{-|
Module      : Math
Description : Mathematical functions
Copyright   : (c) Christopher Howard, 2016
License     : GPL-3
Maintainer  : ch.howard@zoho.com
-}

module Math where

divBySum a b c = a / (b + c)

divideProduct a b c = a * b / c

ratioRadDeg = 180 / pi

radToDeg = (ratioRadDeg *)

mulSV s (x, y) = (s * x, s * y)

join f a = f a a

sqr = join (*)

distrib f g a b = g (f a) (f b)

sumSquares = distrib sqr (+)

pairLen f = distrib f (flip (-))
pairLenFst = pairLen fst
pairLenSnd = pairLen snd

-- vectMag a = sqrt (sum

hypotenuse a b = sqrt (sumSquares a b)

distance a b = hypotenuse (pairLenFst a b) (pairLenSnd a b)

vectMag (a, b) = hypotenuse a b

circleRads = 2 * pi

nan = 0 / 0

isNan = (== nan)

isPos :: (Num a, Ord a) => a -> Bool
isPos = (>= 0)

isNeg :: (Num a, Ord a) => a -> Bool
isNeg = not . isPos

bothPos = distrib isPos (&&)
bothNeg = distrib isNeg (&&)

-- return unit radians
vectorDirection (0, 0) = nan
vectorDirection (x, y)
  | bothPos x y = a
  | isNeg x && isPos y = pi - a
  | bothNeg x y = pi + a
  | otherwise = circleRads - a
  where a = atan (distrib abs (/) y x)


{-
  Assumes source (origin of projectile) is at origin of grid (0, 0) and so
  target center is relative to this. Assumes source is stationary and so
  velocity of target is relative to source.
-}
targetingA s c v = f c 3

  where f n i =
          if moreThanZero i
            then f (g n) (decrem i)
            else vectorDirection (g n)
        g n = addV c (mulSV (distOrigin n / s) v)

inc, increm :: Num a => a -> a
increm = flip (+) 1
inc = increm

dec, decrem :: Num a => a -> a
decrem = flip (-) 1
dec = decrem

origin = (0, 0)

distOrigin = distance origin

addV (x1, y1) (x2, y2) = (x1 + x2, y1 + y2)

subV (x1, y1) (x2, y2) = (x1 - x2, y1 - y2)

remF x y = (a - coerciveTrunc a) * y
  where a = x / y
coerciveTrunc = fromIntegral . truncate

isZero :: (Num a, Eq a) => a -> Bool
isZero = (== 0)

notZero :: (Num a, Eq a) => a -> Bool
notZero = (/= 0)

zeroProtect a b = if isZero b then a else b

appPair f (a, b) = (f a, f b)

neither a b = not (a || b)

zeroOrLess :: (Num a, Ord a) => a -> Bool
zeroOrLess = (<= 0)

moreThanZero :: (Num a, Ord a) => a -> Bool
moreThanZero = (> 0)

-- |Transforms vector to coordinate form.
vecCoord :: Floating t
         => t -- ^ angle
         -> t -- ^ magnitude
         -> (t, t)
vecCoord a b = appPair ((* b) . ($ a)) (cos, sin)

qArc = pi / 2