hgeometry-0.8.0.0: Geometric Algorithms, Data structures, and Data types.

Copyright(C) Frank Staals
Licensesee the LICENSE file
MaintainerFrank Staals
Safe HaskellNone
LanguageHaskell2010

Data.Geometry.Vector

Description

\(d\)-dimensional vectors.

Synopsis

Documentation

data C (n :: Nat) Source #

A proxy which can be used for the coordinates.

Constructors

C 
Instances
Eq (C n) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFixed

Methods

(==) :: C n -> C n -> Bool #

(/=) :: C n -> C n -> Bool #

Ord (C n) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFixed

Methods

compare :: C n -> C n -> Ordering #

(<) :: C n -> C n -> Bool #

(<=) :: C n -> C n -> Bool #

(>) :: C n -> C n -> Bool #

(>=) :: C n -> C n -> Bool #

max :: C n -> C n -> C n #

min :: C n -> C n -> C n #

Read (C n) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFixed

Methods

readsPrec :: Int -> ReadS (C n) #

readList :: ReadS [C n] #

readPrec :: ReadPrec (C n) #

readListPrec :: ReadPrec [C n] #

Show (C n) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFixed

Methods

showsPrec :: Int -> C n -> ShowS #

show :: C n -> String #

showList :: [C n] -> ShowS #

class Additive (Diff p) => Affine (p :: Type -> Type) where #

An affine space is roughly a vector space in which we have forgotten or at least pretend to have forgotten the origin.

a .+^ (b .-. a)  =  b@
(a .+^ u) .+^ v  =  a .+^ (u ^+^ v)@
(a .-. b) ^+^ v  =  (a .+^ v) .-. q@

Minimal complete definition

(.-.), (.+^)

Associated Types

type Diff (p :: Type -> Type) :: Type -> Type #

Methods

(.-.) :: Num a => p a -> p a -> Diff p a infixl 6 #

Get the difference between two points as a vector offset.

(.+^) :: Num a => p a -> Diff p a -> p a infixl 6 #

Add a vector offset to a point.

(.-^) :: Num a => p a -> Diff p a -> p a infixl 6 #

Subtract a vector offset from a point.

Instances
Affine [] 
Instance details

Defined in Linear.Affine

Associated Types

type Diff [] :: Type -> Type #

Methods

(.-.) :: Num a => [a] -> [a] -> Diff [] a #

(.+^) :: Num a => [a] -> Diff [] a -> [a] #

(.-^) :: Num a => [a] -> Diff [] a -> [a] #

Affine Maybe 
Instance details

Defined in Linear.Affine

Associated Types

type Diff Maybe :: Type -> Type #

Methods

(.-.) :: Num a => Maybe a -> Maybe a -> Diff Maybe a #

(.+^) :: Num a => Maybe a -> Diff Maybe a -> Maybe a #

(.-^) :: Num a => Maybe a -> Diff Maybe a -> Maybe a #

Affine Complex 
Instance details

Defined in Linear.Affine

Associated Types

type Diff Complex :: Type -> Type #

Methods

(.-.) :: Num a => Complex a -> Complex a -> Diff Complex a #

(.+^) :: Num a => Complex a -> Diff Complex a -> Complex a #

(.-^) :: Num a => Complex a -> Diff Complex a -> Complex a #

Affine ZipList 
Instance details

Defined in Linear.Affine

Associated Types

type Diff ZipList :: Type -> Type #

Methods

(.-.) :: Num a => ZipList a -> ZipList a -> Diff ZipList a #

(.+^) :: Num a => ZipList a -> Diff ZipList a -> ZipList a #

(.-^) :: Num a => ZipList a -> Diff ZipList a -> ZipList a #

Affine Identity 
Instance details

Defined in Linear.Affine

Associated Types

type Diff Identity :: Type -> Type #

Methods

(.-.) :: Num a => Identity a -> Identity a -> Diff Identity a #

(.+^) :: Num a => Identity a -> Diff Identity a -> Identity a #

(.-^) :: Num a => Identity a -> Diff Identity a -> Identity a #

Affine IntMap 
Instance details

Defined in Linear.Affine

Associated Types

type Diff IntMap :: Type -> Type #

Methods

(.-.) :: Num a => IntMap a -> IntMap a -> Diff IntMap a #

(.+^) :: Num a => IntMap a -> Diff IntMap a -> IntMap a #

(.-^) :: Num a => IntMap a -> Diff IntMap a -> IntMap a #

Affine Vector 
Instance details

Defined in Linear.Affine

Associated Types

type Diff Vector :: Type -> Type #

Methods

(.-.) :: Num a => Vector a -> Vector a -> Diff Vector a #

(.+^) :: Num a => Vector a -> Diff Vector a -> Vector a #

(.-^) :: Num a => Vector a -> Diff Vector a -> Vector a #

Affine Plucker 
Instance details

Defined in Linear.Affine

Associated Types

type Diff Plucker :: Type -> Type #

Methods

(.-.) :: Num a => Plucker a -> Plucker a -> Diff Plucker a #

(.+^) :: Num a => Plucker a -> Diff Plucker a -> Plucker a #

(.-^) :: Num a => Plucker a -> Diff Plucker a -> Plucker a #

Affine Quaternion 
Instance details

Defined in Linear.Affine

Associated Types

type Diff Quaternion :: Type -> Type #

Affine V0 
Instance details

Defined in Linear.Affine

Associated Types

type Diff V0 :: Type -> Type #

Methods

(.-.) :: Num a => V0 a -> V0 a -> Diff V0 a #

(.+^) :: Num a => V0 a -> Diff V0 a -> V0 a #

(.-^) :: Num a => V0 a -> Diff V0 a -> V0 a #

Affine V4 
Instance details

Defined in Linear.Affine

Associated Types

type Diff V4 :: Type -> Type #

Methods

(.-.) :: Num a => V4 a -> V4 a -> Diff V4 a #

(.+^) :: Num a => V4 a -> Diff V4 a -> V4 a #

(.-^) :: Num a => V4 a -> Diff V4 a -> V4 a #

Affine V3 
Instance details

Defined in Linear.Affine

Associated Types

type Diff V3 :: Type -> Type #

Methods

(.-.) :: Num a => V3 a -> V3 a -> Diff V3 a #

(.+^) :: Num a => V3 a -> Diff V3 a -> V3 a #

(.-^) :: Num a => V3 a -> Diff V3 a -> V3 a #

Affine V2 
Instance details

Defined in Linear.Affine

Associated Types

type Diff V2 :: Type -> Type #

Methods

(.-.) :: Num a => V2 a -> V2 a -> Diff V2 a #

(.+^) :: Num a => V2 a -> Diff V2 a -> V2 a #

(.-^) :: Num a => V2 a -> Diff V2 a -> V2 a #

Affine V1 
Instance details

Defined in Linear.Affine

Associated Types

type Diff V1 :: Type -> Type #

Methods

(.-.) :: Num a => V1 a -> V1 a -> Diff V1 a #

(.+^) :: Num a => V1 a -> Diff V1 a -> V1 a #

(.-^) :: Num a => V1 a -> Diff V1 a -> V1 a #

(Eq k, Hashable k) => Affine (HashMap k) 
Instance details

Defined in Linear.Affine

Associated Types

type Diff (HashMap k) :: Type -> Type #

Methods

(.-.) :: Num a => HashMap k a -> HashMap k a -> Diff (HashMap k) a #

(.+^) :: Num a => HashMap k a -> Diff (HashMap k) a -> HashMap k a #

(.-^) :: Num a => HashMap k a -> Diff (HashMap k) a -> HashMap k a #

Ord k => Affine (Map k) 
Instance details

Defined in Linear.Affine

Associated Types

type Diff (Map k) :: Type -> Type #

Methods

(.-.) :: Num a => Map k a -> Map k a -> Diff (Map k) a #

(.+^) :: Num a => Map k a -> Diff (Map k) a -> Map k a #

(.-^) :: Num a => Map k a -> Diff (Map k) a -> Map k a #

Additive f => Affine (Point f) 
Instance details

Defined in Linear.Affine

Associated Types

type Diff (Point f) :: Type -> Type #

Methods

(.-.) :: Num a => Point f a -> Point f a -> Diff (Point f) a #

(.+^) :: Num a => Point f a -> Diff (Point f) a -> Point f a #

(.-^) :: Num a => Point f a -> Diff (Point f) a -> Point f a #

Arity d => Affine (Vector d) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFixed

Associated Types

type Diff (Vector d) :: Type -> Type #

Methods

(.-.) :: Num a => Vector d a -> Vector d a -> Diff (Vector d) a #

(.+^) :: Num a => Vector d a -> Diff (Vector d) a -> Vector d a #

(.-^) :: Num a => Vector d a -> Diff (Vector d) a -> Vector d a #

ImplicitArity d => Affine (VectorFamily d) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamilyPeano

Associated Types

type Diff (VectorFamily d) :: Type -> Type #

Methods

(.-.) :: Num a => VectorFamily d a -> VectorFamily d a -> Diff (VectorFamily d) a #

(.+^) :: Num a => VectorFamily d a -> Diff (VectorFamily d) a -> VectorFamily d a #

(.-^) :: Num a => VectorFamily d a -> Diff (VectorFamily d) a -> VectorFamily d a #

Arity d => Affine (Vector d) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

Associated Types

type Diff (Vector d) :: Type -> Type #

Methods

(.-.) :: Num a => Vector d a -> Vector d a -> Diff (Vector d) a #

(.+^) :: Num a => Vector d a -> Diff (Vector d) a -> Vector d a #

(.-^) :: Num a => Vector d a -> Diff (Vector d) a -> Vector d a #

Arity d => Affine (Point d) Source # 
Instance details

Defined in Data.Geometry.Point

Associated Types

type Diff (Point d) :: Type -> Type #

Methods

(.-.) :: Num a => Point d a -> Point d a -> Diff (Point d) a #

(.+^) :: Num a => Point d a -> Diff (Point d) a -> Point d a #

(.-^) :: Num a => Point d a -> Diff (Point d) a -> Point d a #

Dim n => Affine (V n) 
Instance details

Defined in Linear.Affine

Associated Types

type Diff (V n) :: Type -> Type #

Methods

(.-.) :: Num a => V n a -> V n a -> Diff (V n) a #

(.+^) :: Num a => V n a -> Diff (V n) a -> V n a #

(.-^) :: Num a => V n a -> Diff (V n) a -> V n a #

Affine ((->) b :: Type -> Type) 
Instance details

Defined in Linear.Affine

Associated Types

type Diff ((->) b) :: Type -> Type #

Methods

(.-.) :: Num a => (b -> a) -> (b -> a) -> Diff ((->) b) a #

(.+^) :: Num a => (b -> a) -> Diff ((->) b) a -> b -> a #

(.-^) :: Num a => (b -> a) -> Diff ((->) b) a -> b -> a #

qdA :: (Affine p, Foldable (Diff p), Num a) => p a -> p a -> a #

Compute the quadrance of the difference (the square of the distance)

distanceA :: (Floating a, Foldable (Diff p), Affine p) => p a -> p a -> a #

Distance between two points in an affine space

dot :: (Metric f, 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

norm :: (Metric f, Floating a) => f a -> a #

Compute the norm of a vector in a metric space

signorm :: (Metric f, Floating a) => f a -> f a #

Convert a non-zero vector to unit vector.

isScalarMultipleOf :: (Eq r, Fractional r, Arity d) => Vector d r -> Vector d r -> Bool Source #

Test if v is a scalar multiple of u.

>>> Vector2 1 1 `isScalarMultipleOf` Vector2 10 10
True
>>> Vector2 1 1 `isScalarMultipleOf` Vector2 10 1
False
>>> Vector2 1 1 `isScalarMultipleOf` Vector2 11.1 11.1
True
>>> Vector2 1 1 `isScalarMultipleOf` Vector2 11.1 11.2
False
>>> Vector2 2 1 `isScalarMultipleOf` Vector2 11.1 11.2
False
>>> Vector2 2 1 `isScalarMultipleOf` Vector2 4 2
True
>>> Vector2 2 1 `isScalarMultipleOf` Vector2 4 0
False

scalarMultiple :: (Eq r, Fractional r, Arity d) => Vector d r -> Vector d r -> Maybe r Source #

Get the scalar labmda s.t. v = lambda * u (if it exists)

replicate :: Vector v a => a -> v a #

Replicate value n times.

Examples:

>>> import Data.Vector.Fixed.Boxed (Vec2)
>>> replicate 1 :: Vec2 Int
fromList [1,1]
>>> replicate 2 :: (Double,Double,Double)
(2.0,2.0,2.0)
>>> import Data.Vector.Fixed.Boxed (Vec4)
>>> replicate "foo" :: Vec4 String
fromList ["foo","foo","foo","foo"]

imap :: (Vector v a, Vector v b) => (Int -> a -> b) -> v a -> v b #

Apply function to every element of the vector and its index.

xComponent :: (1 <= d, Arity d) => Lens' (Vector d r) r Source #

yComponent :: (2 <= d, Arity d) => Lens' (Vector d r) r Source #

zComponent :: (3 <= d, Arity d) => Lens' (Vector d r) r Source #