Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	None
Language	Haskell2010

Data.Geometry.PlanarSubdivision.Basic

Description

Synopsis

type VertexId' (s :: k) = VertexId s 'Primal
type FaceId' (s :: k) = FaceId s 'Primal
data VertexData r v = VertexData !(Point 2 r) !v
vData :: forall r v v. Lens (VertexData r v) (VertexData r v) v v
location :: forall r v r. Lens (VertexData r v) (VertexData r v) (Point 2 r) (Point 2 r)
data FaceData h f = FaceData (Seq h) !f
holes :: forall h f h. Lens (FaceData h f) (FaceData h f) (Seq h) (Seq h)
fData :: forall h f f. Lens (FaceData h f) (FaceData h f) f f
data PlanarSubdivision s v e f r = PlanarSubdivision (Vector (Component s r)) (Vector (Raw s (VertexId' (Wrap s)) v)) (Vector (Raw s (Dart (Wrap s)) e)) (Vector (RawFace s f))
type family Wrap (s :: k) :: k where ...
type Component s r = PlaneGraph (Wrap s) (VertexId' s) (Dart s) (FaceId' s) r
data ComponentId s
data PolygonFaceData
- = Inside
- | Outside
data PlanarGraph (s :: k) (w :: World) v e f
data PlaneGraph s v e f r
fromSimplePolygon :: (Ord r, Fractional r) => proxy s -> SimplePolygon p r -> f -> f -> PlanarSubdivision s p () f r
fromConnectedSegments :: (Foldable f, Ord r, Fractional r) => proxy s -> f (LineSegment 2 p r :+ e) -> PlanarSubdivision s (NonEmpty p) e () r
fromPlaneGraph :: forall s v e f r. (Ord r, Fractional r) => PlaneGraph s v e f r -> PlanarSubdivision s v e f r
fromPlaneGraph' :: forall s v e f r. PlaneGraph s v e f r -> Dart s -> PlanarSubdivision s v e f r
numComponents :: PlanarSubdivision s v e f r -> Int
numVertices :: PlanarSubdivision s v e f r -> Int
numEdges :: PlanarSubdivision s v e f r -> Int
numFaces :: PlanarSubdivision s v e f r -> Int
numDarts :: PlanarSubdivision s v e f r -> Int
dual :: forall k (s :: k) (w :: World) v e f. Getter (PlanarGraph s w v e f) (PlanarGraph s (DualOf w) f e v)
components :: forall k (s :: k) v e f r r. Lens (PlanarSubdivision (s :: k) v e f r) (PlanarSubdivision (s :: k) v e f r) (Vector (Component s r)) (Vector (Component s r))
component :: ComponentId s -> Lens' (PlanarSubdivision s v e f r) (Component s r)
vertices' :: PlanarSubdivision s v e f r -> Vector (VertexId' s)
vertices :: PlanarSubdivision s v e f r -> Vector (VertexId' s, VertexData r v)
edges' :: PlanarSubdivision s v e f r -> Vector (Dart s)
edges :: PlanarSubdivision s v e f r -> Vector (Dart s, e)
faces' :: PlanarSubdivision s v e f r -> Vector (FaceId' s)
faces :: PlanarSubdivision s v e f r -> Vector (FaceId' s, FaceData (Dart s) f)
internalFaces :: PlanarSubdivision s v e f r -> Vector (FaceId' s, FaceData (Dart s) f)
darts' :: PlanarSubdivision s v e f r -> Vector (Dart s)
headOf :: Dart s -> PlanarSubdivision s v e f r -> VertexId' s
tailOf :: Dart s -> PlanarSubdivision s v e f r -> VertexId' s
twin :: forall k (s :: k). Dart s -> Dart s
endPoints :: Dart s -> PlanarSubdivision s v e f r -> (VertexId' s, VertexId' s)
incidentEdges :: VertexId' s -> PlanarSubdivision s v e f r -> Vector (Dart s)
incomingEdges :: VertexId' s -> PlanarSubdivision s v e f r -> Vector (Dart s)
outgoingEdges :: VertexId' s -> PlanarSubdivision s v e f r -> Vector (Dart s)
nextIncidentEdge :: Dart s -> PlanarSubdivision s v e f r -> Dart s
neighboursOf :: VertexId' s -> PlanarSubdivision s v e f r -> Vector (VertexId' s)
leftFace :: Dart s -> PlanarSubdivision s v e f r -> FaceId' s
rightFace :: Dart s -> PlanarSubdivision s v e f r -> FaceId' s
outerBoundaryDarts :: FaceId' s -> PlanarSubdivision s v e f r -> Vector (Dart s)
boundaryVertices :: FaceId' s -> PlanarSubdivision s v e f r -> Vector (VertexId' s)
holesOf :: FaceId' s -> PlanarSubdivision s v e f r -> Seq (Dart s)
outerFaceId :: PlanarSubdivision s v e f r -> FaceId' s
boundary' :: Dart s -> PlanarSubdivision s v e f r -> Vector (Dart s)
locationOf :: VertexId' s -> Lens' (PlanarSubdivision s v e f r) (Point 2 r)
class HasDataOf g i where
- type DataOf g i
- dataOf :: i -> Lens' g (DataOf g i)
endPointsOf :: Dart s -> Getter (PlanarSubdivision s v e f r) (VertexData r v, VertexData r v)
endPointData :: Dart s -> PlanarSubdivision s v e f r -> (VertexData r v, VertexData r v)
faceDataOf :: FaceId' s -> Lens' (PlanarSubdivision s v e f r) (FaceData (Dart s) f)
edgeSegment :: Dart s -> PlanarSubdivision s v e f r -> LineSegment 2 v r :+ e
edgeSegments :: PlanarSubdivision s v e f r -> Vector (Dart s, LineSegment 2 v r :+ e)
rawFacePolygon :: FaceId' s -> PlanarSubdivision s v e f r -> SomePolygon v r :+ f
rawFaceBoundary :: FaceId' s -> PlanarSubdivision s v e f r -> SimplePolygon v r :+ f
rawFacePolygons :: PlanarSubdivision s v e f r -> Vector (FaceId' s, SomePolygon v r :+ f)
newtype VertexId (s :: k) (w :: World) = VertexId {
- _unVertexId :: Int
}
newtype FaceId (s :: k) (w :: World) = FaceId {
- _unFaceId :: VertexId s (DualOf w)
}
data Dart (s :: k)
data World
- = Primal
- | Dual
rawVertexData :: forall k (s :: k) v e f r v. Lens (PlanarSubdivision (s :: k) v e f r) (PlanarSubdivision (s :: k) v e f r) (Vector (Raw s (VertexId' (Wrap s)) v)) (Vector (Raw s (VertexId' (Wrap s)) v))
rawDartData :: forall k (s :: k) v e f r e. Lens (PlanarSubdivision (s :: k) v e f r) (PlanarSubdivision (s :: k) v e f r) (Vector (Raw s (Dart (Wrap s)) e)) (Vector (Raw s (Dart (Wrap s)) e))
rawFaceData :: forall k (s :: k) v e f r f. Lens (PlanarSubdivision (s :: k) v e f r) (PlanarSubdivision (s :: k) v e f r) (Vector (RawFace s f)) (Vector (RawFace s f))
vertexData :: Lens (PlanarSubdivision s v e f r) (PlanarSubdivision s v' e f r) (Vector v) (Vector v')
dartData :: Lens (PlanarSubdivision s v e f r) (PlanarSubdivision s v e' f r) (Vector (Dart s, e)) (Vector (Dart s, e'))
faceData :: Lens (PlanarSubdivision s v e f r) (PlanarSubdivision s v e f' r) (Vector f) (Vector f')
dataVal :: Lens (Raw s ia a) (Raw s ia b) a b
dartMapping :: PlanarSubdivision s v e f r -> Vector (Dart (Wrap s), Dart s)
data Raw s ia a = Raw {
- _compId :: !(ComponentId s)
- _idxVal :: !ia
- _dataVal :: !a
}

Documentation

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.

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 Methods toJSON :: VertexData r v -> Value # toEncoding :: VertexData r v -> Encoding # toJSONList :: [VertexData r v] -> Value # toEncodingList :: [VertexData r v] -> Encoding #
(FromJSON r, FromJSON v) => FromJSON (VertexData r v) Source #
Instance details Defined in Data.PlaneGraph.Core Methods parseJSON :: Value -> Parser (VertexData r v) # parseJSONList :: Value -> Parser [VertexData r v] #
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-0.12.0.2-IMXeR0PuShPEjPCARytEWE" '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 #

data FaceData h f Source #

The Face data consists of the data itself and a list of holes

Constructors

FaceData (Seq h) !f

Instances

Instances details

Bifunctor FaceData Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods bimap :: (a -> b) -> (c -> d) -> FaceData a c -> FaceData b d # first :: (a -> b) -> FaceData a c -> FaceData b c # second :: (b -> c) -> FaceData a b -> FaceData a c #
Functor (FaceData h) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods fmap :: (a -> b) -> FaceData h a -> FaceData h b # (<$) :: a -> FaceData h b -> FaceData h a #
Foldable (FaceData h) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods fold :: Monoid m => FaceData h m -> m # foldMap :: Monoid m => (a -> m) -> FaceData h a -> m # foldMap' :: Monoid m => (a -> m) -> FaceData h a -> m # foldr :: (a -> b -> b) -> b -> FaceData h a -> b # foldr' :: (a -> b -> b) -> b -> FaceData h a -> b # foldl :: (b -> a -> b) -> b -> FaceData h a -> b # foldl' :: (b -> a -> b) -> b -> FaceData h a -> b # foldr1 :: (a -> a -> a) -> FaceData h a -> a # foldl1 :: (a -> a -> a) -> FaceData h a -> a # toList :: FaceData h a -> [a] # null :: FaceData h a -> Bool # length :: FaceData h a -> Int # elem :: Eq a => a -> FaceData h a -> Bool # maximum :: Ord a => FaceData h a -> a # minimum :: Ord a => FaceData h a -> a # sum :: Num a => FaceData h a -> a # product :: Num a => FaceData h a -> a #
Traversable (FaceData h) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods traverse :: Applicative f => (a -> f b) -> FaceData h a -> f (FaceData h b) # sequenceA :: Applicative f => FaceData h (f a) -> f (FaceData h a) # mapM :: Monad m => (a -> m b) -> FaceData h a -> m (FaceData h b) # sequence :: Monad m => FaceData h (m a) -> m (FaceData h a) #
(Eq h, Eq f) => Eq (FaceData h f) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods (==) :: FaceData h f -> FaceData h f -> Bool # (/=) :: FaceData h f -> FaceData h f -> Bool #
(Ord h, Ord f) => Ord (FaceData h f) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods compare :: FaceData h f -> FaceData h f -> Ordering # (<) :: FaceData h f -> FaceData h f -> Bool # (<=) :: FaceData h f -> FaceData h f -> Bool # (>) :: FaceData h f -> FaceData h f -> Bool # (>=) :: FaceData h f -> FaceData h f -> Bool # max :: FaceData h f -> FaceData h f -> FaceData h f # min :: FaceData h f -> FaceData h f -> FaceData h f #
(Show h, Show f) => Show (FaceData h f) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods showsPrec :: Int -> FaceData h f -> ShowS # show :: FaceData h f -> String # showList :: [FaceData h f] -> ShowS #
Generic (FaceData h f) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Associated Types type Rep (FaceData h f) :: Type -> Type # Methods from :: FaceData h f -> Rep (FaceData h f) x # to :: Rep (FaceData h f) x -> FaceData h f #
(ToJSON h, ToJSON f) => ToJSON (FaceData h f) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods toJSON :: FaceData h f -> Value # toEncoding :: FaceData h f -> Encoding # toJSONList :: [FaceData h f] -> Value # toEncodingList :: [FaceData h f] -> Encoding #
(FromJSON h, FromJSON f) => FromJSON (FaceData h f) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods parseJSON :: Value -> Parser (FaceData h f) # parseJSONList :: Value -> Parser [FaceData h f] #
type Rep (FaceData h f) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw type Rep (FaceData h f) = D1 ('MetaData "FaceData" "Data.Geometry.PlanarSubdivision.Raw" "hgeometry-0.12.0.2-IMXeR0PuShPEjPCARytEWE" 'False) (C1 ('MetaCons "FaceData" 'PrefixI 'True) (S1 ('MetaSel ('Just "_holes") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Seq h)) :*: S1 ('MetaSel ('Just "_fData") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 f)))

holes :: forall h f h. Lens (FaceData h f) (FaceData h f) (Seq h) (Seq h) Source #

fData :: forall h f f. Lens (FaceData h f) (FaceData h f) f f Source #

data PlanarSubdivision s v e f r Source #

A planarsubdivision is essentially a bunch of plane-graphs; one for every connected component. These graphs store the global ID's (darts, vertexId's, faceId's) in their data values. This essentially gives us a mapping between the two.

note that a face may actually occur in multiple graphs, hence when we store the edges to the the holes, we store the global edgeId's rather than the local edgeId (dart)'s.

invariant: the outerface has faceId 0

Constructors

PlanarSubdivision (Vector (Component s r)) (Vector (Raw s (VertexId' (Wrap s)) v)) (Vector (Raw s (Dart (Wrap s)) e)) (Vector (RawFace s f))

Instances

Instances details

Functor (PlanarSubdivision s v e f) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic Methods fmap :: (a -> b) -> PlanarSubdivision s v e f a -> PlanarSubdivision s v e f b # (<$) :: a -> PlanarSubdivision s v e f b -> PlanarSubdivision s v e f a #
(Eq r, Eq v, Eq e, Eq f) => Eq (PlanarSubdivision s v e f r) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic Methods (==) :: PlanarSubdivision s v e f r -> PlanarSubdivision s v e f r -> Bool # (/=) :: PlanarSubdivision s v e f r -> PlanarSubdivision s v e f r -> Bool #
(Show r, Show v, Show e, Show f) => Show (PlanarSubdivision s v e f r) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic Methods showsPrec :: Int -> PlanarSubdivision s v e f r -> ShowS # show :: PlanarSubdivision s v e f r -> String # showList :: [PlanarSubdivision s v e f r] -> ShowS #
Generic (PlanarSubdivision s v e f r) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic Associated Types type Rep (PlanarSubdivision s v e f r) :: Type -> Type # Methods from :: PlanarSubdivision s v e f r -> Rep (PlanarSubdivision s v e f r) x # to :: Rep (PlanarSubdivision s v e f r) x -> PlanarSubdivision s v e f r #
IsBoxable (PlanarSubdivision s v e f r) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic Methods boundingBox :: PlanarSubdivision s v e f r -> Box (Dimension (PlanarSubdivision s v e f r)) () (NumType (PlanarSubdivision s v e f r)) Source #
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)) #
type Rep (PlanarSubdivision s v e f r) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic type Rep (PlanarSubdivision s v e f r) = D1 ('MetaData "PlanarSubdivision" "Data.Geometry.PlanarSubdivision.Basic" "hgeometry-0.12.0.2-IMXeR0PuShPEjPCARytEWE" 'False) (C1 ('MetaCons "PlanarSubdivision" 'PrefixI 'True) ((S1 ('MetaSel ('Just "_components") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Vector (Component s r))) :: S1 ('MetaSel ('Just "_rawVertexData") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Vector (Raw s (VertexId' (Wrap s)) v)))) :: (S1 ('MetaSel ('Just "_rawDartData") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Vector (Raw s (Dart (Wrap s)) e))) :*: S1 ('MetaSel ('Just "_rawFaceData") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Vector (RawFace s f))))))
type NumType (PlanarSubdivision s v e f r) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic type NumType (PlanarSubdivision s v e f r) = r
type Dimension (PlanarSubdivision s v e f r) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic type Dimension (PlanarSubdivision s v e f r) = 2
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 (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
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 family Wrap (s :: k) :: k where ... Source #

Equations

Wrap s = Wrap' s

type Component s r = PlaneGraph (Wrap s) (VertexId' s) (Dart s) (FaceId' s) r Source #

A connected component.

For every face f, and every hole in this face, the facedata points to a dart d on the hole s.t. this dart has the face f on its left. i.e. leftFace d = f

data ComponentId s Source #

ComponentId type

Instances

Instances details

Bounded (ComponentId s) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods minBound :: ComponentId s # maxBound :: ComponentId s #
Enum (ComponentId s) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods succ :: ComponentId s -> ComponentId s # pred :: ComponentId s -> ComponentId s # toEnum :: Int -> ComponentId s # fromEnum :: ComponentId s -> Int # enumFrom :: ComponentId s -> [ComponentId s] # enumFromThen :: ComponentId s -> ComponentId s -> [ComponentId s] # enumFromTo :: ComponentId s -> ComponentId s -> [ComponentId s] # enumFromThenTo :: ComponentId s -> ComponentId s -> ComponentId s -> [ComponentId s] #
Eq (ComponentId s) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods (==) :: ComponentId s -> ComponentId s -> Bool # (/=) :: ComponentId s -> ComponentId s -> Bool #
Ord (ComponentId s) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods compare :: ComponentId s -> ComponentId s -> Ordering # (<) :: ComponentId s -> ComponentId s -> Bool # (<=) :: ComponentId s -> ComponentId s -> Bool # (>) :: ComponentId s -> ComponentId s -> Bool # (>=) :: ComponentId s -> ComponentId s -> Bool # max :: ComponentId s -> ComponentId s -> ComponentId s # min :: ComponentId s -> ComponentId s -> ComponentId s #
Show (ComponentId s) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods showsPrec :: Int -> ComponentId s -> ShowS # show :: ComponentId s -> String # showList :: [ComponentId s] -> ShowS #
Generic (ComponentId s) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Associated Types type Rep (ComponentId s) :: Type -> Type # Methods from :: ComponentId s -> Rep (ComponentId s) x # to :: Rep (ComponentId s) x -> ComponentId s #
ToJSON (ComponentId s) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods toJSON :: ComponentId s -> Value # toEncoding :: ComponentId s -> Encoding # toJSONList :: [ComponentId s] -> Value # toEncodingList :: [ComponentId s] -> Encoding #
FromJSON (ComponentId s) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods parseJSON :: Value -> Parser (ComponentId s) # parseJSONList :: Value -> Parser [ComponentId s] #
type Rep (ComponentId s) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw type Rep (ComponentId s) = D1 ('MetaData "ComponentId" "Data.Geometry.PlanarSubdivision.Raw" "hgeometry-0.12.0.2-IMXeR0PuShPEjPCARytEWE" 'True) (C1 ('MetaCons "ComponentId" 'PrefixI 'True) (S1 ('MetaSel ('Just "unCI") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Int)))

data PolygonFaceData Source #

Data type that expresses whether or not we are inside or outside the polygon.

Constructors

Inside
Outside

Instances

Instances details

Eq PolygonFaceData Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic Methods (==) :: PolygonFaceData -> PolygonFaceData -> Bool # (/=) :: PolygonFaceData -> PolygonFaceData -> Bool #
Read PolygonFaceData Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic Methods readsPrec :: Int -> ReadS PolygonFaceData # readList :: ReadS [PolygonFaceData] # readPrec :: ReadPrec PolygonFaceData # readListPrec :: ReadPrec [PolygonFaceData] #
Show PolygonFaceData Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic Methods showsPrec :: Int -> PolygonFaceData -> ShowS # show :: PolygonFaceData -> String # showList :: [PolygonFaceData] -> ShowS #

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-I7RuMNUQsKnHc7W9YnEfQ" '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 PlaneGraph s v e f r Source #

Embedded, *connected*, planar graph

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-0.12.0.2-IMXeR0PuShPEjPCARytEWE" '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

fromSimplePolygon Source #

Arguments

:: (Ord r, Fractional r)
=> proxy s
-> SimplePolygon p r
-> f	data inside
-> f	data outside the polygon
-> PlanarSubdivision 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, Fractional r) => proxy s -> f (LineSegment 2 p r :+ e) -> PlanarSubdivision s (NonEmpty p) e () r Source #

Constructs a connected planar subdivision.

pre: the segments form a single connected component running time: $O(n\log n)$

fromPlaneGraph :: forall s v e f r. (Ord r, Fractional r) => PlaneGraph s v e f r -> PlanarSubdivision s v e f r Source #

Constructs a planarsubdivision from a PlaneGraph

runningTime: $O(n)$

fromPlaneGraph' :: forall s v e f r. PlaneGraph s v e f r -> Dart s -> PlanarSubdivision s v e f r Source #

Given a (connected) PlaneGraph and a dart that has the outerface on its left | Constructs a planarsubdivision

runningTime: $O(n)$

numComponents :: PlanarSubdivision s v e f r -> Int Source #

Get the number of vertices

>>> numVertices myGraph
1

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

Get the number of vertices

>>> numVertices myGraph
4

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

Get the number of Edges

>>> numEdges myGraph
6

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

$ O(1) $. Get the number of faces

>>> numFaces myGraph
4

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

Get the number of Darts

>>> numDarts myGraph
12

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.

components :: forall k (s :: k) v e f r r. Lens (PlanarSubdivision (s :: k) v e f r) (PlanarSubdivision (s :: k) v e f r) (Vector (Component s r)) (Vector (Component s r)) Source #

component :: ComponentId s -> Lens' (PlanarSubdivision s v e f r) (Component s r) Source #

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

Enumerate all vertices

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

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

Enumerate all vertices, together with their vertex data

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

Enumerate all edges. We report only the Positive darts

edges :: PlanarSubdivision 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 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+")

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

$ O(n) $. Vector of all primal faces.

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

$ O(n) $. Vector of all primal faces with associated data.

internalFaces :: PlanarSubdivision s v e f r -> Vector (FaceId' s, FaceData (Dart s) f) Source #

Enumerates all faces with their face data exlcluding the outer face

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

Enumerate all darts

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

The vertex this dart is heading in to

running time: $O(1)$

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

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

running time: $O(1)$

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 -> PlanarSubdivision s v e f r -> (VertexId' s, VertexId' s) Source #

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

running time: $O(1)$

incidentEdges :: VertexId' s -> PlanarSubdivision 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 number of edges reported.

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

All edges incident to vertex v in outgoing direction (i.e. pointing away from v) in counterclockwise order around v.

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

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

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

running time: $O(1)$

neighboursOf :: VertexId' s -> PlanarSubdivision 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

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

The face to the left of the dart

running time: $O(1)$.

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

The face to the right of the dart

running time: $O(1)$.

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

The darts on the outer boundary of the face, for internal faces the darts are in clockwise order. For the outer face the darts are in counterclockwise order, and the darts from various components are in no particular order.

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

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

The vertices of the outer boundary of the 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.

holesOf :: FaceId' s -> PlanarSubdivision s v e f r -> Seq (Dart s) Source #

Lists the holes in this face, given as a list of darts to arbitrary darts on those faces. The returned darts are on the outside of the hole, i.e. they are incident to the given input face:

all (\d -> leftFace d ps == fi) $ holesOf fi ps

running time: $O(k)$, where $k$ is the number of darts returned.

outerFaceId :: PlanarSubdivision s v e f r -> FaceId' s Source #

gets the id of the outer face

running time: $O(1)$

boundary' :: Dart s -> PlanarSubdivision 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

locationOf :: VertexId' s -> Lens' (PlanarSubdivision 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 (PlanarSubdivision 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 -> PlanarSubdivision s v e f r -> (VertexData r v, VertexData r v) Source #

data corresponding to the endpoints of the dart

running time: $O(1)$

faceDataOf :: FaceId' s -> Lens' (PlanarSubdivision s v e f r) (FaceData (Dart s) f) Source #

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

Given a dart and the subdivision constructs the line segment representing it

$O(1)$

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

Reports all edges as line segments

rawFacePolygon :: FaceId' s -> PlanarSubdivision s v e f r -> SomePolygon v r :+ f Source #

Constructs the boundary of the given face

$O(k)$, where $k$ is the complexity of the face

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

Constructs the outer boundary of the face

$O(k)$, where $k$ is the complexity of the outer boundary of the face

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

Lists all *internal* faces of the planar subdivision.

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 _unVertexId :: Int

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 Methods toJSON :: VertexId s w -> Value # toEncoding :: VertexId s w -> Encoding # toJSONList :: [VertexId s w] -> Value # toEncodingList :: [VertexId s w] -> Encoding #
FromJSON (VertexId s w)
Instance details Defined in Data.PlanarGraph.Core Methods parseJSON :: Value -> Parser (VertexId s w) # parseJSONList :: Value -> Parser [VertexId s w] #
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-I7RuMNUQsKnHc7W9YnEfQ" '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 _unFaceId :: VertexId s (DualOf w)

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-I7RuMNUQsKnHc7W9YnEfQ" '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 #

rawVertexData :: forall k (s :: k) v e f r v. Lens (PlanarSubdivision (s :: k) v e f r) (PlanarSubdivision (s :: k) v e f r) (Vector (Raw s (VertexId' (Wrap s)) v)) (Vector (Raw s (VertexId' (Wrap s)) v)) Source #

rawDartData :: forall k (s :: k) v e f r e. Lens (PlanarSubdivision (s :: k) v e f r) (PlanarSubdivision (s :: k) v e f r) (Vector (Raw s (Dart (Wrap s)) e)) (Vector (Raw s (Dart (Wrap s)) e)) Source #

rawFaceData :: forall k (s :: k) v e f r f. Lens (PlanarSubdivision (s :: k) v e f r) (PlanarSubdivision (s :: k) v e f r) (Vector (RawFace s f)) (Vector (RawFace s f)) Source #

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

Lens to the facedata of the vertexdata themselves. The indices correspond to the vertexId's

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

lens to access the Dart Data

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

Lens to the facedata of the faces themselves. The indices correspond to the faceIds

dataVal :: Lens (Raw s ia a) (Raw s ia b) a b Source #

get the dataVal of a Raw

dartMapping :: PlanarSubdivision s v e f r -> Vector (Dart (Wrap s), Dart s) Source #

data Raw s ia a Source #

Helper type for the data that we store in a planar subdivision

Constructors

Raw
Fields _compId :: !(ComponentId s) _idxVal :: !ia _dataVal :: !a

Instances

Instances details

Functor (Raw s ia) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods fmap :: (a -> b) -> Raw s ia a -> Raw s ia b # (<$) :: a -> Raw s ia b -> Raw s ia a #
Foldable (Raw s ia) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods fold :: Monoid m => Raw s ia m -> m # foldMap :: Monoid m => (a -> m) -> Raw s ia a -> m # foldMap' :: Monoid m => (a -> m) -> Raw s ia a -> m # foldr :: (a -> b -> b) -> b -> Raw s ia a -> b # foldr' :: (a -> b -> b) -> b -> Raw s ia a -> b # foldl :: (b -> a -> b) -> b -> Raw s ia a -> b # foldl' :: (b -> a -> b) -> b -> Raw s ia a -> b # foldr1 :: (a -> a -> a) -> Raw s ia a -> a # foldl1 :: (a -> a -> a) -> Raw s ia a -> a # toList :: Raw s ia a -> [a] # null :: Raw s ia a -> Bool # length :: Raw s ia a -> Int # elem :: Eq a => a -> Raw s ia a -> Bool # maximum :: Ord a => Raw s ia a -> a # minimum :: Ord a => Raw s ia a -> a # sum :: Num a => Raw s ia a -> a # product :: Num a => Raw s ia a -> a #
Traversable (Raw s ia) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods traverse :: Applicative f => (a -> f b) -> Raw s ia a -> f (Raw s ia b) # sequenceA :: Applicative f => Raw s ia (f a) -> f (Raw s ia a) # mapM :: Monad m => (a -> m b) -> Raw s ia a -> m (Raw s ia b) # sequence :: Monad m => Raw s ia (m a) -> m (Raw s ia a) #
(Eq ia, Eq a) => Eq (Raw s ia a) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods (==) :: Raw s ia a -> Raw s ia a -> Bool # (/=) :: Raw s ia a -> Raw s ia a -> Bool #
(Show ia, Show a) => Show (Raw s ia a) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods showsPrec :: Int -> Raw s ia a -> ShowS # show :: Raw s ia a -> String # showList :: [Raw s ia a] -> ShowS #
Generic (Raw s ia a) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Associated Types type Rep (Raw s ia a) :: Type -> Type # Methods from :: Raw s ia a -> Rep (Raw s ia a) x # to :: Rep (Raw s ia a) x -> Raw s ia a #
(ToJSON ia, ToJSON a) => ToJSON (Raw s ia a) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods toJSON :: Raw s ia a -> Value # toEncoding :: Raw s ia a -> Encoding # toJSONList :: [Raw s ia a] -> Value # toEncodingList :: [Raw s ia a] -> Encoding #
(FromJSON ia, FromJSON a) => FromJSON (Raw s ia a) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw Methods parseJSON :: Value -> Parser (Raw s ia a) # parseJSONList :: Value -> Parser [Raw s ia a] #
type Rep (Raw s ia a) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Raw type Rep (Raw s ia a) = D1 ('MetaData "Raw" "Data.Geometry.PlanarSubdivision.Raw" "hgeometry-0.12.0.2-IMXeR0PuShPEjPCARytEWE" 'False) (C1 ('MetaCons "Raw" 'PrefixI 'True) (S1 ('MetaSel ('Just "_compId") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (ComponentId s)) :: (S1 ('MetaSel ('Just "_idxVal") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 ia) :: S1 ('MetaSel ('Just "_dataVal") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a))))