = crtDynamicAxes gwSpec
lines = zeroLine (lBound^&0) (rBound^&0) `provided`(bBound<0 && tBound>0)
<> zeroLine (0^&bBound) (0^&tBound) `provided`(lBound<0 && rBound>0)
<> foldMap (renderClass $ \x -> (x^&bBound, x^&tBound)) yAxCls
<> foldMap (renderClass $ \y -> (lBound^&y, rBound^&y)) xAxCls
tickLabels
= do (dirq, hAlign, vAlign, acl) <- zip4 [\x -> x^&0, \y -> 0^&y ]
[AlignMid , AlignTop ]
[AlignTop , AlignMid ]
[yAxCls , xAxCls ]
let (AxisClass vaxs _ prc) = head acl
prepAnnotation (Axis{axisPosition=z}) = do
guard(z/=0)
[Annotation (TextAnnotation txt align) place False]
where txt = PlainText . prettyFloatShow prc $ realToFrac z
place = ExactPlace $ dirq z
align = TextAlignment hAlign vAlign
prepAnnotation =<< vaxs
dirLabels = [ if dir^._x > dir^._y
then Annotation (TextAnnotation txt
$ TextAlignment AlignMid AlignBottom)
(ExactPlace $ xFar^&0)
False
else Annotation (TextAnnotation txt
$ TextAlignment AlignBottom AlignMid)
(ExactPlace $ 0^&yFar)
False
| (dir,lbl) <- poLabels
, let txt = PlainText lbl
xFar = if rBound > abs lBound/2
then rBound else lBound
yFar = if tBound > abs bBound/2
then tBound else bBound
]
zeroLine p1 p2 = simpleLine' defLineWidth p1 p2 & Dia.lc Dia.grey
renderClass crd (AxisClass axes strength _)
= foldMap (uncurry (simpleLine' defLineWidth) . crd . axisPosition) axes
& Dia.lcA (Dia.grey `DCol.withOpacity` strength)
noDynamicAxes :: DynamicPlottable
noDynamicAxes = def & axesNecessity .~ superfluent
xAxisLabel :: String -> DynamicPlottable
xAxisLabel str = def & axisLabelRequests .~ [(1^&0, str)]
& axesNecessity .~ 2
yAxisLabel :: String -> DynamicPlottable
yAxisLabel str = def & axisLabelRequests .~ [(0^&1, str)]
& axesNecessity .~ 2
simpleLine :: P2 -> P2 -> PlainGraphicsR2
simpleLine p q = Dia.fromVertices [p,q]
defLineWidth :: Double
defLineWidth = 2
simpleLine' :: Double -> P2 -> P2 -> PlainGraphicsR2
simpleLine' w p q = Dia.fromVertices [p,q] & Dia.lwO w
autoDashLine :: Double -> P2 -> P2 -> PlainGraphicsR2
autoDashLine w p q = simpleLine' (max 1 w) p q
& if w < 1 then Dia.dashingO [w*6, 3] 0 else id
tweakPrerendered :: (PlainGraphicsR2->PlainGraphicsR2) -> DynamicPlottable->DynamicPlottable
tweakPrerendered f = allDynamicPlot %~ (fmap tweak .)
where tweak = getPlot %~ f
opacityFactor :: Double -> DynamicPlottable -> DynamicPlottable
opacityFactor = tweakPrerendered . Dia.opacity
-- | When you “plot” 'xInterval' / 'yInterval', it is ensured that the (initial) view encompasses
-- (at least) the specified range.
-- Note there is nothing special about these “flag” objects: /any/ 'Plottable' can request a
-- certain view, e.g. for a discrete point cloud it's obvious and a function defines at least
-- a @y@-range for a given @x@-range. Only use explicit range when necessary.
xInterval :: (Double, Double) -> DynamicPlottable
-- | Like 'xInterval', this only affects what range is plotted. However, it doesn't merely
-- request that a certain interval /should be visible/, but actually enforces particular
-- values for the left and right boundary. Nothing outside the range will be plotted
-- (unless there is another, contradicting 'forceXRange').
forceXRange :: (Double, Double) -> DynamicPlottable
yInterval, forceYRange :: (Double, Double) -> DynamicPlottable
xInterval (l,r) = mempty & relevantRange_x .~ atLeastInterval (Interval l r)
forceXRange (l,r) = mempty & relevantRange_x .~ MustBeThisRange (Interval l r)
yInterval (b,t) = mempty & relevantRange_y .~ atLeastInterval (Interval b t)
forceYRange (b,t) = mempty & relevantRange_y .~ MustBeThisRange (Interval b t)
-- $interactiveExplanation
-- 'MouseClicks', 'ViewXCenter', 'ViewYResolution' etc. can be used as arguments to some object
-- you 'plot', if you want to plot stuff that depends on user interaction
-- or just on the screen's visible range, for instance to calculate a tangent
-- at the middle of the screen:
--
-- @
-- plotWindow [fnPlot sin, plot $ \\(ViewXCenter xc) x -> sin xc + (x-xc) * cos xc]
-- @
--
-- <<images/examples/sin-ctrd-tangents.gif>>
newtype ViewXCenter = ViewXCenter { getViewXCenter :: Double }
instance (Plottable p) => Plottable (ViewXCenter -> p) where
plot f = def & relevantRange_y .~ OtherDimDependantRange
(\g -> deescalate relevantRange_y g . plot . f . cxI =<< g)
& inherentColours .~ fcxVoid^.inherentColours
& axesNecessity .~ fcxVoid^.axesNecessity
& dynamicPlotWithAxisLabels .~
\lbls g -> _dynamicPlotWithAxisLabels (plot . f $ cx g) lbls g
where cx (GraphWindowSpecR2{..}) = ViewXCenter $ (lBound+rBound)/2
cxI (Interval l r) = ViewXCenter $ (l+r)/2
fcxVoid = plot . f $ ViewXCenter 0.23421 -- Yup, it's magic.
deescalate rfind otherdim p = case p^.rfind of
MustBeThisRange i -> pure i
OtherDimDependantRange ifr -> ifr otherdim
newtype ViewYCenter = ViewYCenter { getViewYCenter :: Double }
instance (Plottable p) => Plottable (ViewYCenter -> p) where
plot f = def & relevantRange_x .~ OtherDimDependantRange
(\g -> deescalate relevantRange_x g . plot . f . cyI =<< g)
& inherentColours .~ fcyVoid^.inherentColours
& axesNecessity .~ fcyVoid^.axesNecessity
& dynamicPlotWithAxisLabels .~
\lbls g -> _dynamicPlotWithAxisLabels (plot . f $ cy g) lbls g
where cy (GraphWindowSpecR2{..}) = ViewYCenter $ (bBound+tBound)/2
cyI (Interval b t) = ViewYCenter $ (b+t)/2
fcyVoid = plot . f $ ViewYCenter 0.319421 -- Alright, alright... the idea is to avoid exact equality with zero or any other number that might come up in some plot object, since such an equality can lead to div-by-zero problems.
deescalate rfind otherdim p = case p^.rfind of
MustBeThisRange i -> pure i
OtherDimDependantRange ifr -> ifr otherdim
newtype ViewWidth = ViewWidth { getViewWidth :: Double }
instance (Plottable p) => Plottable (ViewWidth -> p) where
plot f = def & relevantRange_y .~ OtherDimDependantRange
(\g -> deescalate relevantRange_y g . plot . f . wI =<< g)
& inherentColours .~ fwVoid^.inherentColours
& axesNecessity .~ fwVoid^.axesNecessity
& dynamicPlotWithAxisLabels .~
\lbls g -> _dynamicPlotWithAxisLabels (plot . f $ w g) lbls g
where w (GraphWindowSpecR2{..}) = ViewWidth $ rBound - lBound
wI (Interval l r) = ViewWidth $ r - l
fwVoid = plot . f $ ViewWidth 2.142349
deescalate rfind otherdim p = case p^.rfind of
MustBeThisRange i -> pure i
OtherDimDependantRange ifr -> ifr otherdim
newtype ViewHeight = ViewHeight { getViewHeight :: Double }
instance (Plottable p) => Plottable (ViewHeight -> p) where
plot f = def & relevantRange_x .~ OtherDimDependantRange
(\g -> deescalate relevantRange_x g . plot . f . hI =<< g)
& inherentColours .~ fhVoid^.inherentColours
& axesNecessity .~ fhVoid^.axesNecessity
& dynamicPlotWithAxisLabels .~
\lbls g -> _dynamicPlotWithAxisLabels (plot . f $ h g) lbls g
where h (GraphWindowSpecR2{..}) = ViewHeight $ tBound - bBound
hI (Interval b t) = ViewHeight $ t - b
fhVoid = plot . f $ ViewHeight 1.494213
deescalate rfind otherdim p = case p^.rfind of
MustBeThisRange i -> pure i
OtherDimDependantRange ifr -> ifr otherdim
newtype ViewXResolution = ViewXResolution { getViewXResolution :: Int }
newtype ViewYResolution = ViewYResolution { getViewYResolution :: Int }
newtype MouseClicks = MouseClicks {
getClickPositions :: [(ℝ,ℝ)] -- ^ A history of all clicks that were done
-- in this window; more specifically, of all
-- /left mouse-button release events/ recorded.
}
instance (Plottable p) => Plottable (MouseClicks -> p) where
plot f = go []
where go oldClicks = addInterrupt . plot . f $ MouseClicks oldClicks
where addInterrupt :: DynamicPlottable -> DynamicPlottable
addInterrupt pl = pl
& futurePlots %~ \anim -> \case
interac@(Interactions [] _) -> fmap addInterrupt $ anim interac
Interactions newClicks _ -> pure . go
$ (_releaseLocation<$>newClicks) ++ oldClicks
newtype MousePress = MousePress {
lastMousePressedLocation :: (ℝ,ℝ)
}
instance (Plottable p) => Plottable (MousePress -> p) where
plot f = go Nothing
where go :: Maybe (ℝ,ℝ) -> DynamicPlottable
go Nothing = mempty & futurePlots .~ pure . \case
Interactions [] Nothing -> go Nothing
Interactions (click:_) Nothing -> go . Just $ click^.releaseLocation
Interactions _ (Just current) -> go . Just $ current^.releaseLocation
go (Just lastPressed) = addInterrupt . plot . f $ MousePress lastPressed
where addInterrupt :: DynamicPlottable -> DynamicPlottable
addInterrupt pl = pl
& futurePlots %~ \anim -> \case
Interactions [] Nothing -> fmap addInterrupt $ anim mempty
Interactions (click:_) Nothing
-> pure . go . Just $ click^.releaseLocation
Interactions _ (Just drag)
-> pure . go . Just $ drag^.releaseLocation
newtype MousePressed = MousePressed {
mouseIsPressedAt :: Maybe (ℝ,ℝ)
}
instance (Plottable p) => Plottable (MousePressed -> p) where
plot f = go Nothing
where go :: Maybe (ℝ,ℝ) -> DynamicPlottable
go lastInt = addInterrupt . plot . f $ MousePressed lastInt
where addInterrupt :: DynamicPlottable -> DynamicPlottable
addInterrupt pl = pl
& futurePlots %~ \anim -> \case
Interactions _ Nothing
| isNothing lastInt -> fmap addInterrupt $ anim mempty
| otherwise -> return $ go Nothing
Interactions _ (Just drag)
-> pure . go . Just $ drag^.releaseLocation
-- | Move through a sequence of plottable objects, switching to the next
-- whenever a click is received anywhere on the screen. Similar to 'plotLatest',
-- but does not proceed automatically.
clickThrough :: Plottable p => [p] -> DynamicPlottable
clickThrough [] = mempty
clickThrough [final] = plot final
clickThrough (v:vs) = addInterrupt $ plot v
where addInterrupt :: DynamicPlottable -> DynamicPlottable
addInterrupt pl = pl & futurePlots %~ \anim -> \case
interac@(Interactions [] _) -> fmap addInterrupt $ anim interac
Interactions (_:_) _ -> Just $ clickThrough vs
mouseInteractive :: Plottable p
=> (MouseEvent (ℝ,ℝ) -> s -> s)
-> s
-> (s -> p)
-> DynamicPlottable
mouseInteractive upd initl f = go initl
where go s = addInterrupt . plot $ f s
where addInterrupt :: DynamicPlottable -> DynamicPlottable
addInterrupt pl = pl
& futurePlots %~ \anim -> \case
Interactions _ Nothing
-> fmap addInterrupt $ anim mempty
Interactions _ (Just drag)
-> pure . go $ upd drag s
indexedT :: Hask.Traversable t => t a -> t (Int,a)
indexedT v = (`evalState`0) . Hask.forM v $ \x -> do
i <- get
put $ i+1
return (i,x)
updateAt :: Hask.Traversable t => Int -> (a->a) -> t a -> t a
updateAt iM f v = (`evalState`0) . Hask.forM v $ \x -> do
i <- get
put $ i+1
return $ if i==iM then f x
else x
-- | Plot something dependent on points that the user can interactively move around.
-- The nearest point (Euclidean distance) is always picked to be dragged.
withDraggablePoints :: ∀ p list . (Plottable p, Traversable list)
=> list (ℝ,ℝ) -> (list (ℝ,ℝ) -> p) -> DynamicPlottable
withDraggablePoints pts₀ f = go pts₀
where go :: list (ℝ,ℝ) -> DynamicPlottable
go pts = addInterrupt . plot $ f pts
where addInterrupt :: DynamicPlottable -> DynamicPlottable
addInterrupt pl = pl
& futurePlots %~ \anim -> \case
Interactions _ Nothing -> return $ go pts
Interactions _ (Just drag)
-> let p = drag^.releaseLocation
grabbed = fst . minimumBy
(comparing $ magnitude . (^-^p) . snd)
$ indexedT pts
in return . go $ updateAt grabbed (const p) pts
atExtendOf :: PlainGraphicsR2 -> PlainGraphicsR2 -> PlainGraphicsR2
atExtendOf d₁ = atExtendOf' d₁ 1
atExtendOf' :: PlainGraphicsR2 -> Double -> PlainGraphicsR2 -> PlainGraphicsR2
atExtendOf' d₁ q d₂ = d₂
& Dia.translate ((pux+plx-lux-llx)/2 ^& (puy+ply-luy-lly)/2)
& Dia.scaleX (q*(pux-plx)/(lux-llx))
& Dia.scaleY (q*(puy-ply)/(luy-lly))
where (Just (plx,pux)) = Dia.extentX d₁; (Just (ply,puy)) = Dia.extentY d₁
(Just (llx,lux)) = Dia.extentX d₂; (Just (lly,luy)) = Dia.extentY d₂
waitTill :: UTCTime -> IO ()
waitTill t = do
tnow <- getCurrentTime
threadDelay . max 1000 . round $ diffUTCTime t tnow
* 1e+6 -- threadDelay ticks in microseconds
-- | Limit the refresh / frame rate for this plot object. Useful to slowly
-- study some sequence of plots with 'plotLatest', or to just reduce processor load.
--
-- Note: the argument will probably change to
-- <http://hackage.haskell.org/package/thyme-0.3.5.5/docs/Data-Thyme-Clock.html#t:NominalDiffTime NominalDiffTime> from the <http://hackage.haskell.org/package/thyme thyme>
-- library soon.
plotDelay :: NominalDiffTime -> DynamicPlottable -> DynamicPlottable
plotDelay dly = sustained frameDelay .~ dly
-- | Disable an animation, i.e. take an animated plot and show only the first frame.
freezeAnim :: DynamicPlottable -> DynamicPlottable
freezeAnim = futurePlots .~ const Nothing
-- | Wait with starting the animation until the user has clicked on it.
startFrozen :: DynamicPlottable -> DynamicPlottable
startFrozen = futurePlots %~ \f inta -> if inta==mempty
then Nothing
else f inta