Merge pull request #1 from tavianator/rust

Rewrite in rust

15 files changed, 3079 insertions, 0 deletions

diff --git a/src/color.rs b/src/color.rs
new file mode 100644
index 0000000..64fd82b
--- /dev/null
+++ b/src/color.rs
@@ -0,0 +1,285 @@
+//! Colors and color spaces.
+
+pub mod order;
+pub mod source;
+
+use crate::metric::kd::{Cartesian, CartesianMetric};
+use crate::metric::{Metric, SquaredDistance};
+
+use image::Rgb;
+
+use std::ops::Index;
+
+/// An 8-bit RGB color.
+pub type Rgb8 = Rgb<u8>;
+
+/// A [color space](https://en.wikipedia.org/wiki/Color_space).
+pub trait ColorSpace: Copy + From<Rgb8> + CartesianMetric {
+    /// Compute the average of the given colors.
+    fn average<I: IntoIterator<Item = Self>>(colors: I) -> Self;
+}
+
+/// [sRGB](https://en.wikipedia.org/wiki/SRGB) space.
+#[derive(Clone, Copy, Debug)]
+pub struct RgbSpace([f64; 3]);
+
+impl Index<usize> for RgbSpace {
+    type Output = f64;
+
+    fn index(&self, i: usize) -> &f64 {
+        &self.0[i]
+    }
+}
+
+impl From<Rgb8> for RgbSpace {
+    fn from(rgb8: Rgb8) -> Self {
+        Self([
+            (rgb8[0] as f64) / 255.0,
+            (rgb8[1] as f64) / 255.0,
+            (rgb8[2] as f64) / 255.0,
+        ])
+    }
+}
+
+impl Metric<[f64]> for RgbSpace {
+    type Distance = SquaredDistance;
+
+    fn distance(&self, other: &[f64]) -> Self::Distance {
+        self.0.distance(other)
+    }
+}
+
+impl Metric for RgbSpace {
+    type Distance = SquaredDistance;
+
+    fn distance(&self, other: &Self) -> Self::Distance {
+        self.0.distance(&other.0)
+    }
+}
+
+impl Cartesian for RgbSpace {
+    fn dimensions(&self) -> usize {
+        self.0.dimensions()
+    }
+
+    fn coordinate(&self, i: usize) -> f64 {
+        self.0.coordinate(i)
+    }
+}
+
+impl ColorSpace for RgbSpace {
+    fn average<I: IntoIterator<Item = Self>>(colors: I) -> Self {
+        let mut sum = [0.0, 0.0, 0.0];
+        let mut len: usize = 0;
+        for color in colors.into_iter() {
+            for i in 0..3 {
+                sum[i] += color[i];
+            }
+            len += 1;
+        }
+        for i in 0..3 {
+            sum[i] /= len as f64;
+        }
+        Self(sum)
+    }
+}
+
+/// [CIE XYZ](https://en.wikipedia.org/wiki/CIE_1931_color_space) space.
+#[derive(Clone, Copy, Debug)]
+struct XyzSpace([f64; 3]);
+
+impl Index<usize> for XyzSpace {
+    type Output = f64;
+
+    fn index(&self, i: usize) -> &f64 {
+        &self.0[i]
+    }
+}
+
+/// The inverse of the sRGB gamma function.
+fn srgb_inv_gamma(t: f64) -> f64 {
+    if t <= 0.040449936 {
+        t / 12.92
+    } else {
+        ((t + 0.055) / 1.055).powf(2.4)
+    }
+}
+
+impl From<Rgb8> for XyzSpace {
+    fn from(rgb8: Rgb8) -> Self {
+        let rgb = RgbSpace::from(rgb8);
+
+        let r = srgb_inv_gamma(rgb[0]);
+        let g = srgb_inv_gamma(rgb[1]);
+        let b = srgb_inv_gamma(rgb[2]);
+
+        Self([
+            0.4123808838268995 * r + 0.3575728355732478 * g + 0.1804522977447919 * b,
+            0.2126198631048975 * r + 0.7151387878413206 * g + 0.0721499433963131 * b,
+            0.0193434956789248 * r + 0.1192121694056356 * g + 0.9505065664127130 * b,
+        ])
+    }
+}
+
+/// CIE D50 [white point](https://en.wikipedia.org/wiki/Standard_illuminant).
+const WHITE: XyzSpace = XyzSpace([0.9504060171449392, 0.9999085943425312, 1.089062231497274]);
+
+/// CIE L\*a\*b\* (and L\*u\*v\*) gamma
+fn lab_gamma(t: f64) -> f64 {
+    if t > 216.0 / 24389.0 {
+        t.cbrt()
+    } else {
+        841.0 * t / 108.0 + 4.0 / 29.0
+    }
+}
+
+/// [CIE L\*a\*b\*](https://en.wikipedia.org/wiki/CIELAB_color_space) space.
+#[derive(Clone, Copy, Debug)]
+pub struct LabSpace([f64; 3]);
+
+impl Index<usize> for LabSpace {
+    type Output = f64;
+
+    fn index(&self, i: usize) -> &f64 {
+        &self.0[i]
+    }
+}
+
+impl From<Rgb8> for LabSpace {
+    fn from(rgb8: Rgb8) -> Self {
+        let xyz = XyzSpace::from(rgb8);
+
+        let x = lab_gamma(xyz[0] / WHITE[0]);
+        let y = lab_gamma(xyz[1] / WHITE[1]);
+        let z = lab_gamma(xyz[2] / WHITE[2]);
+
+        let l = 116.0 * y - 16.0;
+        let a = 500.0 * (x - y);
+        let b = 200.0 * (y - z);
+
+        Self([l, a, b])
+    }
+}
+
+impl Metric<[f64]> for LabSpace {
+    type Distance = SquaredDistance;
+
+    fn distance(&self, other: &[f64]) -> Self::Distance {
+        self.0.distance(other)
+    }
+}
+
+impl Metric for LabSpace {
+    type Distance = SquaredDistance;
+
+    fn distance(&self, other: &Self) -> Self::Distance {
+        self.0.distance(&other.0)
+    }
+}
+
+impl Cartesian for LabSpace {
+    fn dimensions(&self) -> usize {
+        self.0.dimensions()
+    }
+
+    fn coordinate(&self, i: usize) -> f64 {
+        self.0.coordinate(i)
+    }
+}
+
+impl ColorSpace for LabSpace {
+    fn average<I: IntoIterator<Item = Self>>(colors: I) -> Self {
+        let mut sum = [0.0, 0.0, 0.0];
+        let mut len: usize = 0;
+        for color in colors.into_iter() {
+            for i in 0..3 {
+                sum[i] += color[i];
+            }
+            len += 1;
+        }
+        for i in 0..3 {
+            sum[i] /= len as f64;
+        }
+        Self(sum)
+    }
+}
+
+/// [CIE L\*u\*v\*](https://en.wikipedia.org/wiki/CIELUV) space.
+#[derive(Clone, Copy, Debug)]
+pub struct LuvSpace([f64; 3]);
+
+impl Index<usize> for LuvSpace {
+    type Output = f64;
+
+    fn index(&self, i: usize) -> &f64 {
+        &self.0[i]
+    }
+}
+
+/// Computes the u' and v' values for L\*u\*v\*.
+fn uv_prime(xyz: &XyzSpace) -> (f64, f64) {
+    let denom = xyz[0] + 15.0 * xyz[1] + 3.0 * xyz[2];
+    if denom == 0.0 {
+        (0.0, 0.0)
+    } else {
+        (4.0 * xyz[0] / denom, 9.0 * xyz[1] / denom)
+    }
+}
+
+impl From<Rgb8> for LuvSpace {
+    fn from(rgb8: Rgb8) -> Self {
+        let xyz = XyzSpace::from(rgb8);
+
+        let (uprime, vprime) = uv_prime(&xyz);
+        let (unprime, vnprime) = uv_prime(&WHITE);
+
+        let l = 116.0 * lab_gamma(xyz[1] / WHITE[1]) - 16.0;
+        let u = 13.0 * l * (uprime - unprime);
+        let v = 13.0 * l * (vprime - vnprime);
+
+        Self([l, u, v])
+    }
+}
+
+impl Metric<[f64]> for LuvSpace {
+    type Distance = SquaredDistance;
+
+    fn distance(&self, other: &[f64]) -> Self::Distance {
+        self.0.distance(other)
+    }
+}
+
+impl Metric for LuvSpace {
+    type Distance = SquaredDistance;
+
+    fn distance(&self, other: &Self) -> Self::Distance {
+        self.0.distance(&other.0)
+    }
+}
+
+impl Cartesian for LuvSpace {
+    fn dimensions(&self) -> usize {
+        self.0.dimensions()
+    }
+
+    fn coordinate(&self, i: usize) -> f64 {
+        self.0.coordinate(i)
+    }
+}
+
+impl ColorSpace for LuvSpace {
+    fn average<I: IntoIterator<Item = Self>>(colors: I) -> Self {
+        let mut sum = [0.0, 0.0, 0.0];
+        let mut len: usize = 0;
+        for color in colors.into_iter() {
+            for i in 0..3 {
+                sum[i] += color[i];
+            }
+            len += 1;
+        }
+        for i in 0..3 {
+            sum[i] /= len as f64;
+        }
+        Self(sum)
+    }
+}
diff --git a/src/color/order.rs b/src/color/order.rs
new file mode 100644
index 0000000..300a556
--- /dev/null
+++ b/src/color/order.rs
@@ -0,0 +1,196 @@
+//! Linear orders for colors.
+
+use super::source::ColorSource;
+use super::Rgb8;
+
+use crate::hilbert::hilbert_point;
+
+use rand::seq::SliceRandom;
+use rand::Rng;
+
+use std::cmp::Ordering;
+
+/// An iterator over all colors from a source.
+#[derive(Debug)]
+struct ColorSourceIter<S> {
+    source: S,
+    coords: Vec<usize>,
+}
+
+impl<S: ColorSource> From<S> for ColorSourceIter<S> {
+    fn from(source: S) -> Self {
+        let coords = vec![0; source.dimensions().len()];
+
+        Self { source, coords }
+    }
+}
+
+impl<S: ColorSource> Iterator for ColorSourceIter<S> {
+    type Item = Rgb8;
+
+    fn next(&mut self) -> Option<Rgb8> {
+        if self.coords.is_empty() {
+            return None;
+        }
+
+        let color = self.source.get_color(&self.coords);
+
+        let dims = self.source.dimensions();
+        for i in 0..dims.len() {
+            self.coords[i] += 1;
+            if self.coords[i] < dims[i] {
+                break;
+            } else if i == dims.len() - 1 {
+                self.coords.clear();
+            } else {
+                self.coords[i] = 0;
+            }
+        }
+
+        Some(color)
+    }
+}
+
+/// Wrapper for sorting colors by hue.
+#[derive(Debug, Eq, PartialEq)]
+struct Hue {
+    /// The quadrant of the hue angle.
+    quad: i32,
+    /// The numerator of the hue calculation.
+    num: i32,
+    /// The denominator of the hue calculation.
+    denom: i32,
+}
+
+impl From<Rgb8> for Hue {
+    fn from(rgb8: Rgb8) -> Self {
+        // The hue angle is atan2(sqrt(3) * (G - B), 2 * R - G - B).  We avoid actually computing
+        // the atan2() as an optimization.
+        let r = rgb8[0] as i32;
+        let g = rgb8[1] as i32;
+        let b = rgb8[2] as i32;
+
+        let num = g - b;
+        let mut denom = 2 * r - g - b;
+        if num == 0 && denom == 0 {
+            denom = 1;
+        }
+
+        let quad = match (num >= 0, denom >= 0) {
+            (true, true) => 0,
+            (true, false) => 1,
+            (false, false) => 2,
+            (false, true) => 3,
+        };
+
+        Self { quad, num, denom }
+    }
+}
+
+impl Ord for Hue {
+    fn cmp(&self, other: &Self) -> Ordering {
+        // Within the same quadrant,
+        //
+        //     atan2(n1, d1) < atan2(n2, d2)  iff
+        //           n1 / d1 < n2 / d2        iff
+        //           n1 * d2 < n2 * d1
+        self.quad
+            .cmp(&other.quad)
+            .then_with(|| (self.num * other.denom).cmp(&(other.num * self.denom)))
+    }
+}
+
+impl PartialOrd for Hue {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+/// Iterate over colors sorted by their hue.
+pub fn hue_sorted<S: ColorSource>(source: S) -> Vec<Rgb8> {
+    let mut colors: Vec<_> = ColorSourceIter::from(source).collect();
+    colors.sort_by_key(|c| Hue::from(*c));
+    colors
+}
+
+/// Iterate over colors in random order.
+pub fn shuffled<S: ColorSource, R: Rng>(source: S, rng: &mut R) -> Vec<Rgb8> {
+    let mut colors: Vec<_> = ColorSourceIter::from(source).collect();
+    colors.shuffle(rng);
+    colors
+}
+
+/// ceil(log_2(n)). for rounding up to powers of 2.
+fn log2(n: usize) -> u32 {
+    let nbits = 8 * std::mem::size_of::<usize>() as u32;
+    nbits - (n - 1).leading_zeros()
+}
+
+/// Iterate over colors in Morton order (Z-order).
+pub fn morton<S: ColorSource>(source: S) -> Vec<Rgb8> {
+    let mut colors = Vec::new();
+
+    let dims = source.dimensions();
+    let ndims = dims.len();
+
+    let nbits = ndims * dims.iter().map(|n| log2(*n) as usize).max().unwrap();
+
+    let size = 1usize << nbits;
+    let mut coords = vec![0; ndims];
+    for i in 0..size {
+        for x in &mut coords {
+            *x = 0;
+        }
+        for j in 0..nbits {
+            let bit = (i >> j) & 1;
+            coords[j % ndims] |= bit << (j / ndims);
+        }
+        if coords.iter().zip(dims.iter()).all(|(x, n)| x < n) {
+            colors.push(source.get_color(&coords));
+        }
+    }
+
+    colors
+}
+
+/// Iterate over colors in Hilbert curve order.
+pub fn hilbert<S: ColorSource>(source: S) -> Vec<Rgb8> {
+    let mut colors = Vec::new();
+
+    let dims = source.dimensions();
+    let ndims = dims.len();
+
+    let bits: Vec<_> = dims.iter().map(|n| log2(*n)).collect();
+    let nbits: u32 = bits.iter().sum();
+    let size = 1usize << nbits;
+
+    let mut coords = vec![0; ndims];
+
+    for i in 0..size {
+        hilbert_point(i, &bits, &mut coords);
+        if coords.iter().zip(dims.iter()).all(|(x, n)| x < n) {
+            colors.push(source.get_color(&coords));
+        }
+    }
+
+    colors
+}
+
+/// Stripe an ordered list of colors, to reduce artifacts in the generated image.
+///
+/// The striped ordering gives every other item first, then every other item from the remaining
+/// items, etc. For example, the striped form of `0..16` is
+/// `[0, 2, 4, 6, 8, 10, 12, 14, 1, 5, 9, 13, 3, 11, 7, 15]`.
+pub fn striped(colors: Vec<Rgb8>) -> Vec<Rgb8> {
+    let len = colors.len();
+    let mut result = Vec::with_capacity(len);
+    let mut stripe = 1;
+    while stripe <= len {
+        for i in ((stripe - 1)..len).step_by(2 * stripe) {
+            result.push(colors[i]);
+        }
+        stripe *= 2;
+    }
+
+    result
+}
diff --git a/src/color/source.rs b/src/color/source.rs
new file mode 100644
index 0000000..bd752d9
--- /dev/null
+++ b/src/color/source.rs
@@ -0,0 +1,76 @@
+//! Sources of colors.
+
+use super::Rgb8;
+
+use image::RgbImage;
+
+/// A source of colors in multidimensional space.
+pub trait ColorSource {
+    /// Get the size of each dimension in this space.
+    fn dimensions(&self) -> &[usize];
+
+    /// Get the color at some particular coordinates.
+    fn get_color(&self, coords: &[usize]) -> Rgb8;
+}
+
+/// The entire RGB space.
+#[derive(Debug)]
+pub struct AllColors {
+    dims: [usize; 3],
+    shifts: [usize; 3],
+}
+
+impl AllColors {
+    /// Create an AllColors source with the given bit depth.
+    pub fn new(bits: usize) -> Self {
+        // Allocate bits from most to least perceptually important
+        let gbits = (bits + 2) / 3;
+        let rbits = (bits + 1) / 3;
+        let bbits = bits / 3;
+
+        Self {
+            dims: [1 << rbits, 1 << gbits, 1 << bbits],
+            shifts: [8 - rbits, 8 - gbits, 8 - bbits],
+        }
+    }
+}
+
+impl ColorSource for AllColors {
+    fn dimensions(&self) -> &[usize] {
+        &self.dims
+    }
+
+    fn get_color(&self, coords: &[usize]) -> Rgb8 {
+        Rgb8::from([
+            (coords[0] << self.shifts[0]) as u8,
+            (coords[1] << self.shifts[1]) as u8,
+            (coords[2] << self.shifts[2]) as u8,
+        ])
+    }
+}
+
+/// Colors extracted from an image.
+#[derive(Debug)]
+pub struct ImageColors {
+    dims: [usize; 2],
+    image: RgbImage,
+}
+
+impl From<RgbImage> for ImageColors {
+    fn from(image: RgbImage) -> Self {
+        Self {
+            dims: [image.width() as usize, image.height() as usize],
+            image: image,
+        }
+    }
+}
+
+impl ColorSource for ImageColors {
+    fn dimensions(&self) -> &[usize] {
+        &self.dims
+    }
+
+    fn get_color(&self, coords: &[usize]) -> Rgb8 {
+        *self.image.get_pixel(coords[0] as u32, coords[1] as u32)
+    }
+}
diff --git a/src/frontier.rs b/src/frontier.rs
new file mode 100644
index 0000000..7143cb7
--- /dev/null
+++ b/src/frontier.rs
@@ -0,0 +1,149 @@
+//! Frontiers on which to place pixels.
+
+pub mod image;
+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 std::cell::Cell;
+use std::rc::Rc;
+
+/// A frontier of pixels.
+pub trait Frontier {
+    /// The width of the image.
+    fn width(&self) -> u32;
+
+    /// The height of the image.
+    fn height(&self) -> u32;
+
+    /// The number of pixels currently on the frontier.
+    fn len(&self) -> usize;
+
+    /// Place the given color on the frontier, and return its position.
+    fn place(&mut self, rgb8: Rgb8) -> Option<(u32, u32)>;
+}
+
+/// A pixel on a frontier.
+#[derive(Debug)]
+struct Pixel<C> {
+    pos: (u32, u32),
+    color: C,
+    deleted: Cell<bool>,
+}
+
+impl<C: ColorSpace> Pixel<C> {
+    fn new(x: u32, y: u32, color: C) -> Self {
+        Self {
+            pos: (x, y),
+            color,
+            deleted: Cell::new(false),
+        }
+    }
+
+    fn delete(&self) {
+        self.deleted.set(true);
+    }
+}
+
+impl<C: Metric> Metric<Pixel<C>> for C {
+    type Distance = C::Distance;
+
+    fn distance(&self, other: &Pixel<C>) -> Self::Distance {
+        self.distance(&other.color)
+    }
+}
+
+impl<C: Metric<[f64]>> Metric<[f64]> for Pixel<C> {
+    type Distance = C::Distance;
+
+    fn distance(&self, other: &[f64]) -> Self::Distance {
+        self.color.distance(other)
+    }
+}
+
+impl<C: Metric> Metric for Pixel<C> {
+    type Distance = C::Distance;
+
+    fn distance(&self, other: &Pixel<C>) -> Self::Distance {
+        self.color.distance(&other.color)
+    }
+}
+
+impl<C: Cartesian> Cartesian for Pixel<C> {
+    fn dimensions(&self) -> usize {
+        self.color.dimensions()
+    }
+
+    fn coordinate(&self, i: usize) -> f64 {
+        self.color.coordinate(i)
+    }
+}
+
+impl<C> SoftDelete for Pixel<C> {
+    fn is_deleted(&self) -> bool {
+        self.deleted.get()
+    }
+}
+
+impl<C: Metric<[f64]>> Metric<[f64]> for Rc<Pixel<C>> {
+    type Distance = C::Distance;
+
+    fn distance(&self, other: &[f64]) -> Self::Distance {
+        (**self).distance(other)
+    }
+}
+
+impl<C: Metric> Metric<Rc<Pixel<C>>> for C {
+    type Distance = C::Distance;
+
+    fn distance(&self, other: &Rc<Pixel<C>>) -> Self::Distance {
+        self.distance(&other.color)
+    }
+}
+
+impl<C: Metric> Metric for Rc<Pixel<C>> {
+    type Distance = C::Distance;
+
+    fn distance(&self, other: &Self) -> Self::Distance {
+        (**self).distance(&**other)
+    }
+}
+
+impl<C: Cartesian> Cartesian for Rc<Pixel<C>> {
+    fn dimensions(&self) -> usize {
+        (**self).dimensions()
+    }
+
+    fn coordinate(&self, i: usize) -> f64 {
+        (**self).coordinate(i)
+    }
+}
+
+impl<C> SoftDelete for Rc<Pixel<C>> {
+    fn is_deleted(&self) -> bool {
+        (**self).is_deleted()
+    }
+}
+
+/// Return all the neighbors of a pixel location.
+fn neighbors(x: u32, y: u32) -> [(u32, u32); 8] {
+    let xm1 = x.wrapping_sub(1);
+    let ym1 = y.wrapping_sub(1);
+    let xp1 = x + 1;
+    let yp1 = y + 1;
+
+    [
+        (xm1, ym1),
+        (xm1, y),
+        (xm1, yp1),
+        (x, ym1),
+        (x, yp1),
+        (xp1, ym1),
+        (xp1, y),
+        (xp1, yp1),
+    ]
+}
diff --git a/src/frontier/image.rs b/src/frontier/image.rs
new file mode 100644
index 0000000..3655580
--- /dev/null
+++ b/src/frontier/image.rs
@@ -0,0 +1,74 @@
+//! Frontier that targets an image.
+
+use super::{Frontier, Pixel};
+
+use crate::color::{ColorSpace, Rgb8};
+use crate::metric::soft::SoftKdTree;
+use crate::metric::NearestNeighbors;
+
+use image::RgbImage;
+
+/// A [Frontier] that places colors on the closest pixel of a target image.
+#[derive(Debug)]
+pub struct ImageFrontier<C: ColorSpace> {
+    nodes: SoftKdTree<Pixel<C>>,
+    width: u32,
+    height: u32,
+    len: usize,
+    deleted: usize,
+}
+
+impl<C: ColorSpace> ImageFrontier<C> {
+    /// Create an ImageFrontier from an image.
+    pub fn new(img: &RgbImage) -> Self {
+        let width = img.width();
+        let height = img.height();
+        let len = (width as usize) * (height as usize);
+
+        Self {
+            nodes: img
+                .enumerate_pixels()
+                .map(|(x, y, p)| Pixel::new(x, y, C::from(*p)))
+                .collect(),
+            width,
+            height,
+            len,
+            deleted: 0,
+        }
+    }
+}
+
+impl<C: ColorSpace> Frontier for ImageFrontier<C> {
+    fn width(&self) -> u32 {
+        self.width
+    }
+
+    fn height(&self) -> u32 {
+        self.height
+    }
+
+    fn len(&self) -> usize {
+        self.len - self.deleted
+    }
+
+    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) {
+            let pos = node.pos;
+
+            node.delete();
+            self.deleted += 1;
+
+            if 32 * self.deleted >= self.len {
+                self.nodes.rebuild();
+                self.len -= self.deleted;
+                self.deleted = 0;
+            }
+
+            Some(pos)
+        } else {
+            None
+        }
+    }
+}
diff --git a/src/frontier/mean.rs b/src/frontier/mean.rs
new file mode 100644
index 0000000..889c5ba
--- /dev/null
+++ b/src/frontier/mean.rs
@@ -0,0 +1,140 @@
+//! Mean selection frontier.
+
+use super::{neighbors, Frontier, Pixel};
+
+use crate::color::{ColorSpace, Rgb8};
+use crate::metric::soft::SoftKdForest;
+use crate::metric::NearestNeighbors;
+
+use std::iter;
+use std::rc::Rc;
+
+/// A pixel on a mean frontier.
+#[derive(Debug)]
+enum MeanPixel<C> {
+    Empty,
+    Fillable(Rc<Pixel<C>>),
+    Filled(C),
+}
+
+impl<C: ColorSpace> MeanPixel<C> {
+    fn filled_color(&self) -> Option<C> {
+        match self {
+            Self::Filled(color) => Some(*color),
+            _ => None,
+        }
+    }
+}
+
+/// A [Frontier] that looks at the average color of each pixel's neighbors.
+pub struct MeanFrontier<C> {
+    pixels: Vec<MeanPixel<C>>,
+    forest: SoftKdForest<Rc<Pixel<C>>>,
+    width: u32,
+    height: u32,
+    len: usize,
+    deleted: usize,
+}
+
+impl<C: ColorSpace> MeanFrontier<C> {
+    /// Create a MeanFrontier with the given dimensions and initial pixel location.
+    pub fn new(width: u32, height: u32, x0: u32, y0: u32) -> Self {
+        let size = (width as usize) * (height as usize);
+        let mut pixels = Vec::with_capacity(size);
+        for _ in 0..size {
+            pixels.push(MeanPixel::Empty);
+        }
+
+        let pixel0 = Rc::new(Pixel::new(x0, y0, C::from(Rgb8::from([0, 0, 0]))));
+        let i = (x0 + y0 * width) as usize;
+        pixels[i] = MeanPixel::Fillable(pixel0.clone());
+
+        Self {
+            pixels,
+            forest: iter::once(pixel0).collect(),
+            width,
+            height,
+            len: 1,
+            deleted: 0,
+        }
+    }
+
+    fn pixel_index(&self, x: u32, y: u32) -> usize {
+        debug_assert!(x < self.width);
+        debug_assert!(y < self.height);
+
+        (x + y * self.width) as usize
+    }
+
+    fn fill(&mut self, x: u32, y: u32, color: C) {
+        let i = self.pixel_index(x, y);
+        match &self.pixels[i] {
+            MeanPixel::Empty => {}
+            MeanPixel::Fillable(pixel) => {
+                pixel.delete();
+                self.deleted += 1;
+            }
+            _ => unreachable!(),
+        }
+        self.pixels[i] = MeanPixel::Filled(color);
+
+        let mut pixels = Vec::new();
+        for &(x, y) in &neighbors(x, y) {
+            if x < self.width && y < self.height {
+                let i = self.pixel_index(x, y);
+                match &self.pixels[i] {
+                    MeanPixel::Empty => {}
+                    MeanPixel::Fillable(pixel) => {
+                        pixel.delete();
+                        self.deleted += 1;
+                    }
+                    MeanPixel::Filled(_) => continue,
+                }
+                let color = C::average(
+                    neighbors(x, y)
+                        .iter()
+                        .filter(|(x, y)| *x < self.width && *y < self.height)
+                        .map(|(x, y)| self.pixel_index(*x, *y))
+                        .map(|i| &self.pixels[i])
+                        .map(MeanPixel::filled_color)
+                        .flatten(),
+                );
+                let pixel = Rc::new(Pixel::new(x, y, color));
+                self.pixels[i] = MeanPixel::Fillable(pixel.clone());
+                pixels.push(pixel);
+            }
+        }
+
+        self.len += pixels.len();
+        self.forest.extend(pixels);
+
+        if 2 * self.deleted >= self.len {
+            self.forest.rebuild();
+            self.len -= self.deleted;
+            self.deleted = 0;
+        }
+    }
+}
+
+impl<C: ColorSpace> Frontier for MeanFrontier<C> {
+    fn width(&self) -> u32 {
+        self.width
+    }
+
+    fn height(&self) -> u32 {
+        self.height
+    }
+
+    fn len(&self) -> usize {
+        self.len - self.deleted
+    }
+
+    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)?;
+
+        self.fill(x, y, color);
+
+        Some((x, y))
+    }
+}
diff --git a/src/frontier/min.rs b/src/frontier/min.rs
new file mode 100644
index 0000000..b22b290
--- /dev/null
+++ b/src/frontier/min.rs
@@ -0,0 +1,150 @@
+//! Minimum selection frontier.
+
+use super::{neighbors, Frontier, Pixel};
+
+use crate::color::{ColorSpace, Rgb8};
+use crate::metric::soft::SoftKdForest;
+use crate::metric::NearestNeighbors;
+
+use rand::Rng;
+
+use std::rc::Rc;
+
+/// A pixel on a min frontier.
+#[derive(Debug)]
+struct MinPixel<C> {
+    pixel: Option<Rc<Pixel<C>>>,
+    filled: bool,
+}
+
+impl<C: ColorSpace> MinPixel<C> {
+    fn new() -> Self {
+        Self {
+            pixel: None,
+            filled: false,
+        }
+    }
+}
+
+/// A [Frontier] that places colors on a neighbor of the closest pixel so far.
+#[derive(Debug)]
+pub struct MinFrontier<C, R> {
+    rng: R,
+    pixels: Vec<MinPixel<C>>,
+    forest: SoftKdForest<Rc<Pixel<C>>>,
+    width: u32,
+    height: u32,
+    x0: u32,
+    y0: u32,
+    len: usize,
+    deleted: usize,
+}
+
+impl<C: ColorSpace, R: Rng> MinFrontier<C, R> {
+    /// Create a MinFrontier with the given dimensions and initial pixel location.
+    pub fn new(rng: R, width: u32, height: u32, x0: u32, y0: u32) -> Self {
+        let size = (width as usize) * (height as usize);
+        let mut pixels = Vec::with_capacity(size);
+        for _ in 0..size {
+            pixels.push(MinPixel::new());
+        }
+
+        Self {
+            rng,
+            pixels,
+            forest: SoftKdForest::new(),
+            width,
+            height,
+            x0,
+            y0,
+            len: 0,
+            deleted: 0,
+        }
+    }
+
+    fn pixel_index(&self, x: u32, y: u32) -> usize {
+        debug_assert!(x < self.width);
+        debug_assert!(y < self.height);
+
+        (x + y * self.width) as usize
+    }
+
+    fn free_neighbor(&mut self, x: u32, y: u32) -> Option<(u32, u32)> {
+        // Pick a pseudo-random neighbor
+        let offset: usize = self.rng.gen();
+
+        let neighbors = neighbors(x, y);
+        for i in 0..8 {
+            let (x, y) = neighbors[(i + offset) % 8];
+            if x < self.width && y < self.height {
+                let i = self.pixel_index(x, y);
+                if !self.pixels[i].filled {
+                    return Some((x, y));
+                }
+            }
+        }
+
+        None
+    }
+
+    fn fill(&mut self, x: u32, y: u32, color: C) -> Option<(u32, u32)> {
+        let i = self.pixel_index(x, y);
+        let pixel = &mut self.pixels[i];
+        if pixel.filled {
+            return None;
+        }
+
+        let rc = Rc::new(Pixel::new(x, y, color));
+        pixel.pixel = Some(rc.clone());
+        pixel.filled = true;
+
+        if self.free_neighbor(x, y).is_some() {
+            self.forest.push(rc);
+            self.len += 1;
+        }
+
+        for &(x, y) in &neighbors(x, y) {
+            if x < self.width && y < self.height && self.free_neighbor(x, y).is_none() {
+                let i = self.pixel_index(x, y);
+                if let Some(pixel) = self.pixels[i].pixel.take() {
+                    pixel.delete();
+                    self.deleted += 1;
+                }
+            }
+        }
+
+        if 2 * self.deleted >= self.len {
+            self.forest.rebuild();
+            self.len -= self.deleted;
+            self.deleted = 0;
+        }
+
+        Some((x, y))
+    }
+}
+
+impl<C: ColorSpace, R: Rng> Frontier for MinFrontier<C, R> {
+    fn width(&self) -> u32 {
+        self.width
+    }
+
+    fn height(&self) -> u32 {
+        self.height
+    }
+
+    fn len(&self) -> usize {
+        self.len - self.deleted
+    }
+
+    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)
+            .map(|(x, y)| self.free_neighbor(x, y).unwrap())
+            .unwrap_or((self.x0, self.y0));
+
+        self.fill(x, y, color)
+    }
+}
diff --git a/src/hilbert.rs b/src/hilbert.rs
new file mode 100644
index 0000000..c0982d4
--- /dev/null
+++ b/src/hilbert.rs
@@ -0,0 +1,136 @@
+//! Implementation of [Compact Hilbert Indices](https://dl.acm.org/doi/10.1109/CISIS.2007.16) by
+//! Chris Hamilton.
+
+/// Right rotation of x by b bits out of n.
+fn rotate_right(x: usize, b: u32, n: u32) -> usize {
+    let l = x & ((1 << b) - 1);
+    let r = x >> b;
+    (l << (n - b)) | r
+}
+
+/// Left rotation of x by b bits out of n.
+fn rotate_left(x: usize, b: u32, n: u32) -> usize {
+    rotate_right(x, n - b, n)
+}
+
+/// Binary reflected Gray code.
+fn gray_code(i: usize) -> usize {
+    i ^ (i >> 1)
+}
+
+/// e(i), the entry point for the ith sub-hypercube.
+fn entry_point(i: usize) -> usize {
+    if i == 0 {
+        0
+    } else {
+        gray_code((i - 1) & !1)
+    }
+}
+
+/// g(i), the inter sub-hypercube direction.
+fn inter_direction(i: usize) -> u32 {
+    // g(i) counts the trailing set bits in i
+    (!i).trailing_zeros()
+}
+
+/// d(i), the intra sub-hypercube direction.
+fn intra_direction(i: usize) -> u32 {
+    if i & 1 != 0 {
+        inter_direction(i)
+    } else if i > 0 {
+        inter_direction(i - 1)
+    } else {
+        0
+    }
+}
+
+/// T transformation inverse
+fn t_inverse(dims: u32, e: usize, d: u32, a: usize) -> usize {
+    rotate_left(a, d, dims) ^ e
+}
+
+/// GrayCodeRankInverse
+fn gray_code_rank_inverse(
+    dims: u32,
+    mu: usize,
+    pi: usize,
+    r: usize,
+    free_bits: u32,
+) -> (usize, usize) {
+    // The inverse rank of r
+    let mut i = 0;
+    // gray_code(i)
+    let mut g = 0;
+
+    let mut j = free_bits - 1;
+    for k in (0..dims).rev() {
+        if mu & (1 << k) == 0 {
+            g |= pi & (1 << k);
+            i |= (g ^ (i >> 1)) & (1 << k);
+        } else {
+            i |= ((r >> j) & 1) << k;
+            g |= (i ^ (i >> 1)) & (1 << k);
+            j = j.wrapping_sub(1);
+        }
+    }
+
+    (i, g)
+}
+
+/// ExtractMask.
+fn extract_mask(bits: &[u32], i: u32) -> (usize, u32) {
+    // The mask
+    let mut mu = 0;
+    // popcount(mu)
+    let mut free_bits = 0;
+
+    let dims = bits.len();
+    for j in (0..dims).rev() {
+        mu <<= 1;
+        if bits[j] > i {
+            mu |= 1;
+            free_bits += 1;
+        }
+    }
+
+    (mu, free_bits)
+}
+
+/// Compute the corresponding point for a Hilbert index (CompactHilbertIndexInverse).
+pub fn hilbert_point(index: usize, bits: &[u32], point: &mut [usize]) {
+    let dims = bits.len() as u32;
+    let max = *bits.iter().max().unwrap();
+    let sum: u32 = bits.iter().sum();
+
+    let mut e = 0;
+    let mut k = 0;
+
+    // Next direction; we use d instead of d + 1 everywhere
+    let mut d = 1;
+
+    for x in point.iter_mut() {
+        *x = 0;
+    }
+
+    for i in (0..max).rev() {
+        let (mut mu, free_bits) = extract_mask(bits, i);
+        mu = rotate_right(mu, d, dims);
+
+        let pi = rotate_right(e, d, dims) & !mu;
+
+        let r = (index >> (sum - k - free_bits)) & ((1 << free_bits) - 1);
+
+        k += free_bits;
+
+        let (w, mut l) = gray_code_rank_inverse(dims, mu, pi, r, free_bits);
+        l = t_inverse(dims, e, d, l);
+
+        for x in point.iter_mut() {
+            *x |= (l & 1) << i;
+            l >>= 1;
+        }
+
+        e = e ^ rotate_right(entry_point(w), d, dims);
+        d = (d + intra_direction(w) + 1) % dims;
+    }
+}
diff --git a/src/main.rs b/src/main.rs
new file mode 100644
index 0000000..f016b4c
--- /dev/null
+++ b/src/main.rs
@@ -0,0 +1,401 @@
+pub mod color;
+pub mod frontier;
+pub mod hilbert;
+pub mod metric;
+
+use crate::color::source::{AllColors, ColorSource, ImageColors};
+use crate::color::{order, ColorSpace, LabSpace, LuvSpace, Rgb8, RgbSpace};
+use crate::frontier::image::ImageFrontier;
+use crate::frontier::mean::MeanFrontier;
+use crate::frontier::min::MinFrontier;
+use crate::frontier::Frontier;
+
+use clap::{self, clap_app, crate_authors, crate_name, crate_version, AppSettings};
+
+use image::{self, Rgba, RgbaImage};
+
+use rand::SeedableRng;
+use rand_pcg::Pcg64;
+
+use term;
+
+use std::cmp;
+use std::error::Error;
+use std::fs;
+use std::io::{self, Write};
+use std::path::PathBuf;
+use std::str::FromStr;
+use std::time::Instant;
+
+/// The color source specified on the command line.
+#[derive(Debug, Eq, PartialEq)]
+enum SourceArg {
+    /// All RGB colors of the given bit depth.
+    AllRgb(u32),
+    /// Take the colors from an image.
+    Image(PathBuf),
+}
+
+/// The order to process colors in.
+#[derive(Debug, Eq, PartialEq)]
+enum OrderArg {
+    /// Sorted by hue.
+    HueSort,
+    /// Shuffled randomly.
+    Random,
+    /// Morton/Z-order.
+    Morton,
+    /// Hilbert curve order.
+    Hilbert,
+}
+
+/// The frontier implementation.
+#[derive(Debug, Eq, PartialEq)]
+enum FrontierArg {
+    /// Pick a neighbor of the closest pixel so far.
+    Min,
+    /// Pick the pixel with the closest mean color of all its neighbors.
+    Mean,
+    /// Target the closest pixel on an image.
+    Image(PathBuf),
+}
+
+/// The color space to operate in.
+#[derive(Debug, Eq, PartialEq)]
+enum ColorSpaceArg {
+    /// sRGB space.
+    Rgb,
+    /// CIE L*a*b* space.
+    Lab,
+    /// CIE L*u*v* space.
+    Luv,
+}
+
+/// Parse an argument into the appropriate type.
+fn parse_arg<F>(arg: Option<&str>) -> clap::Result<Option<F>>
+where
+    F: FromStr,
+    F::Err: Error,
+{
+    match arg.map(|s| s.parse()) {
+        Some(Ok(f)) => Ok(Some(f)),
+        Some(Err(e)) => Err(clap::Error::with_description(
+            &e.to_string(),
+            clap::ErrorKind::InvalidValue,
+        )),
+        None => Ok(None),
+    }
+}
+
+/// The parsed command line arguments.
+#[derive(Debug)]
+struct Args {
+    source: SourceArg,
+    order: OrderArg,
+    stripe: bool,
+    frontier: FrontierArg,
+    space: ColorSpaceArg,
+    width: Option<u32>,
+    height: Option<u32>,
+    x0: Option<u32>,
+    y0: Option<u32>,
+    animate: bool,
+    output: PathBuf,
+    seed: u64,
+}
+
+impl Args {
+    fn parse() -> clap::Result<Self> {
+        let args = clap_app!((crate_name!()) =>
+            (version: crate_version!())
+            (author: crate_authors!())
+            (setting: AppSettings::ColoredHelp)
+            (@group source =>
+                (@arg DEPTH: -b --("bit-depth") +takes_value "Use all DEPTH-bit colors")
+                (@arg INPUT: -i --input +takes_value "Use colors from the INPUT image")
+            )
+            (@group order =>
+                (@arg HUE: -s --hue-sort "Sort colors by hue [default]")
+                (@arg RANDOM: -r --random "Randomize colors")
+                (@arg MORTON: -M --morton "Place colors in Morton order (Z-order)")
+                (@arg HILBERT: -H --hilbert "Place colors in Hilbert curve order")
+            )
+            (@group stripe =>
+                (@arg STRIPE: -t --stripe "Reduce artifacts by iterating through the colors in multiple stripes [default]")
+                (@arg NOSTRIPE: -T --("no-stripe") "Don't stripe")
+            )
+            (@group frontier =>
+                (@arg MODE: -l --selection +takes_value possible_value[min mean] "Specify the selection mode")
+                (@arg TARGET: -g --target +takes_value "Place colors on the closest pixels of the TARGET image")
+            )
+            (@arg SPACE: -c --("color-space") default_value("Lab") possible_value[RGB Lab Luv] "Use the given color space")
+            (@arg WIDTH: -w --width +takes_value "The width of the generated image")
+            (@arg HEIGHT: -h --height +takes_value "The height of the generated image")
+            (@arg X: -x +takes_value "The x coordinate of the first pixel")
+            (@arg Y: -y +takes_value "The y coordinate of the first pixel")
+            (@arg ANIMATE: -a --animate "Generate frames of an animation")
+            (@arg PATH: -o --output default_value("kd-forest.png") "Save the image to PATH")
+            (@arg SEED: -e --seed default_value("0") "Seed the random number generator")
+        )
+        .get_matches_safe()?;
+
+        let source = if let Some(input) = args.value_of("INPUT") {
+            SourceArg::Image(PathBuf::from(input))
+        } else {
+            SourceArg::AllRgb(parse_arg(args.value_of("DEPTH"))?.unwrap_or(24))
+        };
+
+        let order = if args.is_present("RANDOM") {
+            OrderArg::Random
+        } else if args.is_present("MORTON") {
+            OrderArg::Morton
+        } else if args.is_present("HILBERT") {
+            OrderArg::Hilbert
+        } else {
+            OrderArg::HueSort
+        };
+
+        let stripe = !args.is_present("NOSTRIPE") && order != OrderArg::Random;
+
+        let frontier = if let Some(target) = args.value_of("TARGET") {
+            FrontierArg::Image(PathBuf::from(target))
+        } else {
+            match args.value_of("MODE") {
+                Some("min") | None => FrontierArg::Min,
+                Some("mean") => FrontierArg::Mean,
+                _ => unreachable!(),
+            }
+        };
+
+        let space = match args.value_of("SPACE").unwrap() {
+            "RGB" => ColorSpaceArg::Rgb,
+            "Lab" => ColorSpaceArg::Lab,
+            "Luv" => ColorSpaceArg::Luv,
+            _ => unreachable!(),
+        };
+
+        let width = parse_arg(args.value_of("WIDTH"))?;
+        let height = parse_arg(args.value_of("HEIGHT"))?;
+        let x0 = parse_arg(args.value_of("X"))?;
+        let y0 = parse_arg(args.value_of("Y"))?;
+
+        let animate = args.is_present("ANIMATE");
+
+        let mut path = args.value_of("PATH").unwrap();
+        if animate && args.occurrences_of("PATH") == 0 {
+            path = "kd-frames";
+        }
+        let output = PathBuf::from(path);
+
+        let seed = parse_arg(args.value_of("SEED"))?.unwrap_or(0);
+
+        Ok(Self {
+            source,
+            order,
+            stripe,
+            frontier,
+            space,
+            width,
+            height,
+            x0,
+            y0,
+            animate,
+            output,
+            seed,
+        })
+    }
+}
+
+/// main() return type.
+type MainResult = Result<(), Box<dyn Error>>;
+
+/// The kd-forest application itself.
+#[derive(Debug)]
+struct App {
+    args: Args,
+    rng: Pcg64,
+    width: Option<u32>,
+    height: Option<u32>,
+    start_time: Instant,
+}
+
+impl App {
+    /// Make the App.
+    fn new(args: Args) -> Self {
+        let rng = Pcg64::seed_from_u64(args.seed);
+        let width = args.width;
+        let height = args.height;
+        let start_time = Instant::now();
+
+        Self {
+            args,
+            rng,
+            width,
+            height,
+            start_time,
+        }
+    }
+
+    fn run(&mut self) -> MainResult {
+        let colors = match self.args.source {
+            SourceArg::AllRgb(depth) => {
+                self.width.get_or_insert(1u32 << ((depth + 1) / 2));
+                self.height.get_or_insert(1u32 << (depth / 2));
+                self.get_colors(AllColors::new(depth as usize))
+            }
+            SourceArg::Image(ref path) => {
+                let img = image::open(path)?.into_rgb();
+                self.width.get_or_insert(img.width());
+                self.height.get_or_insert(img.height());
+                self.get_colors(ImageColors::from(img))
+            }
+        };
+
+        match self.args.space {
+            ColorSpaceArg::Rgb => self.paint::<RgbSpace>(colors),
+            ColorSpaceArg::Lab => self.paint::<LabSpace>(colors),
+            ColorSpaceArg::Luv => self.paint::<LuvSpace>(colors),
+        }
+    }
+
+    fn get_colors<S: ColorSource>(&mut self, source: S) -> Vec<Rgb8> {
+        let colors = match self.args.order {
+            OrderArg::HueSort => order::hue_sorted(source),
+            OrderArg::Random => order::shuffled(source, &mut self.rng),
+            OrderArg::Morton => order::morton(source),
+            OrderArg::Hilbert => order::hilbert(source),
+        };
+
+        if self.args.stripe {
+            order::striped(colors)
+        } else {
+            colors
+        }
+    }
+
+    fn paint<C: ColorSpace>(&mut self, colors: Vec<Rgb8>) -> MainResult {
+        let width = self.width.unwrap();
+        let height = self.height.unwrap();
+        let x0 = self.args.x0.unwrap_or(width / 2);
+        let y0 = self.args.x0.unwrap_or(height / 2);
+
+        match &self.args.frontier {
+            FrontierArg::Image(ref path) => {
+                let img = image::open(path)?.into_rgb();
+                self.paint_on(colors, ImageFrontier::<C>::new(&img))
+            }
+            FrontierArg::Min => {
+                let rng = Pcg64::from_rng(&mut self.rng)?;
+                self.paint_on(colors, MinFrontier::<C, _>::new(rng, width, height, x0, y0))
+            }
+            FrontierArg::Mean => {
+                self.paint_on(colors, MeanFrontier::<C>::new(width, height, x0, y0))
+            }
+        }
+    }
+
+    fn paint_on<F: Frontier>(&mut self, colors: Vec<Rgb8>, mut frontier: F) -> MainResult {
+        let width = frontier.width();
+        let height = frontier.height();
+        let mut output = RgbaImage::new(width, height);
+
+        let size = cmp::min((width * height) as usize, colors.len());
+        println!("Generating a {}x{} image ({} pixels)", width, height, size);
+
+        if self.args.animate {
+            fs::create_dir_all(&self.args.output)?;
+            output.save(&self.args.output.join("0000.png"))?;
+        }
+
+        let interval = cmp::max(width, height) as usize;
+
+        let mut max_frontier = frontier.len();
+
+        for (i, color) in colors.into_iter().enumerate() {
+            let pos = frontier.place(color);
+            if pos.is_none() {
+                break;
+            }
+
+            let (x, y) = pos.unwrap();
+            let rgba = Rgba([color[0], color[1], color[2], 255]);
+            output.put_pixel(x, y, rgba);
+
+            max_frontier = cmp::max(max_frontier, frontier.len());
+
+            if (i + 1) % interval == 0 {
+                if self.args.animate {
+                    let frame = (i + 1) / interval;
+                    output.save(&self.args.output.join(format!("{:04}.png", frame)))?;
+                }
+
+                if i + 1 < size {
+                    self.print_progress(i + 1, size, frontier.len())?;
+                }
+            }
+        }
+
+        if self.args.animate && size % interval != 0 {
+            let frame = size / interval;
+            output.save(&self.args.output.join(format!("{:04}.png", frame)))?;
+        }
+
+        self.print_progress(size, size, max_frontier)?;
+
+        if !self.args.animate {
+            output.save(&self.args.output)?;
+        }
+
+        Ok(())
+    }
+
+    fn print_progress(&self, i: usize, size: usize, frontier_len: usize) -> io::Result<()> {
+        let mut term = match term::stderr() {
+            Some(term) => term,
+            None => return Ok(()),
+        };
+
+        let progress = 100.0 * (i as f64) / (size as f64);
+        let mut rate = (i as f64) / self.start_time.elapsed().as_secs_f64();
+        let mut unit = "px/s";
+
+        if rate >= 10_000.0 {
+            rate /= 1_000.0;
+            unit = "Kpx/s";
+        }
+
+        if rate >= 10_000.0 {
+            rate /= 1_000.0;
+            unit = "Mpx/s";
+        }
+
+        if rate >= 10_000.0 {
+            rate /= 1_000.0;
+            unit = "Gpx/s";
+        }
+
+        let (frontier_label, newline) = if i == size {
+            ("max frontier size", "\n")
+        } else {
+            ("frontier size", "")
+        };
+
+        term.carriage_return()?;
+        term.delete_line()?;
+
+        write!(
+            term,
+            "{:>6.2}%  | {:4.0} {:>5}  | {}: {}{}",
+            progress, rate, unit, frontier_label, frontier_len, newline,
+        )
+    }
+}
+
+fn main() -> MainResult {
+    let args = match Args::parse() {
+        Ok(args) => args,
+        Err(e) => e.exit(),
+    };
+
+    App::new(args).run()
+}
diff --git a/src/metric.rs b/src/metric.rs
new file mode 100644
index 0000000..268aefd
--- /dev/null
+++ b/src/metric.rs
@@ -0,0 +1,537 @@
+//! [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 ordered_float::OrderedFloat;
+
+use std::cmp::Ordering;
+use std::collections::BinaryHeap;
+use std::iter::FromIterator;
+
+/// 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> + Ord {}
+
+/// A raw numerical distance.
+#[derive(Debug, Clone, Copy, Eq, Ord, PartialEq, PartialOrd)]
+pub struct RawDistance(OrderedFloat<f64>);
+
+impl From<f64> for RawDistance {
+    fn from(value: f64) -> Self {
+        Self(value.into())
+    }
+}
+
+impl From<RawDistance> for f64 {
+    fn from(value: RawDistance) -> Self {
+        value.0.into_inner()
+    }
+}
+
+impl Distance for RawDistance {}
+
+/// A squared distance, to avoid computing square roots unless absolutely necessary.
+#[derive(Debug, Clone, Copy, Eq, Ord, PartialEq, PartialOrd)]
+pub struct SquaredDistance(OrderedFloat<f64>);
+
+impl SquaredDistance {
+    /// Create a SquaredDistance from an already squared value.
+    pub fn from_squared(value: f64) -> Self {
+        Self(value.into())
+    }
+}
+
+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.into_inner().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.  Use [RawDistance] to compare the actual values
+    /// directly, or another type if comparisons can be implemented more efficiently.
+    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.distance.cmp(&other.distance)
+    }
+}
+
+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);
+    }
+}
+
+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
new file mode 100644
index 0000000..c23f9c7
--- /dev/null
+++ b/src/metric/approx.rs
@@ -0,0 +1,131 @@
+//! [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/forest.rs b/src/metric/forest.rs
new file mode 100644
index 0000000..29b6f55
--- /dev/null
+++ b/src/metric/forest.rs
@@ -0,0 +1,159 @@
+//! [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 std::iter::{self, Extend, Flatten, FromIterator};
+
+/// A dynamic wrapper for a static nearest neighbor search data structure.
+///
+/// This type applies [dynamization](https://en.wikipedia.org/wiki/Dynamization) to an arbitrary
+/// nearest neighbor search structure `T`, allowing new items to be added dynamically.
+#[derive(Debug)]
+pub struct Forest<T>(Vec<Option<T>>);
+
+impl<T, U> Forest<U>
+where
+    U: FromIterator<T> + IntoIterator<Item = T>,
+{
+    /// Create a new empty forest.
+    pub fn new() -> Self {
+        Self(Vec::new())
+    }
+
+    /// Add a new item to the forest.
+    pub fn push(&mut self, item: T) {
+        self.extend(iter::once(item));
+    }
+
+    /// Get the number of items in the forest.
+    pub fn len(&self) -> usize {
+        let mut len = 0;
+        for (i, slot) in self.0.iter().enumerate() {
+            if slot.is_some() {
+                len |= 1 << i;
+            }
+        }
+        len
+    }
+}
+
+impl<T, U> Extend<T> for Forest<U>
+where
+    U: FromIterator<T> + IntoIterator<Item = T>,
+{
+    fn extend<I: IntoIterator<Item = T>>(&mut self, items: I) {
+        let mut vec: Vec<_> = items.into_iter().collect();
+        let new_len = self.len() + vec.len();
+
+        for i in 0.. {
+            let bit = 1 << i;
+
+            if bit > new_len {
+                break;
+            }
+
+            if i >= self.0.len() {
+                self.0.push(None);
+            }
+
+            if new_len & bit == 0 {
+                if let Some(tree) = self.0[i].take() {
+                    vec.extend(tree);
+                }
+            } else if self.0[i].is_none() {
+                let offset = vec.len() - bit;
+                self.0[i] = Some(vec.drain(offset..).collect());
+            }
+        }
+
+        debug_assert!(vec.is_empty());
+        debug_assert!(self.len() == new_len);
+    }
+}
+
+impl<T, U> FromIterator<T> for Forest<U>
+where
+    U: FromIterator<T> + IntoIterator<Item = T>,
+{
+    fn from_iter<I: IntoIterator<Item = T>>(items: I) -> Self {
+        let mut forest = Self::new();
+        forest.extend(items);
+        forest
+    }
+}
+
+type IntoIterImpl<T> = Flatten<Flatten<std::vec::IntoIter<Option<T>>>>;
+
+/// An iterator that moves items out of a forest.
+pub struct IntoIter<T: IntoIterator>(IntoIterImpl<T>);
+
+impl<T: IntoIterator> Iterator for IntoIter<T> {
+    type Item = T::Item;
+
+    fn next(&mut self) -> Option<Self::Item> {
+        self.0.next()
+    }
+}
+
+impl<T: IntoIterator> IntoIterator for Forest<T> {
+    type Item = T::Item;
+    type IntoIter = IntoIter<T>;
+
+    fn into_iter(self) -> Self::IntoIter {
+        IntoIter(self.0.into_iter().flatten().flatten())
+    }
+}
+
+impl<T, U, V> NearestNeighbors<T, U> for Forest<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.0
+            .iter()
+            .flatten()
+            .fold(neighborhood, |n, t| t.search(n))
+    }
+}
+
+/// A forest of k-d trees.
+pub type KdForest<T> = Forest<KdTree<T>>;
+
+/// A forest of vantage-point trees.
+pub type VpForest<T> = Forest<VpTree<T>>;
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    use crate::metric::tests::test_nearest_neighbors;
+    use crate::metric::ExhaustiveSearch;
+
+    #[test]
+    fn test_exhaustive_forest() {
+        test_nearest_neighbors(Forest::<ExhaustiveSearch<_>>::from_iter);
+    }
+
+    #[test]
+    fn test_forest_forest() {
+        test_nearest_neighbors(Forest::<Forest<ExhaustiveSearch<_>>>::from_iter);
+    }
+
+    #[test]
+    fn test_kd_forest() {
+        test_nearest_neighbors(KdForest::from_iter);
+    }
+
+    #[test]
+    fn test_vp_forest() {
+        test_nearest_neighbors(VpForest::from_iter);
+    }
+}
diff --git a/src/metric/kd.rs b/src/metric/kd.rs
new file mode 100644
index 0000000..2caf4a3
--- /dev/null
+++ b/src/metric/kd.rs
@@ -0,0 +1,226 @@
+//! [k-d trees](https://en.wikipedia.org/wiki/K-d_tree).
+
+use super::{Metric, NearestNeighbors, Neighborhood};
+
+use ordered_float::OrderedFloat;
+
+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| OrderedFloat::from(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/soft.rs b/src/metric/soft.rs
new file mode 100644
index 0000000..0d7dcdb
--- /dev/null
+++ b/src/metric/soft.rs
@@ -0,0 +1,282 @@
+//! [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 std::iter;
+use std::iter::FromIterator;
+use std::mem;
+
+/// A trait for objects that can be soft-deleted.
+pub trait SoftDelete {
+    /// Check whether this item is deleted.
+    fn is_deleted(&self) -> bool;
+}
+
+/// Blanket [SoftDelete] implementation for references.
+impl<'a, T: SoftDelete> SoftDelete for &'a T {
+    fn is_deleted(&self) -> bool {
+        (*self).is_deleted()
+    }
+}
+
+/// [Neighborhood] wrapper that ignores soft-deleted items.
+#[derive(Debug)]
+struct SoftNeighborhood<N>(N);
+
+impl<T, U, N> Neighborhood<T, U> for SoftNeighborhood<N>
+where
+    T: SoftDelete,
+    U: Metric<T>,
+    N: Neighborhood<T, U>,
+{
+    fn target(&self) -> U {
+        self.0.target()
+    }
+
+    fn contains(&self, distance: f64) -> bool {
+        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 {
+        if item.is_deleted() {
+            self.target().distance(&item)
+        } else {
+            self.0.consider(item)
+        }
+    }
+}
+
+/// A [NearestNeighbors] implementation that supports [soft deletes](https://en.wiktionary.org/wiki/soft_deletion).
+#[derive(Debug)]
+pub struct SoftSearch<T>(T);
+
+impl<T, U> SoftSearch<U>
+where
+    T: SoftDelete,
+    U: FromIterator<T> + IntoIterator<Item = T>,
+{
+    /// Create a new empty soft index.
+    pub fn new() -> Self {
+        Self(iter::empty().collect())
+    }
+
+    /// Push a new item into this index.
+    pub fn push(&mut self, item: T)
+    where
+        U: Extend<T>,
+    {
+        self.0.extend(iter::once(item));
+    }
+
+    /// Rebuild this index, discarding deleted items.
+    pub fn rebuild(&mut self) {
+        let items = mem::replace(&mut self.0, iter::empty().collect());
+        self.0 = items.into_iter().filter(|e| !e.is_deleted()).collect();
+    }
+}
+
+impl<T, U: Extend<T>> Extend<T> for SoftSearch<U> {
+    fn extend<I: IntoIterator<Item = T>>(&mut self, iter: I) {
+        self.0.extend(iter);
+    }
+}
+
+impl<T, U: FromIterator<T>> FromIterator<T> for SoftSearch<U> {
+    fn from_iter<I: IntoIterator<Item = T>>(iter: I) -> Self {
+        Self(U::from_iter(iter))
+    }
+}
+
+impl<T: IntoIterator> IntoIterator for SoftSearch<T> {
+    type Item = T::Item;
+    type IntoIter = T::IntoIter;
+
+    fn into_iter(self) -> Self::IntoIter {
+        self.0.into_iter()
+    }
+}
+
+impl<T, U, V> NearestNeighbors<T, U> for SoftSearch<V>
+where
+    T: SoftDelete,
+    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.0.search(SoftNeighborhood(neighborhood)).0
+    }
+}
+
+/// A k-d forest that supports soft deletes.
+pub type SoftKdForest<T> = SoftSearch<KdForest<T>>;
+
+/// A k-d tree that supports soft deletes.
+pub type SoftKdTree<T> = SoftSearch<KdTree<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>>;
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    use crate::metric::kd::Cartesian;
+    use crate::metric::tests::Point;
+    use crate::metric::Neighbor;
+
+    #[derive(Debug, PartialEq)]
+    struct SoftPoint {
+        point: Point,
+        deleted: bool,
+    }
+
+    impl SoftPoint {
+        fn new(x: f64, y: f64, z: f64) -> Self {
+            Self {
+                point: Point([x, y, z]),
+                deleted: false,
+            }
+        }
+
+        fn deleted(x: f64, y: f64, z: f64) -> Self {
+            Self {
+                point: Point([x, y, z]),
+                deleted: true,
+            }
+        }
+    }
+
+    impl SoftDelete for SoftPoint {
+        fn is_deleted(&self) -> bool {
+            self.deleted
+        }
+    }
+
+    impl Metric for SoftPoint {
+        type Distance = <Point as Metric>::Distance;
+
+        fn distance(&self, other: &Self) -> Self::Distance {
+            self.point.distance(&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 Cartesian for SoftPoint {
+        fn dimensions(&self) -> usize {
+            self.point.dimensions()
+        }
+
+        fn coordinate(&self, i: usize) -> f64 {
+            self.point.coordinate(i)
+        }
+    }
+
+    impl Metric<SoftPoint> for Point {
+        type Distance = <Point as Metric>::Distance;
+
+        fn distance(&self, other: &SoftPoint) -> Self::Distance {
+            self.distance(&other.point)
+        }
+    }
+
+    fn test_index<T>(index: &T)
+    where
+        T: NearestNeighbors<SoftPoint, Point>,
+    {
+        let target = Point([0.0, 0.0, 0.0]);
+
+        assert_eq!(
+            index.nearest(&target),
+            Some(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))
+        );
+
+        assert_eq!(
+            index.k_nearest(&target, 3),
+            vec![
+                Neighbor::new(&SoftPoint::new(1.0, 2.0, 2.0), 3.0),
+                Neighbor::new(&SoftPoint::new(3.0, 4.0, 0.0), 5.0),
+                Neighbor::new(&SoftPoint::new(2.0, 3.0, 6.0), 7.0),
+            ]
+        );
+
+        assert_eq!(
+            index.k_nearest_within(&target, 3, 6.0),
+            vec![
+                Neighbor::new(&SoftPoint::new(1.0, 2.0, 2.0), 3.0),
+                Neighbor::new(&SoftPoint::new(3.0, 4.0, 0.0), 5.0),
+            ]
+        );
+        assert_eq!(
+            index.k_nearest_within(&target, 3, 8.0),
+            vec![
+                Neighbor::new(&SoftPoint::new(1.0, 2.0, 2.0), 3.0),
+                Neighbor::new(&SoftPoint::new(3.0, 4.0, 0.0), 5.0),
+                Neighbor::new(&SoftPoint::new(2.0, 3.0, 6.0), 7.0),
+            ]
+        );
+    }
+
+    fn test_soft_index<T>(index: &mut SoftSearch<T>)
+    where
+        T: Extend<SoftPoint>,
+        T: FromIterator<SoftPoint>,
+        T: IntoIterator<Item = SoftPoint>,
+        T: NearestNeighbors<SoftPoint, Point>,
+    {
+        let points = vec![
+            SoftPoint::deleted(0.0, 0.0, 0.0),
+            SoftPoint::new(3.0, 4.0, 0.0),
+            SoftPoint::new(5.0, 0.0, 12.0),
+            SoftPoint::new(0.0, 8.0, 15.0),
+            SoftPoint::new(1.0, 2.0, 2.0),
+            SoftPoint::new(2.0, 3.0, 6.0),
+            SoftPoint::new(4.0, 4.0, 7.0),
+        ];
+
+        for point in points {
+            index.push(point);
+        }
+        test_index(index);
+
+        index.rebuild();
+        test_index(index);
+    }
+
+    #[test]
+    fn test_soft_kd_forest() {
+        test_soft_index(&mut SoftKdForest::new());
+    }
+
+    #[test]
+    fn test_soft_vp_forest() {
+        test_soft_index(&mut SoftVpForest::new());
+    }
+}
diff --git a/src/metric/vp.rs b/src/metric/vp.rs
new file mode 100644
index 0000000..fae62e5
--- /dev/null
+++ b/src/metric/vp.rs
@@ -0,0 +1,137 @@
+//! [Vantage-point trees](https://en.wikipedia.org/wiki/Vantage-point_tree).
+
+use super::{Metric, NearestNeighbors, Neighborhood};
+
+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| 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);
+    }
+}