hgeometry-0.10.0.0: Geometric Algorithms, Data structures, and Data types.

Data.Geometry.Vector

Contents

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 detailsDefined in Data.Geometry.Vector.VectorFixed Methods(==) :: C n -> C n -> Bool #(/=) :: C n -> C n -> Bool # Ord (C n) Source # Instance detailsDefined in Data.Geometry.Vector.VectorFixed Methodscompare :: 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 detailsDefined in Data.Geometry.Vector.VectorFixed MethodsreadsPrec :: Int -> ReadS (C n) #readList :: ReadS [C n] #readPrec :: ReadPrec (C n) # Show (C n) Source # Instance detailsDefined in Data.Geometry.Vector.VectorFixed MethodsshowsPrec :: 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 detailsDefined in Linear.Affine Associated Typestype Diff [] :: Type -> Type # Methods(.-.) :: Num a => [a] -> [a] -> Diff [] a #(.+^) :: Num a => [a] -> Diff [] a -> [a] #(.-^) :: Num a => [a] -> Diff [] a -> [a] # Instance detailsDefined in Linear.Affine Associated Typestype 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 # Instance detailsDefined in Linear.Affine Associated Typestype 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 # Instance detailsDefined in Linear.Affine Associated Typestype 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 # Instance detailsDefined in Linear.Affine Associated Typestype 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 # Instance detailsDefined in Linear.Affine Associated Typestype 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 # Instance detailsDefined in Linear.Affine Associated Typestype 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 # Instance detailsDefined in Linear.Affine Associated Typestype 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 # Instance detailsDefined in Linear.Affine Associated Typestype Diff Quaternion :: Type -> Type # Methods(.-.) :: Num a => Quaternion a -> Quaternion a -> Diff Quaternion a #(.+^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a #(.-^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a # Instance detailsDefined in Linear.Affine Associated Typestype 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 # Instance detailsDefined in Linear.Affine Associated Typestype 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 # Instance detailsDefined in Linear.Affine Associated Typestype 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 # Instance detailsDefined in Linear.Affine Associated Typestype 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 # Instance detailsDefined in Linear.Affine Associated Typestype 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 detailsDefined in Linear.Affine Associated Typestype 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 detailsDefined in Linear.Affine Associated Typestype 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 detailsDefined in Linear.Affine Associated Typestype 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 detailsDefined in Data.Geometry.Vector.VectorFixed Associated Typestype 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 # Source # Instance detailsDefined in Data.Geometry.Vector.VectorFamilyPeano Associated Typestype 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 detailsDefined in Data.Geometry.Vector.VectorFamily Associated Typestype 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 detailsDefined in Data.Geometry.Point Associated Typestype 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 detailsDefined in Linear.Affine Associated Typestype 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 detailsDefined in Linear.Affine Associated Typestype 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 #

'isScalarmultipleof u v' 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 #

scalarMultiple u v computes 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 #

# Orphan instances

 (Arbitrary r, Arity d) => Arbitrary (Vector d r) Source # Instance details Methodsarbitrary :: Gen (Vector d r) #shrink :: Vector d r -> [Vector d r] #