Safe Haskell	None
Language	Haskell98

Geom2D.CubicBezier.MetaPath

Description

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.

Synopsis

unmetaOpen :: OpenMetaPath Double -> OpenPath Double
unmetaClosed :: ClosedMetaPath Double -> ClosedPath Double
data ClosedMetaPath a = ClosedMetaPath [(Point a, MetaJoin a)]
data OpenMetaPath a = OpenMetaPath [(Point a, MetaJoin a)] (Point a)
data MetaJoin a
- = MetaJoin {
  - metaTypeL :: MetaNodeType a
  - tensionL :: Tension a
  - tensionR :: Tension a
  - metaTypeR :: MetaNodeType a
  }
- | Controls (Point a) (Point a)
data MetaNodeType a
- = Open
- | Curl {
  - curlgamma :: a
  }
- | Direction {
  - nodedir :: Point a
  }
data Tension a
- = Tension {
  - tensionValue :: a
  }
- | TensionAtLeast {
  - tensionValue :: a
  }

Documentation

unmetaOpen :: OpenMetaPath Double -> OpenPath Double Source #

Create a normal path from a metapath.

unmetaClosed :: ClosedMetaPath Double -> ClosedPath Double Source #

data ClosedMetaPath a Source #

Constructors

ClosedMetaPath [(Point a, MetaJoin a)]

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

Instances

Functor ClosedMetaPath Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods fmap :: (a -> b) -> ClosedMetaPath a -> ClosedMetaPath b # (<$) :: a -> ClosedMetaPath b -> ClosedMetaPath a #
Foldable ClosedMetaPath Source #
Instance details 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 Source #
Instance details 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) Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods (==) :: ClosedMetaPath a -> ClosedMetaPath a -> Bool # (/=) :: ClosedMetaPath a -> ClosedMetaPath a -> Bool #
(Show a, Real a) => Show (ClosedMetaPath a) Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods showsPrec :: Int -> ClosedMetaPath a -> ShowS # show :: ClosedMetaPath a -> String # showList :: [ClosedMetaPath a] -> ShowS #

data OpenMetaPath a Source #

Constructors

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

A metapath with endpoints

Instances

Functor OpenMetaPath Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods fmap :: (a -> b) -> OpenMetaPath a -> OpenMetaPath b # (<$) :: a -> OpenMetaPath b -> OpenMetaPath a #
Foldable OpenMetaPath Source #
Instance details 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 Source #
Instance details 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) Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods showsPrec :: Int -> OpenMetaPath a -> ShowS # show :: OpenMetaPath a -> String # showList :: [OpenMetaPath a] -> ShowS #

data MetaJoin a Source #

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 Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods fmap :: (a -> b) -> MetaJoin a -> MetaJoin b # (<$) :: a -> MetaJoin b -> MetaJoin a #
Foldable MetaJoin Source #
Instance details 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 Source #
Instance details 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) Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods (==) :: MetaJoin a -> MetaJoin a -> Bool # (/=) :: MetaJoin a -> MetaJoin a -> Bool #
Show a => Show (MetaJoin a) Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods showsPrec :: Int -> MetaJoin a -> ShowS # show :: MetaJoin a -> String # showList :: [MetaJoin a] -> ShowS #

data MetaNodeType a Source #

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 Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods fmap :: (a -> b) -> MetaNodeType a -> MetaNodeType b # (<$) :: a -> MetaNodeType b -> MetaNodeType a #
Foldable MetaNodeType Source #
Instance details 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 Source #
Instance details 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) Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods (==) :: MetaNodeType a -> MetaNodeType a -> Bool # (/=) :: MetaNodeType a -> MetaNodeType a -> Bool #
Show a => Show (MetaNodeType a) Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods showsPrec :: Int -> MetaNodeType a -> ShowS # show :: MetaNodeType a -> String # showList :: [MetaNodeType a] -> ShowS #

data Tension a Source #

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 Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods fmap :: (a -> b) -> Tension a -> Tension b # (<$) :: a -> Tension b -> Tension a #
Foldable Tension Source #
Instance details 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 Source #
Instance details 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) Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods (==) :: Tension a -> Tension a -> Bool # (/=) :: Tension a -> Tension a -> Bool #
Show a => Show (Tension a) Source #
Instance details Defined in Geom2D.CubicBezier.MetaPath Methods showsPrec :: Int -> Tension a -> ShowS # show :: Tension a -> String # showList :: [Tension a] -> ShowS #