Data.Algebra.Quaternion

Documentation

type QuatF = Quat Float

type QuatD = Quat Double

type QuatR = Quat Rational

type QuatM = Quat Micro

type QuatN = Quat Nano

type QuatP = Quat Pico

data Quat a

Constructors

Quat !a !(V3 a)

Instances

Functor Quat

Defined in Data.Algebra.Quaternion

Methods

fmap :: (a -> b) -> Quat a -> Quat b

(<$) :: a -> Quat b -> Quat a

Foldable Quat

Defined in Data.Algebra.Quaternion

Methods

fold :: Monoid m => Quat m -> m

foldMap :: Monoid m => (a -> m) -> Quat a -> m

foldr :: (a -> b -> b) -> b -> Quat a -> b

foldr' :: (a -> b -> b) -> b -> Quat a -> b

foldl :: (b -> a -> b) -> b -> Quat a -> b

foldl' :: (b -> a -> b) -> b -> Quat a -> b

foldr1 :: (a -> a -> a) -> Quat a -> a

foldl1 :: (a -> a -> a) -> Quat a -> a

toList :: Quat a -> [a]

null :: Quat a -> Bool

length :: Quat a -> Int

elem :: Eq a => a -> Quat a -> Bool

maximum :: Ord a => Quat a -> a

minimum :: Ord a => Quat a -> a

sum :: Num a => Quat a -> a

product :: Num a => Quat a -> a

Distributive Quat

Defined in Data.Algebra.Quaternion

Methods

distribute :: Functor f => f (Quat a) -> Quat (f a)

collect :: Functor f => (a -> Quat b) -> f a -> Quat (f b)

distributeM :: Monad m => m (Quat a) -> Quat (m a)

collectM :: Monad m => (a -> Quat b) -> m a -> Quat (m b)

Representable Quat

Defined in Data.Algebra.Quaternion

Associated Types

type Rep Quat :: Type

Methods

tabulate :: (Rep Quat -> a) -> Quat a

index :: Quat a -> Rep Quat -> a

Show1 Quat

Defined in Data.Algebra.Quaternion

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Quat a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Quat a] -> ShowS

Foldable1 Quat

Defined in Data.Algebra.Quaternion

Methods

fold1 :: Semigroup m => Quat m -> m

foldMap1 :: Semigroup m => (a -> m) -> Quat a -> m

toNonEmpty :: Quat a -> NonEmpty a

Semiring a => Bisemimodule a a (Quat a)

Defined in Data.Algebra.Quaternion

Methods

discale :: a -> a -> Quat a -> Quat a

Semiring a => RightSemimodule a (Quat a)

Defined in Data.Algebra.Quaternion

Methods

rscale :: a -> Quat a -> Quat a

Semiring a => LeftSemimodule a (Quat a)

Defined in Data.Algebra.Quaternion

Methods

lscale :: a -> Quat a -> Quat a

Eq a => Eq (Quat a)

Defined in Data.Algebra.Quaternion

Methods

(==) :: Quat a -> Quat a -> Bool

(/=) :: Quat a -> Quat a -> Bool

Ord a => Ord (Quat a)

Defined in Data.Algebra.Quaternion

Methods

compare :: Quat a -> Quat a -> Ordering

(<) :: Quat a -> Quat a -> Bool

(<=) :: Quat a -> Quat a -> Bool

(>) :: Quat a -> Quat a -> Bool

(>=) :: Quat a -> Quat a -> Bool

max :: Quat a -> Quat a -> Quat a

min :: Quat a -> Quat a -> Quat a

Show a => Show (Quat a)

Defined in Data.Algebra.Quaternion

Methods

showsPrec :: Int -> Quat a -> ShowS

show :: Quat a -> String

showList :: [Quat a] -> ShowS

Generic (Quat a)

Defined in Data.Algebra.Quaternion

Associated Types

type Rep (Quat a) :: Type -> Type

Methods

from :: Quat a -> Rep (Quat a) x

to :: Rep (Quat a) x -> Quat a

Real a => Semigroup (Multiplicative (Quat a))

Defined in Data.Algebra.Quaternion

Methods

(<>) :: Multiplicative (Quat a) -> Multiplicative (Quat a) -> Multiplicative (Quat a)

sconcat :: NonEmpty (Multiplicative (Quat a)) -> Multiplicative (Quat a)

stimes :: Integral b => b -> Multiplicative (Quat a) -> Multiplicative (Quat a)

(Additive - Semigroup) a => Semigroup (Additive (Quat a))

Defined in Data.Algebra.Quaternion

Methods

(<>) :: Additive (Quat a) -> Additive (Quat a) -> Additive (Quat a)

sconcat :: NonEmpty (Additive (Quat a)) -> Additive (Quat a)

stimes :: Integral b => b -> Additive (Quat a) -> Additive (Quat a)

(Additive - Semigroup) a => Semigroup (Quat a)

Defined in Data.Algebra.Quaternion

Methods

(<>) :: Quat a -> Quat a -> Quat a

sconcat :: NonEmpty (Quat a) -> Quat a

stimes :: Integral b => b -> Quat a -> Quat a

Real a => Monoid (Multiplicative (Quat a))

Defined in Data.Algebra.Quaternion

Methods

mempty :: Multiplicative (Quat a)

mappend :: Multiplicative (Quat a) -> Multiplicative (Quat a) -> Multiplicative (Quat a)

mconcat :: [Multiplicative (Quat a)] -> Multiplicative (Quat a)

(Additive - Monoid) a => Monoid (Additive (Quat a))

Defined in Data.Algebra.Quaternion

Methods

mempty :: Additive (Quat a)

mappend :: Additive (Quat a) -> Additive (Quat a) -> Additive (Quat a)

mconcat :: [Additive (Quat a)] -> Additive (Quat a)

(Additive - Monoid) a => Monoid (Quat a)

Defined in Data.Algebra.Quaternion

Methods

mempty :: Quat a

mappend :: Quat a -> Quat a -> Quat a

mconcat :: [Quat a] -> Quat a

(Additive - Group) a => Group (Additive (Quat a))

Defined in Data.Algebra.Quaternion

Methods

inv :: Additive (Quat a) -> Additive (Quat a)

greplicate :: Integer -> Additive (Quat a) -> Additive (Quat a)

(Additive - Group) a => Group (Quat a)

Defined in Data.Algebra.Quaternion

Methods

inv :: Quat a -> Quat a

greplicate :: Integer -> Quat a -> Quat a

(Additive - Group) a => Loop (Additive (Quat a))

Defined in Data.Algebra.Quaternion

Methods

lempty :: Additive (Quat a)

lreplicate :: Natural -> Additive (Quat a) -> Additive (Quat a)

(Additive - Group) a => Loop (Quat a)

Defined in Data.Algebra.Quaternion

Methods

lempty :: Quat a

lreplicate :: Natural -> Quat a -> Quat a

(Additive - Group) a => Quasigroup (Additive (Quat a))

Defined in Data.Algebra.Quaternion

Methods

(//) :: Additive (Quat a) -> Additive (Quat a) -> Additive (Quat a)

(\\) :: Additive (Quat a) -> Additive (Quat a) -> Additive (Quat a)

(Additive - Group) a => Quasigroup (Quat a)

Defined in Data.Algebra.Quaternion

Methods

(//) :: Quat a -> Quat a -> Quat a

(\\) :: Quat a -> Quat a -> Quat a

(Additive - Group) a => Magma (Additive (Quat a))

Defined in Data.Algebra.Quaternion

Methods

(<<) :: Additive (Quat a) -> Additive (Quat a) -> Additive (Quat a)

(Additive - Group) a => Magma (Quat a)

Defined in Data.Algebra.Quaternion

Methods

(<<) :: Quat a -> Quat a -> Quat a

Real a => Ring (Quat a)

Defined in Data.Algebra.Quaternion

Real a => Semiring (Quat a)

Defined in Data.Algebra.Quaternion

Real a => Presemiring (Quat a)

Defined in Data.Algebra.Quaternion

Generic1 Quat

Defined in Data.Algebra.Quaternion

Associated Types

type Rep1 Quat :: k -> Type

Methods

from1 :: Quat a -> Rep1 Quat a

to1 :: Rep1 Quat a -> Quat a

type Rep Quat

Defined in Data.Algebra.Quaternion

type Rep Quat = Maybe E3

type Rep (Quat a)

Defined in Data.Algebra.Quaternion

type Rep (Quat a) = D1 (MetaData "Quat" "Data.Algebra.Quaternion" "rings-0.0.3-21Z3wlGnIMkBc1cJ09ZojY" False) (C1 (MetaCons "Quat" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) SourceUnpack SourceStrict DecidedStrict) (Rec0 (V3 a))))

type Rep1 Quat

Defined in Data.Algebra.Quaternion

type Rep1 Quat = D1 (MetaData "Quat" "Data.Algebra.Quaternion" "rings-0.0.3-21Z3wlGnIMkBc1cJ09ZojY" False) (C1 (MetaCons "Quat" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1 :*: S1 (MetaSel (Nothing :: Maybe Symbol) SourceUnpack SourceStrict DecidedStrict) (Rec1 V3)))

quat :: a -> a -> a -> a -> Quat a

Obtain a Quat from 4 base elements.

scal :: Quat a -> a

Real or scalar part of a quaternion.

vect :: Quat a -> V3 a

qu :: Semiring a => Quat a

The real quaternion.

Represents no rotation.

qu = unit

qi :: Semiring a => Quat a

The i quaternion.

Represents a \( \pi \) radian rotation about the x axis.

>>> rotate (qi :: QuatM) $ V3 1 0 0
V3 1.000000 0.000000 0.000000
>>> rotate (qi :: QuatM) $ V3 0 1 0
V3 0.000000 -1.000000 0.000000
>>> rotate (qi :: QuatM) $ V3 0 0 1
V3 0.000000 0.000000 -1.000000

>>> qi * qj
Quat 0 (V3 0 0 1)

qj :: Semiring a => Quat a

The j quaternion.

Represents a \( \pi \) radian rotation about the y axis.

>>> rotate (qj :: QuatM) $ V3 1 0 0
V3 -1.000000 0.000000 0.000000
>>> rotate (qj :: QuatM) $ V3 0 1 0
V3 0.000000 1.000000 0.000000
>>> rotate (qj :: QuatM) $ V3 0 0 1
V3 0.000000 0.000000 -1.000000

>>> qj * qk
Quat 0 (V3 1 0 0)

qk :: Semiring a => Quat a

The k quaternion.

Represents a \( \pi \) radian rotation about the z axis.

>>> rotate (qk :: QuatM) $ V3 1 0 0
V3 -1.000000 0.000000 0.000000
>>> rotate (qk :: QuatM) $ V3 0 1 0
V3 0.000000 -1.000000 0.000000
>>> rotate (qk :: QuatM) $ V3 0 0 1
V3 0.000000 0.000000 1.000000

>>> qk * qi
Quat 0 (V3 0 1 0)
>>> qi * qj * qk
Quat (-1) (V3 0 0 0)