Add TRANS_SPRING to Tween

[rakkarage]

once again:
#58999
sorry, thanks

Bugsquad edited: godotengine/godot-proposals#4212

[TokageItLab]

I did a quick look into spring tween, but could not find any details about its origin. What I did find is that the formula is similar to the Elastic formula when the spring formula is modified, and that unlike Elastic, the oscillation frequency is accelerated using the cubic of time.

I guessed that the approximate constant was determined to give a good number of about 3 bounds (there may be some additional bounds that are too small to be noticeable) with neat motion, but I don't know what the reason is.

For now, I only review the formulas and leave it to the production team to decide what to do about the license since this algorithm is probably a quote from somewhere.

[rakkarage]

• uses real instead of float like rest of file

[TokageItLab]

I think now the behavior and code style are fine.

Well, it is unclear as to the original source of this code. I leave it to the production team to decide if there is a licensing concern.

[KoBeWi]

Tween cheat sheet with the new transition:

We'll need to update the image in the documentation.

[kleonc]

@KoBeWi How is this cheat sheet generated? It could potentially be improved, like lines could be antialiased and the gaps could be eliminated (there are visible gaps e.g. near zero in elastic).

[KoBeWi]

With this: https://github.com/wandomPewlin/godotTweeningCheatSheet
Note that the tool does not support Godot 4 yet, I was going send the updated code once this PR is merged.

[akien-mga]

Thanks! And congrats for your first merged Godot contribution 🎉