hgeometry-combinatorial-0.9.0.0: Data structures, and Data types.

Data.PlanarGraph

Description

Data type for representing connected planar graphs

Synopsis

# Documentation

>>> :{
let dart i s = Dart (Arc i) (read s)
(aA:aB:aC:aD:aE:aG:_) = take 6 [Arc 0..]
myGraph :: PlanarGraph () Primal () String ()
myGraph = planarGraph [ [ (Dart aA Negative, "a-")
, (Dart aC Positive, "c+")
, (Dart aB Positive, "b+")
, (Dart aA Positive, "a+")
]
, [ (Dart aE Negative, "e-")
, (Dart aB Negative, "b-")
, (Dart aG Positive, "g+")
]
, [ (Dart aE Positive, "e+")
, (Dart aC Negative, "c-")
]
, [ (Dart aG Negative, "g-")
]
]
:}


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.

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

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
 (Eq v, Eq e, Eq f) => Eq (PlanarGraph s w v e f) Source # Instance detailsDefined 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) Source # Instance detailsDefined in Data.PlanarGraph.Core MethodsshowsPrec :: 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) Source # Instance detailsDefined in Data.PlanarGraph.Core Associated Typestype Rep (PlanarGraph s w v e f) :: Type -> Type # Methodsfrom :: 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 # (ToJSON v, ToJSON e, ToJSON f) => ToJSON (PlanarGraph s w v e f) Source # Instance detailsDefined in Data.PlanarGraph.IO MethodstoJSON :: PlanarGraph s w v e f -> Value #toEncoding :: PlanarGraph s w v e f -> Encoding #toJSONList :: [PlanarGraph s w v e f] -> Value #toEncodingList :: [PlanarGraph s w v e f] -> Encoding # (FromJSON v, FromJSON e, FromJSON f) => FromJSON (PlanarGraph s Primal v e f) Source # Instance detailsDefined in Data.PlanarGraph.IO MethodsparseJSON :: Value -> Parser (PlanarGraph s Primal v e f) #parseJSONList :: Value -> Parser [PlanarGraph s Primal v e f] # HasDataOf (PlanarGraph s w v e f) (Dart s) Source # Instance detailsDefined in Data.PlanarGraph.Core Associated Typestype DataOf (PlanarGraph s w v e f) (Dart s) :: Type Source # MethodsdataOf :: Dart s -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (Dart s)) Source # HasDataOf (PlanarGraph s w v e f) (FaceId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core Associated Typestype DataOf (PlanarGraph s w v e f) (FaceId s w) :: Type Source # MethodsdataOf :: FaceId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (FaceId s w)) Source # HasDataOf (PlanarGraph s w v e f) (VertexId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core Associated Typestype DataOf (PlanarGraph s w v e f) (VertexId s w) :: Type Source # MethodsdataOf :: VertexId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (VertexId s w)) Source # type Rep (PlanarGraph s w v e f) Source # Instance detailsDefined in Data.PlanarGraph.Core type Rep (PlanarGraph s w v e f) = D1 (MetaData "PlanarGraph" "Data.PlanarGraph.Core" "hgeometry-combinatorial-0.9.0.0-6qy5VaQ7muxJuEfibyCL9S" 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) Source # Instance detailsDefined in Data.PlanarGraph.Core type DataOf (PlanarGraph s w v e f) (Dart s) = e type DataOf (PlanarGraph s w v e f) (FaceId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core type DataOf (PlanarGraph s w v e f) (FaceId s w) = f type DataOf (PlanarGraph s w v e f) (VertexId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core type DataOf (PlanarGraph s w v e f) (VertexId s w) = v

embedding :: Getter (PlanarGraph s w v e f) (Permutation (Dart s)) Source #

Get the embedding, reprsented as a permutation of the darts, of this graph.

vertexData :: Lens (PlanarGraph s w v e f) (PlanarGraph s w v' e f) (Vector v) (Vector v') Source #

dartData :: Lens (PlanarGraph s w v e f) (PlanarGraph s w v e' f) (Vector (Dart s, e)) (Vector (Dart s, e')) Source #

lens to access the Dart Data

faceData :: Lens (PlanarGraph s w v e f) (PlanarGraph s w v e f') (Vector f) (Vector f') Source #

rawDartData :: Lens (PlanarGraph s w v e f) (PlanarGraph s w v e' f) (Vector e) (Vector e') Source #

edgeData :: Lens (PlanarGraph s w v e f) (PlanarGraph s w v e' f) (Vector (Dart s, e)) (Vector (Dart s, e')) Source #

edgeData is just an alias for dartData

data World Source #

The world in which the graph lives

Constructors

 Primal Dual
Instances
 Source # Instance detailsDefined in Data.PlanarGraph.Core Methods(==) :: World -> World -> Bool #(/=) :: World -> World -> Bool # Source # Instance detailsDefined in Data.PlanarGraph.Core MethodsshowsPrec :: Int -> World -> ShowS #show :: World -> String #showList :: [World] -> ShowS #

type family DualOf (sp :: World) where ... Source #

We can take the dual of a world. For the Primal this gives us the Dual, for the Dual this gives us the Primal.

Equations

 DualOf Primal = Dual DualOf Dual = Primal

# Representing edges: Arcs and Darts

newtype Arc s Source #

An Arc is a directed edge in a planar graph. The type s is used to tie this arc to a particular graph.

Constructors

 Arc Fields_unArc :: Int
Instances
 Bounded (Arc s) Source # Instance detailsDefined in Data.PlanarGraph.Dart MethodsminBound :: Arc s #maxBound :: Arc s # Enum (Arc s) Source # Instance detailsDefined in Data.PlanarGraph.Dart Methodssucc :: Arc s -> Arc s #pred :: Arc s -> Arc s #toEnum :: Int -> Arc s #fromEnum :: Arc s -> Int #enumFrom :: Arc s -> [Arc s] #enumFromThen :: Arc s -> Arc s -> [Arc s] #enumFromTo :: Arc s -> Arc s -> [Arc s] #enumFromThenTo :: Arc s -> Arc s -> Arc s -> [Arc s] # Eq (Arc s) Source # Instance detailsDefined in Data.PlanarGraph.Dart Methods(==) :: Arc s -> Arc s -> Bool #(/=) :: Arc s -> Arc s -> Bool # Ord (Arc s) Source # Instance detailsDefined in Data.PlanarGraph.Dart Methodscompare :: Arc s -> Arc s -> Ordering #(<) :: Arc s -> Arc s -> Bool #(<=) :: Arc s -> Arc s -> Bool #(>) :: Arc s -> Arc s -> Bool #(>=) :: Arc s -> Arc s -> Bool #max :: Arc s -> Arc s -> Arc s #min :: Arc s -> Arc s -> Arc s # Show (Arc s) Source # Instance detailsDefined in Data.PlanarGraph.Dart MethodsshowsPrec :: Int -> Arc s -> ShowS #show :: Arc s -> String #showList :: [Arc s] -> ShowS # Generic (Arc s) Source # Instance detailsDefined in Data.PlanarGraph.Dart Associated Typestype Rep (Arc s) :: Type -> Type # Methodsfrom :: Arc s -> Rep (Arc s) x #to :: Rep (Arc s) x -> Arc s # Arbitrary (Arc s) Source # Instance detailsDefined in Data.PlanarGraph.Dart Methodsarbitrary :: Gen (Arc s) #shrink :: Arc s -> [Arc s] # NFData (Arc s) Source # Instance detailsDefined in Data.PlanarGraph.Dart Methodsrnf :: Arc s -> () # type Rep (Arc s) Source # Instance detailsDefined in Data.PlanarGraph.Dart type Rep (Arc s) = D1 (MetaData "Arc" "Data.PlanarGraph.Dart" "hgeometry-combinatorial-0.9.0.0-6qy5VaQ7muxJuEfibyCL9S" True) (C1 (MetaCons "Arc" PrefixI True) (S1 (MetaSel (Just "_unArc") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Int)))

data Direction Source #

Darts have a direction which is either Positive or Negative (shown as +1 or -1, respectively).

Constructors

 Negative Positive
Instances
 Source # Instance detailsDefined in Data.PlanarGraph.Dart Methods Source # Instance detailsDefined in Data.PlanarGraph.Dart MethodsenumFrom :: Direction -> [Direction] # Source # Instance detailsDefined in Data.PlanarGraph.Dart Methods Source # Instance detailsDefined in Data.PlanarGraph.Dart Methods Source # Instance detailsDefined in Data.PlanarGraph.Dart Methods Source # Instance detailsDefined in Data.PlanarGraph.Dart MethodsshowList :: [Direction] -> ShowS # Source # Instance detailsDefined in Data.PlanarGraph.Dart Associated Typestype Rep Direction :: Type -> Type # Methodsto :: Rep Direction x -> Direction # Source # Instance detailsDefined in Data.PlanarGraph.Dart Methodsshrink :: Direction -> [Direction] # Source # Instance detailsDefined in Data.PlanarGraph.Dart Methodsrnf :: Direction -> () # type Rep Direction Source # Instance detailsDefined in Data.PlanarGraph.Dart type Rep Direction = D1 (MetaData "Direction" "Data.PlanarGraph.Dart" "hgeometry-combinatorial-0.9.0.0-6qy5VaQ7muxJuEfibyCL9S" False) (C1 (MetaCons "Negative" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "Positive" PrefixI False) (U1 :: Type -> Type))

Reverse the direcion

data Dart s Source #

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.

Constructors

 Dart Fields_arc :: !(Arc s) _direction :: !Direction
Instances
 Enum (Dart s) Source # Instance detailsDefined in Data.PlanarGraph.Dart Methodssucc :: 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) Source # Instance detailsDefined in Data.PlanarGraph.Dart Methods(==) :: Dart s -> Dart s -> Bool #(/=) :: Dart s -> Dart s -> Bool # Ord (Dart s) Source # Instance detailsDefined in Data.PlanarGraph.Dart Methodscompare :: 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) Source # Instance detailsDefined in Data.PlanarGraph.Dart MethodsshowsPrec :: Int -> Dart s -> ShowS #show :: Dart s -> String #showList :: [Dart s] -> ShowS # Generic (Dart s) Source # Instance detailsDefined in Data.PlanarGraph.Dart Associated Typestype Rep (Dart s) :: Type -> Type # Methodsfrom :: Dart s -> Rep (Dart s) x #to :: Rep (Dart s) x -> Dart s # Source # Instance detailsDefined in Data.PlanarGraph.Dart Methodsarbitrary :: Gen (Dart s) #shrink :: Dart s -> [Dart s] # NFData (Dart s) Source # Instance detailsDefined in Data.PlanarGraph.Dart Methodsrnf :: Dart s -> () # HasDataOf (PlanarGraph s w v e f) (Dart s) Source # Instance detailsDefined in Data.PlanarGraph.Core Associated Typestype DataOf (PlanarGraph s w v e f) (Dart s) :: Type Source # MethodsdataOf :: Dart s -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (Dart s)) Source # type Rep (Dart s) Source # Instance detailsDefined in Data.PlanarGraph.Dart type Rep (Dart s) = D1 (MetaData "Dart" "Data.PlanarGraph.Dart" "hgeometry-combinatorial-0.9.0.0-6qy5VaQ7muxJuEfibyCL9S" 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) Source # Instance detailsDefined in Data.PlanarGraph.Core type DataOf (PlanarGraph s w v e f) (Dart s) = e

arc :: forall s s. Lens (Dart s) (Dart s) (Arc s) (Arc s) Source #

twin :: Dart s -> Dart s Source #

Get the twin of this dart (edge)

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


test if a dart is Positive

# Vertices

newtype VertexId s (w :: World) Source #

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_unVertexId :: Int
Instances
 Enum (VertexId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core Methodssucc :: 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) Source # Instance detailsDefined in Data.PlanarGraph.Core Methods(==) :: VertexId s w -> VertexId s w -> Bool #(/=) :: VertexId s w -> VertexId s w -> Bool # Ord (VertexId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core Methodscompare :: 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) Source # Instance detailsDefined in Data.PlanarGraph.Core MethodsshowsPrec :: Int -> VertexId s w -> ShowS #show :: VertexId s w -> String #showList :: [VertexId s w] -> ShowS # Generic (VertexId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core Associated Typestype Rep (VertexId s w) :: Type -> Type # Methodsfrom :: VertexId s w -> Rep (VertexId s w) x #to :: Rep (VertexId s w) x -> VertexId s w # ToJSON (VertexId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core MethodstoJSON :: VertexId s w -> Value #toEncoding :: VertexId s w -> Encoding #toJSONList :: [VertexId s w] -> Value #toEncodingList :: [VertexId s w] -> Encoding # FromJSON (VertexId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core MethodsparseJSON :: Value -> Parser (VertexId s w) #parseJSONList :: Value -> Parser [VertexId s w] # NFData (VertexId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core Methodsrnf :: VertexId s w -> () # HasDataOf (PlanarGraph s w v e f) (VertexId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core Associated Typestype DataOf (PlanarGraph s w v e f) (VertexId s w) :: Type Source # MethodsdataOf :: VertexId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (VertexId s w)) Source # type Rep (VertexId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core type Rep (VertexId s w) = D1 (MetaData "VertexId" "Data.PlanarGraph.Core" "hgeometry-combinatorial-0.9.0.0-6qy5VaQ7muxJuEfibyCL9S" True) (C1 (MetaCons "VertexId" PrefixI True) (S1 (MetaSel (Just "_unVertexId") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Int))) type DataOf (PlanarGraph s w v e f) (VertexId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core type DataOf (PlanarGraph s w v e f) (VertexId s w) = v

type VertexId' s = VertexId s Primal Source #

Shorthand for vertices in the primal.

# Building a planar graph

planarGraph :: [[(Dart s, e)]] -> PlanarGraph s Primal () e () Source #

Construct a planar graph, given the darts in cyclic order around each vertex.

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

planarGraph' :: Permutation (Dart s) -> PlanarGraph s w () () () Source #

Construct a planar graph

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

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

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: $$O(n)$$.

toAdjacencyLists :: PlanarGraph s w v e f -> [(VertexId s w, Vector (VertexId s w))] Source #

Produces the adjacencylists for all vertices in the graph. For every vertex, the adjacent vertices are given in counter clockwise order.

Note that in case a vertex u as a self loop, we have that this vertexId occurs twice in the list of neighbours, i.e.: u : [...,u,..,u,...]. Similarly, if there are multiple darts between a pair of edges they occur multiple times.

running time: $$O(n)$$

fromAdjRep :: proxy s -> Gr (Vtx v e) (Face f) -> PlanarGraph s Primal v e f Source #

Read a planar graph, given in JSON format into a planar graph. The adjacencylists should be in counter clockwise order.

running time: $$O(n)$$

toAdjRep :: PlanarGraph s w v e f -> Gr (Vtx v e) (Face f) Source #

Transforms the planar graph into a format taht can be easily converted into JSON format. For every vertex, the adjacent vertices are given in counter clockwise order.

See toAdjacencyLists for notes on how we handle self-loops.

running time: $$O(n)$$

# Quering a planar graph

numVertices :: PlanarGraph s w v e f -> Int Source #

Get the number of vertices

>>> numVertices myGraph
4


numDarts :: PlanarGraph s w v e f -> Int Source #

Get the number of Darts

>>> numDarts myGraph
12


numEdges :: PlanarGraph s w v e f -> Int Source #

Get the number of Edges

>>> numEdges myGraph
6


numFaces :: PlanarGraph s w v e f -> Int Source #

Get the number of faces

>>> numFaces myGraph
4


darts' :: PlanarGraph s w v e f -> Vector (Dart s) Source #

Enumerate all darts

darts :: PlanarGraph s w v e f -> Vector (Dart s, e) Source #

Get all darts together with their data

>>> mapM_ print $darts myGraph (Dart (Arc 0) -1,"a-") (Dart (Arc 2) +1,"c+") (Dart (Arc 1) +1,"b+") (Dart (Arc 0) +1,"a+") (Dart (Arc 4) -1,"e-") (Dart (Arc 1) -1,"b-") (Dart (Arc 3) -1,"d-") (Dart (Arc 5) +1,"g+") (Dart (Arc 4) +1,"e+") (Dart (Arc 3) +1,"d+") (Dart (Arc 2) -1,"c-") (Dart (Arc 5) -1,"g-")  edges' :: PlanarGraph s w v e f -> Vector (Dart s) Source # Enumerate all edges. We report only the Positive darts edges :: PlanarGraph s w v e f -> Vector (Dart s, e) Source # Enumerate all edges with their edge data. We report only the Positive darts. >>> mapM_ print$ edges myGraph
(Dart (Arc 2) +1,"c+")
(Dart (Arc 1) +1,"b+")
(Dart (Arc 0) +1,"a+")
(Dart (Arc 5) +1,"g+")
(Dart (Arc 4) +1,"e+")
(Dart (Arc 3) +1,"d+")


vertices' :: PlanarGraph s w v e f -> Vector (VertexId s w) Source #

Enumerate all vertices

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


vertices :: PlanarGraph s w v e f -> Vector (VertexId s w, v) Source #

Enumerate all vertices, together with their vertex data

faces' :: PlanarGraph s w v e f -> Vector (FaceId s w) Source #

Enumerate all faces in the planar graph

faces :: PlanarGraph s w v e f -> Vector (FaceId s w, f) Source #

All faces with their face data.

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

Traverse the vertices

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

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

Traverses the darts

>>> traverseDarts (\d x -> print (d,x)) myGraph >> pure ()
(Dart (Arc 0) +1,"a+")
(Dart (Arc 0) -1,"a-")
(Dart (Arc 1) +1,"b+")
(Dart (Arc 1) -1,"b-")
(Dart (Arc 2) +1,"c+")
(Dart (Arc 2) -1,"c-")
(Dart (Arc 3) +1,"d+")
(Dart (Arc 3) -1,"d-")
(Dart (Arc 4) +1,"e+")
(Dart (Arc 4) -1,"e-")
(Dart (Arc 5) +1,"g+")
(Dart (Arc 5) -1,"g-")


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

Traverses the faces

>>> traverseFaces (\i x -> print (i,x)) myGraph >> pure ()
(FaceId 0,())
(FaceId 1,())
(FaceId 2,())
(FaceId 3,())


tailOf :: Dart s -> PlanarGraph s w v e f -> VertexId s w Source #

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

running time: $$O(1)$$

headOf :: Dart s -> PlanarGraph s w v e f -> VertexId s w Source #

The vertex this dart is heading in to

running time: $$O(1)$$

endPoints :: Dart s -> PlanarGraph s w v e f -> (VertexId s w, VertexId s w) Source #

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

running time: $$O(1)$$

incidentEdges :: VertexId s w -> PlanarGraph s w v e f -> 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

incomingEdges :: VertexId s w -> PlanarGraph s w v e f -> Vector (Dart s) Source #

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

outgoingEdges :: VertexId s w -> PlanarGraph s w v e f -> Vector (Dart s) Source #

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

neighboursOf :: VertexId s w -> PlanarGraph s w v e f -> Vector (VertexId s w) Source #

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

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

nextIncidentEdge :: Dart s -> PlanarGraph s w v e f -> Dart s Source #

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

running time: $$O(1)$$

prevIncidentEdge :: Dart s -> PlanarGraph s w v e f -> Dart s Source #

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

running time: $$O(1)$$

# Associated Data

class HasDataOf g i where Source #

Associated Types

type DataOf g i Source #

Methods

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

get the data associated with the value i.

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

Instances
 HasDataOf (PlanarGraph s w v e f) (Dart s) Source # Instance detailsDefined in Data.PlanarGraph.Core Associated Typestype DataOf (PlanarGraph s w v e f) (Dart s) :: Type Source # MethodsdataOf :: Dart s -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (Dart s)) Source # HasDataOf (PlanarGraph s w v e f) (FaceId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core Associated Typestype DataOf (PlanarGraph s w v e f) (FaceId s w) :: Type Source # MethodsdataOf :: FaceId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (FaceId s w)) Source # HasDataOf (PlanarGraph s w v e f) (VertexId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core Associated Typestype DataOf (PlanarGraph s w v e f) (VertexId s w) :: Type Source # MethodsdataOf :: VertexId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (VertexId s w)) Source #

endPointDataOf :: Dart s -> Getter (PlanarGraph s w v e f) (v, v) Source #

Data corresponding to the endpoints of the dart

endPointData :: Dart s -> PlanarGraph s w v e f -> (v, v) Source #

Data corresponding to the endpoints of the dart

running time: $$O(1)$$

dual :: Getter (PlanarGraph s w v e f) (PlanarGraph s (DualOf w) f e v) Source #

Get the dual graph of this graph.

# Faces

newtype FaceId s w Source #

The type to reprsent FaceId's

Constructors

 FaceId Fields_unFaceId :: VertexId s (DualOf w)
Instances
 Enum (FaceId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core Methodssucc :: 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) Source # Instance detailsDefined in Data.PlanarGraph.Core Methods(==) :: FaceId s w -> FaceId s w -> Bool #(/=) :: FaceId s w -> FaceId s w -> Bool # Ord (FaceId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core Methodscompare :: 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) Source # Instance detailsDefined in Data.PlanarGraph.Core MethodsshowsPrec :: Int -> FaceId s w -> ShowS #show :: FaceId s w -> String #showList :: [FaceId s w] -> ShowS # ToJSON (FaceId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core MethodstoJSON :: FaceId s w -> Value #toEncoding :: FaceId s w -> Encoding #toJSONList :: [FaceId s w] -> Value #toEncodingList :: [FaceId s w] -> Encoding # FromJSON (FaceId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core MethodsparseJSON :: Value -> Parser (FaceId s w) #parseJSONList :: Value -> Parser [FaceId s w] # HasDataOf (PlanarGraph s w v e f) (FaceId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core Associated Typestype DataOf (PlanarGraph s w v e f) (FaceId s w) :: Type Source # MethodsdataOf :: FaceId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (FaceId s w)) Source # type DataOf (PlanarGraph s w v e f) (FaceId s w) Source # Instance detailsDefined in Data.PlanarGraph.Core type DataOf (PlanarGraph s w v e f) (FaceId s w) = f

type FaceId' s = FaceId s Primal Source #

Shorthand for FaceId's in the primal.

leftFace :: Dart s -> PlanarGraph s w v e f -> FaceId s w Source #

The face to the left of the dart

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


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

rightFace :: Dart s -> PlanarGraph s w v e f -> FaceId s w Source #

The face to the right of the dart

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


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

boundaryDart :: FaceId s w -> PlanarGraph s w v e f -> 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.

boundary :: FaceId s w -> PlanarGraph s w v e f -> 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 -> PlanarGraph s w v e f -> 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

boundaryVertices :: FaceId s w -> PlanarGraph s w v e f -> Vector (VertexId s w) 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.

nextEdge :: Dart s -> PlanarGraph s w v e f -> Dart s Source #

Get the next edge along the face

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

prevEdge :: Dart s -> PlanarGraph s w v e f -> Dart s Source #

Get the previous edge along the face

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