I was mistaken, she really is always facing the camera. You can clearly see this in 0:24 in the video when the camera switches from behind her and she is facing the same way.
But this transparent screen she's being projected on is REALLY transparent!? I don't see it at all. At the beginning of the video there's a light circle around her, perhaps that's the spotlights hitting the screen?
Ok, watching more closely, there are indications that the screen is a flat, very tall, rectangular piece of glass about 3 or 4 meters wide. You can see two vertical lines at the same 0:24 mark and other parts of the video with close ups indicating the glasse's outline.
Wait a second... 3D projection, glasses and mirror illusion. Time Traveller from SEGA anyone? I read somewhere that SEGA owns a good part of the rights for Hatsune, as well as being involved in her animation for the shows. Maybe it's related.
last edit: oh my, the screen isn't that tall at all, it can be seen in all its glory at 2:41
Thanks for clearing this up ^^ I guess the effect is better when viewing the show through a 2d screen than when viewing it live. Of course this statement is unrelated with the context of it being a show.
