hgeometry-0.12.0.1: Geometric Algorithms, Data structures, and Data types.
Copyright(C) Frank Staals
Licensesee the LICENSE file
MaintainerFrank Staals
Safe HaskellNone
LanguageHaskell2010

Data.PlaneGraph.Core

Description

Data type for planar graphs embedded in \(\mathbb{R}^2\). For functions that export faces and edges etc, we assume the graph has a (planar) straight line embedding.

Synopsis

Documentation

>>> import Data.Proxy
>>> import Data.PlaneGraph.AdjRep(Gr(Gr),Face(Face),Vtx(Vtx))
>>> import Data.PlaneGraph.IO(fromAdjRep)
>>> import Data.PlanarGraph.Dart(Dart(..),Arc(..))
>>> :{
let dart i s = Dart (Arc i) (read s)
    small :: Gr (Vtx Int String Int) (Face String)
    small = Gr [ Vtx 0 (Point2 0 0) [ (2,"0->2")
                                    , (1,"0->1")
                                    , (3,"0->3")
                                    ] 0
               , Vtx 1 (Point2 2 2) [ (0,"1->0")
                                    , (2,"1->2")
                                    , (3,"1->3")
                                    ] 1
               , Vtx 2 (Point2 2 0) [ (0,"2->0")
                                    , (1,"2->1")
                                    ] 2
               , Vtx 3 (Point2 (-1) 4) [ (0,"3->0")
                                       , (1,"3->1")
                                       ] 3
               ]
               [ Face (2,1) "OuterFace"
               , Face (0,1) "A"
               , Face (1,0) "B"
               ]
    smallG = fromAdjRep (Proxy :: Proxy ()) small
:}

This represents the following graph. Note that the graph is undirected, the arrows are just to indicate what the Positive direction of the darts is.

newtype PlaneGraph s v e f r Source #

Embedded, *connected*, planar graph

Constructors

PlaneGraph (PlanarGraph s Primal (VertexData r v) e f) 

Instances

Instances details
Functor (PlaneGraph s v e f) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Methods

fmap :: (a -> b) -> PlaneGraph s v e f a -> PlaneGraph s v e f b #

(<$) :: a -> PlaneGraph s v e f b -> PlaneGraph s v e f a #

(Eq r, Eq v, Eq e, Eq f) => Eq (PlaneGraph s v e f r) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Methods

(==) :: PlaneGraph s v e f r -> PlaneGraph s v e f r -> Bool #

(/=) :: PlaneGraph s v e f r -> PlaneGraph s v e f r -> Bool #

(Show r, Show v, Show e, Show f) => Show (PlaneGraph s v e f r) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Methods

showsPrec :: Int -> PlaneGraph s v e f r -> ShowS #

show :: PlaneGraph s v e f r -> String #

showList :: [PlaneGraph s v e f r] -> ShowS #

Generic (PlaneGraph s v e f r) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Associated Types

type Rep (PlaneGraph s v e f r) :: Type -> Type #

Methods

from :: PlaneGraph s v e f r -> Rep (PlaneGraph s v e f r) x #

to :: Rep (PlaneGraph s v e f r) x -> PlaneGraph s v e f r #

(ToJSON v, ToJSON e, ToJSON f, ToJSON r) => ToJSON (PlaneGraph s v e f r) Source # 
Instance details

Defined in Data.PlaneGraph.IO

Methods

toJSON :: PlaneGraph s v e f r -> Value #

toEncoding :: PlaneGraph s v e f r -> Encoding #

toJSONList :: [PlaneGraph s v e f r] -> Value #

toEncodingList :: [PlaneGraph s v e f r] -> Encoding #

(FromJSON v, FromJSON e, FromJSON f, FromJSON r) => FromJSON (PlaneGraph s v e f r) Source # 
Instance details

Defined in Data.PlaneGraph.IO

Methods

parseJSON :: Value -> Parser (PlaneGraph s v e f r) #

parseJSONList :: Value -> Parser [PlaneGraph s v e f r] #

IsBoxable (PlaneGraph s v e f r) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Methods

boundingBox :: PlaneGraph s v e f r -> Box (Dimension (PlaneGraph s v e f r)) () (NumType (PlaneGraph s v e f r)) Source #

HasDataOf (PlaneGraph s v e f r) (FaceId' s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Associated Types

type DataOf (PlaneGraph s v e f r) (FaceId' s) #

Methods

dataOf :: FaceId' s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (FaceId' s)) #

HasDataOf (PlaneGraph s v e f r) (Dart s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Associated Types

type DataOf (PlaneGraph s v e f r) (Dart s) #

Methods

dataOf :: Dart s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (Dart s)) #

HasDataOf (PlaneGraph s v e f r) (VertexId' s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Associated Types

type DataOf (PlaneGraph s v e f r) (VertexId' s) #

Methods

dataOf :: VertexId' s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (VertexId' s)) #

type Rep (PlaneGraph s v e f r) Source # 
Instance details

Defined in Data.PlaneGraph.Core

type Rep (PlaneGraph s v e f r) = D1 ('MetaData "PlaneGraph" "Data.PlaneGraph.Core" "hgeometry-0.12.0.1-744QXwUb5uS54emseMX1Co" 'True) (C1 ('MetaCons "PlaneGraph" 'PrefixI 'True) (S1 ('MetaSel ('Just "_graph") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (PlanarGraph s 'Primal (VertexData r v) e f))))
type NumType (PlaneGraph s v e f r) Source # 
Instance details

Defined in Data.PlaneGraph.Core

type NumType (PlaneGraph s v e f r) = r
type Dimension (PlaneGraph s v e f r) Source # 
Instance details

Defined in Data.PlaneGraph.Core

type Dimension (PlaneGraph s v e f r) = 2
type DataOf (PlaneGraph s v e f r) (FaceId' s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

type DataOf (PlaneGraph s v e f r) (FaceId' s) = f
type DataOf (PlaneGraph s v e f r) (Dart s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

type DataOf (PlaneGraph s v e f r) (Dart s) = e
type DataOf (PlaneGraph s v e f r) (VertexId' s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

type DataOf (PlaneGraph s v e f r) (VertexId' s) = v

graph :: forall k (s :: k) v e f r k (s :: k) v e f r. Iso (PlaneGraph (s :: k) v e f r) (PlaneGraph (s :: k) v e f r) (PlanarGraph s 'Primal (VertexData r v) e f) (PlanarGraph s 'Primal (VertexData r v) e f) Source #

data PlanarGraph (s :: k) (w :: World) v e f #

A *connected* Planar graph with bidirected edges. I.e. the edges (darts) are directed, however, for every directed edge, the edge in the oposite direction is also in the graph.

The types v, e, and f are the are the types of the data associated with the vertices, edges, and faces, respectively.

The orbits in the embedding are assumed to be in counterclockwise order. Therefore, every dart directly bounds the face to its right.

Instances

Instances details
(Eq v, Eq e, Eq f) => Eq (PlanarGraph s w v e f) 
Instance details

Defined in Data.PlanarGraph.Core

Methods

(==) :: PlanarGraph s w v e f -> PlanarGraph s w v e f -> Bool #

(/=) :: PlanarGraph s w v e f -> PlanarGraph s w v e f -> Bool #

(Show v, Show e, Show f) => Show (PlanarGraph s w v e f) 
Instance details

Defined in Data.PlanarGraph.Core

Methods

showsPrec :: Int -> PlanarGraph s w v e f -> ShowS #

show :: PlanarGraph s w v e f -> String #

showList :: [PlanarGraph s w v e f] -> ShowS #

Generic (PlanarGraph s w v e f) 
Instance details

Defined in Data.PlanarGraph.Core

Associated Types

type Rep (PlanarGraph s w v e f) :: Type -> Type #

Methods

from :: PlanarGraph s w v e f -> Rep (PlanarGraph s w v e f) x #

to :: Rep (PlanarGraph s w v e f) x -> PlanarGraph s w v e f #

HasDataOf (PlanarGraph s w v e f) (Dart s) 
Instance details

Defined in Data.PlanarGraph.Core

Associated Types

type DataOf (PlanarGraph s w v e f) (Dart s) #

Methods

dataOf :: Dart s -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (Dart s)) #

HasDataOf (PlanarGraph s w v e f) (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Associated Types

type DataOf (PlanarGraph s w v e f) (VertexId s w) #

Methods

dataOf :: VertexId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (VertexId s w)) #

HasDataOf (PlanarGraph s w v e f) (FaceId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Associated Types

type DataOf (PlanarGraph s w v e f) (FaceId s w) #

Methods

dataOf :: FaceId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (FaceId s w)) #

type Rep (PlanarGraph s w v e f) 
Instance details

Defined in Data.PlanarGraph.Core

type Rep (PlanarGraph s w v e f) = D1 ('MetaData "PlanarGraph" "Data.PlanarGraph.Core" "hgeometry-combinatorial-0.12.0.1-3UsM6nqO83QAAGVLl4vU5w" 'False) (C1 ('MetaCons "PlanarGraph" 'PrefixI 'True) ((S1 ('MetaSel ('Just "_embedding") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Permutation (Dart s))) :*: S1 ('MetaSel ('Just "_vertexData") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Vector v))) :*: (S1 ('MetaSel ('Just "_rawDartData") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Vector e)) :*: (S1 ('MetaSel ('Just "_faceData") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Vector f)) :*: S1 ('MetaSel ('Just "_dual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (PlanarGraph s (DualOf w) f e v))))))
type DataOf (PlanarGraph s w v e f) (Dart s) 
Instance details

Defined in Data.PlanarGraph.Core

type DataOf (PlanarGraph s w v e f) (Dart s) = e
type DataOf (PlanarGraph s w v e f) (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

type DataOf (PlanarGraph s w v e f) (VertexId s w) = v
type DataOf (PlanarGraph s w v e f) (FaceId s w) 
Instance details

Defined in Data.PlanarGraph.Core

type DataOf (PlanarGraph s w v e f) (FaceId s w) = f

data VertexData r v Source #

Note that the functor instance is in v

Constructors

VertexData !(Point 2 r) !v 

Instances

Instances details
Bifunctor VertexData Source # 
Instance details

Defined in Data.PlaneGraph.Core

Methods

bimap :: (a -> b) -> (c -> d) -> VertexData a c -> VertexData b d #

first :: (a -> b) -> VertexData a c -> VertexData b c #

second :: (b -> c) -> VertexData a b -> VertexData a c #

Functor (VertexData r) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Methods

fmap :: (a -> b) -> VertexData r a -> VertexData r b #

(<$) :: a -> VertexData r b -> VertexData r a #

Foldable (VertexData r) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Methods

fold :: Monoid m => VertexData r m -> m #

foldMap :: Monoid m => (a -> m) -> VertexData r a -> m #

foldMap' :: Monoid m => (a -> m) -> VertexData r a -> m #

foldr :: (a -> b -> b) -> b -> VertexData r a -> b #

foldr' :: (a -> b -> b) -> b -> VertexData r a -> b #

foldl :: (b -> a -> b) -> b -> VertexData r a -> b #

foldl' :: (b -> a -> b) -> b -> VertexData r a -> b #

foldr1 :: (a -> a -> a) -> VertexData r a -> a #

foldl1 :: (a -> a -> a) -> VertexData r a -> a #

toList :: VertexData r a -> [a] #

null :: VertexData r a -> Bool #

length :: VertexData r a -> Int #

elem :: Eq a => a -> VertexData r a -> Bool #

maximum :: Ord a => VertexData r a -> a #

minimum :: Ord a => VertexData r a -> a #

sum :: Num a => VertexData r a -> a #

product :: Num a => VertexData r a -> a #

Traversable (VertexData r) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Methods

traverse :: Applicative f => (a -> f b) -> VertexData r a -> f (VertexData r b) #

sequenceA :: Applicative f => VertexData r (f a) -> f (VertexData r a) #

mapM :: Monad m => (a -> m b) -> VertexData r a -> m (VertexData r b) #

sequence :: Monad m => VertexData r (m a) -> m (VertexData r a) #

(Eq r, Eq v) => Eq (VertexData r v) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Methods

(==) :: VertexData r v -> VertexData r v -> Bool #

(/=) :: VertexData r v -> VertexData r v -> Bool #

(Ord r, Ord v) => Ord (VertexData r v) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Methods

compare :: VertexData r v -> VertexData r v -> Ordering #

(<) :: VertexData r v -> VertexData r v -> Bool #

(<=) :: VertexData r v -> VertexData r v -> Bool #

(>) :: VertexData r v -> VertexData r v -> Bool #

(>=) :: VertexData r v -> VertexData r v -> Bool #

max :: VertexData r v -> VertexData r v -> VertexData r v #

min :: VertexData r v -> VertexData r v -> VertexData r v #

(Show r, Show v) => Show (VertexData r v) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Methods

showsPrec :: Int -> VertexData r v -> ShowS #

show :: VertexData r v -> String #

showList :: [VertexData r v] -> ShowS #

Generic (VertexData r v) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Associated Types

type Rep (VertexData r v) :: Type -> Type #

Methods

from :: VertexData r v -> Rep (VertexData r v) x #

to :: Rep (VertexData r v) x -> VertexData r v #

(ToJSON r, ToJSON v) => ToJSON (VertexData r v) Source # 
Instance details

Defined in Data.PlaneGraph.Core

(FromJSON r, FromJSON v) => FromJSON (VertexData r v) Source # 
Instance details

Defined in Data.PlaneGraph.Core

type Rep (VertexData r v) Source # 
Instance details

Defined in Data.PlaneGraph.Core

type Rep (VertexData r v) = D1 ('MetaData "VertexData" "Data.PlaneGraph.Core" "hgeometry-0.12.0.1-744QXwUb5uS54emseMX1Co" 'False) (C1 ('MetaCons "VertexData" 'PrefixI 'True) (S1 ('MetaSel ('Just "_location") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (Point 2 r)) :*: S1 ('MetaSel ('Just "_vData") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 v)))

vData :: forall r v v. Lens (VertexData r v) (VertexData r v) v v Source #

location :: forall r v r. Lens (VertexData r v) (VertexData r v) (Point 2 r) (Point 2 r) Source #

fromSimplePolygon Source #

Arguments

:: proxy s 
-> SimplePolygon p r 
-> f

data inside

-> f

data outside the polygon

-> PlaneGraph s p () f r 

Construct a plane graph from a simple polygon. It is assumed that the polygon is given in counterclockwise order.

the interior of the polygon will have faceId 0

pre: the input polygon is given in counterclockwise order running time: \(O(n)\).

fromConnectedSegments :: (Foldable f, Ord r, Num r) => proxy s -> f (LineSegment 2 p r :+ e) -> PlaneGraph s (NonEmpty p) e () r Source #

Constructs a connected plane graph

pre: The segments form a single connected component

running time: \(O(n\log n)\)

fromAdjacencyLists :: forall k (s :: k) (w :: World) h. (Foldable h, Functor h) => [(VertexId s w, h (VertexId s w))] -> PlanarGraph s w () () () #

Construct a planar graph from a adjacency matrix. For every vertex, all vertices should be given in counter-clockwise order.

pre: No self-loops, and no multi-edges

running time: \(O(n)\).

numVertices :: PlaneGraph s v e f r -> Int Source #

Get the number of vertices

>>> numVertices smallG
4

numEdges :: PlaneGraph s v e f r -> Int Source #

Get the number of Edges

>>> numEdges smallG
5

numFaces :: PlaneGraph s v e f r -> Int Source #

Get the number of faces

>>> numFaces smallG
3

numDarts :: PlaneGraph s v e f r -> Int Source #

Get the number of Darts

>>> numDarts smallG
10

dual :: forall k (s :: k) (w :: World) v e f. Getter (PlanarGraph s w v e f) (PlanarGraph s (DualOf w) f e v) #

Get the dual graph of this graph.

vertices' :: PlaneGraph s v e f r -> Vector (VertexId' s) Source #

Enumerate all vertices

>>> vertices' smallG
[VertexId 0,VertexId 1,VertexId 2,VertexId 3]

vertices :: PlaneGraph s v e f r -> Vector (VertexId' s, VertexData r v) Source #

Enumerate all vertices, together with their vertex data

>>> mapM_ print $ vertices smallG
(VertexId 0,VertexData {_location = Point2 0 0, _vData = 0})
(VertexId 1,VertexData {_location = Point2 2 2, _vData = 1})
(VertexId 2,VertexData {_location = Point2 2 0, _vData = 2})
(VertexId 3,VertexData {_location = Point2 (-1) 4, _vData = 3})

edges' :: PlaneGraph s v e f r -> Vector (Dart s) Source #

Enumerate all edges. We report only the Positive darts

edges :: PlaneGraph s v e f r -> Vector (Dart s, e) Source #

Enumerate all edges with their edge data. We report only the Positive darts.

>>> mapM_ print $ edges smallG
(Dart (Arc 0) +1,"0->2")
(Dart (Arc 1) +1,"0->1")
(Dart (Arc 2) +1,"0->3")
(Dart (Arc 4) +1,"1->2")
(Dart (Arc 3) +1,"1->3")

faces' :: PlaneGraph s v e f r -> Vector (FaceId' s) Source #

Enumerate all faces in the plane graph

faces :: PlaneGraph s v e f r -> Vector (FaceId' s, f) Source #

All faces with their face data.

>>> mapM_ print $ faces smallG
(FaceId 0,"OuterFace")
(FaceId 1,"A")
(FaceId 2,"B")

internalFaces :: (Ord r, Fractional r) => PlaneGraph s v e f r -> Vector (FaceId' s, f) Source #

Reports all internal faces. running time: \(O(n)\)

faces'' :: (Ord r, Fractional r) => PlaneGraph s v e f r -> ((FaceId' s, f), Vector (FaceId' s, f)) Source #

Reports the outerface and all internal faces separately. running time: \(O(n)\)

darts' :: PlaneGraph s v e f r -> Vector (Dart s) Source #

Enumerate all darts

darts :: PlaneGraph s v e f r -> Vector (Dart s, e) Source #

Get all darts together with their data

traverseVertices :: Applicative m => (VertexId' s -> v -> m v') -> PlaneGraph s v e f r -> m (PlaneGraph s v' e f r) Source #

Traverse the vertices

(^.vertexData) $ traverseVertices (i x -> Just (i,x)) smallG Just [(VertexId 0,0),(VertexId 1,1),(VertexId 2,2),(VertexId 3,3)] >>> traverseVertices (i x -> print (i,x)) smallG >> pure () (VertexId 0,0) (VertexId 1,1) (VertexId 2,2) (VertexId 3,3)

traverseDarts :: Applicative m => (Dart s -> e -> m e') -> PlaneGraph s v e f r -> m (PlaneGraph s v e' f r) Source #

Traverses the darts

>>> traverseDarts (\d x -> print (d,x)) smallG >> pure ()
(Dart (Arc 0) +1,"0->2")
(Dart (Arc 0) -1,"2->0")
(Dart (Arc 1) +1,"0->1")
(Dart (Arc 1) -1,"1->0")
(Dart (Arc 2) +1,"0->3")
(Dart (Arc 2) -1,"3->0")
(Dart (Arc 3) +1,"1->3")
(Dart (Arc 3) -1,"3->1")
(Dart (Arc 4) +1,"1->2")
(Dart (Arc 4) -1,"2->1")

traverseFaces :: Applicative m => (FaceId' s -> f -> m f') -> PlaneGraph s v e f r -> m (PlaneGraph s v e f' r) Source #

Traverses the faces

>>> traverseFaces (\i x -> print (i,x)) smallG >> pure ()
(FaceId 0,"OuterFace")
(FaceId 1,"A")
(FaceId 2,"B")

headOf :: Dart s -> PlaneGraph s v e f r -> VertexId' s Source #

The vertex this dart is heading in to

running time: \(O(1)\)

>>> headOf (dart 0 "+1") smallG
VertexId 2

tailOf :: Dart s -> PlaneGraph s v e f r -> VertexId' s Source #

The tail of a dart, i.e. the vertex this dart is leaving from

running time: \(O(1)\)

>>> tailOf (dart 0 "+1") smallG
VertexId 0

twin :: forall k (s :: k). Dart s -> Dart s #

Get the twin of this dart (edge)

>>> twin (dart 0 "+1")
Dart (Arc 0) -1
>>> twin (dart 0 "-1")
Dart (Arc 0) +1

endPoints :: Dart s -> PlaneGraph s v e f r -> (VertexId' s, VertexId' s) Source #

endPoints d g = (tailOf d g, headOf d g)

running time: \(O(1)\)

>>> endPoints (dart 0 "+1") smallG
(VertexId 0,VertexId 2)

incidentEdges :: VertexId' s -> PlaneGraph s v e f r -> Vector (Dart s) Source #

All edges incident to vertex v, in counterclockwise order around v.

running time: \(O(k)\), where \(k\) is the output size

>>> incidentEdges (VertexId 1) smallG
[Dart (Arc 1) -1,Dart (Arc 4) +1,Dart (Arc 3) +1]

incomingEdges :: VertexId' s -> PlaneGraph s v e f r -> Vector (Dart s) Source #

All edges incident to vertex v in incoming direction (i.e. pointing into v) in counterclockwise order around v.

running time: \(O(k)\), where (k) is the total number of incident edges of v

>>> incomingEdges (VertexId 1) smallG
[Dart (Arc 1) +1,Dart (Arc 4) -1,Dart (Arc 3) -1]

outgoingEdges :: VertexId' s -> PlaneGraph s v e f r -> Vector (Dart s) Source #

All edges incident to vertex v in incoming direction (i.e. pointing into v) in counterclockwise order around v.

running time: \(O(k)\), where (k) is the total number of incident edges of v

>>> outgoingEdges (VertexId 1) smallG
[Dart (Arc 1) -1,Dart (Arc 4) +1,Dart (Arc 3) +1]

neighboursOf :: VertexId' s -> PlaneGraph s v e f r -> Vector (VertexId' s) Source #

Gets the neighbours of a particular vertex, in counterclockwise order around the vertex.

running time: \(O(k)\), where \(k\) is the output size

>>> neighboursOf (VertexId 1) smallG
[VertexId 0,VertexId 2,VertexId 3]

nextIncidentEdge :: Dart s -> PlaneGraph s v e f r -> Dart s Source #

Given a dart d that points into some vertex v, report the next dart in the cyclic order around v in clockwise direction.

running time: \(O(1)\)

>>> nextIncidentEdge (dart 1 "+1") smallG
Dart (Arc 2) +1

prevIncidentEdge :: Dart s -> PlaneGraph s v e f r -> Dart s Source #

Given a dart d that points into some vertex v, report the next dart in the cyclic order around v (in clockwise order)

running time: \(O(1)\)

>>> prevIncidentEdge (dart 1 "+1") smallG
Dart (Arc 0) +1

leftFace :: Dart s -> PlaneGraph s v e f r -> FaceId' s Source #

The face to the left of the dart

running time: \(O(1)\).

>>> leftFace (dart 1 "+1") smallG
FaceId 2
>>> leftFace (dart 1 "-1") smallG
FaceId 1
>>> leftFace (dart 2 "+1") smallG
FaceId 0
>>> leftFace (dart 2 "-1") smallG
FaceId 2

rightFace :: Dart s -> PlaneGraph s v e f r -> FaceId' s Source #

The face to the right of the dart

running time: \(O(1)\).

>>> rightFace (dart 1 "+1") smallG
FaceId 1
>>> rightFace (dart 1 "-1") smallG
FaceId 2
>>> rightFace (dart 2 "+1") smallG
FaceId 2
>>> rightFace (dart 2 "-1") smallG
FaceId 0

nextEdge :: Dart s -> PlaneGraph s v e f r -> Dart s Source #

Get the next edge along the face

running time: \(O(1)\).

>>> nextEdge (dart 1 "+1") smallG
Dart (Arc 4) +1

prevEdge :: Dart s -> PlaneGraph s v e f r -> Dart s Source #

Get the previous edge along the face

running time: \(O(1)\).

>>> prevEdge (dart 1 "+1") smallG
Dart (Arc 0) -1

boundary :: FaceId' s -> PlaneGraph s v e f r -> Vector (Dart s) Source #

The darts bounding this face, for internal faces in clockwise order, for the outer face in counter clockwise order.

running time: \(O(k)\), where \(k\) is the output size.

boundary' :: Dart s -> PlaneGraph s v e f r -> Vector (Dart s) Source #

Generates the darts incident to a face, starting with the given dart.

\(O(k)\), where \(k\) is the number of darts reported

boundaryDart :: FaceId' s -> PlaneGraph s v e f r -> Dart s Source #

Gets a dart bounding this face. I.e. a dart d such that the face lies to the right of the dart.

boundaryVertices :: FaceId' s -> PlaneGraph s v e f r -> Vector (VertexId' s) Source #

The vertices bounding this face, for internal faces in clockwise order, for the outer face in counter clockwise order.

running time: \(O(k)\), where \(k\) is the output size.

outerFaceId :: (Ord r, Fractional r) => PlaneGraph s v e f r -> FaceId' s Source #

gets the id of the outer face

running time: \(O(n)\)

outerFaceDart :: (Ord r, Fractional r) => PlaneGraph s v e f r -> Dart s Source #

gets a dart incident to the outer face (in particular, that has the outerface on its left)

running time: \(O(n)\)

locationOf :: VertexId' s -> Lens' (PlaneGraph s v e f r) (Point 2 r) Source #

class HasDataOf g i where #

General interface to accessing vertex data, dart data, and face data.

Associated Types

type DataOf g i #

Methods

dataOf :: i -> Lens' g (DataOf g i) #

get the data associated with the value i.

running time: \(O(1)\) to read the data, \(O(n)\) to write it.

Instances

Instances details
HasDataOf (PlanarGraph s w v e f) (Dart s) 
Instance details

Defined in Data.PlanarGraph.Core

Associated Types

type DataOf (PlanarGraph s w v e f) (Dart s) #

Methods

dataOf :: Dart s -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (Dart s)) #

HasDataOf (PlaneGraph s v e f r) (FaceId' s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Associated Types

type DataOf (PlaneGraph s v e f r) (FaceId' s) #

Methods

dataOf :: FaceId' s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (FaceId' s)) #

HasDataOf (PlaneGraph s v e f r) (Dart s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Associated Types

type DataOf (PlaneGraph s v e f r) (Dart s) #

Methods

dataOf :: Dart s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (Dart s)) #

HasDataOf (PlaneGraph s v e f r) (VertexId' s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Associated Types

type DataOf (PlaneGraph s v e f r) (VertexId' s) #

Methods

dataOf :: VertexId' s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (VertexId' s)) #

HasDataOf (PlanarSubdivision s v e f r) (FaceId' s) Source # 
Instance details

Defined in Data.Geometry.PlanarSubdivision.Basic

Associated Types

type DataOf (PlanarSubdivision s v e f r) (FaceId' s) #

Methods

dataOf :: FaceId' s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (FaceId' s)) #

HasDataOf (PlanarSubdivision s v e f r) (Dart s) Source # 
Instance details

Defined in Data.Geometry.PlanarSubdivision.Basic

Associated Types

type DataOf (PlanarSubdivision s v e f r) (Dart s) #

Methods

dataOf :: Dart s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (Dart s)) #

HasDataOf (PlanarSubdivision s v e f r) (VertexId' s) Source # 
Instance details

Defined in Data.Geometry.PlanarSubdivision.Basic

Associated Types

type DataOf (PlanarSubdivision s v e f r) (VertexId' s) #

Methods

dataOf :: VertexId' s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (VertexId' s)) #

HasDataOf (PlanarGraph s w v e f) (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Associated Types

type DataOf (PlanarGraph s w v e f) (VertexId s w) #

Methods

dataOf :: VertexId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (VertexId s w)) #

HasDataOf (PlanarGraph s w v e f) (FaceId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Associated Types

type DataOf (PlanarGraph s w v e f) (FaceId s w) #

Methods

dataOf :: FaceId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (FaceId s w)) #

endPointsOf :: Dart s -> Getter (PlaneGraph s v e f r) (VertexData r v, VertexData r v) Source #

Getter for the data at the endpoints of a dart

running time: \(O(1)\)

endPointData :: Dart s -> PlaneGraph s v e f r -> (VertexData r v, VertexData r v) Source #

Data corresponding to the endpoints of the dart

running time: \(O(1)\)

vertexData :: Lens (PlaneGraph s v e f r) (PlaneGraph s v' e f r) (Vector v) (Vector v') Source #

faceData :: Lens (PlaneGraph s v e f r) (PlaneGraph s v e f' r) (Vector f) (Vector f') Source #

Lens to access face data

dartData :: Lens (PlaneGraph s v e f r) (PlaneGraph s v e' f r) (Vector (Dart s, e)) (Vector (Dart s, e')) Source #

lens to access the Dart Data

rawDartData :: Lens (PlaneGraph s v e f r) (PlaneGraph s v e' f r) (Vector e) (Vector e') Source #

Lens to access the raw dart data, use at your own risk

edgeSegment :: Dart s -> PlaneGraph s v e f r -> LineSegment 2 v r :+ e Source #

Given a dart and the graph constructs the line segment representing the dart. The segment \(\overline{uv})\) is has \(u\) as its tail and \(v\) as its head.

\(O(1)\)

edgeSegments :: PlaneGraph s v e f r -> Vector (Dart s, LineSegment 2 v r :+ e) Source #

Reports all edges as line segments

>>> mapM_ print $ edgeSegments smallG
(Dart (Arc 0) +1,ClosedLineSegment (Point2 0 0 :+ 0) (Point2 2 0 :+ 2) :+ "0->2")
(Dart (Arc 1) +1,ClosedLineSegment (Point2 0 0 :+ 0) (Point2 2 2 :+ 1) :+ "0->1")
(Dart (Arc 2) +1,ClosedLineSegment (Point2 0 0 :+ 0) (Point2 (-1) 4 :+ 3) :+ "0->3")
(Dart (Arc 4) +1,ClosedLineSegment (Point2 2 2 :+ 1) (Point2 2 0 :+ 2) :+ "1->2")
(Dart (Arc 3) +1,ClosedLineSegment (Point2 2 2 :+ 1) (Point2 (-1) 4 :+ 3) :+ "1->3")

rawFacePolygon :: FaceId' s -> PlaneGraph s v e f r -> SimplePolygon v r :+ f Source #

Alias for rawFace Boundary

runningtime: \(O(k)\), where \(k\) is the size of the face.

rawFaceBoundary :: FaceId' s -> PlaneGraph s v e f r -> SimplePolygon v r :+ f Source #

The polygon describing the face

runningtime: \(O(k)\), where \(k\) is the size of the face.

rawFacePolygons :: PlaneGraph s v e f r -> Vector (FaceId' s, SimplePolygon v r :+ f) Source #

Lists all faces of the plane graph.

newtype VertexId (s :: k) (w :: World) #

A vertex in a planar graph. A vertex is tied to a particular planar graph by the phantom type s, and to a particular world w.

Constructors

VertexId 

Fields

Instances

Instances details
Enum (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Methods

succ :: VertexId s w -> VertexId s w #

pred :: VertexId s w -> VertexId s w #

toEnum :: Int -> VertexId s w #

fromEnum :: VertexId s w -> Int #

enumFrom :: VertexId s w -> [VertexId s w] #

enumFromThen :: VertexId s w -> VertexId s w -> [VertexId s w] #

enumFromTo :: VertexId s w -> VertexId s w -> [VertexId s w] #

enumFromThenTo :: VertexId s w -> VertexId s w -> VertexId s w -> [VertexId s w] #

Eq (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Methods

(==) :: VertexId s w -> VertexId s w -> Bool #

(/=) :: VertexId s w -> VertexId s w -> Bool #

Ord (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Methods

compare :: VertexId s w -> VertexId s w -> Ordering #

(<) :: VertexId s w -> VertexId s w -> Bool #

(<=) :: VertexId s w -> VertexId s w -> Bool #

(>) :: VertexId s w -> VertexId s w -> Bool #

(>=) :: VertexId s w -> VertexId s w -> Bool #

max :: VertexId s w -> VertexId s w -> VertexId s w #

min :: VertexId s w -> VertexId s w -> VertexId s w #

Show (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Methods

showsPrec :: Int -> VertexId s w -> ShowS #

show :: VertexId s w -> String #

showList :: [VertexId s w] -> ShowS #

Generic (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Associated Types

type Rep (VertexId s w) :: Type -> Type #

Methods

from :: VertexId s w -> Rep (VertexId s w) x #

to :: Rep (VertexId s w) x -> VertexId s w #

ToJSON (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

FromJSON (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

NFData (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Methods

rnf :: VertexId s w -> () #

HasDataOf (PlaneGraph s v e f r) (VertexId' s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Associated Types

type DataOf (PlaneGraph s v e f r) (VertexId' s) #

Methods

dataOf :: VertexId' s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (VertexId' s)) #

HasDataOf (PlanarSubdivision s v e f r) (VertexId' s) Source # 
Instance details

Defined in Data.Geometry.PlanarSubdivision.Basic

Associated Types

type DataOf (PlanarSubdivision s v e f r) (VertexId' s) #

Methods

dataOf :: VertexId' s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (VertexId' s)) #

HasDataOf (PlanarGraph s w v e f) (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Associated Types

type DataOf (PlanarGraph s w v e f) (VertexId s w) #

Methods

dataOf :: VertexId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (VertexId s w)) #

type Rep (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

type Rep (VertexId s w) = D1 ('MetaData "VertexId" "Data.PlanarGraph.Core" "hgeometry-combinatorial-0.12.0.1-3UsM6nqO83QAAGVLl4vU5w" 'True) (C1 ('MetaCons "VertexId" 'PrefixI 'True) (S1 ('MetaSel ('Just "_unVertexId") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Int)))
type DataOf (PlaneGraph s v e f r) (VertexId' s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

type DataOf (PlaneGraph s v e f r) (VertexId' s) = v
type DataOf (PlanarSubdivision s v e f r) (VertexId' s) Source # 
Instance details

Defined in Data.Geometry.PlanarSubdivision.Basic

type DataOf (PlanarSubdivision s v e f r) (VertexId' s) = v
type DataOf (PlanarGraph s w v e f) (VertexId s w) 
Instance details

Defined in Data.PlanarGraph.Core

type DataOf (PlanarGraph s w v e f) (VertexId s w) = v

newtype FaceId (s :: k) (w :: World) #

The type to represent FaceId's

Constructors

FaceId 

Fields

Instances

Instances details
Enum (FaceId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Methods

succ :: FaceId s w -> FaceId s w #

pred :: FaceId s w -> FaceId s w #

toEnum :: Int -> FaceId s w #

fromEnum :: FaceId s w -> Int #

enumFrom :: FaceId s w -> [FaceId s w] #

enumFromThen :: FaceId s w -> FaceId s w -> [FaceId s w] #

enumFromTo :: FaceId s w -> FaceId s w -> [FaceId s w] #

enumFromThenTo :: FaceId s w -> FaceId s w -> FaceId s w -> [FaceId s w] #

Eq (FaceId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Methods

(==) :: FaceId s w -> FaceId s w -> Bool #

(/=) :: FaceId s w -> FaceId s w -> Bool #

Ord (FaceId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Methods

compare :: FaceId s w -> FaceId s w -> Ordering #

(<) :: FaceId s w -> FaceId s w -> Bool #

(<=) :: FaceId s w -> FaceId s w -> Bool #

(>) :: FaceId s w -> FaceId s w -> Bool #

(>=) :: FaceId s w -> FaceId s w -> Bool #

max :: FaceId s w -> FaceId s w -> FaceId s w #

min :: FaceId s w -> FaceId s w -> FaceId s w #

Show (FaceId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Methods

showsPrec :: Int -> FaceId s w -> ShowS #

show :: FaceId s w -> String #

showList :: [FaceId s w] -> ShowS #

ToJSON (FaceId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Methods

toJSON :: FaceId s w -> Value #

toEncoding :: FaceId s w -> Encoding #

toJSONList :: [FaceId s w] -> Value #

toEncodingList :: [FaceId s w] -> Encoding #

FromJSON (FaceId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Methods

parseJSON :: Value -> Parser (FaceId s w) #

parseJSONList :: Value -> Parser [FaceId s w] #

HasDataOf (PlaneGraph s v e f r) (FaceId' s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Associated Types

type DataOf (PlaneGraph s v e f r) (FaceId' s) #

Methods

dataOf :: FaceId' s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (FaceId' s)) #

HasDataOf (PlanarSubdivision s v e f r) (FaceId' s) Source # 
Instance details

Defined in Data.Geometry.PlanarSubdivision.Basic

Associated Types

type DataOf (PlanarSubdivision s v e f r) (FaceId' s) #

Methods

dataOf :: FaceId' s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (FaceId' s)) #

HasDataOf (PlanarGraph s w v e f) (FaceId s w) 
Instance details

Defined in Data.PlanarGraph.Core

Associated Types

type DataOf (PlanarGraph s w v e f) (FaceId s w) #

Methods

dataOf :: FaceId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (FaceId s w)) #

type DataOf (PlaneGraph s v e f r) (FaceId' s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

type DataOf (PlaneGraph s v e f r) (FaceId' s) = f
type DataOf (PlanarSubdivision s v e f r) (FaceId' s) Source # 
Instance details

Defined in Data.Geometry.PlanarSubdivision.Basic

type DataOf (PlanarSubdivision s v e f r) (FaceId' s) = f
type DataOf (PlanarGraph s w v e f) (FaceId s w) 
Instance details

Defined in Data.PlanarGraph.Core

type DataOf (PlanarGraph s w v e f) (FaceId s w) = f

data Dart (s :: k) #

A dart represents a bi-directed edge. I.e. a dart has a direction, however the dart of the oposite direction is always present in the planar graph as well.

Instances

Instances details
Enum (Dart s) 
Instance details

Defined in Data.PlanarGraph.Dart

Methods

succ :: Dart s -> Dart s #

pred :: Dart s -> Dart s #

toEnum :: Int -> Dart s #

fromEnum :: Dart s -> Int #

enumFrom :: Dart s -> [Dart s] #

enumFromThen :: Dart s -> Dart s -> [Dart s] #

enumFromTo :: Dart s -> Dart s -> [Dart s] #

enumFromThenTo :: Dart s -> Dart s -> Dart s -> [Dart s] #

Eq (Dart s) 
Instance details

Defined in Data.PlanarGraph.Dart

Methods

(==) :: Dart s -> Dart s -> Bool #

(/=) :: Dart s -> Dart s -> Bool #

Ord (Dart s) 
Instance details

Defined in Data.PlanarGraph.Dart

Methods

compare :: Dart s -> Dart s -> Ordering #

(<) :: Dart s -> Dart s -> Bool #

(<=) :: Dart s -> Dart s -> Bool #

(>) :: Dart s -> Dart s -> Bool #

(>=) :: Dart s -> Dart s -> Bool #

max :: Dart s -> Dart s -> Dart s #

min :: Dart s -> Dart s -> Dart s #

Show (Dart s) 
Instance details

Defined in Data.PlanarGraph.Dart

Methods

showsPrec :: Int -> Dart s -> ShowS #

show :: Dart s -> String #

showList :: [Dart s] -> ShowS #

Generic (Dart s) 
Instance details

Defined in Data.PlanarGraph.Dart

Associated Types

type Rep (Dart s) :: Type -> Type #

Methods

from :: Dart s -> Rep (Dart s) x #

to :: Rep (Dart s) x -> Dart s #

Arbitrary (Dart s) 
Instance details

Defined in Data.PlanarGraph.Dart

Methods

arbitrary :: Gen (Dart s) #

shrink :: Dart s -> [Dart s] #

NFData (Dart s) 
Instance details

Defined in Data.PlanarGraph.Dart

Methods

rnf :: Dart s -> () #

HasDataOf (PlanarGraph s w v e f) (Dart s) 
Instance details

Defined in Data.PlanarGraph.Core

Associated Types

type DataOf (PlanarGraph s w v e f) (Dart s) #

Methods

dataOf :: Dart s -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (Dart s)) #

HasDataOf (PlaneGraph s v e f r) (Dart s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

Associated Types

type DataOf (PlaneGraph s v e f r) (Dart s) #

Methods

dataOf :: Dart s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (Dart s)) #

HasDataOf (PlanarSubdivision s v e f r) (Dart s) Source # 
Instance details

Defined in Data.Geometry.PlanarSubdivision.Basic

Associated Types

type DataOf (PlanarSubdivision s v e f r) (Dart s) #

Methods

dataOf :: Dart s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (Dart s)) #

type Rep (Dart s) 
Instance details

Defined in Data.PlanarGraph.Dart

type Rep (Dart s) = D1 ('MetaData "Dart" "Data.PlanarGraph.Dart" "hgeometry-combinatorial-0.12.0.1-3UsM6nqO83QAAGVLl4vU5w" 'False) (C1 ('MetaCons "Dart" 'PrefixI 'True) (S1 ('MetaSel ('Just "_arc") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (Arc s)) :*: S1 ('MetaSel ('Just "_direction") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Direction)))
type DataOf (PlanarGraph s w v e f) (Dart s) 
Instance details

Defined in Data.PlanarGraph.Core

type DataOf (PlanarGraph s w v e f) (Dart s) = e
type DataOf (PlaneGraph s v e f r) (Dart s) Source # 
Instance details

Defined in Data.PlaneGraph.Core

type DataOf (PlaneGraph s v e f r) (Dart s) = e
type DataOf (PlanarSubdivision s v e f r) (Dart s) Source # 
Instance details

Defined in Data.Geometry.PlanarSubdivision.Basic

type DataOf (PlanarSubdivision s v e f r) (Dart s) = e

data World #

The world in which the graph lives

Constructors

Primal 
Dual 

Instances

Instances details
Eq World 
Instance details

Defined in Data.PlanarGraph.Core

Methods

(==) :: World -> World -> Bool #

(/=) :: World -> World -> Bool #

Show World 
Instance details

Defined in Data.PlanarGraph.Core

Methods

showsPrec :: Int -> World -> ShowS #

show :: World -> String #

showList :: [World] -> ShowS #

type VertexId' (s :: k) = VertexId s 'Primal #

Shorthand for vertices in the primal.

type FaceId' (s :: k) = FaceId s 'Primal #

Shorthand for FaceId's in the primal.

withEdgeDistances :: (Point 2 r -> Point 2 r -> a) -> PlaneGraph s p e f r -> PlaneGraph s p (a :+ e) f r Source #

Labels the edges of a plane graph with their distances, as specified by the distance function.