Hi all,

Take a look at this disaster area, or just scroll down to where I come to the point...

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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?

TIA,

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?