Algorithms.Geometry.DelaunayTriangulation.Types

Defines some geometric types used in the delaunay triangulation

Documentation

type VertexID = Int

Rotating Right - rotate clockwise

type Vertex = CList VertexID

type Adj = IntMap (CList VertexID)

data Triangulation p r

Neighbours are stored in clockwise order: i.e. rotating right moves to the next clockwise neighbour.

Constructors

Triangulation

Fields

• _vertexIds :: Map (Point 2 r) VertexID
• _positions :: Vector (Point 2 r :+ p)
• _neighbours :: Vector (CList VertexID)

Instances

(Eq r, Eq p) => Eq (Triangulation p r)

Defined in Algorithms.Geometry.DelaunayTriangulation.Types

Methods

(==) :: Triangulation p r -> Triangulation p r -> Bool

(/=) :: Triangulation p r -> Triangulation p r -> Bool

(Show r, Show p) => Show (Triangulation p r)

Defined in Algorithms.Geometry.DelaunayTriangulation.Types

Methods

showsPrec :: Int -> Triangulation p r -> ShowS

show :: Triangulation p r -> String

showList :: [Triangulation p r] -> ShowS

type NumType (Triangulation p r)

Defined in Algorithms.Geometry.DelaunayTriangulation.Types

type NumType (Triangulation p r) = r

type Dimension (Triangulation p r)

Defined in Algorithms.Geometry.DelaunayTriangulation.Types

type Dimension (Triangulation p r) = 2

vertexIds :: forall p r. Lens' (Triangulation p r) (Map (Point 2 r) VertexID)

positions :: forall p r p. Lens (Triangulation p r) (Triangulation p r) (Vector ((:+) (Point 2 r) p)) (Vector ((:+) (Point 2 r) p))

neighbours :: forall p r. Lens' (Triangulation p r) (Vector (CList VertexID))

type Mapping p r = (Map (Point 2 r) VertexID, Vector (Point 2 r :+ p))

showDT :: (Show p, Show r) => Triangulation p r -> IO ()

triangulationEdges :: Triangulation p r -> [(Point 2 r :+ p, Point 2 r :+ p)]

tEdges :: Triangulation p r -> [(VertexID, VertexID)]

data ST a b c

Constructors

ST

Fields

• fst' :: !a
• snd' :: !b
• trd' :: !c

type ArcID = Int

type ST' a = ST (Map (VertexID, VertexID) ArcID) ArcID a

ST' is a strict triple (m,a,x) containing:

• m: a Map, mapping edges, represented by a pair of vertexId's (u,v) with u < v, to arcId's.
• a: the next available unused arcID
• x: the data value we are interested in computing

toPlanarSubdivision :: (Ord r, Fractional r) => proxy s -> Triangulation p r -> PlanarSubdivision s p () () r

convert the triangulation into a planarsubdivision

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

toPlaneGraph :: forall proxy s p r. proxy s -> Triangulation p r -> PlaneGraph s p () () r

convert the triangulation into a plane graph

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