```{-# LANGUAGE TupleSections #-}
module Data.GPS.Core
( -- * Types
Distance
, Speed
, Vector
, Trail
, Circle
, Arc
-- * Constants
, north
, south
, east
, west
, circumferenceOfEarth
-- * Coordinate Functions
, distance
, speed
, getVector
, getDMSPair
, divideArea
, interpolate
, circleIntersectionPoints
, intersectionArcsOf
, maximumDistanceOfArc
-- * IO helpers
, writeGPX
-- * Utility
, getUTCTime
, module Data.Geo.GPX
) where

import Data.Time
import Data.Maybe
import Data.List (sortBy)
import Data.Ord (comparing)
import Text.XML.HXT.Core
import Text.XML.XSD.DateTime(DateTime,toUTCTime)
import Data.Geo.GPX
import Data.Lens.Common

-- |Distances are expressed in meters
type Distance = Double

-- |Angles are expressed in radians from North.
-- 	0	== North
-- 	pi/2	== West
-- 	pi 	== South
-- 	(3/2)pi	== East    == - (pi / 2)

-- |Speed is hard coded as meters per second
type Speed = Double

-- | Genearlly a circle indicates a known area in which we are searching
-- (so a center point and maximum possible distance from that point)
type Circle a = (a, Distance)

-- | An arc is represented as a circle, starting heading and ending heading

type Trail a = [a]

getUTCTime :: (TimeL a) => a -> Maybe UTCTime
getUTCTime = fmap toUTCTime . (^. timeL)

distance :: (LatL a, LonL a, LatL b, LonL b) => a -> b -> Distance
distance x y =
deltaLat    = lat2 - lat1
deltaLon    = lon2 - lon1
a = (sin (deltaLat / 2))^2 + cos lat1 * cos lat2 * (sin (deltaLon / 2))^2
c = 2 * atan2 (a**0.5) ((1-a)**0.5)

-- | Direction two points aim toward (0 = North, pi/2 = West, pi = South, 3pi/2 = East)
heading         :: (LatL a, LonL a, LatL b, LonL b) => a -> b -> Heading
atan2	(sin (diffLon) * cos (lat2))
(cos(lat1) * sin (lat2) - sin(lat1) * cos lat2 * cos (diffLon))
where
diffLon = lon2 - lon1

getVector :: (LatL a, LonL a, LatL b, LonL b) => a -> b -> Vector
getVector a b = (distance a b, heading a b)

-- |Given a vector and coordinate, computes a new coordinate.
-- Within some epsilon it should hold that if
--
--
-- then
--
--
-- 	@dist    == distance start dest@
addVector :: (LatL c, LonL c) => Vector -> c -> c
addVector (d,h) p = (lonL ^= longitude (toDegrees lon2))
. (latL ^= latitude  (toDegrees lat2))
\$ p
where
lat2 = asin (sin (lat) * cos (d / radiusOfEarth) + cos(lat)
lon2 = lon + atan2 (sin h * sin (d / radiusOfEarth) * cos lat)
(cos (d/radiusOfEarth) - sin lat * sin lat2)

-- | Speed in meters per second, only if a 'Time' was recorded for each waypoint.
speed :: (LatL loc, LonL loc, TimeL loc, LatL b, LonL b, TimeL b) => loc -> b -> Maybe Speed
speed a b =
case (getUTCTime b, getUTCTime a) of
(Just x, Just y) ->
let timeDiff = realToFrac (diffUTCTime x y)
in if timeDiff == 0 then Nothing else Just \$ (distance a b) / timeDiff
_ -> Nothing

-- |radius of the earth in meters

-- |Circumference of earth (meters)
circumferenceOfEarth :: Double
circumferenceOfEarth = radiusOfEarth * 2 * pi

north = 0

-- |South, being 180 degrees from North, is pi.
south = pi

-- |East is 270 degrees (3 pi / 2)
east = (3 / 2) * pi

-- |West is 90 degrees (pi/2)
west = pi / 2

toDegrees = (*) (180 / pi)

getRadianPairD :: (LatL c, LonL c) => c -> (Double,Double)

getDMSPair :: (LatL c, LonL c) => c -> (Latitude, Longitude)
getDMSPair c = (c ^. latL, c ^. lonL)

-- |Provides a lat/lon pair of doubles in radians
getRadianPair :: (LatL p, LonL p) => p -> (Latitude, Longitude)

toRadians :: Floating f => f -> f
toRadians = (*) (pi / 180)

-- | @interpolate c1 c2 w@ where @0 <= w <= 1@ Gives a point on the line
-- between c1 and c2 equal to c1 when @w == 0@ (weighted linearly
-- toward c2).
interpolate :: (LatL a, LonL a) => a -> a -> Double -> a
interpolate c1 c2 w
| w < 0 || w > 1 = error "Interpolate only works with a weight between zero and one"
| otherwise =
let (h,d) = (heading c1 c2, distance c1 c2)
v = (d * w, h)

-- | Compute the points at which two circles intersect (assumes a flat plain).  If
-- the circles do not intersect or are identical then the result is @Nothing@.
circleIntersectionPoints :: (LatL a, LonL a) => (a, Distance) -> (a, Distance) -> Maybe (a,a)
circleIntersectionPoints (a,r1) (b,r2)
| a ^. latL == b ^. latL && a ^. lonL == b ^. lonL && r1 == r2 = Nothing -- FIXME need approx eq
| r1 + r2 < ab = Nothing
| any isNaN (map (^. latL) pts) || any isNaN (map (^. lonL) pts) = Nothing
| otherwise = Just (p1, p2)
where
ab = distance a b
angABX = acos ( (r1^2 + ab^2 - r2^2) / (2 * r1 * ab) )
ang1 = heading a b + angABX
ang2 = heading a b - angABX
p1 = addVector (r1, ang1) a
p2 = addVector (r1, ang2) a
pts = [p1,p2]

-- | Find the area in which all given circles intersect.  The resulting
-- area is described in terms of the bounding arcs.   All cirlces must
-- intersect at two points.
intersectionArcsOf :: (LatL a, LonL a) => [Circle a] -> [Arc a]
intersectionArcsOf cs =
let isArcWithinCircle circ arc = maximumDistanceOfArc (fst circ) arc <= (snd circ)
isArcWithinAllCircles arc = all (\$ arc) (map isArcWithinCircle cs)
-- getArcs :: Circle a -> Circle a -> [Arc a]
getArcs c1 c2 = concatMap (buildArcsFromPoints c1 c2) . maybeToList \$ circleIntersectionPoints c1 c2
-- buildArcsFromPoints :: (a, a) -> [Arc a]
buildArcsFromPoints c1 c2 (p1,p2) =
let c1h1 = heading (fst c1) p1
c1h2 = heading (fst c1) p2
c2h1 = heading (fst c2) p1
c2h2 = heading (fst c2) p2
in [(c1,c1h1,c1h2), (c1,c1h2, c1h1), (c2,c2h1,c2h2), (c2,c2h2,c2h1)]
in filter isArcWithinAllCircles . concatMap (uncurry getArcs) . choose2 \$ cs

maximumDistanceOfArc :: (LatL a, LonL a) => a -> Arc a -> Distance
maximumDistanceOfArc pnt ((c,r), h1, h2) =
in if ((pcHeading < h1 || pcHeading > h2) && h1 < h2) || ((pcHeading > h2 && pcHeading < h1) && h1 > h2)
then max (distance pnt (addVector (r,h1) c)) (distance pnt (addVector (r,h2) c))
else distance pnt c + r

choose2 :: [a] -> [(a,a)]
choose2 [] = []
choose2 (x:xs) = map (x,) xs ++ choose2 xs

-- |@divideArea vDist hDist nw se@ divides an area into a grid of equally
-- spaced coordinates within the box drawn by the northwest point (nw) and
-- southeast point (se).  Because this uses floating point there might be a
-- different number of points in some rows (the last might be too far east based
-- on a heading from the se point).
divideArea :: (LatL c, LonL c) => Distance -> Distance -> c -> c -> [[c]]
divideArea vDist hDist nw se =
let (top,left)  = (nw ^. latL, nw ^. lonL)
(btm,right) = (se ^. latL, se ^. lonL)
columnOne = takeWhile ( (<= west) . heading se) . iterate (addVector (vDist, south)) \$ nw
buildRow  = takeWhile ((>= north) . heading se) . iterate (addVector (hDist, east))
in map buildRow columnOne

-- |Reads a GPX file (using the GPX library) by simply concatenating all the
-- tracks, segments, and points ('trkpts', 'trksegs', 'trks') into a single 'Trail'.
readGPX :: FilePath -> IO (Trail Wpt)
readGPX = liftM (concatMap (^. trkptsL). concatMap (^. trksegsL) . concatMap (^. trksL)) . readGpxFile

writeGPX :: FilePath -> Trail Wpt -> IO ()
writeGPX fp ps = writeGpxFile fp \$ gpx "1.0" "Haskell GPS Package (via the GPX package)" Nothing [] [] [trk Nothing Nothing Nothing Nothing [] Nothing Nothing Nothing [trkseg ps Nothing]] Nothing

-- writeGpxFile should go in the GPX package
writeGpxFile :: FilePath -> Gpx -> IO ()
writeGpxFile fp gpx = runX_ (constA gpx >>> xpickleDocument (xpickle :: PU Gpx) [] fp)

runX_ t = runX t >> return ()

readGPXSegments :: FilePath -> IO [Trail Wpt]
readGPXSegments = liftM (map (concatMap (^. trkptsL)) . map (^. trksegsL) . concatMap (^. trksL)) . readGpxFile

readGpxFile :: FilePath -> IO [Gpx]
readGpxFile = runX . xunpickleDocument (xpickle :: PU Gpx) [withRemoveWS yes, withValidate no]
```