Copyright	Written by David Himmelstrup
License	Unlicense
Maintainer	lemmih@gmail.com
Stability	experimental
Portability	POSIX
Safe Haskell	None
Language	Haskell2010

Geom2D.CubicBezier.Linear

Description

Convenience wrapper around CubicBezier

Synopsis

newtype AnyBezier a = AnyBezier (Vector (V2 a))
data CubicBezier a = CubicBezier {
- cubicC0 :: !(V2 a)
- cubicC1 :: !(V2 a)
- cubicC2 :: !(V2 a)
- cubicC3 :: !(V2 a)
}
data QuadBezier a = QuadBezier {
- quadC0 :: !(V2 a)
- quadC1 :: !(V2 a)
- quadC2 :: !(V2 a)
}
data OpenPath a = OpenPath [(V2 a, PathJoin a)] (V2 a)
data ClosedPath a = ClosedPath [(V2 a, PathJoin a)]
data PathJoin a
- = JoinLine
- | JoinCurve (V2 a) (V2 a)
data ClosedMetaPath a = ClosedMetaPath [(V2 a, MetaJoin a)]
data OpenMetaPath a = OpenMetaPath [(V2 a, MetaJoin a)] (V2 a)
data MetaJoin a
- = MetaJoin {
  - metaTypeL :: MetaNodeType a
  - tensionL :: Tension a
  - tensionR :: Tension a
  - metaTypeR :: MetaNodeType a
  }
- | Controls (V2 a) (V2 a)
data MetaNodeType a
- = Open
- | Curl {
  - curlgamma :: a
  }
- | Direction {
  - nodedir :: V2 a
  }
data FillRule
- = FillEvenOdd
- | FillNonZero
data Tension a
- = Tension {
  - tensionValue :: a
  }
- | TensionAtLeast {
  - tensionValue :: a
  }
quadToCubic :: Fractional a => QuadBezier a -> CubicBezier a
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)
colinear :: CubicBezier Double -> Double -> Bool
evalBezier :: (GenericBezier b, Unbox a, Fractional a) => b a -> a -> V2 a
evalBezierDeriv :: (Unbox a, Fractional a, GenericBezier b) => b a -> a -> (V2 a, V2 a)
bezierHoriz :: CubicBezier Double -> [Double]
bezierVert :: CubicBezier Double -> [Double]
bezierSubsegment :: (Ord a, Unbox a, Fractional a, GenericBezier b) => b a -> a -> a -> b a
reorient :: (GenericBezier b, Unbox a) => b a -> b a
closedPathCurves :: Fractional a => ClosedPath a -> [CubicBezier a]
openPathCurves :: Fractional a => OpenPath a -> [CubicBezier a]
curvesToClosed :: [CubicBezier a] -> ClosedPath a
closest :: CubicBezier Double -> V2 Double -> Double -> Double
unmetaOpen :: OpenMetaPath Double -> OpenPath Double
unmetaClosed :: ClosedMetaPath Double -> ClosedPath Double
union :: [ClosedPath Double] -> FillRule -> Double -> [ClosedPath Double]
bezierIntersection :: CubicBezier Double -> CubicBezier Double -> Double -> [(Double, Double)]
interpolateVector :: Num a => V2 a -> V2 a -> a -> V2 a
vectorDistance :: Floating a => V2 a -> V2 a -> a
findBezierInflection :: CubicBezier Double -> [Double]
findBezierCusp :: CubicBezier Double -> [Double]

Documentation

newtype AnyBezier a Source #

A bezier curve of any degree.

Constructors

AnyBezier (Vector (V2 a))

Instances

GenericBezier AnyBezier Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods degree :: Unbox a => AnyBezier a -> Int # toVector :: Unbox a => AnyBezier a -> Vector (a, a) # unsafeFromVector :: Unbox a => Vector (a, a) -> AnyBezier a #

data CubicBezier a Source #

A cubic bezier curve.

Constructors

CubicBezier
Fields cubicC0 :: !(V2 a) cubicC1 :: !(V2 a) cubicC2 :: !(V2 a) cubicC3 :: !(V2 a)

Instances

GenericBezier CubicBezier Source #
Instance details Defined in Geom2D.CubicBezier.Linear 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) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods (==) :: CubicBezier a -> CubicBezier a -> Bool # (/=) :: CubicBezier a -> CubicBezier a -> Bool #
Show a => Show (CubicBezier a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods showsPrec :: Int -> CubicBezier a -> ShowS # show :: CubicBezier a -> String # showList :: [CubicBezier a] -> ShowS #

data QuadBezier a Source #

A quadratic bezier curve.

Constructors

QuadBezier
Fields quadC0 :: !(V2 a) quadC1 :: !(V2 a) quadC2 :: !(V2 a)

Instances

GenericBezier QuadBezier Source #
Instance details Defined in Geom2D.CubicBezier.Linear 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) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods (==) :: QuadBezier a -> QuadBezier a -> Bool # (/=) :: QuadBezier a -> QuadBezier a -> Bool #
Show a => Show (QuadBezier a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods showsPrec :: Int -> QuadBezier a -> ShowS # show :: QuadBezier a -> String # showList :: [QuadBezier a] -> ShowS #

data OpenPath a Source #

Open cubicbezier path.

Constructors

OpenPath [(V2 a, PathJoin a)] (V2 a)

Instances

Eq a => Eq (OpenPath a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods (==) :: OpenPath a -> OpenPath a -> Bool # (/=) :: OpenPath a -> OpenPath a -> Bool #
Show a => Show (OpenPath a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods showsPrec :: Int -> OpenPath a -> ShowS # show :: OpenPath a -> String # showList :: [OpenPath a] -> ShowS #

data ClosedPath a Source #

Closed cubicbezier path.

Constructors

ClosedPath [(V2 a, PathJoin a)]

Instances

Eq a => Eq (ClosedPath a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods (==) :: ClosedPath a -> ClosedPath a -> Bool # (/=) :: ClosedPath a -> ClosedPath a -> Bool #
Show a => Show (ClosedPath a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods showsPrec :: Int -> ClosedPath a -> ShowS # show :: ClosedPath a -> String # showList :: [ClosedPath a] -> ShowS #

data PathJoin a Source #

Join two points with either a straight line or a bezier curve with two control points.

Constructors

JoinLine
JoinCurve (V2 a) (V2 a)

Instances

Eq a => Eq (PathJoin a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods (==) :: PathJoin a -> PathJoin a -> Bool # (/=) :: PathJoin a -> PathJoin a -> Bool #
Show a => Show (PathJoin a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods showsPrec :: Int -> PathJoin a -> ShowS # show :: PathJoin a -> String # showList :: [PathJoin a] -> ShowS #

data ClosedMetaPath a Source #

Closed meta path.

Constructors

ClosedMetaPath [(V2 a, MetaJoin a)]

Instances

Eq a => Eq (ClosedMetaPath a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods (==) :: ClosedMetaPath a -> ClosedMetaPath a -> Bool # (/=) :: ClosedMetaPath a -> ClosedMetaPath a -> Bool #
Show a => Show (ClosedMetaPath a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods showsPrec :: Int -> ClosedMetaPath a -> ShowS # show :: ClosedMetaPath a -> String # showList :: [ClosedMetaPath a] -> ShowS #

data OpenMetaPath a Source #

Open meta path

Constructors

OpenMetaPath [(V2 a, MetaJoin a)] (V2 a)

Instances

Eq a => Eq (OpenMetaPath a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods (==) :: OpenMetaPath a -> OpenMetaPath a -> Bool # (/=) :: OpenMetaPath a -> OpenMetaPath a -> Bool #
Show a => Show (OpenMetaPath a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods showsPrec :: Int -> OpenMetaPath a -> ShowS # show :: OpenMetaPath a -> String # showList :: [OpenMetaPath a] -> ShowS #

data MetaJoin a Source #

Join two meta points with either a bezier curve or tension contraints.

Constructors

MetaJoin
Fields metaTypeL :: MetaNodeType a tensionL :: Tension a tensionR :: Tension a metaTypeR :: MetaNodeType a
Controls (V2 a) (V2 a)

Instances

Eq a => Eq (MetaJoin a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods (==) :: MetaJoin a -> MetaJoin a -> Bool # (/=) :: MetaJoin a -> MetaJoin a -> Bool #
Show a => Show (MetaJoin a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods showsPrec :: Int -> MetaJoin a -> ShowS # show :: MetaJoin a -> String # showList :: [MetaJoin a] -> ShowS #

data MetaNodeType a Source #

Node constraint type.

Constructors

Open
Curl
Fields curlgamma :: a
Direction
Fields nodedir :: V2 a

Instances

Eq a => Eq (MetaNodeType a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods (==) :: MetaNodeType a -> MetaNodeType a -> Bool # (/=) :: MetaNodeType a -> MetaNodeType a -> Bool #
Show a => Show (MetaNodeType a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods showsPrec :: Int -> MetaNodeType a -> ShowS # show :: MetaNodeType a -> String # showList :: [MetaNodeType a] -> ShowS #

data FillRule #

Describe the possile filling algorithms. Map the values of the `fill-rule` attributes.

Constructors

FillEvenOdd	Correspond to the `evenodd` value.
FillNonZero	Correspond to the `nonzero` value.

Instances

Eq FillRule
Instance details Defined in Graphics.SvgTree.Types Methods (==) :: FillRule -> FillRule -> Bool # (/=) :: FillRule -> FillRule -> Bool #
Show FillRule
Instance details Defined in Graphics.SvgTree.Types Methods showsPrec :: Int -> FillRule -> ShowS # show :: FillRule -> String # showList :: [FillRule] -> ShowS #
ParseableAttribute FillRule
Instance details Defined in Graphics.SvgTree.XmlParser Methods aparse :: String -> Maybe FillRule aserialize :: FillRule -> Maybe String

data Tension a Source #

The tension value specifies how tense the curve is. A higher value means the curve approaches a line segment, while a lower value means the curve is more round. Metafont doesn't allow values below 3/4.

Constructors

Tension
Fields tensionValue :: a
TensionAtLeast	Like Tension, but keep the segment inside the bounding triangle defined by the control points, if there is one.
Fields tensionValue :: a

Instances

Functor Tension Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods fmap :: (a -> b) -> Tension a -> Tension b # (<$) :: a -> Tension b -> Tension a #
Foldable Tension Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods fold :: Monoid m => Tension m -> m # foldMap :: Monoid m => (a -> m) -> Tension a -> m # foldr :: (a -> b -> b) -> b -> Tension a -> b # foldr' :: (a -> b -> b) -> b -> Tension a -> b # foldl :: (b -> a -> b) -> b -> Tension a -> b # foldl' :: (b -> a -> b) -> b -> Tension a -> b # foldr1 :: (a -> a -> a) -> Tension a -> a # foldl1 :: (a -> a -> a) -> Tension a -> a # toList :: Tension a -> [a] # null :: Tension a -> Bool # length :: Tension a -> Int # elem :: Eq a => a -> Tension a -> Bool # maximum :: Ord a => Tension a -> a # minimum :: Ord a => Tension a -> a # sum :: Num a => Tension a -> a # product :: Num a => Tension a -> a #
Traversable Tension Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods traverse :: Applicative f => (a -> f b) -> Tension a -> f (Tension b) # sequenceA :: Applicative f => Tension (f a) -> f (Tension a) # mapM :: Monad m => (a -> m b) -> Tension a -> m (Tension b) # sequence :: Monad m => Tension (m a) -> m (Tension a) #
Eq a => Eq (Tension a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods (==) :: Tension a -> Tension a -> Bool # (/=) :: Tension a -> Tension a -> Bool #
Show a => Show (Tension a) Source #
Instance details Defined in Geom2D.CubicBezier.Linear Methods showsPrec :: Int -> Tension a -> ShowS # show :: Tension a -> String # showList :: [Tension a] -> ShowS #

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

Convert a quadratic bezier to a cubic bezier.

arcLength :: CubicBezier Double -> Double -> Double -> Double Source #

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

arcLengthParam :: CubicBezier Double -> Double -> Double -> Double Source #

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.

colinear :: CubicBezier Double -> Double -> Bool Source #

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

evalBezier :: (GenericBezier b, Unbox a, Fractional a) => b a -> a -> V2 a Source #

Calculate a value on the bezier curve.

evalBezierDeriv :: (Unbox a, Fractional a, GenericBezier b) => b a -> a -> (V2 a, V2 a) Source #

Calculate a value and the first derivative on the curve.

bezierHoriz :: CubicBezier Double -> [Double] Source #

Find the parameter where the bezier curve is horizontal.

bezierVert :: CubicBezier Double -> [Double] Source #

Find the parameter where the bezier curve is vertical.

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

Return the subsegment between the two parameters.

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

Reorient to the curve B(1-t).

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

Return the closed path as a list of curves.

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

Return the open path as a list of curves.

curvesToClosed :: [CubicBezier a] -> ClosedPath a Source #

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

closest :: CubicBezier Double -> V2 Double -> Double -> Double Source #

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

unmetaOpen :: OpenMetaPath Double -> OpenPath Double Source #

Create a normal path from a metapath.

unmetaClosed :: ClosedMetaPath Double -> ClosedPath Double Source #

Create a normal path from a metapath.

union :: [ClosedPath Double] -> FillRule -> Double -> [ClosedPath Double] Source #

`O((n+m)*log(n+m))`, for n segments and m intersections. Union of paths, removing overlap and rounding to the given tolerance.

bezierIntersection :: CubicBezier Double -> CubicBezier Double -> Double -> [(Double, Double)] Source #

Find the intersections between two Bezier curves, using the Bezier Clip algorithm. Returns the parameters for both curves.

interpolateVector :: Num a => V2 a -> V2 a -> a -> V2 a Source #

Interpolate between two vectors.

vectorDistance :: Floating a => V2 a -> V2 a -> a Source #

Distance between two vectors.

findBezierInflection :: CubicBezier Double -> [Double] Source #

Find inflection points on the curve.

findBezierCusp :: CubicBezier Double -> [Double] Source #

Find the cusps of a bezier.