{-# LANGUAGE DefaultSignatures #-}
{-# LANGUAGE DeriveTraversable #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE RebindableSyntax #-}
{-# LANGUAGE TypeFamilies #-}
{-# OPTIONS_HADDOCK hide #-}
module NumHask.Space.Types
( Space (..),
Union (..),
Intersection (..),
FieldSpace (..),
mid,
project,
Pos (..),
space1,
randomS,
randomSs,
memberOf,
contains,
disjoint,
width,
(+/-),
monotone,
eps,
widen,
widenEps,
scale,
move,
Transform (..),
inverseTransform,
Affinity (..),
(|.),
rotate,
)
where
import NumHask.Prelude hiding (rotate)
import qualified Prelude as P
class Space s where
type Element s :: Type
lower :: s -> Element s
upper :: s -> Element s
singleton :: Element s -> s
singleton Element s
s = Element s
s Element s -> Element s -> s
forall s. Space s => Element s -> Element s -> s
>.< Element s
s
intersection :: s -> s -> s
default intersection :: (Ord (Element s)) => s -> s -> s
intersection s
a s
b = Element s
l Element s -> Element s -> s
forall s. Space s => Element s -> Element s -> s
>.< Element s
u
where
l :: Element s
l = s -> Element s
forall s. Space s => s -> Element s
lower s
a Element s -> Element s -> Element s
forall a. Ord a => a -> a -> a
`max` s -> Element s
forall s. Space s => s -> Element s
lower s
b
u :: Element s
u = s -> Element s
forall s. Space s => s -> Element s
upper s
a Element s -> Element s -> Element s
forall a. Ord a => a -> a -> a
`min` s -> Element s
forall s. Space s => s -> Element s
upper s
b
union :: s -> s -> s
default union :: (Ord (Element s)) => s -> s -> s
union s
a s
b = Element s
l Element s -> Element s -> s
forall s. Space s => Element s -> Element s -> s
>.< Element s
u
where
l :: Element s
l = s -> Element s
forall s. Space s => s -> Element s
lower s
a Element s -> Element s -> Element s
forall a. Ord a => a -> a -> a
`min` s -> Element s
forall s. Space s => s -> Element s
lower s
b
u :: Element s
u = s -> Element s
forall s. Space s => s -> Element s
upper s
a Element s -> Element s -> Element s
forall a. Ord a => a -> a -> a
`max` s -> Element s
forall s. Space s => s -> Element s
upper s
b
normalise :: s -> s
normalise s
s = s -> Element s
forall s. Space s => s -> Element s
lower s
s Element s -> Element s -> s
forall s. Space s => Element s -> Element s -> s
... s -> Element s
forall s. Space s => s -> Element s
upper s
s
infix 3 ...
(...) :: Element s -> Element s -> s
default (...) :: (Ord (Element s)) => Element s -> Element s -> s
(...) Element s
a Element s
b = (Element s
a Element s -> Element s -> Element s
forall a. Ord a => a -> a -> a
`min` Element s
b) Element s -> Element s -> s
forall s. Space s => Element s -> Element s -> s
>.< (Element s
a Element s -> Element s -> Element s
forall a. Ord a => a -> a -> a
`max` Element s
b)
infix 3 >.<
(>.<) :: Element s -> Element s -> s
infixl 7 |.|
(|.|) :: Element s -> s -> Bool
default (|.|) :: (Ord (Element s)) => Element s -> s -> Bool
(|.|) Element s
a s
s = (Element s
a Element s -> Element s -> Bool
forall a. Ord a => a -> a -> Bool
>= s -> Element s
forall s. Space s => s -> Element s
lower s
s) Bool -> Bool -> Bool
&& (s -> Element s
forall s. Space s => s -> Element s
upper s
s Element s -> Element s -> Bool
forall a. Ord a => a -> a -> Bool
>= Element s
a)
infixl 7 |>|
(|>|) :: s -> s -> Bool
default (|>|) :: (Ord (Element s)) => s -> s -> Bool
(|>|) s
s0 s
s1 =
s -> Element s
forall s. Space s => s -> Element s
lower s
s0 Element s -> Element s -> Bool
forall a. Ord a => a -> a -> Bool
>= s -> Element s
forall s. Space s => s -> Element s
upper s
s1
infixl 7 |<|
(|<|) :: s -> s -> Bool
default (|<|) :: (Ord (Element s)) => s -> s -> Bool
(|<|) s
s0 s
s1 =
s -> Element s
forall s. Space s => s -> Element s
lower s
s1 Element s -> Element s -> Bool
forall a. Ord a => a -> a -> Bool
<= s -> Element s
forall s. Space s => s -> Element s
upper s
s0
contains :: (Space s) => s -> s -> Bool
contains :: s -> s -> Bool
contains s
s0 s
s1 =
s -> Element s
forall s. Space s => s -> Element s
lower s
s1 Element s -> s -> Bool
forall s. Space s => Element s -> s -> Bool
|.| s
s0
Bool -> Bool -> Bool
&& s -> Element s
forall s. Space s => s -> Element s
upper s
s1 Element s -> s -> Bool
forall s. Space s => Element s -> s -> Bool
|.| s
s0
disjoint :: (Space s) => s -> s -> Bool
disjoint :: s -> s -> Bool
disjoint s
s0 s
s1 = s
s0 s -> s -> Bool
forall s. Space s => s -> s -> Bool
|>| s
s1 Bool -> Bool -> Bool
|| s
s0 s -> s -> Bool
forall s. Space s => s -> s -> Bool
|<| s
s1
memberOf :: (Space s) => Element s -> s -> Bool
memberOf :: Element s -> s -> Bool
memberOf = Element s -> s -> Bool
forall s. Space s => Element s -> s -> Bool
(|.|)
width :: (Space s, Subtractive (Element s)) => s -> Element s
width :: s -> Element s
width s
s = s -> Element s
forall s. Space s => s -> Element s
upper s
s Element s -> Element s -> Element s
forall a. Subtractive a => a -> a -> a
- s -> Element s
forall s. Space s => s -> Element s
lower s
s
infixl 6 +/-
(+/-) :: (Space s, Subtractive (Element s)) => Element s -> Element s -> s
Element s
a +/- :: Element s -> Element s -> s
+/- Element s
b = Element s
a Element s -> Element s -> Element s
forall a. Subtractive a => a -> a -> a
- Element s
b Element s -> Element s -> s
forall s. Space s => Element s -> Element s -> s
... Element s
a Element s -> Element s -> Element s
forall a. Additive a => a -> a -> a
+ Element s
b
newtype Union a = Union {Union a -> a
getUnion :: a}
instance (Space a) => Semigroup (Union a) where
<> :: Union a -> Union a -> Union a
(<>) (Union a
a) (Union a
b) = a -> Union a
forall a. a -> Union a
Union (a
a a -> a -> a
forall s. Space s => s -> s -> s
`union` a
b)
newtype Intersection a = Intersection {Intersection a -> a
getIntersection :: a}
instance (Space a) => Semigroup (Intersection a) where
<> :: Intersection a -> Intersection a -> Intersection a
(<>) (Intersection a
a) (Intersection a
b) = a -> Intersection a
forall a. a -> Intersection a
Intersection (a
a a -> a -> a
forall s. Space s => s -> s -> s
`union` a
b)
randomS :: (Space s, RandomGen g, Random (Element s)) => s -> g -> (Element s, g)
randomS :: s -> g -> (Element s, g)
randomS s
s = (Element s, Element s) -> g -> (Element s, g)
forall a g. (Random a, RandomGen g) => (a, a) -> g -> (a, g)
randomR (s -> Element s
forall s. Space s => s -> Element s
lower s
s, s -> Element s
forall s. Space s => s -> Element s
upper s
s)
randomSs :: (Space s, RandomGen g, Random (Element s)) => s -> g -> [Element s]
randomSs :: s -> g -> [Element s]
randomSs s
s = (Element s, Element s) -> g -> [Element s]
forall a g. (Random a, RandomGen g) => (a, a) -> g -> [a]
randomRs (s -> Element s
forall s. Space s => s -> Element s
lower s
s, s -> Element s
forall s. Space s => s -> Element s
upper s
s)
class (Space s, Field (Element s)) => FieldSpace s where
type Grid s :: Type
grid :: Pos -> s -> Grid s -> [Element s]
gridSpace :: s -> Grid s -> [s]
data Pos
=
OuterPos
|
InnerPos
|
LowerPos
|
UpperPos
|
MidPos
deriving (Int -> Pos -> ShowS
[Pos] -> ShowS
Pos -> String
(Int -> Pos -> ShowS)
-> (Pos -> String) -> ([Pos] -> ShowS) -> Show Pos
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [Pos] -> ShowS
$cshowList :: [Pos] -> ShowS
show :: Pos -> String
$cshow :: Pos -> String
showsPrec :: Int -> Pos -> ShowS
$cshowsPrec :: Int -> Pos -> ShowS
Show, Pos -> Pos -> Bool
(Pos -> Pos -> Bool) -> (Pos -> Pos -> Bool) -> Eq Pos
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Pos -> Pos -> Bool
$c/= :: Pos -> Pos -> Bool
== :: Pos -> Pos -> Bool
$c== :: Pos -> Pos -> Bool
Eq)
mid :: (Space s, Field (Element s)) => s -> Element s
mid :: s -> Element s
mid s
s = (s -> Element s
forall s. Space s => s -> Element s
lower s
s Element s -> Element s -> Element s
forall a. Additive a => a -> a -> a
+ s -> Element s
forall s. Space s => s -> Element s
upper s
s) Element s -> Element s -> Element s
forall a. Divisive a => a -> a -> a
/ (Element s
forall a. Multiplicative a => a
one Element s -> Element s -> Element s
forall a. Additive a => a -> a -> a
+ Element s
forall a. Multiplicative a => a
one)
project :: (Space s, Field (Element s)) => s -> s -> Element s -> Element s
project :: s -> s -> Element s -> Element s
project s
s0 s
s1 Element s
p =
((Element s
p Element s -> Element s -> Element s
forall a. Subtractive a => a -> a -> a
- s -> Element s
forall s. Space s => s -> Element s
lower s
s0) Element s -> Element s -> Element s
forall a. Divisive a => a -> a -> a
/ (s -> Element s
forall s. Space s => s -> Element s
upper s
s0 Element s -> Element s -> Element s
forall a. Subtractive a => a -> a -> a
- s -> Element s
forall s. Space s => s -> Element s
lower s
s0)) Element s -> Element s -> Element s
forall a. Multiplicative a => a -> a -> a
* (s -> Element s
forall s. Space s => s -> Element s
upper s
s1 Element s -> Element s -> Element s
forall a. Subtractive a => a -> a -> a
- s -> Element s
forall s. Space s => s -> Element s
lower s
s1) Element s -> Element s -> Element s
forall a. Additive a => a -> a -> a
+ s -> Element s
forall s. Space s => s -> Element s
lower s
s1
space1 :: (Space s, Traversable f) => f (Element s) -> s
space1 :: f (Element s) -> s
space1 = (s -> s -> s) -> f s -> s
forall (t :: * -> *) a. Foldable t => (a -> a -> a) -> t a -> a
P.foldr1 s -> s -> s
forall s. Space s => s -> s -> s
union (f s -> s) -> (f (Element s) -> f s) -> f (Element s) -> s
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (Element s -> s) -> f (Element s) -> f s
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Element s -> s
forall s. Space s => Element s -> s
singleton
monotone :: (Space a, Space b) => (Element a -> Element b) -> a -> b
monotone :: (Element a -> Element b) -> a -> b
monotone Element a -> Element b
f a
s = [Element b] -> b
forall s (f :: * -> *).
(Space s, Traversable f) =>
f (Element s) -> s
space1 [Element a -> Element b
f (a -> Element a
forall s. Space s => s -> Element s
lower a
s), Element a -> Element b
f (a -> Element a
forall s. Space s => s -> Element s
upper a
s)]
eps ::
( Space s,
FromRational (Element s),
Field (Element s)
) =>
Element s ->
Element s ->
s
eps :: Element s -> Element s -> s
eps Element s
accuracy Element s
a = Element s
a Element s -> Element s -> s
forall s.
(Space s, Subtractive (Element s)) =>
Element s -> Element s -> s
+/- (Element s
accuracy Element s -> Element s -> Element s
forall a. Multiplicative a => a -> a -> a
* Element s
a Element s -> Element s -> Element s
forall a. Multiplicative a => a -> a -> a
* Element s
1e-6)
widen ::
( Space s,
Ring (Element s)
) =>
Element s ->
s ->
s
widen :: Element s -> s -> s
widen Element s
a s
s = (s -> Element s
forall s. Space s => s -> Element s
lower s
s Element s -> Element s -> Element s
forall a. Subtractive a => a -> a -> a
- Element s
a) Element s -> Element s -> s
forall s. Space s => Element s -> Element s -> s
>.< (s -> Element s
forall s. Space s => s -> Element s
upper s
s Element s -> Element s -> Element s
forall a. Additive a => a -> a -> a
+ Element s
a)
widenEps ::
( Space s,
FromRational (Element s),
Ring (Element s)
) =>
Element s ->
s ->
s
widenEps :: Element s -> s -> s
widenEps Element s
accuracy = Element s -> s -> s
forall s. (Space s, Ring (Element s)) => Element s -> s -> s
widen (Element s
accuracy Element s -> Element s -> Element s
forall a. Multiplicative a => a -> a -> a
* Element s
1e-6)
scale :: (Multiplicative (Element s), Space s) => Element s -> s -> s
scale :: Element s -> s -> s
scale Element s
e s
s = (Element s
e Element s -> Element s -> Element s
forall a. Multiplicative a => a -> a -> a
* s -> Element s
forall s. Space s => s -> Element s
lower s
s) Element s -> Element s -> s
forall s. Space s => Element s -> Element s -> s
... (Element s
e Element s -> Element s -> Element s
forall a. Multiplicative a => a -> a -> a
* s -> Element s
forall s. Space s => s -> Element s
upper s
s)
move :: (Additive (Element s), Space s) => Element s -> s -> s
move :: Element s -> s -> s
move Element s
e s
s = (Element s
e Element s -> Element s -> Element s
forall a. Additive a => a -> a -> a
+ s -> Element s
forall s. Space s => s -> Element s
lower s
s) Element s -> Element s -> s
forall s. Space s => Element s -> Element s -> s
... (Element s
e Element s -> Element s -> Element s
forall a. Additive a => a -> a -> a
+ s -> Element s
forall s. Space s => s -> Element s
upper s
s)
data Transform a = Transform
{ Transform a -> a
ta :: !a,
Transform a -> a
tb :: !a,
Transform a -> a
tc :: !a,
Transform a -> a
td :: !a,
Transform a -> a
te :: !a,
Transform a -> a
tf :: !a
}
deriving (Transform a -> Transform a -> Bool
(Transform a -> Transform a -> Bool)
-> (Transform a -> Transform a -> Bool) -> Eq (Transform a)
forall a. Eq a => Transform a -> Transform a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Transform a -> Transform a -> Bool
$c/= :: forall a. Eq a => Transform a -> Transform a -> Bool
== :: Transform a -> Transform a -> Bool
$c== :: forall a. Eq a => Transform a -> Transform a -> Bool
Eq, Int -> Transform a -> ShowS
[Transform a] -> ShowS
Transform a -> String
(Int -> Transform a -> ShowS)
-> (Transform a -> String)
-> ([Transform a] -> ShowS)
-> Show (Transform a)
forall a. Show a => Int -> Transform a -> ShowS
forall a. Show a => [Transform a] -> ShowS
forall a. Show a => Transform a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [Transform a] -> ShowS
$cshowList :: forall a. Show a => [Transform a] -> ShowS
show :: Transform a -> String
$cshow :: forall a. Show a => Transform a -> String
showsPrec :: Int -> Transform a -> ShowS
$cshowsPrec :: forall a. Show a => Int -> Transform a -> ShowS
Show, a -> Transform b -> Transform a
(a -> b) -> Transform a -> Transform b
(forall a b. (a -> b) -> Transform a -> Transform b)
-> (forall a b. a -> Transform b -> Transform a)
-> Functor Transform
forall a b. a -> Transform b -> Transform a
forall a b. (a -> b) -> Transform a -> Transform b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
-> (forall a b. a -> f b -> f a) -> Functor f
<$ :: a -> Transform b -> Transform a
$c<$ :: forall a b. a -> Transform b -> Transform a
fmap :: (a -> b) -> Transform a -> Transform b
$cfmap :: forall a b. (a -> b) -> Transform a -> Transform b
Functor, Transform a -> Bool
(a -> m) -> Transform a -> m
(a -> b -> b) -> b -> Transform a -> b
(forall m. Monoid m => Transform m -> m)
-> (forall m a. Monoid m => (a -> m) -> Transform a -> m)
-> (forall m a. Monoid m => (a -> m) -> Transform a -> m)
-> (forall a b. (a -> b -> b) -> b -> Transform a -> b)
-> (forall a b. (a -> b -> b) -> b -> Transform a -> b)
-> (forall b a. (b -> a -> b) -> b -> Transform a -> b)
-> (forall b a. (b -> a -> b) -> b -> Transform a -> b)
-> (forall a. (a -> a -> a) -> Transform a -> a)
-> (forall a. (a -> a -> a) -> Transform a -> a)
-> (forall a. Transform a -> [a])
-> (forall a. Transform a -> Bool)
-> (forall a. Transform a -> Int)
-> (forall a. Eq a => a -> Transform a -> Bool)
-> (forall a. Ord a => Transform a -> a)
-> (forall a. Ord a => Transform a -> a)
-> (forall a. Num a => Transform a -> a)
-> (forall a. Num a => Transform a -> a)
-> Foldable Transform
forall a. Eq a => a -> Transform a -> Bool
forall a. Num a => Transform a -> a
forall a. Ord a => Transform a -> a
forall m. Monoid m => Transform m -> m
forall a. Transform a -> Bool
forall a. Transform a -> Int
forall a. Transform a -> [a]
forall a. (a -> a -> a) -> Transform a -> a
forall m a. Monoid m => (a -> m) -> Transform a -> m
forall b a. (b -> a -> b) -> b -> Transform a -> b
forall a b. (a -> b -> b) -> b -> Transform a -> b
forall (t :: * -> *).
(forall m. Monoid m => t m -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. t a -> [a])
-> (forall a. t a -> Bool)
-> (forall a. t a -> Int)
-> (forall a. Eq a => a -> t a -> Bool)
-> (forall a. Ord a => t a -> a)
-> (forall a. Ord a => t a -> a)
-> (forall a. Num a => t a -> a)
-> (forall a. Num a => t a -> a)
-> Foldable t
product :: Transform a -> a
$cproduct :: forall a. Num a => Transform a -> a
sum :: Transform a -> a
$csum :: forall a. Num a => Transform a -> a
minimum :: Transform a -> a
$cminimum :: forall a. Ord a => Transform a -> a
maximum :: Transform a -> a
$cmaximum :: forall a. Ord a => Transform a -> a
elem :: a -> Transform a -> Bool
$celem :: forall a. Eq a => a -> Transform a -> Bool
length :: Transform a -> Int
$clength :: forall a. Transform a -> Int
null :: Transform a -> Bool
$cnull :: forall a. Transform a -> Bool
toList :: Transform a -> [a]
$ctoList :: forall a. Transform a -> [a]
foldl1 :: (a -> a -> a) -> Transform a -> a
$cfoldl1 :: forall a. (a -> a -> a) -> Transform a -> a
foldr1 :: (a -> a -> a) -> Transform a -> a
$cfoldr1 :: forall a. (a -> a -> a) -> Transform a -> a
foldl' :: (b -> a -> b) -> b -> Transform a -> b
$cfoldl' :: forall b a. (b -> a -> b) -> b -> Transform a -> b
foldl :: (b -> a -> b) -> b -> Transform a -> b
$cfoldl :: forall b a. (b -> a -> b) -> b -> Transform a -> b
foldr' :: (a -> b -> b) -> b -> Transform a -> b
$cfoldr' :: forall a b. (a -> b -> b) -> b -> Transform a -> b
foldr :: (a -> b -> b) -> b -> Transform a -> b
$cfoldr :: forall a b. (a -> b -> b) -> b -> Transform a -> b
foldMap' :: (a -> m) -> Transform a -> m
$cfoldMap' :: forall m a. Monoid m => (a -> m) -> Transform a -> m
foldMap :: (a -> m) -> Transform a -> m
$cfoldMap :: forall m a. Monoid m => (a -> m) -> Transform a -> m
fold :: Transform m -> m
$cfold :: forall m. Monoid m => Transform m -> m
Foldable, Functor Transform
Foldable Transform
Functor Transform
-> Foldable Transform
-> (forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Transform a -> f (Transform b))
-> (forall (f :: * -> *) a.
Applicative f =>
Transform (f a) -> f (Transform a))
-> (forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> Transform a -> m (Transform b))
-> (forall (m :: * -> *) a.
Monad m =>
Transform (m a) -> m (Transform a))
-> Traversable Transform
(a -> f b) -> Transform a -> f (Transform b)
forall (t :: * -> *).
Functor t
-> Foldable t
-> (forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> t a -> f (t b))
-> (forall (f :: * -> *) a. Applicative f => t (f a) -> f (t a))
-> (forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> t a -> m (t b))
-> (forall (m :: * -> *) a. Monad m => t (m a) -> m (t a))
-> Traversable t
forall (m :: * -> *) a.
Monad m =>
Transform (m a) -> m (Transform a)
forall (f :: * -> *) a.
Applicative f =>
Transform (f a) -> f (Transform a)
forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> Transform a -> m (Transform b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Transform a -> f (Transform b)
sequence :: Transform (m a) -> m (Transform a)
$csequence :: forall (m :: * -> *) a.
Monad m =>
Transform (m a) -> m (Transform a)
mapM :: (a -> m b) -> Transform a -> m (Transform b)
$cmapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> Transform a -> m (Transform b)
sequenceA :: Transform (f a) -> f (Transform a)
$csequenceA :: forall (f :: * -> *) a.
Applicative f =>
Transform (f a) -> f (Transform a)
traverse :: (a -> f b) -> Transform a -> f (Transform b)
$ctraverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Transform a -> f (Transform b)
$cp2Traversable :: Foldable Transform
$cp1Traversable :: Functor Transform
Traversable)
inverseTransform :: (Eq a, Field a) => Transform a -> Maybe (Transform a)
inverseTransform :: Transform a -> Maybe (Transform a)
inverseTransform (Transform a
a a
b a
c a
d a
e a
f) =
let det :: a
det = a
a a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
e a -> a -> a
forall a. Subtractive a => a -> a -> a
- a
b a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
d
in Maybe (Transform a)
-> Maybe (Transform a) -> Bool -> Maybe (Transform a)
forall a. a -> a -> Bool -> a
bool
( Transform a -> Maybe (Transform a)
forall a. a -> Maybe a
Just
( a -> a -> a -> a -> a -> a -> Transform a
forall a. a -> a -> a -> a -> a -> a -> Transform a
Transform
(a
a a -> a -> a
forall a. Divisive a => a -> a -> a
/ a
det)
(a
d a -> a -> a
forall a. Divisive a => a -> a -> a
/ a
det)
(- (a
a a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
c a -> a -> a
forall a. Additive a => a -> a -> a
+ a
d a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
f) a -> a -> a
forall a. Divisive a => a -> a -> a
/ a
det)
(a
b a -> a -> a
forall a. Divisive a => a -> a -> a
/ a
det)
(a
e a -> a -> a
forall a. Divisive a => a -> a -> a
/ a
det)
(- (a
b a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
c a -> a -> a
forall a. Additive a => a -> a -> a
+ a
e a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
f) a -> a -> a
forall a. Divisive a => a -> a -> a
/ a
det)
)
)
Maybe (Transform a)
forall a. Maybe a
Nothing
(a
det a -> a -> Bool
forall a. Eq a => a -> a -> Bool
== a
forall a. Additive a => a
zero)
class Affinity a b | a -> b where
transform :: Transform b -> a -> a
infix 3 |.
(|.) :: (Affinity a b) => Transform b -> a -> a
|. :: Transform b -> a -> a
(|.) = Transform b -> a -> a
forall a b. Affinity a b => Transform b -> a -> a
transform
instance (Multiplicative a, Additive a) => Affinity (Transform a) a where
transform :: Transform a -> Transform a -> Transform a
transform (Transform a
a' a
b' a
c' a
d' a
e' a
f') (Transform a
a a
b a
c a
d a
e a
f) =
a -> a -> a -> a -> a -> a -> Transform a
forall a. a -> a -> a -> a -> a -> a -> Transform a
Transform
(a
a a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
a' a -> a -> a
forall a. Additive a => a -> a -> a
+ a
b' a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
d)
(a
a' a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
b a -> a -> a
forall a. Additive a => a -> a -> a
+ a
b' a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
e)
(a
a' a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
c a -> a -> a
forall a. Additive a => a -> a -> a
+ a
b' a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
f a -> a -> a
forall a. Additive a => a -> a -> a
+ a
c')
(a
d' a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
a a -> a -> a
forall a. Additive a => a -> a -> a
+ a
e' a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
d)
(a
d' a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
b a -> a -> a
forall a. Additive a => a -> a -> a
+ a
e' a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
e)
(a
d' a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
c a -> a -> a
forall a. Additive a => a -> a -> a
+ a
e' a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
f a -> a -> a
forall a. Additive a => a -> a -> a
+ a
f')
rotate :: (TrigField a) => a -> Transform a
rotate :: a -> Transform a
rotate a
a = a -> a -> a -> a -> a -> a -> Transform a
forall a. a -> a -> a -> a -> a -> a -> Transform a
Transform (a -> a
forall a. TrigField a => a -> a
cos a
a) (- a -> a
forall a. TrigField a => a -> a
sin a
a) a
forall a. Additive a => a
zero (a -> a
forall a. TrigField a => a -> a
sin a
a) (a -> a
forall a. TrigField a => a -> a
cos a
a) a
forall a. Additive a => a
zero