Vector module
=============
This module contains a class for two-dimensional vectors, a strict
datatype to instantiate it, and another instance for signals of the
same type.
> {-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances, TypeSynonymInstances #-}
>
> module Common.Vector where
>
> import Control.Applicative
> import FRP.Elerea.Legacy
> import Graphics.Rendering.OpenGL
>
> data Vec = V { getX :: !GLfloat, getY :: !GLfloat }
>
> infixl 7 ^*.
> infixl 7 .*^
> infixl 7 `dot`
> infixl 7 `cross`
> infixl 6 ^+^
> infixl 6 ^-^
>
> class Vector2D v c | v -> c where
> (^+^) :: v -> v -> v
> (^-^) :: v -> v -> v
> (^*.) :: v -> c -> v
> (.*^) :: c -> v -> v
> vnull :: v
> dot :: v -> v -> c
> cross :: v -> v -> c
>
> instance Vector2D Vec GLfloat where
> V x1 y1 ^+^ V x2 y2 = V (x1+x2) (y1+y2)
> V x1 y1 ^-^ V x2 y2 = V (x1-x2) (y1-y2)
> V x y ^*. t = V (x*t) (y*t)
> t .*^ V x y = V (x*t) (y*t)
> vnull = V 0 0
> V x1 y1 `dot` V x2 y2 = x1*y1+x2*y2
> V x1 y1 `cross` V x2 y2 = x1*y2-x2*y1
>
> instance Vector2D (Signal Vec) (Signal GLfloat) where
> (^+^) = liftA2 (^+^)
> (^-^) = liftA2 (^-^)
> (^*.) = liftA2 (^*.)
> (.*^) = liftA2 (.*^)
> vnull = pure vnull
> dot = liftA2 dot
> cross = liftA2 cross