Graphics.Rasterific.Linear

This module is a reduction of the Linear package from Edward Kmett to match just the need of Rasterific.

If the flag embed_linear is disabled, this module is just a reexport from the real linear package.

Documentation

newtype V1 a

A 1-dimensional vector

Constructors

V1 a

Instances

Functor V1

Methods

fmap :: (a -> b) -> V1 a -> V1 b

(<$) :: a -> V1 b -> V1 a

Applicative V1

Methods

pure :: a -> V1 a

(<*>) :: V1 (a -> b) -> V1 a -> V1 b

(*>) :: V1 a -> V1 b -> V1 b

(<*) :: V1 a -> V1 b -> V1 a

Foldable V1

Methods

fold :: Monoid m => V1 m -> m

foldMap :: Monoid m => (a -> m) -> V1 a -> m

foldr :: (a -> b -> b) -> b -> V1 a -> b

foldr' :: (a -> b -> b) -> b -> V1 a -> b

foldl :: (b -> a -> b) -> b -> V1 a -> b

foldl' :: (b -> a -> b) -> b -> V1 a -> b

foldr1 :: (a -> a -> a) -> V1 a -> a

foldl1 :: (a -> a -> a) -> V1 a -> a

toList :: V1 a -> [a]

null :: V1 a -> Bool

length :: V1 a -> Int

elem :: Eq a => a -> V1 a -> Bool

maximum :: Ord a => V1 a -> a

minimum :: Ord a => V1 a -> a

sum :: Num a => V1 a -> a

product :: Num a => V1 a -> a

Traversable V1

Methods

traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b)

sequenceA :: Applicative f => V1 (f a) -> f (V1 a)

mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b)

sequence :: Monad m => V1 (m a) -> m (V1 a)

Additive V1

Methods

zero :: Num a => V1 a

(^+^) :: Num a => V1 a -> V1 a -> V1 a

(^-^) :: Num a => V1 a -> V1 a -> V1 a

lerp :: Num a => a -> V1 a -> V1 a -> V1 a

R1 V1

Methods

_x :: Functor f => (a -> f a) -> V1 a -> f (V1 a)

Eq a => Eq (V1 a)

Methods

(==) :: V1 a -> V1 a -> Bool

(/=) :: V1 a -> V1 a -> Bool

Num a => Num (V1 a)

Methods

(+) :: V1 a -> V1 a -> V1 a

(-) :: V1 a -> V1 a -> V1 a

(*) :: V1 a -> V1 a -> V1 a

negate :: V1 a -> V1 a

abs :: V1 a -> V1 a

signum :: V1 a -> V1 a

fromInteger :: Integer -> V1 a

Show a => Show (V1 a)

Methods

showsPrec :: Int -> V1 a -> ShowS

show :: V1 a -> String

showList :: [V1 a] -> ShowS

Epsilon a => Epsilon (V1 a)

Methods

nearZero :: V1 a -> Bool

data V2 a

A 2-dimensional vector

>>> pure 1 :: V2 Int
V2 1 1

>>> V2 1 2 + V2 3 4
V2 4 6

>>> V2 1 2 * V2 3 4
V2 3 8

>>> sum (V2 1 2)
3

Constructors

V2 !a !a

Instances

Functor V2

Methods

fmap :: (a -> b) -> V2 a -> V2 b

(<$) :: a -> V2 b -> V2 a

Applicative V2

Methods

pure :: a -> V2 a

(<*>) :: V2 (a -> b) -> V2 a -> V2 b

(*>) :: V2 a -> V2 b -> V2 b

(<*) :: V2 a -> V2 b -> V2 a

Foldable V2

Methods

fold :: Monoid m => V2 m -> m

foldMap :: Monoid m => (a -> m) -> V2 a -> m

foldr :: (a -> b -> b) -> b -> V2 a -> b

foldr' :: (a -> b -> b) -> b -> V2 a -> b

foldl :: (b -> a -> b) -> b -> V2 a -> b

foldl' :: (b -> a -> b) -> b -> V2 a -> b

foldr1 :: (a -> a -> a) -> V2 a -> a

foldl1 :: (a -> a -> a) -> V2 a -> a

toList :: V2 a -> [a]

null :: V2 a -> Bool

length :: V2 a -> Int

elem :: Eq a => a -> V2 a -> Bool

maximum :: Ord a => V2 a -> a

minimum :: Ord a => V2 a -> a

sum :: Num a => V2 a -> a

product :: Num a => V2 a -> a

Traversable V2

Methods

traverse :: Applicative f => (a -> f b) -> V2 a -> f (V2 b)

sequenceA :: Applicative f => V2 (f a) -> f (V2 a)

mapM :: Monad m => (a -> m b) -> V2 a -> m (V2 b)

sequence :: Monad m => V2 (m a) -> m (V2 a)

Metric V2

Methods

dot :: Num a => V2 a -> V2 a -> a

quadrance :: Num a => V2 a -> a

qd :: Num a => V2 a -> V2 a -> a

distance :: Floating a => V2 a -> V2 a -> a

norm :: Floating a => V2 a -> a

signorm :: Floating a => V2 a -> V2 a

Additive V2

Methods

zero :: Num a => V2 a

(^+^) :: Num a => V2 a -> V2 a -> V2 a

(^-^) :: Num a => V2 a -> V2 a -> V2 a

lerp :: Num a => a -> V2 a -> V2 a -> V2 a

R2 V2

Methods

_y :: Functor f => (a -> f a) -> V2 a -> f (V2 a)

R1 V2

Methods

_x :: Functor f => (a -> f a) -> V2 a -> f (V2 a)

PointFoldable Point

Just apply the function

Methods

foldPoints :: (b -> Point -> b) -> b -> Point -> b

Transformable Point

Just apply the function

Methods

transform :: (Point -> Point) -> Point -> Point

transformM :: Monad m => (Point -> m Point) -> Point -> m Point

PlaneBoundable Point

Methods

planeBounds :: Point -> PlaneBound

Eq a => Eq (V2 a)

Methods

(==) :: V2 a -> V2 a -> Bool

(/=) :: V2 a -> V2 a -> Bool

Num a => Num (V2 a)

Methods

(+) :: V2 a -> V2 a -> V2 a

(-) :: V2 a -> V2 a -> V2 a

(*) :: V2 a -> V2 a -> V2 a

negate :: V2 a -> V2 a

abs :: V2 a -> V2 a

signum :: V2 a -> V2 a

fromInteger :: Integer -> V2 a

Show a => Show (V2 a)

Methods

showsPrec :: Int -> V2 a -> ShowS

show :: V2 a -> String

showList :: [V2 a] -> ShowS

Epsilon a => Epsilon (V2 a)

Methods

nearZero :: V2 a -> Bool

data V3 a

A 3-dimensional vector

Constructors

V3 !a !a !a

Instances

Functor V3

Methods

fmap :: (a -> b) -> V3 a -> V3 b

(<$) :: a -> V3 b -> V3 a

Applicative V3

Methods

pure :: a -> V3 a

(<*>) :: V3 (a -> b) -> V3 a -> V3 b

(*>) :: V3 a -> V3 b -> V3 b

(<*) :: V3 a -> V3 b -> V3 a

Foldable V3

Methods

fold :: Monoid m => V3 m -> m

foldMap :: Monoid m => (a -> m) -> V3 a -> m

foldr :: (a -> b -> b) -> b -> V3 a -> b

foldr' :: (a -> b -> b) -> b -> V3 a -> b

foldl :: (b -> a -> b) -> b -> V3 a -> b

foldl' :: (b -> a -> b) -> b -> V3 a -> b

foldr1 :: (a -> a -> a) -> V3 a -> a

foldl1 :: (a -> a -> a) -> V3 a -> a

toList :: V3 a -> [a]

null :: V3 a -> Bool

length :: V3 a -> Int

elem :: Eq a => a -> V3 a -> Bool

maximum :: Ord a => V3 a -> a

minimum :: Ord a => V3 a -> a

sum :: Num a => V3 a -> a

product :: Num a => V3 a -> a

Traversable V3

Methods

traverse :: Applicative f => (a -> f b) -> V3 a -> f (V3 b)

sequenceA :: Applicative f => V3 (f a) -> f (V3 a)

mapM :: Monad m => (a -> m b) -> V3 a -> m (V3 b)

sequence :: Monad m => V3 (m a) -> m (V3 a)

Metric V3

Methods

dot :: Num a => V3 a -> V3 a -> a

quadrance :: Num a => V3 a -> a

qd :: Num a => V3 a -> V3 a -> a

distance :: Floating a => V3 a -> V3 a -> a

norm :: Floating a => V3 a -> a

signorm :: Floating a => V3 a -> V3 a

Additive V3

Methods

zero :: Num a => V3 a

(^+^) :: Num a => V3 a -> V3 a -> V3 a

(^-^) :: Num a => V3 a -> V3 a -> V3 a

lerp :: Num a => a -> V3 a -> V3 a -> V3 a

R2 V3

Methods

_y :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

R1 V3

Methods

_x :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

Eq a => Eq (V3 a)

Methods

(==) :: V3 a -> V3 a -> Bool

(/=) :: V3 a -> V3 a -> Bool

Num a => Num (V3 a)

Methods

(+) :: V3 a -> V3 a -> V3 a

(-) :: V3 a -> V3 a -> V3 a

(*) :: V3 a -> V3 a -> V3 a

negate :: V3 a -> V3 a

abs :: V3 a -> V3 a

signum :: V3 a -> V3 a

fromInteger :: Integer -> V3 a

Show a => Show (V3 a)

Methods

showsPrec :: Int -> V3 a -> ShowS

show :: V3 a -> String

showList :: [V3 a] -> ShowS

Epsilon a => Epsilon (V3 a)

Methods

nearZero :: V3 a -> Bool

data V4 a

A 4-dimensional vector

Constructors

V4 !a !a !a !a

Instances

Functor V4

Methods

fmap :: (a -> b) -> V4 a -> V4 b

(<$) :: a -> V4 b -> V4 a

Applicative V4

Methods

pure :: a -> V4 a

(<*>) :: V4 (a -> b) -> V4 a -> V4 b

(*>) :: V4 a -> V4 b -> V4 b

(<*) :: V4 a -> V4 b -> V4 a

Foldable V4

Methods

fold :: Monoid m => V4 m -> m

foldMap :: Monoid m => (a -> m) -> V4 a -> m

foldr :: (a -> b -> b) -> b -> V4 a -> b

foldr' :: (a -> b -> b) -> b -> V4 a -> b

foldl :: (b -> a -> b) -> b -> V4 a -> b

foldl' :: (b -> a -> b) -> b -> V4 a -> b

foldr1 :: (a -> a -> a) -> V4 a -> a

foldl1 :: (a -> a -> a) -> V4 a -> a

toList :: V4 a -> [a]

null :: V4 a -> Bool

length :: V4 a -> Int

elem :: Eq a => a -> V4 a -> Bool

maximum :: Ord a => V4 a -> a

minimum :: Ord a => V4 a -> a

sum :: Num a => V4 a -> a

product :: Num a => V4 a -> a

Traversable V4

Methods

traverse :: Applicative f => (a -> f b) -> V4 a -> f (V4 b)

sequenceA :: Applicative f => V4 (f a) -> f (V4 a)

mapM :: Monad m => (a -> m b) -> V4 a -> m (V4 b)

sequence :: Monad m => V4 (m a) -> m (V4 a)

Metric V4

Methods

dot :: Num a => V4 a -> V4 a -> a

quadrance :: Num a => V4 a -> a

qd :: Num a => V4 a -> V4 a -> a

distance :: Floating a => V4 a -> V4 a -> a

norm :: Floating a => V4 a -> a

signorm :: Floating a => V4 a -> V4 a

Additive V4

Methods

zero :: Num a => V4 a

(^+^) :: Num a => V4 a -> V4 a -> V4 a

(^-^) :: Num a => V4 a -> V4 a -> V4 a

lerp :: Num a => a -> V4 a -> V4 a -> V4 a

R2 V4

Methods

_y :: Functor f => (a -> f a) -> V4 a -> f (V4 a)

R1 V4

Methods

_x :: Functor f => (a -> f a) -> V4 a -> f (V4 a)

Eq a => Eq (V4 a)

Methods

(==) :: V4 a -> V4 a -> Bool

(/=) :: V4 a -> V4 a -> Bool

Num a => Num (V4 a)

Methods

(+) :: V4 a -> V4 a -> V4 a

(-) :: V4 a -> V4 a -> V4 a

(*) :: V4 a -> V4 a -> V4 a

negate :: V4 a -> V4 a

abs :: V4 a -> V4 a

signum :: V4 a -> V4 a

fromInteger :: Integer -> V4 a

Show a => Show (V4 a)

Methods

showsPrec :: Int -> V4 a -> ShowS

show :: V4 a -> String

showList :: [V4 a] -> ShowS

Epsilon a => Epsilon (V4 a)

Methods

nearZero :: V4 a -> Bool

class R1 t where

Methods

_x :: Lens' (t a) a

Instances

R1 V1

Methods

_x :: Functor f => (a -> f a) -> V1 a -> f (V1 a)

R1 V4

Methods

_x :: Functor f => (a -> f a) -> V4 a -> f (V4 a)

R1 V3

Methods

_x :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

R1 V2

Methods

_x :: Functor f => (a -> f a) -> V2 a -> f (V2 a)

class R2 t where

Methods

_y :: Lens' (t a) a

Instances

R2 V4

Methods

_y :: Functor f => (a -> f a) -> V4 a -> f (V4 a)

R2 V3

Methods

_y :: Functor f => (a -> f a) -> V3 a -> f (V3 a)

R2 V2

Methods

_y :: Functor f => (a -> f a) -> V2 a -> f (V2 a)

class Functor f => Additive f where

A vector is an additive group with additional structure.

Minimal complete definition

zero, (^+^), (^-^), lerp

Methods

zero :: Num a => f a

The zero vector

(^+^) :: Num a => f a -> f a -> f a infixl 6

Compute the sum of two vectors

>>> V2 1 2 ^+^ V2 3 4
V2 4 6

(^-^) :: Num a => f a -> f a -> f a infixl 6

Compute the difference between two vectors

>>> V2 4 5 - V2 3 1
V2 1 4

lerp :: Num a => a -> f a -> f a -> f a

Linearly interpolate between two vectors.

Instances

Additive V1

Methods

zero :: Num a => V1 a

(^+^) :: Num a => V1 a -> V1 a -> V1 a

(^-^) :: Num a => V1 a -> V1 a -> V1 a

lerp :: Num a => a -> V1 a -> V1 a -> V1 a

Additive V4

Methods

zero :: Num a => V4 a

(^+^) :: Num a => V4 a -> V4 a -> V4 a

(^-^) :: Num a => V4 a -> V4 a -> V4 a

lerp :: Num a => a -> V4 a -> V4 a -> V4 a

Additive V3

Methods

zero :: Num a => V3 a

(^+^) :: Num a => V3 a -> V3 a -> V3 a

(^-^) :: Num a => V3 a -> V3 a -> V3 a

lerp :: Num a => a -> V3 a -> V3 a -> V3 a

Additive V2

Methods

zero :: Num a => V2 a

(^+^) :: Num a => V2 a -> V2 a -> V2 a

(^-^) :: Num a => V2 a -> V2 a -> V2 a

lerp :: Num a => a -> V2 a -> V2 a -> V2 a

class Num a => Epsilon a where

Provides a fairly subjective test to see if a quantity is near zero.

>>> nearZero (1e-11 :: Double)
False

>>> nearZero (1e-17 :: Double)
True

>>> nearZero (1e-5 :: Float)
False

>>> nearZero (1e-7 :: Float)
True

Minimal complete definition

nearZero

Methods

nearZero :: a -> Bool

Determine if a quantity is near zero.

Instances

Epsilon Double

abs a <= 1e-12

Methods

nearZero :: Double -> Bool

Epsilon Float

abs a <= 1e-6

Methods

nearZero :: Float -> Bool

Epsilon a => Epsilon (V1 a)

Methods

nearZero :: V1 a -> Bool

Epsilon a => Epsilon (V4 a)

Methods

nearZero :: V4 a -> Bool

Epsilon a => Epsilon (V3 a)

Methods

nearZero :: V3 a -> Bool

Epsilon a => Epsilon (V2 a)

Methods

nearZero :: V2 a -> Bool

class Additive f => Metric f where

Free and sparse inner product/metric spaces.

Minimal complete definition

dot

Methods

dot :: Num a => f a -> f a -> a

Compute the inner product of two vectors or (equivalently) convert a vector f a into a covector f a -> a.

>>> V2 1 2 `dot` V2 3 4
11

quadrance :: Num a => f a -> a

Compute the squared norm. The name quadrance arises from Norman J. Wildberger's rational trigonometry.

qd :: Num a => f a -> f a -> a

Compute the quadrance of the difference

distance :: Floating a => f a -> f a -> a

Compute the distance between two vectors in a metric space

norm :: Floating a => f a -> a

Compute the norm of a vector in a metric space

signorm :: Floating a => f a -> f a

Convert a non-zero vector to unit vector.

Instances

Metric V4

Methods

dot :: Num a => V4 a -> V4 a -> a

quadrance :: Num a => V4 a -> a

qd :: Num a => V4 a -> V4 a -> a

distance :: Floating a => V4 a -> V4 a -> a

norm :: Floating a => V4 a -> a

signorm :: Floating a => V4 a -> V4 a

Metric V3

Methods

dot :: Num a => V3 a -> V3 a -> a

quadrance :: Num a => V3 a -> a

qd :: Num a => V3 a -> V3 a -> a

distance :: Floating a => V3 a -> V3 a -> a

norm :: Floating a => V3 a -> a

signorm :: Floating a => V3 a -> V3 a

Metric V2

Methods

dot :: Num a => V2 a -> V2 a -> a

quadrance :: Num a => V2 a -> a

qd :: Num a => V2 a -> V2 a -> a

distance :: Floating a => V2 a -> V2 a -> a

norm :: Floating a => V2 a -> a

signorm :: Floating a => V2 a -> V2 a

(^*) :: (Functor f, Num a) => f a -> a -> f a infixl 7

Compute the right scalar product

>>> V2 3 4 ^* 2
V2 6 8

(^/) :: (Functor f, Floating a) => f a -> a -> f a infixl 7

Compute division by a scalar on the right.

normalize :: (Floating a, Metric f, Epsilon a) => f a -> f a

Normalize a Metric functor to have unit norm. This function does not change the functor if its norm is 0 or 1.