Geom2D.CubicBezier.Basic

Documentation

data CubicBezier a

A cubic bezier curve.

Constructors

CubicBezier

Fields

• cubicC0 :: !(Point a)
• cubicC1 :: !(Point a)
• cubicC2 :: !(Point a)
• cubicC3 :: !(Point a)

Instances

Functor CubicBezier

Methods

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

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

Foldable CubicBezier

Methods

fold :: Monoid m => CubicBezier m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> CubicBezier a -> a

foldl1 :: (a -> a -> a) -> CubicBezier a -> a

toList :: CubicBezier a -> [a]

null :: CubicBezier a -> Bool

length :: CubicBezier a -> Int

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

maximum :: Ord a => CubicBezier a -> a

minimum :: Ord a => CubicBezier a -> a

sum :: Num a => CubicBezier a -> a

product :: Num a => CubicBezier a -> a

Traversable CubicBezier

Methods

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

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

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

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

GenericBezier CubicBezier

Methods

degree :: Unbox a => CubicBezier a -> Int

toVector :: Unbox a => CubicBezier a -> Vector (a, a)

unsafeFromVector :: Unbox a => Vector (a, a) -> CubicBezier a

Eq a => Eq (CubicBezier a)

Methods

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

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

Show a => Show (CubicBezier a)

Methods

showsPrec :: Int -> CubicBezier a -> ShowS

show :: CubicBezier a -> String

showList :: [CubicBezier a] -> ShowS

Num a => AffineTransform (CubicBezier a) a

Methods

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

data QuadBezier a

A quadratic bezier curve.

Constructors

QuadBezier

Fields

• quadC0 :: !(Point a)
• quadC1 :: !(Point a)
• quadC2 :: !(Point a)

Instances

Functor QuadBezier

Methods

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

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

Foldable QuadBezier

Methods

fold :: Monoid m => QuadBezier m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> QuadBezier a -> a

foldl1 :: (a -> a -> a) -> QuadBezier a -> a

toList :: QuadBezier a -> [a]

null :: QuadBezier a -> Bool

length :: QuadBezier a -> Int

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

maximum :: Ord a => QuadBezier a -> a

minimum :: Ord a => QuadBezier a -> a

sum :: Num a => QuadBezier a -> a

product :: Num a => QuadBezier a -> a

Traversable QuadBezier

Methods

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

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

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

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

GenericBezier QuadBezier

Methods

degree :: Unbox a => QuadBezier a -> Int

toVector :: Unbox a => QuadBezier a -> Vector (a, a)

unsafeFromVector :: Unbox a => Vector (a, a) -> QuadBezier a

Eq a => Eq (QuadBezier a)

Methods

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

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

Show a => Show (QuadBezier a)

Methods

showsPrec :: Int -> QuadBezier a -> ShowS

show :: QuadBezier a -> String

showList :: [QuadBezier a] -> ShowS

Num a => AffineTransform (QuadBezier a) a

Methods

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

data AnyBezier a

A bezier curve of any degree.

Constructors

AnyBezier (Vector (a, a))

Instances

GenericBezier AnyBezier

Methods

degree :: Unbox a => AnyBezier a -> Int

toVector :: Unbox a => AnyBezier a -> Vector (a, a)

unsafeFromVector :: Unbox a => Vector (a, a) -> AnyBezier a

class GenericBezier b where

Minimal complete definition

degree, toVector, unsafeFromVector

Methods

degree :: Unbox a => b a -> Int

toVector :: Unbox a => b a -> Vector (a, a)

unsafeFromVector :: Unbox a => Vector (a, a) -> b a

Instances

GenericBezier AnyBezier

Methods

degree :: Unbox a => AnyBezier a -> Int

toVector :: Unbox a => AnyBezier a -> Vector (a, a)

unsafeFromVector :: Unbox a => Vector (a, a) -> AnyBezier a

GenericBezier QuadBezier

Methods

degree :: Unbox a => QuadBezier a -> Int

toVector :: Unbox a => QuadBezier a -> Vector (a, a)

unsafeFromVector :: Unbox a => Vector (a, a) -> QuadBezier a

GenericBezier CubicBezier

Methods

degree :: Unbox a => CubicBezier a -> Int

toVector :: Unbox a => CubicBezier a -> Vector (a, a)

unsafeFromVector :: Unbox a => Vector (a, a) -> CubicBezier a

data PathJoin a

Constructors

JoinLine

JoinCurve (Point a) (Point a)

Instances

Functor PathJoin

Methods

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

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

Foldable PathJoin

Methods

fold :: Monoid m => PathJoin m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> PathJoin a -> a

foldl1 :: (a -> a -> a) -> PathJoin a -> a

toList :: PathJoin a -> [a]

null :: PathJoin a -> Bool

length :: PathJoin a -> Int

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

maximum :: Ord a => PathJoin a -> a

minimum :: Ord a => PathJoin a -> a

sum :: Num a => PathJoin a -> a

product :: Num a => PathJoin a -> a

Traversable PathJoin

Methods

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

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

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

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

Show a => Show (PathJoin a)

Methods

showsPrec :: Int -> PathJoin a -> ShowS

show :: PathJoin a -> String

showList :: [PathJoin a] -> ShowS

Num a => AffineTransform (PathJoin a) a

Methods

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

data ClosedPath a

Constructors

ClosedPath [(Point a, PathJoin a)]

Instances

Functor ClosedPath

Methods

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

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

Foldable ClosedPath

Methods

fold :: Monoid m => ClosedPath m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> ClosedPath a -> a

foldl1 :: (a -> a -> a) -> ClosedPath a -> a

toList :: ClosedPath a -> [a]

null :: ClosedPath a -> Bool

length :: ClosedPath a -> Int

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

maximum :: Ord a => ClosedPath a -> a

minimum :: Ord a => ClosedPath a -> a

sum :: Num a => ClosedPath a -> a

product :: Num a => ClosedPath a -> a

Traversable ClosedPath

Methods

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

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

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

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

Show a => Show (ClosedPath a)

Methods

showsPrec :: Int -> ClosedPath a -> ShowS

show :: ClosedPath a -> String

showList :: [ClosedPath a] -> ShowS

Num a => AffineTransform (ClosedPath a) a

Methods

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

data OpenPath a

Constructors

OpenPath [(Point a, PathJoin a)] (Point a)

Instances

Functor OpenPath

Methods

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

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

Foldable OpenPath

Methods

fold :: Monoid m => OpenPath m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> OpenPath a -> a

foldl1 :: (a -> a -> a) -> OpenPath a -> a

toList :: OpenPath a -> [a]

null :: OpenPath a -> Bool

length :: OpenPath a -> Int

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

maximum :: Ord a => OpenPath a -> a

minimum :: Ord a => OpenPath a -> a

sum :: Num a => OpenPath a -> a

product :: Num a => OpenPath a -> a

Traversable OpenPath

Methods

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

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

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

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

Show a => Show (OpenPath a)

Methods

showsPrec :: Int -> OpenPath a -> ShowS

show :: OpenPath a -> String

showList :: [OpenPath a] -> ShowS

Monoid (OpenPath a)

Methods

mempty :: OpenPath a

mappend :: OpenPath a -> OpenPath a -> OpenPath a

mconcat :: [OpenPath a] -> OpenPath a

Num a => AffineTransform (OpenPath a) a

Methods

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

class AffineTransform a b | a -> b where

Minimal complete definition

transform

Methods

transform :: Transform b -> a -> a

Instances

Num a => AffineTransform (Polygon a) a

Methods

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

Num a => AffineTransform (Transform a) a

Methods

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

Num a => AffineTransform (Point a) a

Methods

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

Num a => AffineTransform (ClosedPath a) a

Methods

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

Num a => AffineTransform (OpenPath a) a

Methods

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

Num a => AffineTransform (PathJoin a) a

Methods

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

Num a => AffineTransform (QuadBezier a) a

Methods

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

Num a => AffineTransform (CubicBezier a) a

Methods

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

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

Methods

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

anyToCubic :: Unbox a => AnyBezier a -> Maybe (CubicBezier a)

safely convert from AnyBezier to CubicBezier

anyToQuad :: Unbox a => AnyBezier a -> Maybe (QuadBezier a)

safely convert from AnyBezier to QuadBezier

openPathCurves :: Fractional a => OpenPath a -> [CubicBezier a]

Return the open path as a list of curves.

closedPathCurves :: Fractional a => ClosedPath a -> [CubicBezier a]

Return the closed path as a list of curves

curvesToOpen :: [CubicBezier a] -> OpenPath a

Make an open path from a list of curves. The last control point of each curve except the last is ignored.

curvesToClosed :: [CubicBezier a] -> ClosedPath a

Make an open path from a list of curves. The last control point of each curve is ignored.

consOpenPath :: Point a -> PathJoin a -> OpenPath a -> OpenPath a

construct an open path

consClosedPath :: Point a -> PathJoin a -> ClosedPath a -> ClosedPath a

construct a closed path

openClosedPath :: ClosedPath a -> OpenPath a

open a closed path

closeOpenPath :: OpenPath a -> ClosedPath a

close an open path, discarding the last point

bezierParam :: (Ord a, Num a) => a -> Bool

Return True if the param lies on the curve, iff it's in the interval [0, 1].

bezierParamTolerance :: GenericBezier b => b Double -> Double -> Double

Convert a tolerance from the codomain to the domain of the bezier curve, by dividing by the maximum velocity on the curve. The estimate is conservative, but holds for any value on the curve.

reorient :: (GenericBezier b, Unbox a) => b a -> b a

Reorient to the curve B(1-t).

bezierToBernstein :: (GenericBezier b, Unbox a) => b a -> (BernsteinPoly a, BernsteinPoly a)

Give the bernstein polynomial for each coordinate.

evalBezierDerivs :: (GenericBezier b, Unbox a, Fractional a) => b a -> a -> [Point a]

Evaluate the bezier and all its derivatives using the modified horner algorithm.

evalBezier :: (GenericBezier b, Unbox a, Fractional a) => b a -> a -> Point a

Calculate a value on the bezier curve.

evalBezierDeriv :: (Unbox a, Fractional a) => GenericBezier b => b a -> a -> (Point a, Point a)

Calculate a value and the first derivative on the curve.

findBezierTangent :: DPoint -> CubicBezier Double -> [Double]

findBezierTangent p b finds the parameters where the tangent of the bezier curve b has the same direction as vector p.

quadToCubic :: Fractional a => QuadBezier a -> CubicBezier a

Convert a quadratic bezier to a cubic bezier.

bezierHoriz :: CubicBezier Double -> [Double]

Find the parameter where the bezier curve is horizontal.

bezierVert :: CubicBezier Double -> [Double]

Find the parameter where the bezier curve is vertical.

findBezierInflection :: CubicBezier Double -> [Double]

Find inflection points on the curve. Use the formula B_x''(t) * B_y'(t) - B_y''(t) * B_x'(t) = 0 with B_x'(t) the x value of the first derivative at t, B_y''(t) the y value of the second derivative at t

findBezierCusp :: CubicBezier Double -> [Double]

Find the cusps of a bezier.

bezierArc :: Double -> Double -> CubicBezier Double

bezierArc startAngle endAngle approximates an arc on the unit circle with a single cubic béziér curve. Maximum deviation is <0.03% for arcs 90° degrees or less.

arcLength :: CubicBezier Double -> Double -> Double -> Double

@arcLength c t tol finds the arclength of the bezier c at t, within given tolerance tol.

arcLengthParam :: CubicBezier Double -> Double -> Double -> Double

arcLengthParam c len tol finds the parameter where the curve c has the arclength len, within tolerance tol.

splitBezier :: (Unbox a, Fractional a) => GenericBezier b => b a -> a -> (b a, b a)

Split a bezier curve into two curves.

bezierSubsegment :: (Ord a, Unbox a, Fractional a) => GenericBezier b => b a -> a -> a -> b a

Return the subsegment between the two parameters.

splitBezierN :: (Ord a, Unbox a, Fractional a) => GenericBezier b => b a -> [a] -> [b a]

Split a bezier curve into a list of beziers The parameters should be in ascending order or the result is unpredictable.

colinear :: CubicBezier Double -> Double -> Bool

Return False if some points fall outside a line with a thickness of the given tolerance.

closest :: CubicBezier Double -> DPoint -> Double -> Double

Find the closest value on the bezier to the given point, within tolerance. Return the first value found.

findX :: CubicBezier Double -> Double -> Double -> Double

Find the x value of the cubic bezier. The bezier must be monotonically increasing in the X coordinate.