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-rw-r--r--src/color.rs285
-rw-r--r--src/color/order.rs196
-rw-r--r--src/color/source.rs76
-rw-r--r--src/frontier.rs149
-rw-r--r--src/frontier/image.rs74
-rw-r--r--src/frontier/mean.rs140
-rw-r--r--src/frontier/min.rs150
-rw-r--r--src/hilbert.rs136
-rw-r--r--src/main.rs401
-rw-r--r--src/metric.rs537
-rw-r--r--src/metric/approx.rs131
-rw-r--r--src/metric/forest.rs159
-rw-r--r--src/metric/kd.rs226
-rw-r--r--src/metric/soft.rs282
-rw-r--r--src/metric/vp.rs137
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);
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-26 16:08:18 +0000