Simplified easing curves (#15711)

# Objective

Simplify the API surrounding easing curves. Broaden the base of types
that support easing.

## Solution

There is now a single library function, `easing_curve`, which constructs
a unit-parametrized easing curve between two values based on an
`EaseFunction`:
```rust
/// Given a `start` and `end` value, create a curve parametrized over [the unit interval]
/// that connects them, using the given [ease function] to determine the form of the
/// curve in between.
///
/// [the unit interval]: Interval::UNIT
/// [ease function]: EaseFunction
pub fn easing_curve<T: Ease>(start: T, end: T, ease_fn: EaseFunction) -> EasingCurve<T> { //... }
```

As this shows, the type of the output curve is generic only in `T`. In
particular, as long as `T` is `Reflect` (and `FromReflect` etc. — i.e.,
a standard "well-behaved" reflectable type), `EasingCurve<T>` is also
`Reflect`, and there is no special field handling nonsense. Therefore,
`EasingCurve` is the kind of thing that would be able to be easily
changed in an editor. This is made possible by storing the actual
`EaseFunction` on `EasingCurve<T>` instead of indirecting through some
kind of function type (which generally leads to issues with reflection).

The types that can be eased are those that implement a trait `Ease`:
```rust
/// A type whose values can be eased between.
///
/// This requires the construction of an interpolation curve that actually extends
/// beyond the curve segment that connects two values, because an easing curve may
/// extrapolate before the starting value and after the ending value. This is
/// especially common in easing functions that mimic elastic or springlike behavior.
pub trait Ease: Sized {
    /// Given `start` and `end` values, produce a curve with [unlimited domain]
    /// that:
    /// - takes a value equivalent to `start` at `t = 0`
    /// - takes a value equivalent to `end` at `t = 1`
    /// - has constant speed everywhere, including outside of `[0, 1]`
    ///
    /// [unlimited domain]: Interval::EVERYWHERE
    fn interpolating_curve_unbounded(start: &Self, end: &Self) -> impl Curve<Self>;
}
```

(I know, I know, yet *another* interpolation trait. See 'Future
direction'.)

The other existing easing functions from the previous version of this
module have also become new members of `EaseFunction`: `Linear`,
`Steps`, and `Elastic` (which maybe needs a different name). The latter
two are parametrized.

## Testing

Tested using the `easing_functions` example. I also axed the
`cubic_curve` example which was of questionable value and replaced it
with `eased_motion`, which uses this API in the context of animation:


https://github.com/user-attachments/assets/3c802992-6b9b-4b56-aeb1-a47501c29ce2


---

## Future direction

Morally speaking, `Ease` is incredibly similar to `StableInterpolate`.
Probably, we should just merge `StableInterpolate` into `Ease`, and then
make `SmoothNudge` an automatic extension trait of `Ease`. The reason I
didn't do that is that `StableInterpolate` is not implemented for
`VectorSpace` because of concerns about the `Color` types, and I wanted
to avoid controversy. I think that may be a good idea though.

As Alice mentioned before, we should also probably get rid of the
`interpolation` dependency.

The parametrized `Elastic` variant probably also needs some additional
work (e.g. renaming, in/out/in-out variants, etc.) if we want to keep
it.

Author: mweatherley

Cargo.toml

@@ -1300,13 +1300,13 @@ category = "Animation"
 wasm = true
 
 [[example]]
-name = "cubic_curve"
-path = "examples/animation/cubic_curve.rs"
+name = "eased_motion"
+path = "examples/animation/eased_motion.rs"
 doc-scrape-examples = true
 
-[package.metadata.example.cubic_curve]
-name = "Cubic Curve"
-description = "Bezier curve example showing a cube following a cubic curve"
+[package.metadata.example.eased_motion]
+name = "Eased Motion"
+description = "Demonstrates the application of easing curves to animate an object"
 category = "Animation"
 wasm = true
 

crates/bevy_math/src/common_traits.rs

@@ -43,11 +43,11 @@ pub trait VectorSpace:
     /// on the parameter `t`. When `t` is `0`, `self` is recovered. When `t` is `1`, `rhs`
     /// is recovered.
     ///
-    /// Note that the value of `t` is not clamped by this function, so interpolating outside
+    /// Note that the value of `t` is not clamped by this function, so extrapolating outside
     /// of the interval `[0,1]` is allowed.
     #[inline]
-    fn lerp(&self, rhs: Self, t: f32) -> Self {
-        *self * (1. - t) + rhs * t
+    fn lerp(self, rhs: Self, t: f32) -> Self {
+        self * (1. - t) + rhs * t
     }
 }