Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Instances.Affine2d

Contents

SegmentAction implementations
SemigroupAction implementations

Description

Affine2d, Mat2x2 and V2 as a SemigroupAction instance.

Affine2d or Mat2x2 represents \(f: x \rightarrow a x + b\). V2 is the target vector type with scaling information.

REMARK: It is super important to have 1 as the second element in V2. Or else it fails to calculate comopsitional affine transformation.

Synopsis

newtype Affine2d a = Affine2d (Affine2dRepr a)
identAffine2d :: Num a => Affine2d a
type Affine2dRepr a = (a, a)
newtype Mat2x2 a = Mat2x2 (Mat2x2Repr a)
type Mat2x2Repr a = (a, a, a, a)
toMat2x2 :: Num a => a -> a -> Mat2x2 a
unMat2x2 :: Mat2x2 a -> (a, a, a, a)
mapM22 :: (a -> b) -> Mat2x2 a -> Mat2x2 b
mulM22M22 :: Num a => Mat2x2 a -> Mat2x2 a -> Mat2x2 a
invMat2x2 :: Fractional e => Mat2x2 e -> Mat2x2 e
mulM22V2 :: Num a => Mat2x2 a -> V2 a -> V2 a
newtype V2 a = V2 (V2Repr a)
type V2Repr a = (a, a)
toV2 :: Num a => a -> V2 a
unV2 :: V2 a -> a
mapV2 :: (a -> b) -> V2 a -> V2 b

Documentation

newtype Affine2d a #

2D affine transformation \(f: x \rightarrow a x + b\)

The acted target type is V2, which holds the length at the second element.

Composition and dual

\((f_1 \diamond f_2) v := (f_1 . f_2) v\). If yo need foldr [f_l, .., f_r] on segment tree, be sure to wrap Affine2d with Dual.

Constructors

Affine2d (Affine2dRepr a)

Instances

Instances details

Unbox a => Vector Vector (Affine2d a) #
Instance details Defined in Data.Instances.Affine2d Methods basicUnsafeFreeze :: Mutable Vector s (Affine2d a) -> ST s (Vector (Affine2d a)) # basicUnsafeThaw :: Vector (Affine2d a) -> ST s (Mutable Vector s (Affine2d a)) # basicLength :: Vector (Affine2d a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Affine2d a) -> Vector (Affine2d a) # basicUnsafeIndexM :: Vector (Affine2d a) -> Int -> Box (Affine2d a) # basicUnsafeCopy :: Mutable Vector s (Affine2d a) -> Vector (Affine2d a) -> ST s () # elemseq :: Vector (Affine2d a) -> Affine2d a -> b -> b #
Unbox a => MVector MVector (Affine2d a) #
Instance details Defined in Data.Instances.Affine2d Methods basicLength :: MVector s (Affine2d a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Affine2d a) -> MVector s (Affine2d a) # basicOverlaps :: MVector s (Affine2d a) -> MVector s (Affine2d a) -> Bool # basicUnsafeNew :: Int -> ST s (MVector s (Affine2d a)) # basicInitialize :: MVector s (Affine2d a) -> ST s () # basicUnsafeReplicate :: Int -> Affine2d a -> ST s (MVector s (Affine2d a)) # basicUnsafeRead :: MVector s (Affine2d a) -> Int -> ST s (Affine2d a) # basicUnsafeWrite :: MVector s (Affine2d a) -> Int -> Affine2d a -> ST s () # basicClear :: MVector s (Affine2d a) -> ST s () # basicSet :: MVector s (Affine2d a) -> Affine2d a -> ST s () # basicUnsafeCopy :: MVector s (Affine2d a) -> MVector s (Affine2d a) -> ST s () # basicUnsafeMove :: MVector s (Affine2d a) -> MVector s (Affine2d a) -> ST s () # basicUnsafeGrow :: MVector s (Affine2d a) -> Int -> ST s (MVector s (Affine2d a)) #
Num a => Monoid (Affine2d a) #
Instance details Defined in Data.Instances.Affine2d Methods mempty :: Affine2d a # mappend :: Affine2d a -> Affine2d a -> Affine2d a # mconcat :: [Affine2d a] -> Affine2d a #
Num a => Semigroup (Affine2d a) #
Instance details Defined in Data.Instances.Affine2d Methods (<>) :: Affine2d a -> Affine2d a -> Affine2d a # sconcat :: NonEmpty (Affine2d a) -> Affine2d a # stimes :: Integral b => b -> Affine2d a -> Affine2d a #
Show a => Show (Affine2d a) #
Instance details Defined in Data.Instances.Affine2d Methods showsPrec :: Int -> Affine2d a -> ShowS # show :: Affine2d a -> String # showList :: [Affine2d a] -> ShowS #
Eq a => Eq (Affine2d a) #
Instance details Defined in Data.Instances.Affine2d Methods (==) :: Affine2d a -> Affine2d a -> Bool # (/=) :: Affine2d a -> Affine2d a -> Bool #
Ord a => Ord (Affine2d a) #
Instance details Defined in Data.Instances.Affine2d Methods compare :: Affine2d a -> Affine2d a -> Ordering # (<) :: Affine2d a -> Affine2d a -> Bool # (<=) :: Affine2d a -> Affine2d a -> Bool # (>) :: Affine2d a -> Affine2d a -> Bool # (>=) :: Affine2d a -> Affine2d a -> Bool # max :: Affine2d a -> Affine2d a -> Affine2d a # min :: Affine2d a -> Affine2d a -> Affine2d a #
Unbox a => Unbox (Affine2d a) #
Instance details Defined in Data.Instances.Affine2d
Integral a => SegmentAction (Affine2d a) a #
Instance details Defined in Data.Instances.Affine2d Methods segAct :: Affine2d a -> a -> a # segActWithLength :: Int -> Affine2d a -> a -> a #
Num a => SemigroupAction (Affine2d a) a #	Limited to length 1
Instance details Defined in Data.Instances.Affine2d Methods sact :: Affine2d a -> a -> a #
Integral a => SegmentAction (Affine2d a) (Product a) #
Instance details Defined in Data.Instances.Affine2d Methods segAct :: Affine2d a -> Product a -> Product a # segActWithLength :: Int -> Affine2d a -> Product a -> Product a #
Integral a => SegmentAction (Affine2d a) (Sum a) #
Instance details Defined in Data.Instances.Affine2d Methods segAct :: Affine2d a -> Sum a -> Sum a # segActWithLength :: Int -> Affine2d a -> Sum a -> Sum a #
Num a => SegmentAction (Affine2d a) (V2 a) #
Instance details Defined in Data.Instances.Affine2d Methods segAct :: Affine2d a -> V2 a -> V2 a # segActWithLength :: Int -> Affine2d a -> V2 a -> V2 a #
Num a => SemigroupAction (Affine2d a) (V2 a) #
Instance details Defined in Data.Instances.Affine2d Methods sact :: Affine2d a -> V2 a -> V2 a #
newtype MVector s (Affine2d a) #
Instance details Defined in Data.Instances.Affine2d newtype MVector s (Affine2d a) = MV_Affine2d (MVector s (Affine2dRepr a))
newtype Vector (Affine2d a) #
Instance details Defined in Data.Instances.Affine2d newtype Vector (Affine2d a) = V_Affine2d (Vector (Affine2dRepr a))

identAffine2d :: Num a => Affine2d a #

type Affine2dRepr a = (a, a) #

Affine2d represents x -> a x + b.

SegmentAction implementations

SemigroupAction implementations

newtype Mat2x2 a #

2x2 unboxed matrix that works as a 2D affine transformation to V2. Prefer Affine2d for efficiency.

Constructors

Mat2x2 (Mat2x2Repr a)

Instances

Instances details

Unbox a => Vector Vector (Mat2x2 a) #
Instance details Defined in Data.Instances.Affine2d Methods basicUnsafeFreeze :: Mutable Vector s (Mat2x2 a) -> ST s (Vector (Mat2x2 a)) # basicUnsafeThaw :: Vector (Mat2x2 a) -> ST s (Mutable Vector s (Mat2x2 a)) # basicLength :: Vector (Mat2x2 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Mat2x2 a) -> Vector (Mat2x2 a) # basicUnsafeIndexM :: Vector (Mat2x2 a) -> Int -> Box (Mat2x2 a) # basicUnsafeCopy :: Mutable Vector s (Mat2x2 a) -> Vector (Mat2x2 a) -> ST s () # elemseq :: Vector (Mat2x2 a) -> Mat2x2 a -> b -> b #
Unbox a => MVector MVector (Mat2x2 a) #
Instance details Defined in Data.Instances.Affine2d Methods basicLength :: MVector s (Mat2x2 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Mat2x2 a) -> MVector s (Mat2x2 a) # basicOverlaps :: MVector s (Mat2x2 a) -> MVector s (Mat2x2 a) -> Bool # basicUnsafeNew :: Int -> ST s (MVector s (Mat2x2 a)) # basicInitialize :: MVector s (Mat2x2 a) -> ST s () # basicUnsafeReplicate :: Int -> Mat2x2 a -> ST s (MVector s (Mat2x2 a)) # basicUnsafeRead :: MVector s (Mat2x2 a) -> Int -> ST s (Mat2x2 a) # basicUnsafeWrite :: MVector s (Mat2x2 a) -> Int -> Mat2x2 a -> ST s () # basicClear :: MVector s (Mat2x2 a) -> ST s () # basicSet :: MVector s (Mat2x2 a) -> Mat2x2 a -> ST s () # basicUnsafeCopy :: MVector s (Mat2x2 a) -> MVector s (Mat2x2 a) -> ST s () # basicUnsafeMove :: MVector s (Mat2x2 a) -> MVector s (Mat2x2 a) -> ST s () # basicUnsafeGrow :: MVector s (Mat2x2 a) -> Int -> ST s (MVector s (Mat2x2 a)) #
Num a => Monoid (Mat2x2 a) #
Instance details Defined in Data.Instances.Affine2d Methods mempty :: Mat2x2 a # mappend :: Mat2x2 a -> Mat2x2 a -> Mat2x2 a # mconcat :: [Mat2x2 a] -> Mat2x2 a #
Num a => Semigroup (Mat2x2 a) #
Instance details Defined in Data.Instances.Affine2d Methods (<>) :: Mat2x2 a -> Mat2x2 a -> Mat2x2 a # sconcat :: NonEmpty (Mat2x2 a) -> Mat2x2 a # stimes :: Integral b => b -> Mat2x2 a -> Mat2x2 a #
Show a => Show (Mat2x2 a) #
Instance details Defined in Data.Instances.Affine2d Methods showsPrec :: Int -> Mat2x2 a -> ShowS # show :: Mat2x2 a -> String # showList :: [Mat2x2 a] -> ShowS #
Eq a => Eq (Mat2x2 a) #
Instance details Defined in Data.Instances.Affine2d Methods (==) :: Mat2x2 a -> Mat2x2 a -> Bool # (/=) :: Mat2x2 a -> Mat2x2 a -> Bool #
Ord a => Ord (Mat2x2 a) #
Instance details Defined in Data.Instances.Affine2d Methods compare :: Mat2x2 a -> Mat2x2 a -> Ordering # (<) :: Mat2x2 a -> Mat2x2 a -> Bool # (<=) :: Mat2x2 a -> Mat2x2 a -> Bool # (>) :: Mat2x2 a -> Mat2x2 a -> Bool # (>=) :: Mat2x2 a -> Mat2x2 a -> Bool # max :: Mat2x2 a -> Mat2x2 a -> Mat2x2 a # min :: Mat2x2 a -> Mat2x2 a -> Mat2x2 a #
Fractional e => Group (Mat2x2 e) #
Instance details Defined in Data.Instances.Affine2d Methods invert :: Mat2x2 e -> Mat2x2 e #
Unbox a => Unbox (Mat2x2 a) #
Instance details Defined in Data.Instances.Affine2d
Num a => SemigroupAction (Mat2x2 a) (V2 a) #
Instance details Defined in Data.Instances.Affine2d Methods sact :: Mat2x2 a -> V2 a -> V2 a #
newtype MVector s (Mat2x2 a) #
Instance details Defined in Data.Instances.Affine2d newtype MVector s (Mat2x2 a) = MV_Mat2x2 (MVector s (Mat2x2Repr a))
newtype Vector (Mat2x2 a) #
Instance details Defined in Data.Instances.Affine2d newtype Vector (Mat2x2 a) = V_Mat2x2 (Vector (Mat2x2Repr a))

type Mat2x2Repr a = (a, a, a, a) #

Mat2x2 internal unboxed data representaton.

toMat2x2 :: Num a => a -> a -> Mat2x2 a #

unMat2x2 :: Mat2x2 a -> (a, a, a, a) #

mapM22 :: (a -> b) -> Mat2x2 a -> Mat2x2 b #

mulM22M22 :: Num a => Mat2x2 a -> Mat2x2 a -> Mat2x2 a #

Multiplies 2x2 matrix to a 2x2 matrix.

invMat2x2 :: Fractional e => Mat2x2 e -> Mat2x2 e #

\(O(N^2)\) Returns NxN unit matrix, based on Group and Fractional.

mulM22V2 :: Num a => Mat2x2 a -> V2 a -> V2 a #

Multiplies 2x2 matrix to a 2 vector.

newtype V2 a #

Two-dimensional unboxed vector. Implements `Semigroup V2` as sum.

Constructors

V2 (V2Repr a)

Instances

Instances details

Unbox a => Vector Vector (V2 a) #
Instance details Defined in Data.Instances.Affine2d Methods basicUnsafeFreeze :: Mutable Vector s (V2 a) -> ST s (Vector (V2 a)) # basicUnsafeThaw :: Vector (V2 a) -> ST s (Mutable Vector s (V2 a)) # basicLength :: Vector (V2 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V2 a) -> Vector (V2 a) # basicUnsafeIndexM :: Vector (V2 a) -> Int -> Box (V2 a) # basicUnsafeCopy :: Mutable Vector s (V2 a) -> Vector (V2 a) -> ST s () # elemseq :: Vector (V2 a) -> V2 a -> b -> b #
Unbox a => MVector MVector (V2 a) #
Instance details Defined in Data.Instances.Affine2d Methods basicLength :: MVector s (V2 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V2 a) -> MVector s (V2 a) # basicOverlaps :: MVector s (V2 a) -> MVector s (V2 a) -> Bool # basicUnsafeNew :: Int -> ST s (MVector s (V2 a)) # basicInitialize :: MVector s (V2 a) -> ST s () # basicUnsafeReplicate :: Int -> V2 a -> ST s (MVector s (V2 a)) # basicUnsafeRead :: MVector s (V2 a) -> Int -> ST s (V2 a) # basicUnsafeWrite :: MVector s (V2 a) -> Int -> V2 a -> ST s () # basicClear :: MVector s (V2 a) -> ST s () # basicSet :: MVector s (V2 a) -> V2 a -> ST s () # basicUnsafeCopy :: MVector s (V2 a) -> MVector s (V2 a) -> ST s () # basicUnsafeMove :: MVector s (V2 a) -> MVector s (V2 a) -> ST s () # basicUnsafeGrow :: MVector s (V2 a) -> Int -> ST s (MVector s (V2 a)) #
Num a => Monoid (V2 a) #
Instance details Defined in Data.Instances.Affine2d Methods mempty :: V2 a # mappend :: V2 a -> V2 a -> V2 a # mconcat :: [V2 a] -> V2 a #
Num a => Semigroup (V2 a) #
Instance details Defined in Data.Instances.Affine2d Methods (<>) :: V2 a -> V2 a -> V2 a # sconcat :: NonEmpty (V2 a) -> V2 a # stimes :: Integral b => b -> V2 a -> V2 a #
Show a => Show (V2 a) #
Instance details Defined in Data.Instances.Affine2d Methods showsPrec :: Int -> V2 a -> ShowS # show :: V2 a -> String # showList :: [V2 a] -> ShowS #
Eq a => Eq (V2 a) #
Instance details Defined in Data.Instances.Affine2d Methods (==) :: V2 a -> V2 a -> Bool # (/=) :: V2 a -> V2 a -> Bool #
Ord a => Ord (V2 a) #
Instance details Defined in Data.Instances.Affine2d Methods compare :: V2 a -> V2 a -> Ordering # (<) :: V2 a -> V2 a -> Bool # (<=) :: V2 a -> V2 a -> Bool # (>) :: V2 a -> V2 a -> Bool # (>=) :: V2 a -> V2 a -> Bool # max :: V2 a -> V2 a -> V2 a # min :: V2 a -> V2 a -> V2 a #
Unbox a => Unbox (V2 a) #
Instance details Defined in Data.Instances.Affine2d
Num a => SegmentAction (Affine2d a) (V2 a) #
Instance details Defined in Data.Instances.Affine2d Methods segAct :: Affine2d a -> V2 a -> V2 a # segActWithLength :: Int -> Affine2d a -> V2 a -> V2 a #
Num a => SemigroupAction (Affine2d a) (V2 a) #
Instance details Defined in Data.Instances.Affine2d Methods sact :: Affine2d a -> V2 a -> V2 a #
Num a => SemigroupAction (Mat2x2 a) (V2 a) #
Instance details Defined in Data.Instances.Affine2d Methods sact :: Mat2x2 a -> V2 a -> V2 a #
newtype MVector s (V2 a) #
Instance details Defined in Data.Instances.Affine2d newtype MVector s (V2 a) = MV_V2 (MVector s (V2Repr a))
newtype Vector (V2 a) #
Instance details Defined in Data.Instances.Affine2d newtype Vector (V2 a) = V_V2 (Vector (V2Repr a))

type V2Repr a = (a, a) #

V2 internal unboxed data representaton. Be sure to have 1 as the second element on construction.

toV2 :: Num a => a -> V2 a #

unV2 :: V2 a -> a #

mapV2 :: (a -> b) -> V2 a -> V2 b #