module Data.Cross
(
HasNormal(..), normal
, One, Two, Three
, HasCross2(..), HasCross3(..)
) where
import Data.VectorSpace
import Data.MemoTrie
import Data.Basis
import Data.Derivative
class HasNormal v where normalVec :: v -> v
normal :: (HasNormal v, InnerSpace v s, Floating s) => v -> v
normal = normalized . normalVec
type One s = s
type Two s = (s,s)
type Three s = (s,s,s)
class HasCross2 v where cross2 :: v -> v
instance AdditiveGroup u => HasCross2 (u,u) where
cross2 (x,y) = (negateV y,x)
instance ( HasBasis a s, HasTrie (Basis a)
, VectorSpace v s, HasCross2 v) => HasCross2 (a:>v) where
cross2 = fmapD cross2
instance (HasBasis s s, HasTrie (Basis s), Basis s ~ ()) =>
HasNormal (One s :> Two s) where
normalVec v = cross2 (derivative v `untrie` ())
instance ( Num s, VectorSpace s s
, HasBasis s s, HasTrie (Basis s), Basis s ~ ())
=> HasNormal (Two (One s :> s)) where
normalVec = unpairD . normalVec . pairD
class HasCross3 v where cross3 :: v -> v -> v
instance Num s => HasCross3 (s,s,s) where
(ax,ay,az) `cross3` (bx,by,bz) = ( ay * bz az * by
, az * bx ax * bz
, ax * by ay * bx )
instance (HasBasis a s, HasTrie (Basis a), VectorSpace v s, HasCross3 v) => HasCross3 (a:>v) where
cross3 = distrib cross3
instance (Num s, HasTrie (Basis (s, s)), HasBasis s s, Basis s ~ ()) =>
HasNormal (Two s :> Three s) where
normalVec v = d (Left ()) `cross3` d (Right ())
where
d = untrie (derivative v)
instance ( Num s, VectorSpace s s, HasBasis s s, HasTrie (Basis s)
, HasNormal (Two s :> Three s))
=> HasNormal (Three (Two s :> s)) where
normalVec = untripleD . normalVec . tripleD
pairD :: (HasBasis a s, HasTrie (Basis a), VectorSpace b s, VectorSpace c s) =>
(a:>b,a:>c) -> a:>(b,c)
pairD (u,v) = liftD2 (,) u v
tripleD :: (HasBasis a s, HasTrie (Basis a), VectorSpace b s, VectorSpace c s, VectorSpace d s) =>
(a:>b,a:>c,a:>d) -> a:>(b,c,d)
tripleD (u,v,w) = liftD3 (,,) u v w
unpairD :: (HasBasis a s, HasTrie (Basis a), VectorSpace a s, VectorSpace b s, VectorSpace c s) =>
(a :> (b,c)) -> (a:>b, a:>c)
unpairD d = (fst <$>> d, snd <$>> d)
untripleD :: ( HasBasis a s, HasTrie (Basis a) , VectorSpace a s, VectorSpace b s
, VectorSpace c s, VectorSpace d s) =>
(a :> (b,c,d)) -> (a:>b, a:>c, a:>d)
untripleD d =
((\ (a,_,_) -> a) <$>> d, (\ (_,b,_) -> b) <$>> d, (\ (_,_,c) -> c) <$>> d)