Data.Geometry.Point

\(d\)-dimensional points.

Documentation

newtype Point d r

A d-dimensional point.

There are convenience pattern synonyms for 1, 2 and 3 dimensional points.

>>> let f (Point1 x) = x in f (Point1 1)
1
>>> let f (Point2 x y) = x in f (Point2 1 2)
1
>>> let f (Point3 x y z) = z in f (Point3 1 2 3)
3
>>> let f (Point3 x y z) = z in f (Point $ Vector3 1 2 3)
3

Constructors

Point

Fields

• toVec :: Vector d r

Bundled Patterns

pattern Point1 :: r -> Point 1 r

A bidirectional pattern synonym for 1 dimensional points.

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

A bidirectional pattern synonym for 2 dimensional points.

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

A bidirectional pattern synonym for 3 dimensional points.

Instances

Arity d => Functor (Point d)

Defined in Data.Geometry.Point.Internal

Methods

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

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

Arity d => Applicative (Point d)

Defined in Data.Geometry.Point.Internal

Methods

pure :: a -> Point d a

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

liftA2 :: (a -> b -> c) -> Point d a -> Point d b -> Point d c

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

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

Arity d => Foldable (Point d)

Defined in Data.Geometry.Point.Internal

Methods

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

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

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 => Arbitrary1 (Point d)

Defined in Data.Geometry.Point.Internal

Methods

liftArbitrary :: Gen a -> Gen (Point d a)

liftShrink :: (a -> [a]) -> Point d a -> [Point d a]

Arity d => Eq1 (Point d)

Defined in Data.Geometry.Point.Internal

Methods

liftEq :: (a -> b -> Bool) -> Point d a -> Point d b -> Bool

Arity d => Read1 (Point d)

Defined in Data.Geometry.Point.Internal

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Point d a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Point d a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Point d a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Point d a]

Arity d => Show1 (Point d)

Defined in Data.Geometry.Point.Internal

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Point d a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Point d a] -> ShowS

Arity d => Affine (Point d)

Defined in Data.Geometry.Point.Internal

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.Internal

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.Internal

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.Internal

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.Internal

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.Internal

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.Internal

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, Random r) => Random (Point d r)

Defined in Data.Geometry.Point.Internal

Methods

randomR :: RandomGen g => (Point d r, Point d r) -> g -> (Point d r, g)

random :: RandomGen g => g -> (Point d r, g)

randomRs :: RandomGen g => (Point d r, Point d r) -> g -> [Point d r]

randoms :: RandomGen g => g -> [Point d r]

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

Defined in Data.Geometry.Point.Internal

Methods

arbitrary :: Gen (Point d r)

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

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

Defined in Data.Geometry.Point.Internal

Methods

hashWithSalt :: Int -> Point d r -> Int

hash :: Point d r -> Int

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

Defined in Data.Geometry.Point.Internal

Methods

toJSON :: Point d r -> Value

toEncoding :: Point d r -> Encoding

toJSONList :: [Point d r] -> Value

toEncodingList :: [Point d r] -> Encoding

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

Defined in Data.Geometry.Point.Internal

Methods

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

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

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

Defined in Data.Geometry.Point.Internal

Methods

rnf :: Point d r -> ()

(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))

(Ord r, Fractional r) => IsIntersectableWith (Point 2 r) (Cell r)

Defined in Data.Geometry.QuadTree.Cell

Methods

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

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

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

(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

(Ord r, Fractional r, Arity d) => IsIntersectableWith (Point d r) (HalfLine d r)

Defined in Data.Geometry.HalfLine

Methods

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

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

nonEmptyIntersection :: proxy (Point d r) -> proxy (HalfLine d r) -> Intersection (Point d r) (HalfLine 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

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

Defined in Data.Geometry.LineSegment.Internal

Methods

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

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

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

(Ord r, Num r) => IsIntersectableWith (Point 2 r) (LineSegment 2 p r)

Defined in Data.Geometry.LineSegment.Internal

Methods

intersect :: Point 2 r -> LineSegment 2 p r -> Intersection (Point 2 r) (LineSegment 2 p r)

intersects :: Point 2 r -> LineSegment 2 p r -> Bool

nonEmptyIntersection :: proxy (Point 2 r) -> proxy (LineSegment 2 p r) -> Intersection (Point 2 r) (LineSegment 2 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

Field1 (Triangle d p r) (Triangle d p r) (Point d r :+ p) (Point d r :+ p)

Defined in Data.Geometry.Triangle

Methods

_1 :: Lens (Triangle d p r) (Triangle d p r) (Point d r :+ p) (Point d r :+ p)

Field2 (Triangle d p r) (Triangle d p r) (Point d r :+ p) (Point d r :+ p)

Defined in Data.Geometry.Triangle

Methods

_2 :: Lens (Triangle d p r) (Triangle d p r) (Point d r :+ p) (Point d r :+ p)

Field3 (Triangle d p r) (Triangle d p r) (Point d r :+ p) (Point d r :+ p)

Defined in Data.Geometry.Triangle

Methods

_3 :: Lens (Triangle d p r) (Triangle d p r) (Point d r :+ p) (Point d r :+ p)

type Diff (Point d)

Defined in Data.Geometry.Point.Internal

type Diff (Point d) = Vector d

type Rep (Point d r)

Defined in Data.Geometry.Point.Internal

type Rep (Point d r) = D1 ('MetaData "Point" "Data.Geometry.Point.Internal" "hgeometry-0.12.0.2-IMXeR0PuShPEjPCARytEWE" '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.Internal

type NumType (Point d r) = r

type Dimension (Point d r)

Defined in Data.Geometry.Point.Internal

type Dimension (Point d r) = d

type IntersectionOf (Point 2 r) (Cell r)

Defined in Data.Geometry.QuadTree.Cell

type IntersectionOf (Point 2 r) (Cell r) = '[NoIntersection, Point 2 r]

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 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 IntersectionOf (Point d r) (HalfLine d r)

Defined in Data.Geometry.HalfLine

type IntersectionOf (Point d r) (HalfLine d r) = '[NoIntersection, Point d r]

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 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 IntersectionOf (Point d r) (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

type IntersectionOf (Point d r) (LineSegment d p r) = '[NoIntersection, Point d r]

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]

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

Point representing the origin in d dimensions

>>> origin :: Point 4 Int
Point4 0 0 0 0

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

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

Constructs a point from a list of coordinates. The length of the list has to match the dimension exactly.

>>> pointFromList [1,2,3] :: Maybe (Point 3 Int)
Just (Point3 1 2 3)
>>> pointFromList [1] :: Maybe (Point 3 Int)
Nothing
>>> pointFromList [1,2,3,4] :: Maybe (Point 3 Int)
Nothing

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

Project a point down into a lower dimension.

xCoord :: (1 <= d, Arity d, AsAPoint point) => 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, AsAPoint point) => 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, AsAPoint point) => 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

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.Internal

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.Internal

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 (BezierSpline n d)

Defined in Data.Geometry.BezierSpline

Methods

pmap :: (Point (Dimension (BezierSpline n d r)) r -> Point (Dimension (BezierSpline n d s)) s) -> BezierSpline n d r -> BezierSpline n d 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.Core

Methods

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

data CCW

Data type for expressing the orientation of three points, with the option of allowing Colinearities.

Instances

Eq CCW

Defined in Data.Geometry.Point.Orientation.Degenerate

Methods

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

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

Show CCW

Defined in Data.Geometry.Point.Orientation.Degenerate

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.

Be vary of numerical instability: >>> ccw (Point2 0 0.3) (Point2 1 0.6) (Point2 2 (0.9::Double)) CCW

>>> ccw (Point2 0 0.3) (Point2 1 0.6) (Point2 2 (0.9::Rational))
CoLinear

If you can't use Rational, try SafeDouble instead of Double: >>> ccw (Point2 0 0.3) (Point2 1 0.6) (Point2 2 (0.9::SafeDouble)) CoLinear

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.

isCoLinear :: (Eq r, Num r) => Point 2 r -> Point 2 r -> Point 2 r -> Bool

Given three points p q and r determine if the line from p to r via q is straight/colinear.

This is identical to `ccw p q r == CoLinear` but doesn't have the Ord constraint.

pattern CCW :: CCW

CounterClockwise orientation. Also called a left-turn.

pattern CW :: CCW

Clockwise orientation. Also called a right-turn.

pattern CoLinear :: CCW

CoLinear orientation. Also called a straight line.

ccwCmpAround :: (Num r, Ord r) => Point 2 r -> Point 2 r -> Point 2 r -> Ordering

Counter clockwise ordering of the points around c. Points are ordered with respect to the positive x-axis.

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.

cwCmpAround :: (Num r, Ord r) => Point 2 r -> Point 2 r -> Point 2 r -> Ordering

Clockwise ordering of the points around c. Points are ordered with respect to the positive x-axis.

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.

ccwCmpAroundWith :: (Ord r, Num r) => Vector 2 r -> Point 2 r -> Point 2 r -> Point 2 r -> Ordering

Given a zero vector z, a center c, and two points p and q, compute the ccw ordering of p and q around c with this vector as zero direction.

pre: the points p,q /= c

ccwCmpAroundWith' :: (Ord r, Num r) => Vector 2 r -> (Point 2 r :+ c) -> (Point 2 r :+ a) -> (Point 2 r :+ b) -> Ordering

Given a zero vector z, a center c, and two points p and q, compute the ccw ordering of p and q around c with this vector as zero direction.

pre: the points p,q /= c

cwCmpAroundWith :: (Ord r, Num r) => Vector 2 r -> Point 2 r -> Point 2 r -> Point 2 r -> Ordering

Given a zero vector z, a center c, and two points p and q, compute the cw ordering of p and q around c with this vector as zero direction.

pre: the points p,q /= c

cwCmpAroundWith' :: (Ord r, Num r) => Vector 2 r -> (Point 2 r :+ a) -> (Point 2 r :+ b) -> (Point 2 r :+ c) -> Ordering

Given a zero vector z, a center c, and two points p and q, compute the cw ordering of p and q around c with this vector as zero direction.

pre: the points p,q /= c

sortAround :: (Ord r, Num r) => Point 2 r -> [Point 2 r] -> [Point 2 r]

\( O(n log n) \) 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.

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

\( O(n log n) \) 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.

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

\( O(n) \) 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.

data Quadrant

Quadrants of two dimensional points. in CCW order

Constructors

TopRight

TopLeft

BottomLeft

BottomRight

Instances

Bounded Quadrant

Defined in Data.Geometry.Point.Quadrants

Methods

minBound :: Quadrant

maxBound :: Quadrant

Enum Quadrant

Defined in Data.Geometry.Point.Quadrants

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.Quadrants

Methods

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

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

Ord Quadrant

Defined in Data.Geometry.Point.Quadrants

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.Quadrants

Methods

readsPrec :: Int -> ReadS Quadrant

readList :: ReadS [Quadrant]

readPrec :: ReadPrec Quadrant

readListPrec :: ReadPrec [Quadrant]

Show Quadrant

Defined in Data.Geometry.Point.Quadrants

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.

cmpByDistanceTo :: (Ord r, Num r, Arity d) => Point d r -> Point d r -> Point d r -> Ordering

Compare by distance to the first argument

cmpByDistanceTo' :: (Ord r, Num r, Arity d) => (Point d r :+ c) -> (Point d r :+ p) -> (Point d r :+ q) -> Ordering

Compare by distance to the first argument

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

coord :: (1 <= i, i <= d, KnownNat i, Arity d, AsAPoint p) => proxy i -> Lens' (p 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

unsafeCoord :: (Arity d, AsAPoint p) => Int -> Lens' (p 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