Safe Haskell	Safe-Inferred
Language	Haskell2010

SpatialMathT

Synopsis

class Rotation p a | p -> a where
- compose :: Rot f1 f2 p -> Rot f2 f3 p -> Rot f1 f3 p
- rot :: Rot f1 f2 p -> V3T f1 a -> V3T f2 a
- rot' :: Rot f1 f2 p -> V3T f2 a -> V3T f1 a
- toDcm :: Rot f1 f2 p -> Rot f1 f2 (M33 a)
- transpose :: Rot f1 f2 p -> Rot f2 f1 p
newtype Rot f1 f2 r = Rot {
- unR :: r
}
newtype V3T f a = V3T {
- unV :: V3 a
}
class R1 (t :: Type -> Type) where
- _x :: Lens' (t a) a
class R1 t => R2 (t :: Type -> Type) where
- _y :: Lens' (t a) a
- _xy :: Lens' (t a) (V2 a)
class R2 t => R3 (t :: Type -> Type) where
- _z :: Lens' (t a) a
- _xyz :: Lens' (t a) (V3 a)
type M33T f1 f2 a = V3T f1 (V3T f2 a)
cross :: Num a => V3T f a -> V3T f a -> V3T f a
orthonormalize :: Floating a => Rot f1 f2 (M33 a) -> Rot f1 f2 (M33 a)

Documentation

class Rotation p a | p -> a where Source #

Methods

compose :: Rot f1 f2 p -> Rot f2 f3 p -> Rot f1 f3 p Source #

rot :: Rot f1 f2 p -> V3T f1 a -> V3T f2 a Source #

rot' :: Rot f1 f2 p -> V3T f2 a -> V3T f1 a Source #

toDcm :: Rot f1 f2 p -> Rot f1 f2 (M33 a) Source #

transpose :: Rot f1 f2 p -> Rot f2 f1 p Source #

Instances

Instances details

Num a => Rotation (M33 a) a Source #
Instance details Defined in SpatialMathT Methods compose :: Rot f1 f2 (M33 a) -> Rot f2 f3 (M33 a) -> Rot f1 f3 (M33 a) Source # rot :: Rot f1 f2 (M33 a) -> V3T f1 a -> V3T f2 a Source # rot' :: Rot f1 f2 (M33 a) -> V3T f2 a -> V3T f1 a Source # toDcm :: Rot f1 f2 (M33 a) -> Rot f1 f2 (M33 a) Source # transpose :: Rot f1 f2 (M33 a) -> Rot f2 f1 (M33 a) Source #
Num a => Rotation (Quaternion a) a Source #
Instance details Defined in SpatialMathT Methods compose :: Rot f1 f2 (Quaternion a) -> Rot f2 f3 (Quaternion a) -> Rot f1 f3 (Quaternion a) Source # rot :: Rot f1 f2 (Quaternion a) -> V3T f1 a -> V3T f2 a Source # rot' :: Rot f1 f2 (Quaternion a) -> V3T f2 a -> V3T f1 a Source # toDcm :: Rot f1 f2 (Quaternion a) -> Rot f1 f2 (M33 a) Source # transpose :: Rot f1 f2 (Quaternion a) -> Rot f2 f1 (Quaternion a) Source #

newtype Rot f1 f2 r Source #

Constructors

Rot
Fields unR :: r

Instances

Instances details

Generic1 (Rot f1 f2 :: Type -> Type) Source #
Instance details Defined in SpatialMathT Associated Types type Rep1 (Rot f1 f2) :: k -> Type # Methods from1 :: forall (a :: k). Rot f1 f2 a -> Rep1 (Rot f1 f2) a # to1 :: forall (a :: k). Rep1 (Rot f1 f2) a -> Rot f1 f2 a #
Foldable (Rot f1 f2) Source #
Instance details Defined in SpatialMathT Methods fold :: Monoid m => Rot f1 f2 m -> m # foldMap :: Monoid m => (a -> m) -> Rot f1 f2 a -> m # foldMap' :: Monoid m => (a -> m) -> Rot f1 f2 a -> m # foldr :: (a -> b -> b) -> b -> Rot f1 f2 a -> b # foldr' :: (a -> b -> b) -> b -> Rot f1 f2 a -> b # foldl :: (b -> a -> b) -> b -> Rot f1 f2 a -> b # foldl' :: (b -> a -> b) -> b -> Rot f1 f2 a -> b # foldr1 :: (a -> a -> a) -> Rot f1 f2 a -> a # foldl1 :: (a -> a -> a) -> Rot f1 f2 a -> a # toList :: Rot f1 f2 a -> [a] # null :: Rot f1 f2 a -> Bool # length :: Rot f1 f2 a -> Int # elem :: Eq a => a -> Rot f1 f2 a -> Bool # maximum :: Ord a => Rot f1 f2 a -> a # minimum :: Ord a => Rot f1 f2 a -> a # sum :: Num a => Rot f1 f2 a -> a # product :: Num a => Rot f1 f2 a -> a #
Traversable (Rot f1 f2) Source #
Instance details Defined in SpatialMathT Methods traverse :: Applicative f => (a -> f b) -> Rot f1 f2 a -> f (Rot f1 f2 b) # sequenceA :: Applicative f => Rot f1 f2 (f a) -> f (Rot f1 f2 a) # mapM :: Monad m => (a -> m b) -> Rot f1 f2 a -> m (Rot f1 f2 b) # sequence :: Monad m => Rot f1 f2 (m a) -> m (Rot f1 f2 a) #
Functor (Rot f1 f2) Source #
Instance details Defined in SpatialMathT Methods fmap :: (a -> b) -> Rot f1 f2 a -> Rot f1 f2 b # (<$) :: a -> Rot f1 f2 b -> Rot f1 f2 a #
Storable r => Storable (Rot f1 f2 r) Source #
Instance details Defined in SpatialMathT Methods sizeOf :: Rot f1 f2 r -> Int # alignment :: Rot f1 f2 r -> Int # peekElemOff :: Ptr (Rot f1 f2 r) -> Int -> IO (Rot f1 f2 r) # pokeElemOff :: Ptr (Rot f1 f2 r) -> Int -> Rot f1 f2 r -> IO () # peekByteOff :: Ptr b -> Int -> IO (Rot f1 f2 r) # pokeByteOff :: Ptr b -> Int -> Rot f1 f2 r -> IO () # peek :: Ptr (Rot f1 f2 r) -> IO (Rot f1 f2 r) # poke :: Ptr (Rot f1 f2 r) -> Rot f1 f2 r -> IO () #
Generic (Rot f1 f2 r) Source #
Instance details Defined in SpatialMathT Associated Types type Rep (Rot f1 f2 r) :: Type -> Type # Methods from :: Rot f1 f2 r -> Rep (Rot f1 f2 r) x # to :: Rep (Rot f1 f2 r) x -> Rot f1 f2 r #
Num r => Num (Rot f1 f2 r) Source #
Instance details Defined in SpatialMathT Methods (+) :: Rot f1 f2 r -> Rot f1 f2 r -> Rot f1 f2 r # (-) :: Rot f1 f2 r -> Rot f1 f2 r -> Rot f1 f2 r # (*) :: Rot f1 f2 r -> Rot f1 f2 r -> Rot f1 f2 r # negate :: Rot f1 f2 r -> Rot f1 f2 r # abs :: Rot f1 f2 r -> Rot f1 f2 r # signum :: Rot f1 f2 r -> Rot f1 f2 r # fromInteger :: Integer -> Rot f1 f2 r #
Fractional r => Fractional (Rot f1 f2 r) Source #
Instance details Defined in SpatialMathT Methods (/) :: Rot f1 f2 r -> Rot f1 f2 r -> Rot f1 f2 r # recip :: Rot f1 f2 r -> Rot f1 f2 r # fromRational :: Rational -> Rot f1 f2 r #
Show r => Show (Rot f1 f2 r) Source #
Instance details Defined in SpatialMathT Methods showsPrec :: Int -> Rot f1 f2 r -> ShowS # show :: Rot f1 f2 r -> String # showList :: [Rot f1 f2 r] -> ShowS #
Binary r => Binary (Rot f1 f2 r) Source #
Instance details Defined in SpatialMathT Methods put :: Rot f1 f2 r -> Put # get :: Get (Rot f1 f2 r) # putList :: [Rot f1 f2 r] -> Put #
Serialize r => Serialize (Rot f1 f2 r) Source #
Instance details Defined in SpatialMathT Methods put :: Putter (Rot f1 f2 r) # get :: Get (Rot f1 f2 r) #
Eq r => Eq (Rot f1 f2 r) Source #
Instance details Defined in SpatialMathT Methods (==) :: Rot f1 f2 r -> Rot f1 f2 r -> Bool # (/=) :: Rot f1 f2 r -> Rot f1 f2 r -> Bool #
Ord r => Ord (Rot f1 f2 r) Source #
Instance details Defined in SpatialMathT Methods compare :: Rot f1 f2 r -> Rot f1 f2 r -> Ordering # (<) :: Rot f1 f2 r -> Rot f1 f2 r -> Bool # (<=) :: Rot f1 f2 r -> Rot f1 f2 r -> Bool # (>) :: Rot f1 f2 r -> Rot f1 f2 r -> Bool # (>=) :: Rot f1 f2 r -> Rot f1 f2 r -> Bool # max :: Rot f1 f2 r -> Rot f1 f2 r -> Rot f1 f2 r # min :: Rot f1 f2 r -> Rot f1 f2 r -> Rot f1 f2 r #
type Rep1 (Rot f1 f2 :: Type -> Type) Source #
Instance details Defined in SpatialMathT type Rep1 (Rot f1 f2 :: Type -> Type) = D1 ('MetaData "Rot" "SpatialMathT" "SpatialMath-0.2.7.0-GZqIaMCJq0F5jaw9AzNN8p" 'True) (C1 ('MetaCons "Rot" 'PrefixI 'True) (S1 ('MetaSel ('Just "unR") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Rot f1 f2 r) Source #
Instance details Defined in SpatialMathT type Rep (Rot f1 f2 r) = D1 ('MetaData "Rot" "SpatialMathT" "SpatialMath-0.2.7.0-GZqIaMCJq0F5jaw9AzNN8p" 'True) (C1 ('MetaCons "Rot" 'PrefixI 'True) (S1 ('MetaSel ('Just "unR") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 r)))

newtype V3T f a Source #

Constructors

V3T
Fields unV :: V3 a

Instances

Instances details

Generic1 (V3T f :: Type -> TYPE LiftedRep) Source #
Instance details Defined in SpatialMathT Associated Types type Rep1 (V3T f) :: k -> Type # Methods from1 :: forall (a :: k). V3T f a -> Rep1 (V3T f) a # to1 :: forall (a :: k). Rep1 (V3T f) a -> V3T f a #
Foldable (V3T f) Source #
Instance details Defined in SpatialMathT Methods fold :: Monoid m => V3T f m -> m # foldMap :: Monoid m => (a -> m) -> V3T f a -> m # foldMap' :: Monoid m => (a -> m) -> V3T f a -> m # foldr :: (a -> b -> b) -> b -> V3T f a -> b # foldr' :: (a -> b -> b) -> b -> V3T f a -> b # foldl :: (b -> a -> b) -> b -> V3T f a -> b # foldl' :: (b -> a -> b) -> b -> V3T f a -> b # foldr1 :: (a -> a -> a) -> V3T f a -> a # foldl1 :: (a -> a -> a) -> V3T f a -> a # toList :: V3T f a -> [a] # null :: V3T f a -> Bool # length :: V3T f a -> Int # elem :: Eq a => a -> V3T f a -> Bool # maximum :: Ord a => V3T f a -> a # minimum :: Ord a => V3T f a -> a # sum :: Num a => V3T f a -> a # product :: Num a => V3T f a -> a #
Traversable (V3T f) Source #
Instance details Defined in SpatialMathT Methods traverse :: Applicative f0 => (a -> f0 b) -> V3T f a -> f0 (V3T f b) # sequenceA :: Applicative f0 => V3T f (f0 a) -> f0 (V3T f a) # mapM :: Monad m => (a -> m b) -> V3T f a -> m (V3T f b) # sequence :: Monad m => V3T f (m a) -> m (V3T f a) #
Applicative (V3T f) Source #
Instance details Defined in SpatialMathT Methods pure :: a -> V3T f a # (<>) :: V3T f (a -> b) -> V3T f a -> V3T f b # liftA2 :: (a -> b -> c) -> V3T f a -> V3T f b -> V3T f c # (>) :: V3T f a -> V3T f b -> V3T f b # (<*) :: V3T f a -> V3T f b -> V3T f a #
Functor (V3T f) Source #
Instance details Defined in SpatialMathT Methods fmap :: (a -> b) -> V3T f a -> V3T f b # (<$) :: a -> V3T f b -> V3T f a #
Metric (V3T f) Source #
Instance details Defined in SpatialMathT Methods dot :: Num a => V3T f a -> V3T f a -> a # quadrance :: Num a => V3T f a -> a # qd :: Num a => V3T f a -> V3T f a -> a # distance :: Floating a => V3T f a -> V3T f a -> a # norm :: Floating a => V3T f a -> a # signorm :: Floating a => V3T f a -> V3T f a #
R1 (V3T f) Source #
Instance details Defined in SpatialMathT Methods _x :: Lens' (V3T f a) a #
R2 (V3T f) Source #
Instance details Defined in SpatialMathT Methods _y :: Lens' (V3T f a) a # _xy :: Lens' (V3T f a) (V2 a) #
R3 (V3T f) Source #
Instance details Defined in SpatialMathT Methods _z :: Lens' (V3T f a) a # _xyz :: Lens' (V3T f a) (V3 a) #
Additive (V3T f) Source #
Instance details Defined in SpatialMathT Methods zero :: Num a => V3T f a # (^+^) :: Num a => V3T f a -> V3T f a -> V3T f a # (^-^) :: Num a => V3T f a -> V3T f a -> V3T f a # lerp :: Num a => a -> V3T f a -> V3T f a -> V3T f a # liftU2 :: (a -> a -> a) -> V3T f a -> V3T f a -> V3T f a # liftI2 :: (a -> b -> c) -> V3T f a -> V3T f b -> V3T f c #
Storable a => Storable (V3T f a) Source #
Instance details Defined in SpatialMathT Methods sizeOf :: V3T f a -> Int # alignment :: V3T f a -> Int # peekElemOff :: Ptr (V3T f a) -> Int -> IO (V3T f a) # pokeElemOff :: Ptr (V3T f a) -> Int -> V3T f a -> IO () # peekByteOff :: Ptr b -> Int -> IO (V3T f a) # pokeByteOff :: Ptr b -> Int -> V3T f a -> IO () # peek :: Ptr (V3T f a) -> IO (V3T f a) # poke :: Ptr (V3T f a) -> V3T f a -> IO () #
Generic (V3T f a) Source #
Instance details Defined in SpatialMathT Associated Types type Rep (V3T f a) :: Type -> Type # Methods from :: V3T f a -> Rep (V3T f a) x # to :: Rep (V3T f a) x -> V3T f a #
Num a => Num (V3T f a) Source #
Instance details Defined in SpatialMathT Methods (+) :: V3T f a -> V3T f a -> V3T f a # (-) :: V3T f a -> V3T f a -> V3T f a # (*) :: V3T f a -> V3T f a -> V3T f a # negate :: V3T f a -> V3T f a # abs :: V3T f a -> V3T f a # signum :: V3T f a -> V3T f a # fromInteger :: Integer -> V3T f a #
Fractional a => Fractional (V3T f a) Source #
Instance details Defined in SpatialMathT Methods (/) :: V3T f a -> V3T f a -> V3T f a # recip :: V3T f a -> V3T f a # fromRational :: Rational -> V3T f a #
Show a => Show (V3T f a) Source #
Instance details Defined in SpatialMathT Methods showsPrec :: Int -> V3T f a -> ShowS # show :: V3T f a -> String # showList :: [V3T f a] -> ShowS #
Binary a => Binary (V3T f a) Source #
Instance details Defined in SpatialMathT Methods put :: V3T f a -> Put # get :: Get (V3T f a) # putList :: [V3T f a] -> Put #
Serialize a => Serialize (V3T f a) Source #
Instance details Defined in SpatialMathT Methods put :: Putter (V3T f a) # get :: Get (V3T f a) #
Eq a => Eq (V3T f a) Source #
Instance details Defined in SpatialMathT Methods (==) :: V3T f a -> V3T f a -> Bool # (/=) :: V3T f a -> V3T f a -> Bool #
Ord a => Ord (V3T f a) Source #
Instance details Defined in SpatialMathT Methods compare :: V3T f a -> V3T f a -> Ordering # (<) :: V3T f a -> V3T f a -> Bool # (<=) :: V3T f a -> V3T f a -> Bool # (>) :: V3T f a -> V3T f a -> Bool # (>=) :: V3T f a -> V3T f a -> Bool # max :: V3T f a -> V3T f a -> V3T f a # min :: V3T f a -> V3T f a -> V3T f a #
type Rep1 (V3T f :: Type -> TYPE LiftedRep) Source #
Instance details Defined in SpatialMathT type Rep1 (V3T f :: Type -> TYPE LiftedRep) = D1 ('MetaData "V3T" "SpatialMathT" "SpatialMath-0.2.7.0-GZqIaMCJq0F5jaw9AzNN8p" 'True) (C1 ('MetaCons "V3T" 'PrefixI 'True) (S1 ('MetaSel ('Just "unV") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 V3)))
type Rep (V3T f a) Source #
Instance details Defined in SpatialMathT type Rep (V3T f a) = D1 ('MetaData "V3T" "SpatialMathT" "SpatialMath-0.2.7.0-GZqIaMCJq0F5jaw9AzNN8p" 'True) (C1 ('MetaCons "V3T" 'PrefixI 'True) (S1 ('MetaSel ('Just "unV") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (V3 a))))

class R1 (t :: Type -> Type) where #

A space that has at least 1 basis vector _x.

Methods

_x :: Lens' (t a) a #

>>> V1 2 ^._x
2

>>> V1 2 & _x .~ 3
V1 3

Instances

Instances details

R1 Identity
Instance details Defined in Linear.V1 Methods _x :: Lens' (Identity a) a #
R1 Quaternion
Instance details Defined in Linear.Quaternion Methods _x :: Lens' (Quaternion a) a #
R1 V1
Instance details Defined in Linear.V1 Methods _x :: Lens' (V1 a) a #
R1 V2
Instance details Defined in Linear.V2 Methods _x :: Lens' (V2 a) a #
R1 V3
Instance details Defined in Linear.V3 Methods _x :: Lens' (V3 a) a #
R1 V4
Instance details Defined in Linear.V4 Methods _x :: Lens' (V4 a) a #
R1 (V3T f) Source #
Instance details Defined in SpatialMathT Methods _x :: Lens' (V3T f a) a #

class R1 t => R2 (t :: Type -> Type) where #

A space that distinguishes 2 orthogonal basis vectors _x and _y, but may have more.

Minimal complete definition

_xy

Methods

_y :: Lens' (t a) a #

>>> V2 1 2 ^._y
2

>>> V2 1 2 & _y .~ 3
V2 1 3

_xy :: Lens' (t a) (V2 a) #

Instances

Instances details

R2 Quaternion
Instance details Defined in Linear.Quaternion Methods _y :: Lens' (Quaternion a) a # _xy :: Lens' (Quaternion a) (V2 a) #
R2 V2
Instance details Defined in Linear.V2 Methods _y :: Lens' (V2 a) a # _xy :: Lens' (V2 a) (V2 a) #
R2 V3
Instance details Defined in Linear.V3 Methods _y :: Lens' (V3 a) a # _xy :: Lens' (V3 a) (V2 a) #
R2 V4
Instance details Defined in Linear.V4 Methods _y :: Lens' (V4 a) a # _xy :: Lens' (V4 a) (V2 a) #
R2 (V3T f) Source #
Instance details Defined in SpatialMathT Methods _y :: Lens' (V3T f a) a # _xy :: Lens' (V3T f a) (V2 a) #

class R2 t => R3 (t :: Type -> Type) where #

A space that distinguishes 3 orthogonal basis vectors: _x, _y, and _z. (It may have more)

Methods

_z :: Lens' (t a) a #

>>> V3 1 2 3 ^. _z
3

_xyz :: Lens' (t a) (V3 a) #

Instances

Instances details

R3 Quaternion
Instance details Defined in Linear.Quaternion Methods _z :: Lens' (Quaternion a) a # _xyz :: Lens' (Quaternion a) (V3 a) #
R3 V3
Instance details Defined in Linear.V3 Methods _z :: Lens' (V3 a) a # _xyz :: Lens' (V3 a) (V3 a) #
R3 V4
Instance details Defined in Linear.V4 Methods _z :: Lens' (V4 a) a # _xyz :: Lens' (V4 a) (V3 a) #
R3 (V3T f) Source #
Instance details Defined in SpatialMathT Methods _z :: Lens' (V3T f a) a # _xyz :: Lens' (V3T f a) (V3 a) #

type M33T f1 f2 a = V3T f1 (V3T f2 a) Source #

cross :: Num a => V3T f a -> V3T f a -> V3T f a Source #

orthonormalize :: Floating a => Rot f1 f2 (M33 a) -> Rot f1 f2 (M33 a) Source #