So I just saw this today http://www.siliconera.com/2015/01/02/live2d-euclid-gives-2d-anime-a-3d-body-to-swivel-in/ and I really like the results they've gotten. I've followed Live 2D for a while now, but I've only been able to figure out how something like their previous versions would work. I've always wanted to write a rendering engine like the new Live 2D Euclid, but whereas it was pretty easy to figure out what they were doing with the old version (basically just a bunch of textured planes and skewing), I can't figure out how the heck they're doing this new version. Anyone got any ideas how they might be pulling this off?

I can't figure out how the heck they're doing this new version.

There are three interesting clues in that article. The first is the mention that the characters can only be rotated horizontally (it's not possible to view them from above or below). The second is that the video at one point mentions that it requires source illustrations from multiple angles. And the third is the mention that only the characters face (or maybe the whole head) is done via their technology, with the body being modelled with a traditional polygon mesh.

If I had to hazard a guess guess, I'd take their 2D parallax planes approach a little further, and use a restricted form of billboard clouds to simulate 3D. Probably a variant of this paper on animated billboard clouds. Limiting the rotation to a single axis drastically reduces initial computation cost and storage requirements, and it shouldn't be too hard to derive the billboard cloud from a set of source illustrations at various rotations, rather than a polygonal model...

So there's a LOT of artist work going into each character then. If I understand the technique correctly, I'd think that means you'd need the pictures for all the front angles, so front eye layers, front mouth layer, front eyebrows/hair layer, etc. Plus possible two side angle versions of each layer, and some way to match poses or synchronize frames from various angles.

So there's a LOT of artist work going into each character then.

Probably not as much as you'd expect.

I think it's much more like their regular 2D technique, which just separates out elements of a single illustration into layers, so that you can represent small (up to 30º) horizontal rotations by sliding the layers over one another and skewing them for perspective. The difference here is that they take a (small) number of illustrations (probably front, profile and half profile as a minimum), and they reflect those illustrations as necessary to derive the other 9 increments of 30º views.