Data.KdMap.Dynamic

Usage

The KdMap is a variant of Data.KdTree.Dynamic.KdTree where each point in the tree is associated with some data. It is the dynamic variant of Data.KdMap.Static.KdMap.

Here's an example of interleaving point-value insertions and point queries using KdMap, where points are 3D points and values are Strings:

>>> let dkdm = singleton point3dAsList ((Point3D 0.0 0.0 0.0), "First")

>>> let dkdm' = insert dkdm ((Point3D 1.0 1.0 1.0), "Second")

>>> nearest dkdm' (Point3D 0.4 0.4 0.4)
(Point3D {x = 0.0, y = 0.0, z = 0.0}, "First")

>>> let dkdm'' = insert dkdm' ((Point3D 0.5 0.5 0.5), "Third")

>>> nearest dkdm'' (Point3D 0.4 0.4 0.4)
(Point3D {x = 0.5, y = 0.5, z = 0.5}, "Third")

Reference

Types

type PointAsListFn a p = p -> [a]

Converts a point of type p with axis values of type a into a list of axis values [a].

type SquaredDistanceFn a p = p -> p -> a

Returns the squared distance between two points of type p with axis values of type a.

data KdMap a p v

A dynamic k-d tree structure that stores points of type p with axis values of type a. Additionally, each point is associated with a value of type v.

Instances

Functor (KdMap a p)

Foldable (KdMap a p)

Traversable (KdMap a p)

(Show a, Show p, Show v) => Show (KdMap a p v)

Generic (KdMap a p v)

(NFData a, NFData p, NFData v) => NFData (KdMap a p v)

type Rep (KdMap a p v)

Dynamic k-d map construction

empty :: Real a => PointAsListFn a p -> KdMap a p v

Generates an empty KdMap with the default distance function.

singleton :: Real a => PointAsListFn a p -> (p, v) -> KdMap a p v

Generates a KdMap with a single point-value pair using the default distance function.

emptyWithDist :: PointAsListFn a p -> SquaredDistanceFn a p -> KdMap a p v

Generates an empty KdMap with a user-specified distance function.

singletonWithDist :: Real a => PointAsListFn a p -> SquaredDistanceFn a p -> (p, v) -> KdMap a p v

Generates a KdMap with a single point-value pair using a user-specified distance function.

Insertion

insert :: Real a => KdMap a p v -> p -> v -> KdMap a p v

Adds a given point-value pair to a KdMap.

Average time complexity per insert for n inserts: O(log^2(n)).

insertPair :: Real a => KdMap a p v -> (p, v) -> KdMap a p v

Same as insert, but takes point and value as a pair.

batchInsert :: Real a => KdMap a p v -> [(p, v)] -> KdMap a p v

Inserts a list of point-value pairs into the KdMap.

TODO: This will be made far more efficient than simply repeatedly inserting.

Query

nearest :: Real a => KdMap a p v -> p -> (p, v)

Given a KdMap and a query point, returns the point-value pair in the KdMap with the point nearest to the query.

Average time complexity: O(log^2(n)).

inRadius :: Real a => KdMap a p v -> a -> p -> [(p, v)]

Given a KdMap, a query point, and a radius, returns all point-value pairs in the KdTree with points within the given radius of the query point.

Points are not returned in any particular order.

Worst case time complexity: O(n) for n data points.

kNearest :: Real a => KdMap a p v -> Int -> p -> [(p, v)]

Given a KdMap, a query point, and a number k, returns the k point-value pairs with the nearest points to the query.

Neighbors are returned in order of increasing distance from query point.

Average time complexity: log(k) * log^2(n) for k nearest neighbors on a structure with n data points.

Worst case time complexity: n * log(k) for k nearest neighbors on a structure with n data points.

inRange

Arguments

:: Real a

=> KdMap a p v

-> p

lower bounds of range

-> p

upper bounds of range

-> [(p, v)]

point-value pairs within given range

Finds all point-value pairs in a KdMap with points within a given range, where the range is specified as a set of lower and upper bounds.

Points are not returned in any particular order.

Worst case time complexity: O(n) for n data points and a range that spans all the points.

assocs :: KdMap a p v -> [(p, v)]

Returns a list of all the point-value pairs in the KdMap.

Time complexity: O(n) for n data points.

keys :: KdMap a p v -> [p]

Returns all points in the KdMap.

Time complexity: O(n) for n data points.

elems :: KdMap a p v -> [v]

Returns all values in the KdMap.

Time complexity: O(n) for n data points.

null :: KdMap a p v -> Bool

Returns whether the KdMap is empty.

size :: KdMap a p v -> Int

Returns the number of elements in the KdMap.

Time complexity: O(1)

Folds

foldrWithKey :: ((p, v) -> b -> b) -> b -> KdMap a p v -> b

Performs a foldr over each point-value pair in the KdMap.

Utilities

defaultSqrDist :: Num a => PointAsListFn a p -> SquaredDistanceFn a p

A default implementation of squared distance given two points and a PointAsListFn.

Internal (for testing)

subtreeSizes :: KdMap a p v -> [Int]

Returns size of each internal k-d tree that makes up the dynamic structure. For internal testing use.