kd-tree

k-dimensional tree in Rust.

Fast, simple, and easy to use.

Usage

// construct kd-tree
let kdtree = kd_tree::KdTree::build_by_ordered_float(vec![
    [1.0, 2.0, 3.0],
    [3.0, 1.0, 2.0],
    [2.0, 3.0, 1.0],
]);

// search the nearest neighbor
let found = kdtree.nearest(&[3.1, 0.9, 2.1]).unwrap();
assert_eq!(found.item, &[3.0, 1.0, 2.0]);

// search k-nearest neighbors
let found = kdtree.nearests(&[1.5, 2.5, 1.8], 2);
assert_eq!(found[0].item, &[2.0, 3.0, 1.0]);
assert_eq!(found[1].item, &[1.0, 2.0, 3.0]);

// search points within a sphere
let found = kdtree.within_radius(&[2.0, 1.5, 2.5], 1.5);
assert_eq!(found.len(), 2);
assert!(found.iter().any(|&&p| p == [1.0, 2.0, 3.0]));
assert!(found.iter().any(|&&p| p == [3.0, 1.0, 2.0]));

With or without KdPoint

KdPoint trait represents k-dimensional point.

You can live with or without KdPoint.

With KdPoint explicitly

use kd_tree::{KdPoint, KdTree};

// define your own item type.
struct Item {
    point: [f64; 2],
    id: usize,
}

// implement `KdPoint` for your item type.
impl KdPoint for Item {
    type Scalar = f64;
    type Dim = typenum::U2; // 2 dimensional tree.
    fn at(&self, k: usize) -> f64 { self.point[k] }
}

// construct kd-tree from `Vec<Item>`.
// Note: you need to use `build_by_ordered_float()` because f64 doesn't implement `Ord` trait.
let kdtree: KdTree<Item> = KdTree::build_by_ordered_float(vec![
    Item { point: [1.0, 2.0], id: 111 },
    Item { point: [2.0, 3.0], id: 222 },
    Item { point: [3.0, 4.0], id: 333 },
]);

// search nearest item from [1.9, 3.1]
assert_eq!(kdtree.nearest(&[1.9, 3.1]).unwrap().item.id, 222);

With KdPoint implicitly

KdPoint trait is implemented for fixed-sized array of numerical types, such as [f64; 3] or [i32, 2] etc. So you can build kd-trees of those types without custom implementation of KdPoint.

let items: Vec<[i32; 3]> = vec![[1, 2, 3], [3, 1, 2], [2, 3, 1]];
let kdtree = kd_tree::KdTree::build(items);
assert_eq!(kdtree.nearest(&[3, 1, 2]).unwrap().item, &[3, 1, 2]);

KdPoint trait is also implemented for tuple of a KdPoint and an arbitrary type, like (P, T) where P: KdPoint. And a type alias named KdMap<P, T> is defined as KdTree<(P, T)>. So you can build a kd-tree from key-value pairs, as below:

let kdmap: kd_tree::KdMap<[isize; 3], &'static str> = kd_tree::KdMap::build(vec![
    ([1, 2, 3], "foo"),
    ([2, 3, 1], "bar"),
    ([3, 1, 2], "buzz"),
]);
assert_eq!(kdmap.nearest(&[3, 1, 2]).unwrap().item.1, "buzz");

nalgebra feature

KdPoint trait is implemented for nalgebra's vectors and points.

Enable nalgebra feature in your Cargo.toml:

kd-tree = { version = "...", features = ["nalgebra"] }

Then, you can use it as follows:

use nalgebra::Point3;
let items: Vec<Point3<i32>> = vec![
    Point3::new(1, 2, 3),
    Point3::new(3, 1, 2),
    Point3::new(2, 3, 1)
];
let kdtree = kd_tree::KdTree::build(items);
let query = Point3::new(3, 1, 2);
assert_eq!(kdtree.nearest(&query).unwrap().item, &query);

Without KdPoint

use std::collections::HashMap;
let items: HashMap<&'static str, [i32; 2]> = vec![
    ("a", [10, 20]),
    ("b", [20, 10]),
    ("c", [20, 20]),
].into_iter().collect();
let kdtree = kd_tree::KdTree2::build_by_key(items.keys().collect(), |key, k| items[*key][k]);
assert_eq!(kdtree.nearest_by(&[18, 21], |key, k| items[*key][k]).unwrap().item, &&"c");

To own, or not to own

KdSliceN<T, N> and KdTreeN<T, N> are similar to str and String, or Path and PathBuf.

• KdSliceN<T, N> doesn't own its buffer, but KdTreeN<T, N>.
• KdSliceN<T, N> is not Sized, so it must be dealed in reference mannar.
• KdSliceN<T, N> implements Deref to [T].
• KdTreeN<T, N> implements Deref to KdSliceN<T, N>.
• Unlike PathBuf or String, which are mutable, KdTreeN<T, N> is immutable.

&KdSliceN<T, N> can be constructed directly, not via KdTreeN, as below:

let mut items: Vec<[i32; 3]> = vec![[1, 2, 3], [3, 1, 2], [2, 3, 1]];
let kdtree = kd_tree::KdSlice::sort(&mut items);
assert_eq!(kdtree.nearest(&[3, 1, 2]).unwrap().item, &[3, 1, 2]);

KdIndexTreeN

A KdIndexTreeN refers a slice of items, [T], and contains kd-tree of indices to the items, KdTreeN<usize, N>. Unlike KdSlice::sort, KdIndexTree::build doesn't sort input items.

let items = vec![[1, 2, 3], [3, 1, 2], [2, 3, 1]];
let kdtree = kd_tree::KdIndexTree::build(&items);
assert_eq!(kdtree.nearest(&[3, 1, 2]).unwrap().item, &1); // nearest() returns an index of found item.

Features

"serde" feature

[dependencies]
kd-tree = { version = "...", features = ["serde"] }

You can serialize/deserialize KdTree<{serializable type}> with this feature.

let src: KdTree3<[i32; 3]> = KdTree::build(vec![[1, 2, 3], [4, 5, 6]]);

let json = serde_json::to_string(&src).unwrap();
assert_eq!(json, "[[1,2,3],[4,5,6]]");

let dst: KdTree3<[i32; 3]> = serde_json::from_str(&json).unwrap();
assert_eq!(src, dst);

"nalgebra" feature

[dependencies]
kd-tree = { version = "...", features = ["nalgebra"] }

see above

"nalgebra-serde" feature

[dependencies]
kd-tree = { version = "...", features = ["nalgebra-serde"] }

You can serialize/deserialize KdTree<{nalgebra type}> with this feature.

use ::nalgebra as na;

let src: KdTree<na::Point3<f64>> = KdTree::build_by_ordered_float(vec![
    na::Point3::new(1.0, 2.0, 3.0),
    na::Point3::new(4.0, 5.0, 6.0),
]);

let json = serde_json::to_string(&src).unwrap();
assert_eq!(json, "[[1.0,2.0,3.0],[4.0,5.0,6.0]]");

let dst: KdTree3<na::Point3<f64>> = serde_json::from_str(&json).unwrap();
assert_eq!(src, dst);

"rayon" feature

[dependencies]
kd-tree = { version = "...", features = ["rayon"] }

You can build a kd-tree faster with rayon.

let kdtree = KdTree::par_build_by_ordered_float(vec![...]);

License

This library is distributed under the MIT License.