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Workbench

MichalKoutekandFritsH. Post

DelftUniversityofTechnology

email: fm.koutek,f.h.postg@cs.tudelft.nl

Abstract. Inthispaperwepresentadierentviewofuserinteraction

withvirtualworlds.Westartfromthequestion:howcanwebringmore

naturalobjectbehaviorintovirtualenvironments?Currently,objectsin

VRapplications often behave ina veryun-natural way. Incorporation

of physical laws inthe virtual environment, together with monitoring

naturaluseractionsandbehaviorisdesirable.Wepresentsomeprinciples

ofphysicallymorerealisticbehaviorofvirtual objectsandasetofuser

input techniques suitable for semi-immersive VR devices such as the

ResponsiveWorkbench.Weintroducespringsasanewtoolforassisting

directmanipulationofobjectsinVEs.

1 Introduction

Inuser interactionwith virtualworlds,consistentand realisticbehaviorofob-

jectsisveryimportant.Wewantobjectstorespondinanaturalandpredictable

waytoouractions.ButusuallyVEobjectsareweightlessandunsubstantial,and

theymovewithoutfrictionorinertia;thisleadstoaltogether'unphysical'behav-

iorandunpredictableresponses,especiallyinsemi-immersiveenvironmentssuch

as the Responsive Workbench (RWB), where real and virtual worlds co-exist,

andshould followthesamenaturallaws.

Absenceofweightandsubstancemaysometimesbedesirablewhileinspecting

anobjectoryingthroughanenvironment.Butespeciallyinmanipulationtasks,

mechanicallyrealisticbehaviorcanhelptoachieveconsistencyandpredictability.

Awaytoprovidemechanicalresponsesfromavirtualworldisthroughhap-

tic devices [8{11].But haptic devices usually giveforce feedback through an

intermediarydevicewithalimitedrange,andtechnologyforfree-eldhapticin-

teraction,whereobjectsmaybetouchedanywhereinspace,stilldoesnotexist.

Therefore,wewanttoavoidtheuseofaforce-basedhapticinterface.

We will look for a limited set of physical properties and laws of behavior

to makeuserinteractionmorepredictable and intuitive.Wewill introducethe

conceptsofforce,inertia,gravity,contact,surfacefriction,anddampingintothe

virtualworld.Thus, wewill havetoprovideavisualinterfaceto replacedirect

force input.Wewilldothisbytheuseofspringsattached toobjects,basedon

thefollowingassumptions:

{ alinearrelation offorce with spring compression /extension isintuitively

understood and visualized by the spiraling shape of a spring. Thus, even

withoutexertingrealforce,auserhasanintuitivenotionoftransforminga

changeofspringlengthtoaforce.

(2)

dependent. Specic mass of objects should be user specied. A massless

worldcanalwaysbecreatedbysettingallmassesto zero.

{ the table top of the RWB provides a natural ground plane for objects at

rest.

{ stabilityisintroducedbyfrictionanddamping,reducingexcessiveeectsof

inputactionsonobjects,andreducingundesiredoscillations.

{ physicalcontactofobjectsisintuitivelyequivalentwithgeometricintersec-

tion,andsound canbeusedtoprovidecontactfeedback.

Wewillpropose aset ofdynamic interactionprimitiveswith objects,based

on object selection and actions such as lifting/dropping, pushing/pulling, and

throwing/catching. We hypothesize that dynamics in interaction will provide

intuitivelyconsistentandpredictablebehavioroftheobjectsinthevirtualworld,

andthatinteractivemanipulationwillthereforebeeasierandmorenatural.We

will demonstrate the utility of theconcepts from an initial implementation of

a micro-world on the RWB table top bounded by walls around, consisting of

spheresandboxeswhichcanbemanipulatedusingspringsasmanipulatorsand

dynamicsto governbehavior.

Inthis paper, we rstpresentrelated work and providean overviewof 3D

interactiontechniquesin VR.Next,wedescribesomepossibleinteractiontech-

niquesfortheResponsiveWorkbench.Weconcentrateontheuseofdynamicsin

user'sinteractions.Onthecurrentimplementation ofamicro-worldwedemon-

strate thesuggested dynamic interaction in VEs. Finally, we present areasfor

future work.

2 3D Interaction Techniques

Interactionplaysaveryimportantroleinvirtualenvironments.Muchhasbeen

published aboutinteraction techniques in VR but the questfor truly intuitive

andnaturalinteractiontechniques isstillgoingon.

2.1 Related Work

Wehavestudied interactiontechniquesused in fullyimmersive(CAVE,HMD)

and semi-immersivevirtual environments (RWB). Surveys of interaction tech-

niques for VR workbench can be found in [1{3,5]. New methods for remote

translations in immersive VE, especially the CAVE, are presented in [4], but

someofthesemethodscanbeusedontheWorkbench aswell.Inthispaperwe

will not discuss navigationproblems and we will concentrateon selection and

directmanipulation ofobjects.

Theproblemsofmechanicsanddynamicshavebeenstudiedextensivelyfrom

many dierent points of view. It is outside the scope of this paper to review

this eld.Wedo nothavetheintentionto implement afullyrealistic dynamic

manipulation system, but rather a limited set of basic physics to assist the

manipulationof objectsinVE.

(3)

physicallawshavebeenimplementedintoavirtualworld,addressingthepoten-

tialvalue ofvirtual realityforscience education. Howeverdynamic factorsare

notappliedtouserinteraction.Anotherimplementationofvirtualmechanicsis

AERO [7],which isasimulationandanimationsystemofrigidbodies.Springs

areusedinthissystemforcollisionprocessingandforelasticobjectconnection.

Elasticityanddampingfactorsarealsodiscussedinthis paper.

In the VR literature, there is not much published work on incorporating

dynamics in userinteraction. Usually,haptics isused forthis purpose, [8{11].

We introduce springs asanewtool fordirect manipulation ofobjectsin VEs.

Manypeoplehavedonelab-exercisesinphysicswithpracticalexperimentsusing

springs(eg.liftingofanobjectattachedtoaspring).Ithasbeendoneinthereal

worldwith dynamic feedback. In this paperwewill use this asa metaphor to

improvetheuser'sfeelingofmechanicsanddynamicsinvirtualenvironments.

2.2 Interaction Techniques - Overview

We begin with a brief overview of selection and manipulation techniques in

virtual environments. After that we will suggest someinnovations. As we will

focusontheRWBenvironment,navigationisoflittleimportance.Firstwewill

discussselectiontechniques, [1], [2].

Direct picking is the most intuitive and easy way of object selection when

userhastoreachanobjectwiththepointer.Whentheobjectisnotwithinthe

reachofusershandorpointeranothertechniquemustbeused.Inraycasting,a

rayshootsoutfrom user'sngersorpointer andintersections withobjectsare

evaluated.Gaze-directedselection,usercanselectanobjectbylookingatit.The

pointing techniqueallowsthe usertoselectobjectbypointingat itwithnger

orpointerandaninvisiblerayshootsoutfrombetweenuser'seyesandpointer.

Virtual hands give user the possibility to reach distant objects by extending

virtualhandsfasterthentheuser'srealhands.

Once anobjecthasbeen selected,the usercanmanipulate it [1,4].When

anobjectisoutofreach,close manipulationbringsthisobjectneartotheuser.

Popping brings adistant object into user's hands and after manipulations the

objectgoesbacktoitsposition.Copying bringsacopyoftheobjectintouser's

hands,whiletheoriginaldistantobjectfollowsthemanipulationsperformedwith

the copy.Distant manipulation allowsuser to manipulate distant objectswith

toolsat a distance. In tele-manipulation, the user manipulates distant objects

just astheywerecloseto hisbody.This techniquecanbeusedin combination

withvirtualhands.

With the slave method, the manipulated objectfollows translations of the

pointer. A disadvantage is that for largertranslations, the user must perform

a series of translate-release actions. Thestick method connects user's hand or

pointer with object by a ray - stick. The object is attached to this stick and

followstranslationsand rotations (center of rotationisthe user'shand). With

the3Dcross-hair method, theusercantranslateanobjectbydraggingtheray

ofthepointeralongoneofthecross-hairaxes.

(4)

Withtheymethod,thedirectionandthevelocityofapointerisappliedtothe

object.The throttle method usesa metaphor of amotorcycle throttle grip.By

rotatingthe pointer about thedirection of motion(the direction where points

thepointer)thevelocityofmotionisindicated.Forwardandbackwardmotions

arederivedfrom thedirectionofrotation.

Forusewithdynamicinteraction,selectionandmanipulationtechniquesmay

be adapted. We will now discuss the principles of some techniques which are

suitablefordynamicinteractionattheRWB.

3 Suggested Interaction Techniques

Beforewedescribethesuggestedtechniques,wehavetomentionthatourtrack-

ingsystem(tracker daemon)isabletomonitorandalsoevaluatemovementsof

theuser. Itcan detectwhen theuserisat rest, thestartand theend ofuser's

motion.Inaddition,somebasicgesturescanberecognized.Onthetopof this,

morecomplexinteraction techniques canbe built.A specicationofour RWB

environmentandthetrackingsystemisgiveninsection 5.1.

Wewill rstdescribeoursuggestedset of selectiontechniques for dynamic

interaction. Fornear objects we use direct picking. Fordistant objectswe use

ray casting. But if we will think of more natural selection method we should

look into the real world. How doweknow(or how doesthe arm know)which

objectwewant to manipulate? The answeris that it canbe derived from the

path of thehand, orfrom the direction of hand motion. This informationcan

beobtainedfrom thetrackerdaemonbuer. Whenwewantto graban object

we simply move our hand towards to it. This is the principle of the 'I want

this one' IWTO - method. Thepath information and current direction of the

movementofuser'shandarecombinedandinthepredicteddirectionaninvisible

rayisprojectedandintersectionswithobjectsareevaluated.Apossibleselected

candidate changes its colorand if userreally wants this object, just clicksthe

buttononthestyluspointer.Thisisanintuitivetechniquetakenfrom thereal

world,whichcanbeextendedforselectingdistantobjects.

After object selection we will now discuss object manipulation. In simple

caseswhen object iswithin reach of theuser's hand the slave method is used.

Translationandrotationareapplieddirectly totheobject.

Whenthe objectis distant, thestick method together with theray-casting

method could be used. Together with ray-casting works also the cross-plane

methodwhere theobjectisbeingtranslatedbytherayintersections inaplane

with z = const. Similar is the cross-surface method where the ray intersects

surfacesofotherobjects(eg.alandscape).

Whentheuserwantstomanipulateadistantobjectinhisworkingspace,he

cangrabtheobjectneartohimbyarecognizablegesture:afullyextendedhand

bendsin theelbowand movesinto hisworkingsphere.Thismethod workslike

amagnetonobjects.After manipulationanobject canbe releasedwithagiven

speedorsentback to itsoriginal position.Inthis wayan assembling taskcan

beperformed, when userbrings objectsinto his working space and puts them

(5)

Asdiscussedbefore,wewishto introducetheconceptsofforce,inertia,gravity,

contactand surfacefrictiontoprovideavirtualworld inwhichobjectsbehave

more naturally. Objects behave accordingto physical lawsand also the inter-

actionisphysics-based.Weareusingrelevantlawsofmechanicsanddynamics.

Basically,thethreeNewton's laws.

For objectcollisions,there areprinciples ofconservation ofmomentum and

ofenergy,andreversibleconversionbetweenkineticandpotentialenergy.

4.1 Why springs?

In VR it is just as easy to select and manipulate large and heavy objects as

small ones.This may sometimes be advantage, but it is not according to our

expectations. Therefore,wewilltrytogivetheuserafeelingofweightormass

ofobjects.

Weproposetheuseofspringsasalinkbetweenuser'shand andamanipu-

latedobject.Bythis,wecanobtainanaturalvisualfeedbackduringmanipula-

tion.Whentheuserliftsaheavyobject,thespringwillextendproportionallyto

theobject'sweight.Also,accelerationanddecelerationofthemotionwillaect

thevisiblelengthofthespring.

4.2 MethodDescription

A specic mass is assigned to each object. From the volume of an object its

mass is calculated. Tomakeobjects move, forces are needed. In our case, are

actingthe gravityforceand the force exertedby the user.Counter-actingforces

are the friction force with the surfaceand the resistance force of the air. For

stabilityadampingforceisimplemented.Weuseasimpliedimplementationof

thephysicslawsinourvirtualworld.Wewillignoreair-resistance.Wewillalso

only use static friction , when user drags an object overa surface. At small

speeds isconstant. Forsimplicity, we will onlyconsider linearmotion here-

wewill notconsider rotational motion,torques, and angularmomentum.Here

istheoverviewofthelawsofmechanicsdiscussed:

Forcelaw:f

a

=ma=m dv

dt

=m d

2

x

dt 2

Gravitylaw:f

g

=mg

Frictionforce:f

r

=N=:mg

Springforce:f

s

= kx

Dampingforce:f

d

= c:

dx

dt

Momentum: p =mv

LinearMomentum:ma= n

X

F

i

(6)

gravity acceleration, =static friction coeÆcient, k= spring constantand c=

dampingfactor.

Duringusermanipulation, aspring isattached to the center of massof an

object.Thespringconstantkis calculatedforeach objectdierently. Therest

length of the spring x

0

is also calculated automatically from the mass of an

object.Theresultisthatforheavyobjectsastrongerandlongerspringisused,

and a weakerand shorter springfor light objects. If thesame spring constant

andsamerestlengthwouldbeusedforeveryobjectitwouldhaveawrongeect

onusermanipulation.Theuserwouldhavetolifthis handveryhighforheavy

objects with the weak spring. To avoid this, everyobjecthas its own type of

spring.Suchaspringisabletoholdtheattachedobjectwithanextensionof20

% of its rest lengthx

0

. The absolute massof objectsis application dependent

and directly aects the spring constant.The dierence between the springs is

visible, see g.1. Springs are normally only visible during manipulation of a

selectedobject.

Springconstant: k = m:g

x

m

= m:g

0:2x

0

where mg= kx

m

; x

m

= 0:2x

0

Fig.1.(a)Variousobjectsanddierentsprings (b)SpringDamperSystem

4.3 Spring Damper

Toreduceoscillationsduringmanipulationwithanobjectattachedtoaspring,

wehaveimplementedaspring mass-damper system [12].

mx(t)+cx(t)_ +kx(t)=f(t)

Herem is themassof theobject,x(t) is theextension/compression ofthe

spring, f(t) is the force acting on the object only in x(t) direction, k is the

springconstantanddisthedampingfactor.

Whentheobjectisliftedintheairandhangingonthespring,wecanrewrite

themodelthis way:

mx+cx_ +kx=mg; (x=x

s +x

d )

m



x

d +c

_

x

d +kx

s +kx

d

=mg; (kx

s

=mg)

(7)

s d

sionduringthemotion.Thedierentialsystemtosolvewillthenbe:

mx

d +cx_

d +kx

d

=0; x(0)=x

0

; x(0)_ =v

0

More about solutions can be found in [12]. The damping factor plays a

veryimportantrole.Itsvalueisderivedinasimilarwayasthespringconstant,

so that everyobject has its spring and damper. Damping refersto an energy

dissipation mechanism, either intentional or parasitic, such as air friction or

structuraldamping.Thedamperistheenergydissipatingelementofthesystem.

The damping factor measures the ability to damp themotion of the mass. In

g.2,theeect ofthedampingfactorcanbeobserved.

Fig.2.Dampingexamples

4.4 Spring Manipulation Techniques

An objectcan bemanipulated using aset oftechniquesasdescribed below. A

spiralspring isused asahandle, and theobjectwillshowitsmassandinertia

byitsbehaviouraccordingto thelawsofdynamics.

Theactionsareperformedby selectinganobjectbymovingthestyluspen

towardsit,theIWTO method,see section 3.Ataclosedistance, aspring will

bedisplayed betweenthe objectand the user's hand position.Thespring can

beextended orcompressedby keepingthepen buttondepressedwhile moving

thepentowardsorawayfromtheobject.

Virtual forces are thus applied by the user to objects through the virtual

springs, which act as displacement-to-force transducers. The user will see the

extensionorcompressionofaspring,andforcesareinferredbythelinearrelation

of displacementand force. The springconstantsare calculatedas describedin

section 4.2. Theforces maybeexerted onanobjectin anarbitrarydirection.

Theyareassumedtoworkontheobject'scenterofmass,andthustheforceswill

induceonlylinearmotion,andnorotation,asnotorquesareinduced.Thiswas

doneforpracticalreasonsonly.Thelawsgoverningrotationalmotion,torques,

andangularmomentum areverysimilartothose forlinearmotion,andwill be

incorporatedlater.Althoughfrictiononthegroundplanecaninducetorquesand

rollingmotions,these eectsareignoredin thecurrentversionofthesystem.

Theexertedforces are decomposed into liftingforces (perpendicularto the

groundplane),anddraggingforces(paralleltothegroundplane).Toensureeasy

(8)

critically, which means that motion will essentially stop after one cycle. For

clarity,theobjectsareassumedheretorestonthegroundplane,althoughother

horizontalplaneswillhavethesameeects.

Fig.3showsthethree cases:lifting, pullingandpushing. Userexertsaforce

f

u

which is unknown. From the change of extension of the spring x

1

we can

obtainthespringforceF

s

whichmakesobjectattachedtothespringaccelerate

andmove.

Fig.3.Springmanipulationcases

Theset ofdynamicmanipulationtechniquesisdened asfollows:

{ lift:pullthespringupward,untilthespringforceexceedstheobject'sweight,

andthe objectgets anupwardacceleration,counter-acted bythe decrease

on the force caused by the shortening of the spring length. Oscillation is

damped.

{ drop:theobjectisreleasedfromthespringconnectionandfallsdownuntil

ittouchesthegroundplane.

{ pull: pull the spring in a horizontal direction away from the object until

theforceexceedsthestaticfrictionoftheobjectonthegroundsurface.The

object gets a horizontal acceleration and slides over the surface, counter-

actedbyfrictionforce, and thedecreasingforce from theshortening ofthe

spring.

{ push:thesameaspull,but thespringiscompressedtowardtheobject.

{ throw: theobjectreceivesthe initial velocity from theuser's hand and is

thrownin the givendirection,the springdisappears. Thetrajectory ofthe

objectin theairisthenonlyinuencedbythegravityforce andtheobject

isfallingtotheground.

{ catch: stoptheobjectmotionbyblockingit'smotionpath.Thespringbe-

tweentheuser'shandandtheobjectiscompressedandtheobjectdecelerates

andstopsmoving.Oscillationsareagaindamped.

{ swing: acombination oflift-pull-drop.The object behavesasapendulum

onthespring;theswingingmotionisdamped,theobjectismovedthrough

intheair,andisdroppedatthechosenposition.

(9)

motiondata from thetracker.With dropping thepenbutton is releasedwhile

the user's hand is at rest, for throwing the user releasesthe button while the

handismoving.Catchingyingobjectscanbedonebypositioningthehand to

blockthemotionpathandpressingthebutton.

Wherever spring actions are performed (too) far from the user's body, a

'shingrod'techniquecanbeusedtoattachandmovethespringandtheobject.

4.5 Collisions and Constraints

Fornaturalbehaviorin virtualenvironments,thecollisionsand constraintsare

essential.Ofcourse,wecannotstopuser'shandtomovethroughobjects.Butwe

can disableusermanipulation ofanobjectthroughanotherobject.Wecanuse

hereagaintheadvantagesofthe springmanipulation.Themanipulated object

willstayattheplaceofcollisionwiththeotherobject(seecollisionwithawall,

Fig.4) whileuserisstilltryingtopull.Inthiscase,thepullingwillonlyaects

thelengthofthespring,andnomotionisinduced.

Fig.4.Collisionwiththewall

Thebasicconstraintisthegroundplane.Noobjectcangetthroughit.The

groundcanalwaysproduceenoughnormalforce to supportanyobject. Calcu-

lation ofcollisionswiththegroundis thebasicattributeofourmini-world.We

alsohandle collisionsbetweenobjectsinside theworld(spheres,boxes). Elastic

collisions are simulated. We use there the lawof momentum conservation and

thelawofenergyconservation.

5 Experimental Application

Totesttheconceptsofthispaperwehaveimplementedanexperimentalapplica-

tionwhereusercanperformdynamicspringmanipulationwithvirtualobjectsin

amini-world.Themini-worldconsistsofseveralboxesandspheres,surrounded

bywalls,seeFig.5.ThebasicconceptoftheRWBisthattheuserisstandingin

therealworld,wherethephysicallawsapply,andispartlyimmersedinthevir-

tual mini-world which is projectedon theResponsiveWorkbench. Finally, the

user can also observe a visual feedback of dynamic behaviour of manipulated

objects.

(10)

5.1 RWB Environment

TheVRsystemwhichweareusingisbasedontheSGIONYX2,with4xMIPS

R10000,1xIR2graphicspipeandastereoprojectiontable.Forimplementation

wehave used C++, Iris Performer and OpenGL. Our ResponsiveWorkbench

is equipped with aFastrak[13] trackingsystem, to trackthe position and the

orientation of user's head and hand (stylus pointer). A Tracker daemon reads

periodicallyatarateof50Hz thetrackingdataandstoresthem inabuer.

Velocity and accelerationvectorsof the user's hand are calculated.During

our experimentswehavedone measurements onthe trackerdata, g.6. These

dataareusedtogetherwithtimeinformationforcalculationofthespringforce

andforthesimulationofthespring-dampersystem.

0 5 10 15 20 25 30 35

Time samples -49.5594

0.4406 50.4406 100.4406 150.4406

cm

Legend Lifting

x y z

0 5 10 15 20 25 30

Time samples -106.0479

-56.0479 -6.0479 43.9521 93.9521

cm

Legend

Throwing

x y z

Fig.6.Trackerpositionsduringlifting andthrowingmanipulations

5.2 Dynamic ManipulationExamples

Thegures7and8,illustrateaprocedureofdynamicmanipulationofanobject

in themini-world.Onthese pictures,asimplemanipulationtask isperformed:

1)liftingoftheobject,2)translationalmotionintheairand3)droppingofthe

object.Whiletheobjectisin theair,thereisalsoaswingingmotion.

Ingures 9, 10and 11, we show somepictures taken of theactual system

implementedintheRWBenvironment.

(11)

Fig.8.Movinganddroppingofobject

Fig.9.RWB-overview:thedynamicmanipulationwithobjectsinthemini-world

6 Conclusions and Future Work

We have developed a scheme for introduction of dynamic object behaviourin

manipulationofobjectsinvirtualenvironments.Initialresultshaveshownthat

object'sbehaviourappears morenaturaland predictable thanthe 'unphysical'

objectsin mostvirtualenvironments.Also,it seemsthat thedynamicsgivesa

coherent'lookandfeel'toa3Ddirectmanipulationuserinterface.Wecaneasily

dene a long list of extensions for future work in this area. The set of basic

user operations will have to be extended, especially if we want to introduce

rotational motions. The numerical computations for dynamic simulation can

becomeverycomplex,andmayputseriouslimitsonperformance.Bothaccuracy

(12)

and geometric constraint maintenance should beintegrated. A problem which

needs attention is th dierence in direction between the gravity elds in the

virtualandrealenvironment,dueto theangleoftheRWB'stable top.

Fig.10.RWB-detail:Liftingofasphere Fig.11.RWB-detail:Draggingofabox

References

1. R. vande Pol, W. Ribarsky,L. Hodges, F. Post, Interaction Techniques on the

Virtual Workbench, Proc. of Eurographics Virtual Environments '99 workshop,

Springer,Vienna1999.

2. D. Bowman, D. and L. Hodges, An evaluation of Techniques for Grabbing and

ManipulationRemote Objects inImmersiveVirtualEnvironments,Symposiumon

Interactive3D Graphics,1997.

3. L.D. Cutler, B. Frohlich, P. Hanrahan, Two-handed Direct Manipulation on the

ResponsiveWorkbench,SymposiumonInteractive3DGraphics,1997.

4. J.D.Mulder,RemoteObjectTranslationMethodsforImmersiveVirtualEnviron-

ments,Proc.ofEurographicsVirtualEnvironments'98,Springer,1998.

5. D.Bowman,L.Hodges,UserInterfaceConstrainsforImmersiveVirtualEnviron-

mentApplications,Proc.ofIEEEVRAIS,1997,pp.35-38.

6. C.Dede, M.C.Salzman,R.B.Loftin,The development of avirtual worldforlearn-

ing newtonian mechanics, Multimedia, Hypermedia, and Virtual Reality,Berlin:

Springer/Verlag,1996,pp.87-106

NewtonWorld: http://www.virtual.gmu.edu/newton.htm

7. H. Keller, H. Stolz, A. Ziegler, T. Braunl, Virtual Mechanics - Simulation and

AnimationofRigidBodySystems,1996.

Aero:http://www.ee.uwa.edu.au/ braunl/aero/

8. T.M. Massie,J.K. Salisbury,The phantomhaptic interface:A device for probing

virtual objects, Proc. of ASME Haptic Interfaces for Virtual Environments and

Teleoprator Systems,p:295-301,1994.

9. D.C. Ruspini, K.Kolarov, O.Hatib,The haptic display of complexobjects, Pro-

ceedingsofACMSIGGRAPH'97,pages345-352,1997.

10. J.M.Brown,J.E.Colgate,Physics-basedApproachtoHaptic'sDisplayProceedings

ISMCR'94,TopicalWorkshoponVirtualReality,HoustonTX,1994.

11. GrigoreC.Burdea,ForceandTouchFeedbackforVirtualReality,PublishersCity,

ISBN0-471-02141-5,1996.

12. http://links.math.rpi.edu/devmodules/mechanicalosc/springmass/

13. http://www.polhemus.com/ftrakds.htm

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