```{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-}
-----------------------------------------------------------------------------------------
-- |
-- Module      :  FRP.Yampa.Vector2
-- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003
--
-- Maintainer  :  nilsson@cs.yale.edu
-- Stability   :  provisional
-- Portability :  non-portable (GHC extensions)
--
-- 2D vector abstraction (R^2).
--
-- ToDo: Deriving Show, or provide dedicated show instance?
-----------------------------------------------------------------------------------------

module FRP.Yampa.Vector2 (
-- module AFRPVectorSpace,
Vector2,		-- Abstract, instance of VectorSpace
vector2,		-- :: RealFloat a => a -> a -> Vector2 a
vector2X,		-- :: RealFloat a => Vector2 a -> a
vector2Y,		-- :: RealFloat a => Vector2 a -> a
vector2XY,		-- :: RealFloat a => Vector2 a -> (a, a)
vector2Polar,	-- :: RealFloat a => a -> a -> Vector2 a
vector2Rho,		-- :: RealFloat a => Vector2 a -> a
vector2Theta,	-- :: RealFloat a => Vector2 a -> a
vector2RhoTheta,	-- :: RealFloat a => Vector2 a -> (a, a)
vector2Rotate 	-- :: RealFloat a => a -> Vector2 a -> Vector2 a
) where

import FRP.Yampa.VectorSpace
import FRP.Yampa.Forceable

------------------------------------------------------------------------------
-- 2D vector, constructors and selectors.
------------------------------------------------------------------------------

-- Restrict coefficient space to RealFloat (rather than Floating) for now.
-- While unclear if a complex coefficient space would be useful (and if the
-- result really would be a 2d vector), the only thing causing trouble is the
-- use of atan2 in vector2Theta. Maybe atan2 can be generalized?

data RealFloat a => Vector2 a = Vector2 !a !a deriving (Eq,Show)

vector2 :: RealFloat a => a -> a -> Vector2 a
vector2 x y = Vector2 x y

vector2X :: RealFloat a => Vector2 a -> a
vector2X (Vector2 x _) = x

vector2Y :: RealFloat a => Vector2 a -> a
vector2Y (Vector2 _ y) = y

vector2XY :: RealFloat a => Vector2 a -> (a, a)
vector2XY (Vector2 x y) = (x, y)

vector2Polar :: RealFloat a => a -> a -> Vector2 a
vector2Polar rho theta = Vector2 (rho * cos theta) (rho * sin theta)

vector2Rho :: RealFloat a => Vector2 a -> a
vector2Rho (Vector2 x y) = sqrt (x * x + y * y)

vector2Theta :: RealFloat a => Vector2 a -> a
vector2Theta (Vector2 x y) = atan2 y x

vector2RhoTheta :: RealFloat a => Vector2 a -> (a, a)
vector2RhoTheta v = (vector2Rho v, vector2Theta v)

------------------------------------------------------------------------------
-- Vector space instance
------------------------------------------------------------------------------

instance RealFloat a => VectorSpace (Vector2 a) a where
zeroVector = Vector2 0 0

a *^ (Vector2 x y) = Vector2 (a * x) (a * y)

(Vector2 x y) ^/ a = Vector2 (x / a) (y / a)

negateVector (Vector2 x y) = (Vector2 (-x) (-y))

(Vector2 x1 y1) ^+^ (Vector2 x2 y2) = Vector2 (x1 + x2) (y1 + y2)

(Vector2 x1 y1) ^-^ (Vector2 x2 y2) = Vector2 (x1 - x2) (y1 - y2)

(Vector2 x1 y1) `dot` (Vector2 x2 y2) = x1 * x2 + y1 * y2

------------------------------------------------------------------------------