Data.Geometry.Point

\(d\)-dimensional points.

Documentation

>>> :{
let myVector :: Vector 3 Int
    myVector = Vector3 1 2 3
    myPoint = Point myVector
:}

A d-dimensional Point

newtype Point d r

A d-dimensional point.

Constructors

Point

Fields

• toVec :: Vector d r

Instances

Arity d => Functor (Point d)

Defined in Data.Geometry.Point

Methods

fmap :: (a -> b) -> Point d a -> Point d b

(<$) :: a -> Point d b -> Point d a

Arity d => Foldable (Point d)

Defined in Data.Geometry.Point

Methods

fold :: Monoid m => Point d m -> m

foldMap :: Monoid m => (a -> m) -> Point d a -> m

foldr :: (a -> b -> b) -> b -> Point d a -> b

foldr' :: (a -> b -> b) -> b -> Point d a -> b

foldl :: (b -> a -> b) -> b -> Point d a -> b

foldl' :: (b -> a -> b) -> b -> Point d a -> b

foldr1 :: (a -> a -> a) -> Point d a -> a

foldl1 :: (a -> a -> a) -> Point d a -> a

toList :: Point d a -> [a]

null :: Point d a -> Bool

length :: Point d a -> Int

elem :: Eq a => a -> Point d a -> Bool

maximum :: Ord a => Point d a -> a

minimum :: Ord a => Point d a -> a

sum :: Num a => Point d a -> a

product :: Num a => Point d a -> a

Arity d => Traversable (Point d)

Defined in Data.Geometry.Point

Methods

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

sequenceA :: Applicative f => Point d (f a) -> f (Point d a)

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

sequence :: Monad m => Point d (m a) -> m (Point d a)

(Arity d, Ord r) => Semigroup (CWMin (Point d r))

Defined in Data.Geometry.Box.Internal

Methods

(<>) :: CWMin (Point d r) -> CWMin (Point d r) -> CWMin (Point d r)

sconcat :: NonEmpty (CWMin (Point d r)) -> CWMin (Point d r)

stimes :: Integral b => b -> CWMin (Point d r) -> CWMin (Point d r)

(Arity d, Ord r) => Semigroup (CWMax (Point d r))

Defined in Data.Geometry.Box.Internal

Methods

(<>) :: CWMax (Point d r) -> CWMax (Point d r) -> CWMax (Point d r)

sconcat :: NonEmpty (CWMax (Point d r)) -> CWMax (Point d r)

stimes :: Integral b => b -> CWMax (Point d r) -> CWMax (Point d r)

Arity d => Affine (Point d)

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

PointFunctor (Point d)

Defined in Data.Geometry.Point

Methods

pmap :: (Point (Dimension (Point d r)) r -> Point (Dimension (Point d s)) s) -> Point d r -> Point d s

(Eq r, Arity d) => Eq (Point d r)

Defined in Data.Geometry.Point

Methods

(==) :: Point d r -> Point d r -> Bool

(/=) :: Point d r -> Point d r -> Bool

(Ord r, Arity d) => Ord (Point d r)

Defined in Data.Geometry.Point

Methods

compare :: Point d r -> Point d r -> Ordering

(<) :: Point d r -> Point d r -> Bool

(<=) :: Point d r -> Point d r -> Bool

(>) :: Point d r -> Point d r -> Bool

(>=) :: Point d r -> Point d r -> Bool

max :: Point d r -> Point d r -> Point d r

min :: Point d r -> Point d r -> Point d r

(Read r, Arity d) => Read (Point d r)

Defined in Data.Geometry.Point

Methods

readsPrec :: Int -> ReadS (Point d r)

readList :: ReadS [Point d r]

readPrec :: ReadPrec (Point d r)

readListPrec :: ReadPrec [Point d r]

(Show r, Arity d) => Show (Point d r)

Defined in Data.Geometry.Point

Methods

showsPrec :: Int -> Point d r -> ShowS

show :: Point d r -> String

showList :: [Point d r] -> ShowS

Generic (Point d r)

Defined in Data.Geometry.Point

Associated Types

type Rep (Point d r) :: Type -> Type

Methods

from :: Point d r -> Rep (Point d r) x

to :: Rep (Point d r) x -> Point d r

(Arity d, NFData r) => NFData (Point d r)

Defined in Data.Geometry.Point

Methods

rnf :: Point d r -> ()

(Arity d, Arbitrary r) => Arbitrary (Point d r)

Defined in Data.Geometry.Point

Methods

arbitrary :: Gen (Point d r)

shrink :: Point d r -> [Point d r]

(FromJSON r, Arity d, KnownNat d) => FromJSON (Point d r)

Defined in Data.Geometry.Point

Methods

parseJSON :: Value -> Parser (Point d r)

parseJSONList :: Value -> Parser [Point d r]

(ToJSON r, Arity d) => ToJSON (Point d r)

Defined in Data.Geometry.Point

Methods

toJSON :: Point d r -> Value

toEncoding :: Point d r -> Encoding

toJSONList :: [Point d r] -> Value

toEncodingList :: [Point d r] -> Encoding

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Point d r)

Defined in Data.Geometry.Transformation

Methods

transformBy :: Transformation (Dimension (Point d r)) (NumType (Point d r)) -> Point d r -> Point d r

IsBoxable (Point d r)

Defined in Data.Geometry.Box.Internal

Methods

boundingBox :: Point d r -> Box (Dimension (Point d r)) () (NumType (Point d r))

(Eq r, Fractional r, Arity d) => IsIntersectableWith (Point d r) (Line d r)

Defined in Data.Geometry.Line

Methods

intersect :: Point d r -> Line d r -> Intersection (Point d r) (Line d r)

intersects :: Point d r -> Line d r -> Bool

nonEmptyIntersection :: proxy (Point d r) -> proxy (Line d r) -> Intersection (Point d r) (Line d r) -> Bool

(Num r, Eq r, Arity d) => IsIntersectableWith (Point d r) (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

Methods

intersect :: Point d r -> HyperPlane d r -> Intersection (Point d r) (HyperPlane d r)

intersects :: Point d r -> HyperPlane d r -> Bool

nonEmptyIntersection :: proxy (Point d r) -> proxy (HyperPlane d r) -> Intersection (Point d r) (HyperPlane d r) -> Bool

(Num r, Ord r, Arity d) => IsIntersectableWith (Point d r) (HalfSpace d r)

Defined in Data.Geometry.HalfSpace

Methods

intersect :: Point d r -> HalfSpace d r -> Intersection (Point d r) (HalfSpace d r)

intersects :: Point d r -> HalfSpace d r -> Bool

nonEmptyIntersection :: proxy (Point d r) -> proxy (HalfSpace d r) -> Intersection (Point d r) (HalfSpace d r) -> Bool

(Ord r, Num r) => IsIntersectableWith (Point 2 r) (Line 2 r)

Defined in Data.Geometry.Line

Methods

intersect :: Point 2 r -> Line 2 r -> Intersection (Point 2 r) (Line 2 r)

intersects :: Point 2 r -> Line 2 r -> Bool

nonEmptyIntersection :: proxy (Point 2 r) -> proxy (Line 2 r) -> Intersection (Point 2 r) (Line 2 r) -> Bool

(Arity d, Ord r) => IsIntersectableWith (Point d r) (Box d p r)

Defined in Data.Geometry.Box.Internal

Methods

intersect :: Point d r -> Box d p r -> Intersection (Point d r) (Box d p r)

intersects :: Point d r -> Box d p r -> Bool

nonEmptyIntersection :: proxy (Point d r) -> proxy (Box d p r) -> Intersection (Point d r) (Box d p r) -> Bool

(Fractional r, Ord r) => IsIntersectableWith (Point 2 r) (Polygon t p r)

Defined in Data.Geometry.Polygon

Methods

intersect :: Point 2 r -> Polygon t p r -> Intersection (Point 2 r) (Polygon t p r)

intersects :: Point 2 r -> Polygon t p r -> Bool

nonEmptyIntersection :: proxy (Point 2 r) -> proxy (Polygon t p r) -> Intersection (Point 2 r) (Polygon t p r) -> Bool

type Diff (Point d)

Defined in Data.Geometry.Point

type Diff (Point d) = Vector d

type Rep (Point d r)

Defined in Data.Geometry.Point

type Rep (Point d r) = D1 (MetaData "Point" "Data.Geometry.Point" "hgeometry-0.9.0.0-inplace" True) (C1 (MetaCons "Point" PrefixI True) (S1 (MetaSel (Just "toVec") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Vector d r))))

type NumType (Point d r)

Defined in Data.Geometry.Point

type NumType (Point d r) = r

type Dimension (Point d r)

Defined in Data.Geometry.Point

type Dimension (Point d r) = d

type IntersectionOf (Point d r) (Line d r)

Defined in Data.Geometry.Line

type IntersectionOf (Point d r) (Line d r) = NoIntersection ': (Point d r ': ([] :: [Type]))

type IntersectionOf (Point d r) (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

type IntersectionOf (Point d r) (HyperPlane d r) = NoIntersection ': (Point d r ': ([] :: [Type]))

type IntersectionOf (Point d r) (HalfSpace d r)

Defined in Data.Geometry.HalfSpace

type IntersectionOf (Point d r) (HalfSpace d r) = NoIntersection ': (Point d r ': ([] :: [Type]))

type IntersectionOf (Point d r) (Box d p r)

Defined in Data.Geometry.Box.Internal

type IntersectionOf (Point d r) (Box d p r) = NoIntersection ': (Point d r ': ([] :: [Type]))

type IntersectionOf (Point 2 r) (Polygon t p r)

Defined in Data.Geometry.Polygon

type IntersectionOf (Point 2 r) (Polygon t p r) = NoIntersection ': (Point 2 r ': ([] :: [Type]))

readPt :: forall d r. (Arity d, Read r) => ReadP (Point d r)

origin :: (Arity d, Num r) => Point d r

Point representing the origin in d dimensions

>>> origin :: Point 4 Int
Point4 [0,0,0,0]

Accessing points

vector :: Lens' (Point d r) (Vector d r)

Lens to access the vector corresponding to this point.

>>> (point3 1 2 3) ^. vector
Vector3 [1,2,3]
>>> origin & vector .~ Vector3 1 2 3
Point3 [1,2,3]

unsafeCoord :: Arity d => Int -> Lens' (Point d r) r

Get the coordinate in a given dimension. This operation is unsafe in the sense that no bounds are checked. Consider using coord instead.

>>> point3 1 2 3 ^. unsafeCoord 2
2

coord :: forall proxy i d r. (1 <= i, i <= d, ((i - 1) + 1) ~ i, Arity (i - 1), Arity d) => proxy i -> Lens' (Point d r) r

Get the coordinate in a given dimension

>>> point3 1 2 3 ^. coord (C :: C 2)
2
>>> point3 1 2 3 & coord (C :: C 1) .~ 10
Point3 [10,2,3]
>>> point3 1 2 3 & coord (C :: C 3) %~ (+1)
Point3 [1,2,4]

pointFromList :: Arity d => [r] -> Maybe (Point d r)

Constructs a point from a list of coordinates

>>> pointFromList [1,2,3] :: Maybe (Point 3 Int)
Just Point3 [1,2,3]

projectPoint :: (Arity i, Arity d, i <= d) => Point d r -> Point i r

Project a point down into a lower dimension.

Convenience functions to construct 2 and 3 dimensional points

pattern Point2 :: r -> r -> Point 2 r

We provide pattern synonyms Point2 and Point3 for 2 and 3 dimensional points. i.e. we can write:

>>> :{
  let
    f              :: Point 2 r -> r
    f (Point2 x y) = x
  in f (point2 1 2)
:}
1

if we want.

pattern Point3 :: r -> r -> r -> Point 3 r

Similarly, we can write:

>>> :{
  let
    g                :: Point 3 r -> r
    g (Point3 x y z) = z
  in g myPoint
:}
3

point2 :: r -> r -> Point 2 r

Construct a 2 dimensional point

>>> point2 1 2
Point2 [1,2]

_point2 :: Point 2 r -> (r, r)

Destruct a 2 dimensional point

>>> _point2 $ point2 1 2
(1,2)

point3 :: r -> r -> r -> Point 3 r

Construct a 3 dimensional point

>>> point3 1 2 3
Point3 [1,2,3]

_point3 :: Point 3 r -> (r, r, r)

Destruct a 3 dimensional point

>>> _point3 $ point3 1 2 3
(1,2,3)

xCoord :: (1 <= d, Arity d) => Lens' (Point d r) r

Shorthand to access the first coordinate C 1

>>> point3 1 2 3 ^. xCoord
1
>>> point2 1 2 & xCoord .~ 10
Point2 [10,2]

yCoord :: (2 <= d, Arity d) => Lens' (Point d r) r

Shorthand to access the second coordinate C 2

>>> point2 1 2 ^. yCoord
2
>>> point3 1 2 3 & yCoord %~ (+1)
Point3 [1,3,3]

zCoord :: (3 <= d, Arity d) => Lens' (Point d r) r

Shorthand to access the third coordinate C 3

>>> point3 1 2 3 ^. zCoord
3
>>> point3 1 2 3 & zCoord %~ (+1)
Point3 [1,2,4]

Point Functors

class PointFunctor g where

Types that we can transform by mapping a function on each point in the structure

Methods

pmap :: (Point (Dimension (g r)) r -> Point (Dimension (g s)) s) -> g r -> g s

Instances

PointFunctor (Point d)

Defined in Data.Geometry.Point

Methods

pmap :: (Point (Dimension (Point d r)) r -> Point (Dimension (Point d s)) s) -> Point d r -> Point d s

PointFunctor (ConvexPolygon p)

Defined in Data.Geometry.Polygon.Convex

Methods

pmap :: (Point (Dimension (ConvexPolygon p r)) r -> Point (Dimension (ConvexPolygon p s)) s) -> ConvexPolygon p r -> ConvexPolygon p s

PointFunctor (Box d p)

Defined in Data.Geometry.Box.Internal

Methods

pmap :: (Point (Dimension (Box d p r)) r -> Point (Dimension (Box d p s)) s) -> Box d p r -> Box d p s

PointFunctor (LineSegment d p)

Defined in Data.Geometry.LineSegment

Methods

pmap :: (Point (Dimension (LineSegment d p r)) r -> Point (Dimension (LineSegment d p s)) s) -> LineSegment d p r -> LineSegment d p s

PointFunctor (PolyLine d p)

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

PointFunctor (Triangle d p)

Defined in Data.Geometry.Triangle

Methods

pmap :: (Point (Dimension (Triangle d p r)) r -> Point (Dimension (Triangle d p s)) s) -> Triangle d p r -> Triangle d p s

PointFunctor (Polygon t p)

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

Functions specific to Two Dimensional points

data CCW

Constructors

CCW

CoLinear

CW

Instances

Eq CCW

Defined in Data.Geometry.Point

Methods

(==) :: CCW -> CCW -> Bool

(/=) :: CCW -> CCW -> Bool

Show CCW

Defined in Data.Geometry.Point

Methods

showsPrec :: Int -> CCW -> ShowS

show :: CCW -> String

showList :: [CCW] -> ShowS

ccw :: (Ord r, Num r) => Point 2 r -> Point 2 r -> Point 2 r -> CCW

Given three points p q and r determine the orientation when going from p to r via q.

ccw' :: (Ord r, Num r) => (Point 2 r :+ a) -> (Point 2 r :+ b) -> (Point 2 r :+ c) -> CCW

Given three points p q and r determine the orientation when going from p to r via q.

sortArround :: (Ord r, Num r) => (Point 2 r :+ q) -> [Point 2 r :+ p] -> [Point 2 r :+ p]

Sort the points arround the given point p in counter clockwise order with respect to the rightward horizontal ray starting from p. If two points q and r are colinear with p, the closest one to p is reported first. running time: O(n log n)

data Quadrant

Quadrants of two dimensional points. in CCW order

Constructors

TopRight

TopLeft

BottomLeft

BottomRight

Instances

Bounded Quadrant

Defined in Data.Geometry.Point

Methods

minBound :: Quadrant

maxBound :: Quadrant

Enum Quadrant

Defined in Data.Geometry.Point

Methods

succ :: Quadrant -> Quadrant

pred :: Quadrant -> Quadrant

toEnum :: Int -> Quadrant

fromEnum :: Quadrant -> Int

enumFrom :: Quadrant -> [Quadrant]

enumFromThen :: Quadrant -> Quadrant -> [Quadrant]

enumFromTo :: Quadrant -> Quadrant -> [Quadrant]

enumFromThenTo :: Quadrant -> Quadrant -> Quadrant -> [Quadrant]

Eq Quadrant

Defined in Data.Geometry.Point

Methods

(==) :: Quadrant -> Quadrant -> Bool

(/=) :: Quadrant -> Quadrant -> Bool

Ord Quadrant

Defined in Data.Geometry.Point

Methods

compare :: Quadrant -> Quadrant -> Ordering

(<) :: Quadrant -> Quadrant -> Bool

(<=) :: Quadrant -> Quadrant -> Bool

(>) :: Quadrant -> Quadrant -> Bool

(>=) :: Quadrant -> Quadrant -> Bool

max :: Quadrant -> Quadrant -> Quadrant

min :: Quadrant -> Quadrant -> Quadrant

Read Quadrant

Defined in Data.Geometry.Point

Methods

readsPrec :: Int -> ReadS Quadrant

readList :: ReadS [Quadrant]

readPrec :: ReadPrec Quadrant

readListPrec :: ReadPrec [Quadrant]

Show Quadrant

Defined in Data.Geometry.Point

Methods

showsPrec :: Int -> Quadrant -> ShowS

show :: Quadrant -> String

showList :: [Quadrant] -> ShowS

quadrantWith :: (Ord r, 1 <= d, 2 <= d, Arity d) => (Point d r :+ q) -> (Point d r :+ p) -> Quadrant

Quadrants around point c; quadrants are closed on their "previous" boundary (i..e the boundary with the previous quadrant in the CCW order), open on next boundary. The origin itself is assigned the topRight quadrant

quadrant :: (Ord r, Num r, 1 <= d, 2 <= d, Arity d) => (Point d r :+ p) -> Quadrant

Quadrants with respect to the origin

partitionIntoQuadrants :: (Ord r, 1 <= d, 2 <= d, Arity d) => (Point d r :+ q) -> [Point d r :+ p] -> ([Point d r :+ p], [Point d r :+ p], [Point d r :+ p], [Point d r :+ p])

Given a center point c, and a set of points, partition the points into quadrants around c (based on their x and y coordinates). The quadrants are reported in the order topLeft, topRight, bottomLeft, bottomRight. The points are in the same order as they were in the original input lists. Points with the same x-or y coordinate as p, are "rounded" to above.

ccwCmpAround :: (Num r, Ord r) => (Point 2 r :+ qc) -> (Point 2 r :+ p) -> (Point 2 r :+ q) -> Ordering

Counter clockwise ordering of the points around c. Points are ordered with respect to the positive x-axis. Points nearer to the center come before points further away.

cwCmpAround :: (Num r, Ord r) => (Point 2 r :+ qc) -> (Point 2 r :+ p) -> (Point 2 r :+ q) -> Ordering

Clockwise ordering of the points around c. Points are ordered with respect to the positive x-axis. Points nearer to the center come before points further away.

insertIntoCyclicOrder :: (Ord r, Num r) => (Point 2 r :+ q) -> (Point 2 r :+ p) -> CList (Point 2 r :+ p) -> CList (Point 2 r :+ p)

Given a center c, a new point p, and a list of points ps, sorted in counter clockwise order around c. Insert p into the cyclic order. The focus of the returned cyclic list is the new point p.

running time: O(n)

squaredEuclideanDist :: (Num r, Arity d) => Point d r -> Point d r -> r

Squared Euclidean distance between two points

euclideanDist :: (Floating r, Arity d) => Point d r -> Point d r -> r

Euclidean distance between two points