Safe Haskell | Safe-Inferred |
---|---|
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.
Documentation
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 |
A 1-dimensional vector
V1 a |
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