Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	None
Language	Haskell2010

Data.Geometry.Vector.VectorFamily

Contents

d dimensional Vectors
Convenience "constructors"
Indexing vectors
Snoccing and consindg
Specific on 3-dimensional vectors

Description

Implementation of $d$-dimensional vectors. The implementation automatically selects an optimized representation for small (up to size 4) vectors.

Synopsis

newtype Vector (d :: Nat) (r :: *) = MKVector {
- _unV :: VectorFamily (Peano d) r
}
unV :: Iso (Vector d r) (Vector d s) (VectorFamily (Peano d) r) (VectorFamily (Peano d) s)
class (ImplicitArity (Peano d), KnownNat d) => Arity d
pattern Vector :: VectorFamilyF (Peano d) r -> Vector d r
pattern Vector1 :: r -> Vector 1 r
pattern Vector2 :: r -> r -> Vector 2 r
pattern Vector3 :: r -> r -> r -> Vector 3 r
pattern Vector4 :: r -> r -> r -> r -> Vector 4 r
vectorFromList :: Arity d => [r] -> Maybe (Vector d r)
vectorFromListUnsafe :: Arity d => [r] -> Vector d r
destruct :: (Arity d, Arity (d + 1)) => Vector (d + 1) r -> (r, Vector d r)
head :: (Arity d, 1 <= d) => Vector d r -> r
element :: forall proxy i d r. (Arity d, KnownNat i, (i + 1) <= d) => proxy i -> Lens' (Vector d r) r
element' :: forall d r. Arity d => Int -> Traversal' (Vector d r) r
cons :: (Arity d, Arity (d + 1)) => r -> Vector d r -> Vector (d + 1) r
snoc :: (Arity (d + 1), Arity d) => Vector d r -> r -> Vector (d + 1) r
init :: (Arity d, Arity (d + 1)) => Vector (d + 1) r -> Vector d r
last :: forall d r. (KnownNat d, Arity (d + 1)) => Vector (d + 1) r -> r
prefix :: forall i d r. (Arity d, Arity i, i <= d) => Vector d r -> Vector i r
cross :: Num r => Vector 3 r -> Vector 3 r -> Vector 3 r

d dimensional Vectors

newtype Vector (d :: Nat) (r :: *) Source #

Datatype representing d dimensional vectors. The default implementation is based n VectorFixed. However, for small vectors we automatically select a more efficient representation.

Constructors

MKVector
Fields _unV :: VectorFamily (Peano d) r

Instances

Instances details

Arity d => FunctorWithIndex Int (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods imap :: (Int -> a -> b) -> Vector d a -> Vector d b #
Arity d => FoldableWithIndex Int (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods ifoldMap :: Monoid m => (Int -> a -> m) -> Vector d a -> m # ifoldMap' :: Monoid m => (Int -> a -> m) -> Vector d a -> m # ifoldr :: (Int -> a -> b -> b) -> b -> Vector d a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> Vector d a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> Vector d a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> Vector d a -> b #
Arity d => TraversableWithIndex Int (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods itraverse :: Applicative f => (Int -> a -> f b) -> Vector d a -> f (Vector d b) #
Arity d => Functor (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods fmap :: (a -> b) -> Vector d a -> Vector d b # (<$) :: a -> Vector d b -> Vector d a #
Arity d => Applicative (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods pure :: a -> Vector d a # (<>) :: Vector d (a -> b) -> Vector d a -> Vector d b # liftA2 :: (a -> b -> c) -> Vector d a -> Vector d b -> Vector d c # (>) :: Vector d a -> Vector d b -> Vector d b # (<*) :: Vector d a -> Vector d b -> Vector d a #
Arity d => Foldable (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods fold :: Monoid m => Vector d m -> m # foldMap :: Monoid m => (a -> m) -> Vector d a -> m # foldMap' :: Monoid m => (a -> m) -> Vector d a -> m # foldr :: (a -> b -> b) -> b -> Vector d a -> b # foldr' :: (a -> b -> b) -> b -> Vector d a -> b # foldl :: (b -> a -> b) -> b -> Vector d a -> b # foldl' :: (b -> a -> b) -> b -> Vector d a -> b # foldr1 :: (a -> a -> a) -> Vector d a -> a # foldl1 :: (a -> a -> a) -> Vector d a -> a # toList :: Vector d a -> [a] # null :: Vector d a -> Bool # length :: Vector d a -> Int # elem :: Eq a => a -> Vector d a -> Bool # maximum :: Ord a => Vector d a -> a # minimum :: Ord a => Vector d a -> a # sum :: Num a => Vector d a -> a # product :: Num a => Vector d a -> a #
Arity d => Traversable (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods traverse :: Applicative f => (a -> f b) -> Vector d a -> f (Vector d b) # sequenceA :: Applicative f => Vector d (f a) -> f (Vector d a) # mapM :: Monad m => (a -> m b) -> Vector d a -> m (Vector d b) # sequence :: Monad m => Vector d (m a) -> m (Vector d a) #
Arity d => Arbitrary1 (Vector d) Source #
Instance details Defined in Data.Geometry.Vector Methods liftArbitrary :: Gen a -> Gen (Vector d a) # liftShrink :: (a -> [a]) -> Vector d a -> [Vector d a] #
Arity d => Eq1 (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods liftEq :: (a -> b -> Bool) -> Vector d a -> Vector d b -> Bool #
Arity d => Read1 (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Vector d a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Vector d a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Vector d a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Vector d a] #
Arity d => Show1 (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Vector d a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Vector d a] -> ShowS #
Arity d => Affine (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Associated Types type Diff (Vector d) :: Type -> Type # Methods (.-.) :: Num a => Vector d a -> Vector d a -> Diff (Vector d) a # (.+^) :: Num a => Vector d a -> Diff (Vector d) a -> Vector d a # (.-^) :: Num a => Vector d a -> Diff (Vector d) a -> Vector d a #
Arity d => Metric (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods dot :: Num a => Vector d a -> Vector d a -> a # quadrance :: Num a => Vector d a -> a # qd :: Num a => Vector d a -> Vector d a -> a # distance :: Floating a => Vector d a -> Vector d a -> a # norm :: Floating a => Vector d a -> a # signorm :: Floating a => Vector d a -> Vector d a #
Arity d => Additive (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods zero :: Num a => Vector d a # (^+^) :: Num a => Vector d a -> Vector d a -> Vector d a # (^-^) :: Num a => Vector d a -> Vector d a -> Vector d a # lerp :: Num a => a -> Vector d a -> Vector d a -> Vector d a # liftU2 :: (a -> a -> a) -> Vector d a -> Vector d a -> Vector d a # liftI2 :: (a -> b -> c) -> Vector d a -> Vector d b -> Vector d c #
Arity d => Vector (Vector d) r Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods construct :: Fun (Peano (Dim (Vector d))) r (Vector d r) # inspect :: Vector d r -> Fun (Peano (Dim (Vector d))) r b -> b # basicIndex :: Vector d r -> Int -> r #
(Eq r, Arity d) => Eq (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods (==) :: Vector d r -> Vector d r -> Bool # (/=) :: Vector d r -> Vector d r -> Bool #
(Ord r, Arity d) => Ord (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods compare :: Vector d r -> Vector d r -> Ordering # (<) :: Vector d r -> Vector d r -> Bool # (<=) :: Vector d r -> Vector d r -> Bool # (>) :: Vector d r -> Vector d r -> Bool # (>=) :: Vector d r -> Vector d r -> Bool # max :: Vector d r -> Vector d r -> Vector d r # min :: Vector d r -> Vector d r -> Vector d r #
(Read r, Arity d) => Read (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods readsPrec :: Int -> ReadS (Vector d r) # readList :: ReadS [Vector d r] # readPrec :: ReadPrec (Vector d r) # readListPrec :: ReadPrec [Vector d r] #
(Show r, Arity d) => Show (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods showsPrec :: Int -> Vector d r -> ShowS # show :: Vector d r -> String # showList :: [Vector d r] -> ShowS #
(Random r, Arity d) => Random (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector Methods randomR :: RandomGen g => (Vector d r, Vector d r) -> g -> (Vector d r, g) # random :: RandomGen g => g -> (Vector d r, g) # randomRs :: RandomGen g => (Vector d r, Vector d r) -> g -> [Vector d r] # randoms :: RandomGen g => g -> [Vector d r] #
(Arbitrary r, Arity d) => Arbitrary (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector Methods arbitrary :: Gen (Vector d r) # shrink :: Vector d r -> [Vector d r] #
(Arity d, Hashable r) => Hashable (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods hashWithSalt :: Int -> Vector d r -> Int # hash :: Vector d r -> Int #
(ToJSON r, Arity d) => ToJSON (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods toJSON :: Vector d r -> Value # toEncoding :: Vector d r -> Encoding # toJSONList :: [Vector d r] -> Value # toEncodingList :: [Vector d r] -> Encoding #
(FromJSON r, Arity d) => FromJSON (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods parseJSON :: Value -> Parser (Vector d r) # parseJSONList :: Value -> Parser [Vector d r] #
(NFData r, Arity d) => NFData (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods rnf :: Vector d r -> () #
Arity d => Ixed (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily Methods ix :: Index (Vector d r) -> Traversal' (Vector d r) (IxValue (Vector d r)) #
(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Vector d r) Source #
Instance details Defined in Data.Geometry.Transformation Methods transformBy :: Transformation (Dimension (Vector d r)) (NumType (Vector d r)) -> Vector d r -> Vector d r Source #
type Dim (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily type Dim (Vector d) = FromPeano (Peano d)
type Diff (Vector d) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily type Diff (Vector d) = Vector d
type Index (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily type Index (Vector d r) = Int
type IxValue (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily type IxValue (Vector d r) = r
type NumType (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector type NumType (Vector d r) = r
type Dimension (Vector d r) Source #
Instance details Defined in Data.Geometry.Vector type Dimension (Vector d r) = d

unV :: Iso (Vector d r) (Vector d s) (VectorFamily (Peano d) r) (VectorFamily (Peano d) s) Source #

Vectors are isomorphic to a definition determined by VectorFamily.

class (ImplicitArity (Peano d), KnownNat d) => Arity d Source #

Instances

Instances details

(ImplicitArity (Peano d), KnownNat d) => Arity d Source #
Instance details Defined in Data.Geometry.Vector.VectorFamily

Convenience "constructors"

pattern Vector :: VectorFamilyF (Peano d) r -> Vector d r Source #

Constant sized vector with d elements.

pattern Vector1 :: r -> Vector 1 r Source #

Constant sized vector with 1 element.

pattern Vector2 :: r -> r -> Vector 2 r Source #

Constant sized vector with 2 elements.

pattern Vector3 :: r -> r -> r -> Vector 3 r Source #

Constant sized vector with 3 elements.

pattern Vector4 :: r -> r -> r -> r -> Vector 4 r Source #

Constant sized vector with 4 elements.

vectorFromList :: Arity d => [r] -> Maybe (Vector d r) Source #

$ O(n) $ Convert from a list to a non-empty vector.

vectorFromListUnsafe :: Arity d => [r] -> Vector d r Source #

$ O(n) $ Convert from a list to a non-empty vector.

destruct :: (Arity d, Arity (d + 1)) => Vector (d + 1) r -> (r, Vector d r) Source #

$ O(n) $ Pop the first element off a vector.

head :: (Arity d, 1 <= d) => Vector d r -> r Source #

$ O(1) $ First element. Since arity is at least 1, this function is total.

Indexing vectors

element :: forall proxy i d r. (Arity d, KnownNat i, (i + 1) <= d) => proxy i -> Lens' (Vector d r) r Source #

Lens into the i th element

element' :: forall d r. Arity d => Int -> Traversal' (Vector d r) r Source #

Similar to element above. Except that we don't have a static guarantee that the index is in bounds. Hence, we can only return a Traversal

Snoccing and consindg

cons :: (Arity d, Arity (d + 1)) => r -> Vector d r -> Vector (d + 1) r Source #

$ O(n) $ Prepend an element.

snoc :: (Arity (d + 1), Arity d) => Vector d r -> r -> Vector (d + 1) r Source #

Add an element at the back of the vector

init :: (Arity d, Arity (d + 1)) => Vector (d + 1) r -> Vector d r Source #

Get a vector of the first d - 1 elements.

last :: forall d r. (KnownNat d, Arity (d + 1)) => Vector (d + 1) r -> r Source #

$ O(1) $ Last element. Since the vector is non-empty, runtime bounds checks are bypassed.

prefix :: forall i d r. (Arity d, Arity i, i <= d) => Vector d r -> Vector i r Source #

Get a prefix of i elements of a vector

Specific on 3-dimensional vectors

cross :: Num r => Vector 3 r -> Vector 3 r -> Vector 3 r Source #

Cross product of two three-dimensional vectors