Safe Haskell | Safe |
---|---|

Language | Haskell2010 |

- type PointAsListFn a p = p -> [a]
- type SquaredDistanceFn a p = p -> p -> a
- data KdMap a p v
- empty :: Real a => PointAsListFn a p -> KdMap a p v
- emptyWithDist :: Real a => PointAsListFn a p -> SquaredDistanceFn a p -> KdMap a p v
- singleton :: Real a => PointAsListFn a p -> (p, v) -> KdMap a p v
- singletonWithDist :: Real a => PointAsListFn a p -> SquaredDistanceFn a p -> (p, v) -> KdMap a p v
- build :: Real a => PointAsListFn a p -> [(p, v)] -> KdMap a p v
- buildWithDist :: Real a => PointAsListFn a p -> SquaredDistanceFn a p -> [(p, v)] -> KdMap a p v
- insertUnbalanced :: Real a => KdMap a p v -> p -> v -> KdMap a p v
- batchInsertUnbalanced :: Real a => KdMap a p v -> [(p, v)] -> KdMap a p v
- nearest :: Real a => KdMap a p v -> p -> (p, v)
- inRadius :: Real a => KdMap a p v -> a -> p -> [(p, v)]
- kNearest :: Real a => KdMap a p v -> Int -> p -> [(p, v)]
- inRange :: Real a => KdMap a p v -> p -> p -> [(p, v)]
- assocs :: KdMap a p v -> [(p, v)]
- keys :: KdMap a p v -> [p]
- elems :: KdMap a p v -> [v]
- null :: KdMap a p v -> Bool
- size :: KdMap a p v -> Int
- foldrWithKey :: ((p, v) -> b -> b) -> b -> KdMap a p v -> b
- defaultSqrDist :: Num a => PointAsListFn a p -> SquaredDistanceFn a p
- data TreeNode a p v
- = TreeNode {
- _treeLeft :: TreeNode a p v
- _treePoint :: (p, v)
- _axisValue :: a
- _treeRight :: TreeNode a p v

- | Empty

- = TreeNode {
- isValid :: Real a => KdMap a p v -> Bool

# Usage

The `KdMap`

is a variant of `KdTree`

where each point in
the tree is associated with some data. When talking about `KdMap`

s,
we'll refer to the points and their associated data as the *points*
and *values* of the `KdMap`

, respectively. It might help to think
of `KdTree`

and `KdMap`

as being analogous to
`Set`

and `Map`

.

Suppose you wanted to perform point queries on a set of 3D points,
where each point is associated with a `String`

. Here's how to build
a `KdMap`

of the data and perform a nearest neighbor query (if this
doesn't make sense, start with the documentation for
`KdTree`

):

>>> let points = [(Point3d 0.0 0.0 0.0), (Point3d 1.0 1.0 1.0)] >>> let valueStrings = ["First", "Second"] >>> let pointValuePairs =`zip`

points valueStrings >>> let kdm =`build`

point3dAsList pointValuePairs >>>`nearest`

kdm (Point3d 0.1 0.1 0.1) [Point3d {x = 0.0, y = 0.0, z = 0.0}, "First"]

# Reference

## Types

type PointAsListFn a p = p -> [a] Source

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 Source

Returns the squared distance between two points of type
`p`

with axis values of type `a`

.

A *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`

.

*k*-d map construction

emptyWithDist :: Real a => PointAsListFn a p -> SquaredDistanceFn a p -> KdMap a p v Source

Builds an empty `KdMap`

using a user-specified squared distance
function.

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

Builds a `KdMap`

with a single point-value pair.

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

Builds a `KdMap`

with a single point-value pair and a
user-specified squared distance function.

build :: Real a => PointAsListFn a p -> [(p, v)] -> KdMap a p v Source

Builds a `KdTree`

from a list of pairs of points (of type p) and
values (of type v) using a default squared distance function
`defaultSqrDist`

.

Average complexity: *O(n * log(n))* for *n* data points.

Worst case time complexity: *O(n^2)* for *n* data points.

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

buildWithDist :: Real a => PointAsListFn a p -> SquaredDistanceFn a p -> [(p, v)] -> KdMap a p v Source

Builds a `KdMap`

from a list of pairs of points (of type p) and
values (of type v), using a user-specified squared distance
function.

Average time complexity: *O(n * log(n))* for *n* data points.

Worst case time complexity: *O(n^2)* for *n* data points.

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

insertUnbalanced :: Real a => KdMap a p v -> p -> v -> KdMap a p v Source

Inserts a point-value pair into a `KdMap`

. This can potentially
cause the internal tree structure to become unbalanced. If the tree
becomes too unbalanced, point queries will be very inefficient. If
you need to perform lots of point insertions on an already existing
*k*-d map, check out
`Data.KdMap.Dynamic.`

`KdMap`

.

Average complexity: *O(log(n))* for *n* data points.

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

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

Inserts a list of point-value pairs into a `KdMap`

. This can
potentially cause the internal tree structure to become unbalanced,
which leads to inefficient point queries.

Average complexity: *O(n * log(n))* for *n* data points.

Worst case time complexity: *O(n^2)* for *n* data points.

## Query

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

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(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.

:: 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.

TODO: Maybe use known bounds on entire tree structure to be able to automatically count whole portions of tree as being within given range.

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

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] Source

Returns all points in the `KdMap`

.

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

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

Returns all values in the `KdMap`

.

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

size :: KdMap a p v -> Int Source

Returns the number of point-value pairs in the `KdMap`

.

Time complexity: *O(1)*

## Folds

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

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

.

## Utilities

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

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

.

## Advanced

A node of a *k*-d tree structure that stores a point of type `p`

with axis values of type `a`

. Additionally, each point is
associated with a value of type `v`

. Note: users typically will not
need to use this type, but we export it just in case.

TreeNode | |

- _treeLeft :: TreeNode a p v
- _treePoint :: (p, v)
- _axisValue :: a
- _treeRight :: TreeNode a p v
| |

Empty |