Use the acap nearest neighbors implementationHEADmaster

14 files changed, 363 insertions, 1229 deletions

diff --git a/Cargo.lock b/Cargo.lock
index 1b04548..e3eaa1d 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -1,6 +1,16 @@
 # This file is automatically @generated by Cargo.
 # It is not intended for manual editing.
 [[package]]
+name = "acap"
+version = "0.1.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "881ff84781a207a949e7663c7990fe98b9826bb961a2389f8672986c34177da9"
+dependencies = [
+ "num-traits",
+ "rand",
+]
+
+[[package]]
 name = "adler32"
 version = "1.0.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
@@ -87,9 +97,9 @@ checksum = "4785bdd1c96b2a846b2bd7cc02e86b6b3dbf14e7e53446c4f54c92a361040822"
 
 [[package]]
 name = "clap"
-version = "2.33.0"
+version = "2.33.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "5067f5bb2d80ef5d68b4c87db81601f0b75bca627bc2ef76b141d7b846a3c6d9"
+checksum = "bdfa80d47f954d53a35a64987ca1422f495b8d6483c0fe9f7117b36c2a792129"
 dependencies = [
  "ansi_term",
  "atty",
@@ -238,9 +248,9 @@ dependencies = [
 
 [[package]]
 name = "image"
-version = "0.23.4"
+version = "0.23.6"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9117f4167a8f21fa2bb3f17a652a760acd7572645281c98e3b612a26242c96ee"
+checksum = "b5b0553fec6407d63fe2975b794dfb099f3f790bdc958823851af37b26404ab4"
 dependencies = [
  "bytemuck",
  "byteorder",
@@ -255,15 +265,6 @@ dependencies = [
 ]
 
 [[package]]
-name = "inflate"
-version = "0.4.5"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1cdb29978cc5797bd8dcc8e5bf7de604891df2a8dc576973d71a281e916db2ff"
-dependencies = [
- "adler32",
-]
-
-[[package]]
 name = "jpeg-decoder"
 version = "0.1.19"
 source = "registry+https://github.com/rust-lang/crates.io-index"
@@ -277,6 +278,7 @@ dependencies = [
 name = "kd-forest"
 version = "2.0.0"
 dependencies = [
+ "acap",
  "clap",
  "image",
  "rand",
@@ -349,9 +351,9 @@ dependencies = [
 
 [[package]]
 name = "num-rational"
-version = "0.2.4"
+version = "0.3.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "5c000134b5dbf44adc5cb772486d335293351644b801551abe8f75c84cfa4aef"
+checksum = "a5b4d7360f362cfb50dde8143501e6940b22f644be75a4cc90b2d81968908138"
 dependencies = [
  "autocfg",
  "num-integer",
@@ -379,14 +381,14 @@ dependencies = [
 
 [[package]]
 name = "png"
-version = "0.16.3"
+version = "0.16.5"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "2c68a431ed29933a4eb5709aca9800989758c97759345860fa5db3cfced0b65d"
+checksum = "34ccdd66f6fe4b2433b07e4728e9a013e43233120427046e93ceb709c3a439bf"
 dependencies = [
  "bitflags",
  "crc32fast",
  "deflate",
- "inflate",
+ "miniz_oxide",
 ]
 
 [[package]]
@@ -537,9 +539,9 @@ dependencies = [
 
 [[package]]
 name = "tiff"
-version = "0.4.0"
+version = "0.5.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "002351e428db1eb1d8656d4ca61947c3519ac3191e1c804d4600cd32093b77ad"
+checksum = "3f3b8a87c4da944c3f27e5943289171ac71a6150a79ff6bacfff06d159dfff2f"
 dependencies = [
  "byteorder",
  "lzw",
diff --git a/Cargo.toml b/Cargo.toml
index ae6fe88..c1a4bc6 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -5,8 +5,9 @@ authors = ["Tavian Barnes <tavianator@tavianator.com>"]
 edition = "2018"
 
 [dependencies]
-clap = "2.33.0"
-image = "0.23.4"
+acap = "0.1.0"
+clap = "2.33.1"
+image = "0.23.6"
 rand = "0.7.3"
 rand_pcg = "0.2.1"
 term = "0.6.1"
diff --git a/src/color.rs b/src/color.rs
index 5d50aa1..ff113a7 100644
--- a/src/color.rs
+++ b/src/color.rs
@@ -3,8 +3,9 @@
 pub mod order;
 pub mod source;
 
-use crate::metric::kd::{Cartesian, CartesianMetric};
-use crate::metric::{Metric, SquaredDistance};
+use acap::coords::{Coordinates, CoordinateMetric, CoordinateProximity};
+use acap::distance::{Metric, Proximity};
+use acap::euclid::{EuclideanDistance, euclidean_distance};
 
 use image::Rgb;
 
@@ -14,7 +15,11 @@ use std::ops::Index;
 pub type Rgb8 = Rgb<u8>;
 
 /// A [color space](https://en.wikipedia.org/wiki/Color_space).
-pub trait ColorSpace: Copy + From<Rgb8> + CartesianMetric {
+pub trait ColorSpace: Copy + From<Rgb8>
+    + Coordinates
+    + Metric
+    + CoordinateMetric<<Self as Coordinates>::Value, Distance = <Self as Proximity>::Distance>
+{
     /// Compute the average of the given colors.
     fn average<I: IntoIterator<Item = Self>>(colors: I) -> Self;
 }
@@ -41,32 +46,38 @@ impl From<Rgb8> for RgbSpace {
     }
 }
 
-impl Metric<[f64]> for RgbSpace {
-    type Distance = SquaredDistance;
+impl Coordinates for RgbSpace {
+    type Value = f64;
 
-    fn distance(&self, other: &[f64]) -> Self::Distance {
-        self.0.distance(other)
+    fn dims(&self) -> usize {
+        self.0.dims()
+    }
+
+    fn coord(&self, i: usize) -> f64 {
+        self.0.coord(i)
     }
 }
 
-impl Metric for RgbSpace {
-    type Distance = SquaredDistance;
+impl Proximity for RgbSpace {
+    type Distance = EuclideanDistance<f64>;
 
     fn distance(&self, other: &Self) -> Self::Distance {
-        self.0.distance(&other.0)
+        euclidean_distance(&self.0, &other.0)
     }
 }
 
-impl Cartesian for RgbSpace {
-    fn dimensions(&self) -> usize {
-        self.0.dimensions()
-    }
+impl Metric for RgbSpace {}
+
+impl CoordinateProximity<f64> for RgbSpace {
+    type Distance = EuclideanDistance<f64>;
 
-    fn coordinate(&self, i: usize) -> f64 {
-        self.0.coordinate(i)
+    fn distance_to_coords(&self, other: &[f64]) -> Self::Distance {
+        euclidean_distance(&self.0, other)
     }
 }
 
+impl CoordinateMetric<f64> for RgbSpace {}
+
 impl ColorSpace for RgbSpace {
     fn average<I: IntoIterator<Item = Self>>(colors: I) -> Self {
         let mut sum = [0.0, 0.0, 0.0];
@@ -161,32 +172,38 @@ impl From<Rgb8> for LabSpace {
     }
 }
 
-impl Metric<[f64]> for LabSpace {
-    type Distance = SquaredDistance;
+impl Coordinates for LabSpace {
+    type Value = f64;
+
+    fn dims(&self) -> usize {
+        self.0.dims()
+    }
 
-    fn distance(&self, other: &[f64]) -> Self::Distance {
-        self.0.distance(other)
+    fn coord(&self, i: usize) -> f64 {
+        self.0.coord(i)
     }
 }
 
-impl Metric for LabSpace {
-    type Distance = SquaredDistance;
+impl Proximity for LabSpace {
+    type Distance = EuclideanDistance<f64>;
 
     fn distance(&self, other: &Self) -> Self::Distance {
-        self.0.distance(&other.0)
+        euclidean_distance(self.0, other.0)
     }
 }
 
-impl Cartesian for LabSpace {
-    fn dimensions(&self) -> usize {
-        self.0.dimensions()
-    }
+impl Metric for LabSpace {}
 
-    fn coordinate(&self, i: usize) -> f64 {
-        self.0.coordinate(i)
+impl CoordinateProximity<f64> for LabSpace {
+    type Distance = EuclideanDistance<f64>;
+
+    fn distance_to_coords(&self, other: &[f64]) -> Self::Distance {
+        euclidean_distance(&self.0, other)
     }
 }
 
+impl CoordinateMetric<f64> for LabSpace {}
+
 impl ColorSpace for LabSpace {
     fn average<I: IntoIterator<Item = Self>>(colors: I) -> Self {
         let mut sum = [0.0, 0.0, 0.0];
@@ -241,32 +258,38 @@ impl From<Rgb8> for LuvSpace {
     }
 }
 
-impl Metric<[f64]> for LuvSpace {
-    type Distance = SquaredDistance;
+impl Coordinates for LuvSpace {
+    type Value = f64;
+
+    fn dims(&self) -> usize {
+        self.0.dims()
+    }
 
-    fn distance(&self, other: &[f64]) -> Self::Distance {
-        self.0.distance(other)
+    fn coord(&self, i: usize) -> f64 {
+        self.0.coord(i)
     }
 }
 
-impl Metric for LuvSpace {
-    type Distance = SquaredDistance;
+impl Proximity for LuvSpace {
+    type Distance = EuclideanDistance<f64>;
 
     fn distance(&self, other: &Self) -> Self::Distance {
-        self.0.distance(&other.0)
+        euclidean_distance(&self.0, &other.0)
     }
 }
 
-impl Cartesian for LuvSpace {
-    fn dimensions(&self) -> usize {
-        self.0.dimensions()
-    }
+impl Metric for LuvSpace {}
+
+impl CoordinateProximity<f64> for LuvSpace {
+    type Distance = EuclideanDistance<f64>;
 
-    fn coordinate(&self, i: usize) -> f64 {
-        self.0.coordinate(i)
+    fn distance_to_coords(&self, other: &[f64]) -> Self::Distance {
+        euclidean_distance(&self.0, other)
     }
 }
 
+impl CoordinateMetric<f64> for LuvSpace {}
+
 impl ColorSpace for LuvSpace {
     fn average<I: IntoIterator<Item = Self>>(colors: I) -> Self {
         let mut sum = [0.0, 0.0, 0.0];
diff --git a/src/metric/forest.rs b/src/forest.rs
index 887ff12..56dff7e 100644
--- a/src/metric/forest.rs
+++ b/src/forest.rs
@@ -1,8 +1,9 @@
 //! [Dynamization](https://en.wikipedia.org/wiki/Dynamization) for nearest neighbor search.
 
-use super::kd::KdTree;
-use super::vp::VpTree;
-use super::{Metric, NearestNeighbors, Neighborhood};
+use acap::distance::Proximity;
+use acap::kd::FlatKdTree;
+use acap::vp::FlatVpTree;
+use acap::{NearestNeighbors, Neighborhood};
 
 use std::iter::{self, Extend, FromIterator};
 
@@ -129,17 +130,17 @@ impl<T: IntoIterator> IntoIterator for Forest<T> {
     }
 }
 
-impl<T, U, V> NearestNeighbors<T, U> for Forest<V>
+impl<K, V, T> NearestNeighbors<K, V> for Forest<T>
 where
-    U: Metric<T>,
-    V: NearestNeighbors<T, U>,
-    V: IntoIterator<Item = T>,
+    K: Proximity<V>,
+    T: NearestNeighbors<K, V>,
+    T: IntoIterator<Item = V>,
 {
-    fn search<'a, 'b, N>(&'a self, mut neighborhood: N) -> N
+    fn search<'k, 'v, N>(&'v self, mut neighborhood: N) -> N
     where
-        T: 'a,
-        U: 'b,
-        N: Neighborhood<&'a T, &'b U>,
+        K: 'k,
+        V: 'v,
+        N: Neighborhood<&'k K, &'v V>
     {
         for item in &self.buffer {
             neighborhood.consider(item);
@@ -153,17 +154,121 @@ where
 }
 
 /// A forest of k-d trees.
-pub type KdForest<T> = Forest<KdTree<T>>;
+pub type KdForest<T> = Forest<FlatKdTree<T>>;
 
 /// A forest of vantage-point trees.
-pub type VpForest<T> = Forest<VpTree<T>>;
+pub type VpForest<T> = Forest<FlatVpTree<T>>;
 
 #[cfg(test)]
 mod tests {
     use super::*;
 
-    use crate::metric::tests::test_nearest_neighbors;
-    use crate::metric::ExhaustiveSearch;
+    use acap::euclid::Euclidean;
+    use acap::exhaustive::ExhaustiveSearch;
+    use acap::{NearestNeighbors, Neighbor};
+
+    use rand::prelude::*;
+
+    type Point = Euclidean<[f32; 3]>;
+
+    fn test_empty<T, F>(from_iter: &F)
+    where
+        T: NearestNeighbors<Point>,
+        F: Fn(Vec<Point>) -> T,
+    {
+        let points = Vec::new();
+        let index = from_iter(points);
+        let target = Euclidean([0.0, 0.0, 0.0]);
+        assert_eq!(index.nearest(&target), None);
+        assert_eq!(index.nearest_within(&target, 1.0), None);
+        assert!(index.k_nearest(&target, 0).is_empty());
+        assert!(index.k_nearest(&target, 3).is_empty());
+        assert!(index.k_nearest_within(&target, 0, 1.0).is_empty());
+        assert!(index.k_nearest_within(&target, 3, 1.0).is_empty());
+    }
+
+    fn test_pythagorean<T, F>(from_iter: &F)
+    where
+        T: NearestNeighbors<Point>,
+        F: Fn(Vec<Point>) -> T,
+    {
+        let points = vec![
+            Euclidean([3.0, 4.0, 0.0]),
+            Euclidean([5.0, 0.0, 12.0]),
+            Euclidean([0.0, 8.0, 15.0]),
+            Euclidean([1.0, 2.0, 2.0]),
+            Euclidean([2.0, 3.0, 6.0]),
+            Euclidean([4.0, 4.0, 7.0]),
+        ];
+        let index = from_iter(points);
+        let target = Euclidean([0.0, 0.0, 0.0]);
+
+        assert_eq!(
+            index.nearest(&target).expect("No nearest neighbor found"),
+            Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0)
+        );
+
+        assert_eq!(index.nearest_within(&target, 2.0), None);
+        assert_eq!(
+            index.nearest_within(&target, 4.0).expect("No nearest neighbor found within 4.0"),
+            Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0)
+        );
+
+        assert!(index.k_nearest(&target, 0).is_empty());
+        assert_eq!(
+            index.k_nearest(&target, 3),
+            vec![
+                Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0),
+                Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), 5.0),
+                Neighbor::new(&Euclidean([2.0, 3.0, 6.0]), 7.0),
+            ]
+        );
+
+        assert!(index.k_nearest(&target, 0).is_empty());
+        assert_eq!(
+            index.k_nearest_within(&target, 3, 6.0),
+            vec![
+                Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0),
+                Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), 5.0),
+            ]
+        );
+        assert_eq!(
+            index.k_nearest_within(&target, 3, 8.0),
+            vec![
+                Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0),
+                Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), 5.0),
+                Neighbor::new(&Euclidean([2.0, 3.0, 6.0]), 7.0),
+            ]
+        );
+    }
+
+    fn test_random_points<T, F>(from_iter: &F)
+    where
+        T: NearestNeighbors<Point>,
+        F: Fn(Vec<Point>) -> T,
+    {
+        let mut points = Vec::new();
+        for _ in 0..255 {
+            points.push(Euclidean([random(), random(), random()]));
+        }
+        let target = Euclidean([random(), random(), random()]);
+
+        let eindex = ExhaustiveSearch::from_iter(points.clone());
+        let index = from_iter(points);
+
+        assert_eq!(index.k_nearest(&target, 3), eindex.k_nearest(&target, 3));
+    }
+
+    /// Test a [NearestNeighbors] impl.
+    fn test_nearest_neighbors<T, F>(from_iter: F)
+    where
+        T: NearestNeighbors<Point>,
+        F: Fn(Vec<Point>) -> T,
+    {
+        test_empty(&from_iter);
+        test_pythagorean(&from_iter);
+        test_random_points(&from_iter);
+    }
 
     #[test]
     fn test_exhaustive_forest() {
diff --git a/src/frontier.rs b/src/frontier.rs
index c7b7ca5..74c7398 100644
--- a/src/frontier.rs
+++ b/src/frontier.rs
@@ -5,11 +5,13 @@ pub mod mean;
 pub mod min;
 
 use crate::color::{ColorSpace, Rgb8};
-use crate::metric::kd::Cartesian;
-use crate::metric::soft::SoftDelete;
-use crate::metric::Metric;
+use crate::soft::SoftDelete;
+
+use acap::coords::{Coordinates, CoordinateMetric, CoordinateProximity};
+use acap::distance::{Proximity, Metric};
 
 use std::cell::Cell;
+use std::ops::Deref;
 use std::rc::Rc;
 
 /// A frontier of pixels.
@@ -52,23 +54,39 @@ impl<C: ColorSpace> Pixel<C> {
     }
 }
 
-impl<C: Metric> Metric<Pixel<C>> for C {
-    type Distance = C::Distance;
+/// A reference-counted pixel, to work around the coherence rules.
+#[derive(Clone, Debug)]
+struct RcPixel<C>(Rc<Pixel<C>>);
 
-    fn distance(&self, other: &Pixel<C>) -> Self::Distance {
-        self.distance(&other.color)
+impl<C: ColorSpace> RcPixel<C> {
+    fn new(x: u32, y: u32, color: C) -> Self {
+        Self(Rc::new(Pixel::new(x, y, color)))
+    }
+}
+
+impl<C> Deref for RcPixel<C> {
+    type Target = Pixel<C>;
+
+    fn deref(&self) -> &Self::Target {
+        self.0.deref()
     }
 }
 
-impl<C: Metric<[f64]>> Metric<[f64]> for Pixel<C> {
+/// A search target, to work around the coherence rules.
+#[derive(Debug)]
+struct Target<C>(C);
+
+impl<C: Proximity> Proximity<Pixel<C>> for Target<C> {
     type Distance = C::Distance;
 
-    fn distance(&self, other: &[f64]) -> Self::Distance {
-        self.color.distance(other)
+    fn distance(&self, other: &Pixel<C>) -> Self::Distance {
+        self.0.distance(&other.color)
     }
 }
 
-impl<C: Metric> Metric for Pixel<C> {
+impl<C: Metric> Metric<Pixel<C>> for Target<C> {}
+
+impl<C: Proximity> Proximity for Pixel<C> {
     type Distance = C::Distance;
 
     fn distance(&self, other: &Pixel<C>) -> Self::Distance {
@@ -76,13 +94,17 @@ impl<C: Metric> Metric for Pixel<C> {
     }
 }
 
-impl<C: Cartesian> Cartesian for Pixel<C> {
-    fn dimensions(&self) -> usize {
-        self.color.dimensions()
+impl<C: Metric> Metric for Pixel<C> {}
+
+impl<C: Coordinates> Coordinates for Pixel<C> {
+    type Value = C::Value;
+
+    fn dims(&self) -> usize {
+        self.color.dims()
     }
 
-    fn coordinate(&self, i: usize) -> f64 {
-        self.color.coordinate(i)
+    fn coord(&self, i: usize) -> Self::Value {
+        self.color.coord(i)
     }
 }
 
@@ -92,43 +114,63 @@ impl<C> SoftDelete for Pixel<C> {
     }
 }
 
-impl<C: Metric<[f64]>> Metric<[f64]> for Rc<Pixel<C>> {
+impl<C: Proximity> Proximity<RcPixel<C>> for Target<C> {
     type Distance = C::Distance;
 
-    fn distance(&self, other: &[f64]) -> Self::Distance {
-        (**self).distance(other)
+    fn distance(&self, other: &RcPixel<C>) -> Self::Distance {
+        self.0.distance(&other.0.color)
+    }
+}
+
+impl<C: Metric> Metric<RcPixel<C>> for Target<C> {}
+
+impl<C: Coordinates> Coordinates for Target<C> {
+    type Value = C::Value;
+
+    fn dims(&self) -> usize {
+        self.0.dims()
+    }
+
+    fn coord(&self, i: usize) -> Self::Value {
+        self.0.coord(i)
     }
 }
 
-impl<C: Metric> Metric<Rc<Pixel<C>>> for C {
+impl<T, C: CoordinateProximity<T>> CoordinateProximity<T> for Target<C> {
     type Distance = C::Distance;
 
-    fn distance(&self, other: &Rc<Pixel<C>>) -> Self::Distance {
-        self.distance(&other.color)
+    fn distance_to_coords(&self, coords: &[T]) -> Self::Distance {
+        self.0.distance_to_coords(coords)
     }
 }
 
-impl<C: Metric> Metric for Rc<Pixel<C>> {
+impl<T, C: CoordinateMetric<T>> CoordinateMetric<T> for Target<C> {}
+
+impl<C: Proximity> Proximity for RcPixel<C> {
     type Distance = C::Distance;
 
     fn distance(&self, other: &Self) -> Self::Distance {
-        (**self).distance(&**other)
+        (*self.0).distance(&*other.0)
     }
 }
 
-impl<C: Cartesian> Cartesian for Rc<Pixel<C>> {
-    fn dimensions(&self) -> usize {
-        (**self).dimensions()
+impl<C: Metric> Metric for RcPixel<C> {}
+
+impl<C: Coordinates> Coordinates for RcPixel<C> {
+    type Value = C::Value;
+
+    fn dims(&self) -> usize {
+        (*self.0).dims()
     }
 
-    fn coordinate(&self, i: usize) -> f64 {
-        (**self).coordinate(i)
+    fn coord(&self, i: usize) -> Self::Value {
+        (*self.0).coord(i)
     }
 }
 
-impl<C> SoftDelete for Rc<Pixel<C>> {
+impl<C> SoftDelete for RcPixel<C> {
     fn is_deleted(&self) -> bool {
-        (**self).is_deleted()
+        (*self.0).is_deleted()
     }
 }
 
diff --git a/src/frontier/image.rs b/src/frontier/image.rs
index 5642297..18bf620 100644
--- a/src/frontier/image.rs
+++ b/src/frontier/image.rs
@@ -1,16 +1,17 @@
 //! Frontier that targets an image.
 
-use super::{Frontier, Pixel};
+use super::{Frontier, Pixel, Target};
 
 use crate::color::{ColorSpace, Rgb8};
-use crate::metric::soft::SoftKdTree;
-use crate::metric::NearestNeighbors;
+use crate::soft::SoftKdTree;
+
+use acap::NearestNeighbors;
 
 use image::RgbImage;
 
 /// A [Frontier] that places colors on the closest pixel of a target image.
 #[derive(Debug)]
-pub struct ImageFrontier<C: ColorSpace> {
+pub struct ImageFrontier<C> {
     nodes: SoftKdTree<Pixel<C>>,
     width: u32,
     height: u32,
@@ -58,7 +59,7 @@ impl<C: ColorSpace> Frontier for ImageFrontier<C> {
     fn place(&mut self, rgb8: Rgb8) -> Option<(u32, u32)> {
         let color = C::from(rgb8);
 
-        if let Some(node) = self.nodes.nearest(&color).map(|n| n.item) {
+        if let Some(node) = self.nodes.nearest(&Target(color)).map(|n| n.item) {
             let pos = node.pos;
 
             node.delete();
diff --git a/src/frontier/mean.rs b/src/frontier/mean.rs
index 6a32b97..3c441b8 100644
--- a/src/frontier/mean.rs
+++ b/src/frontier/mean.rs
@@ -1,19 +1,19 @@
 //! Mean selection frontier.
 
-use super::{neighbors, Frontier, Pixel};
+use super::{neighbors, Frontier, RcPixel, Target};
 
 use crate::color::{ColorSpace, Rgb8};
-use crate::metric::soft::SoftKdForest;
-use crate::metric::NearestNeighbors;
+use crate::soft::SoftKdForest;
+
+use acap::NearestNeighbors;
 
 use std::iter;
-use std::rc::Rc;
 
 /// A pixel on a mean frontier.
 #[derive(Debug)]
 enum MeanPixel<C> {
     Empty,
-    Fillable(Rc<Pixel<C>>),
+    Fillable(RcPixel<C>),
     Filled(C),
 }
 
@@ -27,9 +27,10 @@ impl<C: ColorSpace> MeanPixel<C> {
 }
 
 /// A [Frontier] that looks at the average color of each pixel's neighbors.
+#[derive(Debug)]
 pub struct MeanFrontier<C> {
     pixels: Vec<MeanPixel<C>>,
-    forest: SoftKdForest<Rc<Pixel<C>>>,
+    forest: SoftKdForest<RcPixel<C>>,
     width: u32,
     height: u32,
     len: usize,
@@ -45,7 +46,7 @@ impl<C: ColorSpace> MeanFrontier<C> {
             pixels.push(MeanPixel::Empty);
         }
 
-        let pixel0 = Rc::new(Pixel::new(x0, y0, C::from(Rgb8::from([0, 0, 0]))));
+        let pixel0 = RcPixel::new(x0, y0, C::from(Rgb8::from([0, 0, 0])));
         let i = (x0 + y0 * width) as usize;
         pixels[i] = MeanPixel::Fillable(pixel0.clone());
 
@@ -99,7 +100,7 @@ impl<C: ColorSpace> MeanFrontier<C> {
                         .map(MeanPixel::filled_color)
                         .flatten(),
                 );
-                let pixel = Rc::new(Pixel::new(x, y, color));
+                let pixel = RcPixel::new(x, y, color);
                 self.pixels[i] = MeanPixel::Fillable(pixel.clone());
                 pixels.push(pixel);
             }
@@ -135,7 +136,7 @@ impl<C: ColorSpace> Frontier for MeanFrontier<C> {
 
     fn place(&mut self, rgb8: Rgb8) -> Option<(u32, u32)> {
         let color = C::from(rgb8);
-        let (x, y) = self.forest.nearest(&color).map(|n| n.item.pos)?;
+        let (x, y) = self.forest.nearest(&Target(color)).map(|n| n.item.pos)?;
 
         self.fill(x, y, color);
 
diff --git a/src/frontier/min.rs b/src/frontier/min.rs
index 269f3b7..95b3321 100644
--- a/src/frontier/min.rs
+++ b/src/frontier/min.rs
@@ -1,19 +1,18 @@
 //! Minimum selection frontier.
 
-use super::{neighbors, Frontier, Pixel};
+use super::{neighbors, Frontier, RcPixel, Target};
 
 use crate::color::{ColorSpace, Rgb8};
-use crate::metric::soft::SoftKdForest;
-use crate::metric::NearestNeighbors;
+use crate::soft::SoftKdForest;
 
-use rand::Rng;
+use acap::NearestNeighbors;
 
-use std::rc::Rc;
+use rand::Rng;
 
 /// A pixel on a min frontier.
 #[derive(Debug)]
 struct MinPixel<C> {
-    pixel: Option<Rc<Pixel<C>>>,
+    pixel: Option<RcPixel<C>>,
     filled: bool,
 }
 
@@ -31,7 +30,7 @@ impl<C: ColorSpace> MinPixel<C> {
 pub struct MinFrontier<C, R> {
     rng: R,
     pixels: Vec<MinPixel<C>>,
-    forest: SoftKdForest<Rc<Pixel<C>>>,
+    forest: SoftKdForest<RcPixel<C>>,
     width: u32,
     height: u32,
     x0: u32,
@@ -94,7 +93,7 @@ impl<C: ColorSpace, R: Rng> MinFrontier<C, R> {
             return None;
         }
 
-        let rc = Rc::new(Pixel::new(x, y, color));
+        let rc = RcPixel::new(x, y, color);
         pixel.pixel = Some(rc.clone());
         pixel.filled = true;
 
@@ -144,7 +143,7 @@ impl<C: ColorSpace, R: Rng> Frontier for MinFrontier<C, R> {
         let color = C::from(rgb8);
         let (x, y) = self
             .forest
-            .nearest(&color)
+            .nearest(&Target(color))
             .map(|n| n.item.pos)
             .map(|(x, y)| self.free_neighbor(x, y).unwrap())
             .unwrap_or((self.x0, self.y0));
diff --git a/src/main.rs b/src/main.rs
index a2f5322..ce54939 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -1,7 +1,8 @@
 pub mod color;
+pub mod forest;
 pub mod frontier;
 pub mod hilbert;
-pub mod metric;
+pub mod soft;
 
 use crate::color::source::{AllColors, ColorSource, ImageColors};
 use crate::color::{order, ColorSpace, LabSpace, LuvSpace, Rgb8, RgbSpace};
diff --git a/src/metric.rs b/src/metric.rs
deleted file mode 100644
index d9938e4..0000000
--- a/src/metric.rs
+++ /dev/null
@@ -1,546 +0,0 @@
-//! [Metric spaces](https://en.wikipedia.org/wiki/Metric_space).
-
-pub mod approx;
-pub mod forest;
-pub mod kd;
-pub mod soft;
-pub mod vp;
-
-use std::cmp::Ordering;
-use std::collections::BinaryHeap;
-use std::iter::FromIterator;
-
-/// A wrapper that converts a partial ordering into a total one by panicking.
-#[derive(Debug, PartialEq, PartialOrd)]
-struct Ordered<T>(T);
-
-impl<T: PartialOrd> Ord for Ordered<T> {
-    fn cmp(&self, other: &Self) -> Ordering {
-        self.partial_cmp(other).unwrap()
-    }
-}
-
-impl<T: PartialEq> Eq for Ordered<T> {}
-
-/// An [order embedding](https://en.wikipedia.org/wiki/Order_embedding) for distances.
-///
-/// Implementations of this trait must satisfy, for all non-negative distances `x` and `y`:
-///
-/// * `x == Self::from(x).into()`
-/// * `x <= y` iff `Self::from(x) <= Self::from(y)`
-///
-/// This trait exists to optimize the common case where distances can be compared more efficiently
-/// than their exact values can be computed.  For example, taking the square root can be avoided
-/// when comparing Euclidean distances (see [SquaredDistance]).
-pub trait Distance: Copy + From<f64> + Into<f64> + PartialOrd {}
-
-impl Distance for f64 {}
-
-/// A squared distance, to avoid computing square roots unless absolutely necessary.
-#[derive(Debug, Clone, Copy, PartialEq, PartialOrd)]
-pub struct SquaredDistance(f64);
-
-impl SquaredDistance {
-    /// Create a SquaredDistance from an already squared value.
-    pub fn from_squared(value: f64) -> Self {
-        Self(value)
-    }
-}
-
-impl From<f64> for SquaredDistance {
-    fn from(value: f64) -> Self {
-        Self::from_squared(value * value)
-    }
-}
-
-impl From<SquaredDistance> for f64 {
-    fn from(value: SquaredDistance) -> Self {
-        value.0.sqrt()
-    }
-}
-
-impl Distance for SquaredDistance {}
-
-/// A [metric space](https://en.wikipedia.org/wiki/Metric_space).
-pub trait Metric<T: ?Sized = Self> {
-    /// The type used to represent distances.
-    type Distance: Distance;
-
-    /// Computes the distance between this point and another point.  This function must satisfy
-    /// three conditions:
-    ///
-    /// * `x.distance(y) == 0` iff `x == y` (identity of indiscernibles)
-    /// * `x.distance(y) == y.distance(x)` (symmetry)
-    /// * `x.distance(z) <= x.distance(y) + y.distance(z)` (triangle inequality)
-    fn distance(&self, other: &T) -> Self::Distance;
-}
-
-/// Blanket [Metric] implementation for references.
-impl<'a, 'b, T, U: Metric<T>> Metric<&'a T> for &'b U {
-    type Distance = U::Distance;
-
-    fn distance(&self, other: &&'a T) -> Self::Distance {
-        (*self).distance(other)
-    }
-}
-
-/// The standard [Euclidean distance](https://en.wikipedia.org/wiki/Euclidean_distance) metric.
-impl Metric for [f64] {
-    type Distance = SquaredDistance;
-
-    fn distance(&self, other: &Self) -> Self::Distance {
-        debug_assert!(self.len() == other.len());
-
-        let mut sum = 0.0;
-        for i in 0..self.len() {
-            let diff = self[i] - other[i];
-            sum += diff * diff;
-        }
-
-        Self::Distance::from_squared(sum)
-    }
-}
-
-/// A nearest neighbor to a target.
-#[derive(Clone, Copy, Debug, PartialEq)]
-pub struct Neighbor<T> {
-    /// The found item.
-    pub item: T,
-    /// The distance from the target.
-    pub distance: f64,
-}
-
-impl<T> Neighbor<T> {
-    /// Create a new Neighbor.
-    pub fn new(item: T, distance: f64) -> Self {
-        Self { item, distance }
-    }
-}
-
-/// A candidate nearest neighbor found during a search.
-#[derive(Debug)]
-struct Candidate<T, D> {
-    item: T,
-    distance: D,
-}
-
-impl<T, D: Distance> Candidate<T, D> {
-    fn new<U>(target: U, item: T) -> Self
-    where
-        U: Metric<T, Distance = D>,
-    {
-        let distance = target.distance(&item);
-        Self { item, distance }
-    }
-
-    fn into_neighbor(self) -> Neighbor<T> {
-        Neighbor::new(self.item, self.distance.into())
-    }
-}
-
-impl<T, D: Distance> PartialOrd for Candidate<T, D> {
-    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
-        self.distance.partial_cmp(&other.distance)
-    }
-}
-
-impl<T, D: Distance> Ord for Candidate<T, D> {
-    fn cmp(&self, other: &Self) -> Ordering {
-        self.partial_cmp(other).unwrap()
-    }
-}
-
-impl<T, D: Distance> PartialEq for Candidate<T, D> {
-    fn eq(&self, other: &Self) -> bool {
-        self.distance.eq(&other.distance)
-    }
-}
-
-impl<T, D: Distance> Eq for Candidate<T, D> {}
-
-/// Accumulates nearest neighbor search results.
-pub trait Neighborhood<T, U: Metric<T>> {
-    /// Returns the target of the nearest neighbor search.
-    fn target(&self) -> U;
-
-    /// Check whether a distance is within this neighborhood.
-    fn contains(&self, distance: f64) -> bool {
-        distance < 0.0 || self.contains_distance(distance.into())
-    }
-
-    /// Check whether a distance is within this neighborhood.
-    fn contains_distance(&self, distance: U::Distance) -> bool;
-
-    /// Consider a new candidate neighbor.
-    fn consider(&mut self, item: T) -> U::Distance;
-}
-
-/// A [Neighborhood] with at most one result.
-#[derive(Debug)]
-struct SingletonNeighborhood<T, U: Metric<T>> {
-    /// The target of the nearest neighbor search.
-    target: U,
-    /// The current threshold distance to the farthest result.
-    threshold: Option<U::Distance>,
-    /// The current nearest neighbor, if any.
-    candidate: Option<Candidate<T, U::Distance>>,
-}
-
-impl<T, U> SingletonNeighborhood<T, U>
-where
-    U: Copy + Metric<T>,
-{
-    /// Create a new single metric result tracker.
-    ///
-    /// * `target`: The target fo the nearest neighbor search.
-    /// * `threshold`: The maximum allowable distance.
-    fn new(target: U, threshold: Option<f64>) -> Self {
-        Self {
-            target,
-            threshold: threshold.map(U::Distance::from),
-            candidate: None,
-        }
-    }
-
-    /// Consider a candidate.
-    fn push(&mut self, candidate: Candidate<T, U::Distance>) -> U::Distance {
-        let distance = candidate.distance;
-
-        if self.contains_distance(distance) {
-            self.threshold = Some(distance);
-            self.candidate = Some(candidate);
-        }
-
-        distance
-    }
-
-    /// Convert this result into an optional neighbor.
-    fn into_option(self) -> Option<Neighbor<T>> {
-        self.candidate.map(Candidate::into_neighbor)
-    }
-}
-
-impl<T, U> Neighborhood<T, U> for SingletonNeighborhood<T, U>
-where
-    U: Copy + Metric<T>,
-{
-    fn target(&self) -> U {
-        self.target
-    }
-
-    fn contains_distance(&self, distance: U::Distance) -> bool {
-        self.threshold.map(|t| distance <= t).unwrap_or(true)
-    }
-
-    fn consider(&mut self, item: T) -> U::Distance {
-        self.push(Candidate::new(self.target, item))
-    }
-}
-
-/// A [Neighborhood] of up to `k` results, using a binary heap.
-#[derive(Debug)]
-struct HeapNeighborhood<T, U: Metric<T>> {
-    /// The target of the nearest neighbor search.
-    target: U,
-    /// The number of nearest neighbors to find.
-    k: usize,
-    /// The current threshold distance to the farthest result.
-    threshold: Option<U::Distance>,
-    /// A max-heap of the best candidates found so far.
-    heap: BinaryHeap<Candidate<T, U::Distance>>,
-}
-
-impl<T, U> HeapNeighborhood<T, U>
-where
-    U: Copy + Metric<T>,
-{
-    /// Create a new metric result tracker.
-    ///
-    /// * `target`: The target fo the nearest neighbor search.
-    /// * `k`: The number of nearest neighbors to find.
-    /// * `threshold`: The maximum allowable distance.
-    fn new(target: U, k: usize, threshold: Option<f64>) -> Self {
-        Self {
-            target,
-            k,
-            threshold: threshold.map(U::Distance::from),
-            heap: BinaryHeap::with_capacity(k),
-        }
-    }
-
-    /// Consider a candidate.
-    fn push(&mut self, candidate: Candidate<T, U::Distance>) -> U::Distance {
-        let distance = candidate.distance;
-
-        if self.contains_distance(distance) {
-            let heap = &mut self.heap;
-
-            if heap.len() == self.k {
-                heap.pop();
-            }
-
-            heap.push(candidate);
-
-            if heap.len() == self.k {
-                self.threshold = self.heap.peek().map(|c| c.distance)
-            }
-        }
-
-        distance
-    }
-
-    /// Convert these results into a vector of neighbors.
-    fn into_vec(self) -> Vec<Neighbor<T>> {
-        self.heap
-            .into_sorted_vec()
-            .into_iter()
-            .map(Candidate::into_neighbor)
-            .collect()
-    }
-}
-
-impl<T, U> Neighborhood<T, U> for HeapNeighborhood<T, U>
-where
-    U: Copy + Metric<T>,
-{
-    fn target(&self) -> U {
-        self.target
-    }
-
-    fn contains_distance(&self, distance: U::Distance) -> bool {
-        self.k > 0 && self.threshold.map(|t| distance <= t).unwrap_or(true)
-    }
-
-    fn consider(&mut self, item: T) -> U::Distance {
-        self.push(Candidate::new(self.target, item))
-    }
-}
-
-/// A [nearest neighbor search](https://en.wikipedia.org/wiki/Nearest_neighbor_search) index.
-///
-/// Type parameters:
-/// * `T`: The search result type.
-/// * `U`: The query type.
-pub trait NearestNeighbors<T, U: Metric<T> = T> {
-    /// Returns the nearest neighbor to `target` (or `None` if this index is empty).
-    fn nearest(&self, target: &U) -> Option<Neighbor<&T>> {
-        self.search(SingletonNeighborhood::new(target, None))
-            .into_option()
-    }
-
-    /// Returns the nearest neighbor to `target` within the distance `threshold`, if one exists.
-    fn nearest_within(&self, target: &U, threshold: f64) -> Option<Neighbor<&T>> {
-        self.search(SingletonNeighborhood::new(target, Some(threshold)))
-            .into_option()
-    }
-
-    /// Returns the up to `k` nearest neighbors to `target`.
-    fn k_nearest(&self, target: &U, k: usize) -> Vec<Neighbor<&T>> {
-        self.search(HeapNeighborhood::new(target, k, None))
-            .into_vec()
-    }
-
-    /// Returns the up to `k` nearest neighbors to `target` within the distance `threshold`.
-    fn k_nearest_within(&self, target: &U, k: usize, threshold: f64) -> Vec<Neighbor<&T>> {
-        self.search(HeapNeighborhood::new(target, k, Some(threshold)))
-            .into_vec()
-    }
-
-    /// Search for nearest neighbors and add them to a neighborhood.
-    fn search<'a, 'b, N>(&'a self, neighborhood: N) -> N
-    where
-        T: 'a,
-        U: 'b,
-        N: Neighborhood<&'a T, &'b U>;
-}
-
-/// A [NearestNeighbors] implementation that does exhaustive search.
-#[derive(Debug)]
-pub struct ExhaustiveSearch<T>(Vec<T>);
-
-impl<T> ExhaustiveSearch<T> {
-    /// Create an empty ExhaustiveSearch index.
-    pub fn new() -> Self {
-        Self(Vec::new())
-    }
-
-    /// Add a new item to the index.
-    pub fn push(&mut self, item: T) {
-        self.0.push(item);
-    }
-
-    /// Get the size of this index.
-    pub fn len(&self) -> usize {
-        self.0.len()
-    }
-
-    /// Check if this index is empty.
-    pub fn is_empty(&self) -> bool {
-        self.0.is_empty()
-    }
-}
-
-impl<T> Default for ExhaustiveSearch<T> {
-    fn default() -> Self {
-        Self::new()
-    }
-}
-
-impl<T> FromIterator<T> for ExhaustiveSearch<T> {
-    fn from_iter<I: IntoIterator<Item = T>>(items: I) -> Self {
-        Self(items.into_iter().collect())
-    }
-}
-
-impl<T> IntoIterator for ExhaustiveSearch<T> {
-    type Item = T;
-    type IntoIter = std::vec::IntoIter<T>;
-
-    fn into_iter(self) -> Self::IntoIter {
-        self.0.into_iter()
-    }
-}
-
-impl<T> Extend<T> for ExhaustiveSearch<T> {
-    fn extend<I: IntoIterator<Item = T>>(&mut self, iter: I) {
-        for value in iter {
-            self.push(value);
-        }
-    }
-}
-
-impl<T, U: Metric<T>> NearestNeighbors<T, U> for ExhaustiveSearch<T> {
-    fn search<'a, 'b, N>(&'a self, mut neighborhood: N) -> N
-    where
-        T: 'a,
-        U: 'b,
-        N: Neighborhood<&'a T, &'b U>,
-    {
-        for e in &self.0 {
-            neighborhood.consider(e);
-        }
-        neighborhood
-    }
-}
-
-#[cfg(test)]
-pub mod tests {
-    use super::*;
-
-    use rand::prelude::*;
-
-    #[derive(Clone, Copy, Debug, PartialEq)]
-    pub struct Point(pub [f64; 3]);
-
-    impl Metric for Point {
-        type Distance = SquaredDistance;
-
-        fn distance(&self, other: &Self) -> Self::Distance {
-            self.0.distance(&other.0)
-        }
-    }
-
-    /// Test a [NearestNeighbors] impl.
-    pub fn test_nearest_neighbors<T, F>(from_iter: F)
-    where
-        T: NearestNeighbors<Point>,
-        F: Fn(Vec<Point>) -> T,
-    {
-        test_empty(&from_iter);
-        test_pythagorean(&from_iter);
-        test_random_points(&from_iter);
-    }
-
-    fn test_empty<T, F>(from_iter: &F)
-    where
-        T: NearestNeighbors<Point>,
-        F: Fn(Vec<Point>) -> T,
-    {
-        let points = Vec::new();
-        let index = from_iter(points);
-        let target = Point([0.0, 0.0, 0.0]);
-        assert_eq!(index.nearest(&target), None);
-        assert_eq!(index.nearest_within(&target, 1.0), None);
-        assert!(index.k_nearest(&target, 0).is_empty());
-        assert!(index.k_nearest(&target, 3).is_empty());
-        assert!(index.k_nearest_within(&target, 0, 1.0).is_empty());
-        assert!(index.k_nearest_within(&target, 3, 1.0).is_empty());
-    }
-
-    fn test_pythagorean<T, F>(from_iter: &F)
-    where
-        T: NearestNeighbors<Point>,
-        F: Fn(Vec<Point>) -> T,
-    {
-        let points = vec![
-            Point([3.0, 4.0, 0.0]),
-            Point([5.0, 0.0, 12.0]),
-            Point([0.0, 8.0, 15.0]),
-            Point([1.0, 2.0, 2.0]),
-            Point([2.0, 3.0, 6.0]),
-            Point([4.0, 4.0, 7.0]),
-        ];
-        let index = from_iter(points);
-        let target = Point([0.0, 0.0, 0.0]);
-
-        assert_eq!(
-            index.nearest(&target),
-            Some(Neighbor::new(&Point([1.0, 2.0, 2.0]), 3.0))
-        );
-
-        assert_eq!(index.nearest_within(&target, 2.0), None);
-        assert_eq!(
-            index.nearest_within(&target, 4.0),
-            Some(Neighbor::new(&Point([1.0, 2.0, 2.0]), 3.0))
-        );
-
-        assert!(index.k_nearest(&target, 0).is_empty());
-        assert_eq!(
-            index.k_nearest(&target, 3),
-            vec![
-                Neighbor::new(&Point([1.0, 2.0, 2.0]), 3.0),
-                Neighbor::new(&Point([3.0, 4.0, 0.0]), 5.0),
-                Neighbor::new(&Point([2.0, 3.0, 6.0]), 7.0),
-            ]
-        );
-
-        assert!(index.k_nearest(&target, 0).is_empty());
-        assert_eq!(
-            index.k_nearest_within(&target, 3, 6.0),
-            vec![
-                Neighbor::new(&Point([1.0, 2.0, 2.0]), 3.0),
-                Neighbor::new(&Point([3.0, 4.0, 0.0]), 5.0),
-            ]
-        );
-        assert_eq!(
-            index.k_nearest_within(&target, 3, 8.0),
-            vec![
-                Neighbor::new(&Point([1.0, 2.0, 2.0]), 3.0),
-                Neighbor::new(&Point([3.0, 4.0, 0.0]), 5.0),
-                Neighbor::new(&Point([2.0, 3.0, 6.0]), 7.0),
-            ]
-        );
-    }
-
-    fn test_random_points<T, F>(from_iter: &F)
-    where
-        T: NearestNeighbors<Point>,
-        F: Fn(Vec<Point>) -> T,
-    {
-        let mut points = Vec::new();
-        for _ in 0..255 {
-            points.push(Point([random(), random(), random()]));
-        }
-        let target = Point([random(), random(), random()]);
-
-        let eindex = ExhaustiveSearch::from_iter(points.clone());
-        let index = from_iter(points);
-
-        assert_eq!(index.k_nearest(&target, 3), eindex.k_nearest(&target, 3));
-    }
-
-    #[test]
-    fn test_exhaustive_index() {
-        test_nearest_neighbors(ExhaustiveSearch::from_iter);
-    }
-}
diff --git a/src/metric/approx.rs b/src/metric/approx.rs
deleted file mode 100644
index c23f9c7..0000000
--- a/src/metric/approx.rs
+++ /dev/null
@@ -1,131 +0,0 @@
-//! [Approximate nearest neighbor search](https://en.wikipedia.org/wiki/Nearest_neighbor_search#Approximate_nearest_neighbor).
-
-use super::{Metric, NearestNeighbors, Neighborhood};
-
-/// An approximate [Neighborhood], for approximate nearest neighbor searches.
-#[derive(Debug)]
-struct ApproximateNeighborhood<N> {
-    inner: N,
-    ratio: f64,
-    limit: usize,
-}
-
-impl<N> ApproximateNeighborhood<N> {
-    fn new(inner: N, ratio: f64, limit: usize) -> Self {
-        Self {
-            inner,
-            ratio,
-            limit,
-        }
-    }
-}
-
-impl<T, U, N> Neighborhood<T, U> for ApproximateNeighborhood<N>
-where
-    U: Metric<T>,
-    N: Neighborhood<T, U>,
-{
-    fn target(&self) -> U {
-        self.inner.target()
-    }
-
-    fn contains(&self, distance: f64) -> bool {
-        if self.limit > 0 {
-            self.inner.contains(self.ratio * distance)
-        } else {
-            false
-        }
-    }
-
-    fn contains_distance(&self, distance: U::Distance) -> bool {
-        self.contains(self.ratio * distance.into())
-    }
-
-    fn consider(&mut self, item: T) -> U::Distance {
-        self.limit = self.limit.saturating_sub(1);
-        self.inner.consider(item)
-    }
-}
-
-/// An [approximate nearest neighbor search](https://en.wikipedia.org/wiki/Nearest_neighbor_search#Approximate_nearest_neighbor)
-/// index.
-///
-/// This wrapper converts an exact nearest neighbor search algorithm into an approximate one by
-/// modifying the behavior of [Neighborhood::contains].  The approximation is controlled by two
-/// parameters:
-///
-/// * `ratio`: The [nearest neighbor distance ratio](https://en.wikipedia.org/wiki/Nearest_neighbor_search#Nearest_neighbor_distance_ratio),
-///   which controls how much closer new candidates must be to be considered.  For example, a ratio
-///   of 2.0 means that a neighbor must be less than half of the current threshold away to be
-///   considered.  A ratio of 1.0 means an exact search.
-///
-/// * `limit`: A limit on the number of candidates to consider.  Typical nearest neighbor algorithms
-///   find a close match quickly, so setting a limit bounds the worst-case search time while keeping
-///   good accuracy.
-#[derive(Debug)]
-pub struct ApproximateSearch<T> {
-    inner: T,
-    ratio: f64,
-    limit: usize,
-}
-
-impl<T> ApproximateSearch<T> {
-    /// Create a new ApproximateSearch index.
-    ///
-    /// * `inner`: The [NearestNeighbors] implementation to wrap.
-    /// * `ratio`: The nearest neighbor distance ratio.
-    /// * `limit`: The maximum number of results to consider.
-    pub fn new(inner: T, ratio: f64, limit: usize) -> Self {
-        Self {
-            inner,
-            ratio,
-            limit,
-        }
-    }
-}
-
-impl<T, U, V> NearestNeighbors<T, U> for ApproximateSearch<V>
-where
-    U: Metric<T>,
-    V: NearestNeighbors<T, U>,
-{
-    fn search<'a, 'b, N>(&'a self, neighborhood: N) -> N
-    where
-        T: 'a,
-        U: 'b,
-        N: Neighborhood<&'a T, &'b U>,
-    {
-        self.inner
-            .search(ApproximateNeighborhood::new(
-                neighborhood,
-                self.ratio,
-                self.limit,
-            ))
-            .inner
-    }
-}
-
-#[cfg(test)]
-mod tests {
-    use super::*;
-
-    use crate::metric::kd::KdTree;
-    use crate::metric::tests::test_nearest_neighbors;
-    use crate::metric::vp::VpTree;
-
-    use std::iter::FromIterator;
-
-    #[test]
-    fn test_approx_kd_tree() {
-        test_nearest_neighbors(|iter| {
-            ApproximateSearch::new(KdTree::from_iter(iter), 1.0, std::usize::MAX)
-        });
-    }
-
-    #[test]
-    fn test_approx_vp_tree() {
-        test_nearest_neighbors(|iter| {
-            ApproximateSearch::new(VpTree::from_iter(iter), 1.0, std::usize::MAX)
-        });
-    }
-}
diff --git a/src/metric/kd.rs b/src/metric/kd.rs
deleted file mode 100644
index 6ea3809..0000000
--- a/src/metric/kd.rs
+++ /dev/null
@@ -1,224 +0,0 @@
-//! [k-d trees](https://en.wikipedia.org/wiki/K-d_tree).
-
-use super::{Metric, NearestNeighbors, Neighborhood, Ordered};
-
-use std::iter::FromIterator;
-
-/// A point in Cartesian space.
-pub trait Cartesian: Metric<[f64]> {
-    /// Returns the number of dimensions necessary to describe this point.
-    fn dimensions(&self) -> usize;
-
-    /// Returns the value of the `i`th coordinate of this point (`i < self.dimensions()`).
-    fn coordinate(&self, i: usize) -> f64;
-}
-
-/// Blanket [Cartesian] implementation for references.
-impl<'a, T: Cartesian> Cartesian for &'a T {
-    fn dimensions(&self) -> usize {
-        (*self).dimensions()
-    }
-
-    fn coordinate(&self, i: usize) -> f64 {
-        (*self).coordinate(i)
-    }
-}
-
-/// Blanket [Metric<[f64]>](Metric) implementation for [Cartesian] references.
-impl<'a, T: Cartesian> Metric<[f64]> for &'a T {
-    type Distance = T::Distance;
-
-    fn distance(&self, other: &[f64]) -> Self::Distance {
-        (*self).distance(other)
-    }
-}
-
-/// Standard cartesian space.
-impl Cartesian for [f64] {
-    fn dimensions(&self) -> usize {
-        self.len()
-    }
-
-    fn coordinate(&self, i: usize) -> f64 {
-        self[i]
-    }
-}
-
-/// Marker trait for cartesian metric spaces.
-pub trait CartesianMetric<T: ?Sized = Self>:
-    Cartesian + Metric<T, Distance = <Self as Metric<[f64]>>::Distance>
-{
-}
-
-/// Blanket [CartesianMetric] implementation for cartesian spaces with compatible metric distance
-/// types.
-impl<T, U> CartesianMetric<T> for U
-where
-    T: ?Sized,
-    U: ?Sized + Cartesian + Metric<T, Distance = <U as Metric<[f64]>>::Distance>,
-{
-}
-
-/// A node in a k-d tree.
-#[derive(Debug)]
-struct KdNode<T> {
-    /// The value stored in this node.
-    item: T,
-    /// The size of the left subtree.
-    left_len: usize,
-}
-
-impl<T: Cartesian> KdNode<T> {
-    /// Create a new KdNode.
-    fn new(item: T) -> Self {
-        Self { item, left_len: 0 }
-    }
-
-    /// Build a k-d tree recursively.
-    fn build(slice: &mut [KdNode<T>], i: usize) {
-        if slice.is_empty() {
-            return;
-        }
-
-        slice.sort_unstable_by_key(|n| Ordered(n.item.coordinate(i)));
-
-        let mid = slice.len() / 2;
-        slice.swap(0, mid);
-
-        let (node, children) = slice.split_first_mut().unwrap();
-        let (left, right) = children.split_at_mut(mid);
-        node.left_len = left.len();
-
-        let j = (i + 1) % node.item.dimensions();
-        Self::build(left, j);
-        Self::build(right, j);
-    }
-
-    /// Recursively search for nearest neighbors.
-    fn recurse<'a, U, N>(
-        slice: &'a [KdNode<T>],
-        i: usize,
-        closest: &mut [f64],
-        neighborhood: &mut N,
-    ) where
-        T: 'a,
-        U: CartesianMetric<&'a T>,
-        N: Neighborhood<&'a T, U>,
-    {
-        let (node, children) = slice.split_first().unwrap();
-        neighborhood.consider(&node.item);
-
-        let target = neighborhood.target();
-        let ti = target.coordinate(i);
-        let ni = node.item.coordinate(i);
-        let j = (i + 1) % node.item.dimensions();
-
-        let (left, right) = children.split_at(node.left_len);
-        let (near, far) = if ti <= ni {
-            (left, right)
-        } else {
-            (right, left)
-        };
-
-        if !near.is_empty() {
-            Self::recurse(near, j, closest, neighborhood);
-        }
-
-        if !far.is_empty() {
-            let saved = closest[i];
-            closest[i] = ni;
-            if neighborhood.contains_distance(target.distance(closest)) {
-                Self::recurse(far, j, closest, neighborhood);
-            }
-            closest[i] = saved;
-        }
-    }
-}
-
-/// A [k-d tree](https://en.wikipedia.org/wiki/K-d_tree).
-#[derive(Debug)]
-pub struct KdTree<T>(Vec<KdNode<T>>);
-
-impl<T: Cartesian> FromIterator<T> for KdTree<T> {
-    /// Create a new k-d tree from a set of points.
-    fn from_iter<I: IntoIterator<Item = T>>(items: I) -> Self {
-        let mut nodes: Vec<_> = items.into_iter().map(KdNode::new).collect();
-        KdNode::build(nodes.as_mut_slice(), 0);
-        Self(nodes)
-    }
-}
-
-impl<T, U> NearestNeighbors<T, U> for KdTree<T>
-where
-    T: Cartesian,
-    U: CartesianMetric<T>,
-{
-    fn search<'a, 'b, N>(&'a self, mut neighborhood: N) -> N
-    where
-        T: 'a,
-        U: 'b,
-        N: Neighborhood<&'a T, &'b U>,
-    {
-        if !self.0.is_empty() {
-            let target = neighborhood.target();
-            let dims = target.dimensions();
-            let mut closest: Vec<_> = (0..dims).map(|i| target.coordinate(i)).collect();
-
-            KdNode::recurse(&self.0, 0, &mut closest, &mut neighborhood);
-        }
-
-        neighborhood
-    }
-}
-
-/// An iterator that the moves values out of a k-d tree.
-#[derive(Debug)]
-pub struct IntoIter<T>(std::vec::IntoIter<KdNode<T>>);
-
-impl<T> Iterator for IntoIter<T> {
-    type Item = T;
-
-    fn next(&mut self) -> Option<T> {
-        self.0.next().map(|n| n.item)
-    }
-}
-
-impl<T> IntoIterator for KdTree<T> {
-    type Item = T;
-    type IntoIter = IntoIter<T>;
-
-    fn into_iter(self) -> Self::IntoIter {
-        IntoIter(self.0.into_iter())
-    }
-}
-
-#[cfg(test)]
-mod tests {
-    use super::*;
-
-    use crate::metric::tests::{test_nearest_neighbors, Point};
-    use crate::metric::SquaredDistance;
-
-    impl Metric<[f64]> for Point {
-        type Distance = SquaredDistance;
-
-        fn distance(&self, other: &[f64]) -> Self::Distance {
-            self.0.distance(other)
-        }
-    }
-
-    impl Cartesian for Point {
-        fn dimensions(&self) -> usize {
-            self.0.dimensions()
-        }
-
-        fn coordinate(&self, i: usize) -> f64 {
-            self.0.coordinate(i)
-        }
-    }
-
-    #[test]
-    fn test_kd_tree() {
-        test_nearest_neighbors(KdTree::from_iter);
-    }
-}
diff --git a/src/metric/vp.rs b/src/metric/vp.rs
deleted file mode 100644
index d6e05df..0000000
--- a/src/metric/vp.rs
+++ /dev/null
@@ -1,137 +0,0 @@
-//! [Vantage-point trees](https://en.wikipedia.org/wiki/Vantage-point_tree).
-
-use super::{Metric, NearestNeighbors, Neighborhood, Ordered};
-
-use std::iter::FromIterator;
-
-/// A node in a VP tree.
-#[derive(Debug)]
-struct VpNode<T> {
-    /// The vantage point itself.
-    item: T,
-    /// The radius of this node.
-    radius: f64,
-    /// The size of the subtree inside the radius.
-    inside_len: usize,
-}
-
-impl<T: Metric> VpNode<T> {
-    /// Create a new VpNode.
-    fn new(item: T) -> Self {
-        Self {
-            item,
-            radius: 0.0,
-            inside_len: 0,
-        }
-    }
-
-    /// Build a VP tree recursively.
-    fn build(slice: &mut [VpNode<T>]) {
-        if let Some((node, children)) = slice.split_first_mut() {
-            let item = &node.item;
-            children.sort_by_cached_key(|n| Ordered(item.distance(&n.item)));
-
-            let (inside, outside) = children.split_at_mut(children.len() / 2);
-            if let Some(last) = inside.last() {
-                node.radius = item.distance(&last.item).into();
-            }
-            node.inside_len = inside.len();
-
-            Self::build(inside);
-            Self::build(outside);
-        }
-    }
-
-    /// Recursively search for nearest neighbors.
-    fn recurse<'a, U, N>(slice: &'a [VpNode<T>], neighborhood: &mut N)
-    where
-        T: 'a,
-        U: Metric<&'a T>,
-        N: Neighborhood<&'a T, U>,
-    {
-        let (node, children) = slice.split_first().unwrap();
-        let (inside, outside) = children.split_at(node.inside_len);
-
-        let distance = neighborhood.consider(&node.item).into();
-
-        if distance <= node.radius {
-            if !inside.is_empty() && neighborhood.contains(distance - node.radius) {
-                Self::recurse(inside, neighborhood);
-            }
-            if !outside.is_empty() && neighborhood.contains(node.radius - distance) {
-                Self::recurse(outside, neighborhood);
-            }
-        } else {
-            if !outside.is_empty() && neighborhood.contains(node.radius - distance) {
-                Self::recurse(outside, neighborhood);
-            }
-            if !inside.is_empty() && neighborhood.contains(distance - node.radius) {
-                Self::recurse(inside, neighborhood);
-            }
-        }
-    }
-}
-
-/// A [vantage-point tree](https://en.wikipedia.org/wiki/Vantage-point_tree).
-#[derive(Debug)]
-pub struct VpTree<T>(Vec<VpNode<T>>);
-
-impl<T: Metric> FromIterator<T> for VpTree<T> {
-    fn from_iter<I: IntoIterator<Item = T>>(items: I) -> Self {
-        let mut nodes: Vec<_> = items.into_iter().map(VpNode::new).collect();
-        VpNode::build(nodes.as_mut_slice());
-        Self(nodes)
-    }
-}
-
-impl<T, U> NearestNeighbors<T, U> for VpTree<T>
-where
-    T: Metric,
-    U: Metric<T>,
-{
-    fn search<'a, 'b, N>(&'a self, mut neighborhood: N) -> N
-    where
-        T: 'a,
-        U: 'b,
-        N: Neighborhood<&'a T, &'b U>,
-    {
-        if !self.0.is_empty() {
-            VpNode::recurse(&self.0, &mut neighborhood);
-        }
-
-        neighborhood
-    }
-}
-
-/// An iterator that moves values out of a VP tree.
-#[derive(Debug)]
-pub struct IntoIter<T>(std::vec::IntoIter<VpNode<T>>);
-
-impl<T> Iterator for IntoIter<T> {
-    type Item = T;
-
-    fn next(&mut self) -> Option<T> {
-        self.0.next().map(|n| n.item)
-    }
-}
-
-impl<T> IntoIterator for VpTree<T> {
-    type Item = T;
-    type IntoIter = IntoIter<T>;
-
-    fn into_iter(self) -> Self::IntoIter {
-        IntoIter(self.0.into_iter())
-    }
-}
-
-#[cfg(test)]
-mod tests {
-    use super::*;
-
-    use crate::metric::tests::test_nearest_neighbors;
-
-    #[test]
-    fn test_vp_tree() {
-        test_nearest_neighbors(VpTree::from_iter);
-    }
-}
diff --git a/src/metric/soft.rs b/src/soft.rs
index d443bfd..3edaa10 100644
--- a/src/metric/soft.rs
+++ b/src/soft.rs
@@ -1,9 +1,11 @@
 //! [Soft deletion](https://en.wiktionary.org/wiki/soft_deletion) for nearest neighbor search.
 
 use super::forest::{KdForest, VpForest};
-use super::kd::KdTree;
-use super::vp::VpTree;
-use super::{Metric, NearestNeighbors, Neighborhood};
+
+use acap::distance::Proximity;
+use acap::kd::FlatKdTree;
+use acap::vp::FlatVpTree;
+use acap::{NearestNeighbors, Neighborhood};
 
 use std::iter;
 use std::iter::FromIterator;
@@ -26,25 +28,24 @@ impl<'a, T: SoftDelete> SoftDelete for &'a T {
 #[derive(Debug)]
 struct SoftNeighborhood<N>(N);
 
-impl<T, U, N> Neighborhood<T, U> for SoftNeighborhood<N>
+impl<K, V, N> Neighborhood<K, V> for SoftNeighborhood<N>
 where
-    T: SoftDelete,
-    U: Metric<T>,
-    N: Neighborhood<T, U>,
+    V: SoftDelete,
+    K: Proximity<V>,
+    N: Neighborhood<K, V>,
 {
-    fn target(&self) -> U {
+    fn target(&self) -> K {
         self.0.target()
     }
 
-    fn contains(&self, distance: f64) -> bool {
+    fn contains<D>(&self, distance: D) -> bool
+    where
+        D: PartialOrd<K::Distance>
+    {
         self.0.contains(distance)
     }
 
-    fn contains_distance(&self, distance: U::Distance) -> bool {
-        self.0.contains_distance(distance)
-    }
-
-    fn consider(&mut self, item: T) -> U::Distance {
+    fn consider(&mut self, item: V) -> K::Distance {
         if item.is_deleted() {
             self.target().distance(&item)
         } else {
@@ -113,17 +114,17 @@ impl<T: IntoIterator> IntoIterator for SoftSearch<T> {
     }
 }
 
-impl<T, U, V> NearestNeighbors<T, U> for SoftSearch<V>
+impl<K, V, T> NearestNeighbors<K, V> for SoftSearch<T>
 where
-    T: SoftDelete,
-    U: Metric<T>,
-    V: NearestNeighbors<T, U>,
+    K: Proximity<V>,
+    V: SoftDelete,
+    T: NearestNeighbors<K, V>,
 {
-    fn search<'a, 'b, N>(&'a self, neighborhood: N) -> N
+    fn search<'k, 'v, N>(&'v self, neighborhood: N) -> N
     where
-        T: 'a,
-        U: 'b,
-        N: Neighborhood<&'a T, &'b U>,
+        K: 'k,
+        V: 'v,
+        N: Neighborhood<&'k K, &'v V>
     {
         self.0.search(SoftNeighborhood(neighborhood)).0
     }
@@ -133,39 +134,41 @@ where
 pub type SoftKdForest<T> = SoftSearch<KdForest<T>>;
 
 /// A k-d tree that supports soft deletes.
-pub type SoftKdTree<T> = SoftSearch<KdTree<T>>;
+pub type SoftKdTree<T> = SoftSearch<FlatKdTree<T>>;
 
 /// A VP forest that supports soft deletes.
 pub type SoftVpForest<T> = SoftSearch<VpForest<T>>;
 
 /// A VP tree that supports soft deletes.
-pub type SoftVpTree<T> = SoftSearch<VpTree<T>>;
+pub type SoftVpTree<T> = SoftSearch<FlatVpTree<T>>;
 
 #[cfg(test)]
 mod tests {
     use super::*;
 
-    use crate::metric::kd::Cartesian;
-    use crate::metric::tests::Point;
-    use crate::metric::Neighbor;
+    use acap::coords::Coordinates;
+    use acap::euclid::{euclidean_distance, Euclidean, EuclideanDistance};
+    use acap::Neighbor;
+
+    type Point = Euclidean<[f32; 3]>;
 
     #[derive(Debug, PartialEq)]
     struct SoftPoint {
-        point: Point,
+        point: [f32; 3],
         deleted: bool,
     }
 
     impl SoftPoint {
-        fn new(x: f64, y: f64, z: f64) -> Self {
+        fn new(x: f32, y: f32, z: f32) -> Self {
             Self {
-                point: Point([x, y, z]),
+                point: [x, y, z],
                 deleted: false,
             }
         }
 
-        fn deleted(x: f64, y: f64, z: f64) -> Self {
+        fn deleted(x: f32, y: f32, z: f32) -> Self {
             Self {
-                point: Point([x, y, z]),
+                point: [x, y, z],
                 deleted: true,
             }
         }
@@ -177,55 +180,49 @@ mod tests {
         }
     }
 
-    impl Metric for SoftPoint {
-        type Distance = <Point as Metric>::Distance;
+    impl Proximity for SoftPoint {
+        type Distance = EuclideanDistance<f32>;
 
         fn distance(&self, other: &Self) -> Self::Distance {
-            self.point.distance(&other.point)
+            euclidean_distance(&self.point, &other.point)
         }
     }
 
-    impl Metric<[f64]> for SoftPoint {
-        type Distance = <Point as Metric>::Distance;
-
-        fn distance(&self, other: &[f64]) -> Self::Distance {
-            self.point.distance(other)
-        }
-    }
+    impl Coordinates for SoftPoint {
+        type Value = <Point as Coordinates>::Value;
 
-    impl Cartesian for SoftPoint {
-        fn dimensions(&self) -> usize {
-            self.point.dimensions()
+        fn dims(&self) -> usize {
+            self.point.dims()
         }
 
-        fn coordinate(&self, i: usize) -> f64 {
-            self.point.coordinate(i)
+        fn coord(&self, i: usize) -> Self::Value {
+            self.point.coord(i)
         }
     }
 
-    impl Metric<SoftPoint> for Point {
-        type Distance = <Point as Metric>::Distance;
+    impl Proximity<SoftPoint> for Point {
+        type Distance = EuclideanDistance<f32>;
 
         fn distance(&self, other: &SoftPoint) -> Self::Distance {
-            self.distance(&other.point)
+            euclidean_distance(&self, &other.point)
         }
     }
 
     fn test_index<T>(index: &T)
     where
-        T: NearestNeighbors<SoftPoint, Point>,
+        T: NearestNeighbors<Point, SoftPoint>,
     {
-        let target = Point([0.0, 0.0, 0.0]);
+        let target = Euclidean([0.0, 0.0, 0.0]);
 
         assert_eq!(
-            index.nearest(&target),
-            Some(Neighbor::new(&SoftPoint::new(1.0, 2.0, 2.0), 3.0))
+            index.nearest(&target).expect("No nearest neighbor found"),
+            Neighbor::new(&SoftPoint::new(1.0, 2.0, 2.0), 3.0)
         );
 
         assert_eq!(index.nearest_within(&target, 2.0), None);
         assert_eq!(
-            index.nearest_within(&target, 4.0),
-            Some(Neighbor::new(&SoftPoint::new(1.0, 2.0, 2.0), 3.0))
+            index.nearest_within(&target, 4.0).expect("No nearest neighbor found within 4.0"),
+            Neighbor::new(&SoftPoint::new(1.0, 2.0, 2.0), 3.0)
         );
 
         assert_eq!(
@@ -259,7 +256,7 @@ mod tests {
         T: Extend<SoftPoint>,
         T: FromIterator<SoftPoint>,
         T: IntoIterator<Item = SoftPoint>,
-        T: NearestNeighbors<SoftPoint, Point>,
+        T: NearestNeighbors<Point, SoftPoint>,
     {
         let points = vec![
             SoftPoint::deleted(0.0, 0.0, 0.0),