Safe Haskell	None
Language	Haskell98

Geom2D.CubicBezier.Basic

Synopsis

data CubicBezier a = CubicBezier {
- cubicC0 :: !(Point a)
- cubicC1 :: !(Point a)
- cubicC2 :: !(Point a)
- cubicC3 :: !(Point a)
}
data QuadBezier a = QuadBezier {
- quadC0 :: !(Point a)
- quadC1 :: !(Point a)
- quadC2 :: !(Point a)
}
data AnyBezier a = AnyBezier (Vector (a, a))
class GenericBezier b where
data PathJoin a
- = JoinLine
- | JoinCurve (Point a) (Point a)
data ClosedPath a = ClosedPath [(Point a, PathJoin a)]
data OpenPath a = OpenPath [(Point a, PathJoin a)] (Point a)
class AffineTransform a b | a -> b where
anyToCubic :: Unbox a => AnyBezier a -> Maybe (CubicBezier a)
anyToQuad :: Unbox a => AnyBezier a -> Maybe (QuadBezier a)
openPathCurves :: Fractional a => OpenPath a -> [CubicBezier a]
closedPathCurves :: Fractional a => ClosedPath a -> [CubicBezier a]
curvesToOpen :: [CubicBezier a] -> OpenPath a
curvesToClosed :: [CubicBezier a] -> ClosedPath a
consOpenPath :: Point a -> PathJoin a -> OpenPath a -> OpenPath a
consClosedPath :: Point a -> PathJoin a -> ClosedPath a -> ClosedPath a
openClosedPath :: ClosedPath a -> OpenPath a
closeOpenPath :: OpenPath a -> ClosedPath a
bezierParam :: (Ord a, Num a) => a -> Bool
bezierParamTolerance :: GenericBezier b => b Double -> Double -> Double
reorient :: (GenericBezier b, Unbox a) => b a -> b a
bezierToBernstein :: (GenericBezier b, Unbox a) => b a -> (BernsteinPoly a, BernsteinPoly a)
evalBezierDerivs :: (GenericBezier b, Unbox a, Fractional a) => b a -> a -> [Point a]
evalBezier :: (GenericBezier b, Unbox a, Fractional a) => b a -> a -> Point a
evalBezierDeriv :: (Unbox a, Fractional a) => GenericBezier b => b a -> a -> (Point a, Point a)
findBezierTangent :: DPoint -> CubicBezier Double -> [Double]
quadToCubic :: Fractional a => QuadBezier a -> CubicBezier a
bezierHoriz :: CubicBezier Double -> [Double]
bezierVert :: CubicBezier Double -> [Double]
findBezierInflection :: CubicBezier Double -> [Double]
findBezierCusp :: CubicBezier Double -> [Double]
bezierArc :: Double -> Double -> CubicBezier Double
arcLength :: CubicBezier Double -> Double -> Double -> Double
arcLengthParam :: CubicBezier Double -> Double -> Double -> Double
splitBezier :: (Unbox a, Fractional a) => GenericBezier b => b a -> a -> (b a, b a)
bezierSubsegment :: (Ord a, Unbox a, Fractional a) => GenericBezier b => b a -> a -> a -> b a
splitBezierN :: (Ord a, Unbox a, Fractional a) => GenericBezier b => b a -> [a] -> [b a]
colinear :: CubicBezier Double -> Double -> Bool
closest :: CubicBezier Double -> DPoint -> Double -> Double
findX :: CubicBezier Double -> Double -> Double -> Double

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 #
Instance details Defined in Geom2D.CubicBezier.Basic Methods fmap :: (a -> b) -> CubicBezier a -> CubicBezier b # (<$) :: a -> CubicBezier b -> CubicBezier a #
Foldable CubicBezier #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D.CubicBezier.Basic 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) #
Instance details Defined in Geom2D.CubicBezier.Basic Methods (==) :: CubicBezier a -> CubicBezier a -> Bool # (/=) :: CubicBezier a -> CubicBezier a -> Bool #
Show a => Show (CubicBezier a) #
Instance details Defined in Geom2D.CubicBezier.Basic Methods showsPrec :: Int -> CubicBezier a -> ShowS # show :: CubicBezier a -> String # showList :: [CubicBezier a] -> ShowS #
Num a => AffineTransform (CubicBezier a) a #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D.CubicBezier.Basic Methods fmap :: (a -> b) -> QuadBezier a -> QuadBezier b # (<$) :: a -> QuadBezier b -> QuadBezier a #
Foldable QuadBezier #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D.CubicBezier.Basic 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) #
Instance details Defined in Geom2D.CubicBezier.Basic Methods (==) :: QuadBezier a -> QuadBezier a -> Bool # (/=) :: QuadBezier a -> QuadBezier a -> Bool #
Show a => Show (QuadBezier a) #
Instance details Defined in Geom2D.CubicBezier.Basic Methods showsPrec :: Int -> QuadBezier a -> ShowS # show :: QuadBezier a -> String # showList :: [QuadBezier a] -> ShowS #
Num a => AffineTransform (QuadBezier a) a #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D.CubicBezier.Basic Methods fmap :: (a -> b) -> PathJoin a -> PathJoin b # (<$) :: a -> PathJoin b -> PathJoin a #
Foldable PathJoin #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D.CubicBezier.Basic 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) #
Instance details Defined in Geom2D.CubicBezier.Basic Methods showsPrec :: Int -> PathJoin a -> ShowS # show :: PathJoin a -> String # showList :: [PathJoin a] -> ShowS #
Num a => AffineTransform (PathJoin a) a #
Instance details Defined in Geom2D.CubicBezier.Basic Methods transform :: Transform a -> PathJoin a -> PathJoin a #

data ClosedPath a #

Constructors

ClosedPath [(Point a, PathJoin a)]

Instances

Functor ClosedPath #
Instance details Defined in Geom2D.CubicBezier.Basic Methods fmap :: (a -> b) -> ClosedPath a -> ClosedPath b # (<$) :: a -> ClosedPath b -> ClosedPath a #
Foldable ClosedPath #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D.CubicBezier.Basic 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) #
Instance details Defined in Geom2D.CubicBezier.Basic Methods showsPrec :: Int -> ClosedPath a -> ShowS # show :: ClosedPath a -> String # showList :: [ClosedPath a] -> ShowS #
Num a => AffineTransform (ClosedPath a) a #
Instance details Defined in Geom2D.CubicBezier.Basic Methods transform :: Transform a -> ClosedPath a -> ClosedPath a #

data OpenPath a #

Constructors

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

Instances

Functor OpenPath #
Instance details Defined in Geom2D.CubicBezier.Basic Methods fmap :: (a -> b) -> OpenPath a -> OpenPath b # (<$) :: a -> OpenPath b -> OpenPath a #
Foldable OpenPath #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D.CubicBezier.Basic 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) #
Instance details Defined in Geom2D.CubicBezier.Basic Methods showsPrec :: Int -> OpenPath a -> ShowS # show :: OpenPath a -> String # showList :: [OpenPath a] -> ShowS #
Semigroup (OpenPath a) #
Instance details Defined in Geom2D.CubicBezier.Basic Methods (<>) :: OpenPath a -> OpenPath a -> OpenPath a # sconcat :: NonEmpty (OpenPath a) -> OpenPath a # stimes :: Integral b => b -> OpenPath a -> OpenPath a #
Monoid (OpenPath a) #
Instance details Defined in Geom2D.CubicBezier.Basic Methods mempty :: OpenPath a # mappend :: OpenPath a -> OpenPath a -> OpenPath a # mconcat :: [OpenPath a] -> OpenPath a #
Num a => AffineTransform (OpenPath a) a #
Instance details Defined in Geom2D.CubicBezier.Basic 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 #
Instance details Defined in Geom2D Methods transform :: Transform a -> Polygon a -> Polygon a #
Num a => AffineTransform (Transform a) a #
Instance details Defined in Geom2D Methods transform :: Transform a -> Transform a -> Transform a #
Num a => AffineTransform (Point a) a #
Instance details Defined in Geom2D Methods transform :: Transform a -> Point a -> Point a #
Num a => AffineTransform (ClosedPath a) a #
Instance details Defined in Geom2D.CubicBezier.Basic Methods transform :: Transform a -> ClosedPath a -> ClosedPath a #
Num a => AffineTransform (OpenPath a) a #
Instance details Defined in Geom2D.CubicBezier.Basic Methods transform :: Transform a -> OpenPath a -> OpenPath a #
Num a => AffineTransform (PathJoin a) a #
Instance details Defined in Geom2D.CubicBezier.Basic Methods transform :: Transform a -> PathJoin a -> PathJoin a #
Num a => AffineTransform (QuadBezier a) a #
Instance details Defined in Geom2D.CubicBezier.Basic Methods transform :: Transform a -> QuadBezier a -> QuadBezier a #
Num a => AffineTransform (CubicBezier a) a #
Instance details Defined in Geom2D.CubicBezier.Basic Methods transform :: Transform a -> CubicBezier a -> CubicBezier a #
(Floating a, Eq a) => AffineTransform (Pen a) a #
Instance details Defined in Geom2D.CubicBezier.Stroke 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.