XVIII IMEKO WORLD CONGRESS Merology for Susinle Developmen Sepemer, 17 22, 2006, Rio de Jneiro, Brzil SCANNING OF FREE-FORM SURFACES BY USING A LASER-STRIPE SENSOR ON A CMM Fernández, P. 1, Álvrez, B. J. 1, Rico, J. C. 1, Blnco, D. 1, Vliño, G. 1 Universiy of Oviedo, Gijón, Spin, jcrlosr@uniovi.es Asrc: This reserch presens working mehodology for developing n uomic plnning sysem of he scnning process of free-form surfces. The surfce hs een modelled using STL form, h permis he uomic recognizing of ny ype of surfce. This work does only consider collision-free orienions h gurnee he visiiliy of he zone o scn nd h re compile wih he consrins imposed y he process prmeers. To speed up he clculion of hese orienions, differen mehods like ck-fce culling nd spce priioning echniques, such s kd-rees, re pplied. Once he spce occupied y he pr is priioned in regions, recursive ry rversl lgorihms re used in order o check for inersecion exclusively he pr ringles (STL h cn poenilly e rversed y ech lser em direcion. Keywords: scnning, lser, CMM 1. INTRODUCTION In recen yers, no conc scnning echniques sed on lser sysems hve supposed n enormous progress [1]. Alhough i is no ye very exended, his echnique provides high speed for poin cquisiion h llows for oining housnds of poins per second. The ime reducion is exrordinry nd consequenly lso he coss ssocied o he inspecion process, minly compred o oher rdiionl conc-ype mehods. Alhough i is rue h some compnies use his scnning echnique lredy, he mjoriy do i mnully, eing he operor who decides ou he elecion of he process prmeers nd he working mehodology o follow. Consequenly, he scnning resuls hve no he expeced quliy nd i is difficul o reproduce idenicl process condiions, even when he scnned prs re idenicl or wih similr chrcerisics. For his reson, here re lo of reserch effors mde in order o nlyse he influence of he prmeers in lser scnning sysems, such s he deph of view nd he view ngle [2] or in order o develop echniques for compensing he chrcerisic errors of his scnning echnology [3]. Oheeserch hs minly focused on he phse of reconsrucing he scnned surfces from clouds of poins [3, 4] nd only few of hem hve pproched he generl prolem of scnning process plnning [5-7]. Fig. 1. Prmeers of he digiizing lser sysem The im of his work is o develop mehodology for 3D scnning of free-form surfces y using CMM. This mehodology hs relion no only wih he surfce geomery or he scnning phs u lso wih he opiml orienion of he scnning sensor nd he process prmeers (lser inensiy, deph of view, disnce eween lser sripe, ec.. Wih ll his informion, i will e possile o define he opiml working sregy for scnning cerin surfce. As consequence, higher quliy resuls re chieved in lower process ime 2. CHARACTERISTICS OF LASER SCANNING SYSTEMS In lser scnning sensors lser sripe of known widh is projeced ono pr surfce nd he refleced em is deeced y CCD cmer. By mens of imge processing sed on ringulion mehod, 3D coordines of he surfce poins re cquired. Fig. 1 shows he min prmeers of he lser sysem used in his work (LC-50 y Meris. Apr from hese prmeers, lser scnning sensor like he one menioned ove fixes he disnce eween lser sripes, he disnce eween poins wihin ech sripe nd he overlp zone eween sripes. To crry ou he scnning process i is necessry relive movemen eween he lser sysem nd he surfce. This movemen consis no only on liner nd/or ngulr displcemens u lso on orienion chnges of he lser hed or he surfce. Hence, he lser sysem used in his work hs een inslled in he moorised hed of CMM (Glol Imge of Brown&Shrpe. This wy, hree possile
liner displcemens (X, Y, Z re ville in cominion wih wo roions (A, B of he mchine hed (PH10MQ. Since he hed orienion chnges re discree (7.5º, 720 differen orienions of he lser sysem cn e chieved wih regrd o he scnning surfce. opiml lser inensiy nd perpendiculr orienion of he hed (wihou sured poins. ( Inerference of he lser em ( Inerference of he refleced lser em Fig. 3. Possile lser inerferences wih he surfce Fig. 2. Experimen for deermining he limi view ngle 3. CONSTRAINTS FOR POINT SCANNING Some of he prmeers shown in Fig. 1 re considered s consrins for scnning poins on surfce. Some of hem re imposed y he sysem mnufcurer wheres oher my e conrolled y he user. Among he conrolled prmeers, he lser em inensiy nd he lser hed orienion snd ou. Influence of lser inensiy in he scnning resuls hs een nlysed y mens of severl experimens. For insnce, i hs een proved h he lser inensiy hs o e deque o he colour of he scnned surfce. This wy, drk coloured surfces need higher inensiy. Moreover, i hs een demonsred h he dispersion rnge of poins over he heoreicl surfce increses wih lser inensiy. In relion o he hed orienion, his ffecs direcly he view ngle, which deermines he zones of he scnned surfce h cn or no e cquired depending on is greer or smller inclinion. The numer of poins cquired hs een considered s crierion o deermine if n orienion is eer hn ny oher. The experimen ws sed on digiizing he sme plnr surfce vrying he A ngle of he lser hed orienion. The higher numer of poins cquired hs een reched for A=0º nd B=0º, regrdless he lser inensiy used. Th is, when he hed is perpendiculr o he surfce. As he hed direcion chnges wih regrd o he surfce, i will e necessry higher inensiy o keep cquiring high numer of poins. This wy, n orienion (limi view ngle for which lser hed does no cquire poins cn e found. Anoher experimen hs een crried ou for deermining he limi view ngle (Fig. 2 y using plnr surfce, in which is inclinion hs een incresed unil no poins were cquired in he enire field of view (FOV. The limi view ngle ws found o e 60º for whie surfce wheres his vlue cn chnge for oher colours. For insnce, he limi view ngle of mellic surfce will scrcely e 15º for n Besides, here re prmeers h cn no e conrolled y he user nd hey re imposed y he equipmen mnufcurer, such s he ringulion ngle. This ngle is mesured eween he inciden nd he refleced lser ems. None of hese lser ems mus inerfere wih he pr o mke possile he cquisiion of poins (Fig. 3. For deermining he ringulion ngle, he device shown in Fig. 4 hs een used. During he scnning of he lower surfce (guge lock, n occlusion zone ppers where he CCD sensor cnno cquire poins ecuse n inerference eween he refleced lser em nd he pr occurs. The ringulion ngle mesured ws found o e ou 25º. There exis severl oher influence fcors such s roughness nd reflecnce of surfce nd mien illuminion h hve no een considered in his work. 4. SCANNING METHODOLOGY The opiml em orienion in lser scnning of surfce is perpendiculr o his surfce, s i occurs in conc inspecion. Alur del resle (mm Longiud de l Zon de Oclusión (mm 10 4,6 20 9,3 30 13,9 40 18,6 Fig. 4. Experimen for deermining he size of he occlusion zone Due o he shpe of free-form surfces, differen poins my e ssocied o differen norml direcions. In order o evlue hese direcions previous surfce discreizion hs een crried ou y mens of he STL model. This form represens he surfce y se of plnr ringles whose verices nd uni norml vecors re known. This simplificion of he surfce is suile for scnning sks
nd i is less compuing ime consuming. This wy, ech ringle cn e considered ssocied o significn poin of he surfce nd he uni norml vecor of he surfce (ringle his poin cn e oined. Since he opiml orienion of he lser hed is perpendiculr o he scnned surfce, he proposed mehodology dels wih deermining he opiml lser hed orienions h re closes o he norml direcion of ech ringle (uni norml vecor n r. However, here cn exis lser hed orienions, non-opiml, h lso llow for scnning he surfce correcly. In oh cses, for hed orienion l r o e considered s vlid, he consrin imposed y he limi view ngle mus e ken ino ccoun. The mesured limi view ngle ws found o e ou 60º. In generl, spce clled locl cone h includes he vlid lser hed orienions for ech ringle of he discreized surfce cn e defined. The direcions of he locl cone mus sisfy he nex condiion: cos 60º < l n 1 (1 Even so, hese orienions l r of he locl cone of ech ringle my inerfere wih oher ringles of he discreized surfce (Fig. 3. Therefore, for deermining if n orienion l r is vlid, he nex condiion mus e checked: r l F i = (2 where F i is ny ringle of he discreized surfce. Moreover possile occlusion zones due o inerference eween he refleced lser em l r ' nd he pr mus e checked (Fig. 3. To crry ou his verificion, he ringulion ngle (25º oined in he experimen of he previous secion hs een used. Similrly o he direcion l r, direcion l r ' of he refleced lser em will e vlid if he nex condiion is sisfied: r l F i = (3 Orienions of he locl cone h sisfy he condiions (2 nd (3 will e wihin more resriced spce clled he glol cone. This nlysis procedure mus e repeed for ech ringle of he STL. The compuion of GAC is complex nd expensive from compuionl poin of view, ecuse i involves he clculion of muliple inersecions. In order o ccelere he compuion, ck-fce culling lgorihm h reduces he numer of ringles o sudy in he glol ccessiiliy nlysis hs lso een implemened. Thus, from he iniil ringulrized model W, suse W is exrced h do no include hose ringles whose visiiliy ccording o n nlysed lser em direcion is compleely locked y oher ringles. In prcice, he idenificion of fces h will e wihin W will e crried ou verifying he ngle eween he fce norml nd he lser em orienion. If his ngle is greer hn π/2, i is necessry o deermine if here is inerference eween fce nd lser em. Oherwise, he fce will e discrded for he glol nlysis of h lser em orienion. V 0 P 0 Fig. 5. Inersecion eween lser em l r nd ringle fce V 0V 1V 2 4.1. Inersecion eween ringulr fces nd inciden/refleced lser em orienions By using he STL form ssocied wih he CAD model of he pr, he fces will e ringles whose verices V 0, V 1 y V 2 nd uni norml vecor n r re known. Firsly, he implemened lgorihm deermines if here exis inersecion eween ech inciden lser em orienion l r nd ll he ringles h consiue he pr oundry. If he nex equion (Fig.5 is sisfied: n l = 0 (4 he orienion will e prllel o he supporing plne of he ringle nd herefore here will e no inersecion. If oh he expression (4 nd he nex condiion re sisfied: n w = 0 (5 hen he lser em orienion will e conined in he plne nd here will no e inersecion eiher. If none of he previous relions is fulfilled, hen here is inersecion eween he inciden lser em nd he supporing plne of he ringle. The inersecion poin P i cn e expressed s: n w r Pi = P0 l (6 n l Finlly, i is necessry o check if his poin P i lies wihin he ringle defined y he hree verices V 0, V 1 nd V 2. This verificion is sed on he lgorihm developed y Möller nd Trumore [8]. From he equion of he supporing plne of he ringle V 0, V 1 nd V 2 : V ( s, = V + s u + v (7 0 poin P i loced on h plne will e wihin he ringle if here exis vlues s i nd i h sisfies he nex equion: P V = s u + v (8 i 0 i i where si 0, i 0 nd si + i 1. The vlues of he prmeers s i nd i cn e deermined from he following expressions: Pi V 2 V 1
s i i = = ( u v ( ri v ( v v ( ri u ( u v 2 ( u u ( v v (9 ( u v ( ri u ( u u ( ri v ( u v 2 ( u u ( v v (10 If he poin lies wihin he ringle hen here will e inersecion nd he nlysis will coninue wih noher ringulr fce. Oherwise, similr verificion mus e done for he refleced lser em orienion. If here is sill no inerference, he lser em orienion (inciden nd refleced will e considered s vlid. 4.2. Inersecions sed on kd-rees The use of spce priioning srucures like kd-rees llows foeducing he numer of inersecion ess. I implies he inersecion esing exclusively wih fces h cn poenilly e rversed y ech lser em orienion (inciden nd refleced. The pr is priioned in regions ounded y plnes nd ech pr fce is ssigned o he region wihin which i is loced. Then, regions rversed y ech lser em orienion re seleced nd only inersecions eween his orienion nd he fces included in hese regions re esed. B A D F H C B E F I H D Fig. 6. Kd-ree represenion of he spce priioning This ype of lgorihms re similr o hose of inry spce-priioning (BSP ree ype developed y Fuchs, Kedem nd Nylor for clculing he visiiliy of group of ojecs from n rirry poin of view [9]. In he kd-ree cse, he division of pr in regions (ounding oxes is crried ou y mens of xis-ligned spliing plnes. This wy, equions of hese plnes re simplified nd consequenly, he clculions of possile inersecions. For deermining he posiion of he spliing plnes, he crierion chosen ws o divide successively ech region in wo regions of he sme size. Regrds o he spliing sequence, he xis-ligned plne h is norml o he greer dimension of he region is lwys chosen in firs plce. The priion of he pr ino successive regions cn e represened y inry ree whose roo node snds for he G I region h encloses he pr compleely (Fig. 6. Inernl ree nodes re regions oined in furher priions nd lef nodes represen regions ino which he pr is finlly divided. Along wih he ssocied region, ech node of he ree sores informion ou he fces included, he plne h will e used for is furher priioning, nd references o is children. The numer of pr sudivisions is equivlen o he numer of levels or deph of he ree. 4.3. Kd-ree rversl Once kd-ree hs een uil i is necessry o pply n lgorihm for idenifying he sequence of lef nodes h re inerseced y ech lser em orienion. This lgorihm is clled ry rversl lgorihm nd ws firs developed nd pplied o BSP ree y Kpln [10]. (1 (2 (3 priion plne Fig. 7. Possile inersecion cses eween he lser em nd he regions deermined y spliing plne The lgorihm chosen in his pper corresponds o vrin of he lgorihm developed y Kpln. In priculr, n lgorihm of recursive ype (recursive ry rversl lgorihm hs een pplied. When ry (lser em orienion eners n inerior node (region of he kd-ree, which hs wo child nodes, he rversl lgorihm decides if oh of hem re o e rversed y he ry nd in which order. According o he posiion of he origin of he ry wih regrd o he spliing plne, he lgorihm clssifies he child nodes of he curren inerior node of he ree s ner node nd fr child nodes. When he ry rverses only he ner child node, hen he lgorihm descends o his node nd recurses pplying iself o his new node. When he ry hs o visi oh child nodes, hen he lgorihm sves he informion ou he fr child node nd descends o he ner child node o repe he checking process. When no fce is found o e inerseced inside he ner child node, he fr child node is rerieved nd he lgorihm srs h fr child node gin. In order o deermine if he ry only rverses he ner child node or oh child nodes, he lgorihm compres he signed disnces from he origin of he ry o he spliing plne ( nd o he enry ( nd exi ( poin of he ry wih regrd o he node (Fig. 7. When he rversl of he ree reches lef node, he lser em orienion is checked for inersecion wih he fces inside h node. If inersecion exiss, his orienion is considered no vlid. Oherwise, i will e necessry o (4
nlyse he inersecion of he orienion wih he res of he nodes h i rverses. A lser em orienion (inciden nd refleced will e vlid if here is no inersecion wih ny fce conined in he nodes h i rverses. Then, in order o reduce he numer of sensor orienions i will e necessry o check if here exis les one direcion h llows for complee scnning of he surfce. This wy, one or more lser hed orienions common o ll glol cones mus e looked up. Among hese orienions, ny of hem cn e chosen o scn he whole surfce. Generlly, he orienion o choose will e he opiml one or he closes o he opiml. Oherwise, if no orienions re found, he scnning of he surfce will e done comining severl lser hed orienions. 5. RESULTS The developed sysem deermines he zones of he surfce h cn e scnned wih differen lser hed orienions. For insnce, Fig. 8 shows, y mens of grey scle, he ringles or zones of he surfce whose norml direcions coincide (drker colour or sepre (ligher colour from differen lser hed orienions. This wy, norml direcions of he lck coloured ringles re coinciden wih he proposed orienion (A, B of he hed. They re opiml orienions. The res of ringles cn e scnned wih his orienion u he scnning quliy ges worse s he hed orienion sepres from he norml of ech ringle (grey coloured. Whie coloured ringles cnno e scnned y he seleced hed orienions (occlusion zones. Fig. 8. Surfce ringles h cn e scnned wih differen lser hed orienions For he sme exmple pr (Pr 1 he locl nd glol cones for ny ringle of he surfce hve een oined. Fig. 9 shows he hed orienion mp ssocied o he locl nd glol cones of wo differen ringles of he pr surfce. To simplify he visulizion of he orienion mp, incremens of 15º hve een considered for ngles A nd B. As cn e seen, ringles 284 nd 708 presen wide locl orienion mps (locl cone h re very similr, where A is exclusively limied y he limi view ngle (60º nd where B vries from 0º o 360º for lmos every vlue of A. This is ecuse he possile inerference eween he hed orienion nd he surfce ringles re no considered for deermining he locl cones. The min difference eween he wo mps is he opiml orienion, which depends on he norml direcion of ech ringle. So, for ringle 284, he opiml orienion corresponds o A=15º nd B=75º or 90º while for ringle 708 i corresponds o A=15º nd B=210º-255º. Differen re lso he orienion mps corresponding o he glol cones of ech ringle. In his cse i is relevn he locion of he nlysed ringle. For ringle 708 which is wy from possile occlusion zones here is no influence of poenil oscles over he inciden nd he refleced lser em. For his reson he glol nd locl cones re coinciden. This no occurs for ringle 284, whose glol cone is widely reduced wih regrd o he locl one, due o is proximiy o he occlusion zone of he surfce. In hese cses mny of he inciden nd refleced lser em orienions inerfere wih he surfce nd herefore hey re elimined. Even for ringle 284 he opiml orienions re elimined when he glol orienion mp is consruced. Similesuls hve een oined for he second pr (Pr 2 included in Fig. 9. 6. CONCLUSIONS They hve een mde he firs moves for developing mehodology which llows for n uomic scnning process plnning pplied o free-form surfces. Discreizion of free-form surfces y STL models llows for pplying he developed mehod o scn ny pr, regrdless of is consiuen surfces. By mens of he STL form i is possile o know he norml direcion for ech ringle nd herefore, he lser em orienions h llow for visulizing nd scnning i. The vlid orienions of lser em re consrined y he limi view ngle nd he ringulion ngle. The former deermines he locl cone orienions nd he ler he glol cone. To ccelere he clculion of possile inersecions ck-fce culling lgorihms nd spce priioning echniques like kd-rees hve een pplied. I consiss on esing for inersecion exclusively he fces h cn poenilly e rversed y ech lser em orienion Orienion (A0,B0 Orienion (A30,B90 (inciden nd refleced. Once he kd-ree hs een uil, Orienion (A45,B45 recursive lgorihm hs een pplied for idenifying he sequence of lef nodes h will e inerseced y ech lser em orienion. The mehod hs een proved nd pplied o severl free-form surfces. This work includes he resuls oined for wo of hese surfces. As fuure work he plnning sysem will e compleed y deermining he group or groups of orienions common o he glol cones ssocied o ll ringles of he surfce. These common orienions will e he minimum se of orienions needed for he complee scnning of he surfce. Once his minimum se hs een deermined, he scnning rjecories cn e eslished. ACKNOWLEDGEMENTS This work is pr of he resuls oined in reserch projec suppored y he Spnish Educion nd Science Minisry (MEC-04-DPI2004-03517 nd FEDER.
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