What does an algorithm which handles mesh-based image morphing look like?

In recent years, the technology of Live2D has become particularly popular and I have been attempting to find any papers or articles which explain what the mathematics for the mesh-based image morphing system are and how they work. Unfortunately, there doesn't seem to be a lot of information on the subject and most of the links I found where just different versions of the same two or three papers and they didn't seem to answer my question.

I am trying to find information on what the algorithm which performs the mesh-based morph/warp looks like. I am aware that there are point-based algorithm which morph between the established points on two different images. (This is not what I am looking for.). I am looking for an algorithm which can freely transform an image based on a non-rectangular mesh. I'm primarily referring to the image warping seen in Live2D Cubism (manual). See below for visuals.

The initial definition of the "artmesh" on top of the image to be morphed:

The vertices in the "artmesh" have now been moved around and the solitary layer has been morphed smoothly to match:

Does anybody know what the algorithm looks like? Sources such as papers, articles or open-source projects would also be appreciated, if possible. As a side note, I am posting this on ComputerGraphics, since I get the feeling that the mesh-based morphing logic may relate to texture projection in 3D graphics. Unfortunately, I'm not experienced enough in that subject to be more specific. I hope you can answer my question. Thank you in advance.

• The primary reason its done thisway is that you have this thing called the graphic card that works on triangles like this without any modifications. Other approaches need more work from devs side. Anyway this is hardly new technology ive used siftware that worked like this in the 1990's perhaps not finding anything is because you dont search back in time enough. Nov 29, 2021 at 11:43