Biomedical Engineering Reference
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mapping, which enables users to explore infinite virtual scenes by real walking, and
does not require information about the virtual scene. If more information about the
user's movements is available, the prediction based on the view direction can be
replaced by more sophisticated strategies.
10.5 Conclusion
In this chapter we have described the basic math required to set up real walking
user interfaces in immersive VEs. We have shown how isometric and nonisometric
transformations can be used to map user movements from a physical workspace to a
virtual scene. While isometric transformations provide natural feedback to physical
user movements, they limit the virtual space a user can explore by real walking to the
size of the tracked physical workspace. We have described how this limitation can be
alleviated by combining walking in a limited interaction volume with other traveling
techniques (e.g., flying). With nonisometric angular, linear, and curvature transfor-
mations we have described how the limitations of interaction space can be broken
to support unlimited omnidirectional walking, although this freedom is bought with
less natural feedback to physical user movements.
Practitioners interested in implementing real walking user interfaces may follow
these rough guidelines:
If the virtual interaction space is smaller or equal to the tracked physical work-
space, isometric transformations should be used, since these will provide optimal
self-motion feedback.
If the virtual places of interest are rather small, but considerably spaced apart in the
virtual scene, isometric mappings should be combined with traveling techniques
based on additional devices or sensors.
If the virtual scene consists of one large area of interest that could be explored by
walking, then redirected walking with nonisometric mappings is recommended.
As explained above when using nonisometric mappings, the virtual view moves
in a different way than the user's head in the tracked physical environment. One
interesting question is how much deviation between these motions is tolerated by
the user. Recently, several experiments have been reported which have identified
detection thresholds for these nonisometric mappings. Interested readers may refer
to works by Steinicke et al. [ 31 , 32 ], Neth et al. [ 19 ] and Engel et al. [ 6 ].
In summary, movements of a user in immersive VEs have to be transferred to
a virtual scene to provide the user with virtual feedback about self-motions, which
can be a faithful simulation of real-world movements, or manipulated using different
approaches. Since each of the approaches has different advantages and limitations, it
depends on the structure of the virtual scene and the application as to which approach
is best suited. In the next chapter, these approaches are discussed in more detail.
 
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