Journal of Virtual Reality and Broadcasting, Volume n(200n), no. n

Real Walking through Virtual Environmentsby Redirection Techniques

Frank Steinicke∗, Gerd Bruder∗, Klaus Hinrichs∗ Jason Jerald ‡ Harald Frenz†, Markus Lappe†

∗Visualization and Computer Graphics (VisCG) Research GroupDepartment of Computer Science, Westfalische Wilhelms-Universitat Munster

Einsteinstraße 62, 48149 Munster, Germanyemail: {fsteini,g brud01,khh}@uni-muenster.de

www: viscg.uni-muenster.de‡ Effective Virtual Environments Group

Department of Computer Science, University of North Carolina,Chapel Hill, North Carolina, USA

email: jjerald@email.unc.eduwww: www.cs.unc.edu† Psychology Department II

Department of Psychology, Westfalische Wilhelms-Universitat MunsterFliednerstraße 21, 48149 Munster, Germany

email: {mlappe,frenzh}@uni-muenster.dewww: wwwpsy.uni-muenster.de/Psychologie.inst2/AELappe

Abstract

We present redirection techniques that support explo-ration of large-scale virtual environments (VEs) bymeans of real walking. We quantify to what degreeusers can unknowingly be redirected in order to guidethem through VEs in which virtual paths differ fromthe physical paths. We further introduce the concept ofdynamic passive haptics by which any number of vir-tual objects can be mapped to real physical proxy propshaving similar haptic properties (i. e., size, shape, andsurface structure), such that the user can sense these

Digital Peer Publishing LicenceAny party may pass on this Work by electronicmeans and make it available for download underthe terms and conditions of the current versionof the Digital Peer Publishing Licence (DPPL).The text of the licence may be accessed andretrieved via Internet athttp://www.dipp.nrw.de/.

First presented at the Virtual Reality International Conference (VRIC)extended and revised for JVRB

virtual objects by touching their real world counter-parts. Dynamic passive haptics provides the user withthe illusion of interacting with a desired virtual objectby redirecting her to the corresponding proxy prop.We describe the concepts of generic redirected walk-ing and dynamic passive haptics and present experi-ments in which we have evaluated these concepts. Fur-thermore, we discuss implications that have been de-rived from a user study, and we present approachesthat derive physical paths which may vary from thevirtual counterparts.

Keywords: Virtual Locomotion User Interfaces,Redirected Walking, Perception

1 Introduction

Walking is the most basic and intuitive way of mov-ing within the real world. Taking advantage of such anactive and dynamic ability to navigate through largeimmersive virtual environments (IVEs) is of greatinterest for many 3D applications demanding loco-motion, such as urban planning, tourism, 3D games

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etc. Although these domains are inherently three-dimensional and their applications would benefit fromexploration by means of real walking, many such VEsystems do not allow users to walk in a natural manner.

In many existing immersive VE systems, the usernavigates with hand-based input devices in order tospecify direction and speed as well as acceleration anddeceleration of movements [WCF+05]. Most IVEsdo not allow real walking [WCF+05]. Many do-mains are inherently three-dimensional and advancedvisual simulations often provide a good sense of lo-comotion, but visual stimuli by itself can hardly ad-dress the vestibular-proprioceptive system. An obvi-ous approach to support real walking through an IVEis to transfer the user’s tracked head movements tochanges of the virtual camera in the virtual world bymeans of a one-to-one mapping. This technique hasthe drawback that the users’ movements are restrictedby a rather limited range of the tracking sensors and asmall workspace in the real world. Therefore conceptsfor virtual locomotion methods are needed that en-able walking over large distances in the virtual worldwhile remaining within a relatively small space in thereal world. Various prototypes of interface deviceshave been developed to prevent a displacement in thereal world. These devices include torus-shaped omni-directional treadmills [BS02, BSH+02], motion footpads, robot tiles [IHT06, IYFN05] and motion car-pets [STU07]. Although these hardware systems rep-resent enormous technological achievements, they arestill very expensive and will not be generally accessi-ble in the foreseeable future. Hence there is a tremen-dous demand for more applicable approaches.

As a solution to this challenge, traveling by ex-ploiting walk-like gestures has been proposed in manydifferent variants, giving the user the impression ofwalking. For example, the walking-in-place ap-proach exploits walk-like gestures to travel through anIVE, while the user remains physically at nearly thesame position [UAW+99, Su07, WNM+06, FWW08].However, real walking has been shown to be a morepresence-enhancing locomotion technique than othernavigation metaphors [UAW+99].

Cognition and perception research suggests thatcost-efficient as well as natural alternatives exist. Itis known from perception psychology that vision of-ten dominates proprioceptive and vestibular sensationwhen different [DB78, Ber00]. Human participantsusing only vision to judge their motion through a vir-tual scene can successfully estimate their momentary

direction of self-motion but are not as good in perceiv-ing their paths of travel [LBvdB99, BIL00]. There-fore, since users tend to unwittingly compensate forsmall inconsistencies during walking, it is possible toguide them along paths in the real world that differfrom the perceived path in the virtual world. Thisso-called redirected walking enables users to explorea virtual world that is considerably larger than thetracked working space [Raz05] (see Figure 1).

In this article, we present an evaluation of redirectedwalking and derive implications for the design pro-cess of a virtual locomotion interface. For this eval-uation, we extend redirected walking by generic as-pects, i. e., support for translations, rotations and cur-vatures. We present a model which describes how hu-mans move through virtual environments. We describea user study that derives optimal parameterizations forthese techniques.

Our virtual locomotion interface allows users to ex-plore 3D environments by means of real walking insuch a way that the user’s presence is not disturbedby a rather small interaction space or physical objectspresent in the real environment. Our approach can beused in any fully-immersive VE-setup without a needfor special hardware to support walking or haptics. Forthese reasons we believe that these techniques makeexploration of VEs more natural and thus ubiquitouslyavailable.

The remainder of this paper is structured as follows.Section 2 summarizes related work. Section 3 de-scribes our concepts of redirected walking and presentthe human locomotion triple–modeling how humansmove through VEs. Section 4 presents a user studywe conducted in order to quantify to what degree userscan be redirected without the user noticing the discrep-ancy. Section 5 discusses implications for the designof a virtual locomotion interface based on the results ofthe previously mentioned study. Section 6 concludesthe paper and gives an overview about future work.

2 Previous Work

Locomotion and perception in IVEs are the focusof many research groups analyzing perception inboth the real world and virtual worlds. For exam-ple, researchers have found that distances in virtualworlds are underestimated in comparison to the realworld [LK03, IAR06, IKP+07], that visual speedduring walking is underestimated in VEs [BSD+05]and that the distance one has traveled is also under-

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estimated [FLKB07]. Sometimes, users have gen-eral difficulties in orienting themselves in virtualworlds [RW07].

The real world remains stationary as we rotate ourheads and we perceive the world to be stable evenwhen the world’s image moves on the retina. Visualand extra-retinal cues help us to perceive the world asstable [Wal87, BvdHV94, Wer94]. Extraretinal cuescome from the vestibular system, proprioception, ourcognitive model of the world, and from an efferencecopy of the motor commands that move the respectivebody parts. When one or more of these cues conflictswith other cues, as is often the case for IVEs (due toincorrect field-of-view, tracking errors, latency, etc.),the virtual world may appear to be spatially unstable.

Experiments demonstrate that subjects tolerate acertain amount of inconsistency between visual andproprioceptive sensation [SBRK08, JPSW08, PWF08,KBMF05, BRP+05, Raz05]

Redirected walking [Raz05] provides a promisingsolution to the problem of limited tracking space andthe challenge of providing users with the ability toexplore an IVE by walking. With this approach, theuser is redirected via manipulations applied to the dis-played scene, causing users to unknowingly compen-sate by repositioning and/or reorienting themselves.

Different approaches to redirect a user in an IVEhave been suggested. An obvious approach is to scaletranslational movements, for example, to cover a vir-tual distance that is larger than the distance walkedin the physical space. Interrante et al. suggestto apply the scaling exclusively to the main walk-ing direction in order to prevent unintended lateralshifts [IRA07]. With most reorientation techniques,the virtual world is imperceptibly rotated around thecenter of a stationary user until she is oriented insuch a way that no physical obstacles are in front ofher [PWF08, Raz05, KBMF05]. Then, the user cancontinue to walk in the desired virtual direction. Al-ternatively, reorientation can also be applied while theuser walks [GNRH05, SBRK08, Raz05]. For instance,if the user wants to walk straight ahead for a long dis-tance in the virtual world, small rotations of the cam-era redirect her to walk unconsciously on an arc in theopposite direction in the real world [Raz05].

Redirection techniques are applied in robotics forcontrolling a remote robot by walking [GNRH05].For such scenarios much effort is required to avoidcollisions and sophisticated path prediction is essen-tial [GNRH05, NHS04]. These techniques guide users

on physical paths for which lengths as well as turn-ing angles of the visually perceived paths are main-tained, but the user observes the discrepancy betweenboth worlds.

Until now not much research has been undertakenin order to identify thresholds which indicate the toler-able amount of deviation between vision and proprio-ception while the user is moving. Preliminary stud-ies [SBRK08, PWF08, Raz05] show that in generalredirected walking works as long as the subjects arenot focused on detecting the manipulation. In theseexperiments, subjects answered afterwards if they no-ticed a manipulation or not. Quantified analyzes havenot been undertaken. Some work has been done in or-der to identify thresholds for detecting scene motionduring head rotation [Wal87, JPSW08], but walkingwas not considered in these experiments.

Besides natural navigation, multi-sensory percep-tion of an IVE increases the user’s sense of pres-ence [IMWB01]. Whereas graphics and sound ren-dering have matured so much that realistic synthe-sis of real world scenarios is possible, generation ofhaptic stimuli still represents a vast area for research.Tremendous effort has been undertaken to support ac-tive haptic feedback by specialized hardware whichgenerates certain haptic stimuli [CD05]. These tech-nologies, such as force feedback devices, can providea compelling sense of touch, but are expensive andlimit the size of the user’s working space due to de-vices and wires. A simpler solution is to use passivehaptic feedback: physical props registered to virtualobjects that provide real haptic feedback to the user.By touching such a prop the user gets the impression ofinteracting with an associated virtual object seen in anHMD [Lin99] (see Figure 2). Passive haptic feedbackis very compelling, but a different physical object isneeded for each virtual object that shall provide hapticfeedback [Ins01]. Since the interaction space is con-strained, only a few physical props can be supported.Moreover, the presence of physical props in the inter-action space prevents exploration of other parts of thevirtual world not represented by the current physicalsetup. For example, a proxy prop that represents a vir-tual object at some location in the VE may occlude theuser when walking through a different location in thevirtual world. Thus exploration of large scale environ-ments and support of passive haptic feedback seem tobe mutually exclusive.

Redirected walking and passive haptics havebeen combined in order to address these chal-

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lenges [KBMF05, SBRK08]. If the user approachesan object in the virtual world she is guided to a corre-sponding physical prop. Otherwise the user is guidedaround obstacles in the working space in order to avoidcollisions. Props do not have to be aligned with theirvirtual world counterparts nor do they have to providehaptic feedback identical to the visual representation.Experiments have shown that physical objects can pro-vide passive haptic feedback for virtual objects with adifferent visual appearance and with similar, but notnecessarily the same, haptic capabilities, or the samealignment [SBRK08, BRP+05] (see Figure 2 (a) and(b)). Hence, virtual objects can be sensed by meansof real proxy props having similar haptic properties,i. e., size, shape and texture and location. The map-ping from virtual to real objects need not be one-to-one. Since the mapping as well as the visualizationof virtual objects can be changed dynamically duringruntime, usually a small number of proxy props suf-fices to represent a much larger number of virtual ob-jects. By redirecting the user to a preassigned proxyobject, the user gets the illusion of interacting with adesired virtual object.

In summary, substantial efforts have been made toallow a user to walk through a IVE which is largerthan the laboratory space and experience the environ-ment with support of passive haptic feedback, but theconcepts can be improved on.

3 Generalized Redirected Walking

Redirected walking can be implemented using gainswhich define how tracked real-world motions aremapped to the VE. These gains are specified with re-spect to a coordinate system. For example, they can bedefined by uniform scaling factors that are applied tothe virtual world registered with the tracking coordi-nate system such that all motions are scaled likewise.

3.1 Human Locomotion Triple

We introduce the human locomotion triple (HLT)(s, u, w) by three normalized vectors—strafe vector s,up vector u and walk-direction vector w. w can bedetermined by the actual walking direction or usingproprioceptive information such as the orientation ofthe limbs or the view direction. In our experimentswe define w by the current tracked walking direction.The strafe vector s, a.k.a. right vector, is orthogonalto the direction of walk and parallel to the walk plane.

virtualdirection

virtualrotation

virtual distance

real curve

realrotation

real distance

backpack

HMD

Figure 1: Redirected walking scenario: a user walksthrough the real environment on a different path witha different length in comparison to the perceived pathin the virtual world.

We define u determining the up vector of the trackedhead orientation. Whereas the direction of walk andthe strafe vector are orthogonal to each other, the upvector u is not constrained to the crossproduct of sand w. Hence, if a user walks up a slope the direc-tion of walk is defined according to the walk plane’sorientation, whereas the up vector is not orthogonalto this tilted plane. When walking on slopes humanstend to lean forward, so the up vector remains parallelto the direction of gravity. As long as the direction ofwalk holds w 6= (0, 1, 0), the HLT composes a coor-dinates system. In the following sections we describehow gains can be applied to the HLT.

3.2 Translation gains

The tracking system detects a change of the user’s realworld position defined by the vector Treal = Pcur −Ppre, where Pcur is the current position and Ppre isthe previous position, Treal is mapped one-to-one tothe virtual camera with respect to the registration be-tween virtual scene and tracking coordinates system.A translation gain gT ∈ R3 is defined for each com-ponent of the HLT (see Section 3.1) by the quotientof the mapped virtual world translation Tvirtual and thetracked real world translation Treal, i. e., gT := Tvirtual

Treal.

Hence, generic gains for translational movements canbe expressed by gT [s], gT [u], gT [w], where each com-ponent is applied to the corresponding vector s, u andw respectively composing the translation. In our ex-periments we have focussed on sensitivity to transla-tion gains in the walk direction gT [w].

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3.3 Rotation gains

Real-world head rotations can be specified by avector consisting of three angles, i. e., Rreal :=(pitchreal, yawreal, rollreal). The tracked orientationchange is applied to the virtual camera. Analogous toSection 3.2, rotation gains are defined for each compo-nent (pitch/yaw/roll) of the rotation and are applied tothe axes of the locomotion triple. A rotation gain gR isdefined by the quotient of the considered componentof a virtual world rotation Rvirtual and the real worldrotation Rreal, i. e., gR := Rvirtual

Rreal. When a rotation gain

gR is applied to a real world rotation α the virtual cam-era is rotated by gR · α instead of α. This means thatif gR = 1 the virtual scene remains stable consideringthe head’s orientation change. In the case gR > 1 thevirtual scene appears to move against the direction ofthe head turn, whereas a gain gR < 1 causes the sceneto rotate in the direction of the head turn. A systemwith no head tracking would result in gR = 0. Rota-tional gains can be expressed by gR[s], gR[u], gR[w],where the gain gR[s] specified for pitch is applied tos, the gain gR[u] specified for yaw is applied to u, andgR[w] specified for roll is applied to w. In our ex-periments we have focussed on rotation gains for yawrotation gR[u].

3.4 Curvature gains

Instead of multiplying gains with translations or rota-tions, offsets can be added to real world movements.Camera manipulations are used if only one kind ofmotion is tracked, for example, user turns the head,but stands still, or the user moves straight ahead with-out head rotations. If the injected manipulations arereasonably small, the user will unknowingly compen-sate for these offsets resulting in walking a curve.The curvature gain gC denotes the resulting bend ofa real path. For example, when the user moves straightahead, a curvature gain that causes reasonably smalliterative camera rotations to one side enforces the userto walk along a curve in the opposite direction in or-der to stay on a straight path in the virtual world. Thecurve is determined by a segment of a circle with ra-dius r, and gC := 1

r . In case no curvature is appliedit is r = ∞ ⇒ gC = 0, whereas if the curvaturecauses the user to rotate by 90◦ clockwise after π

2 mthe user has covered a quarter circle with radius r = 1⇒ gC = 1.

3.5 Displacement Gains

Displacement gains specify the mapping from phys-ical head or body rotations to virtual translations.In some cases it is useful to have a means to in-sert virtual translations while the user turns the heador body but is stationary at the same physical posi-tion. Hence, with displacement gains translations areinjected with respect to rotational user movements,whereas with curvature gains rotations can be in-jected corresponding to translational user movements(see Section 3.4). Three displacement gains are in-troduced: (gD[w], gD[s], gD[u]) ∈ R3, where thecomponents define the contribution of physical yaw,pitch, and roll rotations to the virtual translational dis-placement. For an active physical user rotation ofα := (pitchreal, yawreal, rollreal), the virtual positionis translated in the direction of the virtual vectors w, s,and u accordingly.

3.6 Time-dependant Gains

Up to now only gains have been presented, that definedthe mapping of real-world movements to VE motions.However, not all virtual camera rotations and trans-lations have to be triggered by physical user actions.Time-dependant drifts are an example for this type ofmanipulation. They can be defined just like the othergains described above. The idea behind these gains isto introduce changes to the virtual camera orientationor position over time. The time-dependant rotationgains are ratios in degrees/sec and the correspondingtranslation gains are ratios in m/sec. Time-dependantgains are given by gX = (gX [s], gX [u], gX [w]), whereX is replaced by T/t for time-dependent translationgains and R/t for time-dependent rotation gains.

4 Experiments

In this section we present three sub-experiments inwhich we quantify how much humans can unknow-ingly be redirected. We analyze the appliance oftranslation gT [w], rotation gR[u], and curvature gainsgC [w].

4.1 Experimental Design

4.1.1 Test Scenario

Users were restricted to a 10m × 7m × 2.5m track-ing range. The user’s path always led her clockwise

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realenvironment

HMD

backpack

proxy object

(a) Experimental setup (b) User’s perspective

Figure 2: Combining redirection techniques and dynamic passive haptics. (a) A user touches a table serving asproxy object for (b) a stone block displayed in the virtual world.

or counterclockwise around a 3m × 3m squared areawhich is represented as virtual block in the VE (seeFigure 2 (a), 2 (b) and 3). The visual representation ofthe virtual environment can be changed continuouslybetween different levels of realism (see Figure 2 (b)(insets)).

4.1.2 Participants

A total of 8 (7 male and 1 female) subjects partici-pated in the study. Three of them had previous expe-rience with walking in VEs using an HMD setup. Wearranged them into three groups:

• Three expert users (EU Group) (two of whichwere authors) who knew about the objectives andthe procedure before the study

• Three aware users (AU Group) who knew thatwe would manipulate them, but had no knowl-edge about how the manipulation would be per-formed.

• Two naive users (NU Group) had no knowledgeabout the goals of the experiment and thoughtthey had to report any kind of tracking problems.

The EU and AU group were asked to report ifand how they realized any discrepancy between ac-tions performed in the real world and the correspond-ing transfer in the virtual world. The entire experi-ment took over 1.5 hours (including pre-tests and post-questionnaires) for each subject. Subjects could takebreaks at any time.

4.1.3 Visualization Hardware

We used an Intel computer (host) with dual-core pro-cessors, 4 GB of main memory and an nVidia GeForce8800 for system control and logging purposes. Theparticipants were equipped with a HMD backpackconsisting of a laptop PC (slave) with a GeForce 7700Go graphics card and battery power for at least 60 min-utes (see Figure 1). The scene (illustrated in Figure 2(a)) was rendered using DirectX and our own soft-ware with which the system maintained consistentlya frame rate of 30 frames per second The VE was dis-played on two different head-mounted display (HMD)setups: (1) a ProView SR80 HMD with a resolution of1240× 1024 and a large diagonal optical field of view(FoV) of 80◦, and (2) an eMagin Z800 HMD having aresolution of 800 × 600 with a smaller diagonal FoVof 45◦. During the experiment the room was entirelydarkened in order to reduce the user’s perception of thereal world.

4.1.4 Tracking System and Communication

We used the WorldViz Precise Position Tracker, anactive optical tracking system which provides sub-millimeter precision and sub-centimeter accuracy.With our setup the position of one active infraredmarker can be tracked within an area of approximately10m×7m×2.5m. The update rate of this tracking sys-tem is approximately 60 Hz, providing real-time posi-tional data of the active markers. The positions of themarkers are sent via Wifi to the laptop. For the eval-uation we attached a marker to the HMD, but we also

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tracked hands and feet of the user. Since the marker onthe HMD provides no orientation data, we used an In-tersense InertiaCube2 orientation tracker that providesfull 360◦ tracking range along each axis in space andachieves an update rate of 180 Hz. The InertiaCube2is attached to the HMD and connected to the laptop inthe backpack of the user.

The laptop on the back of the user are equipped withwireless LAN adapters. We used a dual-sided commu-nication: data from the InertiaCube2 and the trackingsystem is sent to the host computer where the observerexperimenter logs all streams and oversees the experi-ment. In order to apply generic redirected walking theexperimenter can send corresponding control inputs tothe laptop. The entire weight of the backpack is about8 kg which is quite heavy. However, no wires disturbthe immersion. No assistant must walk beside the userto keep an eye on the wires. Sensing the wires wouldgive the participant a cue to orient physically, an issuewe had to avoid in our study. The user and the ex-perimenter communicated via a dual head set systemonly. Speakers in the head set provided ambient noisesuch that orientation by means of real-world auditoryfeedback was not possible for the user.

4.2 Material and Methods

We performed preliminary interviews and dis-tance/orientation perception tests with the participantsto reveal their spatial cognition and body awareness.For instance the users had to perform simple distanceestimation tests. After reviewing several distancesranging from 3m to 10m the subjects had to walkalong blindfolded until they estimated that the distanceseen before has been reached. Furthermore they had torotate by specific angles ranging from 45◦ to 270◦ androtate back blindfolded. One objective of the studywas to draw conclusions if and how body awarenessmay affect our virtual locomotion approach. We per-formed the same tests before, during, and after the ex-periments.

We modulated the mapping between movements inthe real and the virtual environment by changing thegains gT [w],gR[u] and gC [w] of the HLT (see Sec-tion 3.1).

We evaluated how these parameters can be modi-fied without the user noticing any changes. We alteredthe sequence and gains for each subject in order to re-duce any falsification caused by learning effects. Af-ter a training, period we used random series starting

user

table

1.50mt1

t2

t3

t4t0

6.00m

(a) Real setup

t1

t2t3

t4

t0avatar

block

6.00m

3.00m

(b) Virtual scene

Figure 3: Illustration of a user’s path during the exper-iment showing (a) path through the real setup and (b)virtual path through the VE and positions at differentpoints in time t0, ..., t4.

with different amounts of discrepancy between the realand virtual world. In a simple up-staircase design weslightly increased the difference each 5 to 20 secondsrandomly until subjects reported visual-proprioceptivediscrepancy–this meant that the perceptual thresholdhad been reached.

Afterwards we performed further tests in order toverify the values derived from the study. All variableswere logged and comments were recorded in orderto reveal how much discrepancy between the virtualand real world can occur without users noticing. Theamount of difference is evaluated on a four-point Lik-ert scale where (0) means no distortion, (1) means aslight, (2) a noticeable and (3) a strong perception ofthe discrepancy.

4.3 Analyses of the Results

The results of the experiment allow us to derive appro-priate parameterizations for general redirected walk-ing. Figure 4 shows the applied gains and the corre-sponding level of perceived discrepancy as describedabove pooled for all subjects. The horizontal linesshow the threshold that we defined for each subtaskin order to ensure the maximal rate of detected manip-ulations.

4.3.1 Rotation Gains

We tested 147 different rotation gains within-subjects.Figure 4 (a) shows the corresponding factors appliedto a 90◦ rotation. The bars show the amount as well ashow strong turns were perceived as manipulated. Thedegree of perception has been classified into not per-ceivable, slightly perceivable, noticeable and strongly

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gR [u ]

(a)

gT [w ]

(b)

gC [w ]

(c)

Figure 4: Evaluation of the generic redirected walking concepts for (a) rotation gains gR[u], (b) translationgains gT [w] and (c) curvature gains gC [w]. Different levels of perceived discrepancy are accumulated. The barsindicate how much users have perceived the manipulated walks. The EU, AU and NU groups are combined inthe diagrams. The horizontal lines indicate the detection thresholds as described in Section 4.3 and [SBJ+08].

perceivable. It points out that when we scaled a 90◦

rotation down to 80◦, which corresponds to a gaingR[u] = 0.88, none of the participants realized thecompression. Even with a compression factor gR[u] =0.77 subjects rarely (11%) recognized the discrepancybetween the physical rotations and the correspondingcamera rotations. If this factor is applied users areforced to physically rotate almost 30◦ more when theyperform a 90◦ virtual rotation.

The subjects adapted to rotation gains very quicklyand they perceived them as correctly mapped rota-tions. We performed a virtual blindfolded turn test.The subjects were asked to turn 135◦ in the virtual en-vironment, where a rotation gain gR[u] = 0.7 had beenapplied, i. e., subjects had to turn physically about190◦ in order to achieve the required virtual rotation.Afterwards, they were asked to turn back to the ini-tial position. When only a black image was displayedthe participants rotated on average 148◦ back. Thisis a clear indication that the users sensed the com-pressed rotations close to a real 135◦ rotation andhence adapted well to the applied gain.

4.3.2 Translation Gains

We tested 216 distances to which different transla-tion gains were applied (see Figure 4 (b)). As men-tioned in Section 1, users tend to underestimate dis-tances in VEs. Consequently subjects underestimatedthe walking speed when a gain below 1.2 was ap-plied. On the opposite, when gT [w] > 1.6 subjectsrecognized the scaled movements immediately. Be-tween these thresholds some subjects overestimated

the walking speed whereas others underestimated it.However, most subjects stated the usage of such a gainonly as slight or noticeable. In particular, the moreusers tended to careen (i.e., sway side to side), the lessthey realized the application of a translation gain. Thismay be due to the fact that when they move the headleft or right the gain also applies to corresponding mo-tion parallax phenomena. This could also be due tothe fact that vestibular stimulation suppresses vection[LT77]. This careening may result in users adaptingmore easily to the scaled motions. One could exploitthis effect during the application of translation gainwhen corresponding tracking events indicate a careen-ing user.

We also performed a virtual blindfolded walk test.The subjects were asked to walk 3m in the VE wheretranslation gains between 0.7 and 1.4 were applied.Afterwards, they were asked to turn, review the walkeddistance and walk back to the initial position, whileonly a blank screen had been displayed. Without anygains applied to the motion users walked back on av-erage 2.7m. For each translation gain the participantswalked too short which is a well-known effect becauseof the described underestimation of distances but alsodue to safety reasons, after each step participants areless oriented and thus tend to walk shorter so that theydo not collide with any objects. However, on averagethey walked 2.2m for a translation gain gT [w] = 1.4,2.5m for gT [w] = 1.3, 2.6m for gT [w] = 1.2, and2.7m for gT [w] = 0.8 as well as for gT [w] = 0.9.When the gain satisfied 0.8 < gT [w] < 1.2 userswalked 2.7m back on average. Thus, it seems partici-

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pants adapted to the translation gains.

4.3.3 Curvature Gains

In total we tested 165 distances to which we applieddifferent curvature gains as illustrated in Figure 4 (c).When gC [w] satisfies 0 < gC [w] < 0.17 the curvaturewas not recognized by the subjects. Hence after 3mwe were able to redirect subjects up to 15◦ left or rightwhile they were walking on a segment of a circle withradius of approximately 6m. As long as gC [w] < 0.33,only 12% of the subjects perceived the difference be-tween real and virtual paths. Furthermore, we no-ticed that the more slowly participants walk the lessthey observed that they walked on a curve instead of astraight line. When they increased the speed they be-gan to careen and realized the bending of the walkeddistance. This might be exploited by adjusting the cur-vature gain with respect to the walking speed. Furtherstudy could explore walking speed.

One subject recognized each time a curvature gainhad been applied. Indeed the user claimed a manipu-lation even when no gain was used, but he identifiedeach bending to the right as well as to the left immedi-ately. Therefore, we did not consider this subject in theanalyses. The spatial cognition pre-tests showed thatthis user is ambidextrous in terms of hands as well asfeet. However, the results for the evaluation of trans-lation as well as rotation gains show that his resultsin these cases fit into the findings of the other partici-pants.

5 Implications for Virtual Locomo-tion Interfaces

In this section we describe implications for the designof a virtual locomotion interface with respect to theresults obtained from the user study described in Sec-tion 4. In order to verify these findings we have con-ducted further tests described in [SBJ+08]. For typi-cal VE setups we want to ensure that only reasonablesituations where users have to be manipulated enor-mously, e. g., to avoid a collision, cause the user toperceive a manipulation.

5.1 Virtual Locomotion Interface Guidelines

Based on the results from Section 4 and [SBJ+08] weformulate some guidelines in order to allow sufficientredirection. These guidelines shall ensure that with

respect to the experiment the appliance of redirectedwalking is perceived in less than 20% of all walks.

1. Users can be turned physically about 41% moreor 10% less than the perceived virtual rotation,

2. distances can be up- or down-scaled by 22%, and

3. users can be redirected on an arc of a circle witha radius greater than 15m while they believe theyare walking straight.

Indeed, perception is a subjective matter, but withthese guidelines only a reasonably small number ofwalks from different users is perceived as manipulated.

In this section we present how the redirection tech-niques described in Section 3 can be implementedsuch that users are guided to particular locations in thephysical space, e g., proxy props, in order to supportpassive haptic feedback or to avoid a collision. Weexplain how a virtual path along which a user walksin the IVE is transformed to a path on which the useractually walks in the real world (see Figure 5 and 6).

5.2 Target Prediction

Before a user can be redirected to a proxy prop sup-porting passive haptic feedback, the target in the vir-tual world which is represented by the prop has tobe predicted. In most redirection techniques [NHS04,RKW01, Su07] only the walking direction is consid-ered for the prediction procedure.

Our approach also takes into account the viewing di-rection. The current direction of walk determines thepredicted path, and the viewing direction is used forverification: if both vector’s projections to the walkingplane differ by more than 45◦, no prediction is made.

x1

t1

t0

predicted path

avatar

z1

αv

dv

Pv

(a) Virtual environ-ment

real path

user

dr=|real path|

t1

t0

10.00m

Prαr

(b) Real environment

Figure 5: Redirection technique: (a) a user in the vir-tual world approaches a virtual wall such that (b) sheis guided to the corresponding proxy prop, i. e., a realwall in the physical space.

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s+

e-

E

Ss-

e+<(s,e)

(a)

s+

e-

Ss-

e+

<(s,e) E

(b)

s+

e-

E

S

e+

s-

(c)

s+ e-

E

Se+s-

(d)

S

Es+

e+

e-

s-

<(s,e)

(e)

Figure 6: Generated paths for different poses of start point S and end point E.

Hence the user is only redirected in order to avoid acollision in the physical space or when she might leavethe tracking area. In order to prevent collisions in thephysical space only the walking direction has to beconsidered because the user does not see the physicalspace due to the HMD.

When the angle between the vectors projected ontothe walking plane is sufficiently small (< 45◦), thewalking direction defines the predicted path. In thiscase a half-line s+ extending from the current posi-tion S in the walking direction (see Figure 6) is testedfor intersections with virtual objects in the user’s frus-tum. These objects are defined in terms of their po-sition, orientation and size in a corresponding scenedescription file (see Section 5.6). The collision detec-tion is realized by means of a ray shooting similar tothe approaches described by Pelligrini [Pel97]. Forsimplicity we consider only the first object hit by thewalking direction w. We approximate each virtual ob-ject that provides passive feedback by a 2D boundingbox. Since these boxes are stored in a quadtree-likedata structure the intersection test can be performed inreal-time (see Section 5.6).

As illustrated in Figure 5 (a) if an intersection isdetected, we store the target object, the intersectionangle αvirtual, the distance to the intersection pointdvirtual, and the relative position of the intersectionpoint Pvirtual on the edge of the bounding box. Fromthese values we can calculate all data required for thepath transformation process as described in the follow-ing section.

5.3 Path Transformation

In robotics, techniques for autonomous robots havebeen developed to compute a path through severalinterpolation points [NHS04, GNRH05]. However,these techniques are optimized for static environments.Highly-dynamic scenes, where an update of the trans-formed path occurs 30 times per second, are not con-

sidered [Su07]. Since the scene-based description filecontains the initial orientation between virtual objectsand proxy props, it is possible to redirect a user tothe desired proxy prop such that the haptic feedback isconsistent with her visual perception. Fast computer-memory access and simple calculations enable consis-tent passive feedback.

As mentioned above, we predict the intersectionangle αvirtual, the distance to the intersection pointdvirtual, and the relative position of the intersectionpoint Pvirtual on the edge of the bounding box of thevirtual object. These values define the target pose E,i. e., position and orientation in the physical world withrespect to the associated proxy prop (see Figure 6) Themain goal of redirected walking is to guide the useralong a real world path (from S to E) which variesas little as possible from the visually perceived path,i. e., ideally a straight line in the physical world fromthe current position to the predicted target location.The real world path is determined by the parametersαreal, dreal and Preal. These parameters are calculatedfrom the corresponding parameters αvirtual, dvirtual andPvirtual in such a way that consistent haptic feedback isensured.

Due to many tracking events per second the startand end points change during a walk, but smooth pathsare guaranteed by our approach. We ensure a smoothpath by constraining the path parameters such that thepath is C1 continuous, starting at the start pose S, andending at the end pose E. A C1 continuous compo-sition of line segments and circular arcs is determinedfrom the corresponding path parameters for the phys-ical path, i. e. αreal, dreal and Preal (see Figure 5 (b)).The trajectories in the real world can be computed asillustrated in Figure 6, considering the start pose S to-gether with the line s through S parallel to the direc-tion of walk, and the end pose E together with the linee through E parallel to the direction of walk. With s+

respectively e+ we denote the half-line of s respec-tively e extending from S respectively E in the direc-

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tion of walk, and with s− respectively e− the otherhalf-line of s respectively e.

In Figure 6 different situations are illustrated thatmay occur for the orientation between S and E. Forinstance, if s+ intersects e− and the intersection anglesatisfies 0 < ∠(s, e) < π/2 as depicted in Figure 6 (a)and (b), the path on which we guide the user from Sto E is composed of a line segment and a circular arc.The center of the circle is located on the line through Sand orthogonal to s, its radius is chosen in such a waythat e is tangent to the circle. Depending on whethere+ or e− touches the circle, the user is guided on aline segment first and then on a circular arc or viceversa. If s+ does not intersect e− two different casesare considered: e− intersects s− or not. If an intersec-tion occurs the path is composed of two circular arcsthat are constrained to have tangents s and e and to in-tersect in one point as illustrated in Figure 6 (c). If nointersection occurs (see Figure 6 (d)) the path is com-posed of a line segment and a circular arc similar toFigure 6 (a). However, if the radius of one of the cir-cles gets too small, i. e., the curvature gets too large, anadditional circular arc is inserted into the path as illus-trated in Figure 6 (e). All other cases can be derivedby symmetrical arrangements or by compositions ofthe described cases.

Figure 5 shows how a path is transformed using thedescribed approaches in order to guide the user to thepredicted target proxy prop, i. e., a physical wall. InFigure 5 (a) an IVE is illustrated. Assuming that theangle between the projections of the viewing direc-tion and direction of walking onto the walking planeis sufficiently small (see Section 5.4), the desired tar-get location in the IVE is determined as described inSection 5.4. The target location is denoted by pointPvirtual at the bottom wall. Moreover, the intersectionangle αvirtual as well as the distance dvirtual to Pvirtual arecalculated. The registration of each virtual object to aphysical proxy prop allows the system to determine thecorresponding values Preal, αreal and dreal, and thus toderive start and end pose S and E are derived. A cor-responding path as illustrated in Figure 5 is composedlike the paths shown in Figure6.

5.4 Physical Obstacles

When guiding a user through the real world, collisionswith the physical setup have to be prevented. Colli-sions in the real world are predicted, similarly to thosein the virtual world, based on the intersection of the

E

S

obstacle c

c+

c-

Figure 7: Corresponding paths around a physical ob-stacle between start- and endpoint poses S and E.

direction of walk and real objects. A ray is cast in thedirection of walk and tested for intersection with realworld objects represented in the scene description file(see Section 5.6). If such a collision is predicted a rea-sonable bypass around an obstacle is determined as il-lustrated in Figure 7. The previous path between S andE is replaced by a chain of three circular arcs: a seg-ment c of a circle which encloses the entire boundingbox of the obstacle, and two additional circular arcs c+

and c−. The circles corresponding to these two seg-ments are constrained to touch the circle around theobstacle. Hence, both circles may have different radii(as illustrated in Figure 7). Circular arc c is boundedby the two touching points, c− is bounded by one ofthe touching points and S and c+ by the other touchingpoint and E.

5.5 Score Function

In the previous sections we have described how a real-world path can be generated such that a user is guidedto a registered proxy prop and unintended collisionsin the real world are avoided. Actually, it is possi-ble to represent a virtual path by many different phys-ical paths. In order to select the best transformed pathwe define a score function for each considered path.The score function expresses the quality of paths interms of matching visual and vestibular/proprioceptivecues or differences/discrepancies of the real and vir-tual worlds.First, we define

scale :=

{dvirtualdreal

− 1, if dvirtual > drealdreal

dvirtual− 1, otherwise

with the length of the virtual path dvirtual > 0 and thelength of the transformed real path dreal > 0. Case dif-ferentiation is done in order to weight up- and down-

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scaling equivalently. Furthermore we define the terms

k1 := 1 + c1 ·maxCurvature2

k2 := 1 + c2 · avgCurvature2

k3 := 1 + c3 · scale2

where maxCurvature denotes the maximal andavgCurvature denotes the average curvature of theentire physical path. The constants c1, c2 and c3 canbe used to weight the terms in order to adjust the termsto the user’s sensitivity. For example, if a user is sus-ceptible to curvatures, c1 and c2 can be increased inorder to give the corresponding terms more weight. Inour setup we use c1 = c2 = 0.4 and c3 = 0.2 incorpo-rating that users are more sensitive to curvature gainsthat to scaling of distances.

We specify the score function as

score :=1

k1 · k2 · k3(1)

This function satisfies 0 ≤ score ≤ 1 for all paths.If score = 1 for a transformed path, the predicted vir-tual path and the transformed path are equal. With in-creasing differences between virtual and transformedpath, the score function decreases and approacheszero. In our experiments most paths generated as de-scribed above achieve scores between 0.4 and 0.9 withan average score of 0.74. Rotation gains are not con-sidered in the score function since when the user turnsthe head no path needs to be transformed in order toguide a user to a proxy prop.

5.6 Virtual and Real Scene Description

In order to register proxy props with virtual objects werepresent the virtual and the physical world by meansof an XML-based description in which all objects arediscretized by a polyhedral representation, e. g., 2Dbounding boxes. We use a two-dimensional represen-tation, i. e., X and Y components only, in order todecrease computational effort. Furthermore, in mostcases a 2D representation is sufficient, e. g., to avoidcollision with physical obstacles. The degree of ap-proximation is defined by the level of discretizationset by the developer. Each real and virtual object isrepresented by line segments representing the edgesof their bounding boxes. As mentioned in Section 2the position, orientation and size of a proxy prop neednot match these characteristics exactly. For most sce-narios a certain deviation is not noticeable by the userwhen she touches proxy props, and both worlds are

. . .<worldData>

<o b j e c t s number =” 3 ”><o b j e c t 0 >

5 <boundingBox><v e r t e x 0 x=” 6 . 0 ” y=” 7 . 0 ”></v e r t e x 0 ><v e r t e x 1 x=” 6 . 0 ” y=” 8 . 5 ”></v e r t e x 1 ><v e r t e x 2 x=” 8 . 5 ” y=” 8 . 5 ”></v e r t e x 2 ><v e r t e x 3 x=” 8 . 5 ” y=” 7 . 0 ”></v e r t e x 3 >

10 </boundingBox><v e r t i c e s >

<v e r t e x 0 x=” 6 . 1 ” y=” 7 . 1 ”></v e r t e x 0 ><v e r t e x 1 x=” 6 . 1 ” y=” 8 . 4 ”></v e r t e x 1 ><v e r t e x 2 x=” 8 . 4 ” y=” 8 . 4 ”></v e r t e x 2 >

15 <v e r t e x 3 x=” 8 . 4 ” y=” 7 . 1 ”></v e r t e x 3 ></ v e r t i c e s >

</ o b j e c t 0 >. . .<b o r d e r s >

20 <v e r t e x 0 x=” 0 . 0 ” y=” 0 . 0 ”></v e r t e x 0 ><v e r t e x 1 x=” 0 . 0 ” y=” 9 . 0 ”></v e r t e x 1 ><v e r t e x 2 x=” 9 . 0 ” y=” 9 . 0 ”></v e r t e x 2 ><v e r t e x 3 x=” 9 . 0 ” y=” 0 . 0 ”></v e r t e x 3 >

</ b o r d e r s >25 . . .

Listing 1: Line-based description of the real world inXML format.

perceived as congruent. If tracked proxy props or reg-istered virtual objects are moved within the workingspace or the virtual world, respectively, changes oftheir poses are updated in our XML-based descrip-tion. Thus, dynamic scenarios where the virtual andthe physical environment may change are consideredin our approach.

Listing 1 shows part of an XML-based descriptionspecifying a virtual world. In lines 5-10 the boundingbox of a real world object is defined. In lines 11-15the vertices of the object are defined in real world co-ordinates. The bounding box provides an additionalsecurity area around the real world object such thatcollisions are avoided. The borders of the entire track-ing space are defined by means of a rectangular area inlines 19-24.

Listing 2 shows part of an XML-based descriptionof a working space. In lines 5-10 the bounding box ofa virtual world object is defined. The registration be-tween this object and proxy props is defined in line 17.The field relatedObjects specifies the number aswell as the objects which serve as proxy props.

6 Conclusions and Future Work

In this paper, we analyzed the users’ sensitivity to redi-rected walking manipulations in several experiments.We introduced a taxonomy of redirection techniques

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Journal of Virtual Reality and Broadcasting, Volume n(200n), no. n

. . .<worldData>

<o b j e c t s number =” 3 ”><o b j e c t 0 >

5 <boundingBox><v e r t e x 0 x=” 0 . 5 ” y=” 7 . 0 ”></v e r t e x 0 ><v e r t e x 1 x=” 0 . 5 ” y=” 9 . 5 ”></v e r t e x 1 ><v e r t e x 2 x=” 2 . 0 ” y=” 9 . 5 ”></v e r t e x 2 ><v e r t e x 3 x=” 2 . 0 ” y=” 7 . 0 ”></v e r t e x 3 >

10 </boundingBox><v e r t i c e s >

<v e r t e x 0 x=” 1 . 9 ” y=” 7 . 1 ”></v e r t e x 0 ><v e r t e x 1 x=” 0 . 6 ” y=” 7 . 1 ”></v e r t e x 1 ><v e r t e x 2 x=” 0 . 6 ” y=” 9 . 4 ”></v e r t e x 2 >

15 <v e r t e x 3 x=” 1 . 9 ” y=” 9 . 4 ”></v e r t e x 3 ></ v e r t i c e s ><r e l a t e d O b j e c t s number=” 1 ” ob j0 =” 0 ”></ r e l a t e d O b j e c t s >. . .

Listing 2: Line-based description of virtual world inXML format.

and tested the corresponding gains in a practical use-ful range for their perceptibility. The results of theconducted experiments show that users can be turnedphysically about 41% more or 10% less than the per-ceived virtual rotation without noticing the difference.

Our results agree with previous findings [JPSW08]that users are more sensitive to scene motion if thescene moves against head rotation than if the scenemoves with head rotation. Walked distances can beup and down scaled by 22%. When applying curva-ture gains users can be redirected such that they un-knowingly walk on an arc of a circle when the radius isgreater or equal to 15m. Certainly, sensitivity to redi-rected walking is a subjective matter, but the resultshave potential to serve as guidelines for the develop-ment of future locomotion interfaces.

We have performed further questionnaires in orderto determine the users’ fear of colliding with physi-cal objects. The subjects revealed their level of fearon a four point Likert-scale (0 corresponds to no fear,4 corresponds to a high level of fear). On average theevaluation approximates 0.6 which shows that the sub-jects felt safe even though they were wearing a HMDand knew that they were being manipulated. Fur-ther post-questionnaires based on a comparable Likert-scale show that the subjects only had marginal posi-tional and orientational indications due to environmen-tal audio (0.6), visible (0.1) or haptic (1.6) cues. Wemeasured simulator sickness by means of Kennedy’sSimulator Sickness Questionnaire (SSQ). The Pre-SSQ score averages for all subjects to 16.3 and thePost-SSQ score to 36.0. For subjects with high Post-

SSQ scores, we conducted a follow-up test on anotherday to identify whether the sickness was caused by theapplied redirected walking manipulations. In this testthe subjects were allowed to walk in the same IVE fora longer period of time while this time no manipula-tions were applied. Each subject who was suscepti-ble to cybersickness in the main experiment, showedthe same symptoms again after approximately 15 min-utes. Although cybersickness is an important concern,the follow-up tests suggest redirected walking does notseem to be a large contributing factor of cybersickness.

In the future we will consider other redirection tech-niques presented in the taxonomy of Section 3, whichhave not been analyzed in the scope of this paper.Moreover, further conditions have to be taken into ac-count and tested for their influence on redirected walk-ing, for example, distant scenes, level of detail, con-trast, etc. Informal tests have motivated that manip-ulations can be intensified in some cases, e. g., whenless objects are close to the camera, which could pro-vide further motions cues while the user walks.

Currently, the tested setup consists of a cuboid-shaped tracked working space (10m×7m×2.5m) anda real table serving as proxy prop for virtual blocks,tables etc. With increasing number of virtual objectsand proxy props more rigorous redirection conceptshave to be applied, and users tend to recognize the in-consistencies more often. However, first experimentsin this setup show that it becomes possible to explorearbitrary IVEs by real walking, while consistent pas-sive haptic feedback is provided. Users can navigatewithin arbitrarily sized IVEs by remaining in a com-parably small physical space, where virtual objectscan be touched. Indeed, unpredicted changes of theuser’s motion may result in strongly curved paths, andthe user will recognize this. Moreover, significant in-consistencies between vision and proprioception maycause cyber sickness [BKH97].

We believe that redirected walking combined withpassive haptic feedback is a promising solution tomake exploration of IVEs more ubiquitously available.E.g., Google Earth or multi-player online games mightbe more useable if they were integrated into IVEs withreal walking capabilities. One drawback of our ap-proach is that proxy props have to be associated man-ually to their virtual counterparts. This informationcould be derived from the virtual scene description au-tomatically. When the HMD is equipped with a cam-era, computer vision techniques could be applied inorder to extract information about the IVE and the real

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world automatically. Furthermore, we would like toevaluate how much visual representation and passivehaptic feedback of proxy props may differ with usersnoticing.

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[Raz05] S. Razzaque, Redirected walking, Ph.D.thesis, University of North Carolina,Chapel Hill, 2005.

[RKW01] S. Razzaque, Z. Kohn, and M. Whitton,Redirected Walking, Proceedings of Eu-rographics, ISBN 1-4244-0906-3, ACMPress, 2001, pp. 289–294.

[RW07] B. Riecke and J. Wiener, Can Peoplenot Tell Left from Right in VR? Point-to-Origin Studies Revealed QualitativeErrors in Visual Path Integration, Pro-ceedings of Virtual Reality, IEEE, 2007,pp. 3–10.

[SBJ+08] F. Steinicke, G. Bruder, J. Jerald,H. Frenz, and M. Lappe, Analyses ofhuman sensitivity to redirected walking,15th ACM Symposium on Virtual Re-ality Software and Technology, 2008,pp. 149–156.

[SBRK08] F. Steinicke, G. Bruder, T. Ropinski, andK.Hinrichs, Moving towards generallyapplicable redirected walking, Proceed-ings of the Virtual Reality InternationalConference (VRIC), 2008, pp. 15–24.

[STU07] M. Schwaiger, T. Thummel, and H. Ul-brich, Cyberwalk: Implementation of aBall Bearing Platform for Humans, Pro-ceedings of HCI, Lecture Notes in Com-puter Science, ISBN 978-3-540-73106-1, vol. 4551, 2007, pp. 926–935.

[Su07] J. Su, Motion Compression for Telepres-ence Locomotion, Presence: Teleopera-tor in Virtual Environments, ISSN 1054-7460 4 (2007), no. 16, 385–398.

[UAW+99] M. Usoh, K. Arthur, M. Whitton,R. Bastos, A. Steed, M. Slater, andF. Brooks, Walking > Walking-in-Place> Flying, in Virtual Environments, Pro-ceedings of 26th annual Conferenceon Computer Graphics and InteractiveTechniques (SIGGRAPH), ISBN 0-201-48560-5, ACM, 1999, pp. 359–364.

[Wal87] H. Wallach, Perceiving a stable environ-ment when one moves, Anual Review ofPsychology, ISSN 0066-4308 38 (1987),1–27.

[WCF+05] M. Whitton, J. Cohn, P. Feasel, S. Zim-mons, S. Razzaque, B. Poulton, andB. McLeod und F. Brooks, Compar-ing VE Locomotion Interfaces, Proceed-ings of IEEE Virtual Reality Conference,ISBN 0-7803-8929-8, IEEE Press, 2005,pp. 123–130.

[Wer94] A. H. Wertheim, Motion perception dur-ing self-motion, the direct versus inferen-tial controversy revisited, Behav. BrainSci., ISSN 0140-525X 17 (1994), no. 2,293–355.

[WNM+06] B. Williams, G. Narasimham, T. P. Mc-Namara, T. H. Carr, J. J. Rieser, andB. Bodenheimer, Updating Orientationin Large Virtual Environments usingScaled Translational Gain, Proceedingsof the 3rd ACM Symposium on Ap-plied Perception in Graphics and Visual-ization, ISBN 1-59593-429-4, vol. 153,ACM Press, 2006, pp. 21–28.

urn:nbn:de:0009-6-348, ISSN 1860-2037