This is the subject of my PhD thesis, and it aims at understanding how bodily discontinuities such as change in perspective or movement redirection – which cannot be replicated in reality – affects the perception of the virtual body as ones own body. So far we have published the following papers on the subject
Debarba, H. G., Molla, E., Herbelin, B., & Boulic, R. (2015, March). Characterizing Embodied Interaction in First and Third Person Perspective Viewpoints. In 3D User Interfaces (3DUI), 2015 IEEE Symposium on (pp. 67-72). IEEE. (32% acceptance rate)
Debarba, H. G., Perrin, S., Herbelin, B., & Boulic, R. (2015, November). Embodied interaction using non-planar projections in immersive virtual reality. In Proceedings of the 21st ACM Symposium on Virtual Reality Software and Technology (pp. 125-128). ACM. (18% acceptance rate)
Currently I am working on the perception of movement redirection, bellow is a video demonstrating an interesting illusion related to this subject. Although the physical object the users touch is cube shaped, they often feel as if the object shape is like the one they see through the head-mounted display.
The implementation is based in the thin plate splines in order to map a regular 3D space into a irregular one. Bellow you can find an interesting reference which explores this effect in a cylinder
Ban, Y., Narumi, T., Tanikawa, T., & Hirose, M. (2014, November). Displaying shapes with various types of surfaces using visuo-haptic interaction. In Proceedings of the 20th ACM Symposium on Virtual Reality Software and Technology (pp. 191-196). ACM.