Poin Cloud Represenaion of 3D Shape for Laser- Plasma Scanning 3D Displa Hiroo Ishikawa and Hideo Saio Keio Universi E-mail {hiroo, saio}@ozawa.ics.keio.ac.jp Absrac- In his paper, a mehod of represening 3D shape for he laser-plasma scanning 3D displa devices using poin cloud in consideraion of hardware is proposed. A new device has been developed for 3D spaial displas. This device generaes plasma luminous bodies produced b laser-induced breakdown in midair. In his mehod, objecs are represened b poin cloud so ha he burden of he z-scanner, which conrols he posiion of he plasma, becomes ligher. Addiionall, he order of drawing 3D wireframe models can be decided in consideraion of he scanner burden. I. INTRODUCTION A new device which is able o emi plasma luminous bod in midair has been developed for a new 3D displa. When a high power laser beam is focused in a gas, ionizaion of he gas occurs. This phenomenon is called laser-induced breakdown and he ionized gas is plasma. The breakdown of air is accompanied b a bluish whie ligh emission [][]. The lighs produced b his device are observed as ligh poins such as he eamples in figure. The advanage of his device is ha ligh poins are drawn in midair wihou an screens. Kimura, Shimada, e al. have alread developed an innovaive 3D displa device Free Space Displa of Poin Cloud b Laser-Plasma, ha generaes 3D images in midair [3]. The device is improved in order o displa objecs on a larger space, and various applicaions are considered [4]. The device coninuall can generae plasma luminous bodies sequeniall using infrared one kiloherz pulse laser recenl. The posiion of plasma luminous bodies can be changed b he z-scanner. When he disance beween he plasma is shor, he scanning locus seems o be epressed b a ligh line. The plasma life span is ver shor. However, he plasma emis high inensive ligh. Therefore a plasma luminous bod can be seen abou. seconds as an aferimage, i.e. abou ligh poins can be seen simulaneousl. When he device scans an objec a inervals of abou. seconds, he sill image can be observed sabl. In order o draw an objec sabl wih hese plasma ligh poins, he number of poins has o be as few as possible. However, when an objec is represened wih fewer poins, wider gaps occur beween he plasma. The z-scanner has o be acivaed quickl o scan snchronized wih he plasma generaion a ha ime; however, here is he burden of he scanner movemen. The z-scanner canno suddenl change is scan direcion. When daa which is beond such movemen resricion is inpu, he ligh poins canno be displaed a he posiion ha we se. Therefore, we propose a mehod of epression in consideraion of he movemen resricion of he z-scanner. In his mehod, he acceleraion of he locus of he scanning becomes smooh and he change of veloci becomes slower. As he resul, he plasma gap is narrow in he par of rapid change. Furhermore, we consider he drawing mehod of 3D objecs epressed b wireframes. When an objec which is epressed wih a wireframe is drawn using sequenial ligh poins, he drawing order will be a problem. When he wireframe can be epressed as an Eulerian graph, which is a graph which visis each edge eacl once, we can draw i efficienl. When he objec isn' an Eulerian graph, however, some pah overlaps occur. Therefore we have o choose he opimized pah which is he lowes cos. We solve his problem b consideraion of he lengh of pahs and he above mehod which we propose. II. DRAWING SYSTEM The drawing ssem mechanism of he device is shown in figure. I consiss of an infrared laser generaor and a zscanner. The laser generaor coninues o creae one kiloherz Fig.. Eperimen scenes of he laser-plasma scanning 3D displa device. These picures are he resul of he previous model of he 3D displa.
pulse laser, and he z-scanner conrols he direcion of he laser beam and he disance of he focus poin. The sequenial plasma luminous bodies are coninuall generaed a he arbirar posiions in midair. When he laser scans, plasma luminous bodies are drawn on he locus of he scan head. The z-scanner is conrolled hrough a D/A converer (YOKOGAWA WE7. The WE7 convers from he inpu digial daa as 3D-coordinaes o analog daa for he z-scanner. The inpu daa represens he posiions of he plasma luminous bodies, and is inpu from a conrol compuer, for eample (.,.,., (.,.,.. The analog daa is volage. III. THE METHOD OF GENERATING DATA A. Generaing Poins Daa An objec which we r o displa has o be represened as single sroke drawing. Then he posiions of he plasma luminous bodies are sampled appropriael from he line. The mehod of sampling hem is as follows. The posiion of he poin which is moving on he single sroke drawing is epressed wih ime in (. I is assumed ha he scanner head posiion moves a equal speed, which is he size of he veloci and is scalar value, on he locus. The posiion of scanner moves a lap wih a period T. The veloci, which is he vecor, and he acceleraion of he scanner are in ( and (3. r ( ( (, (, z( ( d( d( dz( ( v, v, v,, v ( z d d d dv dv dv z a a, a, a z,, (3 d d d The eample of each graph in he case of a square is shown in figure 3 and 4. Here, z(. From hese graphs, i is found ha he veloci change and he acceleraion are high a he corners. So he acceleraion is smoohed wih a simple moving average in (4. Here, he daa is smoohed using neighbor daa whose size is w. ( a, a, a s + w / + w / a u du a u du w w / w w / w + w / w /.(4 az ( u du Afer he acceleraion is smoohed, he veloci is calculaed from he smoohed acceleraion in (5. v (, v s ( and v ( are decide so ha (6 is correc. ( v, v, v s v + a u du v + a u du v + ( ( ( a T T v d, vs d, v T.(5 ( u du d. (6 Afer his process, he acceleraion becomes smooh; however, he corner speed becomes slow. The original speed V( is in (7. The smoohed speed V s ( is in (8. The are shown in he speed graph of figure 4. I can be seen ha he disance of he laser scanning becomes shor from his graph, 6 4-6 -4 - - 4 6-4 6-6 4 posiion ime - Fig.. The drawing ssem mechanism. The 3D displa device consiss of an infrared one kiloherz pulse laser generaor and a zscanner. B conrolling he laser, plasmas are creaed a he required posiion. When man plasma luminous bodies are drawn fas enough ( poin/sec. -4-6 Fig. 3. Locus and posiion of a square. The upper graph is he locus of he scanner. The sar poin is (,-5. The lower graph is he posiions of and coordinaes of he scanner.
so ha he locus which is drawn using he smoohed speed becomes he square wih he smoohed corners. acceleraion veloci v + v + vz (7 V.5 -.5 - - ime ime a( a( a( as( v( v( v( vs( V s v + vs + v (8 Therefore, i is necessar o decide he resampling posiions of he plasma poins based on his speed change. In he speed graph of figure 4, he poin densi is calculaed from he raio of V( and Vs(, so ha he inegral value of V( equals o he inegral value of Vs( a. V(/Vs( is adoped The raio of he poin densi is shown a he lower graph in figure 4. The simulaion resul image using his raio of he poin densi is shown in figure 5. The upper image in figure 5 is he resul using he same number of poins (8 poins a equal inervals o compare wih our mehod. Various D shapes simulaion resuls are shown in figure 6. B. Drawing order for wireframes In he drawing a 3D objec which is epressed b a wireframe model; i is imporan o decide he order of drawing pahs. To solve his problem, we use a graph which is shown in figure 6. In he graph, node n i is creaed from he verices v i of he wireframe model, and edge e ij is creaed from he connecions c ij of wo verices. This is an undireced graph. An opimal roue is searched, and he roue is he order of drawing. The lengh beween verices as he cos of he edge and he angle of corner as he cos of he node are adoped as rouing cos. The following wa of deciding he order of drawing is applied o he graph which is creaed from a wireframe model..5 - speed V( Vs( ime. V(/Vs( raio raio of poin of poin densi. posiion on he ime locus of scanner head Fig. 4. Smoohing eample of a square. The op graph is he veloci; he second is he acceleraion of he scanner. The doed lines are he resul of smoohing (v, v s, a, a s,. The hird graph is he speed of he scanner. The black line is original; he gra line is he resul of smoohing, he doed line is he resul of correcing. The lower graph is he poin densi raio. Fig. 5. The epressing resul of he square. These images are displa simulaion resuls. The number of poins is 8. The upper image o compare wih our mehod is epressed a he equal inervals; he lower is epressed b our mehod.
Calculae he lengh of each edge. Calculae he angle formed b wo edges which are inpu/oupu pah of node n i. Then calculae all he angles for all he combinaions of wo edges. A each node he same process is performed. 3 Search all roues which sar from node n i and pass all edges and reurn o n i. If needed, i is allowable o pass an edge more han once. 4 Calculae he cos of he roues which are seleced 3 b (9. The coss are wo kinds, one is disance cos and he oher is angle cos. Here, L(i is he i-h lis of passed node. The n is he sar node. The n and he n Nm are he same node. The funcion d(n j,n j+ is he disance beween n j and n j+. The funcion angle(n j-,n j,n j+ is he angle which is formed b node n j-, n j and n j+. L( m ( n L n L n disance_cos angele_cos N m j N m j j d( n, n angle( n 5 Decide he roue which has he lowes cos. The disance cos is higher priori han he angle cos. If he disance cos is he same, he angle cos is compared. The angle cos is added o avoid he roue which includes acue angles if possible. Acue angles have high cos because of using a lo of ligh poins. Therefore, he roue which includes acue angles is no seleced, even if he disance cos is he same. j j+ N m j, n j, n j+ (9 The resul of he order deciding is shown in figure 8. The rouing resul is shown in able I. No. -4 of he resul are he opimal roues. No. 5-6 are he sample roues which are he same disance cos bu differen angle cos. IV. EXPERIMENTS A. Poins Daa Generaing Eperimen We generaed he posiion of poins daa for some objecs b he mehod which is proposed in III-A. The resul of drawing a square b a real device ssem is shown in figure 9. The number of plasma luminous bodies is missing, however, because hese phoograph were aken b he camera shuer speed of.5 seconds. As compared wih he equal inervals epression, he displa for he corners of he shapes are mainl differen in our mehod, so ha he sharpness of he corners can be well represened, while here is almos no error of he posiion of he plasma illuminance a oher pars. The resuls of various D shapes are shown in figure. From hese resul, i is found ha he burden of he scanner becomes ligher and he drawing resul becomes sable. Therefore, our mehod is effecive. Furhermore, in he case of square, he corner informaion is imporan for human percepion. I can be seen ha our mehod is effecive for human percepion. B. Drawing order for wireframe eperimen We eperimened o decide he drawing orders of some wireframes b he mehod which is proposed in III-B. As he resul, i is shown in figure ; i is found ha he roue which has an acue angle is avoided from an opimal Fig. 6. The resul of generaing poins. These images are displa simulaion resuls. The lef image is creaed a equal inervals of poins. The righ is creaed b our mehod. The number of poins is 8.
roue b he angle cos. Using his mehod, we can decide easil an opimal roue. V. CONCLUSION We proposed a mehod of epressing objecs in consideraion of he movemen resricion of he z-scanner of 3D spaial displa device. The effeciveness of his mehod was shown b he drawing eperimen b he real displa device ssem. I was found ha a drawing resul is sable a he same ime as he burden of he scanner becomes ligher b using his mehod. We eperimened onl for a square b he real ssem; however, we suppose ha similar resuls are achieved for Fig. 7. The eample of a graph from a wireframe model. The nodes epress he verices of he wireframe, and he edges epress he edges of he wireframe. TABLE I THE RESULT OF ROUT LIST No. Disance cos Angle cos Node lis 6 7 3 6 5 4 8 7 3 4 8 5 6 7 3 4 8 5 4 8 7 3 6 5 -.63 3 4 8 5 6 7 3 4 8 7 3 6 5 365.69 4 4 8 7 3 6 7 3 4 8 5 6 5 5 5 8 4 3 7 6 4 8 7 3 6 5 -.56 6 5 8 4 6 7 3 4 8 7 3 6 5 oher objec daa. In addiion, we suppose ha he mehod of deciding o he drawing order for a wire frame in consideraion of he z scanner resricion is effecive. In his ssem, he objec is drawn b he plasma luminous bodies which are generaed sequeniall, so ha ime lag occurs. Therefore, he number of he poins ha we can perceive simulaneousl is limied when we r o draw a large objec, and we canno recognize he objec. I can be coped b improvemen of he hardware (for eample, he plasma generaor is increased o solve his problem. B he improvemen, i will be able o draw muli objecs simulaneousl, oo. ACKNOWLEDGMENT This work is suppored in par b a Gran-in-Aid for he Global Cener of Ecellence for high-level Global Cooperaion for Leading-Edge Plaform on Access Spaces from he Minisr of Educaion, Culure, Spor, Science, and Technolog in Japan. This work is suppored in par b Core Research of Evoluional Science and Technolog program (CREST on Technolog o Displa 3D Conens ino Free Space from Japan Science and Technolog Agenc (JST. The auhors would like o hank Mr. Hidei Kimura and Dr. Daisuke Ishikawa for of he eperimens. REFERENCES [] C. De Michelis, IEEE J. Quan. Elecron, QE5, pp. 88-, 969. [] J. F. Read, Effecs of High-power Laser Radiaion New York: Academic Press, 97. [3] Kimura, H., Uchiama, T., Yoshikawa, H., Laser produced 3D displa in he air, Proceedings of Emerging echnologies SIGGRAPH 6. Boson, Massachuses: ACM SIGGRAPH, Jul 6. [4] H. Saio, H. Kimura, S. Shimada, T. Naemura, J. Kaahara, S. Jarusirisawad, V. Nozick, H. Ishikawa, T. Murakami, J. Aoki; A. Asano; T. Kimura, M. Kakehaa, F. Sasaki, H. Yashiro, M. Mori, K. Torizuka; K. Ino, Laser-plasma scanning 3D displa for puing digial conens in free space, Proceedings of Inernaional Smposium on Elecronic Imaging, Sereoscopic Displas and Applicaions XIX, 683-7, California, Januar 8. Fig.8 The resul of deciding order of drawing. The lef is one of he lowes cos orders, and he righ is one of he orders which are no seleced. The have he same disance cos, however, he angle cos is differen. The dos are sar node, and lines wih arrow are roues.
Fig. 9. The resul of displaing eperimens. These are real plasma luminous bodies. The lef is he resul of equal inervals. The righ is he resul of our mehod. These picures were aken b he shuer speed of.5 seconds Fig.. The resul of various D shapes.(shuer Speed : he lef image:/8sec,he righ image /4sec Fig. The resul of wireframe (Shuer Speed: he lef image /4sec,ohers /8sec