Add support for polymorphic sampling type.

Cargo.toml

@@ -26,6 +26,9 @@ std = []
 impl-cgmath = ["cgmath"]
 impl-nalgebra = ["nalgebra"]
 
+[dependencies]
+num-traits = "0.2"
+
 [dependencies.nalgebra]
 version = ">=0.14, <0.17"
 optional = true

src/lib.rs

@@ -107,21 +107,24 @@
 #[cfg(feature = "serialization")] extern crate serde;
 #[cfg(feature = "serialization")] #[macro_use] extern crate serde_derive;
 
-#[cfg(feature = "impl-cgmath")] use cgmath::{InnerSpace, Quaternion, Vector2, Vector3, Vector4};
+#[cfg(feature = "impl-cgmath")]
+use cgmath::{
+  BaseFloat, InnerSpace, Quaternion, Vector2, Vector3, Vector4
+};
 
 #[cfg(feature = "impl-nalgebra")] use nalgebra as na;
 #[cfg(feature = "impl-nalgebra")] use nalgebra::core::{DimName, DefaultAllocator, Scalar};
 #[cfg(feature = "impl-nalgebra")] use nalgebra::core::allocator::Allocator;
 
 #[cfg(feature = "std")] use std::cmp::Ordering;
-#[cfg(feature = "std")] use std::f32::consts;
 #[cfg(feature = "std")] use std::ops::{Add, Div, Mul, Sub};
 
 #[cfg(not(feature = "std"))] use alloc::vec::Vec;
 #[cfg(not(feature = "std"))] use core::cmp::Ordering;
-#[cfg(not(feature = "std"))] use core::f32::consts;
 #[cfg(not(feature = "std"))] use core::ops::{Add, Div, Mul, Sub};
 
+use num_traits::{Float, FloatConst};
+
 /// A spline control point.
 ///
 /// This type associates a value at a given interpolation parameter value. It also contains an
@@ -130,23 +133,19 @@
 #[derive(Copy, Clone, Debug)]
 #[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
 #[cfg_attr(feature = "serialization", serde(rename_all = "snake_case"))]
-pub struct Key<T> {
+pub struct Key<T, V> {
   /// Interpolation parameter at which the [`Key`] should be reached.
-  pub t: f32,
+  pub t: T,
   /// Held value.
-  pub value: T,
+  pub value: V,
   /// Interpolation mode.
-  pub interpolation: Interpolation
+  pub interpolation: Interpolation<T>
 }
 
-impl<T> Key<T> {
+impl<T, V> Key<T, V> {
   /// Create a new key.
-  pub fn new(t: f32, value: T, interpolation: Interpolation) -> Self {
+  pub fn new(t: T, value: V, interpolation: Interpolation<T>) -> Self {
-    Key {
+    Key { t, value, interpolation }
-      t: t,
-      value: value,
-      interpolation: interpolation
-    }
   }
 }
 
@@ -154,7 +153,7 @@ impl<T> Key<T> {
 #[derive(Copy, Clone, Debug)]
 #[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
 #[cfg_attr(feature = "serialization", serde(rename_all = "snake_case"))]
-pub enum Interpolation {
+pub enum Interpolation<T> {
   /// Hold a [`Key`] until the time passes the normalized step threshold, in which case the next
   /// key is used.
   ///
@@ -162,7 +161,7 @@ pub enum Interpolation {
   /// between the two keys; the second key will be in used afterwards. If you set it to `1.0`, the
   /// first key will be kept until the next key. Set it to `0.` and the first key will never be
   /// used.*
-  Step(f32),
+  Step(T),
   /// Linear interpolation between a key and the next one.
   Linear,
   /// Cosine interpolation between a key and the next one.
@@ -171,7 +170,7 @@ pub enum Interpolation {
   CatmullRom
 }
 
-impl Default for Interpolation {
+impl<T> Default for Interpolation<T> {
   /// `Interpolation::Linear` is the default.
   fn default() -> Self {
     Interpolation::Linear
@@ -181,12 +180,12 @@ impl Default for Interpolation {
 /// Spline curve used to provide interpolation between control points (keys).
 #[derive(Debug, Clone)]
 #[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
-pub struct Spline<T>(Vec<Key<T>>);
+pub struct Spline<T, V>(Vec<Key<T, V>>);
 
-impl<T> Spline<T> {
+impl<T, V> Spline<T, V> {
   /// Create a new spline out of keys. The keys don’t have to be sorted even though it’s recommended
   /// to provide ascending sorted ones (for performance purposes).
-  pub fn from_vec(mut keys: Vec<Key<T>>) -> Self {
+  pub fn from_vec(mut keys: Vec<Key<T, V>>) -> Self where T: PartialOrd {
     keys.sort_by(|k0, k1| k0.t.partial_cmp(&k1.t).unwrap_or(Ordering::Less));
 
     Spline(keys)
@@ -199,12 +198,12 @@ impl<T> Spline<T> {
   ///
   /// It’s valid to use any iterator that implements `Iterator<Item = Key<T>>`. However, you should
   /// use `Spline::from_vec` if you are passing a `Vec<_>`. This will remove dynamic allocations.
-  pub fn from_iter<I>(iter: I) -> Self where I: Iterator<Item = Key<T>> {
+  pub fn from_iter<I>(iter: I) -> Self where I: Iterator<Item = Key<T, V>>, T: PartialOrd {
     Self::from_vec(iter.collect())
   }
 
   /// Retrieve the keys of a spline.
-  pub fn keys(&self) -> &[Key<T>] {
+  pub fn keys(&self) -> &[Key<T, V>] {
     &self.0
   }
 
@@ -222,7 +221,7 @@ impl<T> Spline<T> {
   /// sampling impossible. For instance, `Interpolate::CatmullRom` requires *four* keys. If you’re
   /// near the beginning of the spline or its end, ensure you have enough keys around to make the
   /// sampling.
-  pub fn sample(&self, t: f32) -> Option<T> where T: Interpolate {
+  pub fn sample(&self, t: T) -> Option<V> where V: Interpolate<T>, T: Float {
     let keys = &self.0;
     let i = search_lower_cp(keys, t)?;
     let cp0 = &keys[i];
@@ -244,18 +243,7 @@ impl<T> Spline<T> {
       Interpolation::Cosine => {
         let cp1 = &keys[i+1];
         let nt = normalize_time(t, cp0, cp1);
-        let cos_nt = {
+        let cos_nt = (1. - (nt * T::PI).cos()) * 0.5;
-          #[cfg(feature = "std")]
-          {
-            (1. - f32::cos(nt * consts::PI)) * 0.5
-          }
-
-          #[cfg(not(feature = "std"))]
-          {
-            use core::intrinsics::cosf32;
-            unsafe { (1. - cosf32(nt * consts::PI)) * 0.5 }
-          }
-        };
 
         Some(Interpolate::lerp(cp0.value, cp1.value, cos_nt))
       }
@@ -310,13 +298,13 @@ impl<T> Spline<T> {
 /// Iterator over spline keys.
 ///
 /// This iterator type assures you to iterate over sorted keys.
-pub struct Iter<'a, T> where T: 'a {
+pub struct Iter<'a, T, V> where T: 'a, V: 'a {
-  anim_param: &'a Spline<T>,
+  anim_param: &'a Spline<T, V>,
   i: usize
 }
 
-impl<'a, T> Iterator for Iter<'a, T> {
+impl<'a, T, V> Iterator for Iter<'a, T, V> {
-  type Item = &'a Key<T>;
+  type Item = &'a Key<T, V>;
 
   fn next(&mut self) -> Option<Self::Item> {
     let r = self.anim_param.0.get(self.i);
@@ -329,9 +317,9 @@ impl<'a, T> Iterator for Iter<'a, T> {
   }
 }
 
-impl<'a, T> IntoIterator for &'a Spline<T> {
+impl<'a, T, V> IntoIterator for &'a Spline<T, V> {
-  type Item = &'a Key<T>;
+  type Item = &'a Key<T, V>;
-  type IntoIter = Iter<'a, T>;
+  type IntoIter = Iter<'a, T, V>;
 
   fn into_iter(self) -> Self::IntoIter {
     Iter {
@@ -343,18 +331,22 @@ impl<'a, T> IntoIterator for &'a Spline<T> {
 
 /// Keys that can be interpolated in between. Implementing this trait is required to perform
 /// sampling on splines.
-pub trait Interpolate: Copy {
+///
+/// `T` is the variable used to sample with. Typical implementations use `f32` or `f64`, but you’re
+/// free to use the ones you like.
+pub trait Interpolate<T>: Copy where T: Copy + Float {
   /// Linear interpolation.
-  fn lerp(a: Self, b: Self, t: f32) -> Self;
+  fn lerp(a: Self, b: Self, t: T) -> Self;
+
   /// Cubic hermite interpolation.
   ///
   /// Default to `Self::lerp`.
-  fn cubic_hermite(_: (Self, f32), a: (Self, f32), b: (Self, f32), _: (Self, f32), t: f32) -> Self {
+  fn cubic_hermite(_: (Self, T), a: (Self, T), b: (Self, T), _: (Self, T), t: T) -> Self {
     Self::lerp(a.0, b.0, t)
   }
 }
 
-impl Interpolate for f32 {
+impl Interpolate<f32> for f32 {
   fn lerp(a: Self, b: Self, t: f32) -> Self {
     a * (1. - t) + b * t
   }
@@ -364,42 +356,58 @@ impl Interpolate for f32 {
   }
 }
 
-#[cfg(feature = "impl-cgmath")]
+impl Interpolate<f32> for f64 {
-impl Interpolate for Vector2<f32> {
   fn lerp(a: Self, b: Self, t: f32) -> Self {
+    a * (1. - t as f64) + b * t as f64
+  }
+
+  fn cubic_hermite(
+    (x, tx): (Self, f32),
+    (a, ta): (Self, f32),
+    (b, tb): (Self, f32),
+    (y, ty): (Self, f32),
+    t: f32
+  ) -> Self {
+    cubic_hermite((x, tx as f64), (a, ta as f64), (b, tb as f64), (y, ty as f64), t as f64)
+  }
+}
+
+#[cfg(feature = "impl-cgmath")]
+impl<T> Interpolate<T> for Vector2<T> where T: BaseFloat {
+  fn lerp(a: Self, b: Self, t: T) -> Self {
     a.lerp(b, t)
   }
 
-  fn cubic_hermite(x: (Self, f32), a: (Self, f32), b: (Self, f32), y: (Self, f32), t: f32) -> Self {
+  fn cubic_hermite(x: (Self, T), a: (Self, T), b: (Self, T), y: (Self, T), t: T) -> Self {
     cubic_hermite(x, a, b, y, t)
   }
 }
 
 #[cfg(feature = "impl-cgmath")]
-impl Interpolate for Vector3<f32> {
+impl<T> Interpolate<T> for Vector3<T> where T: BaseFloat {
-  fn lerp(a: Self, b: Self, t: f32) -> Self {
+  fn lerp(a: Self, b: Self, t: T) -> Self {
     a.lerp(b, t)
   }
 
-  fn cubic_hermite(x: (Self, f32), a: (Self, f32), b: (Self, f32), y: (Self, f32), t: f32) -> Self {
+  fn cubic_hermite(x: (Self, T), a: (Self, T), b: (Self, T), y: (Self, T), t: T) -> Self {
     cubic_hermite(x, a, b, y, t)
   }
 }
 
 #[cfg(feature = "impl-cgmath")]
-impl Interpolate for Vector4<f32> {
+impl<T> Interpolate<T> for Vector4<T> where T: BaseFloat {
-  fn lerp(a: Self, b: Self, t: f32) -> Self {
+  fn lerp(a: Self, b: Self, t: T) -> Self {
     a.lerp(b, t)
   }
 
-  fn cubic_hermite(x: (Self, f32), a: (Self, f32), b: (Self, f32), y: (Self, f32), t: f32) -> Self {
+  fn cubic_hermite(x: (Self, T), a: (Self, T), b: (Self, T), y: (Self, T), t: T) -> Self {
     cubic_hermite(x, a, b, y, t)
   }
 }
 
 #[cfg(feature = "impl-cgmath")]
-impl Interpolate for Quaternion<f32> {
+impl<T> Interpolate<T> for Quaternion<T> where T: BaseFloat {
-  fn lerp(a: Self, b: Self, t: f32) -> Self {
+  fn lerp(a: Self, b: Self, t: T) -> Self {
     a.nlerp(b, t)
   }
 }
@@ -460,32 +468,38 @@ impl Interpolate for na::Vector6<f32> {
   }
 }
 
-// Default implementation of Interpolate::cubic_hermit.
+// Default implementation of Interpolate::cubic_hermite.
-pub(crate) fn cubic_hermite<T>(x: (T, f32), a: (T, f32), b: (T, f32), y: (T, f32), t: f32) -> T
+//
-    where T: Copy + Add<Output = T> + Sub<Output = T> + Mul<f32, Output = T> + Div<f32, Output = T> {
+// `V` is the value being interpolated. `T` is the sampling value (also sometimes called time).
-  // time stuff
+pub(crate) fn cubic_hermite<V, T>(x: (V, T), a: (V, T), b: (V, T), y: (V, T), t: T) -> V
+where V: Copy + Add<Output = V> + Sub<Output = V> + Mul<T, Output = V> + Div<T, Output = V>,
+      T: Mul<Output = T> + Mul<f32, Output = T> + Add<Output = T> + Add<f32, Output = T> + Sub<Output = T> {
+  // sampler stuff
   let t2 = t* t;
   let t3 = t2 * t;
-  let two_t3 = 2. * t3;
+  let two_t3 = t3 * 2.;
-  let three_t2 = 3. * t2;
+  let three_t2 = t2 * 3.;
 
   // tangents
   let m0 = (b.0 - x.0) / (b.1 - x.1);
 	let m1 = (y.0 - a.0) / (y.1 - a.1);
 
-  a.0 * (two_t3 - three_t2 + 1.) + m0 * (t3 - 2. * t2 + t) + b.0 * (-two_t3 + three_t2) + m1 * (t3 - t2)
+  a.0 * (two_t3 - three_t2 + 1.) + m0 * (t3 - t2 * 2. + t) + b.0 * (three_t2 - two_t3) + m1 * (t3 - t2)
 }
 
 // Normalize a time ([0;1]) given two control points.
 #[inline(always)]
-pub(crate) fn normalize_time<T>(t: f32, cp: &Key<T>, cp1: &Key<T>) -> f32 {
+pub(crate) fn normalize_time<T, V>(
+  t: T,
+  cp: &Key<T, V>,
+  cp1: &Key<T, V>
+) -> T where T: PartialEq + Sub<Output = T> + Div<Output = T> {
   assert!(cp1.t != cp.t, "overlapping keys");
-
   (t - cp.t) / (cp1.t - cp.t)
 }
 
 // Find the lower control point corresponding to a given time.
-fn search_lower_cp<T>(cps: &[Key<T>], t: f32) -> Option<usize> {
+fn search_lower_cp<T, V>(cps: &[Key<T, V>], t: T) -> Option<usize> where T: PartialOrd {
   let mut i = 0;
   let len = cps.len();