Red Arrow: old algorithm (linear interpolation)
Green Arrow: barycentric coordinates

I wonder if it may be best to make an option to let the developer choose between the old and new algorithm, that way existing particle effects won't be changed.

I believe it's unnecessary to expend additional time and maintenance on an outdated, obsolete algorithm. The new algorithm is demonstrably clearer and more efficient, offering significant improvements that will ultimately benefit all developers.

My focus is on providing the best possible tools, and maintaining two separate algorithms would divert resources that could be better spent on further enhancing the new solution. I'm confident that transitioning to the new algorithm will lead to a more streamlined and performant experience for everyone.

If you disagree with my implementation, I can close this PR and create my own EmitterShape class, since the JME architecture allows it. However, this would result in the loss of this functionality for the JME community.

My worry is that the differing behavior may result in existing particle effects behaving different visually after this change.

This may cause an app with a well-tweaked particle emitter to now have that particle emitter behaving differently. Whether that current algorithm is right/wrong or better/worse is not as important as making sure that existing particle emitters still behave the way the developer expects.

I'd have to see a side-by-side comparison of a few particle emitters with the new compared to old algorithm to see if the visual difference is noticeable enough that it may break existing particle effects.

MY concerns may be overly cautious. But maybe @riccardobl has some insight to offer since he has more experience than I do working with the backend of particle emitters.

If the emission was deterministic i would have suggested to deprecate the old class and to implement a new shape, but it is not, so imo in this case we can merge the patch as it is.

I see this more as a bug fix, because someone using this emission shape is already expecting a random uniform emission anyway, the only difference is that the previous one was not so uniform.