Geom2D.CubicBezier.MetaPath

This module implements an extension to paths as used in D.E.Knuth's Metafont. Metafont gives an alternate way to specify paths using bezier curves. I'll give a brief overview of the metafont curves. A more in depth explanation can be found in The MetafontBook.

Each spline has a tension parameter, which is a relative measure of the length of the curve. You can specify the tension for the left side and the right side of the spline separately. By default metafont gives a tension of 1, which gives a good looking curve. Tensions shouldn't be less than 3/4, but this implementation doesn't check for it. If you want to avoid points of inflection on the spline, you can use TensionAtLeast instead of Tension, which will adjust the length of the control points so they fall into the bounding triangle, if such a triangle exist.

You can either give directions for each node, or let metafont find them. Metafont will solve a set of equations to find the directions. You can also let metafont find directions at corner points by setting the curl, which is how much the point curls at that point. At endpoints a curl of 1 is implied when it is not given.

Metafont will then find the control points from the path for you. You can also specify the control points explicitly.

Here is an example path from the metafont program text:

z0..z1..tension atleast 1..{curl 2}z2..z3{-1,-2}..tension 3 and 4..z4..controls z45 and z54..z5

This path is equivalent to:

z0{curl 1}..tension atleast 1 and atleast 1..{curl 2}z2{curl 2}..tension 1 and 1..
{-1,-2}z3{-1,-2}..tension 3 and 4..z4..controls z45 and z54..z5

This path can be used with the following datatype:

OpenMetaPath [ (z0, MetaJoin Open (Tension 1) (Tension 1) Open)
             , (z1, MetaJoin Open (TensionAtLeast 1) (TensionAtLeast 1) (Curl 2))
             , (z2, MetaJoin Open (Tension 1) (Tension 1) Open)
             , (z3, MetaJoin (Direction (Point (-1) (-2))) (Tension 3) (Tension 4) Open)
             , (z4, Controls z45 z54)
             ] z5

Cyclic paths are similar, but use the CyclicMetaPath contructor. There is no ending point, since the ending point will be the same as the first point.

Documentation

unmetaOpen :: OpenMetaPath Double -> OpenPath Double

Create a normal path from a metapath.

unmetaClosed :: ClosedMetaPath Double -> ClosedPath Double

data ClosedMetaPath a

Constructors

ClosedMetaPath [(Point a, MetaJoin a)]

A metapath with cycles. The last join joins the last point with the first.

Instances

Functor ClosedMetaPath

Defined in Geom2D.CubicBezier.MetaPath

Methods

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

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

Foldable ClosedMetaPath

Defined in Geom2D.CubicBezier.MetaPath

Methods

fold :: Monoid m => ClosedMetaPath m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> ClosedMetaPath a -> a

foldl1 :: (a -> a -> a) -> ClosedMetaPath a -> a

toList :: ClosedMetaPath a -> [a]

null :: ClosedMetaPath a -> Bool

length :: ClosedMetaPath a -> Int

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

maximum :: Ord a => ClosedMetaPath a -> a

minimum :: Ord a => ClosedMetaPath a -> a

sum :: Num a => ClosedMetaPath a -> a

product :: Num a => ClosedMetaPath a -> a

Traversable ClosedMetaPath

Defined in Geom2D.CubicBezier.MetaPath

Methods

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

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

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

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

Eq a => Eq (ClosedMetaPath a)

Defined in Geom2D.CubicBezier.MetaPath

Methods

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

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

(Show a, Real a) => Show (ClosedMetaPath a)

Defined in Geom2D.CubicBezier.MetaPath

Methods

showsPrec :: Int -> ClosedMetaPath a -> ShowS

show :: ClosedMetaPath a -> String

showList :: [ClosedMetaPath a] -> ShowS

data OpenMetaPath a

Constructors

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

A metapath with endpoints

Instances

Functor OpenMetaPath

Defined in Geom2D.CubicBezier.MetaPath

Methods

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

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

Foldable OpenMetaPath

Defined in Geom2D.CubicBezier.MetaPath

Methods

fold :: Monoid m => OpenMetaPath m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> OpenMetaPath a -> a

foldl1 :: (a -> a -> a) -> OpenMetaPath a -> a

toList :: OpenMetaPath a -> [a]

null :: OpenMetaPath a -> Bool

length :: OpenMetaPath a -> Int

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

maximum :: Ord a => OpenMetaPath a -> a

minimum :: Ord a => OpenMetaPath a -> a

sum :: Num a => OpenMetaPath a -> a

product :: Num a => OpenMetaPath a -> a

Traversable OpenMetaPath

Defined in Geom2D.CubicBezier.MetaPath

Methods

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

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

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

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

(Show a, Real a) => Show (OpenMetaPath a)

Defined in Geom2D.CubicBezier.MetaPath

Methods

showsPrec :: Int -> OpenMetaPath a -> ShowS

show :: OpenMetaPath a -> String

showList :: [OpenMetaPath a] -> ShowS

data MetaJoin a

Constructors

MetaJoin

Fields

• metaTypeL :: MetaNodeType a

  The nodetype going out of the previous point. The metafont default is Open.

• tensionL :: Tension a

  The tension going out of the previous point. The metafont default is 1.

• tensionR :: Tension a

  The tension going into the next point. The metafont default is 1.

• metaTypeR :: MetaNodeType a

  The nodetype going into the next point. The metafont default is Open.

Controls (Point a) (Point a)

Specify the control points explicitly.

Instances

Functor MetaJoin

Defined in Geom2D.CubicBezier.MetaPath

Methods

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

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

Foldable MetaJoin

Defined in Geom2D.CubicBezier.MetaPath

Methods

fold :: Monoid m => MetaJoin m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> MetaJoin a -> a

foldl1 :: (a -> a -> a) -> MetaJoin a -> a

toList :: MetaJoin a -> [a]

null :: MetaJoin a -> Bool

length :: MetaJoin a -> Int

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

maximum :: Ord a => MetaJoin a -> a

minimum :: Ord a => MetaJoin a -> a

sum :: Num a => MetaJoin a -> a

product :: Num a => MetaJoin a -> a

Traversable MetaJoin

Defined in Geom2D.CubicBezier.MetaPath

Methods

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

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

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

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

Eq a => Eq (MetaJoin a)

Defined in Geom2D.CubicBezier.MetaPath

Methods

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

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

Show a => Show (MetaJoin a)

Defined in Geom2D.CubicBezier.MetaPath

Methods

showsPrec :: Int -> MetaJoin a -> ShowS

show :: MetaJoin a -> String

showList :: [MetaJoin a] -> ShowS

data MetaNodeType a

Constructors

Open

An open node has no direction specified. If it is an internal node, the curve will keep the same direction going into and going out from the node. If it is an endpoint or corner point, it will have curl of 1.

Curl

The node becomes and endpoint or a corner point. The curl specifies how much the segment curves. A curl of gamma means that the curvature is gamma times that of the following node.

Fields

• curlgamma :: a

Direction

The node has a given direction.

Fields

• nodedir :: Point a

Instances

Functor MetaNodeType

Defined in Geom2D.CubicBezier.MetaPath

Methods

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

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

Foldable MetaNodeType

Defined in Geom2D.CubicBezier.MetaPath

Methods

fold :: Monoid m => MetaNodeType m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> MetaNodeType a -> a

foldl1 :: (a -> a -> a) -> MetaNodeType a -> a

toList :: MetaNodeType a -> [a]

null :: MetaNodeType a -> Bool

length :: MetaNodeType a -> Int

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

maximum :: Ord a => MetaNodeType a -> a

minimum :: Ord a => MetaNodeType a -> a

sum :: Num a => MetaNodeType a -> a

product :: Num a => MetaNodeType a -> a

Traversable MetaNodeType

Defined in Geom2D.CubicBezier.MetaPath

Methods

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

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

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

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

Eq a => Eq (MetaNodeType a)

Defined in Geom2D.CubicBezier.MetaPath

Methods

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

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

Show a => Show (MetaNodeType a)

Defined in Geom2D.CubicBezier.MetaPath

Methods

showsPrec :: Int -> MetaNodeType a -> ShowS

show :: MetaNodeType a -> String

showList :: [MetaNodeType a] -> ShowS

data Tension a

Constructors

Tension

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.

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

Defined in Geom2D.CubicBezier.MetaPath

Methods

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

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

Foldable Tension

Defined in Geom2D.CubicBezier.MetaPath

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

Defined in Geom2D.CubicBezier.MetaPath

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)

Defined in Geom2D.CubicBezier.MetaPath

Methods

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

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

Show a => Show (Tension a)

Defined in Geom2D.CubicBezier.MetaPath

Methods

showsPrec :: Int -> Tension a -> ShowS

show :: Tension a -> String

showList :: [Tension a] -> ShowS