Data.Geometry.Vector.VectorFixed

Documentation

data C (n :: Nat)

A proxy which can be used for the coordinates.

Constructors

C

Instances

Eq (C n)

Defined in Data.Geometry.Vector.VectorFixed

Methods

(==) :: C n -> C n -> Bool

(/=) :: C n -> C n -> Bool

Ord (C n)

Defined in Data.Geometry.Vector.VectorFixed

Methods

compare :: C n -> C n -> Ordering

(<) :: C n -> C n -> Bool

(<=) :: C n -> C n -> Bool

(>) :: C n -> C n -> Bool

(>=) :: C n -> C n -> Bool

max :: C n -> C n -> C n

min :: C n -> C n -> C n

Read (C n)

Defined in Data.Geometry.Vector.VectorFixed

Methods

readsPrec :: Int -> ReadS (C n)

readList :: ReadS [C n]

readPrec :: ReadPrec (C n)

readListPrec :: ReadPrec [C n]

Show (C n)

Defined in Data.Geometry.Vector.VectorFixed

Methods

showsPrec :: Int -> C n -> ShowS

show :: C n -> String

showList :: [C n] -> ShowS

d dimensional Vectors

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

Datatype representing d dimensional vectors. Our implementation wraps the implementation provided by fixed-vector.

Constructors

Vector

Fields

• _unV :: Vec d r

Instances

Arity d => Functor (Vector d)

Defined in Data.Geometry.Vector.VectorFixed

Methods

fmap :: (a -> b) -> Vector d a -> Vector d b

(<$) :: a -> Vector d b -> Vector d a

Arity d => Applicative (Vector d)

Defined in Data.Geometry.Vector.VectorFixed

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)

Defined in Data.Geometry.Vector.VectorFixed

Methods

fold :: Monoid m => Vector d m -> 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)

Defined in Data.Geometry.Vector.VectorFixed

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 => Affine (Vector d)

Defined in Data.Geometry.Vector.VectorFixed

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)

Defined in Data.Geometry.Vector.VectorFixed

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)

Defined in Data.Geometry.Vector.VectorFixed

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

Defined in Data.Geometry.Vector.VectorFixed

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)

Defined in Data.Geometry.Vector.VectorFixed

Methods

(==) :: Vector d r -> Vector d r -> Bool

(/=) :: Vector d r -> Vector d r -> Bool

(Ord r, Arity d) => Ord (Vector d r)

Defined in Data.Geometry.Vector.VectorFixed

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

(Show r, Arity d) => Show (Vector d r)

Defined in Data.Geometry.Vector.VectorFixed

Methods

showsPrec :: Int -> Vector d r -> ShowS

show :: Vector d r -> String

showList :: [Vector d r] -> ShowS

Generic (Vector d r)

Defined in Data.Geometry.Vector.VectorFixed

Associated Types

type Rep (Vector d r) :: Type -> Type

Methods

from :: Vector d r -> Rep (Vector d r) x

to :: Rep (Vector d r) x -> Vector d r

(ToJSON r, Arity d) => ToJSON (Vector d r)

Defined in Data.Geometry.Vector.VectorFixed

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, KnownNat d) => FromJSON (Vector d r)

Defined in Data.Geometry.Vector.VectorFixed

Methods

parseJSON :: Value -> Parser (Vector d r)

parseJSONList :: Value -> Parser [Vector d r]

(Arity d, NFData r) => NFData (Vector d r)

Defined in Data.Geometry.Vector.VectorFixed

Methods

rnf :: Vector d r -> ()

type Dim (Vector d)

Defined in Data.Geometry.Vector.VectorFixed

type Dim (Vector d) = d

type Diff (Vector d)

Defined in Data.Geometry.Vector.VectorFixed

type Diff (Vector d) = Vector d

type Rep (Vector d r)

Defined in Data.Geometry.Vector.VectorFixed

type Rep (Vector d r) = D1 (MetaData "Vector" "Data.Geometry.Vector.VectorFixed" "hgeometry-0.10.0.0-58coE6gW4i4HcLJr7kmg1f" True) (C1 (MetaCons "Vector" PrefixI True) (S1 (MetaSel (Just "_unV") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Vec d r))))

unV :: Lens' (Vector d r) (Vec d r)

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

Lens into the i th element

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

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

vectorFromList :: Arity d => [a] -> Maybe (Vector d a)

vectorFromListUnsafe :: Arity d => [a] -> Vector d a

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

Get the head and tail of a vector

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

Cross product of two three-dimensional vectors

toV2 :: Vector 2 a -> V2 a

Vonversion to a Linear.V2

toV3 :: Vector 3 a -> V3 a

Conversion to a Linear.V3

fromV3 :: V3 a -> Vector 3 a

Conversion from a Linear.V3

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

Add an element at the back of the vector

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

Get a vector of the first d - 1 elements.

last :: forall d r. (Arity 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

Get a prefix of i elements of a vector

Functions specific to two and three dimensional vectors.

v2 :: r -> r -> Vector 2 r

Construct a 2 dimensional vector

v3 :: r -> r -> r -> Vector 3 r

Construct a 3 dimensional vector

_unV2 :: Vector 2 r -> (r, r)

Destruct a 2 dim vector into a pair

_unV3 :: Vector 3 r -> (r, r, r)

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

Pattern synonym for two and three dim vectors

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

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