hgeometry-0.7.0.0: Geometric Algorithms, Data structures, and Data types.

Copyright(c) Frank Staals
LicenseSee LICENCE file
Safe HaskellNone
LanguageHaskell2010

Data.Geometry

Description

 
Synopsis

Documentation

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.

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"]

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

Distance between two points in an affine space

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

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

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

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 [] :: * -> * #

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 :: * -> * #

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 :: * -> * #

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 :: * -> * #

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 :: * -> * #

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 :: * -> * #

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 :: * -> * #

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 :: * -> * #

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 :: * -> * #

Affine V0 
Instance details

Defined in Linear.Affine

Associated Types

type Diff V0 :: * -> * #

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 :: * -> * #

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 :: * -> * #

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 :: * -> * #

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 :: * -> * #

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) :: * -> * #

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) :: * -> * #

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) :: * -> * #

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) # 
Instance details

Defined in Data.Geometry.Vector.VectorFixed

Associated Types

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

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) # 
Instance details

Defined in Data.Geometry.Vector.VectorFamilyPeano

Associated Types

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

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) # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

Associated Types

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

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) # 
Instance details

Defined in Data.Geometry.Point

Associated Types

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

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) :: * -> * #

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 :: * -> *) 
Instance details

Defined in Linear.Affine

Associated Types

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

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 #

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.

outer :: (Functor f, Functor g, Num a) => f a -> g a -> f (g a) #

Outer (tensor) product of two vectors

unit :: (Additive t, Num a) => ASetter' (t a) a -> t a #

Create a unit vector.

>>> unit _x :: V2 Int
V2 1 0

scaled :: (Traversable t, Num a) => t a -> t (t a) #

Produce a diagonal (scale) matrix from a vector.

>>> scaled (V2 2 3)
V2 (V2 2 0) (V2 0 3)

basisFor :: (Traversable t, Num a) => t b -> [t a] #

Produce a default basis for a vector space from which the argument is drawn.

basis :: (Additive t, Traversable t, Num a) => [t a] #

Produce a default basis for a vector space. If the dimensionality of the vector space is not statically known, see basisFor.

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

Compute division by a scalar on the right.

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

Compute the left scalar product

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

sumV :: (Foldable f, Additive v, Num a) => f (v a) -> v a #

Sum over multiple vectors

>>> sumV [V2 1 1, V2 3 4]
V2 4 5

negated :: (Functor f, Num a) => f a -> f a #

Compute the negation of a vector

>>> negated (V2 2 4)
V2 (-2) (-4)

newtype E (t :: * -> *) #

Basis element

Constructors

E 

Fields

  • el :: forall x (f :: * -> *). Functor f => (x -> f x) -> t x -> f (t x)
     
Instances
FunctorWithIndex (E Plucker) Plucker 
Instance details

Defined in Linear.Plucker

Methods

imap :: (E Plucker -> a -> b) -> Plucker a -> Plucker b #

imapped :: (Indexable (E Plucker) p, Settable f) => p a (f b) -> Plucker a -> f (Plucker b) #

FunctorWithIndex (E Quaternion) Quaternion 
Instance details

Defined in Linear.Quaternion

Methods

imap :: (E Quaternion -> a -> b) -> Quaternion a -> Quaternion b #

imapped :: (Indexable (E Quaternion) p, Settable f) => p a (f b) -> Quaternion a -> f (Quaternion b) #

FunctorWithIndex (E V0) V0 
Instance details

Defined in Linear.V0

Methods

imap :: (E V0 -> a -> b) -> V0 a -> V0 b #

imapped :: (Indexable (E V0) p, Settable f) => p a (f b) -> V0 a -> f (V0 b) #

FunctorWithIndex (E V4) V4 
Instance details

Defined in Linear.V4

Methods

imap :: (E V4 -> a -> b) -> V4 a -> V4 b #

imapped :: (Indexable (E V4) p, Settable f) => p a (f b) -> V4 a -> f (V4 b) #

FunctorWithIndex (E V3) V3 
Instance details

Defined in Linear.V3

Methods

imap :: (E V3 -> a -> b) -> V3 a -> V3 b #

imapped :: (Indexable (E V3) p, Settable f) => p a (f b) -> V3 a -> f (V3 b) #

FunctorWithIndex (E V2) V2 
Instance details

Defined in Linear.V2

Methods

imap :: (E V2 -> a -> b) -> V2 a -> V2 b #

imapped :: (Indexable (E V2) p, Settable f) => p a (f b) -> V2 a -> f (V2 b) #

FunctorWithIndex (E V1) V1 
Instance details

Defined in Linear.V1

Methods

imap :: (E V1 -> a -> b) -> V1 a -> V1 b #

imapped :: (Indexable (E V1) p, Settable f) => p a (f b) -> V1 a -> f (V1 b) #

FoldableWithIndex (E Plucker) Plucker 
Instance details

Defined in Linear.Plucker

Methods

ifoldMap :: Monoid m => (E Plucker -> a -> m) -> Plucker a -> m #

ifolded :: (Indexable (E Plucker) p, Contravariant f, Applicative f) => p a (f a) -> Plucker a -> f (Plucker a) #

ifoldr :: (E Plucker -> a -> b -> b) -> b -> Plucker a -> b #

ifoldl :: (E Plucker -> b -> a -> b) -> b -> Plucker a -> b #

ifoldr' :: (E Plucker -> a -> b -> b) -> b -> Plucker a -> b #

ifoldl' :: (E Plucker -> b -> a -> b) -> b -> Plucker a -> b #

FoldableWithIndex (E Quaternion) Quaternion 
Instance details

Defined in Linear.Quaternion

Methods

ifoldMap :: Monoid m => (E Quaternion -> a -> m) -> Quaternion a -> m #

ifolded :: (Indexable (E Quaternion) p, Contravariant f, Applicative f) => p a (f a) -> Quaternion a -> f (Quaternion a) #

ifoldr :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b #

ifoldl :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b #

ifoldr' :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b #

ifoldl' :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b #

FoldableWithIndex (E V0) V0 
Instance details

Defined in Linear.V0

Methods

ifoldMap :: Monoid m => (E V0 -> a -> m) -> V0 a -> m #

ifolded :: (Indexable (E V0) p, Contravariant f, Applicative f) => p a (f a) -> V0 a -> f (V0 a) #

ifoldr :: (E V0 -> a -> b -> b) -> b -> V0 a -> b #

ifoldl :: (E V0 -> b -> a -> b) -> b -> V0 a -> b #

ifoldr' :: (E V0 -> a -> b -> b) -> b -> V0 a -> b #

ifoldl' :: (E V0 -> b -> a -> b) -> b -> V0 a -> b #

FoldableWithIndex (E V4) V4 
Instance details

Defined in Linear.V4

Methods

ifoldMap :: Monoid m => (E V4 -> a -> m) -> V4 a -> m #

ifolded :: (Indexable (E V4) p, Contravariant f, Applicative f) => p a (f a) -> V4 a -> f (V4 a) #

ifoldr :: (E V4 -> a -> b -> b) -> b -> V4 a -> b #

ifoldl :: (E V4 -> b -> a -> b) -> b -> V4 a -> b #

ifoldr' :: (E V4 -> a -> b -> b) -> b -> V4 a -> b #

ifoldl' :: (E V4 -> b -> a -> b) -> b -> V4 a -> b #

FoldableWithIndex (E V3) V3 
Instance details

Defined in Linear.V3

Methods

ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m #

ifolded :: (Indexable (E V3) p, Contravariant f, Applicative f) => p a (f a) -> V3 a -> f (V3 a) #

ifoldr :: (E V3 -> a -> b -> b) -> b -> V3 a -> b #

ifoldl :: (E V3 -> b -> a -> b) -> b -> V3 a -> b #

ifoldr' :: (E V3 -> a -> b -> b) -> b -> V3 a -> b #

ifoldl' :: (E V3 -> b -> a -> b) -> b -> V3 a -> b #

FoldableWithIndex (E V2) V2 
Instance details

Defined in Linear.V2

Methods

ifoldMap :: Monoid m => (E V2 -> a -> m) -> V2 a -> m #

ifolded :: (Indexable (E V2) p, Contravariant f, Applicative f) => p a (f a) -> V2 a -> f (V2 a) #

ifoldr :: (E V2 -> a -> b -> b) -> b -> V2 a -> b #

ifoldl :: (E V2 -> b -> a -> b) -> b -> V2 a -> b #

ifoldr' :: (E V2 -> a -> b -> b) -> b -> V2 a -> b #

ifoldl' :: (E V2 -> b -> a -> b) -> b -> V2 a -> b #

FoldableWithIndex (E V1) V1 
Instance details

Defined in Linear.V1

Methods

ifoldMap :: Monoid m => (E V1 -> a -> m) -> V1 a -> m #

ifolded :: (Indexable (E V1) p, Contravariant f, Applicative f) => p a (f a) -> V1 a -> f (V1 a) #

ifoldr :: (E V1 -> a -> b -> b) -> b -> V1 a -> b #

ifoldl :: (E V1 -> b -> a -> b) -> b -> V1 a -> b #

ifoldr' :: (E V1 -> a -> b -> b) -> b -> V1 a -> b #

ifoldl' :: (E V1 -> b -> a -> b) -> b -> V1 a -> b #

TraversableWithIndex (E Plucker) Plucker 
Instance details

Defined in Linear.Plucker

Methods

itraverse :: Applicative f => (E Plucker -> a -> f b) -> Plucker a -> f (Plucker b) #

itraversed :: (Indexable (E Plucker) p, Applicative f) => p a (f b) -> Plucker a -> f (Plucker b) #

TraversableWithIndex (E Quaternion) Quaternion 
Instance details

Defined in Linear.Quaternion

Methods

itraverse :: Applicative f => (E Quaternion -> a -> f b) -> Quaternion a -> f (Quaternion b) #

itraversed :: (Indexable (E Quaternion) p, Applicative f) => p a (f b) -> Quaternion a -> f (Quaternion b) #

TraversableWithIndex (E V0) V0 
Instance details

Defined in Linear.V0

Methods

itraverse :: Applicative f => (E V0 -> a -> f b) -> V0 a -> f (V0 b) #

itraversed :: (Indexable (E V0) p, Applicative f) => p a (f b) -> V0 a -> f (V0 b) #

TraversableWithIndex (E V4) V4 
Instance details

Defined in Linear.V4

Methods

itraverse :: Applicative f => (E V4 -> a -> f b) -> V4 a -> f (V4 b) #

itraversed :: (Indexable (E V4) p, Applicative f) => p a (f b) -> V4 a -> f (V4 b) #

TraversableWithIndex (E V3) V3 
Instance details

Defined in Linear.V3

Methods

itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b) #

itraversed :: (Indexable (E V3) p, Applicative f) => p a (f b) -> V3 a -> f (V3 b) #

TraversableWithIndex (E V2) V2 
Instance details

Defined in Linear.V2

Methods

itraverse :: Applicative f => (E V2 -> a -> f b) -> V2 a -> f (V2 b) #

itraversed :: (Indexable (E V2) p, Applicative f) => p a (f b) -> V2 a -> f (V2 b) #

TraversableWithIndex (E V1) V1 
Instance details

Defined in Linear.V1

Methods

itraverse :: Applicative f => (E V1 -> a -> f b) -> V1 a -> f (V1 b) #

itraversed :: (Indexable (E V1) p, Applicative f) => p a (f b) -> V1 a -> f (V1 b) #

class Functor f => Additive (f :: * -> *) where #

A vector is an additive group with additional structure.

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.

liftU2 :: (a -> a -> a) -> f a -> f a -> f a #

Apply a function to merge the 'non-zero' components of two vectors, unioning the rest of the values.

  • For a dense vector this is equivalent to liftA2.
  • For a sparse vector this is equivalent to unionWith.

liftI2 :: (a -> b -> c) -> f a -> f b -> f c #

Apply a function to the components of two vectors.

Instances
Additive [] 
Instance details

Defined in Linear.Vector

Methods

zero :: Num a => [a] #

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

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

lerp :: Num a => a -> [a] -> [a] -> [a] #

liftU2 :: (a -> a -> a) -> [a] -> [a] -> [a] #

liftI2 :: (a -> b -> c) -> [a] -> [b] -> [c] #

Additive Maybe 
Instance details

Defined in Linear.Vector

Methods

zero :: Num a => Maybe a #

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

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

lerp :: Num a => a -> Maybe a -> Maybe a -> Maybe a #

liftU2 :: (a -> a -> a) -> Maybe a -> Maybe a -> Maybe a #

liftI2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c #

Additive Complex 
Instance details

Defined in Linear.Vector

Methods

zero :: Num a => Complex a #

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

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

lerp :: Num a => a -> Complex a -> Complex a -> Complex a #

liftU2 :: (a -> a -> a) -> Complex a -> Complex a -> Complex a #

liftI2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c #

Additive ZipList 
Instance details

Defined in Linear.Vector

Methods

zero :: Num a => ZipList a #

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

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

lerp :: Num a => a -> ZipList a -> ZipList a -> ZipList a #

liftU2 :: (a -> a -> a) -> ZipList a -> ZipList a -> ZipList a #

liftI2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c #

Additive Identity 
Instance details

Defined in Linear.Vector

Methods

zero :: Num a => Identity a #

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

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

lerp :: Num a => a -> Identity a -> Identity a -> Identity a #

liftU2 :: (a -> a -> a) -> Identity a -> Identity a -> Identity a #

liftI2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c #

Additive IntMap 
Instance details

Defined in Linear.Vector

Methods

zero :: Num a => IntMap a #

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

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

lerp :: Num a => a -> IntMap a -> IntMap a -> IntMap a #

liftU2 :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a #

liftI2 :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c #

Additive Vector 
Instance details

Defined in Linear.Vector

Methods

zero :: Num a => Vector a #

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

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

lerp :: Num a => a -> Vector a -> Vector a -> Vector a #

liftU2 :: (a -> a -> a) -> Vector a -> Vector a -> Vector a #

liftI2 :: (a -> b -> c) -> Vector a -> Vector b -> Vector c #

Additive Plucker 
Instance details

Defined in Linear.Plucker

Methods

zero :: Num a => Plucker a #

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

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

lerp :: Num a => a -> Plucker a -> Plucker a -> Plucker a #

liftU2 :: (a -> a -> a) -> Plucker a -> Plucker a -> Plucker a #

liftI2 :: (a -> b -> c) -> Plucker a -> Plucker b -> Plucker c #

Additive Quaternion 
Instance details

Defined in Linear.Quaternion

Methods

zero :: Num a => Quaternion a #

(^+^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a #

(^-^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a #

lerp :: Num a => a -> Quaternion a -> Quaternion a -> Quaternion a #

liftU2 :: (a -> a -> a) -> Quaternion a -> Quaternion a -> Quaternion a #

liftI2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c #

Additive V0 
Instance details

Defined in Linear.V0

Methods

zero :: Num a => V0 a #

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

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

lerp :: Num a => a -> V0 a -> V0 a -> V0 a #

liftU2 :: (a -> a -> a) -> V0 a -> V0 a -> V0 a #

liftI2 :: (a -> b -> c) -> V0 a -> V0 b -> V0 c #

Additive V4 
Instance details

Defined in Linear.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 #

liftU2 :: (a -> a -> a) -> V4 a -> V4 a -> V4 a #

liftI2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c #

Additive V3 
Instance details

Defined in Linear.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 #

liftU2 :: (a -> a -> a) -> V3 a -> V3 a -> V3 a #

liftI2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #

Additive V2 
Instance details

Defined in Linear.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 #

liftU2 :: (a -> a -> a) -> V2 a -> V2 a -> V2 a #

liftI2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c #

Additive V1 
Instance details

Defined in Linear.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 #

liftU2 :: (a -> a -> a) -> V1 a -> V1 a -> V1 a #

liftI2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c #

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

Defined in Linear.Vector

Methods

zero :: Num a => HashMap k a #

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

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

lerp :: Num a => a -> HashMap k a -> HashMap k a -> HashMap k a #

liftU2 :: (a -> a -> a) -> HashMap k a -> HashMap k a -> HashMap k a #

liftI2 :: (a -> b -> c) -> HashMap k a -> HashMap k b -> HashMap k c #

Ord k => Additive (Map k) 
Instance details

Defined in Linear.Vector

Methods

zero :: Num a => Map k a #

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

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

lerp :: Num a => a -> Map k a -> Map k a -> Map k a #

liftU2 :: (a -> a -> a) -> Map k a -> Map k a -> Map k a #

liftI2 :: (a -> b -> c) -> Map k a -> Map k b -> Map k c #

Additive f => Additive (Point f) 
Instance details

Defined in Linear.Affine

Methods

zero :: Num a => Point f a #

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

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

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

liftU2 :: (a -> a -> a) -> Point f a -> Point f a -> Point f a #

liftI2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c #

Arity d => Additive (Vector d) # 
Instance details

Defined in Data.Geometry.Vector.VectorFixed

Methods

zero :: Num a => Vector d a #

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

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

lerp :: Num a => a -> Vector d a -> Vector d a -> Vector d a #

liftU2 :: (a -> a -> a) -> Vector d a -> Vector d a -> Vector d a #

liftI2 :: (a -> b -> c) -> Vector d a -> Vector d b -> Vector d c #

ImplicitArity d => Additive (VectorFamily d) # 
Instance details

Defined in Data.Geometry.Vector.VectorFamilyPeano

Methods

zero :: Num a => VectorFamily d a #

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

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

lerp :: Num a => a -> VectorFamily d a -> VectorFamily d a -> VectorFamily d a #

liftU2 :: (a -> a -> a) -> VectorFamily d a -> VectorFamily d a -> VectorFamily d a #

liftI2 :: (a -> b -> c) -> VectorFamily d a -> VectorFamily d b -> VectorFamily d c #

Arity d => Additive (Vector d) # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

Methods

zero :: Num a => Vector d a #

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

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

lerp :: Num a => a -> Vector d a -> Vector d a -> Vector d a #

liftU2 :: (a -> a -> a) -> Vector d a -> Vector d a -> Vector d a #

liftI2 :: (a -> b -> c) -> Vector d a -> Vector d b -> Vector d c #

Dim n => Additive (V n) 
Instance details

Defined in Linear.V

Methods

zero :: Num a => V n a #

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

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

lerp :: Num a => a -> V n a -> V n a -> V n a #

liftU2 :: (a -> a -> a) -> V n a -> V n a -> V n a #

liftI2 :: (a -> b -> c) -> V n a -> V n b -> V n c #

Additive ((->) b :: * -> *) 
Instance details

Defined in Linear.Vector

Methods

zero :: Num a => b -> a #

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

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

lerp :: Num a => a -> (b -> a) -> (b -> a) -> b -> a #

liftU2 :: (a -> a -> a) -> (b -> a) -> (b -> a) -> b -> a #

liftI2 :: (a -> b0 -> c) -> (b -> a) -> (b -> b0) -> b -> c #

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 #

newtype Vector (d :: Nat) (r :: *) Source #

Datatype representing d dimensional vectors. The default implementation is based n VectorFixed. However, for small vectors we automatically select a more efficient representation.

Constructors

MKVector 

Fields

Instances
Arity d => Functor (Vector d) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

Methods

fmap :: (a -> b) -> Vector d a -> Vector d b #

(<$) :: a -> Vector d b -> Vector d a #

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

Defined in Data.Geometry.Vector.VectorFamily

Methods

pure :: a -> Vector d a #

(<*>) :: Vector d (a -> b) -> Vector d a -> Vector d b #

liftA2 :: (a -> b -> c) -> Vector d a -> Vector d b -> Vector d c #

(*>) :: Vector d a -> Vector d b -> Vector d b #

(<*) :: Vector d a -> Vector d b -> Vector d a #

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

Defined in Data.Geometry.Vector.VectorFamily

Methods

fold :: Monoid m => Vector d m -> m #

foldMap :: Monoid m => (a -> m) -> Vector d a -> m #

foldr :: (a -> b -> b) -> b -> Vector d a -> b #

foldr' :: (a -> b -> b) -> b -> Vector d a -> b #

foldl :: (b -> a -> b) -> b -> Vector d a -> b #

foldl' :: (b -> a -> b) -> b -> Vector d a -> b #

foldr1 :: (a -> a -> a) -> Vector d a -> a #

foldl1 :: (a -> a -> a) -> Vector d a -> a #

toList :: Vector d a -> [a] #

null :: Vector d a -> Bool #

length :: Vector d a -> Int #

elem :: Eq a => a -> Vector d a -> Bool #

maximum :: Ord a => Vector d a -> a #

minimum :: Ord a => Vector d a -> a #

sum :: Num a => Vector d a -> a #

product :: Num a => Vector d a -> a #

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

Defined in Data.Geometry.Vector.VectorFamily

Methods

traverse :: Applicative f => (a -> f b) -> Vector d a -> f (Vector d b) #

sequenceA :: Applicative f => Vector d (f a) -> f (Vector d a) #

mapM :: Monad m => (a -> m b) -> Vector d a -> m (Vector d b) #

sequence :: Monad m => Vector d (m a) -> m (Vector d a) #

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

Defined in Data.Geometry.Vector.VectorFamily

Associated Types

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

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 => Metric (Vector d) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

Methods

dot :: Num a => Vector d a -> Vector d a -> a #

quadrance :: Num a => Vector d a -> a #

qd :: Num a => Vector d a -> Vector d a -> a #

distance :: Floating a => Vector d a -> Vector d a -> a #

norm :: Floating a => Vector d a -> a #

signorm :: Floating a => Vector d a -> Vector d a #

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

Defined in Data.Geometry.Vector.VectorFamily

Methods

zero :: Num a => Vector d a #

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

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

lerp :: Num a => a -> Vector d a -> Vector d a -> Vector d a #

liftU2 :: (a -> a -> a) -> Vector d a -> Vector d a -> Vector d a #

liftI2 :: (a -> b -> c) -> Vector d a -> Vector d b -> Vector d c #

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

Defined in Data.Geometry.Vector.VectorFamily

Methods

construct :: Fun (Peano (Dim (Vector d))) r (Vector d r) #

inspect :: Vector d r -> Fun (Peano (Dim (Vector d))) r b -> b #

basicIndex :: Vector d r -> Int -> r #

(Eq r, Arity d) => Eq (Vector d r) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

Methods

(==) :: Vector d r -> Vector d r -> Bool #

(/=) :: Vector d r -> Vector d r -> Bool #

(Ord r, Arity d) => Ord (Vector d r) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

Methods

compare :: Vector d r -> Vector d r -> Ordering #

(<) :: Vector d r -> Vector d r -> Bool #

(<=) :: Vector d r -> Vector d r -> Bool #

(>) :: Vector d r -> Vector d r -> Bool #

(>=) :: Vector d r -> Vector d r -> Bool #

max :: Vector d r -> Vector d r -> Vector d r #

min :: Vector d r -> Vector d r -> Vector d r #

(Arity d, Show r) => Show (Vector d r) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

Methods

showsPrec :: Int -> Vector d r -> ShowS #

show :: Vector d r -> String #

showList :: [Vector d r] -> ShowS #

(Arbitrary r, Arity d) => Arbitrary (Vector d r) # 
Instance details

Defined in Test.QuickCheck.HGeometryInstances

Methods

arbitrary :: Gen (Vector d r) #

shrink :: Vector d r -> [Vector d r] #

(ToJSON r, Arity d) => ToJSON (Vector d r) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

Methods

toJSON :: Vector d r -> Value #

toEncoding :: Vector d r -> Encoding #

toJSONList :: [Vector d r] -> Value #

toEncodingList :: [Vector d r] -> Encoding #

(FromJSON r, Arity d) => FromJSON (Vector d r) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

Methods

parseJSON :: Value -> Parser (Vector d r) #

parseJSONList :: Value -> Parser [Vector d r] #

(NFData r, Arity d) => NFData (Vector d r) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

Methods

rnf :: Vector d r -> () #

Arity d => Ixed (Vector d r) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

Methods

ix :: Index (Vector d r) -> Traversal' (Vector d r) (IxValue (Vector d r)) #

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Vector d r) Source # 
Instance details

Defined in Data.Geometry.Transformation

Methods

transformBy :: Transformation (Dimension (Vector d r)) (NumType (Vector d r)) -> Vector d r -> Vector d r Source #

type Dim (Vector d) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

type Dim (Vector d) = FromPeano (Peano d)
type Diff (Vector d) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

type Diff (Vector d) = Diff (VectorFamily (Peano d))
type Index (Vector d r) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

type Index (Vector d r) = Int
type IxValue (Vector d r) Source # 
Instance details

Defined in Data.Geometry.Vector.VectorFamily

type IxValue (Vector d r) = r
type NumType (Vector d r) Source # 
Instance details

Defined in Data.Geometry.Vector

type NumType (Vector d r) = r
type Dimension (Vector d r) Source # 
Instance details

Defined in Data.Geometry.Vector

type Dimension (Vector d r) = d

pattern Vector4 :: r -> r -> r -> r -> Vector 4 r Source #

pattern Vector3 :: r -> r -> r -> Vector 3 r Source #

pattern Vector2 :: r -> r -> Vector 2 r Source #

pattern Vector1 :: r -> Vector 1 r Source #

pattern Vector :: VectorFamilyF (Peano d) r -> Vector d r Source #

unV :: Lens (Vector d r) (Vector d s) (VectorFamily (Peano d) r) (VectorFamily (Peano d) s) Source #

vectorFromList :: Arity d => [r] -> Maybe (Vector d r) Source #

destruct :: (Arity d, Arity (d + 1)) => Vector (d + 1) r -> (r, Vector d r) Source #

element :: forall proxy i d r. (Arity d, KnownNat i, (i + 1) <= d) => proxy i -> Lens' (Vector d r) r Source #

Lens into the i th element

element' :: forall d r. Arity d => Int -> Traversal' (Vector d r) r Source #

Similar to element above. Except that we don't have a static guarantee that the index is in bounds. Hence, we can only return a Traversal

snoc :: (Arity (d + 1), Arity d) => Vector d r -> r -> Vector (d + 1) r Source #

Add an element at the back of the vector

init :: (Arity d, Arity (d + 1)) => Vector (d + 1) r -> Vector d r Source #

Get a vector of the first d - 1 elements.

prefix :: forall i d r. (Arity d, Arity i, i <= d) => Vector d r -> Vector i r Source #

Get a prefix of i elements of a vector

cross :: Num r => Vector 3 r -> Vector 3 r -> Vector 3 r Source #

Cross product of two three-dimensional vectors

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)

newtype PolyLine d p r Source #

A Poly line in R^d

Constructors

PolyLine 

Fields

Instances
Arity d => Bifunctor (PolyLine d) Source # 
Instance details

Defined in Data.Geometry.PolyLine

Methods

bimap :: (a -> b) -> (c -> d0) -> PolyLine d a c -> PolyLine d b d0 #

first :: (a -> b) -> PolyLine d a c -> PolyLine d b c #

second :: (b -> c) -> PolyLine d a b -> PolyLine d a c #

Arity d => Functor (PolyLine d p) Source # 
Instance details

Defined in Data.Geometry.PolyLine

Methods

fmap :: (a -> b) -> PolyLine d p a -> PolyLine d p b #

(<$) :: a -> PolyLine d p b -> PolyLine d p a #

PointFunctor (PolyLine d p) Source # 
Instance details

Defined in Data.Geometry.PolyLine

Methods

pmap :: (Point (Dimension (PolyLine d p r)) r -> Point (Dimension (PolyLine d p s)) s) -> PolyLine d p r -> PolyLine d p s Source #

(Eq r, Eq p, Arity d) => Eq (PolyLine d p r) Source # 
Instance details

Defined in Data.Geometry.PolyLine

Methods

(==) :: PolyLine d p r -> PolyLine d p r -> Bool #

(/=) :: PolyLine d p r -> PolyLine d p r -> Bool #

(Ord r, Ord p, Arity d) => Ord (PolyLine d p r) Source # 
Instance details

Defined in Data.Geometry.PolyLine

Methods

compare :: PolyLine d p r -> PolyLine d p r -> Ordering #

(<) :: PolyLine d p r -> PolyLine d p r -> Bool #

(<=) :: PolyLine d p r -> PolyLine d p r -> Bool #

(>) :: PolyLine d p r -> PolyLine d p r -> Bool #

(>=) :: PolyLine d p r -> PolyLine d p r -> Bool #

max :: PolyLine d p r -> PolyLine d p r -> PolyLine d p r #

min :: PolyLine d p r -> PolyLine d p r -> PolyLine d p r #

(Show r, Show p, Arity d) => Show (PolyLine d p r) Source # 
Instance details

Defined in Data.Geometry.PolyLine

Methods

showsPrec :: Int -> PolyLine d p r -> ShowS #

show :: PolyLine d p r -> String #

showList :: [PolyLine d p r] -> ShowS #

Semigroup (PolyLine d p r) Source # 
Instance details

Defined in Data.Geometry.PolyLine

Methods

(<>) :: PolyLine d p r -> PolyLine d p r -> PolyLine d p r #

sconcat :: NonEmpty (PolyLine d p r) -> PolyLine d p r #

stimes :: Integral b => b -> PolyLine d p r -> PolyLine d p r #

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (PolyLine d p r) Source # 
Instance details

Defined in Data.Geometry.PolyLine

Methods

transformBy :: Transformation (Dimension (PolyLine d p r)) (NumType (PolyLine d p r)) -> PolyLine d p r -> PolyLine d p r Source #

Arity d => IsBoxable (PolyLine d p r) Source # 
Instance details

Defined in Data.Geometry.PolyLine

Methods

boundingBox :: PolyLine d p r -> Box (Dimension (PolyLine d p r)) () (NumType (PolyLine d p r)) Source #

(IpeWriteText r, IpeWrite p) => IpeWrite (PolyLine 2 p r) Source # 
Instance details

Defined in Data.Geometry.Ipe.Writer

Methods

ipeWrite :: PolyLine 2 p r -> Maybe (Node Text Text) Source #

IpeWriteText r => IpeWriteText (PolyLine 2 () r) Source # 
Instance details

Defined in Data.Geometry.Ipe.Writer

Methods

ipeWriteText :: PolyLine 2 () r -> Maybe Text Source #

HasDefaultFromIpe (PolyLine 2 () r) Source # 
Instance details

Defined in Data.Geometry.Ipe.FromIpe

Associated Types

type DefaultFromIpe (PolyLine 2 () r) :: * -> * Source #

Methods

defaultFromIpe :: r0 ~ NumType (PolyLine 2 () r) => Prism' (IpeObject r0) (PolyLine 2 () r :+ IpeAttributes (DefaultFromIpe (PolyLine 2 () r)) r0) Source #

HasDefaultIpeOut (PolyLine 2 p r) Source # 
Instance details

Defined in Data.Geometry.Ipe.IpeOut

Associated Types

type DefaultIpeOut (PolyLine 2 p r) :: * -> * Source #

type NumType (PolyLine d p r) Source # 
Instance details

Defined in Data.Geometry.PolyLine

type NumType (PolyLine d p r) = r
type Dimension (PolyLine d p r) Source # 
Instance details

Defined in Data.Geometry.PolyLine

type Dimension (PolyLine d p r) = d
type DefaultFromIpe (PolyLine 2 () r) Source # 
Instance details

Defined in Data.Geometry.Ipe.FromIpe

type DefaultFromIpe (PolyLine 2 () r) = Path
type DefaultIpeOut (PolyLine 2 p r) Source # 
Instance details

Defined in Data.Geometry.Ipe.IpeOut

type DefaultIpeOut (PolyLine 2 p r) = Path

points :: forall d p r d p r. Iso (PolyLine d p r) (PolyLine d p r) (Seq2 ((:+) (Point d r) p)) (Seq2 ((:+) (Point d r) p)) Source #

fromPoints' :: Monoid p => [Point d r] -> PolyLine d p r Source #

pre: The input list contains at least two points. All extra vields are initialized with mempty.

fromLineSegment :: LineSegment d p r -> PolyLine d p r Source #

We consider the line-segment as closed.

asLineSegment :: PolyLine d p r -> LineSegment d p r Source #

Convert to a closed line segment by taking the first two points.

asLineSegment' :: PolyLine d p r -> Maybe (LineSegment d p r) Source #

Stricter version of asLineSegment that fails if the Polyline contains more than two points.

type SomePolygon p r = Either (Polygon Simple p r) (Polygon Multi p r) Source #

Either a simple or multipolygon

data Polygon (t :: PolygonType) p r where Source #

Constructors

SimplePolygon :: CSeq (Point 2 r :+ p) -> Polygon Simple p r 
MultiPolygon :: CSeq (Point 2 r :+ p) -> [Polygon Simple p r] -> Polygon Multi p r 
Instances
Bitraversable (Polygon t) Source # 
Instance details

Defined in Data.Geometry.Polygon

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Polygon t a b -> f (Polygon t c d) #

Bifoldable (Polygon t) Source # 
Instance details

Defined in Data.Geometry.Polygon

Methods

bifold :: Monoid m => Polygon t m m -> m #

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Polygon t a b -> m #

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Polygon t a b -> c #

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Polygon t a b -> c #

Bifunctor (Polygon t) Source # 
Instance details

Defined in Data.Geometry.Polygon

Methods

bimap :: (a -> b) -> (c -> d) -> Polygon t a c -> Polygon t b d #

first :: (a -> b) -> Polygon t a c -> Polygon t b c #

second :: (b -> c) -> Polygon t a b -> Polygon t a c #

PointFunctor (Polygon t p) Source # 
Instance details

Defined in Data.Geometry.Polygon

Methods

pmap :: (Point (Dimension (Polygon t p r)) r -> Point (Dimension (Polygon t p s)) s) -> Polygon t p r -> Polygon t p s Source #

HasDefaultFromIpe (MultiPolygon () r) Source # 
Instance details

Defined in Data.Geometry.Ipe.FromIpe

Associated Types

type DefaultFromIpe (MultiPolygon () r) :: * -> * Source #

HasDefaultFromIpe (SimplePolygon () r) Source # 
Instance details

Defined in Data.Geometry.Ipe.FromIpe

Associated Types

type DefaultFromIpe (SimplePolygon () r) :: * -> * Source #

HasDefaultIpeOut (SomePolygon p r) Source # 
Instance details

Defined in Data.Geometry.Ipe.IpeOut

Associated Types

type DefaultIpeOut (SomePolygon p r) :: * -> * Source #

(Eq p, Eq r) => Eq (Polygon t p r) Source # 
Instance details

Defined in Data.Geometry.Polygon

Methods

(==) :: Polygon t p r -> Polygon t p r -> Bool #

(/=) :: Polygon t p r -> Polygon t p r -> Bool #

(Show p, Show r) => Show (Polygon t p r) Source # 
Instance details

Defined in Data.Geometry.Polygon

Methods

showsPrec :: Int -> Polygon t p r -> ShowS #

show :: Polygon t p r -> String #

showList :: [Polygon t p r] -> ShowS #

(NFData p, NFData r) => NFData (Polygon t p r) Source # 
Instance details

Defined in Data.Geometry.Polygon

Methods

rnf :: Polygon t p r -> () #

Fractional r => IsTransformable (Polygon t p r) Source # 
Instance details

Defined in Data.Geometry.Polygon

Methods

transformBy :: Transformation (Dimension (Polygon t p r)) (NumType (Polygon t p r)) -> Polygon t p r -> Polygon t p r Source #

IsBoxable (Polygon t p r) Source # 
Instance details

Defined in Data.Geometry.Polygon

Methods

boundingBox :: Polygon t p r -> Box (Dimension (Polygon t p r)) () (NumType (Polygon t p r)) Source #

IpeWriteText r => IpeWriteText (Polygon t () r) Source # 
Instance details

Defined in Data.Geometry.Ipe.Writer

Methods

ipeWriteText :: Polygon t () r -> Maybe Text Source #

HasDefaultIpeOut (Polygon t p r) Source # 
Instance details

Defined in Data.Geometry.Ipe.IpeOut

Associated Types

type DefaultIpeOut (Polygon t p r) :: * -> * Source #

type NumType (SomePolygon p r) Source # 
Instance details

Defined in Data.Geometry.Polygon

type NumType (SomePolygon p r) = r
type Dimension (SomePolygon p r) Source # 
Instance details

Defined in Data.Geometry.Polygon

type Dimension (SomePolygon p r) = 2
type DefaultFromIpe (MultiPolygon () r) Source # 
Instance details

Defined in Data.Geometry.Ipe.FromIpe

type DefaultFromIpe (SimplePolygon () r) Source # 
Instance details

Defined in Data.Geometry.Ipe.FromIpe

type DefaultIpeOut (SomePolygon p r) Source # 
Instance details

Defined in Data.Geometry.Ipe.IpeOut

type IntersectionOf (Line 2 r) (Boundary (Polygon t p r)) Source # 
Instance details

Defined in Data.Geometry.Polygon

type IntersectionOf (Line 2 r) (Boundary (Polygon t p r)) = Seq (Either (Point 2 r) (LineSegment 2 () r)) ': ([] :: [*])
type NumType (Polygon t p r) Source # 
Instance details

Defined in Data.Geometry.Polygon

type NumType (Polygon t p r) = r
type Dimension (Polygon t p r) Source # 
Instance details

Defined in Data.Geometry.Polygon

type Dimension (Polygon t p r) = 2
type DefaultIpeOut (Polygon t p r) Source # 
Instance details

Defined in Data.Geometry.Ipe.IpeOut

type DefaultIpeOut (Polygon t p r) = Path

data PolygonType Source #

We distinguish between simple polygons (without holes) and Polygons with holes.

Constructors

Simple 
Multi 

bitraverseVertices :: (Applicative f, Traversable t) => (p -> f q) -> (r -> f s) -> t (Point 2 r :+ p) -> f (t (Point 2 s :+ q)) Source #

outerBoundary :: forall t p r. Lens' (Polygon t p r) (CSeq (Point 2 r :+ p)) Source #

polygonHoles :: forall p r. Lens' (Polygon Multi p r) [Polygon Simple p r] Source #

outerVertex :: Int -> Lens' (Polygon t p r) (Point 2 r :+ p) Source #

Access the i^th vertex on the outer boundary

holeList :: Polygon t p r -> [Polygon Simple p r] Source #

Get all holes in a polygon

polygonVertices :: Polygon t p r -> NonEmpty (Point 2 r :+ p) Source #

The vertices in the polygon. No guarantees are given on the order in which they appear!

outerBoundaryEdges :: Polygon t p r -> CSeq (LineSegment 2 p r) Source #

The edges along the outer boundary of the polygon. The edges are half open.

running time: \(O(n)\)

listEdges :: Polygon t p r -> [LineSegment 2 p r] Source #

Lists all edges. The edges on the outer boundary are given before the ones on the holes. However, no other guarantees are given on the order.

running time: \(O(n)\)

withIncidentEdges :: Polygon t p r -> Polygon t (Two (LineSegment 2 p r)) r Source #

Pairs every vertex with its incident edges. The first one is its predecessor edge, the second one its successor edge.

>>> mapM_ print . polygonVertices $ withIncidentEdges simplePoly
Point2 [0 % 1,0 % 1] :+ SP LineSegment (Closed (Point2 [1 % 1,11 % 1] :+ ())) (Closed (Point2 [0 % 1,0 % 1] :+ ())) LineSegment (Closed (Point2 [0 % 1,0 % 1] :+ ())) (Closed (Point2 [10 % 1,0 % 1] :+ ()))
Point2 [10 % 1,0 % 1] :+ SP LineSegment (Closed (Point2 [0 % 1,0 % 1] :+ ())) (Closed (Point2 [10 % 1,0 % 1] :+ ())) LineSegment (Closed (Point2 [10 % 1,0 % 1] :+ ())) (Closed (Point2 [10 % 1,10 % 1] :+ ()))
Point2 [10 % 1,10 % 1] :+ SP LineSegment (Closed (Point2 [10 % 1,0 % 1] :+ ())) (Closed (Point2 [10 % 1,10 % 1] :+ ())) LineSegment (Closed (Point2 [10 % 1,10 % 1] :+ ())) (Closed (Point2 [5 % 1,15 % 1] :+ ()))
Point2 [5 % 1,15 % 1] :+ SP LineSegment (Closed (Point2 [10 % 1,10 % 1] :+ ())) (Closed (Point2 [5 % 1,15 % 1] :+ ())) LineSegment (Closed (Point2 [5 % 1,15 % 1] :+ ())) (Closed (Point2 [1 % 1,11 % 1] :+ ()))
Point2 [1 % 1,11 % 1] :+ SP LineSegment (Closed (Point2 [5 % 1,15 % 1] :+ ())) (Closed (Point2 [1 % 1,11 % 1] :+ ())) LineSegment (Closed (Point2 [1 % 1,11 % 1] :+ ())) (Closed (Point2 [0 % 1,0 % 1] :+ ()))

toEdges :: CSeq (Point 2 r :+ p) -> CSeq (LineSegment 2 p r) Source #

Given the vertices of the polygon. Produce a list of edges. The edges are half-open.

onBoundary :: (Fractional r, Ord r) => Point 2 r -> Polygon t p r -> Bool Source #

Test if q lies on the boundary of the polygon. Running time: O(n)

>>> point2 1 1 `onBoundary` simplePoly
False
>>> point2 0 0 `onBoundary` simplePoly
True
>>> point2 10 0 `onBoundary` simplePoly
True
>>> point2 5 13 `onBoundary` simplePoly
False
>>> point2 5 10 `onBoundary` simplePoly
False
>>> point2 10 5 `onBoundary` simplePoly
True
>>> point2 20 5 `onBoundary` simplePoly
False

TODO: testcases multipolygon

inPolygon :: forall t p r. (Fractional r, Ord r) => Point 2 r -> Polygon t p r -> PointLocationResult Source #

Check if a point lies inside a polygon, on the boundary, or outside of the polygon. Running time: O(n).

>>> point2 1 1 `inPolygon` simplePoly
Inside
>>> point2 0 0 `inPolygon` simplePoly
OnBoundary
>>> point2 10 0 `inPolygon` simplePoly
OnBoundary
>>> point2 5 13 `inPolygon` simplePoly
Inside
>>> point2 5 10 `inPolygon` simplePoly
Inside
>>> point2 10 5 `inPolygon` simplePoly
OnBoundary
>>> point2 20 5 `inPolygon` simplePoly
Outside

TODO: Add some testcases with multiPolygons TODO: Add some more onBoundary testcases

insidePolygon :: (Fractional r, Ord r) => Point 2 r -> Polygon t p r -> Bool Source #

Test if a point lies strictly inside the polgyon.

area :: Fractional r => Polygon t p r -> r Source #

Compute the area of a polygon

signedArea :: Fractional r => SimplePolygon p r -> r Source #

Compute the signed area of a simple polygon. The the vertices are in clockwise order, the signed area will be negative, if the verices are given in counter clockwise order, the area will be positive.

centroid :: Fractional r => SimplePolygon p r -> Point 2 r Source #

Compute the centroid of a simple polygon.

isCounterClockwise :: (Eq r, Fractional r) => Polygon t p r -> Bool Source #

Test if the outer boundary of the polygon is in clockwise or counter clockwise order.

running time: \(O(n)\)

toClockwiseOrder :: (Eq r, Fractional r) => Polygon t p r -> Polygon t p r Source #

Orient the outer boundary to clockwise order

toCounterClockWiseOrder :: (Eq r, Fractional r) => Polygon t p r -> Polygon t p r Source #

Orient the outer boundary to counter clockwise order

asSimplePolygon :: Polygon t p r -> SimplePolygon p r Source #

Convert a Polygon to a simple polygon by forgetting about any holes.

cmpExtreme :: (Num r, Ord r) => Vector 2 r -> (Point 2 r :+ p) -> (Point 2 r :+ q) -> Ordering Source #

Comparison that compares which point is larger in the direction given by the vector u.

extremesLinear :: (Ord r, Num r) => Vector 2 r -> Polygon t p r -> (Point 2 r :+ p, Point 2 r :+ p) Source #

Finds the extreme points, minimum and maximum, in a given direction

running time: \(O(n)\)

numberVertices :: Polygon t p r -> Polygon t (SP Int p) r Source #

assigns unique integer numbers to all vertices. Numbers start from 0, and are increasing along the outer boundary. The vertices of holes will be numbered last, in the same order.

>>> numberVertices simplePoly
SimplePolygon CSeq [Point2 [0 % 1,0 % 1] :+ SP 0 (),Point2 [10 % 1,0 % 1] :+ SP 1 (),Point2 [10 % 1,10 % 1] :+ SP 2 (),Point2 [5 % 1,15 % 1] :+ SP 3 (),Point2 [1 % 1,11 % 1] :+ SP 4 ()]