{-# LANGUAGE DeriveDataTypeable #-}

{-
Copyright (c) 2014, Markus Barenhoff <alios@alios.org>
All rights reserved.

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      names of its contributors may be used to endorse or promote products
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
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-}

module Data.Geodetic.GreatCircle where

import Data.Geodetic.GeodeticModel

import qualified Prelude ()
import Numeric.Units.Dimensional.TF.Prelude
import Data.Typeable
import Data.Fixed (mod')


data CourseDirection = CourseEast | CourseWest
                     deriving (Show, Eq, Typeable)
               
-- | greate circle distance
gcDist :: (GeodeticModel m t) =>
          GeodeticCoordinate m t -> GeodeticCoordinate m t -> Length t
gcDist c1 c2 = 
  let φ1 = longitude c1
      λ1 = latitude c1
      φ2 = longitude c2
      λ2 = latitude c2
      dλ = abs $ λ1 - λ2
      a1 = (cos φ1 * sin dλ)
      a2 = (cos φ2 * sin φ1) - (sin φ2 * cos φ1 * cos dλ)
      a = sqrt ((a1 * a1) + (a2 *a2))     
      b = (sin φ2 * sin φ1) + (cos φ2 * cos φ1 * cos dλ)      
      dσ = atan (a / b)
      r = 6371.01 *~ kilo meter
  in r * dσ


-- | greate circle course
gcCourse :: (Real t, GeodeticModel a t) =>
            CourseDirection -> GeodeticCoordinate a t -> GeodeticCoordinate a t
            -> PlaneAngle t
gcCourse d c1 c2=
  let jb = longitude c2
      dg = gcDist c1 c2 / (1 *~ meter)
      ja = longitude c1
      ar = ((sin jb) - (cos dg) * (sin ja)) / ((cos ja) * (sin dg))
      d360 = (360 *~ degree)
      c = case d of
        CourseWest -> ar
        CourseEast -> d360 - ar
  in ((c /~ degree) `mod'` 360) *~ degree
  

