.github/dependabot.yml

@@ -1,25 +0,0 @@
-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

@@ -1,38 +1,50 @@
 name: CI
-on: [push, pull_request]
+on: [push]
 
 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 test --verbose --all-features
+        run: |
+          . ~/.cargo/env
+          cargo test --verbose --all-features
 
-  quality:
+  check-readme:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v1
-      - name: Install dependencies
+      - name: Install cargo-sync-readme
-        run: |
+        run: cargo install --force cargo-sync-readme
-          cargo install --force cargo-sync-readme
+      - name: Check
-          rustup component add rustfmt
+        run: cargo sync-readme -c
-      - name: cargo sync-readme
-        run: |
-          cargo sync-readme -c
-      - name: rustfmt
-        run: cargo fmt -- --check

CHANGELOG.md

@@ -1,219 +1,4 @@
-# Changelog
+# 2.2.0
-
-* [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
-
-- Sampling now requires the value of the key to be `Linear<T>` for `Interpolate<T>`. That is needed
-  to ease some interpolation mode (especially Bézier).
-
-## Patch changes
-
-- Fix Bézier interpolation when the next key is Bézier too.
-
-# 2.2
 
 > Mon Oct 17th 2019
 
@@ -241,7 +26,7 @@
 - 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
+# 2.0.0
 
 > Mon Sep 23rd 2019
 

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "splines"
-version = "4.3.1"
+version = "2.2.0"
 license = "BSD-3-Clause"
 authors = ["Dimitri Sabadie <dimitri.sabadie@gmail.com>"]
 description = "Spline interpolation made easy"
@@ -11,32 +11,28 @@ repository = "https://github.com/phaazon/splines"
 documentation = "https://docs.rs/splines"
 readme = "README.md"
 
-edition = "2021"
+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" }
 
 [features]
 default = ["std"]
 impl-cgmath = ["cgmath"]
-impl-glam = ["glam"]
+impl-nalgebra = ["alga", "nalgebra", "num-traits"]
-impl-nalgebra = ["nalgebra"]
+serialization = ["serde", "serde_derive"]
-serialization = ["serde"]
+std = []
-std = ["nalgebra/std"]
 
 [dependencies]
-cgmath = { version = ">=0.17, <0.19", optional = true }
+alga = { version = "0.9", optional = true }
-glam = { version = ">=0.10, <0.25", optional = true }
+cgmath = { version = "0.17", optional = true }
-nalgebra = { version = ">=0.21, <0.33", default-features = false, optional = true }
+nalgebra = { version = ">=0.14, <0.19", optional = true }
-serde = { version = "1", features = ["derive"], optional = true }
+num-traits = { version = "0.2", optional = true }
-
+serde =  { version = "1", optional = true }
-[dev-dependencies]
+serde_derive = { version = "1", optional = true }
-float-cmp = ">=0.6, < 0.10"
-serde_json = "1"
 
 [package.metadata.docs.rs]
-features = ["std", "cgmath", "glam", "nalgebra", "serde"]
+all-features = true
-
-[[example]]
-name = "hello-world"
-
-[[example]]
-name = "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](https://docs.rs/splines/latest/splines/interpolate/) for further details.
+implement. See [the documentation of this module](crate::interpolate) for further details.
 
 # Features and customization
 
@@ -83,19 +83,16 @@ 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:
 
-  - **Serde.**
+  - **Serialization / deserialization.**
     - This feature implements both the `Serialize` and `Deserialize` traits from `serde` for all
       types exported by this crate.
-    - Enable with the `"serde"` feature.
+    - Enable with the `"serialization"` feature.
   - **[cgmath](https://crates.io/crates/cgmath) implementors.**
     - Adds some useful implementations of `Interpolate` for some cgmath types.
-    - Enable with the `"cgmath"` feature.
+    - Enable with the `"impl-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 `"nalgebra"` feature.
+    - Enable with the `"impl-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/01-hello-world/Cargo.toml

@@ -0,0 +1,7 @@
+[package]
+name = "hello-world"
+version = "0.2.0"
+authors = ["Dimitri Sabadie <dimitri.sabadie@gmail.com>"]
+
+[dependencies]
+splines = "1.0.0-rc.2"

examples/01-hello-world/src/main.rs

@@ -3,10 +3,7 @@ extern crate splines;
 use splines::{Interpolation, Key, Spline};
 
 fn main() {
-  let keys = vec![
+  let keys = vec![Key::new(0., 0., Interpolation::default()), Key::new(5., 1., Interpolation::default())];
-    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/02-serialization/Cargo.toml

@@ -0,0 +1,8 @@
+[package]
+name = "serialization"
+version = "0.2.0"
+authors = ["Dimitri Sabadie <dimitri.sabadie@gmail.com>"]
+
+[dependencies]
+serde_json = "1"
+splines =  { version = "1.0.0-rc.2", features = ["serialization"] }

examples/02-serialization/src/main.rs

@@ -1,12 +1,11 @@
-#[macro_use]
+#[macro_use] extern crate serde_json;
-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,

examples/Cargo.toml

@@ -0,0 +1,9 @@
+[workspace]
+
+members = [
+  "01-hello-world",
+  "02-serialization"
+]
+
+[patch.crates-io]
+splines = { path = ".." }

rustfmt.toml

@@ -1,15 +0,0 @@
-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

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

src/glam.rs

@@ -1,8 +0,0 @@
-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

@@ -28,220 +28,270 @@
 //! [`Trigo`]: crate::interpolate::Trigo
 //! [num-traits]: https://crates.io/crates/num-traits
 
-#[cfg(not(feature = "std"))]
+#[cfg(feature = "std")] use std::f32;
-use core::f32;
+#[cfg(not(feature = "std"))] use core::f32;
-#[cfg(not(feature = "std"))]
+#[cfg(not(feature = "std"))] use core::intrinsics::cosf32;
-use core::f64;
+#[cfg(feature = "std")] use std::f64;
-#[cfg(not(feature = "std"))]
+#[cfg(not(feature = "std"))] use core::f64;
-use core::intrinsics::cosf32;
+#[cfg(not(feature = "std"))] use core::intrinsics::cosf64;
-#[cfg(not(feature = "std"))]
+#[cfg(feature = "std")] use std::ops::{Add, Mul, Sub};
-use core::intrinsics::cosf64;
+#[cfg(not(feature = "std"))] use core::ops::{Add, Mul, Sub};
-#[cfg(not(feature = "std"))]
-use core::ops::{Add, Mul, Sub};
-#[cfg(feature = "std")]
-use std::f32;
-#[cfg(feature = "std")]
-use std::f64;
 
-/// Types that can be used as interpolator in splines.
+/// Keys that can be interpolated in between. Implementing this trait is required to perform
+/// sampling on splines.
 ///
-/// An interpolator value is like the fabric on which control keys (and sampled values) live on.
+/// `T` is the variable used to sample with. Typical implementations use [`f32`] or [`f64`], but
-pub trait Interpolator: Sized + Copy + PartialOrd {
+/// you’re free to use the ones you like. Feel free to have a look at [`Spline::sample`] for
-  /// Normalize the interpolator.
+/// instance to know which trait your type must implement to be usable.
-  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.
 ///
-/// `T` is the interpolator used to sample with. Typical implementations use [`f32`] or [`f64`], but
+/// [`Spline::sample`]: crate::spline::Spline::sample
-/// 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(t: T, a: Self, b: Self) -> Self;
+  fn lerp(a: Self, b: Self, t: T) -> Self;
-
-  /// Cosine interpolation.
-  fn cosine(t: T, a: Self, b: Self) -> Self;
 
   /// Cubic hermite interpolation.
-  fn cubic_hermite(t: T, x: (T, Self), a: (T, Self), b: (T, Self), y: (T, Self)) -> Self;
+  ///
+  /// 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)
+  }
 
   /// 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;
 }
 
-#[macro_export]
+/// Set of types that support additions and subtraction.
-macro_rules! impl_Interpolate {
+///
-  ($t:ty, $v:ty, $pi:expr) => {
+/// The [`Copy`] trait is also a supertrait as it’s likely to be used everywhere.
-    impl $crate::interpolate::Interpolate<$t> for $v {
+pub trait Additive:
-      fn step(t: $t, threshold: $t, a: Self, b: Self) -> Self {
+  Copy +
-        if t < threshold {
+  Add<Self, Output = Self> +
-          a
+  Sub<Self, Output = Self> {
-        } else {
+}
-          b
+
-        }
+impl<T> Additive for T
+where T: Copy +
+         Add<Self, Output = Self> +
+         Sub<Self, Output = Self> {
+}
+
+/// Set of additive types that support outer multiplication and division, making them linear.
+pub trait Linear<T>: Additive {
+  /// Apply an outer multiplication law.
+  fn outer_mul(self, t: T) -> Self;
+
+  /// Apply an outer division law.
+  fn outer_div(self, t: T) -> Self;
+}
+
+macro_rules! impl_linear_simple {
+  ($t:ty) => {
+    impl Linear<$t> for $t {
+      fn outer_mul(self, t: $t) -> Self {
+        self * t
       }
 
-      #[cfg(feature = "std")]
+      /// Apply an outer division law.
-      fn cosine(t: $t, a: Self, b: Self) -> Self {
+      fn outer_div(self, t: $t) -> Self {
-        let cos_nt = (1. - (t * $pi).cos()) * 0.5;
+        self / t
-        <Self as $crate::interpolate::Interpolate<$t>>::lerp(cos_nt, a, b)
       }
-      #[cfg(not(feature = "std"))]
+    }
-      fn cosine(t: $t, a: Self, b: Self) -> Self {
+  }
-        unimplemented!();
+}
+
+impl_linear_simple!(f32);
+impl_linear_simple!(f64);
+
+macro_rules! impl_linear_cast {
+  ($t:ty, $q:ty) => {
+    impl Linear<$t> for $q {
+      fn outer_mul(self, t: $t) -> Self {
+        self * t as $q
       }
 
-      fn lerp(t: $t, a: Self, b: Self) -> Self {
+      /// 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();
+
+  // mirror the “output” tangent based on the next key “input” tangent
+  let v_ = b + b - v;
+
+  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 {
         a * (1. - t) + b * t
       }
 
-      fn cubic_hermite(t: $t, x: ($t, Self), a: ($t, Self), b: ($t, Self), y: ($t, Self)) -> Self {
+      fn cubic_hermite(x: (Self, $t), a: (Self, $t), b: (Self, $t), y: (Self, $t), t: $t) -> Self {
-        // sampler stuff
+        cubic_hermite_def(x, a, b, y, 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) / (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(t: $t, a: Self, u: Self, b: Self) -> Self {
+      fn quadratic_bezier(a: Self, u: Self, b: Self, t: $t) -> Self {
-        let one_t = 1. - t;
+        quadratic_bezier_def(a, u, b, 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 {
+      fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: $t) -> Self {
-        let one_t = 1. - t;
+        cubic_bezier_def(a, u, v, b, 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)
       }
     }
-  };
+  }
 }
 
-#[macro_export]
+impl_interpolate_simple!(f32);
-macro_rules! impl_InterpolateT {
+impl_interpolate_simple!(f64);
-  ($t:ty, $v:ty, $pi:expr) => {
+
-    impl $crate::interpolate::Interpolate<$t> for $v {
+macro_rules! impl_interpolate_via {
-      fn step(t: $t, threshold: $t, a: Self, b: Self) -> Self {
+  ($t:ty, $v:ty) => {
-        if t < threshold {
+    impl Interpolate<$t> for $v {
-          a
+      fn lerp(a: Self, b: Self, t: $t) -> Self {
-        } else {
+        a * (1. - t as $v) + b * t as $v
-          b
-        }
       }
 
-      #[cfg(feature = "std")]
+      fn cubic_hermite((x, xt): (Self, $t), (a, at): (Self, $t), (b, bt): (Self, $t), (y, yt): (Self, $t), t: $t) -> Self {
-      fn cosine(t: $t, a: Self, b: Self) -> Self {
+        cubic_hermite_def((x, xt as $v), (a, at as $v), (b, bt as $v), (y, yt as $v), t as $v)
-        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 lerp(t: $t, a: Self, b: Self) -> Self {
+      fn quadratic_bezier(a: Self, u: Self, b: Self, t: $t) -> Self {
-        let t = Self::from(t);
+        quadratic_bezier_def(a, u, b, t as $v)
-        a * (1. - t) + b * t
       }
 
-      fn cubic_hermite(t: $t, x: ($t, Self), a: ($t, Self), b: ($t, Self), y: ($t, Self)) -> Self {
+      fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: $t) -> Self {
-        // sampler stuff
+        cubic_bezier_def(a, u, v, b, t as $v)
-        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!(f32, f32, f32::consts::PI);
+impl_interpolate_via!(f32, f64);
-impl_Interpolate!(f64, f64, f64::consts::PI);
+impl_interpolate_via!(f64, f32);
-impl_InterpolateT!(f32, f64, f32::consts::PI);

src/interpolation.rs

@@ -1,18 +1,13 @@
 //! Available interpolation modes.
 
-#[cfg(any(feature = "serialization", feature = "serde"))]
+#[cfg(feature = "serialization")] use serde_derive::{Deserialize, Serialize};
-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(
+#[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
-  any(feature = "serialization", feature = "serde"),
+#[cfg_attr(feature = "serialization", serde(rename_all = "snake_case"))]
-  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.
@@ -24,16 +19,12 @@ 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
@@ -49,7 +40,6 @@ 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
@@ -62,6 +52,8 @@ 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

@@ -11,13 +11,9 @@ use crate::{Key, Spline};
 /// Iterator over spline keys.
 ///
 /// This iterator type is guaranteed to iterate over sorted keys.
-pub struct Iter<'a, T, V>
+pub struct Iter<'a, T, V> where T: 'a, V: 'a {
-where
-  T: 'a,
-  V: 'a,
-{
   spline: &'a Spline<T, V>,
-  i: usize,
+  i: usize
 }
 
 impl<'a, T, V> Iterator for Iter<'a, T, V> {
@@ -39,6 +35,10 @@ 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 carried value that can be
+//! A control point associates to a “sampling value” (a.k.a. time) a carriede 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.
 ///
@@ -18,27 +18,20 @@ use serde::{Deserialize, Serialize};
 ///
 /// [`Interpolation`]: crate::interpolation::Interpolation
 #[derive(Copy, Clone, Debug, Eq, PartialEq)]
-#[cfg_attr(
+#[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
-  any(feature = "serialization", feature = "serde"),
+#[cfg_attr(feature = "serialization", serde(rename_all = "snake_case"))]
-  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 {
+    Key { t, value, interpolation }
-      t,
-      value,
-      interpolation,
-    }
   }
 }

src/lib.rs

@@ -84,19 +84,16 @@
 //!
 //! So here’s a list of currently supported features and how to enable them:
 //!
-//!   - **Serde.**
+//!   - **Serialization / deserialization.**
 //!     - This feature implements both the `Serialize` and `Deserialize` traits from `serde` for all
 //!       types exported by this crate.
-//!     - Enable with the `"serde"` feature.
+//!     - Enable with the `"serialization"` feature.
 //!   - **[cgmath](https://crates.io/crates/cgmath) implementors.**
 //!     - Adds some useful implementations of `Interpolate` for some cgmath types.
-//!     - Enable with the `"cgmath"` feature.
+//!     - Enable with the `"impl-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 `"nalgebra"` feature.
+//!     - Enable with the `"impl-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.
@@ -108,31 +105,15 @@
 #![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"))]
+#[cfg(not(feature = "std"))] extern crate alloc;
-extern crate alloc;
 
-#[cfg(any(feature = "impl-cgmath", feature = "cgmath"))]
+#[cfg(feature = "impl-cgmath")] mod 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(any(feature = "impl-nalgebra", feature = "nalgebra"))]
+#[cfg(feature = "impl-nalgebra")] mod nalgebra;
-mod nalgebra;
 pub mod spline;
 
 pub use crate::interpolate::Interpolate;

src/nalgebra.rs

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

src/spline.rs

@@ -1,19 +1,15 @@
 //! Spline curves and operations.
 
-// #[cfg(feature = "std")]
+#[cfg(feature = "serialization")] use serde_derive::{Deserialize, Serialize};
-use crate::interpolate::{Interpolate, Interpolator};
+#[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::{Interpolate, Additive, One, Trigo};
 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).
 ///
@@ -27,42 +23,24 @@ use std::cmp::Ordering;
 ///     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, Default)]
+#[derive(Debug, Clone)]
-#[cfg_attr(
+#[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
-  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)
+  fn internal_sort(&mut self) where T: PartialOrd {
-  where
+    self.0.sort_by(|k0, k1| k0.t.partial_cmp(&k1.t).unwrap_or(Ordering::Less));
-    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
+  pub fn from_vec(keys: Vec<Key<T, V>>) -> Self where T: PartialOrd {
-  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.
   ///
@@ -70,11 +48,7 @@ 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
+  pub fn from_iter<I>(iter: I) -> Self where I: Iterator<Item = Key<T, V>>, T: PartialOrd {
-  where
-    I: Iterator<Item = Key<T, V>>,
-    T: PartialOrd,
-  {
     Self::from_vec(iter.collect())
   }
 
@@ -110,38 +84,38 @@ 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<SampledWithKey<V>>
+  pub fn sample_with_key(&self, t: T) -> Option<(V, &Key<T, V>, Option<&Key<T, V>>)>
-  where
+  where T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
-    T: Interpolator,
+        V: Interpolate<T> {
-    V: Interpolate<T>,
-  {
     let keys = &self.0;
     let i = search_lower_cp(keys, t)?;
     let cp0 = &keys[i];
 
-    let value = match cp0.interpolation {
+    match cp0.interpolation {
       Interpolation::Step(threshold) => {
         let cp1 = &keys[i + 1];
-        let nt = t.normalize(cp0.t, cp1.t);
+        let nt = normalize_time(t, cp0, cp1);
-        let value = V::step(nt, threshold, cp0.value, cp1.value);
+        let value = if nt < threshold { cp0.value } else { cp1.value };
 
-        Some(value)
+        Some((value, cp0, Some(cp1)))
       }
 
       Interpolation::Linear => {
         let cp1 = &keys[i + 1];
-        let nt = t.normalize(cp0.t, cp1.t);
+        let nt = normalize_time(t, cp0, cp1);
-        let value = V::lerp(nt, cp0.value, cp1.value);
+        let value = Interpolate::lerp(cp0.value, cp1.value, nt);
 
-        Some(value)
+        Some((value, cp0, Some(cp1)))
       }
 
       Interpolation::Cosine => {
+        let two_t = T::one() + T::one();
         let cp1 = &keys[i + 1];
-        let nt = t.normalize(cp0.t, cp1.t);
+        let nt = normalize_time(t, cp0, cp1);
-        let value = V::cosine(nt, cp0.value, cp1.value);
+        let cos_nt = (T::one() - (nt * T::pi()).cos()) / two_t;
+        let value = Interpolate::lerp(cp0.value, cp1.value, cos_nt);
 
-        Some(value)
+        Some((value, cp0, Some(cp1)))
       }
 
       Interpolation::CatmullRom => {
@@ -153,47 +127,46 @@ impl<T, V> Spline<T, V> {
           let cp1 = &keys[i + 1];
           let cpm0 = &keys[i - 1];
           let cpm1 = &keys[i + 2];
-          let nt = t.normalize(cp0.t, cp1.t);
+          let nt = normalize_time(t, cp0, cp1);
-          let value = V::cubic_hermite(
+          let value = Interpolate::cubic_hermite((cpm0.value, cpm0.t), (cp0.value, cp0.t), (cp1.value, cp1.t), (cpm1.value, cpm1.t), nt);
-            nt,
-            (cpm0.t, cpm0.value),
-            (cp0.t, cp0.value),
-            (cp1.t, cp1.value),
-            (cpm1.t, cpm1.value),
-          );
 
-          Some(value)
+          Some((value, cp0, Some(cp1)))
         }
       }
 
-      Interpolation::Bezier(u) | Interpolation::StrokeBezier(_, u) => {
+      Interpolation::Bezier(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 = t.normalize(cp0.t, cp1.t);
+        let nt = normalize_time(t, cp0, cp1);
 
-        let value = match cp1.interpolation {
+        let value =
-          Interpolation::Bezier(v) => V::cubic_bezier_mirrored(nt, cp0.value, u, v, cp1.value),
+          if let Interpolation::Bezier(v) = cp1.interpolation {
+            Interpolate::cubic_bezier(cp0.value, u, v, cp1.value, nt)
+          } else {
+            Interpolate::quadratic_bezier(cp0.value, u, cp1.value, nt)
+          };
 
-          Interpolation::StrokeBezier(v, _) => V::cubic_bezier(nt, cp0.value, u, v, cp1.value),
+        Some((value, cp0, Some(cp1)))
-
-          _ => V::quadratic_bezier(nt, cp0.value, u, cp1.value),
-        };
-
-        Some(value)
       }
-    };
 
-    value.map(|value| SampledWithKey { value, key: i })
+      Interpolation::StrokeBezier(input, output) => {
+        let cp1 = &keys[i + 1];
+        let nt = normalize_time(t, cp0, cp1);
+        let value = Interpolate::cubic_bezier(cp0.value, input, output, cp1.value, nt);
+
+        Some((value, cp0, Some(cp1)))
+      }
+
+      Interpolation::__NonExhaustive => unreachable!(),
+    }
   }
 
   /// Sample a spline at a given time.
   ///
   pub fn sample(&self, t: T) -> Option<V>
-  where
+  where T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
-    T: Interpolator,
+        V: Interpolate<T> {
-    V: Interpolate<T>,
+    self.sample_with_key(t).map(|(v, _, _)| v)
-  {
-    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
@@ -207,33 +180,23 @@ 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<SampledWithKey<V>>
+  pub fn clamped_sample_with_key(&self, t: T) -> Option<(V, &Key<T, V>, Option<&Key<T, V>>)>
-  where
+  where T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
-    T: Interpolator,
+        V: Interpolate<T> {
-    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 sampled = SampledWithKey {
+        let second = if self.0.len() >= 2 { Some(&self.0[1]) } else { None };
-          value: first.value,
+        Some((first.value, &first, second))
-          key: 0,
-        };
-        Some(sampled)
       } else {
         let last = self.0.last().unwrap();
 
         if t >= last.t {
-          let sampled = SampledWithKey {
+          Some((last.value, &last, None))
-            value: last.value,
-            key: self.0.len() - 1,
-          };
-          Some(sampled)
         } else {
           None
         }
@@ -243,18 +206,13 @@ 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
+  where T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
-    T: Interpolator,
+        V: Interpolate<T> {
-    V: Interpolate<T>,
+    self.clamped_sample_with_key(t).map(|(v, _, _)| v)
-  {
-    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>)
+  pub fn add(&mut self, key: Key<T, V>) where T: PartialOrd {
-  where
-    T: PartialOrd,
-  {
     self.0.push(key);
     self.internal_sort();
   }
@@ -277,10 +235,14 @@ 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));
@@ -296,27 +258,16 @@ 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,
@@ -324,21 +275,46 @@ 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.
-// 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 {
-fn search_lower_cp<T, V>(cps: &[Key<T, V>], t: T) -> Option<usize>
+  let mut i = 0;
-where
-  T: PartialOrd,
-{
   let len = cps.len();
+
   if len < 2 {
     return None;
   }
-  match cps.binary_search_by(|key| key.t.partial_cmp(&t).unwrap()) {
+
-    Err(i) if i >= len => None,
+  loop {
-    Err(i) if i == 0 => None,
+    let cp = &cps[i];
-    Err(i) => Some(i - 1),
+    let cp1 = &cps[i+1];
-    Ok(i) if i == len - 1 => None,
+
-    Ok(i) => Some(i),
+    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
+    }
   }
+
+  Some(i)
 }

tests/cgmath.rs

@@ -1,43 +0,0 @@
-#![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/mod.rs

@@ -1,4 +1,7 @@
-use splines::{spline::SampledWithKey, Interpolation, Key, Spline};
+use splines::{Interpolation, Key, Spline};
+
+#[cfg(feature = "impl-cgmath")] use cgmath as cg;
+#[cfg(feature = "impl-nalgebra")] use nalgebra as na;
 
 #[test]
 fn step_interpolation_f32() {
@@ -13,14 +16,8 @@ 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!(
+  assert_eq!(spline.sample_with_key(0.2), Some((10., &start, Some(&end))));
-    spline.sample_with_key(0.2),
+  assert_eq!(spline.clamped_sample_with_key(1.), Some((10., &end, None)));
-    Some(SampledWithKey { value: 10., key: 0 })
-  );
-  assert_eq!(
-    spline.clamped_sample_with_key(1.),
-    Some(SampledWithKey { value: 10., key: 1 })
-  );
 }
 
 #[test]
@@ -36,14 +33,8 @@ 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!(
+  assert_eq!(spline.sample_with_key(0.2), Some((10., &start, Some(&end))));
-    spline.sample_with_key(0.2),
+  assert_eq!(spline.clamped_sample_with_key(1.), Some((10., &end, None)));
-    Some(SampledWithKey { value: 10., key: 0 })
-  );
-  assert_eq!(
-    spline.clamped_sample_with_key(1.),
-    Some(SampledWithKey { value: 10., key: 1 })
-  );
 }
 
 #[test]
@@ -158,6 +149,34 @@ fn several_interpolations_several_keys() {
   assert_eq!(spline.clamped_sample(11.), Some(4.));
 }
 
+#[cfg(feature = "impl-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 = "impl-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

@@ -1,16 +0,0 @@
-#![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);
-}