dynamic-plot-0.1.4.0: Graphics/Dynamic/Plot/R2.hs
-- |
-- Module : Graphics.Dynamic.Plot.R2
-- Copyright : (c) Justus Sagemüller 2013-2015
-- License : GPL v3
--
-- Maintainer : (@) sagemueller $ geo.uni-koeln.de
-- 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 #-}
module Graphics.Dynamic.Plot.R2 (
-- * Interactive display
plotWindow
-- * Plottable objects
-- ** Class
, Plottable(..)
-- ** Simple function plots
, fnPlot, paramPlot
, continFnPlot
, tracePlot
, lineSegPlot
, PlainGraphicsR2
, shapePlot
, diagramPlot
-- ** Legend captions
, legendName
-- ** View selection
, xInterval, yInterval, forceXRange, forceYRange
-- ** View dependance
, ViewXCenter(..), ViewYCenter(..), ViewWidth(..), ViewHeight(..)
, ViewXResolution(..), ViewYResolution(..)
-- ** Auxiliary plot objects
, dynamicAxes, noDynamicAxes
-- ** Plot type
, DynamicPlottable
-- ** Legacy
, PlainGraphics(..)
) 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.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 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)
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.Concurrent.Async
import Control.DeepSeq
import Data.List (foldl', sort, sortBy, partition, zip4)
import qualified Data.List.NonEmpty as NE
import qualified Data.Vector as Arr
import Data.Maybe
import Data.Semigroup
import Data.Default
import Data.Foldable (fold, foldMap)
import qualified Data.Foldable as Hask
import Data.Function (on)
import Data.Ord (comparing)
import Data.VectorSpace
import Data.Basis
import Data.AffineSpace
import Data.LinearMap.HerMetric
import Data.Manifold.PseudoAffine
import Data.Function.Differentiable
import Data.Manifold.Types
import Data.Manifold.TreeCover
import Data.Manifold.Web
import qualified Data.Map.Lazy as Map
import Data.Tagged
import Text.Printf
import Data.IORef
import System.IO
import System.Exit
import System.Process
import Data.Time
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 PlainGraphics where
plot (PlainGraphics d) = def {
relevantRange_x = atLeastInterval rlx
, relevantRange_y = atLeastInterval rly
, axesNecessity = -1
, dynamicPlot = plot
}
where bb = DiaBB.boundingBox d
(rlx,rly) = case DiaBB.getCorners bb of
Just (c1, c2)
-> ( c1^._x ... c2^._x
, c1^._y ... c2^._y )
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) { isTintableMonochromic = True, axesNecessity = 0 }
-- | Plot a generic 'Dia.Diagram'.
diagramPlot :: PlainGraphicsR2 -> DynamicPlottable
diagramPlot d = plot $ PlainGraphics d
instance Plottable (R-->R) where
plot f = def { relevantRange_y = OtherDimDependantRange yRangef
, isTintableMonochromic = True
, axesNecessity = 1
, dynamicPlot = plot }
where yRangef (Option Nothing) = Option Nothing
yRangef (Option (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
([],[]) -> Option 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
1000
( const . metricFromLength
$ (rBound-lBound)/fromIntegral xResolution
, 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
, isTintableMonochromic = True
, axesNecessity = 1
, dynamicPlot = 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
, 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 = projector (recip δx, 0) ^+^ projector (0, recip δy)
δx = w / fromIntegral xResolution
δy = h / fromIntegral yResolution
resoFunc (x,y)
| x >= lBound, x <= rBound, y >= bBound, y <= tBound = ε
| otherwise = projector (recip qx,0) ^+^ projector (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
, isTintableMonochromic = True
, axesNecessity = 1
, dynamicPlot = plot
}
where
xr = wsp * fromIntegral gSplN
plot (GraphWindowSpecR2{..}) = 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 (`metric'`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
, isTintableMonochromic = True
, axesNecessity = 1
, dynamicPlot = plot
}
where plot (GraphWindowSpecR2{..}) = 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 = metriScale' σ $ turnLeft v
trStRange (Right pts) = (`foldMap`pts)
$ \(p, DevBoxes dv _)
-> let δxm = metric' dv $ 1^&0
δym = metric' 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 zeroV 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 { isTintableMonochromic = True }
| otherwise = def {
relevantRange_x = atLeastInterval' $ foldMap (pure . spInterval . fst) (concat ps)
, relevantRange_y = atLeastInterval' $ foldMap (pure . spInterval . snd) (concat ps)
, isTintableMonochromic = True
, axesNecessity = 1
, dynamicPlot = 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 -> [DualSpace 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
| metrics' dev δs > 0.5 || (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
, isTintableMonochromic = True
, axesNecessity = 1
, dynamicPlot = plot
}
where plot _ = mkPlot $ foldMap axLine eigVs
where axLine eigV = simpleLine (ctr .-~^ eigV) (ctr .+~^ eigV)
(xRange,yRange) = shadeExtends shade
ctr = shade^.shadeCtr
eigVs = eigenSpan $ shade^.shadeExpanse
instance Plottable (Shade (R,R)) where
plot sh = plot (coerceShade sh :: Shade P2)
instance Plottable (Shade' (R,R)) where
plot shade = def {
isTintableMonochromic = True
, axesNecessity = 1
, dynamicPlot = plot
}
where plot _ = mkPlot $ Dia.circle 1
& Dia.scaleX w₁ & Dia.scaleY w₂
& Dia.rotate ϑ
& Dia.opacity 0.2
& Dia.moveTo ctr
ctr = Dia.p2 $ shade^.shadeCtr
[ev₁@(e₁x,e₁y),ev₂] = eigenSpan' $ shade^.shadeNarrowness
ϑ = atan2 e₁y e₁x Dia.@@ Dia.rad
w₁ = recip $ magnitude ev₁; w₂ = recip $ magnitude ev₂
instance Plottable (ConvexSet (R,R)) where
plot EmptyConvex = mempty
plot (ConvexSet hull intersects)
= plot [ plot intersects
& tweakDiagram (Dia.opacity
(1 / fromIntegral (length intersects)) )
, plot hull
& tweakDiagram ( Dia.lwO 3
>>> Dia.opacity 1
>>> Dia.fcA (Dia.withOpacity Dia.grey 0.01) ) ]
instance Plottable (Shade' P2) where
plot sh = plot (coerceShade sh :: Shade' (R,R))
instance Plottable (Shaded ℝ ℝ) where
plot tr | length trivs' >= 2
= def { relevantRange_x = atLeastInterval $ Interval xmin xmax
, relevantRange_y = atLeastInterval $ Interval ymin ymax
, isTintableMonochromic = True
, axesNecessity = 1
, dynamicPlot = plot
}
where plot grWS@(GraphWindowSpecR2{..}) = 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]<*>[_topological<$>allLeaves, _untopological<$>allLeaves]
lLoop ps@(p:_) = Dia.fromVertices $ ps++[p]
leafPoints = sortBy (comparing (^._x))
$ (\(x`WithAny`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
, isTintableMonochromic = True
, axesNecessity = 1
, dynamicPlot = 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 ((xc,Shade' yc yce), [(δxo, Shade' yo _)])
= case tryMetricAsLength yce of
Option (Just ry) ->
( [ ( (xc, dirSort 0 δxo)
, ( (yc, ry)
, denseLinear $ \δx -> δx * (yo-yc)/δxo ) ) ], [] )
Option Nothing ->
( [], [(xc, dirSort 0 δxo)] )
mkTriv ((xc,Shade' yc yce), [(δxl, Shade' yl _), (δxr, Shade' yr _)])
= case tryMetricAsLength yce of
Option (Just ry) ->
( [ ( (xc, dirSort δxl δxr)
, ( (yc, ry)
, denseLinear $ \δx -> δx * η ) ) ], [] )
Option 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 (SimpleTree P2) where
plot (GenericTree Nothing) = plot ([] :: [SimpleTree P2])
plot (GenericTree (Just (ctr, root)))
= def{
relevantRange_x = atLeastInterval xRange
, relevantRange_y = atLeastInterval yRange
, isTintableMonochromic = True
, axesNecessity = 1
, dynamicPlot = plot
}
where plot _ = 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 (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
type GraphWindowSpec = GraphWindowSpecR2
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
data Plot = Plot {
plotAnnotations :: [Annotation]
, getPlot :: PlainGraphicsR2
}
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
data DynamicPlottable = DynamicPlottable {
relevantRange_x, relevantRange_y :: RangeRequest R
, isTintableMonochromic :: Bool
, 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
, legendEntries :: [LegendEntry]
, dynamicPlot :: GraphWindowSpec -> Plot
}
instance Semigroup DynamicPlottable where
DynamicPlottable rx₁ ry₁ tm₁ oc₁ ax₁ le₁ dp₁
<> DynamicPlottable rx₂ ry₂ tm₂ oc₂ ax₂ le₂ dp₂
= DynamicPlottable
(rx₁<>rx₂) (ry₁<>ry₂) (tm₁||tm₂) (oc₁+oc₂) (ax₁+ax₂) (le₁++le₂) (dp₁<>dp₂)
instance Monoid DynamicPlottable where
mempty = DynamicPlottable mempty mempty False 0 0 [] mempty
mappend = (<>)
instance Default DynamicPlottable where def = mempty
data GraphViewState = GraphViewState {
lastStableView :: Maybe (GraphWindowSpec, Plot)
, realtimeView, nextTgtView :: Async Plot
, graphColor :: Maybe AColour
}
legendName :: String -> DynamicPlottable -> DynamicPlottable
legendName n d = d { legendEntries = LegendEntry (PlainText n) mempty : legendEntries d }
data RangeRequest r
= OtherDimDependantRange (Option (Interval r) -> Option (Interval r))
| MustBeThisRange (Interval r)
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 mempty
mappend = (<>)
otherDimDependence :: (Interval r->Interval r) -> RangeRequest r
otherDimDependence = OtherDimDependantRange . fmap
atLeastInterval :: Interval r -> RangeRequest r
atLeastInterval = atLeastInterval' . pure
atLeastInterval' :: Option (Interval r) -> RangeRequest r
atLeastInterval' = OtherDimDependantRange . const
-- | 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:
--
-- @
-- plotWindow [ fnPlot cos
-- , tracePlot [(x,y) | x<-[-1,-0.96..1]
-- , y<-[0,0.01..1]
-- , abs (x^2 + y^2 - 1) < 0.01 ]]
-- @
--
-- This gives such a plot window:
--
-- <<images/examples/cos-encircle-points.png>>
--
-- And that can with the mouse wheel be zoomed/browsed, like
--
-- <<images/examples/cos-encircle-points.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,
-- in particular, 'fnPlot' makes heavy use of <http://hackage.haskell.org/package/hmatrix hmatrix>
-- and thus <http://www.gnu.org/software/gsl/ GSL>.
-- 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 [dynamicAxes]
plotWindow graphs' = do
dgStore <- newIORef $ mempty
let defColourScheme = defaultColourScheme
([viewTgt, viewState], graphs) <- do
let window₀ = autoDefaultView graphs'
assignGrViews :: [DynamicPlottable] -> [Colour] -> Double
-> IO [(DynamicPlottable, GraphViewState)]
assignGrViews (g@DynamicPlottable{..}:gs) (c:cs) axn = do
v <- async $ return $! dynamicPlot window₀
fmap ((g, GraphViewState { lastStableView = Nothing
, realtimeView = v, nextTgtView = v
, graphColor = cl }
) : ) $ assignGrViews gs cs' (axn + axesNecessity)
where (cl, cs')
| isTintableMonochromic = (Just $ defColourScheme c, cs)
| otherwise = (Nothing, c:cs)
assignGrViews [] _ axesNeed
| axesNeed > 0 = assignGrViews [dynamicAxes] [grey] (-1)
| otherwise = return []
graphs'' = sortBy (comparing occlusiveness) graphs'
w <- mapM newIORef $ replicate 2 window₀
gs <- newIORef =<< assignGrViews graphs'' defaultColourSeq 0
return (w,gs)
GTK.initGUI
window <- GTK.windowNew
mouseAnchor <- newIORef Nothing
refreshDraw <- do
drawA <- GTK.drawingAreaNew
GTK.onExpose drawA $ \_ -> do
(canvasX,canvasY) <- GTK.widgetGetSize drawA
modifyIORef viewTgt $ \view -> view{ xResolution = fromIntegral canvasX
, yResolution = fromIntegral canvasY }
dia <- readIORef dgStore
let oldSize = Dia.size dia
scaledDia = Dia.bg Dia.black
. Dia.scaleX (fromInt canvasX / 2)
. Dia.scaleY (-fromInt canvasY / 2)
. Dia.translate (1 ^& (-1))
. Dia.withEnvelope (Dia.rect 2 2 :: PlainGraphicsR2)
$ 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.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 -> 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 := defResX
, GTK.windowDefaultHeight := defResY
, GTK.containerChild := drawA
]
GTK.widgetShowAll window
return $ GTK.widgetQueueDraw drawA
let updateRTView, updateTgtView :: (GraphWindowSpec -> GraphWindowSpec) -> IO ()
updateRTView updRealView = do
vstOld <- readIORef viewState
let newRealView = updRealView vstOld
grViewsOld <- readIORef graphs
writeIORef graphs <=< forM grViewsOld $
\(o@DynamicPlottable{..}, gv) -> do
newRt <- async $ return $! dynamicPlot newRealView
poll (realtimeView gv) >>= \case
Just(Right vw) -> return (o
, gv{ realtimeView = newRt, lastStableView = Just (vstOld, vw) })
_ -> do
cancel $ realtimeView gv
poll (nextTgtView gv) >>= \case
Just(Right vw) -> do
ttvn <- readIORef viewTgt
return (o, gv{ realtimeView = newRt, lastStableView = Just (ttvn, vw) })
_ -> return (o, gv{ realtimeView = newRt })
writeIORef viewState newRealView
updateTgtView updTgtView = do
newTgtView <- updTgtView <$> readIORef viewTgt
grViewsOld <- readIORef graphs
writeIORef graphs <=< forM grViewsOld $
\(o@DynamicPlottable{..}, gv) -> do
newTt <- async $ return $! dynamicPlot newTgtView
cancel $ nextTgtView gv
return (o, gv{ nextTgtView = newTt })
writeIORef viewTgt newTgtView
t₀ <- getCurrentTime
lastFrameTime <- newIORef t₀
let refreshScreen = do
currentView@(GraphWindowSpecR2{..}) <- readIORef viewState
let normaliseView :: PlainGraphicsR2 -> PlainGraphicsR2
normaliseView = (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
textTK txSiz asp = TextTK defaultTxtStyle txSiz asp 0.2 0.2
renderComp (DynamicPlottable{..}, GraphViewState{..}) = do
plt <- poll realtimeView >>= \case
Just (Right pl) -> return $ Just pl
_ -> case lastStableView of
Just (_, vw) -> return $ Just vw
_ -> poll nextTgtView >> return Nothing
case plt of
Nothing -> return mempty
Just Plot{..} -> let
antTK = DiagramTK { viewScope = currentView
, textTools = textTK txtSize aspect }
txtSize = h * fontPts / fromIntegral yResolution
aspect = w * fromIntegral yResolution
/ (h * fromIntegral xResolution)
fontPts = 12
transform :: PlainGraphicsR2 -> PlainGraphicsR2
transform = normaliseView . clr
where clr | Just c <- graphColor = Dia.lcA c . Dia.fcA c
| otherwise = id
in do
renderedAnnot <- mapM (prerenderAnnotation antTK) plotAnnotations
return . transform $ fold renderedAnnot <> getPlot
gvStates <- readIORef graphs
waitAny $ map (realtimeView . snd) gvStates
thePlot <- (mconcat . reverse) <$> mapM renderComp (reverse gvStates)
theLegend <- prerenderLegend (textTK 10 1) colourScheme
$ (\(p,g) -> (,) <$> legendEntries p <*> [graphColor g]) =<< gvStates
writeIORef dgStore $ ( theLegend & Dia.scaleX (0.1 / sqrt (fromIntegral xResolution))
& Dia.scaleY (0.1 / sqrt (fromIntegral yResolution))
& (`Dia.place`(0.75^&0.75)) )
<> thePlot
refreshDraw
let mainLoop = do
t <- getCurrentTime
δt <- fmap (diffUTCTime t) $ readIORef lastFrameTime
writeIORef lastFrameTime t
do vt <- readIORef viewTgt
updateRTView $ \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
(readIORef graphs >>=) . mapM_ -- cancel remaining threads
$ \(_, GraphViewState{..}) -> cancel realtimeView >> cancel nextTgtView
GTK.mainQuit
GTK.timeoutAdd mainLoop 100
GTK.mainGUI
readIORef viewState
autoDefaultView :: [DynamicPlottable] -> GraphWindowSpec
autoDefaultView graphs = GraphWindowSpecR2 l r b t defResX defResY defaultColourScheme
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 mempty
defRng (Option (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) / 6
defResX, defResY :: Integral i => i
defResX = 640
defResY = 480
data ScrollAction = ScrollZoomIn | ScrollZoomOut
defaultScrollBehaviour :: Event.ScrollDirection -> ScrollAction
defaultScrollBehaviour Event.ScrollUp = ScrollZoomIn
defaultScrollBehaviour Event.ScrollDown = ScrollZoomOut
defaultDragButton :: Event.MouseButton
defaultDragButton = Event.MiddleButton
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
, isTintableMonochromic = True
, axesNecessity = 1
, dynamicPlot = 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) = simpleLine p q <> 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)
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 . ( WithField ℝ PseudoAffine m
, HasMetric (Needle (Interior m)) )
=> AgentVal (-->) m ℝ -> AgentVal (-->) m ℝ )
-> DynamicPlottable
fnPlot f = plot fd
where fd :: ℝ --> ℝ
fd = alg f
-- | Plot a continuous, “parametric function”, i.e. mapping the real line to a path in ℝ².
paramPlot :: (∀ m . ( WithField ℝ PseudoAffine m
, HasMetric (Needle (Interior 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
, HasMetric (Needle (Interior 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{
isTintableMonochromic = True
, dynamicPlot = mkFrame
}
where mkFrame (GraphWindowSpecR2{..}) = case fscrut xm of
Option (Just ((ym,y'm), δOδx²))
| Option (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{..}) = 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
, dynamicPlot = plot }
where plot gwSpec@(GraphWindowSpecR2{..}) = Plot labels 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
labels = 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
zeroLine p1 p2 = simpleLine p1 p2 & Dia.lc Dia.grey
renderClass crd (AxisClass axes strength _)
= foldMap (uncurry simpleLine . crd . axisPosition) axes
& Dia.lcA (Dia.grey `DCol.withOpacity` strength)
noDynamicAxes :: DynamicPlottable
noDynamicAxes = def { axesNecessity = superfluent }
simpleLine :: P2 -> P2 -> PlainGraphicsR2
simpleLine = simpleLine' 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
tweakDiagram :: (PlainGraphicsR2->PlainGraphicsR2) -> DynamicPlottable->DynamicPlottable
tweakDiagram f fig = fig { dynamicPlot = tweak . dynamicPlot fig }
where tweak pl = pl { getPlot = f $ getPlot pl }
opacityFactor :: Double -> DynamicPlottable -> DynamicPlottable
opacityFactor = tweakDiagram . 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 }
-- | 'ViewXCenter', 'ViewYResolution' etc. can be used as arguments to some object
-- you 'plot', if its rendering is to depend explicitly on the screen's visible range.
-- You should not need to do that manually except for special applications (the
-- standard plot objects like 'fnPlot' already take the range into account anyway)
-- – e.g. comparing with the linear regression /of all visible points/
-- from some sample with some function's tangent /at the screen center/.
--
-- @
-- 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
, isTintableMonochromic = isTintableMonochromic fcxVoid
, axesNecessity = axesNecessity fcxVoid
, dynamicPlot = \g -> dynamicPlot (plot . f $ cx g) 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 rfind p 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
, isTintableMonochromic = isTintableMonochromic fcyVoid
, axesNecessity = axesNecessity fcyVoid
, dynamicPlot = \g -> dynamicPlot (plot . f $ cy g) 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 rfind p 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
, isTintableMonochromic = isTintableMonochromic fwVoid
, axesNecessity = axesNecessity fwVoid
, dynamicPlot = \g -> dynamicPlot (plot . f $ w g) 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 rfind p 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
, isTintableMonochromic = isTintableMonochromic fhVoid
, axesNecessity = axesNecessity fhVoid
, dynamicPlot = \g -> dynamicPlot (plot . f $ h g) 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 rfind p of
MustBeThisRange i -> pure i
OtherDimDependantRange ifr -> ifr otherdim
newtype ViewXResolution = ViewXResolution { getViewXResolution :: Int }
newtype ViewYResolution = ViewYResolution { getViewYResolution :: Int }
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