> JavaFX unnecessarily restricts interpolation in the following ways:
> 1. `Interpolatable` implementations often clamp intermediate values to the 
> interpolation factor range [0,1].
> 2. `SplineInterpolator` doesn't accept Y coordinates outside of [0,1] for its 
> control points. While this was probably done so that the computed 
> interpolation factor doesn't exceed [0,1], the restriction goes far beyond 
> that. For example, the following function is not representable, even though 
> its values are all within the [0,1] range:<br>
>    <img 
> src="https://github.com/user-attachments/assets/368b6142-052d-4ead-8a59-cbddf4a19660";
>  width="400"/><br>
>    The following function is also not representable, but would be very useful 
> for [bouncy animations](https://easings.net/#easeOutBack):<br>
>    <img 
> src="https://github.com/user-attachments/assets/af02b044-ae4c-4250-b181-72178ad9f3f3";
>  width="400"/>
> 
> Fortunately, there is no technical reason why JavaFX can't support the full 
> range of animations that can be represented with a cubic Beziér interpolation 
> function.
> 
> This PR includes the following changes:
> 1. The specification of `Interpolatable` is changed to require 
> implementations to accept interpolation factors outside of [0,1].
> 2. All implementations of `Interpolatable` now correctly return intermediate 
> values outside of [0,1].
> 3. `SplineInterpolator` now accepts control points with any Y coordinate.
> 
> Here's how the result looks like for the previously unrepresentable 
> interpolation function `cubic-bezier(0.34, 2.2, 0.64, 1)`:<br>
> <img 
> src="https://github.com/user-attachments/assets/72c10d0d-71b4-4bb5-b58c-ae377279b0fd";
>  width="500"/>

Michael Strauß has updated the pull request with a new target base due to a 
merge or a rebase. The incremental webrev excludes the unrelated changes 
brought in by the merge/rebase. The pull request contains three additional 
commits since the last revision:

 - Merge branch 'master' into feature/relaxed-interpolation
 - javadoc
 - Allow interpolation outside of range [0,1]

-------------

Changes:
  - all: https://git.openjdk.org/jfx/pull/1822/files
  - new: https://git.openjdk.org/jfx/pull/1822/files/92d06d7e..26208229

Webrevs:
 - full: https://webrevs.openjdk.org/?repo=jfx&pr=1822&range=02
 - incr: https://webrevs.openjdk.org/?repo=jfx&pr=1822&range=01-02

  Stats: 18401 lines in 224 files changed: 15325 ins; 2250 del; 826 mod
  Patch: https://git.openjdk.org/jfx/pull/1822.diff
  Fetch: git fetch https://git.openjdk.org/jfx.git pull/1822/head:pull/1822

PR: https://git.openjdk.org/jfx/pull/1822

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