fix no_std

Prepare v4.3.1.

.github/dependabot.yml

@@ -0,0 +1,25 @@
+version: 2
+updates:
+- package-ecosystem: cargo
+  directory: "/."
+  schedule:
+    interval: daily
+    time: "04:00"
+  open-pull-requests-limit: 10
+  target-branch: master
+  reviewers:
+  - phaazon
+  assignees:
+  - phaazon
+  labels:
+  - dependency-update
+  ignore:
+  - dependency-name: glam
+    versions:
+    - 0.13.0
+  - dependency-name: nalgebra
+    versions:
+    - 0.25.0
+  - dependency-name: cgmath
+    versions:
+    - 0.18.0

.github/workflows/ci.yaml

@@ -1,50 +1,38 @@
 name: CI
-on: [push]
+on: [push, pull_request]
 
 jobs:
   build-linux:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v1
-      - name: Build
-        run: |
-          cargo build --verbose --all-features
       - name: Test
-        run: |
-          cargo test --verbose --all-features
-
+        run: cargo test --verbose --all-features
 
   build-windows:
     runs-on: windows-latest
     steps:
       - uses: actions/checkout@v1
-      - name: Build
-        run: |
-          cargo build --verbose --all-features
       - name: Test
-        run: |
-          cargo test --verbose --all-features
+        run: cargo test --verbose --all-features
 
   build-macosx:
     runs-on: macOS-latest
     steps:
       - uses: actions/checkout@v1
-      - name: Rust requirements
-        run: curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh -s -- -y --profile=minimal
-      - name: Build
-        run: |
-          . ~/.cargo/env
-          cargo build --verbose --all-features
       - name: Test
-        run: |
-          . ~/.cargo/env
-          cargo test --verbose --all-features
+        run: cargo test --verbose --all-features
 
-  check-readme:
+  quality:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v1
-      - name: Install cargo-sync-readme
-        run: cargo install --force cargo-sync-readme
-      - name: Check
-        run: cargo sync-readme -c
+      - name: Install dependencies
+        run: |
+          cargo install --force cargo-sync-readme
+          rustup component add rustfmt
+      - name: cargo sync-readme
+        run: |
+          cargo sync-readme -c
+      - name: rustfmt
+        run: cargo fmt -- --check

CHANGELOG.md

@@ -1,6 +1,208 @@
-# 3.0.0
+# Changelog
 
-> Sun Oct 20th 2019
+* [4.3.1](#431)
+* [4.3](#43)
+* [4.2](#42)
+* [4.1.1](#411)
+* [4.1](#41)
+* [4.0.3](#403)
+* [4.0.2](#402)
+* [4.0.1](#401)
+* [4.0](#40)
+  * [Major changes](#major-changes)
+  * [Patch changes](#patch-changes)
+* [3.5.4](#354)
+* [3.5.3](#353)
+* [3.5.2](#352)
+* [3.5.1](#351)
+* [3.5](#35)
+* [3.4.2](#342)
+* [3.4.1](#341)
+* [3.4](#34)
+* [3.3](#33)
+* [3.2](#32)
+* [3.1](#31)
+* [3.0](#30)
+  * [Major changes](#major-changes-1)
+  * [Patch changes](#patch-changes-1)
+* [2.2](#22)
+* [2.1.1](#211)
+* [2.1](#21)
+* [2.0.1](#201)
+* [2.0](#20)
+  * [Major changes](#major-changes-2)
+  * [Minor changes](#minor-changes)
+* [1.0](#10)
+  * [Major changes](#major-changes-3)
+  * [Minor changes](#minor-changes-1)
+  * [Patch changes](#patch-changes-2)
+* [0.2.3](#023)
+* [0.2.2](#022)
+* [0.2.1](#021)
+* [0.2](#02)
+* [0.1.1](#011)
+* [0.1](#01)
+
+# 4.3.1
+
+> Nov 22, 2023
+
+- Add `Default` implementation for `Spline`. [c6ba847](https://github.com/phaazon/splines/commit/c6ba847)
+
+# 4.3
+
+> Sep 23, 2023
+
+- Add support for `glam-0.23` and `glam-0.24`. [cdc48a4](https://github.com/phaazon/splines/commit/cdc48a4)
+- Add `Spline::clear` to clear a spline keys without deallocating its internal storage. [eca09f1](https://github.com/phaazon/splines/commit/eca09f1)
+
+# 4.2
+
+> Feb 1, 2023
+
+- Add support for `glam-0.22`.
+- Add support for `nalgebra-0.32`.
+- Add deprecation lints for `impl-*` feature gates. Those shouldn’t be used anymore and the `*` variant should be 
+  preferred. For instance, if you used `impl-cgmath`, you should just use the `cgmath` feature gate now.
+
+# 4.1.1
+
+> Jul 27, 2022
+
+- Internal enhancement of sampling splines by looking for control points. That brings the lookup from _O(N)_ to
+  _O(log(N))_. That is super embarassing because it should have been the default from the very first commit. Sorry
+  about that.
+- Fix hermite cubic interpolation.
+- Add support for `glam-0.21`.
+- Add support for `nalgebra-0.31`.
+
+# 4.1
+
+> Mar 28, 2022
+
+- Support for edition 2021.
+- Bump `float-cmp` dependency.
+- Bump `glam` dependency.
+- Bump `nalgebra` dependency.
+- Simplify the CI.
+
+# 4.0.3
+
+> Jul 11, 2021
+
+- Add more implementors for `Interpolate`.
+
+# 4.0.2
+
+> Jul 11, 2021
+
+- **Yanked.**
+
+# 4.0.1
+
+> Jul 11, 2021
+
+- Add support up to `glam-0.17`.
+- Add support up to `nalgebra-0.27`.
+- Replace the name of some feature gates:
+  - `serialization` becomes `serde`.
+  - `impl-*` becomes `*`.
+  - The previous feature gates are kept around to prevent a breaking change but will eventually be removed in the next
+    major update.
+
+# 4.0
+
+> Mar 05, 2021
+
+## Major changes
+
+- Switch the `Interpolation` enum to `#[non_exhaustive]` to allow adding more interpolation modes (if any) in the
+  future.
+- Introduce `SampledWithKey`, which is a more elegant / typed way to access a sample along with its associated key
+  index.
+- Refactor the `Interpolate` trait and add the `Interpolator` trait.
+
+## Patch changes
+
+- Highly simplify the various implementors (`cgmath`, `nalgebra` and `glam`) so that maintenance is easy.
+- Expose the `impl_Interpolate` macro, allowing to implement the API all at once if a type implements the various
+  `std::ops:*` traits. Since most of the crates do, this macro makes it really easy to add support for a crate.
+- Drop `simba` as a direct dependency.
+- Drop `num-traits` as a direct dependency.
+
+# 3.5.4
+
+> Feb 27, 2021
+
+- Support of `cgmath-0.18`.
+
+# 3.5.3
+
+> Jan 16, 2021
+
+- Resynchronize and fix links in the README (fix in `cargo sync-readme`).
+
+# 3.5.2
+
+> Fri Jan 01, 2021
+
+- Support of `nalgebra-0.24`.
+
+# 3.5.1
+
+> Dec 5th, 2020
+
+- Support of `glam-0.11`.
+
+# 3.5
+
+> Nov 23rd, 2020
+
+- Add support for [glam](https://crates.io/crates/glam) via the `"impl-glam"` feature gate.
+- Support of `nalgebra-0.23`.
+
+# 3.4.2
+
+> Oct 24th, 2020
+
+- Support of `simba-0.3`.
+
+# 3.4.1
+
+> Sep 5th, 2020
+
+- Support of `simba-0.2`.
+- Support of `nalgebra-0.22`.
+
+# 3.4
+
+> Thu May 21st 2020
+
+- Add support for `float-cmp-0.7` and `float-cmp-0.8`. Because this uses a SemVer range, if you
+  already have a `Cargo.lock`, don’t forget to update `splines` with `cargo update --aggressive`.
+
+# 3.3
+
+> Thu Apr 10th 2020
+
+- Add support for `nalgebra-0.21`.
+
+# 3.2
+
+> Thu Mar 19th 2020
+
+- Add support for `nalgebra-0.20`.
+- Add support for `float-cmp-0.6`.
+
+# 3.1
+
+> Sat Jan 26th 2020
+
+- Add support for `nalgebra-0.19`.
+
+# 3.0
+
+> Tue Oct 22th 2019
 
 ## Major changes
 
@@ -11,7 +213,7 @@
 
 - Fix Bézier interpolation when the next key is Bézier too.
 
-# 2.2.0
+# 2.2
 
 > Mon Oct 17th 2019
 
@@ -39,7 +241,7 @@
 - Fix the cubic Bézier curve interpolation. The “output” tangent is now taken by mirroring the
   next key’s tangent around its control point.
 
-# 2.0.0
+# 2.0
 
 > Mon Sep 23rd 2019
 

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "splines"
-version = "3.0.0"
+version = "4.3.1"
 license = "BSD-3-Clause"
 authors = ["Dimitri Sabadie <dimitri.sabadie@gmail.com>"]
 description = "Spline interpolation made easy"
@@ -11,39 +11,32 @@ repository = "https://github.com/phaazon/splines"
 documentation = "https://docs.rs/splines"
 readme = "README.md"
 
-edition = "2018"
-
-[badges]
-travis-ci = { repository = "phaazon/splines", branch = "master" }
-is-it-maintained-issue-resolution = { repository = "phaazon/splines" }
-is-it-maintained-open-issues = { repository = "phaazon/splines" }
-maintenance = { status = "actively-developed" }
+edition = "2021"
 
 [features]
 default = ["std"]
 impl-cgmath = ["cgmath"]
-impl-nalgebra = ["alga", "nalgebra", "num-traits"]
-serialization = ["serde", "serde_derive"]
-std = []
+impl-glam = ["glam"]
+impl-nalgebra = ["nalgebra"]
+serialization = ["serde"]
+std = ["nalgebra/std"]
 
 [dependencies]
-alga = { version = "0.9", optional = true }
-cgmath = { version = "0.17", optional = true }
-nalgebra = { version = ">=0.14, <0.19", optional = true }
-num-traits = { version = "0.2", optional = true }
-serde =  { version = "1", optional = true }
-serde_derive = { version = "1", optional = true }
+cgmath = { version = ">=0.17, <0.19", optional = true }
+glam = { version = ">=0.10, <0.25", optional = true }
+nalgebra = { version = ">=0.21, <0.33", default-features = false, optional = true }
+serde = { version = "1", features = ["derive"], optional = true }
 
 [dev-dependencies]
-float-cmp = "0.5"
+float-cmp = ">=0.6, < 0.10"
 serde_json = "1"
 
 [package.metadata.docs.rs]
-all-features = true
+features = ["std", "cgmath", "glam", "nalgebra", "serde"]
 
 [[example]]
 name = "hello-world"
 
 [[example]]
 name = "serialization"
-required-features = ["serialization"]
+required-features = ["serde"]

README.md

@@ -24,7 +24,7 @@ is picked from its lower control point.
 
 # Quickly create splines
 
-```
+```rust
 use splines::{Interpolation, Key, Spline};
 
 let start = Key::new(0., 0., Interpolation::Linear);
@@ -46,7 +46,7 @@ value.
 
 If you try to sample in out-of-bounds sampling parameter, you’ll get no value.
 
-```
+```rust
 assert_eq!(spline.sample(0.), Some(0.));
 assert_eq!(spline.clamped_sample(1.), Some(10.));
 assert_eq!(spline.sample(1.1), None);
@@ -56,7 +56,7 @@ It’s possible that you want to get a value even if you’re out-of-bounds. Thi
 important for simulations / animations. Feel free to use the `Spline::clamped_interpolation` for
 that purpose.
 
-```
+```rust
 assert_eq!(spline.clamped_sample(-0.9), Some(0.)); // clamped to the first key
 assert_eq!(spline.clamped_sample(1.1), Some(10.)); // clamped to the last key
 ```
@@ -66,7 +66,7 @@ assert_eq!(spline.clamped_sample(1.1), Some(10.)); // clamped to the last key
 [`Spline`] curves are parametered both by the carried value (being interpolated) but also the
 sampling type. It’s very typical to use `f32` or `f64` but really, you can in theory use any
 kind of type; that type must, however, implement a contract defined by a set of traits to
-implement. See [the documentation of this module](crate::interpolate) for further details.
+implement. See [the documentation of this module](https://docs.rs/splines/latest/splines/interpolate/) for further details.
 
 # Features and customization
 
@@ -83,16 +83,19 @@ not. It’s especially important to see how it copes with the documentation.
 
 So here’s a list of currently supported features and how to enable them:
 
-  - **Serialization / deserialization.**
+  - **Serde.**
     - This feature implements both the `Serialize` and `Deserialize` traits from `serde` for all
       types exported by this crate.
-    - Enable with the `"serialization"` feature.
+    - Enable with the `"serde"` feature.
   - **[cgmath](https://crates.io/crates/cgmath) implementors.**
     - Adds some useful implementations of `Interpolate` for some cgmath types.
-    - Enable with the `"impl-cgmath"` feature.
+    - Enable with the `"cgmath"` feature.
+  - **[glam](https://crates.io/crates/glam) implementors.**
+    - Adds some useful implementations of `Interpolate` for some glam types.
+    - Enable with the `"glam"` feature.
   - **[nalgebra](https://crates.io/crates/nalgebra) implementors.**
     - Adds some useful implementations of `Interpolate` for some nalgebra types.
-    - Enable with the `"impl-nalgebra"` feature.
+    - Enable with the `"nalgebra"` feature.
   - **Standard library / no standard library.**
     - It’s possible to compile against the standard library or go on your own without it.
     - Compiling with the standard library is enabled by default.

examples/hello-world.rs

@@ -3,7 +3,10 @@ extern crate splines;
 use splines::{Interpolation, Key, Spline};
 
 fn main() {
-  let keys = vec![Key::new(0., 0., Interpolation::default()), Key::new(5., 1., Interpolation::default())];
+  let keys = vec![
+    Key::new(0., 0., Interpolation::default()),
+    Key::new(5., 1., Interpolation::default()),
+  ];
   let spline = Spline::from_vec(keys);
 
   println!("value at 0: {:?}", spline.clamped_sample(0.));

examples/serialization.rs

@@ -1,11 +1,12 @@
-#[macro_use] extern crate serde_json;
+#[macro_use]
+extern crate serde_json;
 extern crate splines;
 
 use serde_json::from_value;
 use splines::Spline;
 
 fn main() {
-  let value = json!{
+  let value = json! {
     [
       {
         "t": 0,

rustfmt.toml

@@ -0,0 +1,15 @@
+edition = "2018"
+
+fn_params_layout = "Tall"
+force_explicit_abi = true
+hard_tabs = false
+max_width = 100
+merge_derives = true
+newline_style = "Unix"
+remove_nested_parens = true
+reorder_imports = true
+reorder_modules = true
+tab_spaces = 2
+use_field_init_shorthand = true
+use_small_heuristics = "Default"
+use_try_shorthand = true

src/cgmath.rs

@@ -1,86 +1,15 @@
-use cgmath::{
-  BaseFloat, BaseNum, InnerSpace, Quaternion, Vector1, Vector2, Vector3, Vector4, VectorSpace
-};
+use crate::impl_Interpolate;
 
-use crate::interpolate::{
-  Additive, Interpolate, Linear, One, cubic_bezier_def, cubic_hermite_def, quadratic_bezier_def
-};
+use cgmath::{Quaternion, Vector1, Vector2, Vector3, Vector4};
 
-macro_rules! impl_interpolate_vec {
-  ($($t:tt)*) => {
-    impl<T> Linear<T> for $($t)*<T> where T: BaseNum {
-      #[inline(always)]
-      fn outer_mul(self, t: T) -> Self {
-        self * t
-      }
+impl_Interpolate!(f32, Vector1<f32>, std::f32::consts::PI);
+impl_Interpolate!(f32, Vector2<f32>, std::f32::consts::PI);
+impl_Interpolate!(f32, Vector3<f32>, std::f32::consts::PI);
+impl_Interpolate!(f32, Vector4<f32>, std::f32::consts::PI);
+impl_Interpolate!(f32, Quaternion<f32>, std::f32::consts::PI);
 
-      #[inline(always)]
-      fn outer_div(self, t: T) -> Self {
-        self / t
-      }
-    }
-
-    impl<T> Interpolate<T> for $($t)*<T>
-    where Self: InnerSpace<Scalar = T>, T: Additive + BaseFloat + One {
-      #[inline(always)]
-      fn lerp(a: Self, b: Self, t: T) -> Self {
-        a.lerp(b, t)
-      }
-
-      #[inline(always)]
-      fn cubic_hermite(x: (Self, T), a: (Self, T), b: (Self, T), y: (Self, T), t: T) -> Self {
-        cubic_hermite_def(x, a, b, y, t)
-      }
-
-      #[inline(always)]
-      fn quadratic_bezier(a: Self, u: Self, b: Self, t: T) -> Self {
-        quadratic_bezier_def(a, u, b, t)
-      }
-
-      #[inline(always)]
-      fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: T) -> Self {
-        cubic_bezier_def(a, u, v, b, t)
-      }
-    }
-  }
-}
-
-impl_interpolate_vec!(Vector1);
-impl_interpolate_vec!(Vector2);
-impl_interpolate_vec!(Vector3);
-impl_interpolate_vec!(Vector4);
-
-impl<T> Linear<T> for Quaternion<T> where T: BaseFloat {
-  #[inline(always)]
-  fn outer_mul(self, t: T) -> Self {
-    self * t
-  }
-
-  #[inline(always)]
-  fn outer_div(self, t: T) -> Self {
-    self / t
-  }
-}
-
-impl<T> Interpolate<T> for Quaternion<T>
-where Self: InnerSpace<Scalar = T>, T: Additive + BaseFloat + One {
-  #[inline(always)]
-  fn lerp(a: Self, b: Self, t: T) -> Self {
-    a.nlerp(b, t)
-  }
-
-  #[inline(always)]
-  fn cubic_hermite(x: (Self, T), a: (Self, T), b: (Self, T), y: (Self, T), t: T) -> Self {
-    cubic_hermite_def(x, a, b, y, t)
-  }
-
-  #[inline(always)]
-  fn quadratic_bezier(a: Self, u: Self, b: Self, t: T) -> Self {
-    quadratic_bezier_def(a, u, b, t)
-  }
-
-  #[inline(always)]
-  fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: T) -> Self {
-    cubic_bezier_def(a, u, v, b, t)
-  }
-}
+impl_Interpolate!(f64, Vector1<f64>, std::f64::consts::PI);
+impl_Interpolate!(f64, Vector2<f64>, std::f64::consts::PI);
+impl_Interpolate!(f64, Vector3<f64>, std::f64::consts::PI);
+impl_Interpolate!(f64, Vector4<f64>, std::f64::consts::PI);
+impl_Interpolate!(f64, Quaternion<f64>, std::f64::consts::PI);

src/glam.rs

@@ -0,0 +1,8 @@
+use crate::impl_Interpolate;
+use glam::{Quat, Vec2, Vec3, Vec3A, Vec4};
+
+impl_Interpolate!(f32, Vec2, std::f32::consts::PI);
+impl_Interpolate!(f32, Vec3, std::f32::consts::PI);
+impl_Interpolate!(f32, Vec3A, std::f32::consts::PI);
+impl_Interpolate!(f32, Vec4, std::f32::consts::PI);
+impl_Interpolate!(f32, Quat, std::f32::consts::PI);

src/interpolate.rs

@@ -28,267 +28,220 @@
 //! [`Trigo`]: crate::interpolate::Trigo
 //! [num-traits]: https://crates.io/crates/num-traits
 
-#[cfg(feature = "std")] use std::f32;
-#[cfg(not(feature = "std"))] use core::f32;
-#[cfg(not(feature = "std"))] use core::intrinsics::cosf32;
-#[cfg(feature = "std")] use std::f64;
-#[cfg(not(feature = "std"))] use core::f64;
-#[cfg(not(feature = "std"))] use core::intrinsics::cosf64;
-#[cfg(feature = "std")] use std::ops::{Add, Mul, Sub};
-#[cfg(not(feature = "std"))] use core::ops::{Add, Mul, Sub};
+#[cfg(not(feature = "std"))]
+use core::f32;
+#[cfg(not(feature = "std"))]
+use core::f64;
+#[cfg(not(feature = "std"))]
+use core::intrinsics::cosf32;
+#[cfg(not(feature = "std"))]
+use core::intrinsics::cosf64;
+#[cfg(not(feature = "std"))]
+use core::ops::{Add, Mul, Sub};
+#[cfg(feature = "std")]
+use std::f32;
+#[cfg(feature = "std")]
+use std::f64;
 
-/// Keys that can be interpolated in between. Implementing this trait is required to perform
-/// sampling on splines.
+/// Types that can be used as interpolator in splines.
 ///
-/// `T` is the variable used to sample with. Typical implementations use [`f32`] or [`f64`], but
-/// you’re free to use the ones you like. Feel free to have a look at [`Spline::sample`] for
-/// instance to know which trait your type must implement to be usable.
+/// An interpolator value is like the fabric on which control keys (and sampled values) live on.
+pub trait Interpolator: Sized + Copy + PartialOrd {
+  /// Normalize the interpolator.
+  fn normalize(self, start: Self, end: Self) -> Self;
+}
+
+macro_rules! impl_Interpolator {
+  ($t:ty) => {
+    impl Interpolator for $t {
+      fn normalize(self, start: Self, end: Self) -> Self {
+        (self - start) / (end - start)
+      }
+    }
+  };
+}
+
+impl_Interpolator!(f32);
+impl_Interpolator!(f64);
+
+/// Values that can be interpolated. Implementing this trait is required to perform sampling on splines.
 ///
-/// [`Spline::sample`]: crate::spline::Spline::sample
-pub trait Interpolate<T>: Sized + Copy + Linear<T> {
+/// `T` is the interpolator used to sample with. Typical implementations use [`f32`] or [`f64`], but
+/// you’re free to use the ones you like.
+pub trait Interpolate<T>: Sized + Copy {
+  /// Step interpolation.
+  fn step(t: T, threshold: T, a: Self, b: Self) -> Self;
+
   /// Linear interpolation.
-  fn lerp(a: Self, b: Self, t: T) -> Self;
+  fn lerp(t: T, a: Self, b: Self) -> Self;
+
+  /// Cosine interpolation.
+  fn cosine(t: T, a: Self, b: Self) -> Self;
 
   /// Cubic hermite interpolation.
-  ///
-  /// Default to [`lerp`].
-  ///
-  /// [`lerp`]: Interpolate::lerp
-  fn cubic_hermite(_: (Self, T), a: (Self, T), b: (Self, T), _: (Self, T), t: T) -> Self {
-    Self::lerp(a.0, b.0, t)
-  }
+  fn cubic_hermite(t: T, x: (T, Self), a: (T, Self), b: (T, Self), y: (T, Self)) -> Self;
 
   /// Quadratic Bézier interpolation.
-  fn quadratic_bezier(a: Self, u: Self, b: Self, t: T) -> Self;
+  ///
+  /// `a` is the first point; `b` is the second point and `u` is the tangent of `a` to the curve.
+  fn quadratic_bezier(t: T, a: Self, u: Self, b: Self) -> Self;
 
   /// Cubic Bézier interpolation.
-  fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: T) -> Self;
+  ///
+  /// `a` is the first point; `b` is the second point; `u` is the output tangent of `a` to the curve and `v` is the
+  /// input tangent of `b` to the curve.
+  fn cubic_bezier(t: T, a: Self, u: Self, v: Self, b: Self) -> Self;
+
+  /// Cubic Bézier interpolation – special case for non-explicit second tangent.
+  ///
+  /// This version does the same computation as [`Interpolate::cubic_bezier`] but computes the second tangent by
+  /// inversing it (typical when the next point uses a Bézier interpolation, where input and output tangents are
+  /// mirrored for the same key).
+  fn cubic_bezier_mirrored(t: T, a: Self, u: Self, v: Self, b: Self) -> Self;
 }
 
-/// Set of types that support additions and subtraction.
-///
-/// The [`Copy`] trait is also a supertrait as it’s likely to be used everywhere.
-pub trait Additive:
-  Copy +
-  Add<Self, Output = Self> +
-  Sub<Self, Output = Self> {
-}
-
-impl<T> Additive for T
-where T: Copy +
-         Add<Self, Output = Self> +
-         Sub<Self, Output = Self> {
-}
-
-/// Set of additive types that support outer multiplication and division, making them linear.
-pub trait Linear<T>: Additive {
-  /// Apply an outer multiplication law.
-  fn outer_mul(self, t: T) -> Self;
-
-  /// Apply an outer division law.
-  fn outer_div(self, t: T) -> Self;
-}
-
-macro_rules! impl_linear_simple {
-  ($t:ty) => {
-    impl Linear<$t> for $t {
-      fn outer_mul(self, t: $t) -> Self {
-        self * t
+#[macro_export]
+macro_rules! impl_Interpolate {
+  ($t:ty, $v:ty, $pi:expr) => {
+    impl $crate::interpolate::Interpolate<$t> for $v {
+      fn step(t: $t, threshold: $t, a: Self, b: Self) -> Self {
+        if t < threshold {
+          a
+        } else {
+          b
+        }
       }
 
-      /// Apply an outer division law.
-      fn outer_div(self, t: $t) -> Self {
-        self / t
+      #[cfg(feature = "std")]
+      fn cosine(t: $t, a: Self, b: Self) -> Self {
+        let cos_nt = (1. - (t * $pi).cos()) * 0.5;
+        <Self as $crate::interpolate::Interpolate<$t>>::lerp(cos_nt, a, b)
       }
-    }
-  }
-}
-
-impl_linear_simple!(f32);
-impl_linear_simple!(f64);
-
-macro_rules! impl_linear_cast {
-  ($t:ty, $q:ty) => {
-    impl Linear<$t> for $q {
-      fn outer_mul(self, t: $t) -> Self {
-        self * t as $q
+      #[cfg(not(feature = "std"))]
+      fn cosine(t: $t, a: Self, b: Self) -> Self {
+        unimplemented!();
       }
 
-      /// Apply an outer division law.
-      fn outer_div(self, t: $t) -> Self {
-        self / t as $q
-      }
-    }
-  }
-}
-
-impl_linear_cast!(f32, f64);
-impl_linear_cast!(f64, f32);
-
-/// Types with a neutral element for multiplication.
-pub trait One {
-  /// The neutral element for the multiplicative monoid — typically called `1`.
-  fn one() -> Self;
-}
-
-macro_rules! impl_one_float {
-  ($t:ty) => {
-    impl One for $t {
-      #[inline(always)]
-      fn one() -> Self {
-        1.
-      }
-    }
-  }
-}
-
-impl_one_float!(f32);
-impl_one_float!(f64);
-
-/// Types with a sane definition of π and cosine.
-pub trait Trigo {
-  /// π.
-  fn pi() -> Self;
-
-  /// Cosine of the argument.
-  fn cos(self) -> Self;
-}
-
-impl Trigo for f32 {
-  #[inline(always)]
-  fn pi() -> Self {
-    f32::consts::PI
-  }
-
-  #[inline(always)]
-  fn cos(self) -> Self {
-    #[cfg(feature = "std")]
-    {
-      self.cos()
-    }
-
-    #[cfg(not(feature = "std"))]
-    {
-      unsafe { cosf32(self) }
-    }
-  }
-}
-
-impl Trigo for f64 {
-  #[inline(always)]
-  fn pi() -> Self {
-    f64::consts::PI
-  }
-
-  #[inline(always)]
-  fn cos(self) -> Self {
-    #[cfg(feature = "std")]
-    {
-      self.cos()
-    }
-
-    #[cfg(not(feature = "std"))]
-    {
-      unsafe { cosf64(self) }
-    }
-  }
-}
-
-/// Default implementation of [`Interpolate::cubic_hermite`].
-///
-/// `V` is the value being interpolated. `T` is the sampling value (also sometimes called time).
-pub fn cubic_hermite_def<V, T>(x: (V, T), a: (V, T), b: (V, T), y: (V, T), t: T) -> V
-where V: Linear<T>,
-      T: Additive + Mul<T, Output = T> + One {
-  // some stupid generic constants, because Rust doesn’t have polymorphic literals…
-  let one_t = T::one();
-  let two_t = one_t + one_t; // lolololol
-  let three_t = two_t + one_t; // megalol
-
-  // sampler stuff
-  let t2 = t * t;
-  let t3 = t2 * t;
-  let two_t3 = t3 * two_t;
-  let three_t2 = t2 * three_t;
-
-  // tangents
-  let m0 = (b.0 - x.0).outer_div(b.1 - x.1);
-  let m1 = (y.0 - a.0).outer_div(y.1 - a.1);
-
-  a.0.outer_mul(two_t3 - three_t2 + one_t) + m0.outer_mul(t3 - t2 * two_t + t) + b.0.outer_mul(three_t2 - two_t3) + m1.outer_mul(t3 - t2)
-}
-
-/// Default implementation of [`Interpolate::quadratic_bezier`].
-///
-/// `V` is the value being interpolated. `T` is the sampling value (also sometimes called time).
-pub fn quadratic_bezier_def<V, T>(a: V, u: V, b: V, t: T) -> V
-where V: Linear<T>,
-      T: Additive + Mul<T, Output = T> + One {
-  let one_t = T::one() - t;
-  let one_t_2 = one_t * one_t;
-  u + (a - u).outer_mul(one_t_2) + (b - u).outer_mul(t * t)
-}
-
-/// Default implementation of [`Interpolate::cubic_bezier`].
-///
-/// `V` is the value being interpolated. `T` is the sampling value (also sometimes called time).
-pub fn cubic_bezier_def<V, T>(a: V, u: V, v: V, b: V, t: T) -> V
-where V: Linear<T>,
-      T: Additive + Mul<T, Output = T> + One {
-  let one_t = T::one() - t;
-  let one_t_2 = one_t * one_t;
-  let one_t_3 = one_t_2 * one_t;
-  let three = T::one() + T::one() + T::one();
-
-  a.outer_mul(one_t_3) + u.outer_mul(three * one_t_2 * t) + v.outer_mul(three * one_t * t * t) + b.outer_mul(t * t * t)
-}
-
-macro_rules! impl_interpolate_simple {
-  ($t:ty) => {
-    impl Interpolate<$t> for $t {
-      fn lerp(a: Self, b: Self, t: $t) -> Self {
+      fn lerp(t: $t, a: Self, b: Self) -> Self {
         a * (1. - t) + b * t
       }
 
-      fn cubic_hermite(x: (Self, $t), a: (Self, $t), b: (Self, $t), y: (Self, $t), t: $t) -> Self {
-        cubic_hermite_def(x, a, b, y, t)
+      fn cubic_hermite(t: $t, x: ($t, Self), a: ($t, Self), b: ($t, Self), y: ($t, Self)) -> Self {
+        // sampler stuff
+        let two_t = t * 2.;
+        let three_t = t * 3.;
+        let t2 = t * t;
+        let t3 = t2 * t;
+        let two_t3 = t2 * two_t;
+        let two_t2 = t * two_t;
+        let three_t2 = t * three_t;
+
+        // tangents
+        let m0 = (b.1 - x.1) / (b.0 - x.0) * (b.0 - a.0);
+        let m1 = (y.1 - a.1) / (y.0 - a.0) * (b.0 - a.0);
+
+        a.1 * (two_t3 - three_t2 + 1.)
+          + m0 * (t3 - two_t2 + t)
+          + b.1 * (three_t2 - two_t3)
+          + m1 * (t3 - t2)
       }
 
-      fn quadratic_bezier(a: Self, u: Self, b: Self, t: $t) -> Self {
-        quadratic_bezier_def(a, u, b, t)
+      fn quadratic_bezier(t: $t, a: Self, u: Self, b: Self) -> Self {
+        let one_t = 1. - t;
+        let one_t2 = one_t * one_t;
+
+        u + (a - u) * one_t2 + (b - u) * t * t
       }
 
-      fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: $t) -> Self {
-        cubic_bezier_def(a, u, v, b, t)
+      fn cubic_bezier(t: $t, a: Self, u: Self, v: Self, b: Self) -> Self {
+        let one_t = 1. - t;
+        let one_t2 = one_t * one_t;
+        let one_t3 = one_t2 * one_t;
+        let t2 = t * t;
+
+        a * one_t3 + (u * one_t2 * t + v * one_t * t2) * 3. + b * t2 * t
+      }
+
+      fn cubic_bezier_mirrored(t: $t, a: Self, u: Self, v: Self, b: Self) -> Self {
+        <Self as $crate::interpolate::Interpolate<$t>>::cubic_bezier(t, a, u, b + b - v, b)
       }
     }
-  }
+  };
 }
 
-impl_interpolate_simple!(f32);
-impl_interpolate_simple!(f64);
-
-macro_rules! impl_interpolate_via {
-  ($t:ty, $v:ty) => {
-    impl Interpolate<$t> for $v {
-      fn lerp(a: Self, b: Self, t: $t) -> Self {
-        a * (1. - t as $v) + b * t as $v
+#[macro_export]
+macro_rules! impl_InterpolateT {
+  ($t:ty, $v:ty, $pi:expr) => {
+    impl $crate::interpolate::Interpolate<$t> for $v {
+      fn step(t: $t, threshold: $t, a: Self, b: Self) -> Self {
+        if t < threshold {
+          a
+        } else {
+          b
+        }
       }
 
-      fn cubic_hermite((x, xt): (Self, $t), (a, at): (Self, $t), (b, bt): (Self, $t), (y, yt): (Self, $t), t: $t) -> Self {
-        cubic_hermite_def((x, xt as $v), (a, at as $v), (b, bt as $v), (y, yt as $v), t as $v)
+      #[cfg(feature = "std")]
+      fn cosine(t: $t, a: Self, b: Self) -> Self {
+        let cos_nt = (1. - (t * $pi).cos()) * 0.5;
+        <Self as $crate::interpolate::Interpolate<$t>>::lerp(cos_nt, a, b)
+      }
+      #[cfg(not(feature = "std"))]
+      fn cosine(t: $t, a: Self, b: Self) -> Self {
+        unimplemented!()
       }
 
-      fn quadratic_bezier(a: Self, u: Self, b: Self, t: $t) -> Self {
-        quadratic_bezier_def(a, u, b, t as $v)
+      fn lerp(t: $t, a: Self, b: Self) -> Self {
+        let t = Self::from(t);
+        a * (1. - t) + b * t
       }
 
-      fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: $t) -> Self {
-        cubic_bezier_def(a, u, v, b, t as $v)
+      fn cubic_hermite(t: $t, x: ($t, Self), a: ($t, Self), b: ($t, Self), y: ($t, Self)) -> Self {
+        // sampler stuff
+        let t = Self::from(t);
+        let two_t = t * 2.;
+        let three_t = t * 3.;
+        let t2 = t * t;
+        let t3 = t2 * t;
+        let two_t3 = t2 * two_t;
+        let two_t2 = t * two_t;
+        let three_t2 = t * three_t;
+
+        // tangents
+        let m0 = (b.1 - x.1) / (Self::from(b.0 - x.0)) * (Self::from(b.0 - a.0));
+        let m1 = (y.1 - a.1) / (Self::from(y.0 - a.0)) * (Self::from(b.0 - a.0));
+
+        a.1 * (two_t3 - three_t2 + 1.)
+          + m0 * (t3 - two_t2 + t)
+          + b.1 * (three_t2 - two_t3)
+          + m1 * (t3 - t2)
+      }
+
+      fn quadratic_bezier(t: $t, a: Self, u: Self, b: Self) -> Self {
+        let t = Self::from(t);
+        let one_t = 1. - t;
+        let one_t2 = one_t * one_t;
+
+        u + (a - u) * one_t2 + (b - u) * t * t
+      }
+
+      fn cubic_bezier(t: $t, a: Self, u: Self, v: Self, b: Self) -> Self {
+        let t = Self::from(t);
+        let one_t = 1. - t;
+        let one_t2 = one_t * one_t;
+        let one_t3 = one_t2 * one_t;
+        let t2 = t * t;
+
+        a * one_t3 + (u * one_t2 * t + v * one_t * t2) * 3. + b * t2 * t
+      }
+
+      fn cubic_bezier_mirrored(t: $t, a: Self, u: Self, v: Self, b: Self) -> Self {
+        <Self as $crate::interpolate::Interpolate<$t>>::cubic_bezier(t, a, u, b + b - v, b)
       }
     }
-  }
+  };
 }
 
-impl_interpolate_via!(f32, f64);
-impl_interpolate_via!(f64, f32);
+impl_Interpolate!(f32, f32, f32::consts::PI);
+impl_Interpolate!(f64, f64, f64::consts::PI);
+impl_InterpolateT!(f32, f64, f32::consts::PI);

src/interpolation.rs

@@ -1,13 +1,18 @@
 //! Available interpolation modes.
 
-#[cfg(feature = "serialization")] use serde_derive::{Deserialize, Serialize};
+#[cfg(any(feature = "serialization", feature = "serde"))]
+use serde::{Deserialize, Serialize};
 
 /// Available kind of interpolations.
 ///
 /// Feel free to visit each variant for more documentation.
+#[non_exhaustive]
 #[derive(Copy, Clone, Debug, Eq, PartialEq)]
-#[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
-#[cfg_attr(feature = "serialization", serde(rename_all = "snake_case"))]
+#[cfg_attr(
+  any(feature = "serialization", feature = "serde"),
+  derive(Deserialize, Serialize),
+  serde(rename_all = "snake_case")
+)]
 pub enum Interpolation<T, V> {
   /// Hold a [`Key`] until the sampling value passes the normalized step threshold, in which
   /// case the next key is used.
@@ -19,12 +24,16 @@ pub enum Interpolation<T, V> {
   ///
   /// [`Key`]: crate::key::Key
   Step(T),
+
   /// Linear interpolation between a key and the next one.
   Linear,
+
   /// Cosine interpolation between a key and the next one.
   Cosine,
+
   /// Catmull-Rom interpolation, performing a cubic Hermite interpolation using four keys.
   CatmullRom,
+
   /// Bézier interpolation.
   ///
   /// A control point that uses such an interpolation is associated with an extra point. The segmant
@@ -40,6 +49,7 @@ pub enum Interpolation<T, V> {
   ///   point and the current control point’s associated point. This is called _quadratic Bézer
   ///   interpolation_ and it kicks ass too, but a bit less than cubic.
   Bezier(V),
+
   /// A special Bézier interpolation using an _input tangent_ and an _output tangent_.
   ///
   /// With this kind of interpolation, a control point has an input tangent, which has the same role
@@ -52,8 +62,6 @@ pub enum Interpolation<T, V> {
   ///
   /// Stroke Bézier interpolation is always a cubic Bézier interpolation by default.
   StrokeBezier(V, V),
-  #[doc(hidden)]
-  __NonExhaustive
 }
 
 impl<T, V> Default for Interpolation<T, V> {

src/iter.rs

@@ -11,9 +11,13 @@ use crate::{Key, Spline};
 /// Iterator over spline keys.
 ///
 /// This iterator type is guaranteed to iterate over sorted keys.
-pub struct Iter<'a, T, V> where T: 'a, V: 'a {
+pub struct Iter<'a, T, V>
+where
+  T: 'a,
+  V: 'a,
+{
   spline: &'a Spline<T, V>,
-  i: usize
+  i: usize,
 }
 
 impl<'a, T, V> Iterator for Iter<'a, T, V> {
@@ -35,10 +39,6 @@ impl<'a, T, V> IntoIterator for &'a Spline<T, V> {
   type IntoIter = Iter<'a, T, V>;
 
   fn into_iter(self) -> Self::IntoIter {
-    Iter {
-      spline: self,
-      i: 0
-    }
+    Iter { spline: self, i: 0 }
   }
 }
-

src/key.rs

@@ -1,14 +1,14 @@
 //! Spline control points.
 //!
-//! A control point associates to a “sampling value” (a.k.a. time) a carriede value that can be
+//! A control point associates to a “sampling value” (a.k.a. time) a carried value that can be
 //! interpolated along the curve made by the control points.
 //!
 //! Splines constructed with this crate have the property that it’s possible to change the
 //! interpolation mode on a key-based way, allowing you to implement and encode complex curves.
 
-#[cfg(feature = "serialization")] use serde_derive::{Deserialize, Serialize};
-
 use crate::interpolation::Interpolation;
+#[cfg(any(feature = "serialization", feature = "serde"))]
+use serde::{Deserialize, Serialize};
 
 /// A spline control point.
 ///
@@ -18,20 +18,27 @@ use crate::interpolation::Interpolation;
 ///
 /// [`Interpolation`]: crate::interpolation::Interpolation
 #[derive(Copy, Clone, Debug, Eq, PartialEq)]
-#[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
-#[cfg_attr(feature = "serialization", serde(rename_all = "snake_case"))]
+#[cfg_attr(
+  any(feature = "serialization", feature = "serde"),
+  derive(Deserialize, Serialize),
+  serde(rename_all = "snake_case")
+)]
 pub struct Key<T, V> {
   /// Interpolation parameter at which the [`Key`] should be reached.
   pub t: T,
   /// Carried value.
   pub value: V,
   /// Interpolation mode.
-  pub interpolation: Interpolation<T, V>
+  pub interpolation: Interpolation<T, V>,
 }
 
 impl<T, V> Key<T, V> {
   /// Create a new key.
   pub fn new(t: T, value: V, interpolation: Interpolation<T, V>) -> Self {
-    Key { t, value, interpolation }
+    Key {
+      t,
+      value,
+      interpolation,
+    }
   }
 }

src/lib.rs

@@ -84,16 +84,19 @@
 //!
 //! So here’s a list of currently supported features and how to enable them:
 //!
-//!   - **Serialization / deserialization.**
+//!   - **Serde.**
 //!     - This feature implements both the `Serialize` and `Deserialize` traits from `serde` for all
 //!       types exported by this crate.
-//!     - Enable with the `"serialization"` feature.
+//!     - Enable with the `"serde"` feature.
 //!   - **[cgmath](https://crates.io/crates/cgmath) implementors.**
 //!     - Adds some useful implementations of `Interpolate` for some cgmath types.
-//!     - Enable with the `"impl-cgmath"` feature.
+//!     - Enable with the `"cgmath"` feature.
+//!   - **[glam](https://crates.io/crates/glam) implementors.**
+//!     - Adds some useful implementations of `Interpolate` for some glam types.
+//!     - Enable with the `"glam"` feature.
 //!   - **[nalgebra](https://crates.io/crates/nalgebra) implementors.**
 //!     - Adds some useful implementations of `Interpolate` for some nalgebra types.
-//!     - Enable with the `"impl-nalgebra"` feature.
+//!     - Enable with the `"nalgebra"` feature.
 //!   - **Standard library / no standard library.**
 //!     - It’s possible to compile against the standard library or go on your own without it.
 //!     - Compiling with the standard library is enabled by default.
@@ -105,15 +108,31 @@
 #![cfg_attr(not(feature = "std"), no_std)]
 #![cfg_attr(not(feature = "std"), feature(alloc))]
 #![cfg_attr(not(feature = "std"), feature(core_intrinsics))]
+#![cfg_attr(
+  any(
+    feature = "impl-cgmath",
+    feature = "impl-glam",
+    feature = "impl-nalgebra"
+  ),
+  deprecated(
+    since = "4.2.0",
+    note = "you are using an impl-* feature gate; please switch to * (e.g. impl-cgmath becomes cgmath)"
+  )
+)]
 
-#[cfg(not(feature = "std"))] extern crate alloc;
+#[cfg(not(feature = "std"))]
+extern crate alloc;
 
-#[cfg(feature = "impl-cgmath")] mod cgmath;
+#[cfg(any(feature = "impl-cgmath", feature = "cgmath"))]
+mod cgmath;
+#[cfg(any(feature = "impl-glam", feature = "glam"))]
+mod glam;
 pub mod interpolate;
 pub mod interpolation;
 pub mod iter;
 pub mod key;
-#[cfg(feature = "impl-nalgebra")] mod nalgebra;
+#[cfg(any(feature = "impl-nalgebra", feature = "nalgebra"))]
+mod nalgebra;
 pub mod spline;
 
 pub use crate::interpolate::Interpolate;

src/nalgebra.rs

@@ -1,64 +1,27 @@
-use alga::general::{ClosedAdd, ClosedDiv, ClosedMul, ClosedSub};
-use nalgebra::{Scalar, Vector, Vector1, Vector2, Vector3, Vector4, Vector5, Vector6};
-use num_traits as nt;
-use std::ops::Mul;
+#[cfg(not(feature = "std"))]
+use core::f32;
+#[cfg(not(feature = "std"))]
+use core::f64;
+#[cfg(feature = "std")]
+use std::f32;
+#[cfg(feature = "std")]
+use std::f64;
 
-use crate::interpolate::{
-  Interpolate, Linear, Additive, One, cubic_bezier_def, cubic_hermite_def, quadratic_bezier_def
-};
+use crate::impl_Interpolate;
+use nalgebra::{Quaternion, Vector1, Vector2, Vector3, Vector4, Vector5, Vector6};
 
-macro_rules! impl_interpolate_vector {
-  ($($t:tt)*) => {
-    // implement Linear
-    impl<T> Linear<T> for $($t)*<T> where T: Scalar + ClosedAdd + ClosedSub + ClosedMul + ClosedDiv {
-      #[inline(always)]
-      fn outer_mul(self, t: T) -> Self {
-        self * t
-      }
+impl_Interpolate!(f32, Vector1<f32>, f32::consts::PI);
+impl_Interpolate!(f32, Vector2<f32>, f32::consts::PI);
+impl_Interpolate!(f32, Vector3<f32>, f32::consts::PI);
+impl_Interpolate!(f32, Vector4<f32>, f32::consts::PI);
+impl_Interpolate!(f32, Vector5<f32>, f32::consts::PI);
+impl_Interpolate!(f32, Vector6<f32>, f32::consts::PI);
+impl_Interpolate!(f32, Quaternion<f32>, f32::consts::PI);
 
-      #[inline(always)]
-      fn outer_div(self, t: T) -> Self {
-        self / t
-      }
-    }
-
-    impl<T, V> Interpolate<T> for $($t)*<V>
-    where Self: Linear<T>,
-          T: Additive + One + Mul<T, Output = T>,
-          V: nt::One +
-             nt::Zero +
-             Additive +
-             Scalar +
-             ClosedAdd +
-             ClosedMul +
-             ClosedSub +
-             Interpolate<T> {
-      #[inline(always)]
-      fn lerp(a: Self, b: Self, t: T) -> Self {
-        Vector::zip_map(&a, &b, |c1, c2| Interpolate::lerp(c1, c2, t))
-      }
-
-      #[inline(always)]
-      fn cubic_hermite(x: (Self, T), a: (Self, T), b: (Self, T), y: (Self, T), t: T) -> Self {
-        cubic_hermite_def(x, a, b, y, t)
-      }
-
-      #[inline(always)]
-      fn quadratic_bezier(a: Self, u: Self, b: Self, t: T) -> Self {
-        quadratic_bezier_def(a, u, b, t)
-      }
-
-      #[inline(always)]
-      fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: T) -> Self {
-        cubic_bezier_def(a, u, v, b, t)
-      }
-    }
-  }
-}
-
-impl_interpolate_vector!(Vector1);
-impl_interpolate_vector!(Vector2);
-impl_interpolate_vector!(Vector3);
-impl_interpolate_vector!(Vector4);
-impl_interpolate_vector!(Vector5);
-impl_interpolate_vector!(Vector6);
+impl_Interpolate!(f64, Vector1<f64>, f64::consts::PI);
+impl_Interpolate!(f64, Vector2<f64>, f64::consts::PI);
+impl_Interpolate!(f64, Vector3<f64>, f64::consts::PI);
+impl_Interpolate!(f64, Vector4<f64>, f64::consts::PI);
+impl_Interpolate!(f64, Vector5<f64>, f64::consts::PI);
+impl_Interpolate!(f64, Vector6<f64>, f64::consts::PI);
+impl_Interpolate!(f64, Quaternion<f64>, f64::consts::PI);

src/spline.rs

@@ -1,15 +1,19 @@
 //! Spline curves and operations.
 
-#[cfg(feature = "serialization")] use serde_derive::{Deserialize, Serialize};
-#[cfg(not(feature = "std"))] use alloc::vec::Vec;
-#[cfg(feature = "std")] use std::cmp::Ordering;
-#[cfg(feature = "std")] use std::ops::{Div, Mul};
-#[cfg(not(feature = "std"))] use core::ops::{Div, Mul};
-#[cfg(not(feature = "std"))] use core::cmp::Ordering;
-
-use crate::interpolate::{Additive, Interpolate, One, Trigo};
+// #[cfg(feature = "std")]
+use crate::interpolate::{Interpolate, Interpolator};
 use crate::interpolation::Interpolation;
 use crate::key::Key;
+#[cfg(not(feature = "std"))]
+use alloc::vec::Vec;
+#[cfg(not(feature = "std"))]
+use core::cmp::Ordering;
+#[cfg(not(feature = "std"))]
+use core::ops::{Div, Mul};
+#[cfg(any(feature = "serialization", feature = "serde"))]
+use serde::{Deserialize, Serialize};
+#[cfg(feature = "std")]
+use std::cmp::Ordering;
 
 /// Spline curve used to provide interpolation between control points (keys).
 ///
@@ -23,24 +27,42 @@ use crate::key::Key;
 ///     for the required interpolation mode, you get `None`.
 ///   - [`Spline::clamped_sample`]: behaves like [`Spline::sample`] but will return either the first
 ///     or last key if out of bound; it will return `None` if not enough key.
-#[derive(Debug, Clone)]
-#[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
+#[derive(Debug, Clone, Default)]
+#[cfg_attr(
+  any(feature = "serialization", feature = "serde"),
+  derive(Deserialize, Serialize)
+)]
 pub struct Spline<T, V>(pub(crate) Vec<Key<T, V>>);
 
 impl<T, V> Spline<T, V> {
   /// Internal sort to ensure invariant of sorting keys is valid.
-  fn internal_sort(&mut self) where T: PartialOrd {
-    self.0.sort_by(|k0, k1| k0.t.partial_cmp(&k1.t).unwrap_or(Ordering::Less));
+  fn internal_sort(&mut self)
+  where
+    T: PartialOrd,
+  {
+    self
+      .0
+      .sort_by(|k0, k1| k0.t.partial_cmp(&k1.t).unwrap_or(Ordering::Less));
   }
 
   /// 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(keys: Vec<Key<T, V>>) -> Self where T: PartialOrd {
+  pub fn from_vec(keys: Vec<Key<T, V>>) -> Self
+  where
+    T: PartialOrd,
+  {
     let mut spline = Spline(keys);
     spline.internal_sort();
     spline
   }
 
+  /// Clear the spline by removing all keys. Keeps the underlying allocated storage, so adding
+  /// new keys should be faster than creating a new [`Spline`]
+  #[inline]
+  pub fn clear(&mut self) {
+    self.0.clear()
+  }
+
   /// Create a new spline by consuming an `Iterater<Item = Key<T>>`. They keys don’t have to be
   /// sorted.
   ///
@@ -48,7 +70,11 @@ impl<T, V> Spline<T, V> {
   ///
   /// 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`].
-  pub fn from_iter<I>(iter: I) -> Self where I: Iterator<Item = Key<T, V>>, T: PartialOrd {
+  pub fn from_iter<I>(iter: I) -> Self
+  where
+    I: Iterator<Item = Key<T, V>>,
+    T: PartialOrd,
+  {
     Self::from_vec(iter.collect())
   }
 
@@ -84,38 +110,38 @@ impl<T, V> Spline<T, V> {
   /// sampling impossible. For instance, [`Interpolation::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_with_key(&self, t: T) -> Option<(V, &Key<T, V>, Option<&Key<T, V>>)>
-  where T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
-        V: Additive + Interpolate<T> {
+  pub fn sample_with_key(&self, t: T) -> Option<SampledWithKey<V>>
+  where
+    T: Interpolator,
+    V: Interpolate<T>,
+  {
     let keys = &self.0;
     let i = search_lower_cp(keys, t)?;
     let cp0 = &keys[i];
 
-    match cp0.interpolation {
+    let value = match cp0.interpolation {
       Interpolation::Step(threshold) => {
         let cp1 = &keys[i + 1];
-        let nt = normalize_time(t, cp0, cp1);
-        let value = if nt < threshold { cp0.value } else { cp1.value };
+        let nt = t.normalize(cp0.t, cp1.t);
+        let value = V::step(nt, threshold, cp0.value, cp1.value);
 
-        Some((value, cp0, Some(cp1)))
+        Some(value)
       }
 
       Interpolation::Linear => {
         let cp1 = &keys[i + 1];
-        let nt = normalize_time(t, cp0, cp1);
-        let value = Interpolate::lerp(cp0.value, cp1.value, nt);
+        let nt = t.normalize(cp0.t, cp1.t);
+        let value = V::lerp(nt, cp0.value, cp1.value);
 
-        Some((value, cp0, Some(cp1)))
+        Some(value)
       }
 
       Interpolation::Cosine => {
-        let two_t = T::one() + T::one();
         let cp1 = &keys[i + 1];
-        let nt = normalize_time(t, cp0, cp1);
-        let cos_nt = (T::one() - (nt * T::pi()).cos()) / two_t;
-        let value = Interpolate::lerp(cp0.value, cp1.value, cos_nt);
+        let nt = t.normalize(cp0.t, cp1.t);
+        let value = V::cosine(nt, cp0.value, cp1.value);
 
-        Some((value, cp0, Some(cp1)))
+        Some(value)
       }
 
       Interpolation::CatmullRom => {
@@ -127,44 +153,47 @@ impl<T, V> Spline<T, V> {
           let cp1 = &keys[i + 1];
           let cpm0 = &keys[i - 1];
           let cpm1 = &keys[i + 2];
-          let nt = normalize_time(t, cp0, cp1);
-          let value = Interpolate::cubic_hermite((cpm0.value, cpm0.t), (cp0.value, cp0.t), (cp1.value, cp1.t), (cpm1.value, cpm1.t), nt);
+          let nt = t.normalize(cp0.t, cp1.t);
+          let value = V::cubic_hermite(
+            nt,
+            (cpm0.t, cpm0.value),
+            (cp0.t, cp0.value),
+            (cp1.t, cp1.value),
+            (cpm1.t, cpm1.value),
+          );
 
-          Some((value, cp0, Some(cp1)))
+          Some(value)
         }
       }
 
       Interpolation::Bezier(u) | Interpolation::StrokeBezier(_, u) => {
         // We need to check the next control point to see whether we want quadratic or cubic Bezier.
         let cp1 = &keys[i + 1];
-        let nt = normalize_time(t, cp0, cp1);
+        let nt = t.normalize(cp0.t, cp1.t);
 
-        let value =
-          match cp1.interpolation {
-            Interpolation::Bezier(v) => {
-              Interpolate::cubic_bezier(cp0.value, u, cp1.value + cp1.value - v, cp1.value, nt)
-            }
+        let value = match cp1.interpolation {
+          Interpolation::Bezier(v) => V::cubic_bezier_mirrored(nt, cp0.value, u, v, cp1.value),
 
-            Interpolation::StrokeBezier(v, _) => {
-              Interpolate::cubic_bezier(cp0.value, u, v, cp1.value, nt)
-            }
+          Interpolation::StrokeBezier(v, _) => V::cubic_bezier(nt, cp0.value, u, v, cp1.value),
 
-            _ => Interpolate::quadratic_bezier(cp0.value, u, cp1.value, nt)
-          };
+          _ => V::quadratic_bezier(nt, cp0.value, u, cp1.value),
+        };
 
-        Some((value, cp0, Some(cp1)))
+        Some(value)
       }
+    };
 
-      Interpolation::__NonExhaustive => unreachable!(),
-    }
+    value.map(|value| SampledWithKey { value, key: i })
   }
 
   /// Sample a spline at a given time.
   ///
   pub fn sample(&self, t: T) -> Option<V>
-  where T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
-        V: Additive + Interpolate<T> {
-    self.sample_with_key(t).map(|(v, _, _)| v)
+  where
+    T: Interpolator,
+    V: Interpolate<T>,
+  {
+    self.sample_with_key(t).map(|sampled| sampled.value)
   }
 
   /// Sample a spline at a given time with clamping, returning the interpolated value along with its
@@ -178,23 +207,33 @@ impl<T, V> Spline<T, V> {
   /// # Error
   ///
   /// This function returns [`None`] if you have no key.
-  pub fn clamped_sample_with_key(&self, t: T) -> Option<(V, &Key<T, V>, Option<&Key<T, V>>)>
-  where T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
-        V: Additive + Interpolate<T> {
+  pub fn clamped_sample_with_key(&self, t: T) -> Option<SampledWithKey<V>>
+  where
+    T: Interpolator,
+    V: Interpolate<T>,
+  {
     if self.0.is_empty() {
       return None;
     }
 
     self.sample_with_key(t).or_else(move || {
       let first = self.0.first().unwrap();
+
       if t <= first.t {
-        let second = if self.0.len() >= 2 { Some(&self.0[1]) } else { None };
-        Some((first.value, &first, second))
+        let sampled = SampledWithKey {
+          value: first.value,
+          key: 0,
+        };
+        Some(sampled)
       } else {
         let last = self.0.last().unwrap();
 
         if t >= last.t {
-          Some((last.value, &last, None))
+          let sampled = SampledWithKey {
+            value: last.value,
+            key: self.0.len() - 1,
+          };
+          Some(sampled)
         } else {
           None
         }
@@ -204,13 +243,18 @@ impl<T, V> Spline<T, V> {
 
   /// Sample a spline at a given time with clamping.
   pub fn clamped_sample(&self, t: T) -> Option<V>
-  where T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
-        V: Additive + Interpolate<T> {
-    self.clamped_sample_with_key(t).map(|(v, _, _)| v)
+  where
+    T: Interpolator,
+    V: Interpolate<T>,
+  {
+    self.clamped_sample_with_key(t).map(|sampled| sampled.value)
   }
 
   /// Add a key into the spline.
-  pub fn add(&mut self, key: Key<T, V>) where T: PartialOrd {
+  pub fn add(&mut self, key: Key<T, V>)
+  where
+    T: PartialOrd,
+  {
     self.0.push(key);
     self.internal_sort();
   }
@@ -233,14 +277,10 @@ impl<T, V> Spline<T, V> {
   /// That function makes sense only if you want to change the interpolator (i.e. [`Key::t`]) of
   /// your key. If you just want to change the interpolation mode or the carried value, consider
   /// using the [`Spline::get_mut`] method instead as it will be way faster.
-  pub fn replace<F>(
-    &mut self,
-    index: usize,
-    f: F
-  ) -> Option<Key<T, V>>
+  pub fn replace<F>(&mut self, index: usize, f: F) -> Option<Key<T, V>>
   where
     F: FnOnce(&Key<T, V>) -> Key<T, V>,
-    T: PartialOrd
+    T: PartialOrd,
   {
     let key = self.remove(index)?;
     self.add(f(&key));
@@ -256,16 +296,27 @@ impl<T, V> Spline<T, V> {
   pub fn get_mut(&mut self, index: usize) -> Option<KeyMut<T, V>> {
     self.0.get_mut(index).map(|key| KeyMut {
       value: &mut key.value,
-      interpolation: &mut key.interpolation
+      interpolation: &mut key.interpolation,
     })
   }
 }
 
+/// A sampled value along with its key index.
+#[derive(Clone, Debug, Eq, Hash, PartialEq)]
+pub struct SampledWithKey<V> {
+  /// Sampled value.
+  pub value: V,
+
+  /// Key index.
+  pub key: usize,
+}
+
 /// A mutable [`Key`].
 ///
 /// Mutable keys allow to edit the carried values and the interpolation mode but not the actual
 /// interpolator value as it would invalidate the internal structure of the [`Spline`]. If you
 /// want to achieve this, you’re advised to use [`Spline::replace`].
+#[derive(Debug)]
 pub struct KeyMut<'a, T, V> {
   /// Carried value.
   pub value: &'a mut V,
@@ -273,46 +324,21 @@ pub struct KeyMut<'a, T, V> {
   pub interpolation: &'a mut Interpolation<T, V>,
 }
 
-// Normalize a time ([0;1]) given two control points.
-#[inline(always)]
-pub(crate) fn normalize_time<T, V>(
-  t: T,
-  cp: &Key<T, V>,
-  cp1: &Key<T, V>
-) -> T where T: Additive + Div<T, Output = T> + PartialEq {
-  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, V>(cps: &[Key<T, V>], t: T) -> Option<usize> where T: PartialOrd {
-  let mut i = 0;
+// It has the property to have a timestamp smaller or equal to t
+fn search_lower_cp<T, V>(cps: &[Key<T, V>], t: T) -> Option<usize>
+where
+  T: PartialOrd,
+{
   let len = cps.len();
-
   if len < 2 {
     return None;
   }
-
-  loop {
-    let cp = &cps[i];
-    let cp1 = &cps[i+1];
-
-    if t >= cp1.t {
-      if i >= len - 2 {
-        return None;
-      }
-
-      i += 1;
-    } else if t < cp.t {
-      if i == 0 {
-        return None;
-      }
-
-      i -= 1;
-    } else {
-      break; // found
-    }
+  match cps.binary_search_by(|key| key.t.partial_cmp(&t).unwrap()) {
+    Err(i) if i >= len => None,
+    Err(i) if i == 0 => None,
+    Err(i) => Some(i - 1),
+    Ok(i) if i == len - 1 => None,
+    Ok(i) => Some(i),
   }
-
-  Some(i)
 }

tests/cgmath.rs

@@ -0,0 +1,43 @@
+#![cfg(feature = "cgmath")]
+
+use cgmath as cg;
+use splines::{Interpolation, Key, Spline};
+
+#[test]
+fn cgmath_vector_interpolation() {
+  use splines::Interpolate;
+
+  let start = cg::Vector2::new(0.0, 0.0);
+  let mid = cg::Vector2::new(0.5, 0.5);
+  let end = cg::Vector2::new(1.0, 1.0);
+
+  assert_eq!(Interpolate::lerp(0., start, end), start);
+  assert_eq!(Interpolate::lerp(1., start, end), end);
+  assert_eq!(Interpolate::lerp(0.5, start, end), mid);
+}
+
+#[test]
+fn stroke_bezier_straight() {
+  use float_cmp::approx_eq;
+
+  let keys = vec![
+    Key::new(
+      0.0,
+      cg::Vector2::new(0., 1.),
+      Interpolation::StrokeBezier(cg::Vector2::new(0., 1.), cg::Vector2::new(0., 1.)),
+    ),
+    Key::new(
+      5.0,
+      cg::Vector2::new(5., 1.),
+      Interpolation::StrokeBezier(cg::Vector2::new(5., 1.), cg::Vector2::new(5., 1.)),
+    ),
+  ];
+  let spline = Spline::from_vec(keys);
+
+  assert!(approx_eq!(f32, spline.clamped_sample(0.0).unwrap().y, 1.));
+  assert!(approx_eq!(f32, spline.clamped_sample(1.0).unwrap().y, 1.));
+  assert!(approx_eq!(f32, spline.clamped_sample(2.0).unwrap().y, 1.));
+  assert!(approx_eq!(f32, spline.clamped_sample(3.0).unwrap().y, 1.));
+  assert!(approx_eq!(f32, spline.clamped_sample(4.0).unwrap().y, 1.));
+  assert!(approx_eq!(f32, spline.clamped_sample(5.0).unwrap().y, 1.));
+}

tests/integ.rs

@@ -1,8 +1,4 @@
-use float_cmp::approx_eq;
-use splines::{Interpolation, Key, Spline};
-
-#[cfg(feature = "cgmath")] use cgmath as cg;
-#[cfg(feature = "nalgebra")] use nalgebra as na;
+use splines::{spline::SampledWithKey, Interpolation, Key, Spline};
 
 #[test]
 fn step_interpolation_f32() {
@@ -17,8 +13,14 @@ fn step_interpolation_f32() {
   assert_eq!(spline.sample(0.9), Some(10.));
   assert_eq!(spline.sample(1.), None);
   assert_eq!(spline.clamped_sample(1.), Some(10.));
-  assert_eq!(spline.sample_with_key(0.2), Some((10., &start, Some(&end))));
-  assert_eq!(spline.clamped_sample_with_key(1.), Some((10., &end, None)));
+  assert_eq!(
+    spline.sample_with_key(0.2),
+    Some(SampledWithKey { value: 10., key: 0 })
+  );
+  assert_eq!(
+    spline.clamped_sample_with_key(1.),
+    Some(SampledWithKey { value: 10., key: 1 })
+  );
 }
 
 #[test]
@@ -34,8 +36,14 @@ fn step_interpolation_f64() {
   assert_eq!(spline.sample(0.9), Some(10.));
   assert_eq!(spline.sample(1.), None);
   assert_eq!(spline.clamped_sample(1.), Some(10.));
-  assert_eq!(spline.sample_with_key(0.2), Some((10., &start, Some(&end))));
-  assert_eq!(spline.clamped_sample_with_key(1.), Some((10., &end, None)));
+  assert_eq!(
+    spline.sample_with_key(0.2),
+    Some(SampledWithKey { value: 10., key: 0 })
+  );
+  assert_eq!(
+    spline.clamped_sample_with_key(1.),
+    Some(SampledWithKey { value: 10., key: 1 })
+  );
 }
 
 #[test]
@@ -150,51 +158,6 @@ fn several_interpolations_several_keys() {
   assert_eq!(spline.clamped_sample(11.), Some(4.));
 }
 
-#[cfg(feature = "cgmath")]
-#[test]
-fn stroke_bezier_straight() {
-  let keys = vec![
-    Key::new(0.0, cg::Vector2::new(0., 1.), Interpolation::StrokeBezier(cg::Vector2::new(0., 1.), cg::Vector2::new(0., 1.))),
-    Key::new(5.0, cg::Vector2::new(5., 1.), Interpolation::StrokeBezier(cg::Vector2::new(5., 1.), cg::Vector2::new(5., 1.)))
-  ];
-  let spline = Spline::from_vec(keys);
-
-  assert!(approx_eq!(f32, spline.clamped_sample(0.0).unwrap().y, 1.));
-  assert!(approx_eq!(f32, spline.clamped_sample(1.0).unwrap().y, 1.));
-  assert!(approx_eq!(f32, spline.clamped_sample(2.0).unwrap().y, 1.));
-  assert!(approx_eq!(f32, spline.clamped_sample(3.0).unwrap().y, 1.));
-  assert!(approx_eq!(f32, spline.clamped_sample(4.0).unwrap().y, 1.));
-  assert!(approx_eq!(f32, spline.clamped_sample(5.0).unwrap().y, 1.));
-}
-
-#[cfg(feature = "cgmath")]
-#[test]
-fn cgmath_vector_interpolation() {
-  use splines::Interpolate;
-
-  let start = cg::Vector2::new(0.0, 0.0);
-  let mid = cg::Vector2::new(0.5, 0.5);
-  let end = cg::Vector2::new(1.0, 1.0);
-
-  assert_eq!(Interpolate::lerp(start, end, 0.0), start);
-  assert_eq!(Interpolate::lerp(start, end, 1.0), end);
-  assert_eq!(Interpolate::lerp(start, end, 0.5), mid);
-}
-
-#[cfg(feature = "nalgebra")]
-#[test]
-fn nalgebra_vector_interpolation() {
-  use splines::Interpolate;
-
-  let start = na::Vector2::new(0.0, 0.0);
-  let mid = na::Vector2::new(0.5, 0.5);
-  let end = na::Vector2::new(1.0, 1.0);
-
-  assert_eq!(Interpolate::lerp(start, end, 0.0), start);
-  assert_eq!(Interpolate::lerp(start, end, 1.0), end);
-  assert_eq!(Interpolate::lerp(start, end, 0.5), mid);
-}
-
 #[test]
 fn add_key_empty() {
   let mut spline: Spline<f32, f32> = Spline::from_vec(vec![]);

tests/nalgebra.rs

@@ -0,0 +1,16 @@
+#![cfg(feature = "nalgebra")]
+
+use nalgebra as na;
+
+#[test]
+fn nalgebra_vector_interpolation() {
+  use splines::Interpolate;
+
+  let start = na::Vector2::new(0.0, 0.0);
+  let mid = na::Vector2::new(0.5, 0.5);
+  let end = na::Vector2::new(1.0, 1.0);
+
+  assert_eq!(Interpolate::lerp(0., start, end), start);
+  assert_eq!(Interpolate::lerp(1., start, end), end);
+  assert_eq!(Interpolate::lerp(0.5, start, end), mid);
+}