Geom2D

Basic 2 dimensional geometry functions.

Documentation

module Data.VectorSpace

module Data.Cross

pattern MV_Point :: MVector s (a, a) -> MVector s (Point a)

pattern V_Point :: Vector (a, a) -> Vector (Point a)

class AffineTransform a b | a -> b where

Methods

transform :: Transform b -> a -> a

Instances

Num a => AffineTransform (Polygon a) a

Defined in Geom2D

Methods

transform :: Transform a -> Polygon a -> Polygon a

Num a => AffineTransform (Transform a) a

Defined in Geom2D

Methods

transform :: Transform a -> Transform a -> Transform a

Num a => AffineTransform (Point a) a

Defined in Geom2D

Methods

transform :: Transform a -> Point a -> Point a

Num a => AffineTransform (ClosedPath a) a

Defined in Geom2D.CubicBezier.Basic

Methods

transform :: Transform a -> ClosedPath a -> ClosedPath a

Num a => AffineTransform (OpenPath a) a

Defined in Geom2D.CubicBezier.Basic

Methods

transform :: Transform a -> OpenPath a -> OpenPath a

Num a => AffineTransform (PathJoin a) a

Defined in Geom2D.CubicBezier.Basic

Methods

transform :: Transform a -> PathJoin a -> PathJoin a

Num a => AffineTransform (QuadBezier a) a

Defined in Geom2D.CubicBezier.Basic

Methods

transform :: Transform a -> QuadBezier a -> QuadBezier a

Num a => AffineTransform (CubicBezier a) a

Defined in Geom2D.CubicBezier.Basic

Methods

transform :: Transform a -> CubicBezier a -> CubicBezier a

(Floating a, Eq a) => AffineTransform (Pen a) a

Defined in Geom2D.CubicBezier.Stroke

Methods

transform :: Transform a -> Pen a -> Pen a

data Polygon a

Constructors

Polygon [Point a]

Instances

Functor Polygon

Defined in Geom2D

Methods

fmap :: (a -> b) -> Polygon a -> Polygon b

(<$) :: a -> Polygon b -> Polygon a

Foldable Polygon

Defined in Geom2D

Methods

fold :: Monoid m => Polygon m -> m

foldMap :: Monoid m => (a -> m) -> Polygon a -> m

foldr :: (a -> b -> b) -> b -> Polygon a -> b

foldr' :: (a -> b -> b) -> b -> Polygon a -> b

foldl :: (b -> a -> b) -> b -> Polygon a -> b

foldl' :: (b -> a -> b) -> b -> Polygon a -> b

foldr1 :: (a -> a -> a) -> Polygon a -> a

foldl1 :: (a -> a -> a) -> Polygon a -> a

toList :: Polygon a -> [a]

null :: Polygon a -> Bool

length :: Polygon a -> Int

elem :: Eq a => a -> Polygon a -> Bool

maximum :: Ord a => Polygon a -> a

minimum :: Ord a => Polygon a -> a

sum :: Num a => Polygon a -> a

product :: Num a => Polygon a -> a

Traversable Polygon

Defined in Geom2D

Methods

traverse :: Applicative f => (a -> f b) -> Polygon a -> f (Polygon b)

sequenceA :: Applicative f => Polygon (f a) -> f (Polygon a)

mapM :: Monad m => (a -> m b) -> Polygon a -> m (Polygon b)

sequence :: Monad m => Polygon (m a) -> m (Polygon a)

Eq a => Eq (Polygon a)

Defined in Geom2D

Methods

(==) :: Polygon a -> Polygon a -> Bool

(/=) :: Polygon a -> Polygon a -> Bool

Show a => Show (Polygon a)

Defined in Geom2D

Methods

showsPrec :: Int -> Polygon a -> ShowS

show :: Polygon a -> String

showList :: [Polygon a] -> ShowS

Num a => AffineTransform (Polygon a) a

Defined in Geom2D

Methods

transform :: Transform a -> Polygon a -> Polygon a

data Line a

Constructors

Line (Point a) (Point a)

Instances

Functor Line

Defined in Geom2D

Methods

fmap :: (a -> b) -> Line a -> Line b

(<$) :: a -> Line b -> Line a

Foldable Line

Defined in Geom2D

Methods

fold :: Monoid m => Line m -> m

foldMap :: Monoid m => (a -> m) -> Line a -> m

foldr :: (a -> b -> b) -> b -> Line a -> b

foldr' :: (a -> b -> b) -> b -> Line a -> b

foldl :: (b -> a -> b) -> b -> Line a -> b

foldl' :: (b -> a -> b) -> b -> Line a -> b

foldr1 :: (a -> a -> a) -> Line a -> a

foldl1 :: (a -> a -> a) -> Line a -> a

toList :: Line a -> [a]

null :: Line a -> Bool

length :: Line a -> Int

elem :: Eq a => a -> Line a -> Bool

maximum :: Ord a => Line a -> a

minimum :: Ord a => Line a -> a

sum :: Num a => Line a -> a

product :: Num a => Line a -> a

Traversable Line

Defined in Geom2D

Methods

traverse :: Applicative f => (a -> f b) -> Line a -> f (Line b)

sequenceA :: Applicative f => Line (f a) -> f (Line a)

mapM :: Monad m => (a -> m b) -> Line a -> m (Line b)

sequence :: Monad m => Line (m a) -> m (Line a)

Eq a => Eq (Line a)

Defined in Geom2D

Methods

(==) :: Line a -> Line a -> Bool

(/=) :: Line a -> Line a -> Bool

Show a => Show (Line a)

Defined in Geom2D

Methods

showsPrec :: Int -> Line a -> ShowS

show :: Line a -> String

showList :: [Line a] -> ShowS

data Transform a

A transformation (x, y) -> (ax + by + c, dx + ey + d)

Constructors

Transform

Fields

• xformA :: !a
• xformB :: !a
• xformC :: !a
• xformD :: !a
• xformE :: !a
• xformF :: !a

Instances

Functor Transform

Defined in Geom2D

Methods

fmap :: (a -> b) -> Transform a -> Transform b

(<$) :: a -> Transform b -> Transform a

Foldable Transform

Defined in Geom2D

Methods

fold :: Monoid m => Transform m -> m

foldMap :: Monoid m => (a -> m) -> Transform a -> m

foldr :: (a -> b -> b) -> b -> Transform a -> b

foldr' :: (a -> b -> b) -> b -> Transform a -> b

foldl :: (b -> a -> b) -> b -> Transform a -> b

foldl' :: (b -> a -> b) -> b -> Transform a -> b

foldr1 :: (a -> a -> a) -> Transform a -> a

foldl1 :: (a -> a -> a) -> Transform a -> a

toList :: Transform a -> [a]

null :: Transform a -> Bool

length :: Transform a -> Int

elem :: Eq a => a -> Transform a -> Bool

maximum :: Ord a => Transform a -> a

minimum :: Ord a => Transform a -> a

sum :: Num a => Transform a -> a

product :: Num a => Transform a -> a

Traversable Transform

Defined in Geom2D

Methods

traverse :: Applicative f => (a -> f b) -> Transform a -> f (Transform b)

sequenceA :: Applicative f => Transform (f a) -> f (Transform a)

mapM :: Monad m => (a -> m b) -> Transform a -> m (Transform b)

sequence :: Monad m => Transform (m a) -> m (Transform a)

Eq a => Eq (Transform a)

Defined in Geom2D

Methods

(==) :: Transform a -> Transform a -> Bool

(/=) :: Transform a -> Transform a -> Bool

Show a => Show (Transform a)

Defined in Geom2D

Methods

showsPrec :: Int -> Transform a -> ShowS

show :: Transform a -> String

showList :: [Transform a] -> ShowS

Num a => AffineTransform (Transform a) a

Defined in Geom2D

Methods

transform :: Transform a -> Transform a -> Transform a

type DPoint = Point Double

data Point a

Constructors

Point

Fields

• pointX :: !a
• pointY :: !a

Instances

Functor Point

Defined in Geom2D

Methods

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

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

Foldable Point

Defined in Geom2D

Methods

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

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

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

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

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

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

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

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

toList :: Point a -> [a]

null :: Point a -> Bool

length :: Point a -> Int

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

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

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

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

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

Traversable Point

Defined in Geom2D

Methods

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

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

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

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

Unbox a => Vector Vector (Point a)

Defined in Geom2D

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Point a) -> m (Vector (Point a))

basicUnsafeThaw :: PrimMonad m => Vector (Point a) -> m (Mutable Vector (PrimState m) (Point a))

basicLength :: Vector (Point a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Point a) -> Vector (Point a)

basicUnsafeIndexM :: Monad m => Vector (Point a) -> Int -> m (Point a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Point a) -> Vector (Point a) -> m ()

elemseq :: Vector (Point a) -> Point a -> b -> b

Unbox a => MVector MVector (Point a)

Defined in Geom2D

Methods

basicLength :: MVector s (Point a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (Point a) -> MVector s (Point a)

basicOverlaps :: MVector s (Point a) -> MVector s (Point a) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Point a))

basicInitialize :: PrimMonad m => MVector (PrimState m) (Point a) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> Point a -> m (MVector (PrimState m) (Point a))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Point a) -> Int -> m (Point a)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Point a) -> Int -> Point a -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (Point a) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (Point a) -> Point a -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Point a) -> MVector (PrimState m) (Point a) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Point a) -> MVector (PrimState m) (Point a) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Point a) -> Int -> m (MVector (PrimState m) (Point a))

Eq a => Eq (Point a)

Defined in Geom2D

Methods

(==) :: Point a -> Point a -> Bool

(/=) :: Point a -> Point a -> Bool

Ord a => Ord (Point a)

Defined in Geom2D

Methods

compare :: Point a -> Point a -> Ordering

(<) :: Point a -> Point a -> Bool

(<=) :: Point a -> Point a -> Bool

(>) :: Point a -> Point a -> Bool

(>=) :: Point a -> Point a -> Bool

max :: Point a -> Point a -> Point a

min :: Point a -> Point a -> Point a

Show a => Show (Point a)

Defined in Geom2D

Methods

showsPrec :: Int -> Point a -> ShowS

show :: Point a -> String

showList :: [Point a] -> ShowS

Unbox a => Unbox (Point a)

Defined in Geom2D

Floating e => HasNormal (Point e)

Defined in Geom2D

Methods

normalVec :: Point e -> Point e

Num e => VectorSpace (Point e)

Defined in Geom2D

Associated Types

type Scalar (Point e) :: Type

Methods

(*^) :: Scalar (Point e) -> Point e -> Point e

(AdditiveGroup e, Num e) => InnerSpace (Point e)

Defined in Geom2D

Methods

(<.>) :: Point e -> Point e -> Scalar (Point e)

Num e => AdditiveGroup (Point e)

Defined in Geom2D

Methods

zeroV :: Point e

(^+^) :: Point e -> Point e -> Point e

negateV :: Point e -> Point e

(^-^) :: Point e -> Point e -> Point e

Num a => AffineTransform (Point a) a

Defined in Geom2D

Methods

transform :: Transform a -> Point a -> Point a

newtype MVector s (Point a)

Defined in Geom2D

newtype MVector s (Point a) = MV_Point (MVector s (a, a))

newtype Vector (Point a)

Defined in Geom2D

newtype Vector (Point a) = V_Point (Vector (a, a))

type Scalar (Point e)

Defined in Geom2D

type Scalar (Point e) = e

($*) :: AffineTransform a b => Transform b -> a -> a infixr 5

Operator for applying a transformation.

inverse :: (Eq a, Fractional a) => Transform a -> Maybe (Transform a)

Calculate the inverse of a transformation.

lineEquation :: Floating t => Line t -> (t, t, t)

Return the parameters (a, b, c) for the normalised equation of the line: a*x + b*y + c = 0.

lineDistance :: Floating a => Line a -> Point a -> a

Return the signed distance from a point to the line. If the distance is negative, the point lies to the right of the line

closestPoint :: Fractional a => Line a -> Point a -> Point a

Return the point on the line closest to the given point.

lineIntersect :: (Ord a, Floating a) => Line a -> Line a -> a -> Maybe (Point a)

Calculate the intersection of two lines. If the determinant is less than tolerance (parallel or coincident lines), return Nothing.

vectorMag :: Floating a => Point a -> a

The lenght of the vector.

vectorMagSquare :: Floating a => Point a -> a

The lenght of the vector.

vectorAngle :: RealFloat a => Point a -> a

The angle of the vector, in the range (-pi, pi].

dirVector :: Floating a => a -> Point a

The unitvector with the given angle.

normVector :: Floating a => Point a -> Point a

The unit vector with the same direction.

(^.^) :: Num a => Point a -> Point a -> a

Dot product of two vectors.

vectorCross :: Num a => Point a -> Point a -> a

Cross product of two vectors.

vectorDistance :: Floating a => Point a -> Point a -> a

Distance between two vectors.

interpolateVector :: Num a => Point a -> Point a -> a -> Point a

Interpolate between two vectors.

rotateScaleVec :: Num a => Point a -> Transform a

Create a transform that rotates by the angle of the given vector and multiplies with the magnitude of the vector.

flipVector :: Num a => Point a -> Point a

reflect the vector over the X-axis.

turnAround :: Num a => Point a -> Point a

rotateVec :: Floating a => Point a -> Transform a

Create a transform that rotates by the angle of the given vector with the x-axis

rotate :: Floating s => s -> Transform s

Create a transform that rotates by the given angle (radians).

rotate90L :: Floating s => Transform s

Rotate vector 90 degrees left.

rotate90R :: Floating s => Transform s

Rotate vector 90 degrees right.

translate :: Num a => Point a -> Transform a

Create a transform that translates by the given vector.

idTrans :: Num a => Transform a

The identity transformation.