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

Data.PlanarGraph.Core

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. # Representing The World

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

dualDualIdentity :: forall w. DualOf (DualOf w) :~: w Source #

The Dual of the Dual is the Primal.

# VertexId's

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.

# FaceId's

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.

# The graph type itself

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.

Constructors

 PlanarGraph Fields_embedding :: Permutation (Dart s) _vertexData :: Vector v _rawDartData :: Vector e _faceData :: Vector f _dual :: PlanarGraph s (DualOf w) f e v
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

## lenses and getters

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 #

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

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

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

Get the dual graph of this graph.

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

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

updateData :: forall s w v e f v' e' f'. (Vector v -> Vector v') -> (Vector e -> Vector e') -> (Vector f -> Vector f') -> PlanarGraph s w v e f -> PlanarGraph s w v' e' f' Source #

Helper function to update the data in a planar graph. Takes care to update both the data in the original graph as well as in the dual.

updateData' :: DualOf (DualOf w) ~ w => (Vector v -> Vector v') -> (Vector e -> Vector e') -> (Vector f -> Vector f') -> PlanarGraph s w v e f -> PlanarGraph s w v' e' f' Source #

The function that does the actual work for updateData

reorderEdgeData :: Foldable f => f (Dart s, e) -> Vector e Source #

Reorders the edge data to be in the right order to set edgeData

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,())  ## Constructing a Planar graph planarGraph' :: Permutation (Dart s) -> PlanarGraph s w () () () Source # Construct a planar graph running time: $$O(n)$$. planarGraph :: [[(Dart s, e)]] -> PlanarGraph s Primal () e () Source # Construct a planar graph, given the darts in cyclic order around each vertex. running time: $$O(n)$$. 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: $$O(n)$$ ## Convenience functions 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  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 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+")


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: $$O(1)$$

# Access 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: $$O(1)$$

# The Dual graph

computeDual :: forall s w v e f. PlanarGraph s w v e f -> PlanarGraph s (DualOf w) f e v Source #

The dual of this graph

>>> :{
 let fromList = V.fromList
answer = fromList [ fromList [dart 0 "-1"]
, fromList [dart 2 "+1",dart 4 "+1",dart 1 "-1",dart 0 "+1"]
, fromList [dart 1 "+1",dart 3 "-1",dart 2 "-1"]
, fromList [dart 4 "-1",dart 3 "+1",dart 5 "+1",dart 5 "-1"]
]

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