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//! k-dimensional tree. //! //! # 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])); //! ``` mod nearest; mod nearests; mod sort; mod tests; mod within; use nearest::*; use nearests::*; use sort::*; use std::cmp::Ordering; use std::marker::PhantomData; use typenum::Unsigned; use within::*; /// A trait to represent k-dimensional point. /// /// # Example /// ``` /// struct MyItem { /// point: [f64; 3], /// id: usize, /// } /// impl kd_tree::KdPoint for MyItem { /// type Scalar = f64; /// type Dim = typenum::U3; /// fn at(&self, k: usize) -> f64 { self.point[k] } /// } /// let kdtree: kd_tree::KdTree<MyItem> = kd_tree::KdTree::build_by_ordered_float(vec![ /// MyItem { point: [1.0, 2.0, 3.0], id: 111 }, /// MyItem { point: [3.0, 1.0, 2.0], id: 222 }, /// MyItem { point: [2.0, 3.0, 1.0], id: 333 }, /// ]); /// assert_eq!(kdtree.nearest(&[3.1, 0.1, 2.2]).unwrap().item.id, 222); /// ``` pub trait KdPoint { type Scalar: num_traits::NumAssign + Copy + PartialOrd; type Dim: Unsigned; fn dim() -> usize { <Self::Dim as Unsigned>::to_usize() } fn at(&self, i: usize) -> Self::Scalar; } #[derive(Debug, Clone, Copy, PartialEq, Eq)] pub struct ItemAndDistance<'a, T, Scalar> { pub item: &'a T, pub squared_distance: Scalar, } /// A slice of kd-tree. /// This type implements [`std::ops::Deref`] to `[T]`. /// This is an unsized type, meaning that it must always be used as a reference. /// For an owned version of this type, see [`KdTree`]. #[derive(Debug, PartialEq, Eq)] pub struct KdSliceN<T, N: Unsigned>(PhantomData<N>, [T]); pub type KdSlice<T> = KdSliceN<T, <T as KdPoint>::Dim>; impl<T, N: Unsigned> std::ops::Deref for KdSliceN<T, N> { type Target = [T]; fn deref(&self) -> &[T] { &self.1 } } impl<T: Clone, N: Unsigned> std::borrow::ToOwned for KdSliceN<T, N> { type Owned = KdTreeN<T, N>; fn to_owned(&self) -> Self::Owned { KdTreeN(PhantomData, self.1.to_vec()) } } impl<T, N: Unsigned> KdSliceN<T, N> { pub fn items(&self) -> &[T] { &self.1 } unsafe fn new_unchecked(items: &[T]) -> &Self { &*(items as *const _ as *const Self) } /// # Example /// ``` /// struct Item { /// point: [i32; 3], /// id: usize, /// } /// let mut items: Vec<Item> = vec![ /// Item { point: [1, 2, 3], id: 111 }, /// Item { point: [3, 1, 2], id: 222 }, /// Item { point: [2, 3, 1], id: 333 }, /// ]; /// let kdtree = kd_tree::KdSlice3::sort_by(&mut items, |item1, item2, k| item1.point[k].cmp(&item2.point[k])); /// assert_eq!(kdtree.nearest_by(&[3, 1, 2], |item, k| item.point[k]).unwrap().item.id, 222); /// ``` pub fn sort_by<F>(items: &mut [T], compare: F) -> &Self where F: Fn(&T, &T, usize) -> Ordering + Copy, { kd_sort_by(items, N::to_usize(), compare); unsafe { Self::new_unchecked(items) } } /// # Example /// ``` /// struct Item { /// point: [f64; 3], /// id: usize, /// } /// let mut items: Vec<Item> = vec![ /// Item { point: [1.0, 2.0, 3.0], id: 111 }, /// Item { point: [3.0, 1.0, 2.0], id: 222 }, /// Item { point: [2.0, 3.0, 1.0], id: 333 }, /// ]; /// use ordered_float::OrderedFloat; /// let kdtree = kd_tree::KdSlice3::sort_by_key(&mut items, |item, k| OrderedFloat(item.point[k])); /// assert_eq!(kdtree.nearest_by(&[3.1, 0.9, 2.1], |item, k| item.point[k]).unwrap().item.id, 222); /// ``` pub fn sort_by_key<Key: Ord, F>(items: &mut [T], kd_key: F) -> &Self where F: Fn(&T, usize) -> Key + Copy, { Self::sort_by(items, |item1, item2, k| { kd_key(item1, k).cmp(&kd_key(item2, k)) }) } /// # Example /// ``` /// use kd_tree::KdSlice; /// let mut items: Vec<[f64; 3]> = vec![[1.0, 2.0, 3.0], [3.0, 1.0, 2.0], [2.0, 3.0, 1.0]]; /// let kdtree: &KdSlice<[f64; 3]> = KdSlice::sort_by_ordered_float(&mut items); /// assert_eq!(kdtree.nearest(&[3.1, 0.9, 2.1]).unwrap().item, &[3.0, 1.0, 2.0]); /// ``` pub fn sort_by_ordered_float(points: &mut [T]) -> &Self where T: KdPoint<Dim = N>, T::Scalar: num_traits::Float, { Self::sort_by_key(points, |item, k| ordered_float::OrderedFloat(item.at(k))) } /// # Example /// ``` /// use kd_tree::KdSlice; /// let mut items: Vec<[i32; 3]> = vec![[1, 2, 3], [3, 1, 2], [2, 3, 1]]; /// let kdtree: &KdSlice<[i32; 3]> = KdSlice::sort(&mut items); /// assert_eq!(kdtree.nearest(&[3, 1, 2]).unwrap().item, &[3, 1, 2]); /// ``` pub fn sort(points: &mut [T]) -> &Self where T: KdPoint<Dim = N>, T::Scalar: Ord, { Self::sort_by_key(points, |item, k| item.at(k)) } /// Returns the nearest item from the input point. Returns `None` if `self.is_empty()`. /// # Example /// ``` /// struct Item { /// point: [f64; 3], /// id: usize, /// } /// let mut items: Vec<Item> = vec![ /// Item { point: [1.0, 2.0, 3.0], id: 111 }, /// Item { point: [3.0, 1.0, 2.0], id: 222 }, /// Item { point: [2.0, 3.0, 1.0], id: 333 }, /// ]; /// use ordered_float::OrderedFloat; /// let kdtree = kd_tree::KdSlice3::sort_by_key(&mut items, |item, k| OrderedFloat(item.point[k])); /// assert_eq!(kdtree.nearest_by(&[3.1, 0.9, 2.1], |item, k| item.point[k]).unwrap().item.id, 222); /// ``` pub fn nearest_by<Q: KdPoint<Dim = N>>( &self, query: &Q, coord: impl Fn(&T, usize) -> Q::Scalar + Copy, ) -> Option<ItemAndDistance<T, Q::Scalar>> { if self.is_empty() { None } else { Some(kd_nearest_by(self.items(), query, coord)) } } /// Returns the nearest item from the input point. Returns `None` if `self.is_empty()`. /// # Example /// ``` /// 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]); /// ``` pub fn nearest( &self, query: &impl KdPoint<Scalar = T::Scalar, Dim = N>, ) -> Option<ItemAndDistance<T, T::Scalar>> where T: KdPoint<Dim = N>, { if self.is_empty() { None } else { Some(kd_nearest(self.items(), query)) } } /* /// # Example /// ``` /// let kdtree = kd_tree::KdTree3::build(vec![[1, 2, 3], [3, 1, 2], [2, 3, 1]]); /// let key = [3, 1, 2]; /// assert_eq!(kdtree.nearest_with(|p, k| key[k] - p[k]).item, &[3, 1, 2]); /// ``` pub fn nearest_with<Scalar>( &self, kd_difference: impl Fn(&T, usize) -> Scalar + Copy, ) -> ItemAndDistance<T, Scalar> where Scalar: num_traits::NumAssign + Copy + PartialOrd, { kd_nearest_with(self.items(), N::to_usize(), kd_difference) } */ /// Returns the nearest item from the input point. Returns `None` if `self.is_empty()`. /// # Example /// ``` /// struct Item { /// point: [f64; 3], /// id: usize, /// } /// let mut items: Vec<Item> = vec![ /// Item { point: [1.0, 2.0, 3.0], id: 111 }, /// Item { point: [3.0, 1.0, 2.0], id: 222 }, /// Item { point: [2.0, 3.0, 1.0], id: 333 }, /// ]; /// use ordered_float::OrderedFloat; /// let kdtree = kd_tree::KdSlice3::sort_by_key(&mut items, |item, k| OrderedFloat(item.point[k])); /// let nearests = kdtree.nearests_by(&[2.5, 2.0, 1.4], 2, |item, k| item.point[k]); /// assert_eq!(nearests.len(), 2); /// assert_eq!(nearests[0].item.id, 333); /// assert_eq!(nearests[1].item.id, 222); /// ``` pub fn nearests_by<Q: KdPoint<Dim = N>>( &self, query: &Q, num: usize, coord: impl Fn(&T, usize) -> Q::Scalar + Copy, ) -> Vec<ItemAndDistance<T, Q::Scalar>> { kd_nearests_by(self.items(), query, num, coord) } /// Returns kNN(k nearest neighbors) from the input point. /// # Example /// ``` /// let mut items: Vec<[i32; 3]> = vec![[1, 2, 3], [3, 1, 2], [2, 3, 1], [3, 2, 2]]; /// let kdtree = kd_tree::KdSlice::sort(&mut items); /// let nearests = kdtree.nearests(&[3, 1, 2], 2); /// assert_eq!(nearests.len(), 2); /// assert_eq!(nearests[0].item, &[3, 1, 2]); /// assert_eq!(nearests[1].item, &[3, 2, 2]); /// ``` pub fn nearests( &self, query: &impl KdPoint<Scalar = T::Scalar, Dim = N>, num: usize, ) -> Vec<ItemAndDistance<T, T::Scalar>> where T: KdPoint<Dim = N>, { kd_nearests(self.items(), query, num) } pub fn within_by_cmp(&self, compare: impl Fn(&T, usize) -> Ordering + Copy) -> Vec<&T> { kd_within_by_cmp(&self, N::to_usize(), compare) } pub fn within_by<Q: KdPoint<Dim = N>>( &self, query: &[Q; 2], coord: impl Fn(&T, usize) -> Q::Scalar + Copy, ) -> Vec<&T> { assert!((0..Q::dim()).all(|k| query[0].at(k) <= query[1].at(k))); self.within_by_cmp(|item, k| { let a = coord(item, k); if a < query[0].at(k) { Ordering::Less } else if a > query[1].at(k) { Ordering::Greater } else { Ordering::Equal } }) } /// search points within a rectangular region pub fn within(&self, query: &[impl KdPoint<Scalar = T::Scalar, Dim = N>; 2]) -> Vec<&T> where T: KdPoint<Dim = N>, { self.within_by(query, |item, k| item.at(k)) } pub fn within_radius_by<Q: KdPoint<Dim = N>>( &self, query: &Q, radius: Q::Scalar, coord: impl Fn(&T, usize) -> Q::Scalar + Copy, ) -> Vec<&T> { let mut results = self.within_by_cmp(|item, k| { let coord = coord(item, k); if coord < query.at(k) - radius { Ordering::Less } else if coord > query.at(k) + radius { Ordering::Greater } else { Ordering::Equal } }); results.retain(|item| { let mut distance = <Q::Scalar as num_traits::Zero>::zero(); for k in 0..N::to_usize() { let diff = coord(item, k) - query.at(k); distance += diff * diff; } distance < radius * radius }); results } /// search points within k-dimensional sphere pub fn within_radius( &self, query: &impl KdPoint<Scalar = T::Scalar, Dim = N>, radius: T::Scalar, ) -> Vec<&T> where T: KdPoint<Dim = N>, { self.within_radius_by(query, radius, |item, k| item.at(k)) } } /// An owned kd-tree. /// This type implements [`std::ops::Deref`] to [`KdSlice`]. #[derive(Debug, Clone, PartialEq, Eq, Default)] pub struct KdTreeN<T, N: Unsigned>(PhantomData<N>, Vec<T>); pub type KdTree<T> = KdTreeN<T, <T as KdPoint>::Dim>; impl<T, N: Unsigned> std::ops::Deref for KdTreeN<T, N> { type Target = KdSliceN<T, N>; fn deref(&self) -> &Self::Target { unsafe { KdSliceN::new_unchecked(&self.1) } } } impl<T, N: Unsigned> AsRef<KdSliceN<T, N>> for KdTreeN<T, N> { fn as_ref(&self) -> &KdSliceN<T, N> { self } } impl<T, N: Unsigned> std::borrow::Borrow<KdSliceN<T, N>> for KdTreeN<T, N> { fn borrow(&self) -> &KdSliceN<T, N> { self } } impl<T, N: Unsigned> Into<Vec<T>> for KdTreeN<T, N> { fn into(self) -> Vec<T> { self.1 } } impl<T, N: Unsigned> KdTreeN<T, N> { pub fn into_vec(self) -> Vec<T> { self.1 } /// # Example /// ``` /// struct Item { /// point: [i32; 3], /// id: usize, /// } /// let kdtree = kd_tree::KdTree3::build_by( /// vec![ /// Item { point: [1, 2, 3], id: 111 }, /// Item { point: [3, 1, 2], id: 222 }, /// Item { point: [2, 3, 1], id: 333 }, /// ], /// |item1, item2, k| item1.point[k].cmp(&item2.point[k]) /// ); /// assert_eq!(kdtree.nearest_by(&[3, 1, 2], |item, k| item.point[k]).unwrap().item.id, 222); /// ``` pub fn build_by<F>(mut items: Vec<T>, compare: F) -> Self where F: Fn(&T, &T, usize) -> Ordering + Copy, { kd_sort_by(&mut items, N::to_usize(), compare); Self(PhantomData, items) } /// # Example /// ``` /// struct Item { /// point: [f64; 3], /// id: usize, /// } /// let kdtree = kd_tree::KdTree3::build_by_key( /// vec![ /// Item { point: [1.0, 2.0, 3.0], id: 111 }, /// Item { point: [3.0, 1.0, 2.0], id: 222 }, /// Item { point: [2.0, 3.0, 1.0], id: 333 }, /// ], /// |item, k| ordered_float::OrderedFloat(item.point[k]) /// ); /// assert_eq!(kdtree.nearest_by(&[3.1, 0.9, 2.1], |item, k| item.point[k]).unwrap().item.id, 222); /// ``` pub fn build_by_key<Key, F>(items: Vec<T>, kd_key: F) -> Self where Key: Ord, F: Fn(&T, usize) -> Key + Copy, { Self::build_by(items, |item1, item2, k| { kd_key(item1, k).cmp(&kd_key(item2, k)) }) } /// # Example /// ``` /// use kd_tree::KdTree; /// let kdtree: KdTree<[f64; 3]> = KdTree::build_by_ordered_float(vec![ /// [1.0, 2.0, 3.0], [3.0, 1.0, 2.0], [2.0, 3.0, 1.0] /// ]); /// assert_eq!(kdtree.nearest(&[3.1, 0.9, 2.1]).unwrap().item, &[3.0, 1.0, 2.0]); /// ``` pub fn build_by_ordered_float(points: Vec<T>) -> Self where T: KdPoint<Dim = N>, T::Scalar: num_traits::Float, { Self::build_by_key(points, |item, k| ordered_float::OrderedFloat(item.at(k))) } /// # Example /// ``` /// use kd_tree::KdTree; /// let kdtree: KdTree<[i32; 3]> = KdTree::build(vec![[1, 2, 3], [3, 1, 2], [2, 3, 1]]); /// assert_eq!(kdtree.nearest(&[3, 1, 2]).unwrap().item, &[3, 1, 2]); /// ``` pub fn build(points: Vec<T>) -> Self where T: KdPoint<Dim = N>, T::Scalar: Ord, { Self::build_by_key(points, |item, k| item.at(k)) } } /// This type refers a slice of items, `[T]`, and contains kd-tree of indices to the items, `KdTree<usize, N>`. /// Unlike [`KdSliceN::sort`], [`KdIndexTreeN::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 items. /// ``` #[derive(Debug, Clone, PartialEq, Eq)] pub struct KdIndexTreeN<'a, T, N: Unsigned> { source: &'a [T], kdtree: KdTreeN<usize, N>, } pub type KdIndexTree<'a, T> = KdIndexTreeN<'a, T, <T as KdPoint>::Dim>; impl<'a, T, N: Unsigned> KdIndexTreeN<'a, T, N> { pub fn source(&self) -> &'a [T] { self.source } pub fn indices(&self) -> &KdSliceN<usize, N> { &self.kdtree } pub fn item(&self, i: usize) -> &'a T { &self.source[i] } pub fn build_by<F>(source: &'a [T], compare: F) -> Self where F: Fn(&T, &T, usize) -> Ordering + Copy, { Self { source, kdtree: KdTreeN::build_by((0..source.len()).collect(), |i1, i2, k| { compare(&source[*i1], &source[*i2], k) }), } } pub fn build_by_key<Key, F>(source: &'a [T], kd_key: F) -> Self where Key: Ord, F: Fn(&T, usize) -> Key + Copy, { Self::build_by(source, |item1, item2, k| { kd_key(item1, k).cmp(&kd_key(item2, k)) }) } pub fn build_by_ordered_float(points: &'a [T]) -> Self where T: KdPoint<Dim = N>, T::Scalar: num_traits::Float, { Self::build_by_key(points, |item, k| ordered_float::OrderedFloat(item.at(k))) } pub fn build(points: &'a [T]) -> Self where T: KdPoint<Dim = N>, T::Scalar: Ord, { Self::build_by_key(points, |item, k| item.at(k)) } pub fn nearest_by<Q: KdPoint<Dim = N>>( &self, query: &Q, coord: impl Fn(&T, usize) -> Q::Scalar + Copy, ) -> Option<ItemAndDistance<usize, Q::Scalar>> { self.kdtree .nearest_by(query, |&index, k| coord(&self.source[index], k)) } /// # Example /// ``` /// let mut items: Vec<[i32; 3]> = vec![[1, 2, 3], [3, 1, 2], [2, 3, 1]]; /// let kdtree = kd_tree::KdIndexTree3::build(&items); /// assert_eq!(kdtree.nearest(&[3, 1, 2]).unwrap().item, &1); /// ``` pub fn nearest( &self, query: &impl KdPoint<Scalar = T::Scalar, Dim = N>, ) -> Option<ItemAndDistance<usize, T::Scalar>> where T: KdPoint<Dim = N>, { self.nearest_by(query, |item, k| item.at(k)) } pub fn nearests_by<Q: KdPoint<Dim = N>>( &self, query: &Q, num: usize, coord: impl Fn(&T, usize) -> Q::Scalar + Copy, ) -> Vec<ItemAndDistance<usize, Q::Scalar>> { self.kdtree .nearests_by(query, num, |&index, k| coord(&self.source[index], k)) } /// Returns kNN(k nearest neighbors) from the input point. /// # Example /// ``` /// let mut items: Vec<[i32; 3]> = vec![[1, 2, 3], [3, 1, 2], [2, 3, 1], [3, 2, 2]]; /// let kdtree = kd_tree::KdIndexTree::build(&mut items); /// let nearests = kdtree.nearests(&[3, 1, 2], 2); /// assert_eq!(nearests.len(), 2); /// assert_eq!(nearests[0].item, &1); /// assert_eq!(nearests[1].item, &3); /// ``` pub fn nearests( &self, query: &impl KdPoint<Scalar = T::Scalar, Dim = N>, num: usize, ) -> Vec<ItemAndDistance<usize, T::Scalar>> where T: KdPoint<Dim = N>, { self.nearests_by(query, num, |item, k| item.at(k)) } pub fn within_by_cmp(&self, compare: impl Fn(&T, usize) -> Ordering + Copy) -> Vec<&usize> { self.kdtree .within_by_cmp(|&index, k| compare(&self.source[index], k)) } pub fn within_by<Q: KdPoint<Dim = N>>( &self, query: &[Q; 2], coord: impl Fn(&T, usize) -> Q::Scalar + Copy, ) -> Vec<&usize> { self.kdtree .within_by(query, |&index, k| coord(&self.source[index], k)) } pub fn within(&self, query: &[impl KdPoint<Scalar = T::Scalar, Dim = N>; 2]) -> Vec<&usize> where T: KdPoint<Dim = N>, { self.within_by(query, |item, k| item.at(k)) } pub fn within_radius_by<Q: KdPoint<Dim = N>>( &self, query: &Q, radius: Q::Scalar, coord: impl Fn(&T, usize) -> Q::Scalar + Copy, ) -> Vec<&usize> { self.kdtree .within_radius_by(query, radius, |&index, k| coord(&self.source[index], k)) } pub fn within_radius( &self, query: &impl KdPoint<Scalar = T::Scalar, Dim = N>, radius: T::Scalar, ) -> Vec<&usize> where T: KdPoint<Dim = N>, { self.within_radius_by(query, radius, |item, k| item.at(k)) } } macro_rules! define_kdtree_aliases { ($($dim:literal),*) => { $( paste::paste! { pub type [<KdSlice $dim>]<T> = KdSliceN<T, typenum::[<U $dim>]>; pub type [<KdTree $dim>]<T> = KdTreeN<T, typenum::[<U $dim>]>; pub type [<KdIndexTree $dim>]<'a, T> = KdIndexTreeN<'a, T, typenum::[<U $dim>]>; } )* }; } define_kdtree_aliases!(1, 2, 3, 4, 5, 6, 7, 8); macro_rules! impl_kd_points { ($($len:literal),*) => { $( paste::paste!{ impl<T: num_traits::NumAssign + Copy + PartialOrd> KdPoint for [T; $len] { type Scalar = T; type Dim = typenum::[<U $len>]; fn at(&self, i: usize) -> T { self[i] } } } )* }; } impl_kd_points!(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16); impl<P: KdPoint, T> KdPoint for (P, T) { type Scalar = P::Scalar; type Dim = P::Dim; fn at(&self, k: usize) -> Self::Scalar { self.0.at(k) } } /// kd-tree of key-value pairs. /// ``` /// 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"); /// ``` pub type KdMap<P, T> = KdTree<(P, T)>; /// kd-tree slice of key-value pairs. /// ``` /// let mut items: Vec<([isize; 3], &'static str)> = vec![ /// ([1, 2, 3], "foo"), /// ([2, 3, 1], "bar"), /// ([3, 1, 2], "buzz"), /// ]; /// let kdmap = kd_tree::KdMapSlice::sort(&mut items); /// assert_eq!(kdmap.nearest(&[3, 1, 2]).unwrap().item.1, "buzz"); /// ``` pub type KdMapSlice<P, T> = KdSlice<(P, T)>;