#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702
#endif
module Linear.V3
( V3(..)
, cross, triple
, R1(..)
, R2(..)
, R3(..)
) where
import Control.Applicative
import Data.Data
import Data.Distributive
import Data.Foldable
import Data.Functor.Bind
import Data.Traversable
import Data.Semigroup
import Data.Semigroup.Foldable
import Data.Semigroup.Traversable
import Foreign.Ptr (castPtr)
import Foreign.Storable (Storable(..))
import GHC.Arr (Ix(..))
#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702
import GHC.Generics (Generic)
#endif
#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706
import GHC.Generics (Generic1)
#endif
import Linear.Core
import Linear.Epsilon
import Linear.Metric
import Linear.V2
import Linear.Vector
data V3 a = V3 !a !a !a deriving (Eq,Ord,Show,Read,Data,Typeable
#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702
,Generic
#endif
#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706
,Generic1
#endif
)
instance Functor V3 where
fmap f (V3 a b c) = V3 (f a) (f b) (f c)
a <$ _ = V3 a a a
instance Foldable V3 where
foldMap f (V3 a b c) = f a `mappend` f b `mappend` f c
instance Traversable V3 where
traverse f (V3 a b c) = V3 <$> f a <*> f b <*> f c
instance Foldable1 V3 where
foldMap1 f (V3 a b c) = f a <> f b <> f c
instance Traversable1 V3 where
traverse1 f (V3 a b c) = V3 <$> f a <.> f b <.> f c
instance Apply V3 where
V3 a b c <.> V3 d e f = V3 (a d) (b e) (c f)
instance Applicative V3 where
pure a = V3 a a a
V3 a b c <*> V3 d e f = V3 (a d) (b e) (c f)
instance Additive V3 where
zero = pure 0
liftU2 = liftA2
liftI2 = liftA2
instance Bind V3 where
V3 a b c >>- f = V3 a' b' c' where
V3 a' _ _ = f a
V3 _ b' _ = f b
V3 _ _ c' = f c
instance Monad V3 where
return a = V3 a a a
V3 a b c >>= f = V3 a' b' c' where
V3 a' _ _ = f a
V3 _ b' _ = f b
V3 _ _ c' = f c
instance Num a => Num (V3 a) where
(+) = liftA2 (+)
() = liftA2 ()
(*) = liftA2 (*)
negate = fmap negate
abs = fmap abs
signum = fmap signum
fromInteger = pure . fromInteger
instance Fractional a => Fractional (V3 a) where
recip = fmap recip
(/) = liftA2 (/)
fromRational = pure . fromRational
instance Metric V3 where
dot (V3 a b c) (V3 d e f) = a * d + b * e + c * f
instance Distributive V3 where
distribute f = V3 (fmap (\(V3 x _ _) -> x) f) (fmap (\(V3 _ y _) -> y) f) (fmap (\(V3 _ _ z) -> z) f)
class R2 t => R3 t where
_z :: Functor f => (a -> f a) -> t a -> f (t a)
_xyz :: Functor f => (V3 a -> f (V3 a)) -> t a -> f (t a)
instance R1 V3 where
_x f (V3 a b c) = (\a' -> V3 a' b c) <$> f a
instance R2 V3 where
_y f (V3 a b c) = (\b' -> V3 a b' c) <$> f b
_xy f (V3 a b c) = (\(V2 a' b') -> V3 a' b' c) <$> f (V2 a b)
instance R3 V3 where
_z f (V3 a b c) = V3 a b <$> f c
_xyz = id
instance Core V3 where
core f = V3 (f _x) (f _y) (f _z)
instance Storable a => Storable (V3 a) where
sizeOf _ = 3 * sizeOf (undefined::a)
alignment _ = alignment (undefined::a)
poke ptr (V3 x y z) = do poke ptr' x
pokeElemOff ptr' 1 y
pokeElemOff ptr' 2 z
where ptr' = castPtr ptr
peek ptr = V3 <$> peek ptr' <*> peekElemOff ptr' 1 <*> peekElemOff ptr' 2
where ptr' = castPtr ptr
cross :: Num a => V3 a -> V3 a -> V3 a
cross (V3 a b c) (V3 d e f) = V3 (b*fc*e) (c*da*f) (a*eb*d)
triple :: Num a => V3 a -> V3 a -> V3 a -> a
triple a b c = dot a (cross b c)
instance Epsilon a => Epsilon (V3 a) where
nearZero = nearZero . quadrance
instance Ix a => Ix (V3 a) where
range (V3 l1 l2 l3,V3 u1 u2 u3) =
[V3 i1 i2 i3 | i1 <- range (l1,u1)
, i2 <- range (l2,u2)
, i3 <- range (l3,u3)
]
unsafeIndex (V3 l1 l2 l3,V3 u1 u2 u3) (V3 i1 i2 i3) =
unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * (
unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) *
unsafeIndex (l1,u1) i1)
inRange (V3 l1 l2 l3,V3 u1 u2 u3) (V3 i1 i2 i3) =
inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
inRange (l3,u3) i3