Prepare 3.3.0.

bump nalgebra

.dependabot/config.yml

@@ -0,0 +1,12 @@
+version: 1
+update_configs:
+  - package_manager: "rust:cargo"
+    directory: "."
+    update_schedule: "live"
+    target_branch: "master"
+    default_reviewers:
+      - "phaazon"
+    default_assignees:
+      - "phaazon"
+    default_labels:
+      - "dependency-update"

.github/workflows/ci.yaml

@@ -1,5 +1,5 @@
 name: CI
-on: [push]
+on: [push, pull_request]
 
 jobs:
   build-linux:
@@ -8,12 +8,10 @@ jobs:
       - uses: actions/checkout@v1
       - name: Build
         run: |
-          cargo build --verbose
+          cargo build --verbose --all-features
-          cargo build --verbose --features bezier
       - name: Test
         run: |
-          cargo test --verbose
+          cargo test --verbose --all-features
-          cargo test --verbose --features bezier
 
   build-windows:
     runs-on: windows-latest
@@ -21,31 +19,36 @@ jobs:
       - uses: actions/checkout@v1
       - name: Build
         run: |
-          cargo build --verbose
+          cargo build --verbose --all-features
-          cargo build --verbose --features bezier
       - name: Test
         run: |
-          cargo test --verbose
+          cargo test --verbose --all-features
-          cargo test --verbose --features bezier
 
   build-macosx:
-    runs-on: macosx-latest
+    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 build --verbose
+          . ~/.cargo/env
-          cargo build --verbose --features bezier
+          cargo build --verbose --all-features
       - name: Test
         run: |
-          cargo test --verbose
+          . ~/.cargo/env
-          cargo test --verbose --features bezier
+          cargo test --verbose --all-features
 
-  check-readme:
+  quality:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v1
-      - name: Install cargo-sync-readme
+      - name: Install dependencies
-        run: cargo install --force cargo-sync-readme
+        run: |
-      - name: Check
+          cargo install --force cargo-sync-readme
-        run: cargo sync-readme -c
+          rustup component add rustfmt
+      - name: cargo sync-readme
+        run: |
+          cargo sync-readme -c
+      - name: rustfmt
+        run: cargo fmt -- --check

CHANGELOG.md

@@ -1,6 +1,80 @@
+# 3.3
+
+> Thu Apr 0th 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
+
+- Add `Interpolation::StrokeBezier`.
+
+# 2.1.1
+
+> Mon Oct 17th 2019
+
+- Licensing support in the crate.
+
+# 2.1
+
+> Mon Sep 30th 2019
+
+- Add `Spline::sample_with_key` and `Spline::clamped_sample_with_key`. Those methods allow one to
+  perform the regular `Spline::sample` and `Spline::clamped_sample` but also retreive the base
+  key that was used to perform the interpolation. The key can be inspected to get the base time,
+  interpolation, etc. The next key is also returned, if present.
+
+# 2.0.1
+
+> Tue Sep 24th 2019
+
+- 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
+
+> Mon Sep 23rd 2019
+
+## Major changes
+
+- Add support for [Bézier curves](https://en.wikipedia.org/wiki/B%C3%A9zier_curve).
+- Because of Bézier curves, the `Interpolation` type now has one more type variable to know how we
+  should interpolate with Bézier.
+
+## Minor changes
+
+- Add `Spline::get`, `Spline::get_mut` and `Spline::replace`.
+
 # 1.0
 
-> Sun Sep 22th 2019
+> Sun Sep 22nd 2019
 
 ## Major changes
 

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "splines"
-version = "1.1.0"
+version = "3.3.0"
 license = "BSD-3-Clause"
 authors = ["Dimitri Sabadie <dimitri.sabadie@gmail.com>"]
 description = "Spline interpolation made easy"
@@ -21,19 +21,29 @@ maintenance = { status = "actively-developed" }
 
 [features]
 default = ["std"]
-bezier = []
 impl-cgmath = ["cgmath"]
-impl-nalgebra = ["alga", "nalgebra", "num-traits"]
+impl-nalgebra = ["nalgebra", "num-traits", "simba"]
 serialization = ["serde", "serde_derive"]
 std = []
 
 [dependencies]
-alga = { version = "0.9", optional = true }
 cgmath = { version = "0.17", optional = true }
-nalgebra = { version = ">=0.14, <0.19", optional = true }
+nalgebra = { version = "0.21", optional = true }
 num-traits = { version = "0.2", optional = true }
 serde =  { version = "1", optional = true }
 serde_derive = { version = "1", optional = true }
+simba = { version = "0.1.2", optional = true }
+
+[dev-dependencies]
+float-cmp = "0.6"
+serde_json = "1"
 
 [package.metadata.docs.rs]
 all-features = true
+
+[[example]]
+name = "hello-world"
+
+[[example]]
+name = "serialization"
+required-features = ["serialization"]

LICENSE

@@ -0,0 +1,30 @@
+Copyright (c) 2019, Dimitri Sabadie <dimitri.sabadie@gmail.com>
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+    * Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+
+    * Redistributions in binary form must reproduce the above
+      copyright notice, this list of conditions and the following
+      disclaimer in the documentation and/or other materials provided
+      with the distribution.
+
+    * Neither the name of Dimitri Sabadie <dimitri.sabadie@gmail.com> nor the names of other
+      contributors may be used to endorse or promote products derived
+      from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

README.md

@@ -98,12 +98,6 @@ So here’s a list of currently supported features and how to enable them:
     - Compiling with the standard library is enabled by default.
     - Use `default-features = []` in your `Cargo.toml` to disable.
     - Enable explicitly with the `"std"` feature.
-  - **Extra interpolation modes.**
-    - In order not to introduce breaking changes, some feature-gates are added to augment the
-      [`Interpolation`] enum.
-    - Those feature-gates will disappear on the next major release of the crate.
-    - The following lists all currently available:
-      - `"bezier"`: [Bézier curves](https://en.wikipedia.org/wiki/B%C3%A9zier_curve).
 
 [`Interpolation`]: crate::interpolation::Interpolation
 

examples/01-hello-world/Cargo.toml

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

examples/02-serialization/Cargo.toml

@@ -1,8 +0,0 @@
-[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/Cargo.toml

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

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_args_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

@@ -1,8 +1,10 @@
 use cgmath::{
-  BaseFloat, BaseNum, InnerSpace, Quaternion, Vector1, Vector2, Vector3, Vector4, VectorSpace
+  BaseFloat, BaseNum, InnerSpace, Quaternion, Vector1, Vector2, Vector3, Vector4, VectorSpace,
 };
 
-use crate::interpolate::{Additive, Interpolate, Linear, One, cubic_hermite_def};
+use crate::interpolate::{
+  cubic_bezier_def, cubic_hermite_def, quadratic_bezier_def, Additive, Interpolate, Linear, One,
+};
 
 macro_rules! impl_interpolate_vec {
   ($($t:tt)*) => {
@@ -29,6 +31,16 @@ macro_rules! impl_interpolate_vec {
       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)
+      }
     }
   }
 }
@@ -38,7 +50,10 @@ impl_interpolate_vec!(Vector2);
 impl_interpolate_vec!(Vector3);
 impl_interpolate_vec!(Vector4);
 
-impl<T> Linear<T> for Quaternion<T> where T: BaseFloat {
+impl<T> Linear<T> for Quaternion<T>
+where
+  T: BaseFloat,
+{
   #[inline(always)]
   fn outer_mul(self, t: T) -> Self {
     self * t
@@ -51,7 +66,10 @@ impl<T> Linear<T> for Quaternion<T> where T: BaseFloat {
 }
 
 impl<T> Interpolate<T> for Quaternion<T>
-where Self: InnerSpace<Scalar = T>, T: Additive + BaseFloat + One {
+where
+  Self: InnerSpace<Scalar = T>,
+  T: Additive + BaseFloat + One,
+{
   #[inline(always)]
   fn lerp(a: Self, b: Self, t: T) -> Self {
     a.nlerp(b, t)
@@ -61,4 +79,14 @@ where Self: InnerSpace<Scalar = T>, T: Additive + BaseFloat + One {
   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/interpolate.rs

@@ -28,14 +28,22 @@
 //! [`Trigo`]: crate::interpolate::Trigo
 //! [num-traits]: https://crates.io/crates/num-traits
 
-#[cfg(feature = "std")] use std::f32;
+#[cfg(not(feature = "std"))]
-#[cfg(not(feature = "std"))] use core::f32;
+use core::f32;
-#[cfg(not(feature = "std"))] use core::intrinsics::cosf32;
+#[cfg(not(feature = "std"))]
-#[cfg(feature = "std")] use std::f64;
+use core::f64;
-#[cfg(not(feature = "std"))] use core::f64;
+#[cfg(not(feature = "std"))]
-#[cfg(not(feature = "std"))] use core::intrinsics::cosf64;
+use core::intrinsics::cosf32;
-#[cfg(feature = "std")] use std::ops::{Add, Mul, Sub};
+#[cfg(not(feature = "std"))]
-#[cfg(not(feature = "std"))] use core::ops::{Add, Mul, Sub};
+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;
+#[cfg(feature = "std")]
+use std::ops::{Add, Mul, Sub};
 
 /// Keys that can be interpolated in between. Implementing this trait is required to perform
 /// sampling on splines.
@@ -45,7 +53,7 @@
 /// instance to know which trait your type must implement to be usable.
 ///
 /// [`Spline::sample`]: crate::spline::Spline::sample
-pub trait Interpolate<T>: Sized + Copy {
+pub trait Interpolate<T>: Sized + Copy + Linear<T> {
   /// Linear interpolation.
   fn lerp(a: Self, b: Self, t: T) -> Self;
 
@@ -68,17 +76,9 @@ pub trait Interpolate<T>: Sized + Copy {
 /// 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:
+pub trait Additive: Copy + Add<Self, Output = Self> + Sub<Self, Output = Self> {}
-  Copy +
-  Add<Self, Output = Self> +
-  Sub<Self, Output = Self> {
-}
 
-impl<T> Additive for T
+impl<T> Additive for T where T: Copy + Add<Self, Output = Self> + Sub<Self, Output = Self> {}
-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 {
@@ -101,7 +101,7 @@ macro_rules! impl_linear_simple {
         self / t
       }
     }
-  }
+  };
 }
 
 impl_linear_simple!(f32);
@@ -119,7 +119,7 @@ macro_rules! impl_linear_cast {
         self / t as $q
       }
     }
-  }
+  };
 }
 
 impl_linear_cast!(f32, f64);
@@ -139,7 +139,7 @@ macro_rules! impl_one_float {
         1.
       }
     }
-  }
+  };
 }
 
 impl_one_float!(f32);
@@ -198,8 +198,10 @@ impl Trigo for f64 {
 ///
 /// `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>,
+where
-      T: Additive + Mul<T, Output = T> + One {
+  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
@@ -215,15 +217,20 @@ where V: Linear<T>,
   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)
+  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>,
+where
-      T: Additive + Mul<T, Output = T> + One {
+  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)
@@ -233,14 +240,19 @@ where V: Linear<T>,
 ///
 /// `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>,
+where
-      T: Additive + Mul<T, Output = T> + One {
+  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)
+  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 {
@@ -262,33 +274,45 @@ macro_rules! impl_interpolate_simple {
         cubic_bezier_def(a, u, v, b, t)
       }
     }
-  }
+  };
 }
 
 impl_interpolate_simple!(f32);
 impl_interpolate_simple!(f64);
 
-//macro_rules! impl_interpolate_via {
+macro_rules! impl_interpolate_via {
-//  ($t:ty, $v:ty) => {
+  ($t:ty, $v:ty) => {
-//    impl Interpolate<$t> for $v {
+    impl Interpolate<$t> for $v {
-//      fn lerp(a: Self, b: Self, t: $t) -> Self {
+      fn lerp(a: Self, b: Self, t: $t) -> Self {
-//        a * (1. - t as $v) + b * t as $v
+        a * (1. - t as $v) + b * t as $v
-//      }
+      }
-//
+
-//      fn cubic_hermite((x, xt): (Self, $t), (a, at): (Self, $t), (b, bt): (Self, $t), (y, yt): (Self, $t), t: $t) -> Self {
+      fn cubic_hermite(
-//        cubic_hermite_def((x, xt as $v), (a, at as $v), (b, bt as $v), (y, yt as $v), t as $v)
+        (x, xt): (Self, $t),
-//      }
+        (a, at): (Self, $t),
-//
+        (b, bt): (Self, $t),
-//      fn quadratic_bezier(a: Self, u: Self, b: Self, t: $t) -> Self {
+        (y, yt): (Self, $t),
-//        $t::quadratic_bezier(a as $t, u as $t, b as $t, t)
+        t: $t,
-//      }
+      ) -> Self {
-//
+        cubic_hermite_def(
-//      fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: $t) -> Self {
+          (x, xt as $v),
-//        $t::cubic_bezier(a as $t, u as $t, v as $t, b as $t, t)
+          (a, at as $v),
-//      }
+          (b, bt as $v),
-//    }
+          (y, yt as $v),
-//  }
+          t as $v,
-//}
+        )
-//
+      }
-//impl_interpolate_via!(f32, f64);
+
-//impl_interpolate_via!(f64, f32);
+      fn quadratic_bezier(a: Self, u: Self, b: Self, t: $t) -> Self {
+        quadratic_bezier_def(a, u, b, t as $v)
+      }
+
+      fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: $t) -> Self {
+        cubic_bezier_def(a, u, v, b, t as $v)
+      }
+    }
+  };
+}
+
+impl_interpolate_via!(f32, f64);
+impl_interpolate_via!(f64, f32);

src/interpolation.rs

@@ -1,6 +1,7 @@
 //! Available interpolation modes.
 
-#[cfg(feature = "serialization")] use serde_derive::{Deserialize, Serialize};
+#[cfg(feature = "serialization")]
+use serde_derive::{Deserialize, Serialize};
 
 /// Available kind of interpolations.
 ///
@@ -9,7 +10,7 @@
 #[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
 #[cfg_attr(feature = "serialization", serde(rename_all = "snake_case"))]
 pub enum Interpolation<T, V> {
-  /// Hold a [`Key<T, _>`] until the sampling value passes the normalized step threshold, in which
+  /// Hold a [`Key`] until the sampling value passes the normalized step threshold, in which
   /// case the next key is used.
   ///
   /// > Note: if you set the threshold to `0.5`, the first key will be used until half the time
@@ -17,7 +18,7 @@ pub enum Interpolation<T, V> {
   /// > first key will be kept until the next key. Set it to `0.` and the first key will never be
   /// > used.
   ///
-  /// [`Key<T, _>`]: crate::key::Key
+  /// [`Key`]: crate::key::Key
   Step(T),
   /// Linear interpolation between a key and the next one.
   Linear,
@@ -39,11 +40,21 @@ pub enum Interpolation<T, V> {
   ///   tangent used for the next control point is defined as the segment connecting that control
   ///   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.
-  #[cfg(feature = "bezier")]
   Bezier(V),
-  #[cfg(not(any(feature = "bezier")))]
+  /// 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
+  /// as the one defined by [`Interpolation::Bezier`], and an output tangent, which has the same
+  /// role defined by the next key’s [`Interpolation::Bezier`] if present, normally.
+  ///
+  /// What it means is that instead of setting the output tangent as the next key’s Bézier tangent,
+  /// this interpolation mode allows you to manually set the output tangent. That will yield more
+  /// control on the tangents but might generate discontinuities. Use with care.
+  ///
+  /// Stroke Bézier interpolation is always a cubic Bézier interpolation by default.
+  StrokeBezier(V, V),
   #[doc(hidden)]
-  _V(std::marker::PhantomData<V>),
+  __NonExhaustive,
 }
 
 impl<T, V> Default for Interpolation<T, V> {
@@ -52,4 +63,3 @@ impl<T, V> Default for Interpolation<T, V> {
     Interpolation::Linear
   }
 }
-

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 {
+    Iter { spline: self, i: 0 }
-      spline: self,
-      i: 0
-    }
   }
 }
-

src/key.rs

@@ -6,7 +6,8 @@
 //! 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};
+#[cfg(feature = "serialization")]
+use serde_derive::{Deserialize, Serialize};
 
 use crate::interpolation::Interpolation;
 
@@ -26,12 +27,16 @@ pub struct Key<T, V> {
   /// 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

@@ -99,12 +99,6 @@
 //!     - Compiling with the standard library is enabled by default.
 //!     - Use `default-features = []` in your `Cargo.toml` to disable.
 //!     - Enable explicitly with the `"std"` feature.
-//!   - **Extra interpolation modes.**
-//!     - In order not to introduce breaking changes, some feature-gates are added to augment the
-//!       [`Interpolation`] enum.
-//!     - Those feature-gates will disappear on the next major release of the crate.
-//!     - The following lists all currently available:
-//!       - `"bezier"`: [Bézier curves](https://en.wikipedia.org/wiki/B%C3%A9zier_curve).
 //!
 //! [`Interpolation`]: crate::interpolation::Interpolation
 
@@ -112,14 +106,17 @@
 #![cfg_attr(not(feature = "std"), feature(alloc))]
 #![cfg_attr(not(feature = "std"), feature(core_intrinsics))]
 
-#[cfg(not(feature = "std"))] extern crate alloc;
+#[cfg(not(feature = "std"))]
+extern crate alloc;
 
-#[cfg(feature = "impl-cgmath")] mod cgmath;
+#[cfg(feature = "impl-cgmath")]
+mod cgmath;
 pub mod interpolate;
 pub mod interpolation;
 pub mod iter;
 pub mod key;
-#[cfg(feature = "impl-nalgebra")] mod nalgebra;
+#[cfg(feature = "impl-nalgebra")]
+mod nalgebra;
 pub mod spline;
 
 pub use crate::interpolate::Interpolate;

src/nalgebra.rs

@@ -1,14 +1,22 @@
-use alga::general::{ClosedAdd, ClosedDiv, ClosedMul, ClosedSub};
 use nalgebra::{Scalar, Vector, Vector1, Vector2, Vector3, Vector4, Vector5, Vector6};
 use num_traits as nt;
+use simba::scalar::{ClosedAdd, ClosedDiv, ClosedMul, ClosedSub};
 use std::ops::Mul;
 
-use crate::interpolate::{Interpolate, Linear, Additive, One, cubic_hermite_def};
+use crate::interpolate::{
+  cubic_bezier_def, cubic_hermite_def, quadratic_bezier_def, Additive, Interpolate, Linear, One,
+};
 
 macro_rules! impl_interpolate_vector {
   ($($t:tt)*) => {
     // implement Linear
-    impl<T> Linear<T> for $($t)*<T> where T: Scalar + ClosedAdd + ClosedSub + ClosedMul + ClosedDiv {
+    impl<T> Linear<T> for $($t)*<T>
+    where T: Scalar +
+             Copy +
+             ClosedAdd +
+             ClosedSub +
+             ClosedMul +
+             ClosedDiv {
       #[inline(always)]
       fn outer_mul(self, t: T) -> Self {
         self * t
@@ -40,6 +48,16 @@ macro_rules! impl_interpolate_vector {
       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/spline.rs

@@ -1,13 +1,19 @@
 //! Spline curves and operations.
 
-#[cfg(feature = "serialization")] use serde_derive::{Deserialize, Serialize};
+#[cfg(not(feature = "std"))]
-#[cfg(not(feature = "std"))] use alloc::vec::Vec;
+use alloc::vec::Vec;
-#[cfg(feature = "std")] use std::cmp::Ordering;
+#[cfg(not(feature = "std"))]
-#[cfg(feature = "std")] use std::ops::{Div, Mul};
+use core::cmp::Ordering;
-#[cfg(not(feature = "std"))] use core::ops::{Div, Mul};
+#[cfg(not(feature = "std"))]
-#[cfg(not(feature = "std"))] use core::cmp::Ordering;
+use core::ops::{Div, Mul};
+#[cfg(feature = "serialization")]
+use serde_derive::{Deserialize, Serialize};
+#[cfg(feature = "std")]
+use std::cmp::Ordering;
+#[cfg(feature = "std")]
+use std::ops::{Div, Mul};
 
-use crate::interpolate::{Interpolate, Additive, One, Trigo};
+use crate::interpolate::{Additive, Interpolate, One, Trigo};
 use crate::interpolation::Interpolation;
 use crate::key::Key;
 
@@ -29,13 +35,21 @@ 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 {
+  fn internal_sort(&mut self)
-    self.0.sort_by(|k0, k1| k0.t.partial_cmp(&k1.t).unwrap_or(Ordering::Less));
+  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
@@ -48,7 +62,11 @@ 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())
   }
 
@@ -69,7 +87,8 @@ impl<T, V> Spline<T, V> {
     self.0.is_empty()
   }
 
-  /// Sample a spline at a given time.
+  /// Sample a spline at a given time, returning the interpolated value along with its associated
+  /// key.
   ///
   /// The current implementation, based on immutability, cannot perform in constant time. This means
   /// that sampling’s processing complexity is currently *O(log n)*. It’s possible to achieve *O(1)*
@@ -83,10 +102,11 @@ 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>>)>
-  pub fn sample(&self, t: T) -> Option<V>
+  where
-  where T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
+    T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
-        V: Interpolate<T> {
+    V: Additive + Interpolate<T>,
+  {
     let keys = &self.0;
     let i = search_lower_cp(keys, t)?;
     let cp0 = &keys[i];
@@ -95,14 +115,17 @@ impl<T, V> Spline<T, V> {
       Interpolation::Step(threshold) => {
         let cp1 = &keys[i + 1];
         let nt = normalize_time(t, cp0, cp1);
-        Some(if nt < threshold { cp0.value } else { cp1.value })
+        let value = if nt < threshold { cp0.value } else { cp1.value };
+
+        Some((value, cp0, Some(cp1)))
       }
 
       Interpolation::Linear => {
         let cp1 = &keys[i + 1];
         let nt = normalize_time(t, cp0, cp1);
+        let value = Interpolate::lerp(cp0.value, cp1.value, nt);
 
-        Some(Interpolate::lerp(cp0.value, cp1.value, nt))
+        Some((value, cp0, Some(cp1)))
       }
 
       Interpolation::Cosine => {
@@ -110,8 +133,9 @@ impl<T, V> Spline<T, V> {
         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);
 
-        Some(Interpolate::lerp(cp0.value, cp1.value, cos_nt))
+        Some((value, cp0, Some(cp1)))
       }
 
       Interpolation::CatmullRom => {
@@ -124,35 +148,54 @@ impl<T, V> Spline<T, V> {
           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,
+          );
 
-          Some(Interpolate::cubic_hermite((cpm0.value, cpm0.t), (cp0.value, cp0.t), (cp1.value, cp1.t), (cpm1.value, cpm1.t), nt))
+          Some((value, cp0, Some(cp1)))
         }
       }
 
-      #[cfg(feature = "bezier")]
+      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 = normalize_time(t, cp0, cp1);
 
-        if let Interpolation::Bezier(v) = cp1.interpolation {
+        let value = match cp1.interpolation {
-          Some(Interpolate::cubic_bezier(cp0.value, u, v, cp1.value, nt))
+          Interpolation::Bezier(v) => {
-          //let one_nt = T::one() - nt;
+            Interpolate::cubic_bezier(cp0.value, u, cp1.value + cp1.value - v, cp1.value, nt)
-          //let one_nt_2 = one_nt * one_nt;
+          }
-          //let one_nt_3 = one_nt_2 * one_nt;
+
-          //let three_one_nt_2 = one_nt_2 + one_nt_2 + one_nt_2; // one_nt_2 * 3
+          Interpolation::StrokeBezier(v, _) => {
-          //let r = cp0.value * one_nt_3;
+            Interpolate::cubic_bezier(cp0.value, u, v, cp1.value, nt)
-        } else {
+          }
-          Some(Interpolate::quadratic_bezier(cp0.value, u, cp1.value, nt))
+
-        }
+          _ => Interpolate::quadratic_bezier(cp0.value, u, cp1.value, nt),
+        };
+
+        Some((value, cp0, Some(cp1)))
       }
 
-      #[cfg(not(any(feature = "bezier")))]
+      Interpolation::__NonExhaustive => unreachable!(),
-      Interpolation::_V(_) => unreachable!()
     }
   }
 
-  /// Sample a spline at a given time with clamping.
+  /// 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)
+  }
+
+  /// Sample a spline at a given time with clamping, returning the interpolated value along with its
+  /// associated key.
   ///
   /// # Return
   ///
@@ -162,22 +205,29 @@ impl<T, V> Spline<T, V> {
   /// # Error
   ///
   /// This function returns [`None`] if you have no key.
-  pub fn clamped_sample(&self, t: T) -> Option<V>
+  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,
+  where
-        V: Interpolate<T> {
+    T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
+    V: Additive + Interpolate<T>,
+  {
     if self.0.is_empty() {
       return None;
     }
 
-    self.sample(t).or_else(move || {
+    self.sample_with_key(t).or_else(move || {
       let first = self.0.first().unwrap();
       if t <= first.t {
-        Some(first.value)
+        let second = if self.0.len() >= 2 {
+          Some(&self.0[1])
+        } else {
+          None
+        };
+        Some((first.value, &first, second))
       } else {
         let last = self.0.last().unwrap();
 
         if t >= last.t {
-          Some(last.value)
+          Some((last.value, &last, None))
         } else {
           None
         }
@@ -185,8 +235,20 @@ 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)
+  }
+
   /// 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();
   }
@@ -199,21 +261,67 @@ impl<T, V> Spline<T, V> {
       Some(self.0.remove(index))
     }
   }
+
+  /// Update a key and return the key already present.
+  ///
+  /// The key is updated — if present — with the provided function.
+  ///
+  /// # Notes
+  ///
+  /// 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>>
+  where
+    F: FnOnce(&Key<T, V>) -> Key<T, V>,
+    T: PartialOrd,
+  {
+    let key = self.remove(index)?;
+    self.add(f(&key));
+    Some(key)
+  }
+
+  /// Get a key at a given index.
+  pub fn get(&self, index: usize) -> Option<&Key<T, V>> {
+    self.0.get(index)
+  }
+
+  /// Mutably get a key at a given index.
+  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,
+    })
+  }
+}
+
+/// 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`].
+pub struct KeyMut<'a, T, V> {
+  /// Carried value.
+  pub value: &'a mut V,
+  /// Interpolation mode to use for that key.
+  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>(
+pub(crate) fn normalize_time<T, V>(t: T, cp: &Key<T, V>, cp1: &Key<T, V>) -> T
-  t: T,
+where
-  cp: &Key<T, V>,
+  T: Additive + Div<T, Output = T> + PartialEq,
-  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 {
+fn search_lower_cp<T, V>(cps: &[Key<T, V>], t: T) -> Option<usize>
+where
+  T: PartialOrd,
+{
   let mut i = 0;
   let len = cps.len();
 
@@ -223,7 +331,7 @@ fn search_lower_cp<T, V>(cps: &[Key<T, V>], t: T) -> Option<usize> where T: Part
 
   loop {
     let cp = &cps[i];
-    let cp1 = &cps[i+1];
+    let cp1 = &cps[i + 1];
 
     if t >= cp1.t {
       if i >= len - 2 {

tests/mod.rs

@@ -1,7 +1,9 @@
 use splines::{Interpolation, Key, Spline};
 
-#[cfg(feature = "impl-cgmath")] use cgmath as cg;
+#[cfg(feature = "cgmath")]
-#[cfg(feature = "impl-nalgebra")] use nalgebra as na;
+use cgmath as cg;
+#[cfg(feature = "nalgebra")]
+use nalgebra as na;
 
 #[test]
 fn step_interpolation_f32() {
@@ -16,6 +18,8 @@ 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!(spline.sample_with_key(0.2), Some((10., &start, Some(&end))));
+  assert_eq!(spline.clamped_sample_with_key(1.), Some((10., &end, None)));
 }
 
 #[test]
@@ -31,6 +35,8 @@ 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!(spline.sample_with_key(0.2), Some((10., &start, Some(&end))));
+  assert_eq!(spline.clamped_sample_with_key(1.), Some((10., &end, None)));
 }
 
 #[test]
@@ -145,7 +151,34 @@ fn several_interpolations_several_keys() {
   assert_eq!(spline.clamped_sample(11.), Some(4.));
 }
 
-#[cfg(feature = "impl-cgmath")]
+#[cfg(feature = "cgmath")]
+#[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.));
+}
+
+#[cfg(feature = "cgmath")]
 #[test]
 fn cgmath_vector_interpolation() {
   use splines::Interpolate;
@@ -159,7 +192,7 @@ fn cgmath_vector_interpolation() {
   assert_eq!(Interpolate::lerp(start, end, 0.5), mid);
 }
 
-#[cfg(feature = "impl-nalgebra")]
+#[cfg(feature = "nalgebra")]
 #[test]
 fn nalgebra_vector_interpolation() {
   use splines::Interpolate;