Merge pull request #33 from phaazon/feature/stroke-bezier

Add Interpolation::StrokeBezier.

.github/workflows/ci.yaml

@@ -8,12 +8,11 @@ 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
@@ -21,25 +20,25 @@ 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:
     runs-on: ubuntu-latest

CHANGELOG.md

@@ -1,10 +1,43 @@
-# 1.1.1
+# 2.2.0
 
-> Mon Sep 22rd 2019
+> 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.
+
+# 2.0.0
+
+> 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 support for [Bézier curves](https://en.wikipedia.org/wiki/B%C3%A9zier_curve). This is
-  normally a breaking change so it’s currently disabled by default and available via the
-  `"bezier"` feature-gate.
 - Add `Spline::get`, `Spline::get_mut` and `Spline::replace`.
 
 # 1.0

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "splines"
-version = "1.1.1"
+version = "2.2.0"
 license = "BSD-3-Clause"
 authors = ["Dimitri Sabadie <dimitri.sabadie@gmail.com>"]
 description = "Spline interpolation made easy"
@@ -21,7 +21,6 @@ maintenance = { status = "actively-developed" }
 
 [features]
 default = ["std"]
-bezier = []
 impl-cgmath = ["cgmath"]
 impl-nalgebra = ["alga", "nalgebra", "num-traits"]
 serialization = ["serde", "serde_derive"]

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
 

src/cgmath.rs

@@ -32,13 +32,11 @@ macro_rules! impl_interpolate_vec {
         cubic_hermite_def(x, a, b, y, t)
       }
 
-      #[cfg(feature = "bezier")]
       #[inline(always)]
       fn quadratic_bezier(a: Self, u: Self, b: Self, t: T) -> Self {
         quadratic_bezier_def(a, u, b, t)
       }
 
-      #[cfg(feature = "bezier")]
       #[inline(always)]
       fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: T) -> Self {
         cubic_bezier_def(a, u, v, b, t)
@@ -76,13 +74,11 @@ where Self: InnerSpace<Scalar = T>, T: Additive + BaseFloat + One {
     cubic_hermite_def(x, a, b, y, t)
   }
 
-  #[cfg(feature = "bezier")]
   #[inline(always)]
   fn quadratic_bezier(a: Self, u: Self, b: Self, t: T) -> Self {
     quadratic_bezier_def(a, u, b, t)
   }
 
-  #[cfg(feature = "bezier")]
   #[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

@@ -59,11 +59,9 @@ pub trait Interpolate<T>: Sized + Copy {
   }
 
   /// Quadratic Bézier interpolation.
-  #[cfg(feature = "bezier")]
   fn quadratic_bezier(a: Self, u: Self, b: Self, t: T) -> Self;
 
   /// Cubic Bézier interpolation.
-  #[cfg(feature = "bezier")]
   fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: T) -> Self;
 }
 
@@ -223,7 +221,6 @@ where V: Linear<T>,
 /// Default implementation of [`Interpolate::quadratic_bezier`].
 ///
 /// `V` is the value being interpolated. `T` is the sampling value (also sometimes called time).
-#[cfg(feature = "bezier")]
 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 {
@@ -235,7 +232,6 @@ where V: Linear<T>,
 /// Default implementation of [`Interpolate::cubic_bezier`].
 ///
 /// `V` is the value being interpolated. `T` is the sampling value (also sometimes called time).
-#[cfg(feature = "bezier")]
 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 {
@@ -244,7 +240,10 @@ where V: Linear<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)
+  // 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 {
@@ -258,12 +257,10 @@ macro_rules! impl_interpolate_simple {
         cubic_hermite_def(x, a, b, y, t)
       }
 
-      #[cfg(feature = "bezier")]
       fn quadratic_bezier(a: Self, u: Self, b: Self, t: $t) -> Self {
         quadratic_bezier_def(a, u, b, t)
       }
 
-      #[cfg(feature = "bezier")]
       fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: $t) -> Self {
         cubic_bezier_def(a, u, v, b, t)
       }
@@ -285,12 +282,10 @@ macro_rules! impl_interpolate_via {
         cubic_hermite_def((x, xt as $v), (a, at as $v), (b, bt as $v), (y, yt as $v), t as $v)
       }
 
-      #[cfg(feature = "bezier")]
       fn quadratic_bezier(a: Self, u: Self, b: Self, t: $t) -> Self {
         quadratic_bezier_def(a, u, b, t as $v)
       }
 
-      #[cfg(feature = "bezier")]
       fn cubic_bezier(a: Self, u: Self, v: Self, b: Self, t: $t) -> Self {
         cubic_bezier_def(a, u, v, b, t as $v)
       }

src/interpolation.rs

@@ -5,7 +5,6 @@
 /// Available kind of interpolations.
 ///
 /// Feel free to visit each variant for more documentation.
-#[cfg(feature = "bezier")]
 #[derive(Copy, Clone, Debug, Eq, PartialEq)]
 #[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
 #[cfg_attr(feature = "serialization", serde(rename_all = "snake_case"))]
@@ -40,48 +39,26 @@ 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),
+  /// 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)]
+  __NonExhaustive
 }
 
-/// Available kind of interpolations.
-///
-/// Feel free to visit each variant for more documentation.
-#[cfg(not(feature = "bezier"))]
-#[derive(Copy, Clone, Debug, Eq, PartialEq)]
-#[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
-#[cfg_attr(feature = "serialization", serde(rename_all = "snake_case"))]
-pub enum Interpolation<T> {
-  /// 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
-  /// > between the two keys; the second key will be in used afterwards. If you set it to `1.0`, the
-  /// > first key will be kept until the next key. Set it to `0.` and the first key will never be
-  /// > used.
-  ///
-  /// [`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,
-}
-
-#[cfg(feature = "bezier")]
 impl<T, V> Default for Interpolation<T, V> {
   /// [`Interpolation::Linear`] is the default.
   fn default() -> Self {
     Interpolation::Linear
   }
 }
-
-#[cfg(not(feature = "bezier"))]
-impl<T> Default for Interpolation<T> {
-  /// [`Interpolation::Linear`] is the default.
-  fn default() -> Self {
-    Interpolation::Linear
-  }
-}

src/key.rs

@@ -17,7 +17,6 @@ use crate::interpolation::Interpolation;
 /// key and the next one – if existing. Have a look at [`Interpolation`] for further details.
 ///
 /// [`Interpolation`]: crate::interpolation::Interpolation
-#[cfg(feature = "bezier")]
 #[derive(Copy, Clone, Debug, Eq, PartialEq)]
 #[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
 #[cfg_attr(feature = "serialization", serde(rename_all = "snake_case"))]
@@ -30,36 +29,9 @@ pub struct Key<T, V> {
   pub interpolation: Interpolation<T, V>
 }
 
-/// A spline control point.
-///
-/// This type associates a value at a given interpolation parameter value. It also contains an
-/// interpolation mode used to determine how to interpolate values on the segment defined by this
-/// key and the next one – if existing. Have a look at [`Interpolation`] for further details.
-///
-/// [`Interpolation`]: crate::interpolation::Interpolation
-#[cfg(not(feature = "bezier"))]
-#[derive(Copy, Clone, Debug, Eq, PartialEq)]
-#[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
-#[cfg_attr(feature = "serialization", 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>
-}
-
 impl<T, V> Key<T, V> {
   /// Create a new key.
-  #[cfg(feature = "bezier")]
   pub fn new(t: T, value: V, interpolation: Interpolation<T, V>) -> Self {
     Key { t, value, interpolation }
   }
-
-  /// Create a new key.
-  #[cfg(not(feature = "bezier"))]
-  pub fn new(t: T, value: V, interpolation: Interpolation<T>) -> Self {
-    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
 

src/nalgebra.rs

@@ -43,13 +43,11 @@ macro_rules! impl_interpolate_vector {
         cubic_hermite_def(x, a, b, y, t)
       }
 
-      #[cfg(feature = "bezier")]
       #[inline(always)]
       fn quadratic_bezier(a: Self, u: Self, b: Self, t: T) -> Self {
         quadratic_bezier_def(a, u, b, t)
       }
 
-      #[cfg(feature = "bezier")]
       #[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

@@ -69,7 +69,8 @@ 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)*
@@ -83,8 +84,7 @@ 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 T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
         V: Interpolate<T> {
     let keys = &self.0;
@@ -95,14 +95,17 @@ 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 +113,9 @@ 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 => {
@@ -124,32 +128,49 @@ 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) => {
         // 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 =
-          Some(Interpolate::cubic_bezier(cp0.value, u, v, cp1.value, nt))
+          if let Interpolation::Bezier(v) = cp1.interpolation {
-          //let one_nt = T::one() - nt;
+            Interpolate::cubic_bezier(cp0.value, u, v, cp1.value, nt)
-          //let one_nt_2 = one_nt * one_nt;
+          } else {
-          //let one_nt_3 = one_nt_2 * one_nt;
+            Interpolate::quadratic_bezier(cp0.value, u, cp1.value, nt)
-          //let three_one_nt_2 = one_nt_2 + one_nt_2 + one_nt_2; // one_nt_2 * 3
+          };
-          //let r = cp0.value * one_nt_3;
+
-        } else {
+        Some((value, cp0, Some(cp1)))
-          Some(Interpolate::quadratic_bezier(cp0.value, u, cp1.value, nt))
-        }
       }
+
+      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 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: 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
   ///
@@ -159,22 +180,23 @@ 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,
         V: 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
         }
@@ -182,6 +204,13 @@ 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 T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T> + PartialOrd,
+        V: 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 {
     self.0.push(key);
@@ -243,10 +272,7 @@ pub struct KeyMut<'a, T, V> {
   /// Carried value.
   pub value: &'a mut V,
   /// Interpolation mode to use for that key.
-  #[cfg(feature = "bezier")]
   pub interpolation: &'a mut Interpolation<T, V>,
-  #[cfg(not(feature = "bezier"))]
-  pub interpolation: &'a mut Interpolation<T>,
 }
 
 // Normalize a time ([0;1]) given two control points.

tests/mod.rs

@@ -16,6 +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!(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 +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!(spline.sample_with_key(0.2), Some((10., &start, Some(&end))));
+  assert_eq!(spline.clamped_sample_with_key(1.), Some((10., &end, None)));
 }
 
 #[test]