Biomedical Engineering Reference
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perspectives and natural interaction metaphors can provide users with a compelling
experience similar to interactions in the real world, which cannot be simulated using
any other existing technology. In this context, the most natural technique for explor-
ing a virtual world is real walking , which provides a greater sense of presence than
other virtual traveling techniques [ 4 , 24 ], such as flying or walking in-place [ 36 ],
and naturally stimulates human spatial wayfinding and cognitive map building [ 27 ].
As described in Part 1, walking is a form of natural locomotion, which encom-
passes repetitive motions of legs or body for active self-propulsion [ 9 ], such that
users in immersive VEs receive proprioceptive, kinesthetic and efferent copy sig-
nals from their physical movements, supporting the perception of self-motion in the
virtual world.
In order to provide users with an unimpaired sense of place and plausibility during
self-motions [ 29 ], virtual reality (VR) applications have to maintain simultaneous
awareness of coordinate systems and transformations in both the real and virtual
world. In this chapter, we describe the basic transformations that can be used to
implement real walking user interfaces in VR laboratory workspaces. In particular,
we show how the sense of moving in computer graphics environments can be stim-
ulated with sequences of frame to frame changes of the position and orientation of a
user in a VR workspace. If the changes from one frame to the next are large, we talk
of teleportation , whereas if the changes are considerable small, the feedback from
the virtual world causes a sensory flow (e.g., optic flow [ 15 ] or acoustic flow [ 30 ]),
which engenders the sense of continuous motion.
We distinguish between two main characteristics of real walking user interfaces:
Isometric transformations describe mappings that preserve motion distances and
angles when movements of a tracked user in the physical workspace are mapped
to changes of a virtual representation.
Nonisometric transformations, in contrast, describe different mapping approaches
to introduce a discrepancy between user movements and virtual feedback.
It is generally assumed that human spatial perception and cognition in virtual
worlds is optimally supported in isometric user interfaces, since sensory motion
feedback from the user's physical movements (e.g., proprioceptive and vestibular
motion cues) match feedback from the virtual world (e.g., optic and acoustic flow).
However, isometric user interfaces have a severe practical problem: With such map-
pings the size of the physical workspace limits the size of the virtual scene that a
user can explore by natural walking. We show how such limitations can be alleviated
with multimodal interfaces that combine walking over short distances with traveling
over long distances. We introduce nonisometric mapping strategies that provide a
different solution to the problem of unrestricted omnidirectional walking by guid-
ing users on a different path in the real world than experienced in the virtual scene.
Nonisometric mappings for walking user interfaces are encompassed under the term
redirected walking [ 23 ].
The remainder of this chapter is structured as follows. Section 10.2 gives a short
introduction to workspaces and coordinate systems in VR laboratories. In Sect. 10.3
 
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