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

Data.Geometry.PlanarSubdivision.Basic

Description

Description : Basic data types to represent a PlanarSubdivision

Synopsis

type VertexId' s = VertexId s Primal
type FaceId' s = 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 (Raw s (FaceId' (Wrap s)) f))
type family Wrap (s :: k) :: k where ...
type Component s r = PlaneGraph (Wrap s) (VertexId' s) (Dart s) (FaceData (Dart s) (FaceId' s)) r
data ComponentId s
data PolygonFaceData
- = Inside
- | Outside
data PlanarGraph s (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
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 :: Getter (PlanarGraph s w v e f) (PlanarGraph s (DualOf w) f e v)
components :: forall s v e f r r. Lens (PlanarSubdivision s v e f r) (PlanarSubdivision s 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 :: (Ord r, Fractional r) => 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 :: 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)
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 (w :: World) = VertexId {
- _unVertexId :: Int
}
newtype FaceId s w = FaceId {
- _unFaceId :: VertexId s (DualOf w)
}
data Dart s
data World
- = Primal
- | Dual
rawVertexData :: forall s v e f r v. Lens (PlanarSubdivision s v e f r) (PlanarSubdivision s v e f r) (Vector (Raw s (VertexId' (Wrap s)) v)) (Vector (Raw s (VertexId' (Wrap s)) v))
rawDartData :: forall s v e f r e. Lens (PlanarSubdivision s v e f r) (PlanarSubdivision s v e f r) (Vector (Raw s (Dart (Wrap s)) e)) (Vector (Raw s (Dart (Wrap s)) e))
rawFaceData :: forall s v e f r f. Lens (PlanarSubdivision s v e f r) (PlanarSubdivision s v e f r) (Vector (Raw s (FaceId' (Wrap s)) f)) (Vector (Raw s (FaceId' (Wrap 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 = VertexId s Primal Source #

Shorthand for vertices in the primal.

type FaceId' s = FaceId s Primal Source #

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

Bifunctor VertexData Source #
Instance details Defined in Data.PlaneGraph 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 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 Methods fold :: Monoid m => VertexData r m -> 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 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 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 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 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 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 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 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 type Rep (VertexData r v) = D1 (MetaData "VertexData" "Data.PlaneGraph" "hgeometry-0.8.0.0-2B18HmKepFxHOPvqiUEkND" 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

Bifunctor FaceData Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic 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.Basic 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.Basic Methods fold :: Monoid m => FaceData h m -> 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.Basic 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.Basic 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.Basic 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.Basic 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.Basic 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.Basic 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.Basic 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.Basic type Rep (FaceData h f) = D1 (MetaData "FaceData" "Data.Geometry.PlanarSubdivision.Basic" "hgeometry-0.8.0.0-2B18HmKepFxHOPvqiUEkND" 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 (Raw s (FaceId' (Wrap s)) f))

Instances

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) :: Type Source # Methods dataOf :: FaceId' s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (FaceId' s)) Source #
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) :: Type Source # Methods dataOf :: Dart s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (Dart s)) Source #
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) :: Type Source # Methods dataOf :: VertexId' s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (VertexId' s)) Source #
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-0.8.0.0-2B18HmKepFxHOPvqiUEkND" 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 (Raw s (FaceId' (Wrap 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) (FaceData (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 #

Instances

Bounded (ComponentId s) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic Methods minBound :: ComponentId s # maxBound :: ComponentId s #
Enum (ComponentId s) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic 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.Basic Methods (==) :: ComponentId s -> ComponentId s -> Bool # (/=) :: ComponentId s -> ComponentId s -> Bool #
Ord (ComponentId s) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic 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.Basic 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.Basic 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.Basic 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.Basic Methods parseJSON :: Value -> Parser (ComponentId s) # parseJSONList :: Value -> Parser [ComponentId s] #
type Rep (ComponentId s) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic type Rep (ComponentId s) = D1 (MetaData "ComponentId" "Data.Geometry.PlanarSubdivision.Basic" "hgeometry-0.8.0.0-2B18HmKepFxHOPvqiUEkND" 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

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 (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 details Defined in Data.PlanarGraph 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 details Defined in Data.PlanarGraph 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) Source #
Instance details Defined in Data.PlanarGraph 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 #
(ToJSON v, ToJSON e, ToJSON f) => ToJSON (PlanarGraph s w v e f) Source #
Instance details Defined in Data.PlanarGraph Methods toJSON :: 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 details Defined in Data.PlanarGraph Methods parseJSON :: 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 details Defined in Data.PlanarGraph Associated Types type DataOf (PlanarGraph s w v e f) (Dart s) :: Type Source # Methods dataOf :: 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) (VertexId s w) Source #
Instance details Defined in Data.PlanarGraph Associated Types type DataOf (PlanarGraph s w v e f) (VertexId s w) :: Type Source # Methods dataOf :: VertexId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (VertexId s w)) Source #
HasDataOf (PlanarGraph s w v e f) (FaceId s w) Source #
Instance details Defined in Data.PlanarGraph Associated Types type DataOf (PlanarGraph s w v e f) (FaceId s w) :: Type Source # Methods dataOf :: FaceId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (FaceId s w)) Source #
type Rep (PlanarGraph s w v e f) Source #
Instance details Defined in Data.PlanarGraph type Rep (PlanarGraph s w v e f) = D1 (MetaData "PlanarGraph" "Data.PlanarGraph" "hgeometry-0.8.0.0-2B18HmKepFxHOPvqiUEkND" 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 details Defined in Data.PlanarGraph type DataOf (PlanarGraph s w v e f) (Dart s) = e
type DataOf (PlanarGraph s w v e f) (VertexId s w) Source #
Instance details Defined in Data.PlanarGraph type DataOf (PlanarGraph s w v e f) (VertexId s w) = v
type DataOf (PlanarGraph s w v e f) (FaceId s w) Source #
Instance details Defined in Data.PlanarGraph 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

Functor (PlaneGraph s v e f) Source #
Instance details Defined in Data.PlaneGraph 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 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 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 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 r, ToJSON v, ToJSON e, ToJSON f) => ToJSON (PlaneGraph s v e f r) Source #
Instance details Defined in Data.PlaneGraph 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 r, FromJSON v, FromJSON e, FromJSON f) => FromJSON (PlaneGraph s v e f r) Source #
Instance details Defined in Data.PlaneGraph 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 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 Associated Types type DataOf (PlaneGraph s v e f r) (FaceId' s) :: Type Source # Methods dataOf :: FaceId' s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (FaceId' s)) Source #
HasDataOf (PlaneGraph s v e f r) (Dart s) Source #
Instance details Defined in Data.PlaneGraph Associated Types type DataOf (PlaneGraph s v e f r) (Dart s) :: Type Source # Methods dataOf :: Dart s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (Dart s)) Source #
HasDataOf (PlaneGraph s v e f r) (VertexId' s) Source #
Instance details Defined in Data.PlaneGraph Associated Types type DataOf (PlaneGraph s v e f r) (VertexId' s) :: Type Source # Methods dataOf :: VertexId' s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (VertexId' s)) Source #
type Rep (PlaneGraph s v e f r) Source #
Instance details Defined in Data.PlaneGraph type Rep (PlaneGraph s v e f r) = D1 (MetaData "PlaneGraph" "Data.PlaneGraph" "hgeometry-0.8.0.0-2B18HmKepFxHOPvqiUEkND" 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 type NumType (PlaneGraph s v e f r) = r
type Dimension (PlaneGraph s v e f r) Source #
Instance details Defined in Data.PlaneGraph 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 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 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 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 planar subdivision from a simple polygon

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: $O(n)$

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 #

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

Get the dual graph of this graph.

components :: forall s v e f r r. Lens (PlanarSubdivision s v e f r) (PlanarSubdivision s 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 #

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

internalFaces :: (Ord r, Fractional r) => 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 :: 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

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

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

All outgoing edges incident to vertex v, in counterclockwise order around 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 in clockwise order, for the outer face in counter clockwise 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.

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 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 details Defined in Data.PlanarGraph Associated Types type DataOf (PlanarGraph s w v e f) (Dart s) :: Type Source # Methods dataOf :: Dart s -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (Dart s)) Source #
HasDataOf (PlaneGraph s v e f r) (FaceId' s) Source #
Instance details Defined in Data.PlaneGraph Associated Types type DataOf (PlaneGraph s v e f r) (FaceId' s) :: Type Source # Methods dataOf :: FaceId' s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (FaceId' s)) Source #
HasDataOf (PlaneGraph s v e f r) (Dart s) Source #
Instance details Defined in Data.PlaneGraph Associated Types type DataOf (PlaneGraph s v e f r) (Dart s) :: Type Source # Methods dataOf :: Dart s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (Dart s)) Source #
HasDataOf (PlaneGraph s v e f r) (VertexId' s) Source #
Instance details Defined in Data.PlaneGraph Associated Types type DataOf (PlaneGraph s v e f r) (VertexId' s) :: Type Source # Methods dataOf :: VertexId' s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (VertexId' s)) 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) :: Type Source # Methods dataOf :: FaceId' s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (FaceId' s)) Source #
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) :: Type Source # Methods dataOf :: Dart s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (Dart s)) Source #
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) :: Type Source # Methods dataOf :: VertexId' s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (VertexId' s)) Source #
HasDataOf (PlanarGraph s w v e f) (VertexId s w) Source #
Instance details Defined in Data.PlanarGraph Associated Types type DataOf (PlanarGraph s w v e f) (VertexId s w) :: Type Source # Methods dataOf :: VertexId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (VertexId s w)) Source #
HasDataOf (PlanarGraph s w v e f) (FaceId s w) Source #
Instance details Defined in Data.PlanarGraph Associated Types type DataOf (PlanarGraph s w v e f) (FaceId s w) :: Type Source # Methods dataOf :: FaceId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (FaceId s w)) Source #

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: $O(1)$

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 faces of the planar subdivision.

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 details Defined in Data.PlanarGraph 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) Source #
Instance details Defined in Data.PlanarGraph Methods (==) :: VertexId s w -> VertexId s w -> Bool # (/=) :: VertexId s w -> VertexId s w -> Bool #
Ord (VertexId s w) Source #
Instance details Defined in Data.PlanarGraph 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) Source #
Instance details Defined in Data.PlanarGraph Methods showsPrec :: Int -> VertexId s w -> ShowS # show :: VertexId s w -> String # showList :: [VertexId s w] -> ShowS #
Generic (VertexId s w) Source #
Instance details Defined in Data.PlanarGraph 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) Source #
Instance details Defined in Data.PlanarGraph 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) Source #
Instance details Defined in Data.PlanarGraph Methods parseJSON :: Value -> Parser (VertexId s w) # parseJSONList :: Value -> Parser [VertexId s w] #
NFData (VertexId s w) Source #
Instance details Defined in Data.PlanarGraph Methods rnf :: VertexId s w -> () #
HasDataOf (PlaneGraph s v e f r) (VertexId' s) Source #
Instance details Defined in Data.PlaneGraph Associated Types type DataOf (PlaneGraph s v e f r) (VertexId' s) :: Type Source # Methods dataOf :: VertexId' s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (VertexId' s)) Source #
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) :: Type Source # Methods dataOf :: VertexId' s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (VertexId' s)) Source #
HasDataOf (PlanarGraph s w v e f) (VertexId s w) Source #
Instance details Defined in Data.PlanarGraph Associated Types type DataOf (PlanarGraph s w v e f) (VertexId s w) :: Type Source # Methods dataOf :: 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 details Defined in Data.PlanarGraph type Rep (VertexId s w) = D1 (MetaData "VertexId" "Data.PlanarGraph" "hgeometry-0.8.0.0-2B18HmKepFxHOPvqiUEkND" 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 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) Source #
Instance details Defined in Data.PlanarGraph type DataOf (PlanarGraph s w v e f) (VertexId s w) = v

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 details Defined in Data.PlanarGraph 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) Source #
Instance details Defined in Data.PlanarGraph Methods (==) :: FaceId s w -> FaceId s w -> Bool # (/=) :: FaceId s w -> FaceId s w -> Bool #
Ord (FaceId s w) Source #
Instance details Defined in Data.PlanarGraph 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) Source #
Instance details Defined in Data.PlanarGraph Methods showsPrec :: Int -> FaceId s w -> ShowS # show :: FaceId s w -> String # showList :: [FaceId s w] -> ShowS #
ToJSON (FaceId s w) Source #
Instance details Defined in Data.PlanarGraph 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) Source #
Instance details Defined in Data.PlanarGraph 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 Associated Types type DataOf (PlaneGraph s v e f r) (FaceId' s) :: Type Source # Methods dataOf :: FaceId' s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (FaceId' s)) 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) :: Type Source # Methods dataOf :: FaceId' s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (FaceId' s)) Source #
HasDataOf (PlanarGraph s w v e f) (FaceId s w) Source #
Instance details Defined in Data.PlanarGraph Associated Types type DataOf (PlanarGraph s w v e f) (FaceId s w) :: Type Source # Methods dataOf :: FaceId s w -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (FaceId s w)) Source #
type DataOf (PlaneGraph s v e f r) (FaceId' s) Source #
Instance details Defined in Data.PlaneGraph 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) Source #
Instance details Defined in Data.PlanarGraph type DataOf (PlanarGraph s w v e f) (FaceId s w) = f

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.

Instances

Enum (Dart s) Source #
Instance details Defined in Data.PlanarGraph 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) Source #
Instance details Defined in Data.PlanarGraph Methods (==) :: Dart s -> Dart s -> Bool # (/=) :: Dart s -> Dart s -> Bool #
Ord (Dart s) Source #
Instance details Defined in Data.PlanarGraph 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) Source #
Instance details Defined in Data.PlanarGraph Methods showsPrec :: Int -> Dart s -> ShowS # show :: Dart s -> String # showList :: [Dart s] -> ShowS #
Generic (Dart s) Source #
Instance details Defined in Data.PlanarGraph 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) Source #
Instance details Defined in Test.QuickCheck.HGeometryInstances Methods arbitrary :: Gen (Dart s) # shrink :: Dart s -> [Dart s] #
NFData (Dart s) Source #
Instance details Defined in Data.PlanarGraph Methods rnf :: Dart s -> () #
HasDataOf (PlanarGraph s w v e f) (Dart s) Source #
Instance details Defined in Data.PlanarGraph Associated Types type DataOf (PlanarGraph s w v e f) (Dart s) :: Type Source # Methods dataOf :: Dart s -> Lens' (PlanarGraph s w v e f) (DataOf (PlanarGraph s w v e f) (Dart s)) Source #
HasDataOf (PlaneGraph s v e f r) (Dart s) Source #
Instance details Defined in Data.PlaneGraph Associated Types type DataOf (PlaneGraph s v e f r) (Dart s) :: Type Source # Methods dataOf :: Dart s -> Lens' (PlaneGraph s v e f r) (DataOf (PlaneGraph s v e f r) (Dart s)) Source #
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) :: Type Source # Methods dataOf :: Dart s -> Lens' (PlanarSubdivision s v e f r) (DataOf (PlanarSubdivision s v e f r) (Dart s)) Source #
type Rep (Dart s) Source #
Instance details Defined in Data.PlanarGraph type Rep (Dart s) = D1 (MetaData "Dart" "Data.PlanarGraph" "hgeometry-0.8.0.0-2B18HmKepFxHOPvqiUEkND" 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 details Defined in Data.PlanarGraph 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 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 Source #

The world in which the graph lives

Constructors

Primal
Dual

Instances

Eq World Source #
Instance details Defined in Data.PlanarGraph Methods (==) :: World -> World -> Bool # (/=) :: World -> World -> Bool #
Show World Source #
Instance details Defined in Data.PlanarGraph Methods showsPrec :: Int -> World -> ShowS # show :: World -> String # showList :: [World] -> ShowS #

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

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

rawFaceData :: forall s v e f r f. Lens (PlanarSubdivision s v e f r) (PlanarSubdivision s v e f r) (Vector (Raw s (FaceId' (Wrap s)) f)) (Vector (Raw s (FaceId' (Wrap 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 #

Constructors

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

Instances

Functor (Raw s ia) Source #
Instance details Defined in Data.Geometry.PlanarSubdivision.Basic 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.Basic Methods fold :: Monoid m => Raw s ia m -> 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.Basic 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.Basic 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.Basic 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.Basic 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.Basic 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.Basic 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.Basic type Rep (Raw s ia a) = D1 (MetaData "Raw" "Data.Geometry.PlanarSubdivision.Basic" "hgeometry-0.8.0.0-2B18HmKepFxHOPvqiUEkND" 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))))