Safe Haskell | None |
---|---|
Language | Haskell2010 |
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.
Synopsis
- newtype V1 a = V1 a
- data V2 a = V2 !a !a
- data V3 a = V3 !a !a !a
- data V4 a = V4 !a !a !a !a
- class R1 t where
- _x :: Lens' (t a) a
- class R2 t where
- _y :: Lens' (t a) a
- class Functor f => Additive f where
- class Num a => Epsilon a where
- class Additive f => Metric f where
- (^*) :: (Functor f, Num a) => f a -> a -> f a
- (^/) :: (Functor f, Floating a) => f a -> a -> f a
- normalize :: (Floating a, Metric f, Epsilon a) => f a -> f a
Documentation
A 1-dimensional vector
V1 a |
Instances
Functor V1 Source # | |
Applicative V1 Source # | |
Foldable V1 Source # | |
Defined in Graphics.Rasterific.Linear 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 # elem :: Eq a => a -> V1 a -> Bool # maximum :: Ord a => V1 a -> a # | |
Traversable V1 Source # | |
Additive V1 Source # | |
R1 V1 Source # | |
Defined in Graphics.Rasterific.Linear | |
Eq a => Eq (V1 a) Source # | |
Num a => Num (V1 a) Source # | |
Show a => Show (V1 a) Source # | |
Epsilon a => Epsilon (V1 a) Source # | |
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
V2 !a !a |
Instances
A 3-dimensional vector
V3 !a !a !a |
Instances
Functor V3 Source # | |
Applicative V3 Source # | |
Foldable V3 Source # | |
Defined in Graphics.Rasterific.Linear 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 # elem :: Eq a => a -> V3 a -> Bool # maximum :: Ord a => V3 a -> a # | |
Traversable V3 Source # | |
Metric V3 Source # | |
Additive V3 Source # | |
R2 V3 Source # | |
Defined in Graphics.Rasterific.Linear | |
R1 V3 Source # | |
Defined in Graphics.Rasterific.Linear | |
Eq a => Eq (V3 a) Source # | |
Num a => Num (V3 a) Source # | |
Show a => Show (V3 a) Source # | |
Epsilon a => Epsilon (V3 a) Source # | |
A 4-dimensional vector
V4 !a !a !a !a |
Instances
Functor V4 Source # | |
Applicative V4 Source # | |
Foldable V4 Source # | |
Defined in Graphics.Rasterific.Linear 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 # elem :: Eq a => a -> V4 a -> Bool # maximum :: Ord a => V4 a -> a # | |
Traversable V4 Source # | |
Metric V4 Source # | |
Additive V4 Source # | |
R2 V4 Source # | |
Defined in Graphics.Rasterific.Linear | |
R1 V4 Source # | |
Defined in Graphics.Rasterific.Linear | |
Eq a => Eq (V4 a) Source # | |
Num a => Num (V4 a) Source # | |
Show a => Show (V4 a) Source # | |
Epsilon a => Epsilon (V4 a) Source # | |
Instances
R1 V1 Source # | |
Defined in Graphics.Rasterific.Linear | |
R1 V4 Source # | |
Defined in Graphics.Rasterific.Linear | |
R1 V3 Source # | |
Defined in Graphics.Rasterific.Linear | |
R1 V2 Source # | |
Defined in Graphics.Rasterific.Linear |
class Functor f => Additive f where Source #
A vector is an additive group with additional structure.
The zero vector
(^+^) :: Num a => f a -> f a -> f a infixl 6 Source #
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 Source #
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 Source #
Linearly interpolate between two vectors.
class Num a => Epsilon a where Source #
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
class Additive f => Metric f where Source #
Free and sparse inner product/metric spaces.
dot :: Num a => f a -> f a -> a Source #
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 Source #
Compute the squared norm. The name quadrance arises from Norman J. Wildberger's rational trigonometry.
qd :: Num a => f a -> f a -> a Source #
Compute the quadrance of the difference
distance :: Floating a => f a -> f a -> a Source #
Compute the distance between two vectors in a metric space
norm :: Floating a => f a -> a Source #
Compute the norm of a vector in a metric space
signorm :: Floating a => f a -> f a Source #
Convert a non-zero vector to unit vector.
(^*) :: (Functor f, Num a) => f a -> a -> f a infixl 7 Source #
Compute the right scalar product
>>>
V2 3 4 ^* 2
V2 6 8