Virtual 3D Sculpting

Transcription

1 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. Virul D Sculping Jnis P.Y. Wong Rynson W.H. Lu Lizhung M Deprmen of Compuer Science, Ciy Universiy of Hong Kong, Hong Kong Se Key Lborory of CAD&CG, Zhejing Universiy, Hngzhou, P.R. Chin Absrc This pper presens virul sculping mehod for inercive D objec deformion. The mehod is bsed on he use of n elecronic glove. A prmeric conrol hnd surfce defined by n Open-Uniform B-Spline ensor produc surfce is firs creed o model he hnd gesure. The geomeric ribues of he objec in he Eucliden D spce re hen mpped o he prmeric domin of he conrol hnd surfce hrough Ry-Projecion mehod. By minining he disnce beween he mpped pirs, chnge of hnd gesure cn be efficienly rnsferred o conrol he deformion of he objec. 1 Inroducion Mos deformion sysems developed so fr mke use of rdiionl inpu devices. They rely grely on he skillfulness of he user o mnipule he sysem, nd hey py lile enion on he inerfce for inercion wih he objec. Mos of he mehods developed concenre on deforming free-form surfces by modifying eiher he conrol poins or he smple poins one by one. The operions become edious when hese mehods re pplied o compliced surfces hving lrge number of conrol poins. Besides, hese deformion sysems usully work wih inerfces consrined by some inermediry devices such s keybords, mice nd joysicks. These devices wih only one, wo or hree degrees of freedom re ofen ill-suied for he compliced modeling nd deformion sks such s risic sculping. In order o fcilie more inuiive inercions wihin he virul world, i is desirble o be ble o deec ll he degrees of freedom of he humn hnd by sensing individul finger moions. Therefore, we believe h he glove device is he mos nurl inercive inpu ool for objec modificion or deformion. I consiss of sensors for mesuring he movemen of ech finger. Commercil models include VPL DGlove, Virex CyberGlove TM, Mel s PowerGlove nd Exos Dexerous Hnd Mser. These gloves hve sensors h mesure he ngles of some or ll finger joins. Some of hese gloves lso work wih D rckers o loce he posiion of he user s hnd. The DGloves from VPL uses he hnd s he user s mnipulive exension ino he virul environmen [1]. By pnomiming reches nd grbs, he user cuses he hnd o rech nd grb objecs in he virul environmen, nd cn move round in he virul spce by poining in he desired direcion nd flying o he desinion by recognizing finger posures. The mjor dvnge of his model of inercion is nurlness. However, in his model, he glove funcions s lile more hn D joysick wih severl buons where lile of he dexeriy nd nurlness h chrcerize our hnds hve been explored o he modeling sks. In his pper, we propose mehod for virul sculping bsed on he use of glove device. The ouline of he res of he pper is s follows. Secion 2 compres exising objec modeling nd deformion lgorihms. Secion 1

2 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. presens some of he echniques used in our mehod in deil. Secion 4 presens some resuls from our prooype nd discusses he performnce of our mehod. Finlly, secion 5 concludes he pper nd presens possible fuure works. 2 Bckgrounds Mny echniques nd sysems hve been developed for objec modeling nd deformion. Here, we discuss some of he imporn ones nd compre heir differences. Solid modeling is minly concerned wih ssembling primiive objecs or scenes, no free-form models. An exmple is JDCAD [2]. This is sysem buil on he MR Toolki []. I inroduces inercion echniques bsed on he use of hnd-held b, which is six-degree-of-freedom D mgneic rcking device, nd keybord. Unlike he work described in his pper, he sysem is used for he creion of mechnicl componens by ssembling primiive volumes using he echnique of Consrucive Solid Geomery (CSG). Kurmnn nd Engeli in [4] proposed spil pproch for inercive modeling o suppor rchiecurl design in VR environmen. By using he mouse or oher D inpu devices, he user my inerc wih he sysem in D. This enbles he user o formule design ides in D spce. Similr o JDCAD, his sysem llows ssembling of predefined building elemens or furniure for rchiecurl design. I lso inroduces he concep of posiive (solid) nd negive (spce) volumes o spil modeling for he rchiecs o consruc design ides. This mehod is useful for oulining vgue ides during he concepul design phse where concepul decisions re mde nd mjor consrins re esblished. However, i is no suible for risic free-form deformion. Free-Form Deformion lgorihms, on he oher hnd, chnge he geomeric ribues of n objec flexibly under some resricions reled o he properies of he objec (e.g. coninuiy). The mos well known mehod for objec deformion is he Free-Form Deformion (FFD). I ws firs proposed by Sederberg nd Prry [5]. Since hen, here hs been lo of enhncemen works from he originl FFD [,7]. Bsiclly, ll of hem deform n objec by deforming he spce round i. The objec is firs embedded in or mpped o D solid lice defined by some prmeric funcion. Deformion of he objec cn hen be chieved by deforming he conrol poins of he D lice. Free-form deformion is powerful modeling echnique h cn deform surfce primiives of ny ypes or degrees. However, deforming n objec hrough mnipuling conrol poins is no inuiive o use. Direc Mnipulion of FFDs [] llows he user o move he smple poins on he objec model nd uomiclly compues he necessry lerion o he conrol poins of he FFDs. However, his echnique involves he compuion of les squres, which re compuionlly very expensive. In ddiion, he problem could be very complex when more hn one verex poin is o be moved he sme ime, nd he soluion my no be unique. Similr o oher FFDs, his echnique only ckles he modificion of conrol poins one by one. The FFD echnique hs been implemened wih n elsic inpu device which hs he sme shpe s he conrol volume ( cube) nd provides cile feedbck [9]. The D model embedded cn be deformed by deforming he cubic inpu device. Alhough he cubic inpu device provides beer inerfce, he nure of he underlying lgorihm sill hinders he nurlness of he deformion inercion. 2

3 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. Kmeym in [1] discussed rubber pd wih cile sensor shee, which cn deec user s shpe deforming cions. The sysem crees grid surfce d nd provides mehod for convering he inpu shpe d ino solid modeling form. The limiions of he mehod re h he iniil shpe of he surfce o be deformed hs o be he sme s h of he cile sensor shee, i.e. fl, nd only vericl deformion of he surfce grid is llowed. These limiions imply h he sysem hs very limied scope of pplicions nd is no suible for highly complex modeling sks like sculping. Glyen nd Hughes [11] proposed volumeric pproch for virul sculping wih D rcker. They described i s D pining sysem in which he objec is represened by voxel d. Sculping is induced by modifying he vlues in he voxel rry, similr o he pin brush funcion of pin progrm, by moving he D rcker hrough spce. The resuln voxel d is convered o polygonl surfce using mrching-cube lgorihm. The models creed re sid o be free-form nd my hve complex opology. This pproch is useful for conrolling he shpe by modifying poin or smll pr of n objec, bu no suible for globl deformions. Li e l. [12] lso described prooype sysem for creing nd ediing NURBS surfces. Insed of developing deformion sysem, heir objecive ws o provide n efficien echnique for rendering deformble NURBS surfces. Recenly, hey hve exended heir work for he rendering of ny deformble prmeric free-form surfces [1]. The Virul Sculping Mehod The min objecive of our reserch is o develop Virul D Sculping sysem o fcilie objec deformion in virul environmen wih nurl nd rel ime inercion similr o sculping in he rel world. To modify he shpe of n objec, he users my prefer o simply flex he hnd nd he fingers. Therefore, he glove device h cpures he hnd gesure by rcking finger bend ngles is believed o be he mos nurl nd he mos expressive inpu device o fcilie he sk. Here, we presen mehod for virul sculping in D spce bsed on he use of he CyberGlove TM for direc objec/surfce modeling or deformion. The min ide of he lgorihm is o mke use of he d colleced from he CyberGlove TM o cree prmeric conrol hnd surfce, which is bsiclly n Open-Uniform bicubic B-Spline ensor produc surfce. An objec o be deformed is mpped o his conrol hnd surfce by novel Ry-Projecion mehod. To improve he performnce of his mpping process, Two-Pss Projecion echnique is developed. By minining he mpping relionship beween he conrol hnd surfce nd he objec, he chnge in he user s hnd gesure cn be effecively pssed o conrol he deformion of he objec. In he following subsecions, we presen he mehod in deil..1 Deecion nd Deducion of Finger Joins Posiions In our implemenion, we hve doped he CyberGlove TM from Virul Technologies for hnd gesure inpu nd he FASTRAK sysem from Polhemus for hnd posiion nd orienion inpu. The CyberGlove TM hnd model could be considered s n riculed rigid body sysem composed of rigid bone segmens conneced by joins. A humn hnd consiss of 17 cive joins nd hs 29 degrees of freedom: 2 degrees of freedom in he hnd joins bove he wris, nd degrees of freedom in he free moion of he plm.

4 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. To idenify he d poins h define he hnd gesure, we index he d poins s J, where =,..., nd b b =,...,. The inner d poins J, b where = 1,..., 5 nd b = 1,..., 5 represen he min gesure of he hnd. The firs dimension refers o he five fingers, i.e., humb, index, middle, ring nd pinkie. The second dimension refers o he firs, second nd hird d poins of ech finger sring from he fingerip. Due o he limiions of he CyberGlove, only 5 finger join posiions cn be deermined direcly from he glove device; oher join posiions re deduced from he mesured join posiions. The sofwre librry of he CyberGlove TM provides he rnsformion mrices of he 5 riculed rigid segmens comprising he virul hnd model [14]. These mrices hold he rnsformions o successive join origins. Hence, he mrix for he coordine sysem of he nex join cn be obined by pplying he specific rnsformion mrix o he curren join poin. From hese rnsformion mrices, we cn deermine he 5 finger join poins. The CyberGlove TM we use in his work hs only 1 sensors nd i does no explicily mesure he posiions of he joins neres o he fingerips. We predic hese d poins by king ino ccoun he coupling exising beween finger join ngles θ 5 nd θ 4 shown in Figure -1(b). Experimenl mesuremens show h he generl coupling formul is of he form [15]: θ 2 5 = 1θ 4 + 2θ 4 where θ 5 is he flexion ngle of he disl join of ny of he fingers, excep for he humb nd he prmeers, 1, nd 2 depend on he hnd chrcerisics of individul users. The oher 5 d poins defining he lower plm of he hnd re deduced from he wris nd he joins neres o he wris. By using Polhemus rcker, he wris posiion nd he hnd orienion cn be obined. The firs d poin posiion of ech finger is hen se o he posiion wo-hird from he wris o he join neres o i s shown in Figure -1(). x unis x unis exended border d poins prediced fingerip d poins finger join d poins (from CyberGlove TM ) J,5 J,4 θ 5 θ 4 L 4 L deduced lower plm d poins J, θ L 2 1/ J,2 : 1/ : 2/ wris 2/ () θ (b) Figure -1 () Finger join poins nd, nd (b) he prmeers of finger. 4

5 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. Now, we hve 5 5 d poins represening he feure gesure of he hnd. We hen exend he d poins o 7 7 simply by exending he ls segmens in ech of he dimensions on he edge by x uni(s). This border pr is used o model he elsic propery of he objec. The more elsic he objec is, he smller is he prmeer x nd hence he nrrower is he border. This cn effecively preserve he coninuiy of he objec when locl modificion is pplied o i. We will explin his in deil in secion.4..2 Consrucion of he Conrol Hnd Surfce To consruc he prmeric conrol hnd surfce, we hve employed echnique clled inerpoling mehod [1]. This is o fi n Open-Uniform B-Spline ensor produc surfce ( u v ) Allocing kno vecors U= {,,,,, u, u, u,,1,1,1,1 } wo dimensions, nd u5 H b, b,, by: u nd V={,,,, v, v, v, v,,1,1,1,1 } in he v5 Resolving 9 9 unknown conrol poins P i, j, where i =,..., nd j =,...,, such h he surfce is ble o inerpole ll 7 7 d poins, b where u, v 1. Therefore,, b, b J,, some prmeric coordine ( v ) u b, b,,, m n ( u, b, v, b ) = J b = Nui ( u, b ) Nv j ( v, b ) H, i= j= P i, j (-1) u v where Nu i ( ) nd Nv j ( ) re he cubic bsis funcions priculr prmeer vlues u in U-dimension nd v in V-dimension, respecively. P, re he conrol poins of he hnd surfce h fulfil he condiion of i j inerpoling J J,, J, b. Equion (-1) cn be rewrien in he mrix form s: J J,, Nu = Nu ( u ) Nu ( u ) ( u ) Nu ( u ) P P,, P P,, Nv Nv ( v ) Nv ( v ) ( v ) Nv ( v ) To improve he efficiency of he clculion, we do no deermine he inverse of he mrices implicily. Insed, we simplify he problem by considering he ensor produc nure of he conrol hnd surfce. We firs inroduce se of inermedie conrol poins, b E, where =,..., nd b =,...,, such h: (-2) E E,, E E,, Nu = Nu Then, Equion (-2) becomes: ( u ) Nu ( u ) P ( ) ( ) u Nu u P P,, P,, (-) J J,, J J,, E = E,, E E,, Nv Nv ( v ) Nv ( v ) ( v ) Nv ( v ) The 2D inerpolion problem is now reduced o wo ses of 1D inerpolion problems. Ech rh row of Equion (-4) is 1D inerpolion problem of n isoprmeric curve C v r () v wih kno vecor (-4) 5

6 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. v {,,,, v 1, v2, v, v4, v5,1,1,1,1 } such h i inerpoles he d poins s C r ( vi ) Jr, i =. Afer solving he inermedie conrol poins E, in Equion (-4), P i, j in Equion (-) cn be solved in similr wy. b Hence, by considering he ensor produc nure of he conrol hnd surfce, he 2D inerpolion problem in Equion (-2), which represens 7 7 liner equions, is now broken down ino D curve inerpolion problems. By crefully selecing he kno vlues u nd v b h define he surfce, he sysem of equions cn be furher simplified. Recll he locl suppor properies of he B-Spline surfce h for ech d poins J, he inerior knos defining he conrol hnd surfce, here re only hree nonzero cubic bsis funcions s shown in Figure -2. i j S ( u ) N ( u ) E + N 1( u ) E 1 N 2( u ) E 2 i = i i i i+ i i+ + i+ i i+ (-5) Non-zero bsis funcion erms inernl kno l N N1 N 2 N N 4 N 5 N N 7 N u1 u2 u u4 u 5 1 Figure -2 Bsis funcions of cubic B-Spline. We pproxime he kno vlues ech d poin by he chord lengh rios beween successive d poins [17]. These rios re verged row by row nd column by column ccordingly in he wo dimensions. The inerior knos of he kno vecors re se o coincide wih he verged chord lengh rio of he d poins. As resul, he mrix of he B-Spline bsis funcions cn effecively be reduced o ridigonl mrix nd he sysem of equions cn be resolved efficienly by numericl mehods [1].. Mpping of Objec Verices o he Conrol Hnd Surfce The mpping mehod we developed is referred o s Ry-Projecion. In his mehod, we consider he objec o be deformed s embedded in he exended 2D prmeric spce of he conrol hnd surfce. To esblish he mpping, rys re projeced from poin clled he cener of projecion, P c, hrough ech of he geomeric ribues (sy objec verices), V, of he virul objec o be deformed ono he conrol hnd surfce s shown in Figure -. Wih his projecion, V in he Eucliden D spce is mpped o ( u, v) in he 2D prmeric spce of he conrol hnd surfce s shown in Figure -4. The mpping relionship remins unchnged during he deformion process. However, compuing he inersecion of ry wih prmeric surfce is compuionlly very expensive. In order o speed up hese inersecion clculions, we propose o pproxime he prmeric surfce by polygonl hnd model, which we refer o s he D ringuled hnd model. This model is consruced by ringuling he d poins J,. i j

7 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. J, Border N, Border hnd surfce d c V V b objec surfce objec verices ry inersecion poins finger join posiions P c exended join posiions Figure - Ry-Projecion. u ( b u, v ) 1 Prmeric domin v 1 y S(1,1) S u, v ) ( b S(1,) conrol hnd surfce S(,1) V S(,) Eucliden D spce z objec (verices) x Figure -4 Mpping of he spil domin of he objec surfce o he prmeric domin of he conrol hnd surfce. Recll h he hnd is modeled by ensor produc surfce inerpoling hrough hese d poins. Therefore, we esselle he surfce by joining neighboring d poins in U nd V dimensions s shown in Figure -5. This resuls in erhedron mesh wih erhedrons. Since he four verices of erhedron my no be on single plne, we furher brek ech of he erhedrons ino wo ringles. As resul, D ringuled hnd model wih 2 ringles, ri, is formed nd ech ringle is defined on plne T i, j,, i, j, T ( P N ) + d i, j, : i, j, i, j, = (-) where i =,..., 5, j =,..., 5 nd =, 1. P is ny poin on he plne T. d is he offse of he plne from he origin, nd N i, j, is he norml of he plne. i, j, i, j, 7

8 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. To deermine he inersecion of ry wih he D ringuled hnd model, we firs define ry from P c hrough verex V s: [ V P c ] I R projeced R : P = V + k (-7) where P is poin on clculed s follows: R some sclr vrible k. The ry-inersecion poin of R nd T cn be i, j, V proj d = V N i, j, i, j, + N i, j, [ ] [ ] c I V P V c I V P Since projeced ry inersecing wih one of he 2 plnes does no necessrily men h i inersecs wih he corresponding ringle in he D ringuled hnd model, clipping ess re necessry o deermine if proj V flls inside ri or no. Therefore, in he wors cse, for n objec consising of n verices, he mpping i, j, process my involve mximum of 2 n projecions, inersecion ess nd clipping operions. To minimize he number of projecions nd inersecion ess, we sepre he ry-inersecion clculions ino wo psses. In pss 1, we deermine which ringle of he D ringuled hnd model he ry inersecs. In pss 2, he ry-inersecion poin is deermined nd he prmeric coordine is ssigned ccordingly. (-) plne π N, 2D bse mesh J, (sme poin) D ringuled hnd model Figure -5 P c Two-Pss Projecion. Pss 1: Deerminion of he Inersecion Tringle To deermine he ringle h ry inersecs he D ringulr hnd model, we firs define plne π hrough he cener of he plm J, nd hving he sme norml s h of he cener of plm, N,. By ry-projecing ll 7 7 d poins ono π, corresponding 2D bse mesh on he plne is consruced s shown in Figure -5. Ech objec verex V is hen ry-projeced o π nd he ringle on he 2D bse mesh h he ry inersecs is deermined. This inersecing ringle on π indices he inersecion of he corresponding ringle on he D ringuled hnd model.

9 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. Pss 2: Deerminion of he Ry-Inersecion Poin A second ry-projecion is mde o find ou he ry-inersecion poin on he corresponding ringle of he D ringuled hnd model by solving k in Equion (-7). Aferwrds, he poin is rnsformed o he 2D locl coordine defined by he corresponding plne i, j, evlued by he brycenric coordine mehod [19]. T nd he prmeric coordine ( v) u, of he verex is.4 Sculping Trnsformion We now go ino he deil on how he objec cn be deformed. Figure - shows how he chnge of hnd gesure cn be pssed o deform he objec verices. Consider ime when n objec is mpped o he conrol hnd surfce. Le he iniil posiion of verex be V, he prmeric coordine h V mpped o by using ry-projecion be u, ) nd he corresponding mpped ry-inersecion poin on he ( v conrol hnd surfce be S ( u, v ). V cn be wrien s: [ V S ( u, v ] I V = S ( u, v ) + V S ( u, v ) ) (-) where V S ( u, v) is he vecor from S ( u, v ) o V. [ V S ( u, v ) nd V S ( u, v ) re he uni vecor nd he mgniude, respecively. ] I d Border Border S ( u b, v b) S ( u, v ) S ( u b, v b) hnd movemen V b V S ( u, v ) objec reshpe d hnd surfce objec surfce d b V b V finger join posiions mpped ry-inersecion poins objec verices Figure - Objec Verex Modificion. By he bove definiion of ry-projecion, he uni vecor [ V S ( u, v ) P c ] equls [ ] I P c S ( u, v ) I. Le d = V S ( u, v ). A ime, he relionship of V nd S ( u, v ) cn be rewrien s: [ P c S ( u, v ] I V = S ( u, v ) + d ) (-9) Here, d represens he disnce beween he mpped ry-inersecion poin, S ( u, v ), nd he objec verex, V, he ime h he mpping is esblished, i.e. ime. We minin his mpping by keeping d 9

10 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. unchnged hroughou he deformion process. Afer his relionship is esblished, deformion cn be iniied by chnging he hnd gesure i.e. S ( u, v). Le us consider he siuion ime, h he chnge of he conrol hnd surfce leds o he chnge of he ( Eucliden D coordine of S ( u, v ) o S u, v ). The sculping rnsformion for he objec verex ime cn be evlued ccordingly s [ Pc S ( u, v ] I V = S ( u, v ) + d ) (-1) Recll h he conrol hnd surfce is consruced wih border by exending x uni(s) from he edge of he finger join d. This prevens undesirble sudden chnge in he objec surfce nd minins he coninuiy he edge when locl deformion is pplied o he objec. A he border, where u, u ], u [ u 5,1], v, v ] or v [ v 5,1], we inroduce weighing funcion which is cubic Bernsein-Bézier bsis funcion, w ( u, v), s shown in Figure -7. This weighing funcion is for preserving he coninuiy of he deformion long he border nd he resul is shown in Ple 1. The corresponding sculping rnsformion he border region is given by: [ 1 [ 1 V = w u ( v ) S ( u, v ) + d [ P S ( u, v )] 1 w( u, v ) ( ) V, c I + w(u,v) (-11) u 1 u 1 u 2 u u 4 u 5 v 1 v 2 v v 4 v 5 1 v effecive region border region Figure -7 Illusrion of he Smooh Weighing Funcion w ( u, v)..5 Conrol of Sculping Region Wih ry-projecion, he sculping region cn be very flexible. We cn chnge i by chnging he locion of he cener of projecion, P c. Three possible deformion effecs cn be produced. When P c is se o infiniy in he direcion of he norml of he plm, ll he projecion rys my be considered s prllel o ech oher. This is referred o s prllel projecion nd is shown in Figure -(). The sculping [ c ] I region will be he sme size s he conrol hnd surfce. Under his circumsnce, d P S ( u, v ) V S( u, v ), nd he sculping rnsformion becomes equls V = S ( u, v) + ( V S( u, v)) (-12) Th is, V = S u, v ). This implies h he chnge of he conrol hnd surfce pplies direcly o he ( verices of he objec nd i provides similr effec of ouching nd deforming he objec. Mgnified Sculping cn be produced by seing he cener of projecion, P c, o he bck of he 1

11 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. conrol hnd surfce s shown in Figure -(). This enlrges he size of he effecive region nd mgnifies he mgniude of deformion h he hnd pssed o he objec. Ple 2 demonsres he Mgnified Sculping experimen. If he cener of projecion, P c, is se o in fron of boh he conrol hnd surfce nd he objec being deformed, Reduced Sculping is resuled nd his is illusred in Figure -(b). This will reduces he size of he effecive region nd he mgniude of he deformion. Experimenl resul for Reduced Sculping is demonsred in Ple. mpped ry-inersecion poins P c hnd surfce objec surfce objec verices P c () (b) (c) Figure - Sculping Regions: () Prllel Projecion, (b) Reduced Sculping, nd (c) Mgnified Sculping. 4 Resuls nd Discussions We hve implemened he lgorihm in C++ wih OpenInvenor nd OpenGL. We esed i on SGI Indigo 2 worksion wih 2MHz MIPS 44 CPU nd he Exreme grphics cceleror using 5 differen models. Here we show nd discuss some of he experimens. Ple 2 shows he experimen of grsping epo model nd Ple demonsres he deformion of humn fce model. Ech window shows he conrol hnd surfce, he objec being deformed nd colored cluser in he middle. There re five colored riculed sicks represening he finger segmens of he user s hnd. The red one is he humb nd he green one is he pinkie. The surfce wih colored poins disribued cross is he conrol hnd surfce. I is divided s erhedron mesh. The colored poins on he conrol hnd surfce nd he colored verices on he objec indice he corresponding mpping beween hem. (For simpliciy, only hose regions h exer deformion effec on he objec re shown.) This helps recognize he exc conrol of differen regions of he conrol hnd surfce pplied o he objec. Here, he whie poins corresponding o he border region nd oher colored poins revel he deformion conrol of he effecive region o he objec. The cluser of colored poins loced beween he conrol hnd surfce nd he objec is for esy reference only. In Ple 2, he cener of projecion is se he bck of he hnd which produces mgnifying conrol. In Ple, he cener of projecion is se in fron of boh he hnd nd he objec nd hus reducing he deformion effec exered on he objec. The upper windows of boh ples show he mpping of he conrol hnd surfce o he objec before he deformion srs nd he models re in heir iniil shpe. The lower windows show he sculping effecs induced by chnging he hnd gesure. Using our prooype sysem, we experienced sculping conrol on severl models. Ple 4 shows some of he oupu models resuled from he experimens. 11

12 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. To evlue he performnce of our mehod, we mesured he processing ime for he wo min sges during sculping. Sge 1 concerns wih he mpping of objec verices o he conrol hnd surfce. Sge 2 is he objec deformion process. Some of he performnce resuls re shown in Tble 4-1. From he ble, he performnce of sge 1 is bou.5ms per verex nd h for sge 2 is bou.5ms per verex. In ddiion, by employing he inerpolion mehod described in secion.2, he consrucion ime for he conrol hnd surfce is reduced from pproximely 1s down o below.1s. These resuls show h our mehod could provide rel ime inercive experience for objec deformion nd we believe h he new mehod is efficien enough for he sk of Virul D Sculping. Model No. of Verices Tol Time --- Sge Sge Averge ime per verex Tol Time Averge ime per verex Buon 71.5s.5ms.5s.5ms Tepo (high res.) 21 1.s.4ms.11s.55ms Tepo (low res.) 529.2s.49ms.s.55ms Apple 7.45s.52ms.5s.5ms Fce 227.s.ms.1s.55ms Tble 4-1 Performnce of he Mehod. 5 Conclusion We hve presened he Virul D Sculping mehod for inercive D objec deformion, bsed on he use of he glove device. The min ide of our mehod is o cree prmeric conrol hnd surfce defined by n Open-Uniform B-Spline ensor produc surfce, inerpoling hrough he d poins h defined he user s hnd. Ech geomeric ribue of he objec in he Eucliden D spce is mpped o he prmeric domin of he conrol hnd surfce hrough Ry-Projecion mehod. By minining he disnces of ll he mpped pirs, chnge of hnd gesure cn be effecively pssed o conrol he deformion of he objec. In ddiion, he ry-projecion mehod lso llows he size of he effecive deformion region o be chnged simply by chnging he posiion of he cener of projecion. The mjor conribuions of he new mehod cn be summrized s follows: The new mehod is one of he few h mke use of essenilly ll he degrees of freedom vilble in glove devices o conrol somehing oher hn n nimed hnd. The mehod provides wy for simulneously conrolling se of feure poins of he objec. The mehod is efficien nd cn be pplied o objecs of ny represenions. As fuure work, we re currenly developing n objec modeling nd ediing sysem bsed on he mehod developed here. The sysem is designed o llow he creion of complex objecs by siching ogeher muliple surfce pches nd he ediing of surfce properies such s colors nd exures. References [1] D. Surmn nd D. Zelzer. A Survey of Glove-bsed Inpu. IEEE Compuer Grphics nd Applicions, pp. -9, [2] J. Ling nd M. Green. JDCAD: A Highly Inercive D Modeling Sysem. Compuers & Grphics, 1(4), pp ,

13 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. [] C. Shw, M. Green, J. Ling, nd Y. Sun. Decoupled Simulion in Virul Reliy wih MR Toolki. ACM Trnscions on Informion Sysems, 11(), pp , My 199. [4] D. Kurmnn nd M. Engeli. Modeling Virul Spce in Archiecure. Proceedings of ACM Symposium on Virul Reliy Sofwre nd Technology, pp. 77-2, July 199. [5] T. Sederberg nd S. Prry. Free-Form Deformion of Solid Geomeric Models. ACM Compuer Grphics, 2(4), pp , Augus 19. [] S. Coquillr. Exended Free-Form Deformion: A Sculping Tool for D Geomeric Modeling. ACM Compuer Grphics, 24(4), pp , Augus 199. [7] H. J. Lmousin nd W. N. Wggenspck. NURBS-Bsed Free-Form Deformions. IEEE Compuer Grphics nd Applicions, pp. 59-5, [] W. Hsu, J. Hughes, nd H. Kufmn. Direc Mnipulion of Free-Form Deformion. ACM Compuer Grphics, 2(2), pp , July [9] T. Murkmi nd N. Nkejim. Direc nd Inuiive Inpu Device for -D shpe Deformion. ACM CHI 94, pp , [1] K. Kmeym. Virul Cly Modeling Sysem. ACM Symposium on Virul Reliy Sofwre nd Technology, pp , Sep [11] T. Glyen nd J. Hughes. Sculping: An inercive volumeric modeling echnique. ACM Compuer Grphics, 25(4), pp , [12] F. Li, R. Lu, nd M. Green. Inercive Rendering of Deforming NURBS Surfces. EUROGRAPHICS 97, 1(), pp. 47-5, Sepember [1] F. Li, R. Lu. Rel-Time Rendering of Deformble Prmeric Free-Form Surfces. ACM Symposium on Virul Reliy Sofwre nd Technology (o pper), December [14] VirulHnd TM Sofwre Librry Reference Mnul. Virul Technologies. [15] G. Burde, J. Zhung, E. Roskos, D. Silver nd N. Lngrn, A Porble Dexrous Mser wih Force Feedbck, Presence: Teleoperors nd Virul Environmens, 1(1), pp.1-2, [1] G. Frin. Curves nd Surfces for Compuer Aided Geomeric Design A Prcicl Guide, 4 h Ediion. Acdemic Press, [17] L. Piegl nd W. Tiller. The NURBS Book. Springer-Verlg, [1] G. Engeln-Mullges nd F. Uhlig. Numericl Algorihms wih C. Springer, pp. 9-92, 199. Ple 1 Effecs of Applying Differen Weighings he Border. 1

14 In Journl of Visulizion nd Compuer Animion, John Wiley & Sons, 11(), pp , July 2. Ple 2 Mgnified Sculping. Ple Reduced Sculping. Ple 4 Some Oupus. 14