RFR: 8358820: Allow interpolation outside of range [0,1]

[Nir Lisker]

On Fri, 6 Jun 2025 23:23:05 GMT, Michael Strauß <mstrauss at openjdk.org> wrote:

> 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.

Noting that this proposed change supersedes the previous changes that were done for for https://bugs.openjdk.org/browse/JDK-8226911. The proposed behavioral change makes sense.

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PR Comment: https://git.openjdk.org/jfx/pull/1822#issuecomment-2952868294