```{-# LANGUAGE ScopedTypeVariables, Rank2Types #-}
module Lseed.Geometry where

import Lseed.Data
import Lseed.Data.Functions
import Lseed.Constants
import Lseed.Geometry.Generator
import Data.List
import Data.Maybe
import Data.Ord
import qualified Data.Map as M
import Data.Traversable (mapM,forM)
import Prelude hiding (mapM)
import Data.STRef
import Control.Applicative

type Point = (Double, Double)
type Line  = (Point, Point)

lineLength ((x1,y1),(x2,y2)) = sqrt ((x1-x2)^2 + (y1-y2)^2)

-- | from http://www.pdas.com/lineint.htm
crossPoint :: Line -> Line -> Maybe Point
crossPoint ((x1,y1),(x2,y2)) ((x3,y3),(x4,y4)) =
let a1 = y2-y1
b1 = x1-x2
c1 = x2*y1 - x1*y2  -- { a1*x + b1*y + c1 = 0 is line 1 }
a2 = y4-y3
b2 = x3-x4
c2 = x4*y3 - x3*y4  -- { a2*x + b2*y + c2 = 0 is line 2 }
denom = a1*b2 - a2*b1
in if abs denom > eps
then let x = (b1*c2 - b2*c1)/denom
y = (a2*c1 - a1*c2)/denom
in if  x1 <= x && x <= x2 &&
y1 <= y && y <= y2 &&
x3 <= x && x <= x4 &&
y3 <= y && y <= y4
then Just (x,y)
else Nothing
else Nothing

plantedToLines :: Planted a -> [(Line, a)]
plantedToLines planted = runGeometryGenerator (plantPosition planted, 0) 0 \$
plantToGeometry (phenotype planted)

plantToGeometry :: Plant a -> GeometryGenerator a ()
plantToGeometry (Plant x len ang _ ps) = rotated ang \$ do
translated (0,len * stipeLength) \$ mapM_ plantToGeometry ps

-- | Lines are annotated with its plant, identified by the extra data
gardenToLines :: Garden a -> [(Line, a)]
gardenToLines = concatMap (\planted -> plantedToLines planted)

-- | Add lightning from a given angle
lightenLines :: Double -> [(Line, a)] -> [(Line, a, Double)]
lightenLines angle lines = let (lighted,_) = allKindsOfStuffWithAngle angle lines
in lighted

lightPolygons :: Double -> [(Line, a)] -> [(Point,Point,Point,Point,Double)]
lightPolygons angle lines = let (_,polygons) = allKindsOfStuffWithAngle angle lines
in polygons

allKindsOfStuffWithAngle :: forall a. Double -> [(Line, a)] ->
( [(Line, a, Double)]
, [(Point,Point,Point,Point,Double)] )
allKindsOfStuffWithAngle angle lines = (lighted, polygons)
where projectLine :: Line -> (Double, Double)
projectLine (p1, p2) = (projectPoint p1, projectPoint p2)
projectTan :: Double
projectTan = 1 / tan (pi-angle)
projectPoint :: Point -> Double
projectPoint (x,y) = x + y * projectTan

-- False means Beginning of Line
sweepPoints :: [(Double, Bool, (Line, a))]
sweepPoints = sortBy (comparing (\(a,b,_)->(a,b))) \$ concatMap (\l@((p1,p2),i) ->
if abs (projectPoint p1 - projectPoint p2) < eps
then []
else if projectPoint p1 < projectPoint p2
then [(projectPoint p1,False,l), (projectPoint p2,True,l)]
else [(projectPoint p2,False,l), (projectPoint p1,True,l)]
) lines

-- Find all crossing points
crossings :: [Double]
crossings = case mapAccumL step [] sweepPoints of
([],crosses) -> nub (sort (concat crosses))
_            -> error "Lines left open after sweep"
where	-- accumulator is open lines, return is list of cross points
step :: [Line] -> (Double, Bool, (Line, a)) -> ([Line], [Double])
step [] (_, True, _)      = error \$ "Line ends with no lines open"
-- Beginning of a new line, mark it as open, and mark it as a cross-point
step ol (x, False, (l,_)) = (l:ol, [x])
-- End of a line. Calculate crosses with all open line, and remove it from the
-- list of open lines
step ol (x, True, (l,_)) =
let ol' = delete l ol
crosses = map projectPoint \$ mapMaybe (crossPoint l) ol'
in (ol', x:crosses)

-- Cross points inverval
intervals = zip crossings (tail crossings)

unlighted = map (\(l,i) -> (l,i,0)) lines

unprojectPoint x (p1@(x1,y1),p2@(x2,y2)) =
let t = (x - projectPoint p1) /
(projectPoint p2 - projectPoint p1)
in (x1 + t * (x2-x1), y1 + t * (y2-y1))

lineAtRay x l = let (x1',x2') = projectLine l
in abs (x1' - x2') > eps && -- avoid lines that parallel to the rays
(x1' <= x && x <= x2' || x2' <= x && x <= x1')

aboveFirst x l1 l2 =
let (_,y1) = unprojectPoint x l1
(_,y2) = unprojectPoint x l2
in y2 `compare` y1

lighted :: [(Line, a, Double)]
lighted = foldl go unlighted intervals
where go llines (x1,x2) = curlines' ++ otherlines
where -- Calculation based on the ray at the mid point
mid = (x1 + x2) / 2
-- Light intensity
width = abs ((x2 - x1) * sin angle)
(curlines, otherlines) = partition (\(l,_,_) -> lineAtRay mid l)
llines
sorted = sortBy (\(l1,_,_) (l2,_,_) -> aboveFirst mid l1 l2)
curlines
curlines' = snd \$ mapAccumL shine width sorted
shine intensity (l,i,amount) = (intensity * lightFalloff,
(l,i,amount + (1-lightFalloff) * intensity))

polygons = concatMap go intervals
where go (x1,x2) = if null sorted then [nothingPoly] else lightedPolys
where mid = (x1 + x2) / 2
curlines = filter (lineAtRay mid) (map fst lines)
sorted = sortBy (aboveFirst mid) curlines
ceiling = ((0,10),(1,10))
floor = ((0,0),(1,0))
nothingPoly = let p1 = unprojectPoint x1 ceiling
p2 = unprojectPoint x1 floor
p3 = unprojectPoint x2 floor
p4 = unprojectPoint x2 ceiling
in (p1,p2,p3,p4,1)
firstPoly = let p1 = unprojectPoint x1 ceiling
p2 = unprojectPoint x1 (head sorted)
p3 = unprojectPoint x2 (head sorted)
p4 = unprojectPoint x2 ceiling
in (p1,p2,p3,p4)
lastPoly =  let p1 = unprojectPoint x1 (last sorted)
p2 = unprojectPoint x1 floor
p3 = unprojectPoint x2 floor
p4 = unprojectPoint x2 (last sorted)
in (p1,p2,p3,p4)
polys = zipWith (\l1 l2 ->
let p1 = unprojectPoint x1 l1
p2 = unprojectPoint x1 l2
p3 = unprojectPoint x2 l2
p4 = unprojectPoint x2 l1
in (p1,p2,p3,p4)) sorted (tail sorted)
polys' = [firstPoly] ++ polys ++ [lastPoly]
lightedPolys = snd \$ mapAccumL shine 1 polys'
shine intensity (p1,p2,p3,p4) = ( intensity * lightFalloff
, (p1,p2,p3,p4,intensity))

-- | Annotates each piece of the garden with the amount of line it attacts
lightenGarden :: Angle -> Garden a -> Garden (a, Double)
lightenGarden angle = mapLine (lightenLines angle) 0 (+)

-- | Helper to apply a function that works on lines to a garden
mapLine :: (forall b. [(Line, b)] -> [(Line, b, c)]) ->
c -> (c -> c -> c) -> Garden a -> Garden (a,c)
mapLine process init combine garden = runST \$ do
gardenWithPointers <- mapM (mapM (\d -> (,) d <\$> newSTRef init)) garden
let linesWithPointers = gardenToLines gardenWithPointers
let processedLines = process linesWithPointers
-- Update values via the STRef
forM_ processedLines \$ \(_,(_,stRef),result) -> modifySTRef stRef (combine result)
-- Undo the STRefs
mapM (mapM (\(d,stRef) -> (,) d <\$> readSTRef stRef)) gardenWithPointers

```