```{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE ScopedTypeVariables        #-}
{-# OPTIONS -Wall #-}

--------------------------------------------------------------------------------
-- |
-- Module      :  Wumpus.Tree.Design
-- Copyright   :  (c) Stephen Tetley 2010-2011
--
-- Maintainer  :  Stephen Tetley <stephen.tetley@gmail.com>
-- Stability   :  highly unstable
-- Portability :  GHC
--
-- A variant of the tree drawing algorithm from
-- Andrew Kennedy - Functional Pearls Drawing Trees 1996.
--
-- Acknowledgment - although based on Andrew Kennedy\'s algorithm,
-- this version uses absolute extents rather than relative ones
-- and is a somewhat different in detail if not in spirit to the
-- original.
--
-- Any mistakes are mine of course.
--
--------------------------------------------------------------------------------

module Wumpus.Tree.Design
(

-- * Design a tree
UW
, CoordTree
, design

-- * Post transform a tree design
, scaleTree
, orientateTree

)
where

import Wumpus.Tree.Base

import Wumpus.Basic.Kernel              -- package: wumpus-basic

import Wumpus.Core                      -- package: wumpus-core

import Data.List
import Data.Maybe
import Data.Tree

-- | Tree unit width.
--
-- Trees are designed with 1.0 as the ideal width between nodes.
-- This is represented as a specific newtype so it can be
-- contextually scaled after the design, before the tree is drawn.
--
newtype UW = UW { getUW :: Double }
deriving (Eq,Ord,Num,Floating,Fractional,Real,RealFrac,RealFloat)

instance Show UW where
showsPrec p d = showsPrec p (getUW d)

instance InterpretUnit UW where
normalize _ = realToFrac
dinterp   _ = realToFrac

-- | Tree annotated with positions.
--
-- This is the result of 'design'.
--
type CoordTree a = Tree (Point2 UW, a)

-- | XPos is an absolute position
--
type XPos = UW

type XTree a = Tree (XPos, a)

-- | Delta - difference in X-positions.
--
type Delta = UW

-- A horizontal span.
--
data HSpan = HSpan !UW !UW
deriving (Eq,Ord,Show)

outsideMerge :: HSpan -> HSpan -> HSpan
outsideMerge (HSpan p _) (HSpan _ q) = HSpan p q

moveSpan :: Delta -> HSpan -> HSpan
moveSpan d (HSpan p q) = HSpan (p+d) (q+d)

newtype Extent = Extent { span_list :: [HSpan] }
deriving (Eq,Show)

extlink :: UW -> Extent -> Extent
extlink a (Extent as) = Extent \$ (HSpan a a) :as

-- note is this just for left ... ?
--
midtop :: UW -> Extent -> XPos
midtop r (Extent [])        = r
midtop _ (Extent (HSpan p q:_)) = p + (0.5*(q-p))

-- merge \"moving right\"...
--
mergeMR :: Delta -> Extent -> Extent -> Extent
mergeMR dx (Extent xs) (Extent ys) = Extent \$ step xs ys
where
step ps     []     = ps
step []     qs     = map (moveSpan dx) qs
step (p:ps) (q:qs) = outsideMerge p (moveSpan dx q) : step ps qs

-- dx is negative...
--
mergeML :: Delta-> Extent -> Extent -> Extent
mergeML dx (Extent xs) (Extent ys) = Extent \$ step xs ys
where
step ps     []     = map (moveSpan dx) ps
step []     qs     = qs
step (p:ps) (q:qs) = outsideMerge (moveSpan dx p) q : step ps qs

extentZero :: Extent
extentZero = Extent []

extentOne :: XPos -> Extent
extentOne x = Extent [HSpan x x]

-- 'moveTree' is now recursive...
--
moveTree :: Delta -> XTree a -> XTree a
moveTree dx (Node (x,a) subtrees) = Node ((x+dx),a) subtrees'
where
subtrees' = map (moveTree dx) subtrees

fit :: Extent -> Extent -> UW
fit a b = go (span_list a) (span_list b) 0.0
where
go (HSpan _ p:ps) (HSpan q _:qs) acc = go ps qs (max acc (p - q + 1.0))
go _          _                  acc = acc

-- Fitting the children of a node...

fitleft :: [(XTree a,Extent)] -> ([XTree a], Extent)
fitleft []           = ([],extentZero)
fitleft ((l,ext):xs) = (l:ts,ext') -- left-most child unchanged
where
(ext',ts)        = mapAccumL step ext xs

step aex (t,ex)  = let dx = fit aex ex
in (mergeMR dx aex ex, moveTree dx t)

fitright :: [(XTree a, Extent)] -> ([XTree a], Extent)
fitright = post . foldr fn Nothing
where
post                        = fromMaybe ([],extentZero)
fn (t,ex) Nothing           = Just ([t],ex)
fn (t,ex) (Just (ts,aex))   = Just (t':ts,aex')
where
dx     = negate \$ fit ex aex
t'     = moveTree dx t
aex'   = mergeML dx ex aex

-- | Design the tree from the left.
--
-- Left and right tree designs are merged.
--
designl :: forall a. Tree a -> (XTree a, Extent)
designl (Node a [])   = (Node (0.0,a)  [],    extentOne 0.0)
designl (Node a kids) = (Node (xpos,a) kids', ext1)
where
xs              :: [(XTree a, Extent)]
xs              = map designl kids

kids'           :: [XTree a]
ext0, ext1      :: Extent
(kids',ext0)    = fitleft xs

xpos            = midtop 0.0 ext0

-- | Design the tree from the right.
--
-- Right and left tree designs are merged.
--
designr :: forall a. XPos -> Tree a -> (XTree a, Extent)
designr r (Node a [])   = (Node (r,a)  [],    extentOne r)
designr r (Node a kids) = (Node (xpos,a) kids', ext1)
where
xs              :: [(XTree a, Extent)]
xs              = map (designr r) kids

kids'           :: [XTree a]
ext0, ext1      :: Extent
(kids',ext0)    = fitright xs

xpos            = midtop r ext0

-- | Design a tree, properly balancing the child nodes oriented
-- at root.
--
-- As the design has no y-positions (but by recursion they can be
-- counted) and x-positions are respective to the unit distance
-- 1.0 separating nodes it is rescaled as a post-processing step
-- into drawable coordinates.
--
design :: Tree a -> CoordTree a
design t = rootOrientate zeroPt \$ decorateYPosns 0 t3
where
(t1,ext)                    = designl t
(_, HSpan xmin xmax)        = stats ext
width                       = xmax - xmin
(t2,_)                      = designr width t

-- reconcile the left and right drawings...
t3                          = treeZipWith zfn t1 t2
zfn (x0,a) (x1,_)           = (mean x0 x1,a)

-- Originally the tree has no y-positions, recurse through the
--
decorateYPosns :: UW -> Tree (XPos, a) -> CoordTree a
decorateYPosns lvl (Node (xpos,a) kids) = Node (pt,a) kids'
where
pt    = P2 xpos lvl
kids' = map (decorateYPosns (lvl-1)) kids

rootOrientate :: Point2 UW -> CoordTree a -> CoordTree a
rootOrientate (P2 ox oy) (Node (P2 x0 y0, val) kids) =
Node (P2 ox oy, val) \$ map (mv (ox-x0) (oy-y0)) kids
where
mv dx dy (Node (P2 x y, a) ks) = let ks' = map (mv dx dy) ks
in Node (P2 (x+dx) (y+dy), a) ks'

-- find height and width
--
stats :: Extent -> (Int, HSpan)
stats (Extent [])     = (0,HSpan 0 0)
stats (Extent (e:es)) = foldr fn (1,e) es
where
fn s1 (h, acc_span) = (h+1, minmaxMerge s1 acc_span)

mean :: Fractional u => u -> u -> u
mean x y = (x+y) / 2.0

minmaxMerge :: HSpan -> HSpan -> HSpan
minmaxMerge (HSpan p q) (HSpan p' q') = HSpan (min p p') (max q q')

treeZipWith :: (a -> b -> c) -> Tree a -> Tree b -> Tree c
treeZipWith f (Node a xs) (Node b ys) = Node (f a b) (step xs ys)
where
step (p:ps) (q:qs) = treeZipWith f p q : step ps qs
step _      _      = []

--------------------------------------------------------------------------------
-- Post design transformations...

-- | 'scaleTree' : @ sibling_distance * level_distance * CoordTree -> Tree @
--
-- Scale a CoordTree - this forms a tree where the node label
-- is a pair of @Point2 u@ and an @a@ (usually a LocImage).
--
scaleTree :: (DrawingCtxM m, InterpretUnit u)
=> u -> u -> CoordTree a -> m (Tree (Point2 u, a))
scaleTree sib_dist lvl_dist tree =
getFontSize >>= \sz ->
let fn = mkFun sz in return \$ fmap (bimapL fn) tree
where
mkFun sz = \(P2 x y) -> let ux = sib_dist * (dinterp sz \$ realToFrac x)
uy = lvl_dist * (dinterp sz \$ realToFrac y)
in P2 ux uy

-- | Orientate the Tree according to it\'s drawing direction.
--
-- This is a rotation about the root node.
--
orientateTree :: (Real u, Floating u)
=> TreeDirection -> Tree (Point2 u, a) -> Tree (Point2 u, a)
orientateTree TREE_DOWN  tree = tree
orientateTree TREE_UP    tree = rotateAboutRoot pi tree
orientateTree TREE_LEFT  tree = rotateAboutRoot (1.5*pi) tree
orientateTree TREE_RIGHT tree = rotateAboutRoot (0.5*pi) tree

rotateAboutRoot :: (Real u, Floating u)
=> Radian -> Tree (Point2 u, a) -> Tree (Point2 u, a)
rotateAboutRoot ang (Node (ogin,val) kids) =
Node (ogin, val) \$ map step kids
where
step (Node (v0, a) ks) = Node (rotA v0, a) \$ map step ks