Take a look at this disaster area, or just scroll down to where I come to the point...
type SankeyBrain = (P2,CircleFrac,Double) -- like a turtle plus width
data SankeyWorld tb = SankeyWorld ((Trail R2,Trail R2),tb) --outgoing and returning trails, plus brain
emptySankey :: SankeyWorld SankeyBrain
emptySankey = SankeyWorld ((mempty,mempty),(origin,0,0))
sankeyFrom:: CircleFrac -> Double -> SankeyWorld SankeyBrain
sankeyFrom a w = SankeyWorld ((mempty,mempty),(p2 (0,0),a,w)) -- kick off with an angle and width
instance Monad SankeyWorld where
return a = SankeyWorld ((mempty,mempty), a) --never use this
(SankeyWorld l) >>= f = let (SankeyWorld r) = f (snd l) in -- out = left then right, return = right then left
SankeyWorld ( (((fst.fst) l <> (fst.fst) r),((snd.fst) r <> (snd.fst) l)),(snd r) )
sankeyVia :: Double -> SankeyBrain -> SankeyWorld SankeyBrain
sankeyVia d (p,a,w) =
let -- draw parallel lines and move them into place
l1 = hrule 1 # scaleX d # translateX (d/2) # translateY (w/2) # rotate a # translate (origin .-. p)
l2 = hrule 1 # scaleX (-d) # translateX (d/2) # translateY (-w/2) # rotate a # translate (origin .-. p)
in SankeyWorld ( ( l1 , l2 ) , ( p .+^ (unitX # scale d # rotate a), a, w) )
sankeyTo :: SankeyBrain -> SankeyWorld SankeyBrain
sankeyTo (p,a,w) = SankeyWorld ( --arrow at the end of the flow
( hrule w # translateX (w/2) # translateY (w/2) # rotate (-1/8::CircleFrac) # scale (0.7071) # rotate a # translate (origin .-. p)
, hrule (-w) # translateX (w/2) # translateY (-w/2) # rotate (1/8::CircleFrac) # scale (0.7071) # rotate a # translate (origin .-. p)
), (p,a,w))
sankeyTurn r a' (p,a,w) = let (outr, inr, qu) = if a'>=0 then (r, -w-r, -0.25::CircleFrac) else (-w-r, r, 0.25::CircleFrac) in
SankeyWorld ( -- turn a corner with nice round edges
( arc' outr (a+qu) (a+a'+qu) # translate (unitY # rotate (a+a' )# scale w)
, arc' inr (a+a'+qu) (a+qu) # translate (unitY # rotate (a+a' )# scale w)
),(p,a+a',w))
-- bump...
sankeySplit :: [(Double, SankeyBrain -> SankeyWorld SankeyBrain)] -> SankeyBrain -> SankeyWorld SankeyBrain
sankeySplit fs (p,a,w) = let (placed,_) = ( foldl ( \(l,t) -> \(i,c) -> ( l++[( ( p .+^ (unitY # rotate a # scale (((t+i/2)-0.5)*w)), a, w*i) ,c )],t+i) ) ([],0) fs ) in
foldl (\(SankeyWorld ((lo,lr),lb)) -> \(SankeyWorld ((ro,rr),rb)) -> SankeyWorld ( ( lo <> ro , rr <> lr ), rb ) ) emptySankey $ map (\(b,f)-> f b) placed
SankeyWorld ((turtb,turta),_) =
{- This is the bit that fails:
sankeyFrom 0 5 >>= sankeyVia 5 >>=
sankeySplit
[ (0.3, sankeyVia 10 )
, (0.7, sankeyVia 15 )
]
-}
sankeyFrom 0 5 >>= sankeyVia 5 >>= sankeyTurn 1 (-0.125) >>= sankeyVia 10 >>= sankeyTurn 1 (0.25) >>= sankeyTo -- >>= turn 0.25 >>= forward 10 >>= turn 0.25 >>= forward 20 >>= turn 0.25 >>= forward 10
pic3 = (strokeT (close ( turtb<>turta) )) # fc red
======================
The idea is that SankeyWorld is a monad containing two trails (outbound and inbound) and a turtle-like state. I bind it onto functions like SankeyBrain -> SankeyWorld, whereby >>= passes the state across. >>= draws the left hand outward trail, then the right hand outward trail, then the right hand inward trail, then the left hand inward trail, so it all makes a nice polygon and I can colour it in.
sankeyFrom angle width is already a monad, sankeyVia length is such a function and I could have sankeyTo contain () in place of the brain (i.e. state) cos you're not supposed to continue from it.
The tricky bit is splitting the flow. I want a function that takes the brain, splits the width according to named shares and shoves each share into a function SankeyBrain -> SankeyWorld that might have lots more stages and splits downwind.
It was all going fine until I discovered that if I can say m >>= f, then I can't say f >>= f. So I don't know how to write the bits after the split. Silly me. But what should I do instead to model Sankey diagrams splitting? Is MonadPlus the trick? If so, am I gonna have to make [SankeyWorld] a monad as well?
Adrian.
PS: I rarely have any use for the polymorphism of the parameter to Monad. In this case, it's a SankeyBrain, end of story. Is there a simpler kind of monad that doesn't throw this complication at me?