I have a set of independent meshes whose results I would like to project onto another non-hierachally related mesh. Until now, I've been accomplishing this by finding the nearest-distance node in the input meshes (by minimizing the $L_2$ error) and assigning its values to the target mesh. This seems to be the most often used way of approaching the problem (ref1, ref2) but due to the requirements of this project I would like to implement something quicker if possible.
As such, I was wondering if there were other, faster, methods for projecting mesh results onto another mesh. Unfortunately, I can't enforce that the input meshes and the target mesh will be related, since the results of the input mesh will be transformed (rotated / translated) during runtime. This takes out the majority of mesh projection methods that I'm at least aware of, which is why I'd like to go to the community for help.
I understand that my current method likely retains the most accuracy as far as grid projection methods go, but I'm okay with trading accuracy for speed.