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authorTavian Barnes <tavianator@tavianator.com>2020-05-28 14:42:37 -0400
committerTavian Barnes <tavianator@tavianator.com>2020-06-24 10:02:23 -0400
commite9b3012520ba580b6e798512b2318df48d45c3b7 (patch)
treea4140cc38dace728e7da1995e2ccada2b10796c5
parent82df66b852fd2e16f3ab5cc0b4bbf32034ee49db (diff)
downloadacap-e9b3012520ba580b6e798512b2318df48d45c3b7.tar.xz
euclid: Implement Euclidean distance
-rw-r--r--src/euclid.rs390
-rw-r--r--src/lib.rs2
2 files changed, 392 insertions, 0 deletions
diff --git a/src/euclid.rs b/src/euclid.rs
new file mode 100644
index 0000000..fa82e9c
--- /dev/null
+++ b/src/euclid.rs
@@ -0,0 +1,390 @@
+//! Euclidean space.
+
+use crate::coords::{Coordinates, CoordinateMetric, CoordinateProximity};
+use crate::distance::{Distance, Metric, Proximity, Value};
+
+use num_traits::zero;
+
+use std::cmp::Ordering;
+use std::convert::TryFrom;
+
+/// A point in Euclidean space.
+///
+/// This wrapper equips any [coordinate space] with the [Euclidean distance] metric.
+///
+/// [coordinate space]: [Coordinates]
+/// [Euclidean distance]: https://en.wikipedia.org/wiki/Euclidean_distance
+#[derive(Clone, Copy, Debug, Eq, PartialEq)]
+pub struct Euclidean<T>(pub T);
+
+impl<T> Euclidean<T> {
+ /// Wrap a point.
+ pub fn new(point: T) -> Self {
+ Self(point)
+ }
+
+ /// Unwrap a point.
+ pub fn inner(&self) -> &T {
+ &self.0
+ }
+
+ /// Unwrap a point.
+ pub fn into_inner(self) -> T {
+ self.0
+ }
+}
+
+impl<T: Coordinates> Coordinates for Euclidean<T> {
+ type Value = T::Value;
+
+ fn dims(&self) -> usize {
+ self.0.dims()
+ }
+
+ fn coord(&self, i: usize) -> Self::Value {
+ self.0.coord(i)
+ }
+}
+
+/// Compute the Euclidean distance between two points.
+pub fn euclidean_distance<T, U>(x: T, y: U) -> EuclideanDistance<T::Value>
+where
+ T: Coordinates,
+ U: Coordinates<Value = T::Value>,
+{
+ debug_assert!(x.dims() == y.dims());
+
+ let mut sum = zero();
+ for i in 0..x.dims() {
+ let diff = x.coord(i) - y.coord(i);
+ sum += diff * diff;
+ }
+
+ EuclideanDistance::from_squared(sum)
+}
+
+/// The Euclidean distance function.
+impl<T> Proximity for Euclidean<T>
+where
+ T: Coordinates,
+ EuclideanDistance<T::Value>: Distance,
+{
+ type Distance = EuclideanDistance<T::Value>;
+
+ fn distance(&self, other: &Self) -> Self::Distance {
+ euclidean_distance(self, other)
+ }
+}
+
+impl<T> Proximity<T> for Euclidean<T>
+where
+ T: Coordinates,
+ EuclideanDistance<T::Value>: Distance,
+{
+ type Distance = EuclideanDistance<T::Value>;
+
+ fn distance(&self, other: &T) -> Self::Distance {
+ euclidean_distance(self, other)
+ }
+}
+
+impl<T> Proximity<Euclidean<T>> for T
+where
+ T: Coordinates,
+ EuclideanDistance<T::Value>: Distance,
+{
+ type Distance = EuclideanDistance<T::Value>;
+
+ fn distance(&self, other: &Euclidean<T>) -> Self::Distance {
+ euclidean_distance(self, other)
+ }
+}
+
+/// Euclidean distance is a metric.
+impl<T> Metric for Euclidean<T>
+where
+ T: Coordinates,
+ EuclideanDistance<T::Value>: Distance,
+{}
+
+impl<T> Metric<T> for Euclidean<T>
+where
+ T: Coordinates,
+ EuclideanDistance<T::Value>: Distance,
+{}
+
+impl<T> Metric<Euclidean<T>> for T
+where
+ T: Coordinates,
+ EuclideanDistance<T::Value>: Distance,
+{}
+
+impl<T> CoordinateProximity<T::Value> for Euclidean<T>
+where
+ T: Coordinates,
+ EuclideanDistance<T::Value>: Distance,
+{
+ type Distance = EuclideanDistance<T::Value>;
+
+ fn distance_to_coords(&self, coords: &[T::Value]) -> Self::Distance {
+ euclidean_distance(self, coords)
+ }
+}
+
+impl<T> CoordinateMetric<T::Value> for Euclidean<T>
+where
+ T: Coordinates,
+ EuclideanDistance<T::Value>: Distance,
+{}
+
+/// A [Euclidean distance].
+///
+/// This type stores the squared value of the Euclidean distance, to avoid computing expensive
+/// square roots until absolutely necessary.
+///
+/// # use acap::distance::Distance;
+/// # use acap::euclid::EuclideanDistance;
+/// # use std::convert::TryFrom;
+/// let a = EuclideanDistance::try_from(3).unwrap();
+/// let b = EuclideanDistance::try_from(4).unwrap();
+/// let c = EuclideanDistance::from_squared(a.squared_value() + b.squared_value());
+/// assert!(a < c && b < c);
+/// assert_eq!(c.value(), 5.0f32);
+///
+/// [Euclidean distance]: https://en.wikipedia.org/wiki/Euclidean_distance
+#[derive(Clone, Copy, Debug, PartialEq, PartialOrd)]
+pub struct EuclideanDistance<T>(T);
+
+impl<T: Value> EuclideanDistance<T> {
+ /// Createa a `EuclideanDistance` from an already-squared value.
+ pub fn from_squared(value: T) -> Self {
+ debug_assert!(!value.is_negative());
+ Self(value)
+ }
+
+ /// Get the squared distance value.
+ pub fn squared_value(self) -> T {
+ self.0
+ }
+}
+
+/// Error type for failed conversions from negative numbers to [EuclideanDistance].
+#[derive(Debug)]
+pub struct NegativeDistanceError;
+
+/// Implement EuclideanDistance for a floating-point type.
+macro_rules! float_distance {
+ ($f:ty) => {
+ impl TryFrom<$f> for EuclideanDistance<$f> {
+ type Error = NegativeDistanceError;
+
+ #[inline]
+ fn try_from(value: $f) -> Result<Self, Self::Error> {
+ if value >= 0.0 {
+ Ok(Self(value * value))
+ } else {
+ Err(NegativeDistanceError)
+ }
+ }
+ }
+
+ impl From<EuclideanDistance<$f>> for $f {
+ #[inline]
+ fn from(value: EuclideanDistance<$f>) -> $f {
+ value.0.sqrt()
+ }
+ }
+
+ impl PartialOrd<$f> for EuclideanDistance<$f> {
+ #[inline]
+ fn partial_cmp(&self, other: &$f) -> Option<Ordering> {
+ if let Ok(rhs) = Self::try_from(*other) {
+ self.partial_cmp(&rhs)
+ } else {
+ Some(Ordering::Greater)
+ }
+ }
+ }
+
+ impl PartialOrd<EuclideanDistance<$f>> for $f {
+ #[inline]
+ fn partial_cmp(&self, other: &EuclideanDistance<$f>) -> Option<Ordering> {
+ if let Ok(lhs) = EuclideanDistance::try_from(*self) {
+ lhs.partial_cmp(other)
+ } else {
+ Some(Ordering::Less)
+ }
+ }
+ }
+
+ impl PartialEq<$f> for EuclideanDistance<$f> {
+ #[inline]
+ fn eq(&self, other: &$f) -> bool {
+ self.partial_cmp(other) == Some(Ordering::Equal)
+ }
+ }
+
+ impl PartialEq<EuclideanDistance<$f>> for $f {
+ #[inline]
+ fn eq(&self, other: &EuclideanDistance<$f>) -> bool {
+ self.partial_cmp(other) == Some(Ordering::Equal)
+ }
+ }
+
+ impl Distance for EuclideanDistance<$f> {
+ type Value = $f;
+ }
+ }
+}
+
+float_distance!(f32);
+float_distance!(f64);
+
+/// Implement EuclideanDistance for an integer type.
+macro_rules! int_distance {
+ ($i:ty, $f:ty, $ff:ty) => {
+ impl TryFrom<$i> for EuclideanDistance<$i> {
+ type Error = NegativeDistanceError;
+
+ #[inline]
+ fn try_from(value: $i) -> Result<Self, Self::Error> {
+ if value >= 0 {
+ Ok(Self(value * value))
+ } else {
+ Err(NegativeDistanceError)
+ }
+ }
+ }
+
+ impl From<EuclideanDistance<$i>> for $f {
+ #[inline]
+ fn from(value: EuclideanDistance<$i>) -> Self {
+ (value.0 as $ff).sqrt() as $f
+ }
+ }
+
+ impl PartialOrd<$i> for EuclideanDistance<$i> {
+ #[inline]
+ fn partial_cmp(&self, other: &$i) -> Option<Ordering> {
+ if let Ok(rhs) = Self::try_from(*other) {
+ self.partial_cmp(&rhs)
+ } else {
+ Some(Ordering::Greater)
+ }
+ }
+ }
+
+ impl PartialOrd<EuclideanDistance<$i>> for $i {
+ #[inline]
+ fn partial_cmp(&self, other: &EuclideanDistance<$i>) -> Option<Ordering> {
+ if let Ok(lhs) = EuclideanDistance::try_from(*self) {
+ lhs.partial_cmp(other)
+ } else {
+ Some(Ordering::Less)
+ }
+ }
+ }
+
+ impl PartialEq<$i> for EuclideanDistance<$i> {
+ #[inline]
+ fn eq(&self, other: &$i) -> bool {
+ self.partial_cmp(other) == Some(Ordering::Equal)
+ }
+ }
+
+ impl PartialEq<EuclideanDistance<$i>> for $i {
+ #[inline]
+ fn eq(&self, other: &EuclideanDistance<$i>) -> bool {
+ self.partial_cmp(other) == Some(Ordering::Equal)
+ }
+ }
+
+ impl PartialOrd<$f> for EuclideanDistance<$i> {
+ #[inline]
+ fn partial_cmp(&self, other: &$f) -> Option<Ordering> {
+ if *other >= 0.0 {
+ let lhs = self.0 as $ff;
+ let mut rhs = *other as $ff;
+ rhs *= rhs;
+ lhs.partial_cmp(&rhs)
+ } else {
+ Some(Ordering::Greater)
+ }
+ }
+ }
+
+ impl PartialOrd<EuclideanDistance<$i>> for $f {
+ #[inline]
+ fn partial_cmp(&self, other: &EuclideanDistance<$i>) -> Option<Ordering> {
+ if *other >= 0.0 {
+ let mut lhs = *self as $ff;
+ lhs *= lhs;
+ let rhs = other.0 as $ff;
+ lhs.partial_cmp(&rhs)
+ } else {
+ Some(Ordering::Greater)
+ }
+ }
+ }
+
+ impl PartialEq<$f> for EuclideanDistance<$i> {
+ #[inline]
+ fn eq(&self, other: &$f) -> bool {
+ self.partial_cmp(other) == Some(Ordering::Equal)
+ }
+ }
+
+ impl PartialEq<EuclideanDistance<$i>> for $f {
+ #[inline]
+ fn eq(&self, other: &EuclideanDistance<$i>) -> bool {
+ self.partial_cmp(other) == Some(Ordering::Equal)
+ }
+ }
+
+ impl Distance for EuclideanDistance<$i> {
+ type Value = $f;
+ }
+ }
+}
+
+int_distance!(i16, f32, f32);
+int_distance!(i32, f32, f64);
+int_distance!(i64, f64, f64);
+int_distance!(isize, f64, f64);
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+
+ #[test]
+ fn test_i32() {
+ let five = euclidean_distance([0, 0], [3, 4]);
+ assert_eq!(five, EuclideanDistance::from_squared(25));
+ assert_eq!(five, 5.0f32);
+
+ let thirteen = Euclidean([0, 0]).distance(&Euclidean([5, 12]));
+ assert_eq!(thirteen, EuclideanDistance::from_squared(169));
+ assert_eq!(thirteen, 13.0f32);
+
+ assert!(five < thirteen);
+ assert!(five < 13);
+ assert!(5 < thirteen);
+ assert!(-5 < thirteen);
+ }
+
+ #[test]
+ fn test_f64() {
+ let five = euclidean_distance([0.0, 0.0], [3.0, 4.0]);
+ assert_eq!(five, EuclideanDistance::from_squared(25.0));
+ assert_eq!(five, 5.0);
+
+ let thirteen = Euclidean([0.0, 0.0]).distance(&Euclidean([5.0, 12.0]));
+ assert_eq!(thirteen, EuclideanDistance::from_squared(169.0));
+ assert_eq!(thirteen, 13.0);
+
+ assert!(five < thirteen);
+ assert!(five < 13.0);
+ assert!(5.0 < thirteen);
+ assert!(-5.0 < thirteen);
+ }
+}
diff --git a/src/lib.rs b/src/lib.rs
index 1532211..e18025b 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -4,6 +4,8 @@
pub mod coords;
pub mod distance;
+pub mod euclid;
pub use coords::Coordinates;
pub use distance::{Distance, Metric, Proximity};
+pub use euclid::{euclidean_distance, Euclidean, EuclideanDistance};