cubicbezier-0.6.0.3: Efficient manipulating of 2D cubic bezier curves.

Safe HaskellNone
LanguageHaskell98

Geom2D.CubicBezier.Basic

Synopsis

Documentation

data CubicBezier a #

A cubic bezier curve.

Constructors

CubicBezier 

Fields

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) # 
Show a => Show (CubicBezier a) # 
Num a => AffineTransform (CubicBezier a) a # 

data QuadBezier a #

A quadratic bezier curve.

Constructors

QuadBezier 

Fields

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) # 
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

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) # 
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 # 
(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.