Extracting Skeletal Curves from 3D Scattered Data
17
0
0
Texte intégral
(2)
(3)
(4) ! "
(5) #$ %&' (
(6) ! "
(7) $ . )+*-,/.10324,6587:9. ;=<(>@?8>A,B0 ?DCFEG. HI>KJMLN./O3P. Q R. USVWVWX1YX[Z\Z^]`_Wacb/dfe ZhgiVWjlkmanogipgqZ^_Wa. rs[t[uhv a\XlwWb^Xx yWZ^XKz|{`{#}. ~& . ISSN 0249-6399. apport de recherche. ;D2S0,,6>./>KT. R. 0,B0.
(8)
(9)
(10) "!$#%& ' (*) +,-."/0)1- 2 334654%78789;:
(11) <>=@?BADC
(12) 7@EF3
(13) G%HI<J"E;KLEM78:
(14) <8N O,PRS8Q T S U VXWZY\[]S>^`_%a[]bdceY P ceTfTgSihjTf_%a P bkYlS%m bkTg_%n%S8omqu plc\YqY S>r S>o>mlaiceO YMYq_sbkoto`_%YMaiS>o ^]c%vZS[wex-y Wjz { _%|q|Fce^t[,plS^]S8a P S>^`a P S}Y~%UeesVXotS>|l[tS>T q^]S 8%LV >Ug|q_sneS>o. +>q%% S bkY\[t^tclpqqaiSg_TgS>[ P clp c\^[ P SfaiceYMo][`^tqa[]bdceY c%o`sSdS[`_saq^t%S8o,^tceT_%YqYlc\^]n\_%YlbdS8p aic%ddS>ai[tb c\Y cs o`aP _%[][]S8^]S8p¡pqP _%[t_¢|Fc%bkY\[togd£\bkYlnceY¡O,_P otq^]_%aS%¤ O,P S>otSa>q^t%S>o Tf_@£ P _@%S_¢[t^tSS bksSBo][`^tqa[tq^tS+[tca>_%|l[`q^]SBq^`_%Yqa P bkYln o _%|FS>ootqa _%o q cLclp¥%S>o`otSko¤ So`sS> S>[t_s¦a>q^t%S>o*a>_%Y§MSMo]S8p6c\^plb ¨;S8^]S8Ye[_e|q|ldbda>_s[tb c\Yqo*^t_eYln%bkYlnB^]c\T©o`q^Z_eaiS ^tS>aceª Yqot[t^`qai[tb c\Y+[tcfP ceLvZS8ai[,^]S8aiP ceneYlbd[]bdceYR¤ O,P Sc\o"Yl_% £YBbdbkY\Yq[]|qS8^tl_e[>aimM[t[ b c\SY_sYldS>n%S>c\pl^]S8bdp[ bkT«o[ [tP _%S"%otS>So,dS>_fa[]otbdSce["Y c%cs®U%_¬}pq_%|M[tce_*bdY\|F[`c%obk¤¦YeWj[[¯ ^]S>P [tbkqa P ^`Yq^]o,S8|q_^]S8otSo]S8[,Y\cs[°
(15) [ aP MS,^]^]ecLS>c%o,[_%c%^`F^`_%[ YlP neS S>[`p^]S>bkS%Y¤ _fª [tYl^tSSSbdn otP [tF^`ceq^aiP [`qcL^tcLS%p ¤ n\^t_e| P bkoaiceYMo][`^tqa[]S8pc%S8^±[ P S o]S>[csP |Fc%bkY\[to []caceTf|ql[tSnePSclplS>otbkaplbkot[t_%YMaiS>oFS[j¯ SS8Y+[ P S ^]cLc%[ |McebdY\[,_%YMp+[ P S*c%[O,P P S>^ |Fc%bkY\[to>¤6²c\YqP YlS8ai[]S8p§ S>%S>±o]S>[tocs,[ SplbdP ot[t_eYqaiSTg_e|³_%^tS[ S8Y§Si´l[t^`_%a[]S8p¥_eYqp§ce^tne_eYlbdS>pbkY¡_[t^tSS+ot[t^`qa[tq^tS%¤ S aS>Y\[]S8^toc%[ S>otS* S>%Sko,otS[to,aceYqot[]bd[tq[]S [ Sot%SdS[t_%µaq^t%S8o¤ ¶·\¸®¹tº » ¼% Lbdo`q_sdbd>_s[tb c\YRmlot%SdS[`_sµaM^]eS%mqai£LdbdYMpq^]bka_%µplS>aceTf|Fceotb [tb c\YRmln%S8YlS>^`_sdb >S>pai£L bkYqplS8^to>mq^tS>aic\Yqot[t^`qai[tb c\Y. ½k¾gÀ]¿ ÁIÂ8à À¿ Ä ÅkÁIÆÈÇÉ Ê ÝËÞ Î ß¦Ì@Ì@Î àÍÏÎ Î ÐFáÍZÎ ÑÈâgÑÈÒÏÎ ãÓ8ä%ÔÖÎÕIÞ ×Î àØÙÌ@Î8ÑÈåçØÛæ±Ú8ÎÎ Ü ß
(16) Ñ Î ËÎàÎ è¦Î ߦΠäsÎ8éiêìëií.ä8î;ïìâ ÞRð ÒÏÓ@ñÙÍjòÏÚìÑÖó é8ôõLÍZñÙÍZösÒÏÑÖÕï>ô ð Î îlÎe÷tøìù,úÏëÏùÏëÏû,ü@Ó8ÕÖÓ@ÑÖÒÏÔÈýZÒÏösÍ à®ÍZó@Íjþ%ôsü@ÑIÚìÌ@ýZÍ -ÿ
(17)
(18)
(19) ÿ
(20) dÿ
(21) !
(22) ÿ
(23) "#%$ '&)($ !* ,+.- eÿ
(24) /10 2 34 eÿ 5- 0 $ 67 $8$:9 2 8;
(25) 3 5<- 0 $ 67. .
(26) . . . s s. v[u. v. s. su[u. . u s . s s. l
(27) I v. s. souhss[v.
(28)
(29) i&g 0/ ,& ¥"! ! i° ° > / "! / &g g! ·
(30) · yc\qo|M^]c\|Mc\o]c\Yqo±qYqS-T S>r [ P clplS-aiceYMo][`^tlbko`_%Y\[±plS8oaceq^`MS8ooLlSdS[t[]S8o _ Q |q_%^t[]bk^pqSk_plc\YqY S>r Sp qY+YLq_%n%S plS|McebdY\[to_%|q|q^tc@´lbdTf_eYe[ qYqS+otM^Z_eaiSUs¬g¤²S8oaic\q^tFS>o|MS8^tTgS[t[]S8Ye[ plSaic\Yqo][`^tqbd^tSqYlS+_e|q|q^tc@´LbkTf_s[tb c\Ya£\dbkP Yqpq^tbLlS plS+d_6o`q^]_%aSplS c\LvZS[>¤ ±d S8o|MS8l%S8Y\[_@%cebd^ qYqS+o][`^tMai[tM^]S+_e^tFce^tS>o`aiS8Y\[]S|Mc\q^Tgclp S>r bko]S8^plS8o S>T q^t_eYqa S8T S8Y\[to aceTfª TgSpq_%YqodSa_eoplS>o,_%bdo`o]S8_%L´+o`_%YqnelbkYqo>¤ |q_e^][tbd^*p qY¥S>YMo]S8TldSplS|McebdY\[`o Us¬gmµ _sdn%c\^]bd[ P T S ceM^tYlbd[ qY¥S>YqotS>T ldSfpqSaiceM^tFS>o*ot[t^`qai[`q^lP Sr S>o*otceqo-c\^tTgS p _%^`q^tS%¤ °_+oqS>r S8ai[]bdceY |M^lS8r _sk_%ldSp qY¢pqS>o-|McebdY\[to*|FS>^`TgS[pqSgp S r FYlbk^"k_+^`_%abdYqSplSg _%^`q^tS% ¤ -Y6n\^t_e| SplS %cebdotbdYM_sn%S aceYqot[t^`lbd[o`q^ S8Yqo]S8TldS*plS>o,|Fc%bkY\[to S>ot[,l[]bd bkolS-r |FceM^ a>_skaldS>^ dS>oplbko][`_%YqaS>on
(31) Sr clp S8r o] b LlS>o¦S>Y\[t^tSdS |McebdY\[,^`_%aibkYlSS[ S8o _el[t^tS>o|McebdY\[to>¤¬S8o±S8Yqo]S8TldS>oplSYlbd%S8_%L´faic\YqYlSi´lS8o±o`q^
(32) Qk_a_e^][tSplSplbkot[t_%YMaiSotceY\[¦S´L[`^t_%b [`o
(33) S[ o][`^tMai[tM^lS8r o
(34) o]c\qo
(35) c\^tTgS p _%^`q^tS%¤ .S8o,aic\q^tFS>o,o LlSdS[t[]S8o,o]c\Ye["_% c\^toaceYqot[t^`lbd[]S>o _|q_e^][tbd^plS8o"aiS8Y\[t^tS>oplSaiS8o,Ylbd%S>_eL´R¤ ! » > ¹ # " · aic\q^tFS $o LlS> S>[][tS%mqp S8r aic\Tg|Fceotbd[]bdceY+a£L bkYqpq^tb LlSemMai£LdbdYMpq^]S8on
(36) S8r Y S8r ^t_% bkolS>r o>ms^]S8aiceYMo][`^tqa[]bdceY.
(37) U.
(38) !"#%$'&)(*+ ,%- "./(0%1. g &/6
(39) i&g 54 O,P S*plS8ota>^]bk|l[]bdceYcs.c\LvZS>a[to ¯,b [ P a£\dbkYqpq^tbda>_s®o P _e|MS8o P _%oMS>S>Y+Si´l[]S8Yqo]bd%S> £qotS>p+bdY+[ P S*aic\Tf|ql[]S8^±Lbko]bdceYaic\TgT qYlbd[j£ 6 ª87 Uqmqw ª87:9 smMw 7:9 ; m < 7>=@? ; m 7 { wLACBI¤WZY_ F^`ot[_%|M|q^]c@´lbkTf_s[]bdceYgbd[bkocs[]S8Y+aceY\%S8Ylb S8Y\[¦[]cgT clplS>R_o P _%|FS_eo_ neS>YlS8^t_% bdS8pai£LdbdYMpl6 u S>^> ¤ O,P bdobko¦|q _e^][tbda>ld_e^]d£^tSdS_%Y\[bdYg[ P S"aiceY\[tSi´l[cs;^tP S>aceYqot[t^`qa[]bdceYc%;_eYq_s[tceTgbda>_slo P _%|FS>o^tceT ² O pq_%[t_Bce^*o`a_eYqYlS>^ Ez DReLm \lmRGy FHFJI ACBI¤ y-qTgS>^tceqo*¯ ce^`Lo _@eSgFSS8Y§plceYlSgc\^c\LvZS>a[ plS>o`a^tbd|q[]bdceY¥qo]bkYln [`^]S>SihI bksSP o][`^tMai[tM^]S8o 6 w ,wL%ULm FS>%ULm±y*²,wL ; m
(40) y_%> Aqm
(41) y*²,wLACBce^fa£\dbkYqpq^tbda>_s,^]S8|q^tS>otS>Y\P [t_%[]bdceYqo 6 7 {
(42) wL ABLKϤ P _sª [ Tf_%%S>o [ SBqotS+cs-ai£L bkYqpq^tbka_s plS>o`a^tbk|l[]bdceYqog_%YMp³n%S8YlS>^`_sdb >S>p³a£\dbkYqplS>^`ogo]c¢|Fce|Mld_e^bko [ S>bd^g^]S>d_%[]bd%SBo]bkTf|l bkaibd[j£%¤ neP S>YlS8^t_% bdS8p a£\dbkYqplP S>^¦bdo¦|M_%^`_%TgS[tS>^tb >S>P p\£g_ ot|lbkYfaq^t%S[tc%n%S>[ P S8^¯,b [ P _ o]S>[
(43) csRa^tP ceo`o
(44) o]S8ai[tb c\Yqo 6 Gª 7 CU BI¤¬S8|MS8YqplbkYln ceY [ S_%|q|q bka_%[]bdceYRmL[ P S^]S8aic%S8^]£gcsotMa |q_e^t_eTgS[]S8^toqo`q_% d£^] S Llbd^tS>o dS>o`o ¯c\^tf[ _%Yb [,¯ ceqdpBMS-c\^,_ Tgce^tS*n%S8YlS>^`_s plS8ota>^]bk|l[tb c\Y+c%_fo P _%|FS%¤ P z6clplS> bkYlngcs°o _e|MS8o¯,bd[ bkTg|q bkaibd["otM^Z_eaiS>o plS FYlS>pB\£_ o`sS> S>[]c\Y P _%o_%dotc FSS8Y+S´l|q ceb [tS>pbdY ? ^t_e| P bkao 6 7 elm 7 wLM BM
(45) [ P So`q^Z_eaiS8oc%°[ P S ceLvZS8ai[`o,_%^tS[ P S>YplS FYlS>pB_%obkotcshjotq^]_%aS>ocs MSkpqYqai[tb c\Yqo,neS>YlS8^t_%[]S>p\£[ P S*neSceTgS>[t^tbda |q^tbkT bd[]bd%S8o
(46) [ P _s[
(47) c\^tT}P [ P S"o`sS> S>[]ceYµ¤ ª YfbdTf|l6 d7 bdaO b [? ^]S8aiceYM= o][`^t?-qªa[]bdceYcsµo P P _%|FS>o^tceT}_ otP S[
(48) c%P µUs¬o`a_%[][]S8^]S8p |Fc%bkY\[toqo]bkYln_ neSceTgS>[tP ^tbda*o`sSdS[tceY _%o,P FSS8YP |q^]c\|Mc\o]S8pbkY elm ² ACBI¤
(49) WZYB[ S>bd^"_e|q|q^tce_ea mL[ S neSceTgS>[t^tbda-ot%SdS[tceYbdo,qqb d[ qotbkYln[ HS N
(50) c\^]P c\Ylc%b®n\^t_e| c%[ Spq_s[`_f|McebdY\[to>¤ z6c\o][cs±[ Sfo][`qplbdS>o*plceYqS bkY¢TgS>pqbda>_sbdTf_snebdYqnot[t_%^t["^tceTec%kqTgSbkTf_sn%S8ootc+[ P _s[-[ P S [`^t_eplb [tb c\Yq_sTgS>plbk_s
(51) _s´Lbko [`^t_eYqoZc\^tT a_eYBFS_e|q|ldb S8p 6 Gy FHFJI ACBI¤ u bdo`O,qP |q_%[]Pb O _sȤ P6 u Qz D®eR Bqo]S_+plb ¨®S>^tS>Y\["_e|q|q^tce_%a P []caceTf|ql[tS_P aiS8Y\[t^`_s _s´Lbko bdYqotbkplS|qqdTgceYM_%^t£[`^]S>Sot[t^`qai[`q^]S8o¤ Sbk^_% nece^tb [ T1qo]S8o _^]S8aq^`otb eS^]S>n%bdceY§ne^tc¯,bkYln []cn%c¢plc¯"Y¡[ S[t^tSS ec%kqª TgS%¤ ª q^`_%Yqa P bdYlnf^tSn%bdceY+bdo"S>YqaceqY\[]S8^]S8p¯ P S8YB[ P SqY\Lbko]bd[]S8pBotS[c%ec@´LS>doo`|ldb [,bkY\[]cf[j¯cplbkovZc%bkYBotS[`o¤ oc\|q|FceotS>p[tcf%c@´lSdb >S>ppM_s[t_ ¯ S-ot[t_e^][^]c\T _%YqYlce^tne_eYlbdS>p+aidceqp+cs|Fc%bkY\[too`_%Tf|ldS>pc\Y+_gotM^Z_eaiS*_%Yqp+¯S*plc Ylce[^tS>ot[tP ^tbda["ceM^totSd%S8o,[]cBT S8plbka_s_%|M|l bka_%P []bdceYqo>¤ O cqotS_+a£L bkYqpq^tbda>_sT clP plS>°[tc+P ^tS>|q^tS>otS>Y\["[ P S o`q^]_%aiSem;_+Us¬ aq^t%S bkYqotbdplS-[ S-a c\qpcs|MceP bdY\[to ^tS>|q^tS>otS>Y\[]bkYln[ PS-ceLvZS8ai[T qot[ FS-o`P |FS>aib MS8pR¤ S>Y+[ S*o]S>[c%.Us¬ |Fc%6 7 bkYe{ [`o±bko n%bd%S8Y_%o _otS[ c%P ®¬ |lk_%YM_%^ota>_%Yqo>m[ S,a>q^]eSplS FYlS8p \£ P[ SaS>Y\[t^tc%bkpqo°csMS8_%a ¬ o]S8ai[tb c\Ya_eYFS,P qo]S8p SÈ_%obdY PwL ACBLKÏU¤ Tc= ¯S>%S8^m [ bdPobkTf|ldb S8o _gaic\Yqotbdot[]S8Ye[ ce^tbdS>Y\[t_%[]bdceYfcs[ S*a^tceo`o]hIotS>aP []bdceYq_%F|lk_%YlS8o^tSk_s[tb eSd£f[]cg[ S |Fceotb [tb c\Ycs°[ S*celvZS>ai[>¤ bdneM^]S o c¯"o°[j¯ c|Fceo`otbdldS^]S>d_%[]bd%S ce^tb S8Ye[`_s[tb c\Yqo¤² S8_%^t £*[ S ;^tot[aceY Fneq^`_s[tb c\VY SÖW_ KµbkoYlc%[_%pM_%|l[tS>pR¤¦w\ceTgS>[]bkT S8omeMS8a_%Mo]S c%P [ P P SFS>Yqp o = P _e|MS c%[ P ScelvZS>ai[>mqbd["bdoSeS>YbdTf|Fceo`o]bkldS[]c FYMp _f@_% bkpBce^tb S8Y\[t_s[tb c\Yc\^,[ P So]S8ai[tb c\Yq_s.|qd_eYlS>o>mM_%o,ce^ [ S ce^`otS-c% bdneq^tSf >q¤ 2. 3. a. =. b. b n\q^]Sf MXZYZ[H\1],^_\[R`Pabc\1] d^ef[)g\h\i jHklf] mJ[)gnio\iRjH]8\1pq1`ri)d,]Rs. ª [ P celn P bd[bdo S>o`otS>Y\[]bk_s;[]c FYqpB_ o`lbd[t_el S*_´lbko±bkYce^`plS>^[]cfplS>otbdneY_ n%S8YlS>^`_sdb >S>pa£L bkYqplS8^mL[ P bdobkoto`lS-¯ _eo^`_%^tSd£ lp bko`aqo`o]S8pR¤
(52) WZYB|q^t_eai[tbda>_s®a_%otS>o [ P bdo[`P _%o`a_eY+FS []S8plb c\qo_%o,P TgS>Y\[tb c\YlS>pB\£y_s8_%^tbd_eP YtO_%Ö¤ O,6 y*P ²,wL ; mly-_s>Almly*²,wl ACBI¤ y-_s>P_e^]bk_%YuO _sȤ |q^tce|FceotS _gS¯ []S8a Ylb LlS>o,[tc_%l[tceTf_s[tS [ S plS[tS>^`T bkYq_%[]bdceYBcs
(53) [ S_´lbko¤ S£Tg_%bdYq £B|q^]S8o]S8Y\[,[j¯c TgS[ clpqoRM. a. b. = bdneq^tSgvMwi xyq] d,pqz\e{)]o\1p|vm ef{e}\ef[Rgtp\efg~Jj/i efgi ] \[ `Uefg]"q1^eiiR i q1eiRg i l}v^z]8Wqz\^j/i efgi %e\he\>\1[YgVefgtmiR\1] m l eg])X ]>j/iegi ] \ [ `efg]"q1^eioi gWm/^z]>k]"qk],gWm ed,p liRq\1kle^^efg~kliRg] \ `r[)q@^z]>\1] d,[RgWm/l],{C],l[R`q]"d,pqz\ef[)gniRq]8\1[ YgJeg0kli efg leg] \,sU|xPX ]>qz\^yi %e\@[R`+efg]"q1^eii gWm/^z]:k]"qk]"gm ed,p l}i q\1kle^^efg~Hkli g]8iRq]:g[R^y\1p ef^_i |lf]:`r[Rq^z]:\1p|vm%ef{%e\ef[)gni lf~)[Rq1ef^zjns. [ P S F^`o][gceYqSBaceYqotbdot[to bkY _¥^]S8aq^`o]bd%Sotq;plbdLbdotb c\Y¡c%[ P P SotS[gcspq_%[t_|McebdY\[to>¤ ª [fS>_ea P o][tS>| [ P P SotMqP o]S>[tPogcs pq_s[`_¢|Fc%bkY\[tofO,_%^tP So`|ldb [\£³_|lk_%YqS|FS>^`|MS8Yqplbkalk_%^g[]c¥[ Sbk^gTf_%bdY _´lbdo csbdYlS8^][tbd_P_%Yqp |q_%o`otbdYln[ ^tceqn [ Sbk^ q_%^t£laiS8Ye[tS>^>¤ S^]S8otld[]bkYln_s´Lbko
(54) bko±_ |Fc%d£L bkYlSaceTf|Mc\o]S8pfcsRTf_sbkY_´lS>o
(55) c%µ|q_%^t[to
(56) c%R[ S"bkYlbd[]bk_s;pq_s[`_o]S>[
(57) csµ|Fc%bkYe[`o ß°ß Ì>éiïÏêìû .
(58) #% W"P%
(59) rZ )% W ;. SÖaiZ¤ = bdneq^tSgq¤ _WKì¤ O,P S _el[ P ce^`o^tS>aiceneYlbdS[ P S>bd^*TgS[ P clp¢plcLS>o-Ylce[_sd¯_@£Lo¯c\^tB_%YMp6o P c¯_+aic\qY\[]S8^]S´l_eTf|l S ¯ P S>^tS"[ P STf_sbkY_´lbko¦c%µbdYlS8^][tbd_Mme^tS>|q^tS>otS>Y\[tS>pfbkYpq_%o P S8pf bkYlS"bkY = b n\q^tSl¤ RmLa_%YMYlc%[±FSMo]S8p[]c ;Yqp[ P SaiS8Y\[t^`_s _´lbko¤ [ P So]S8aiceYMp¥TgS>[ P clp§¯ ce^`\o-c\Y³o]S>[ cs"pq_s[`_ |McebdY\[`o n%bd%S8Y¥\£¥|ld_eYq_%^s¬ o`a_eYqo _%Yqp§bd[qotS>o[ P S[`^]bk_%Yln\lk_s[]bdceY aic\Tg|Ml[]S8pB\£ 7 cebdo`o]c\YqYq_%[ o TgS>[ P clp 6 7 ceb 99 B._%o,_eY_e|q|q^tc@´LbkTf_s[tb c\Ycs[ P S [tqqqd_e^,o P _e|MSe¤ WZ Y³P [ P bkoP |q_e|MS8^m¯ S|q^]S8o]S8Y\[_6TgS[ P P clp§¯ P bda P _%l[tceTf_s[tbda>_sd £¥aiceTf|qq[]S>o _6otS[c%,U%¬ a>q^]eS>o bkY³_6adqot[]S8^P c%,|Fc%bkY\[to>¤ O,P S8S8o]YfS[ aqS"^t%|FS8c%obkY\Tf[to
(60) _@£¢dbdS,c\ce^tYgT1_ _ otq[t^]^tS_%SaSo][[`^tqS8ao]S"[tqa>^tqS^]eb ,S>o[ P TfSB_@£otqF^]S"_%qaSotS>apf_e_%Y³o
(61) M_sSB´LS8o]oS>S>ceY³^
(62) _%_ o a£\
(63) _ dbk ]Yq[`pq^]^tS>bdSa>_scsq,_%n%|MS8|qYl^]S>c@^`´l_sbkdTfbd_sS>[]p§bdceaY£\dcsbk®Yq[plS>S"^`o o` qq¤ ^]O,_%aP S%S ¤ TgP S[ P Pclp¯c\^tP Lo bkYqplS>|FS>= YMplS>Y\[]d£Bcs°[ P SFS>YqpqbdYlnc%[ P So`q^Z_eaiSe¤ ª o"_faic\YqotS LlS>YMaiS*b [¯,b d.^tSP [tM^tYB_P aic\^t^tS>a[ ^tP S>o`ld[ce^ [ So _%|FSgo c¯"Y6c\Y bdneq^tS l¤ R¤ WZY¢c\^tplS8^-[]ccel[`_sbkY¢o`_s[tbdo]£LbdYln^tS>o`l [`o-¯STf_%%SgotceTgS £l|Fc%[ S>otbdo*c\Y6[ SfbdYq|Ml[ adqot[]S8^,cs|McebdY\[` o M %¤ O,P Spq_%[t_f|McebdY\[`o,o P c\lkpBFSo`_%Tf|ldS>pceYB_gaS>^t[t_%bdY SÖqYM\Yqc¯"YK otM^Z_eaiS%¤ l¤ O,P SP ot_eTg|q bkYlP n*o P c\P lkpFSpqceYlS bdY otMa P _P ¯ _@£*[ P _s[[ P S,plbko][`_%YqaS FS[j¯ SS8YYlS>b n P Mc\^°|Fc%bkY\[tobkoo`Tf_sdL¯,b [ P ^tS>o`|MS8ai[ []cf[ S ¯,bdpl[ cs[ S [`qqlk_%^"|M_%^t[to cs[ So`q^]_%aS%¤ O,P S6aceTf|ql[`_s[tb c\Y c%[ P S6_´lS>ogbkoq_%otS>p ceY _§ai£L bkYqpq^tbka_s,plS8aic\Tg|Fceotbd[]bdceY cs[ P S6o`q^Z_eaiS^]S8|q^tS>otS>Y\[]bkYln¥[ P S6otS[fcs U%¬ |FP c%bkYe[`o¤ ª SbkY\[t^tclpqqaiS8p¥[ P Sa£\dbkYqpq^tbda>_s±plS8aic\Tg|FP ceotbd[]bdceYcs,_ o P _e|MSbkY 6 °_s8e\m N P ACB±[tc¢aic\Tg|Ml[]S_s´LS8o*ª bdYMo]bkplS |Fc%d£ S>pq^`_q¤ otbdYqn%dS+_´lbko¯,bd FS+ceq[t_sbkYlS8p§ce^ S>_ea ai£L bkYqpq^tbka_s |q_%^t[ _eototclaibk_s[tS>p¥[]c[ bkofplS>aceTf|Mc\o]bd[]bdceYµ¤ og_%Y bkYq|ql[*|q_e^t_eT S>[]S8^m;[ P Sfai£LdbdYMpq^]bka_%°plS8aic\P Tg|Fceotbd[]bdce Y [`_%sS8o_o]bkYln%dS |Fc%bkY\[a>_sd S8p [ P S # "v#
(64) ¤ O,P bkootceq^`aiS |McebdP Y\[ Tf_@£+FS*bdY\[]S8^t_eai[tP b eSd£6 plS>otb ? n\Yq_s[tS>pO,e£+P [ S P qotS>^>¤ PS_e^]S*_sko]cfaM^t^tS>Y\[]d£¯ ce^`ebkYln ceYB_ plS_%ld["otSdS>ai[tb c\YP M_%otS>pc\Y+[ S plbk_%TgS>[]S>^"cs¦_o _%|FS ² wL%CU BI¤ Sa cebdaS-c%
(65) [ S6 otceM^taS*|FP c%bkY\["bko"a^tb [tbda>_s.otbkYqaiSbd["¯,bd °plS[tS>^`T bkYlS[ SaP £\dbkYqpq^tbda>_s plS8aic\Tg|Fceotbd[]bdceYRo¤ Tc\|MSl d£%mR_eo¯_%o|McebdY\[]S8p6c\l[bkY N- ACB
(66) [ S plS8aiceTf|Fceotb [tb c\Y bkoYlce[eS>^t£otS>YMo]bd[]bd%S[tc+[ Sg|M^]S8aibko]S dcla_s= [tb c\YfcsR[ P Sotceq^`aiS"|Fc%bkY\[¤WZY\[tlbd[]bd%S> £eme[ P Sotceq^`aiS"|Fc%bkY\[±aic\^t^tS>o`|FceYqpg[]c _|Mced_e^
(67) Si´l[`^]S8T bd[j£gcsµ[ P So P _%|FS_%oo P c¯"Y c\Y bdneq^tS Uq¤. source. =. . B i. b n\q^tS*U MX ]8\1[)pqzd]:k[Refg^i gWm/^z]:d,[Rqq] \1k[)gm efg~/d lefgWm q1ed"i l m] d[)jHk[C\e^ef[)g s. O,P SaceTf|ql[`_s[tb c\Y+c%[ P SUs¬a>q^]eS>obko,Tf_%plS bkYceq^,ot[]S8|qomq_eob dkqo][`^t_%[]S8pbkY = bdneM^]S ; ¤ ? bd%S8Y_fotS[,c%pq_%[t_f|Fc%bkYe[`om %¤ Sqqb kp¥[ P S O, P
(68) f"# #RP #).u%P c%c\^tplS8^
(69) ¤ O,PP bko*bko _BYqceYce^tb S8Ye[tP S>p¢ne^`_%| P ¯ P ceotSf%P S>^t[]bkaiS8o*_%^tPS [ P SfbdYq|Ml[ pq_s[`_|Fc%bkY\[to>¤ SgS>pqn%S>o _@eS[ Sgce^`T S ;m "! KìmR¯ S8^]#S "!
(70) bdo-c\YlS c%[ $S YlS>_e^]S8o][*YlS>b n Fce^`ocs±[ Sf%S>^t[]S´% ce&^ bko"c\YlSc%[ P #S §YqS>_%^tS>ot[YlS>b n P P Mc\^to,c%¦P [ P S %S8^][tSi´ '!Ȥ"WZY neS>YlS8^t_%ÖmFb [¯,b dYlc%[-MSg|Mc\ototbdq S[tcplS>[]S8^tTgbkYlS _ otqb [`_%ldS |Mce £Ln%c\Yq_sµo`q^]_%aS^tceT [ bkone^`_%| _%obd["Tf_@£+FSYlceYB|lk_%Yq_e^¤ l¤ = ^tceT [ P P bko Yl"S#)bdn. P"
(71) Fce ^ P cL(cLpg n\O,^t_eP | P _%Yqp_o]c\q^taS"P |McebdY\[>m\¯ SaceYqot[t^`qai[_plbko][`_%YqP aSTf_%|_eYqpP _%Yc\^]P bdS>Y\[tS>pfP otMlneP ^`_%| P a_% dS>p [ S ¤ S n%SclplS8o]bka
(72) n\^t_e| bko.c\l[t_%bdYlS8p\£ aic\Tg|Ml[]bkYlno c\^][tS>ot[°|q_%[ ocsq[ SYlSbdn Fce^ cLcLp ne^`_%|P P FS[j¯ SS>Y_% µeS>^t[]bkaiS8o,_%YqpB[ P So]c\q^taS |McebdY\[¤ O,P Splbko][`_%YqaSTf_%|Bbdoo]bkTf|l £[ P S S8Yln%[ P c%[ P S>otSo P ce^t[]S8o][ |q_s[ o>¤ O,P SfaiceYMo][`^tqa[]bdceY c%±[ P SfYqSbdn P Mc\^ P c\clp n\^t_e| P m;[ P Splbkot[t_%YMaiSfTg_e|¢_eYqp6[ P S neSclplS8o]bkan\^t_e| P _%^tS pqS>o`a^tbdFS>p¢bdY plS[`_sbddobkYo]S8ai[tb c\YUM¤ Þ è°ß Þ Ë.
(73) .
(74) !"#%$'&)(*+ ,%- "./(0%1. source 3D points. neighborhood graph. =. bdneq^tS. geodesic graph. levels. skeleton. ; MX ]:j/iefgn\^z]"k\[ `+[)pqjH],^z[%mvs. Uq¤ S q^t[ O,P P S8^aic\Tf|ql[]S S>%S>.o]S>[tocs
(75) [ P S plbko][`_%YqaSTf_%| qotbkYln[ P Sn%S>clplS>otbda*n\^t_eP| P mF¯ P S>^tSBb ko_qotS>^plS ;P YlS>p _sklS%¤ Sf S>%S¦otS[`o*_%^tSgaceTf|Mc\o]S8p6c% |Fc%bkYe[`o P _s[*_aiceYMo][`_%Y\[-pqbdot[t_eYqaiS ^]c\T = [ SfotceP M^taS%¤ SaiceYMYlS>a[-[ S>otS |McebdY\[`o"ceY¢_|q^tc@´LbkTgb [j£Ba^tb [tS>^tb c\Y _%YqpbkplS8Ye[tb £[ S aceYqYlS8ai[tS>p6aceTf|Mc\YlS>Y\[`o¤ ce^"S8_%a dSeSÈmM¯ S _skotcaiceTf|qq[]S [ P SaS>Y\[t^tc%bkpqo csSeS>^t£csb [`o"aic\YqYlS8ai[]S8paceTf|FceYlS8Ye[`o¤ ; ¤ O,P S_´lS>og_%^tS FYM_sd £³c\l[t_%bdYlS8p \£¡aic\YqYlS8ai[]bkYln[ P S aiS8Y\[t^tc%bkpqoc%o`qaaS>o`o]bd%SdSeSkof_%og|q^]S>Lb c\qo]d£³aic\Tg|Ml[]S8pR¤ P S>Y6[ P Sg S>%S>doaiceY\[`_sbkYqootSeS>^`_s.aceYqYlS8ai[tS>p6aceTf|Mc\YlS>Y\[`om;[ P Sfaic\YqYlS8ai[]bdceYc%¦[ P SgaiS8Ye[`^]cebdpMo_%^tSq_eo]S8p6q|FceY [ P S|M_s[ P ocs[ P S neSclplS>otbkan\^t_e| P ¤ w\[]S8|qo"Uf_%YMp ; _e^]S*plbkota>qototS>pbkYBotS>a[]bdceY ; _%YqpSi´q_eTg|q S8o,_%^tS-|q^tcLbdpqS>pbdYotS>ai[tb c\YBq¤ O,P SaceTf|ql[`_s[tb c\Y6cs[ P SfYqSbdn P Mc\^ P c\clp¢ne^`_%| P bdo*[ P STgceot[-S´q|MS8Yqo]bd%Sot[]S8|R¤wLbdYqaS[ P SYlS>b n P Mc\^ P cLclp6n\^t_e| P pqc\S8o Ylce[,plS>|FS>YqpceY+[ P S a P cebdaSc%.[ P S*otceM^taS|Fc%bkYe[>ml[ P S ;qotS>^a>_%Y+otSdS>a[ pqb P ¨®S>^tS>Y\[,o]c\q^`aiS|Fc%bkY\[to>mq_%Yqp+[ P S ace^`^]S8ot|FceYqpqbdYln _s´LS8oaceTf|ql[`_s[]bdceY¯,bdd.ceYq £BbdY\ec%d%Sot[]S>|lmFU+_%Yqp ¤w\bdTgbdd_e^]d£%m®_%o[ S Y\MTFS>^ cs¦plbkota>^]S>[]bd>_s[tb c\Y |McebdY\[`o"bkoqotS>p c\Yl £bdYBot[]S>|Uf_%YMp ; mqplb ¨;S8^]S8Ye[,_%dlS8ocs Tf_@£+FS [t^tbdS>p¯,b [ P cel["_eai[`q_sd £^]S8aiceTf|qq[]bkYlno][tS>|qo _eYqpBq¤ ( 1"&/ "! i. S _e^]Sneb eS>Y _otS[cs¦pq_%[t_+|Fc%bkY\[t o
(76) o`_%Tf|ldS>pceY¢_%Y qYqLYlc¯"Y o`q^]_%a!S _eYqp _%YbkY\[]SneS>&^
(77) ¤ O,P S YlS>b n P Mc\^ P cLclpne^`_%| P"$#&%(' )+* bko"_%YBqYqpqbd^tS>a[]S>pBn\^t_e| P plS FYlS8pB_eo c%d cH¯ M [ P S eS>^t[]bkaiS8oc% " #&%(' ),* _%^tS*[ P S |Fc%bkY\[to,c%-
(78) ^ S. /t0m 21K¦bdo_%Y+S>plneSc% "$#3%(' ),* b °Sbd[ P S>(^ /bkoc\YlSc%.[ P S ¢YqS>_%^tS>ot[|Fc%bkY\[to cs4 51bk6Y
(79) ce7^ 51bko ceYlS-cs.[ P S _|q_%bdo YlS8_%^tS>ot[,|McebdY\[to"cs4 / bk8Y
(80) ¤ WZY³c\^tpqS>^ [tcP aic\Tf|ql[]S+[ P S YlS>_e^]S8Po][|Fc%bkY\[to cs,S>_ea P %S>^t[]S´Rm°¯ S+qotS_6o`q; plbd\bkotb c\Y§cs"[ P So`|q_%aP SbdY\[]c%c@´lSko>¤ P S o`q;plb LbkplS6[ S6S>YMaidceotbdYln¡Fc@´ c% [ S¢pM_s[t_³|Fc%bkY\[to+bd:Y 9<;=9<;>9 %c@´lSko _eYqp _%o`otcLabd_%[]SS>_ea pq_s[`_³|McebdY\[¯,bd[ [ P Sec@´lSaceY\[t_%bdYlP bkYln¡bd[¤ O,P SotS>_e^ta P c%[ P S YlS>_e^]S8o][+YqSbdn P Mc\^tocs_ pM_s[t_ |McebdY\6[ bdoBTf_%pl) S¥\£ Lbko]bd[]bkYln [ P S e@ c@´LS>do aidceotS+[t)c¢[ Sc\YlSaceY\[t_%bdYlbkYl?n ª _%YMp P TgcLbdYln_@¯ _@£¥|q^]cene^tS>o`o]bd%S> £¥qY\[]bd ) |McebdY\[tuo S +@md¤ ¤d¤ K_e^]Sc\qYqpR¤ °S[ «Tf_sA´ CB / B SÈplbko][`_%YqaV S S / DKKì¤ o¯ S _@eS_sk^]S8_%pl£ c\qYqp |Fc%bkY\[to S +md¤d¤ ¤ K*dcla_s[tS>p³_%[_6plbko][`_%YqaS c¯ S>^ce^ S \M_sR[]c @ @ ^tO,ceE T P °ml¯S _%^tS*otP q^tS-[ P P _%[ [ P S YlS8_%^tS>ot[ YqSbdn P Mc\^tocs- M@ S> c\Ylnf[]cf[ P S o`| P S8^]GS P FSH4 @ K aiS8Ye[tS>^tS>p+bd8Y _%P Yqp c%°^t_eplbkqo ¤ S>Y¯S-o]S8_%^`a P _sdF[ Spq_%[t_ |McebdY\[toFSdceYlnebdYqn[]Ic FSH4 K±_eYqp¯ SS´L[`^t_eai[¦[ S 6YlS>_e^]S8o][ |McebdY\[toceY[ bko otO,SP [>mMqotbdYln_ LlbkaÏP+otce^t[c\Y[ P Splbko][`_%YqaP S*@P _%dqS>" o>¤#&%(' ),* S P Y\MTFS>^ §o celP kpMSa ceotS>YBotqa [P _s[ bko"_P aic\YqYlS>a[]S8pn\^t_e| P ¤ O,P bdo"a =P c%bkaiSplS8|MS8Yqpqo,c\Y[ P S^tSn\l d_eP^]bd[j£ c%P µ[ S-ot_eTg|q bkYlnc%µ[ S-pq_s[`_|McebdY\[`o±c\Yf[ S-otq^]_%aS%P ¤WZY[ SSi´q_eTg|q S8o|q^tS>otS>Y\[tS>pfbkY b n\q^]S > ¯ S= qotS>p q¤ S>P Y [ S pq_%[t_|Fc%bkY\[to_e^]SYqc%[qYqb c\P ^tTgd£Bo`|q^tS>_%pBceS>^[ S o`q^Z_eaiS k_%P ^tn%S8^@_%dqS>oTf_@£BP MSYqS>aiS8oto`_%^t£%¤ P c\^,bkYqo][`_%YqaS%mFbdY [ S a>_%otScss¬$|lk_%YM_%^o`a_eYqo¯,bd[ _6o`Tg_% dS>^ ^]S8o]cedq[]bdceY§bkYqo]bkplS[ SBota>_%Y³|lk_%YlS8o[ _%Y MS>[j¯S>S>Y³[ Sa>^]c\oto]hIotS>a[]bdceYqo¯S c\qYqp¥[ P P _%[ __%d=lSfc% _eo-d_e^]neSg_eo*%+¯_%o YqS>aiS8oto`_%^t£[]cceq[t_sbkY¥_aceYqYlS8ai[tS>pne^`_%| P ¤ O,P bko*¯ _eo*[ P Sa_eo]S ce^*[ P S c\LvZS>a["o c¯"YbkY bdneq^tSf 8l¤ J Lõ K@Í
(81) ÌÓ M7N%ÍZ4Ñ O ó@ÍZö%ÍZÌ@ó8ÔÒÏÌ.Õ K@Í
(82) ÌÓ M(NsÍZѵÒìÜMØÙÌ@ö@Ó8Õ.óÚ`ÕÈÚ ösÒÏØÙÌÕÖÔtÎ ß°ß Ì >éiïÏêìû.
(83) #% W"P%
(84) rZ )% W A. %S>Y¢[ P c\ln P " #&%(' ),* Tg_@£MSYlc\Y|qd_eYq_%^-¯ SgS´q|MS8ai[ [ P SfYqSbdn P Mc\^ P c\clpne^`_%| P []c FS_+_%bd^ _e|q|q^tc@´lbdTf_s[tb c\Y cs [ P SO qYqLYlcP ¯"YBotM^ZP _eaiP S%¤ O,P _%[,bdo"[ P S S8pln%S8oc% " #&%(' ),P * o P celkPp bdS P ceY[ P So`q^]P _%aS%¤ c%neS[ S>^¯,bd[ [ So]S> S8ai[]S8po]c\q^taS |McebdY\[ mM[ SYlSbdn Fce^ cLcLpne^`_%| bko"qotS>pB[]caceTf|ql[tS[ P S n%SclplS8o]bka-ne^`_%| P #&%(' ) ' D* ¤ O,P Sn%S>cLpqS>otbdagne^`_%| P bkoaic\Tf|Mc\o]S8p¢c% neSclplS>otbkag|M_s[ P o*cs[ P S+YqSbdn P Mc\^ P c\clp¢ne^`_%| P S>Tf_%YM_s[]bkYlnB^tceT©[ P S pq_%[t_|McebdY\[to _%Yqp vZc%bkYlbdYqn6[ P Sotceq^`aiS|Fc%bkY\[¤ O,P S+dS>Ylne[ P cs_eY³S>pqn%Sc%"[ P SBYlSbdn P Fce^ P cLcLp¥n\^t_e| P bdo [t_esS8Y³_%o[ P S qaidbdpqS>_%Yplbkot[t_%YMaiS MS>[j¯S>S>YBbd[to,S8Yqpq|Fc%bkYe[`o¤ SqotS [ P S ¬b v]Lo][`^t__% nece^tb [ P T 6 ² { %% B.[]cfS ab S8Y\[]d£aic\Tf|ql[]S [ P S>otS |q_%[ P o,_eYqp[ P S>bd^dS>Ylne[ P ¤ u ^]S8aibko]S> £emL[ P S ¬-b v]Lot[t^`_f_sdn%ce^tbd[ P T ^`qYqo bk Y S *dc%n UK_eYqpaceTf|ql[tS [ P S*neSclplS>otbkaplbkot[t_%YMaiS ^tP ceT _%P Y\£+|Fc%bkYe[,[tc[ P S o]c\q^taS-_eo,¯ Sdµ_%o"_fP |Fc%bkYe[tS>^,[tc[ P SYqSi´lP["|McebdY\[,bkY _g n%SclplS8o]bka*|q_s[ P vZP c%bkYlbdYqnP [ P Sotceq^`aiSe¤
(85) yceP []S [ _s[[ S>^tS*Tf_@£P S´Lbkot[O,otPSeS>^`_s;n%S>cLpqS>otbda-|q_s[ ^tceT _f|Fc%bkY\[ [tc [ Sotceq^`aiSe¤ S o]bkTf|l £qo]S*[ S |q_s[ ^tS[`q^tYqS>p+\£[ S ¬-b v]Lot[t^`_f_sdn%ceP ^tbd[ TB¤ Splbko][`_%YqaS Tg_e|+bkY\[t^tclP pqqaiS8p+bkYo]S8aiP [tb c\Y bdopl S FYqS>p+P ce^SeP S>^t£pq_s[`_f|McebdY\[,[]cFS b [`on%S>cLpqS>otbda plbkot[t_%YMaiSg[]c+[ Sfo]c\q^taS%¤Wj[bko-Si´l[]S8YqplS>p6[]cB[ SgS>plneS>ocs¦[ S neSclplS8o]bkan\^t_e| ¯,b [ _o]bkTf|l SgdbdYlS8_%^bdY\[tS>^`|Mced_%[]bdceYcs [ P S ª S>YqpM|McebdY\["plbko][`_%YqaS P _sklS>P oc%°[ P S S>plneS>P o>¤ P P o¯S6o`q|q|FceotS>p [ _s[[ S S>plneScs*[ S¢YqSbdn Mc\^ c\clp ne^`_%| P P o P celkp P bdS ceY [ P S6O,otP q^]_%aS%m [ P S neSclplS8o]bka|q_s[ P o |q^tSLP bdceqotd£+aic\TgP |Ml[]S8pB_e^]S*bkY\[]S>YMplP S>p[tc_%|q|q^tc@P ´lbdTf_%[]S-n%SclplS8o]bka*|q_s[ o,c\Y[ So`q^Z_eaiSe¤ 6 Su ai9 c\Tg|Mlu [t_%;[]bdceuYBcsn%S>cLpqO,S>otP bda |q_%[ oP ce^ |Mce £ S8pq^`_so`q6^]_%aS>u o 9 _@%S+FSS8Y³[ SBotMLvZS>a[csYLqTgS8^]c\qo|qMl bka_%[]bdceYqo z¢z \@m < O m S>pq\R BȤ S _% nece^tb [ P T pl6 S>o`a^tbkMS8p¢bkY z6P z ) P B±aiceTf|qq[]S>o*S´q_%ai[*neSclplS>otbka plbkot[t_%YMaiS>o*qq[ P bdo _%dotcS´q|MS8Yqo]bd%Se¤ ccel[`_sbkY_P _eo][tS>^ _% nece^tb [ TBm °_s8e\m P N- A)B P _@%Sa ceotS>YB[]c+aceTf|ql[tS_%Y _e|q|q^tc@´lbdTf_s[tb c\Y+c%¦ª [ Sn%SclplS8o]bka plbkP o][`_%YqaSceY _+|Mce £ S8pq^]c\P YRm aceYqotP bdpqS>^tbdPYln§c\Yl £ [ P S6n\^t_e| aceTf|FceP otS>p cs*b [`o%S8^][tbdaS>o_eYqp bd[tPoS>plneS>o>¤ oYlce[]bkaiS8p bkY [ P S6|q^]S>Lb c\qoo]S8ai[tb c\YRm[ S YlS>b n Mc\^ cLclpne^`_%| bdoYlc%[ _ |Fc%d£ S>pq^`_s¦_e|q|q^tc@´LbkTf_s[tb c\Y6cs[ Sotq^]_%aSplS>o`a^tbdFS>p§\£6[ S+otS[*cs,pq_s[`_ |McebdY\[`omo]c [ P _s[,¯ S a_%P YBc\Yl #&£%(ai' ) ce' TfD|q* q[]S_%|M|q^]c@´lbkTf_s[]bdceYMo±c%[ P P S n%S>" cLpq#&%(S>ot' bd),a-* plbko][`_%YqaS>o>¤ P P P P ª YyS´qc%_%[]TfSf|l[ dS _s[ cs_gneSclplS>otbkbko a_Bn\^tai_ece| YMP YlbkS>o"a[]o S>P pc¯"otMY l= nebd^`ne_%M| ^]Scs ce^,_fotS[,o]bkcsYqapqSf_s_%[` _f|M[ ceSfbdY\n%[toScl^]plS>n%S8o]bko]bkag[tS>|q^tS>_sp[ c\o*Yo _g_e^]S8SgT[ q ^ Sf s¤ otceM^taS |Fc%bkYe[>¤. bdneq^tS MX ]G~R]"[%m]"\e}d8~)qzi kV[ `Zio`}]"jopq"s
(86) Um~)]"\yj/i qC] m0efgVq] mni q]Glf[%d"i^z] mi ^hjem-m e\^_iRgd,]:[R`+^z]G\1[)pqzd]Gk[ efg%^iRgme^_\ jH[C\^ym%e}\^_i g^hk[ efg%^ s =. , i! / "! ª []S>^aceTf|ql[tbdYqn¢[ P SneSclplS>otbkane^`_%| P _%Yqp [ P Splbko][`_%YqaSTf_%|µm¦¯SBSi´l[`^t_eai[¡ S>%S> otS[`o¤ O,P SYLqTFS>^I§bkogn%bd%S>Y \£¥[ P SBqo]S8^ []cot|FS>aP b £¥[ P SBYLqTFS>^P cs"|McebdY\[`oqotS>p§[tP c¢_%|q|M^]c@´lP bkTg_%[]Sf[ P S P c\Yln%S8o][ _´lP bdo>¤ O,P S+aP P cebdaScs §TMo][FS Tf_%pqS-aceYqotbdpqS>^tbdYlO,n P [ S YLqT MS8^ _eYqp[ S- cla>_s[]bdceYMoc%.[ S*M^t_eYqa S>o P _%YMpcs°[ S o`T cLce[ YlS8O,otPo c%.[ S o`sS> @ S>[t_s®aM^]@e S>o[]c FSaic\Tg|Ml[]S8pR¤ qo otSeS>^`_sP [t^tbk_sko-a>_%Y¥M6 S@ YlS8ai S8oto`_%@ ^t£ []cceqP [t_sbkY6@ [ S FS>ot[-P _%dlSfc% ®¤ S P ¢ S>%Sko md¤¤¤>m _e^] S qYqb c\^tTgd£plbdot[t^tbkql[]S8pceS>^
(87) [ SbkY\[]S8^]_s BIm\¯ S>^tS bko±[ SS= ´l[t^tS>TMT csO,µP [ S-plP bkot[t_%YMaiSTf_e|_%Yqp P _eYq p ¡_%^tS*[j¯c|FS>P^`aiS8Ye[`_sneSaicL S aibdS>!P Y\[`o¤ P SMo]S8p U «_%Yq p L@ ceY b n\q^]S @l¤ Sbd[ dS%S>.otS[ / bko"[ S otS[,c%|Fc%bkYe[`o,ceY[ S n%SclplS8o]bka-ne^`_%| P ¯ ceotS SÖSi´l[]S8YqplS8p K plbko][`_%YqaS-bko / ¤ ySi´l[mO ¯ SYqSS>p [tc§|M_%^t[]bd[]bdceY S>_ea dSeP S"otS[ P / bkYeP [tc¡otMqo]S>[to$P a" ce^`##^]"S8$ ot' |F* ceYqpqbdYln¥[]c³[ P S6plb ¨;S8^]S8Y\[q^t_eYqa P P S8o c%-[ P S o`q^]_%aiSe¤ c¥P plc¢otcMmO,¯ P S F^`o][aceYqot[t^`qa[[ SB" YlS##bd"n $ ' F* ce^ P cLclp§ne^`_%| m
(88) bkYq\bkYln6SeS>^t£|Fc%bkY\[cs / ¯,b [ bd[to [j¯c a c\o]S8o][*P YlSPbdn Fce^`P o¤ S8YRmR¯SfP ^tS>Tgc%S ^tceT P [ SfS>plneS>o c\Yln%S8^[ P _%Y_+aS>^t[t_sbkY6dP S>Yqn%[ P&% / ¤ % / P bdo*plS>[]S8P ^tTgbkYlS>P p qotbkYln*[ S £l|Mce[ S8o]bko SÈ KµceY [ SpM_s[t_-|Fc%bkYe[` o M°[ S,plbkot[t_%YMaiSMS>[j¯S>S>Yg|McebdY\[tobko
(89) otTf_% L¯,bd[ ^]S8ot|FS>a[°[tc-[ S¯,bdpq[ csF[ S [`qqlk_%^"|M_%^t[to>¤WZY|q^`P _%a[]bkaiS % / bkPo"aic\Tg|Ml[]S8pB\£+Mo]bk= Ylnf[ P STgS8plbd_eYBcs[ P SPplbkot[t^tbdqq[]P bdceYBcs[ P Splbkot[t_%YMaiS _sklS>oc%[ P S otS>aceYqpYqS>_%^tS>ot[±YlS>b n Mc\^
(90) csµS8_%a |Fc%bkYe[ bkYqo]bkpl S / ¤ bdYM_sd £eme¯ S|q_e^][tb [tb c\Yf[ bkone^`_%| bkY\[]cbd[to aic\YqYlS8ai[]S8paic\Tf|Mc\YlS>Y\[to>¤ ' ó@Ú`ÕIÚ8ôsýZÒÏÓ@ÑÕÈÍZ)Ô (Òì+ Ü *ÏÚìØLâ*ÍZÌ@ÍÒÏÌ\0Ïô Í]ÞÒð ó@âÍZÔÈØÙ2ý õ0Ï,Î ÑÈ*8Úì.Î ö - K*Ú`ØÙÌ@ÕÖÔÈÔÒÏÕÈÍ]Ì Úìó*ßµÍZÒìÔÈÜqÍ]Úì.Õ K@ÑÈý ͦK Ì@àRÍZ3Ø ÍZ0CÌiKÕÈNsÍZÒÏÑ]ÑÈÎ ØÙ.Ì 00ÏÑIÚìö KN%ÍZý]ÚìÓ@ÔÖ1Í 4RÍ
(91) Ì8Í]ÍZó*ÕÖÒ KÚZòiͱ.Õ K@2Í 0ÏÍZÒ>ó@ÍZÔÖØÙý±ö@Ú`Õ K@5Ô 4 K@ÍZÌ / -Í KÚZòiÍý K8ÒÏÔÈÍZÌ-ÕÖÒ,Ó@ÔÈÍ.Õ K@1 N@ÑIÚìÌ8ý K@ÍZÔÚìÑÖÍ
(92) ó@ÍjÕÈÍZýjÕÈÍZó\Î . . Þ è°ß Þ Ë.
(93) .
(94) !"#%$'&)(*+ ,%- "./(0%1. ,O P bkoa>_%YFSplceYlSbdYB[]bkTgSYlS8_%^t £dbkYlS>_e^"qotbdYln[ P SqYqb c\YLh;Yqp_sdn%ce^tbd[ P T 6 ² { %CBI¤ S_skotcaiceTf|qq[]S [ P SaiS8Ye[`^]cebdp c%S8O,_%a P P aiceYMYlS>a[]S>pBaic\Tf|Mc\YlS>Y\[,\£+[t_e\bdYlnf[ P Sq_%^t£laiS8Ye[tS>^ csPb [`o"|Fc%bkYe[`o¤ So`sSdS[`_s,aM^]eS>og_%^tSaic\Yqot[t^`qai[tS>p \£¡aceYqYlS8ai[tbdYln¥[ SBaS>Y\[t^tc%bkpqo cs-o`qa>aiS>o`otb eS+dS%S> otS[`o¤ P S>Y [ P SdSeS otS[`o P _@eS*otSeS>^`_sµaceYqYlS8ai[tS>p aic\Tf|Mc\YlS>Y\[to"¯SMo]' S [ P Sne' S $ clplS>otbka-|M_sP[ Po" []caiceYMYlS>a[,[ P SgaiS>Y\[`^]cebdpqoRM¦P b ¦_f S>%So]S>[ / bkP o / m\¯S-o]S> S8ai[ _%S8^][tSi´fcsµ[ SneSclplS>otbka,ne^`_%| |q_e^][tb [tb c\YlS>pbdY\[]c / aceYqYlS8ai[tS>paceTf|Mc\YlS>Y\[`Go SH / / m\ce^±S>_ea ¯ P c\o]S+S>plneS+aic\Ye[`_sbkYqo_¢|McebdY\[c% / ' 1 O,_%YqP p³¯ Sce dc¯ b [`on%S>clplS>P otbda+|q_s[ P []c6[ P SotceM^taS|McebdY\[ MYe[tb ¯ P SP S>YqaceqY\P [tS>^ _eY§S>plneS+aic\Ye[`_sbkP YlbkYln6_6|FP c%bkYe[cs / ¤ ' bko|Fc%bkY\[ FSdceYln\o P []c¢[ S+P aceYqYqP S>ai[tS>p³aceP Tf|Mc\YlS>Y\[c% / f¯ bka bdoSbd[ S8^ _eototclaibk_s[]P S8p+[tcf[ Sq^`_%YMP a aceY\[t_%bdYlbkYln / 1 ce^ cla>_s[]S8p_s[[ Sqbd^t[ cs[ bko"q^`_%YMa ¤ WZYB[ P S F^tot[,a_eo]Seml[ SaP ce^`^]S8ot|FceYqP pqbdYlngaiS8Ye[`^]cebdpMo,_%^tS*aceYqYqS>ai[tS>pR¤ WZY¢[ Sfo]S8aic\YqP p¢a>_%otS%m®[ Sfq^`_%YqP a bdYlnP YlclplS bko*q_%aÏ%S>p6MP |6ceYqS dSeSÈm®_eobdddqot[t^`_s[tS>p¢bdY = bdneM^]S AvMb ±[ P SgaceYqYqS>ai[tS>P p aceTf|Mc\YlS>Y\[ bko [ S cla_%[]bdceY¥cs[ Slbd^t[ c% YlS>¯ M^t_eYqa S>o>mµbd[ bdoplS>aceTf|Mc\o]S8p¢bkY\[]
(95) c YlS>¯ aceTf|FceYlS8Ye[`o qotbdYln [ S neSclplS>otbkane^`_%| P _%Yqp³[ P S aic\YqYlS>a[]S8p¡aic\Tg|FceYqS>Y\[to P cs /*aic\^t^tS>o`|FceYqplP bkYln [tc¢[ P S>otSq^`_%Yqa P S>o>¤ "YqS¯«aiS8Y\[t^tc%bkpqo_e^]S aceTf|ql[tS>p _s[dSeS 6_eYqp _%^tS6aiceYMYlS>a[]S>p [tc³[ S¢aS>Y\[t^tc%bkpqofc%-[ S¢aic\^t^tS>o`|FceYqplbkYln§aic\YqYlS>a[]S8p aceTf|FceYlS8Ye[`ocs dSeS ì¤ b [ P [ P bko P |q^tcLaS>o`om.¯SfS>YMotq^tSf[ P Sg_eai[ [ P P_s[ [ P Sfo`sS> S>[t_%¦aq^t%S8o-ot[t_@£¢bdYqotbkplSf[ P Sc\LvZS>a[-¯ P ceotSfo`q^]_%aS bko _e|q|q^tc@´LbkTf_s[tS>p+\£[ SU%¬pq_s[`_g|Fc%bkY\[to,bkYTgceot[ c%[ Sa_eo]S8o¤ S i−1 Sc i, 1. S’c i−1, 1. Sc i, 2. Sc i+1, 1. Sc i+1, 2. Sc i, 1 Sc i+1, 1. S’c i−1, 2 Sc i, 2 Sc i+1, 2. geodesic paths. =. bdneq^tS/AvM ],`}^ x e\ylf[%d"i^z] mVi ^y^z]:| efq1^zn[R`Pi|qziRgWdzs yef~R%^ x Pe\ym] d,[RjHk[C\1] mJeg^z[o^-Y [/d,[RjHk[)g]"g^_\,x ! " J i gWm# ! " ' iRgm0^z]:d[)qq] \1k[RgWm efg~/d,]"g^zq[Rem\i q]8d,[)gg] d^z]"mJY@e^z^z]h^Y [d,]"g^zq[Rem\@[ `+l],{C],l%$'&)()s %S>Y\[`q_sd £g¯ S-Tf_@£_%|q|M^]c@´lbkTg_%[]S"[ P S*_´lS>o¯,b [ P o`|ldbdYlS*aM^]eS>o _%o o P c¯"Yce^[ P SS>T q^ ceY = bdneq^tS _%Yqp 9+* ¤ S qotS_fo]bkTf|ldS M[][tbdYln|M^]claiS8pqq^tS^tceT 6 wla P %lm b k ; B.[]caic\Tf|ql[]S [ P S>otS ot|q bkYlS>o,^]c\T [ P SaceYqYqS>ai[tS>paiS8Y\[t^tc%bkpqo¤. bdneM^]SWM ],`^ x,(.-Glf]"{C]l\1],^_\yd,[RjHkp^z]"mJ[Rg0^z]:~R]"[%m]"\e}d:~RqziRk[R` i`}]"jopq"syef~R%^ x+^z]:d,[Rqq] \1k[)gm efg~/i e\,s _%a P _´lbkoc%[ P S[`^]S>Sot[t^`qai[`q^]SBaic\^t^tS>o`|Mc\Yqp§[]c§_6[`qqlk_%^f|q_e^][ cs"[ P SBo`q^]_%aS%¤ O,P SMYlb c\Y¡c%[ P S8o]S[tqMld_e^ |q_e^][`o,c\^tT_plS8aic\Tg|F6 ceotbd[]bdceYcs¦[ P S[ P S o`P q^]_%aS%¤ S F^`ot["bdY\[`^]clpqqaS>p [ P bkoplS8aic\Tg|FceP otbd[]bdceYBce^|MP ce £ P S8pq^`_s°o`q^]_%aS>o bkY_B|q6 ^tSLbdceqo¯c\^t ; °_s8eLm N ACBȤWZY6[ O,bdo*P ¯ ce^`_+otbdTf|ldb FS>p¥plbdo`a^tSO,[tPS eS>^`o]bdceYc%±[ Sgz¢ce^`o]S [ S>ce^t£ bdo*plS>%Sdce|FS>p SÈaÏZ¤ F S>^`e\Pm F ²z¢ B¦ce^ Mo]Sc% z6c\^totS Sc\^]£6bkY¥Lbdo`q_sdbd>_s[tb c\Y Kì¤ Sn%SclplS8o]bkagplbdot[t_eYqaiS[tc6_o]c\q^taSf%S>^t[]S´6ceY _§|Fc%d£ P S>pq^tceY bdoaceTfP |ql[tS>pRm _%Yq= p _¢eS>^t[]S´¡O,Pbdoad_eototb FS>p _eof^]S>nelk_%^gce^fa>^]bd[]bka_%_eaace^`plbdYqn¢[]c§[ P S aiP ceY MnePq^`_sP [tb c\Y³cs plbkot[t_%YMaiS>o±csRbd[to±YqSbdn P Mc\^t8o SÖotSS bdneq^tS O,KϤ P Sai£LdbdYMpq^]bka_%MP plS8aiceTf|Fceotb [tb c\Ygbdocel[`_sbkYlS>pf\£fal[t[]bkYln[ ^]c\ln [ SdSeP S otS[`o_eototclaibk_s[]S8pB[]c[ S a>^]bd[]bka_%P °|Fc%bkYe[`oP ¤ S S>%S>°otS[tocs¦[ P SneSclplS>otbka plbdot[t_eYqaiS _%^tSP S aibdS>Y\[t £BSi´l[t^`_%a[]S8p ª qo]bkYln[ S _ep@v]_%aS>Yqa£MS>[j¯S>S>Y+_%aiS8o cs.[ S |Mce £ S8pq^]c\YR¤WZYc\q^P a_%otP S-[ bko_%p@v]_eaiS>YMai£^tSk_s[]bdceYMo P bk|bkoYlc%[,P _@_sbdk_%ldS%¤ oO,_gP ^]S8otld[ |Fc%bkY\[to a_eYqYlce[-FSaik_%o`o]b MS8p¢_%o*^tSn\ld_e^c\^*a^tb [tbda>_s¯ bka ¯ celkp6bkY[tq^`Y|M^]cLbkplS [ Sq^`_%Yqa bkYlnB|McebdY\[to>¤ SfceYld£ / Õ K8ÑÈÍZͱáÚ`Ì8þ8ÍÍZý]Ô.ÚìÒìÌÜMÌ8üqÒì3Ø 0ÏÕÈØÙÓ8ýZÑÈÍ Í¦.Õ úKÚ`ÚìÕ]ÑÖôlÍØÙòiÌ ÍZ)ÑÕ (K@ØÙýZÔ
(96) ñÙÒÏý]ÔÈÚìͦÔÖÍiÚìôeÌ@Õ óK8Í,Õ K@Ú`ͦþ8ØÙ.Ô ÔM,ý]Ò>Ó8ÒìÑÖ.Õ òÏK@Ú`ÍZÕÖѵÓ@ÑÖÒÏÍÌ@ͦØÙÔö@òiÑÈÍZÍZ)ÑÔÈ( ÍZÌiñÙÕÈÒ ÍZ4³ó*ØÙÚìÌÌ@óül3Ø ÷t0Ïê,Ó@ÑÈñÙÍ
(97) ÍZòiøÍZñÙØÙÔ¦ÔRÚìÕ K@ÑÖÍ Í ÔÈNs1Ó ÍZ0,ÔÖÕ.ýZÒÏØÙÍ]Ì@ÌiÍÏÕ
(98) Î ÕÖÒCÒ N8ÕÈÚìØÙÌÕ K@Í 3Ô 2ÏÍZñÙÍjÕIÚìñFý]Ó8ÑÖòi5Í 4.Õ K@Í ß°ß Ì >éiïÏêìû =.
(99) #% W"P%
(100) rZ )% W 9. =. bdneq^tS 9 M be v]"q]"g^yg pjo|]"q@[ `+lf]"{C],l\pW\1] m0^z[d,[)jHkp^z]^z]8i %e\y[ `+^z]>`r],jopq:x nq] md,pq{C] |lfp]8dpq{C]s . . −. −. +. +. −. −. − x. −. +. −.
(101) . −. + x. n ],llf[Y d,pq{C] iRgm. . x +. −. −. −. −. −. = bdneq^tS"vMP^z]@l]`}^zjH[C\^U{C]"q1^z]e\ q]"~)p l}i q i gWm^z]y[ ^z]"qPi q]d,q1e^ed"il+r^z] & q] \1k] d^ef{C]l h i)\\1[%dei ^z]"mH^z[8i>{)]"q1^z],Gegm ed"i^z] \ ^zWi^^z]8~R]"[%m] \edm e\^_iRgd,]o|],^-Y ]"],gn^z]G{C]"q1^z],iRgmV^z]G\1[)pqzd]Ge\~Rq] i ^z]"qq] \1k] d^ef{C]l l[ YZ]"q_y^zWi gn^z]8~)],[%m] \edm%e}\^_i gWd,] |],^YZ]"]"g^z]:\1[)pqzd,]GiRgmJs . Þ è°ß Þ Ë.
(102)
(103) !"#%$'&)(*+ ,%- "./(0%1. . [tce|Fc%dc%n%bka_%qbkYLce^`Tf_s[]bdceYf_@_sbdk_%ldS,_%^tS,[ P SYqSbdn P Mc\^ P c\clpgne^`_%| P _eYqpfP [ P Sn%SclplS8o]bkane^`_%| P ¤.WZYfc\^tplS8^
(104) []c plS[tS>ai[a^tb [tbda>_s |Fc%bkY\[to ¯ Saiceqdp¥bkYe[`^]clpqMaiS_B cla_%
(105) ce^`plS>^tbkYlnB_e^]c\qYqp¥_B%S>^t[]S´¢¯,bd[ _%Y¥_%|q|M^]c@´lbkTg_%[]Sg[t_eYln%S8Ye[ |lk_%YqS_%o`o]claibk_s[tS>p_%o bkY 6 T¬-¬ O,I¦eP ) BI¤§WZY¡[ P bdoga_eo]S¯S¯c\ldp P _@%S[tc¢S8P YLce^`aiSB_6n%dceM_sac P S8^]S8YqaiSP cs"[ P bdogdcla_s ce^`plS8^]bkYln6c\Y³[ P SB¯ P ce S o`q^]_%aiSe¤ bdoa_%YBFS_%oSi´q|FS>Yqotbd%S _%oS8YLce^`aibkYlnf[ S ne c\q_sRaceYqotbdot[]S8Yqai£+cs[ S [`_%YlneS>Y\[,|ld_eYlS*ce^tb S8Y\[t_s[tb c\Yqo_%o,plc\YlS bkY 6 TP ¬H¬ I
(106) \) BȤz6ce^tSª ceS>^[ P bko,¯ celkpYlc%["FSeS>^t£+^]S> bk_%q S otbdYqaSYlSbd[ P S>^,[ P SYlSbdn P Fce^ P cLclp+n\^t_e| P YqPce^,[ P S n%S>cLpqS>otbda n\^t_e| _%^tS|ld_eYq_%^>¤ ko]cFmotbkYqaiSc\q^|qM^t|FceotSbko[]cqP lbd [o`sS> S>[t_%±aq^t%S8o_%YMp³YlP c%[[tc¢^tS>aic\Yqot[t^`qai[ [ So`q^]_%aiSbd[bko ^tS>_eo]c\Yq_%ldS-[]c|q^tc\bkplS _f|q^tcLaS>pqM^]S*dS>o`oSi´q|MS8Yqotb eS-[ _%YB_^tS>aic\Yqot[t^`qai[tb c\Y+TgS[ clpR¤ "! Ï! S_%|q|q bdS>pBceM^,ot%SdS[]c\Ylbd>_s[tb c\Y+TgS[ P clpBceYB_gotS[,c%S´q_%Tf|ldS>o,|q^tS>otS>Y\[]S8p^tceT = bdneM^]Sf > []c = bdneq^tSf 8v M. =. bdneq^tSf > M(.-Glf]"{C]l\1],^_\i gWm0^z]:d,[)qq]"\1k[)gWm%efg~/\ C],lf],^_ildpq{C] \ [RgVioj/i gniRgm0[RgVio[Rqz\1])s. b n\qP ^]S = b n\q^tS 8 o P c¯"o[j¯cfTgcLpqSkoc%_gTf_%YB_%Yqp_ P c\^totS%¤ O,P S8o]S*TgclplSko_%^tS-|qMl bka*plceTf_%bdYT clplS>do c\qYqp ceY[ S S>|q_%n%S8ocs
(107) ²£lFS>^t¯ _e^]SM O,P S*Tf_eY P _%o[ P So]c\q^taS-|Fc%bkY\[, cla>_s[]S8p_%[,[ P S [tce|cs P bko P S>_epR¤ O,P S P c\^totS¯_%ogota>_%YqYlS8p§^tceT Tf_%Y\£c\^]bdS>Y\[`_s[]bdceYMo^tS>o`l [tbdYqn¢bkY l 8 dbdYlS8_%^ ota>_%Yqo ¯ P bka P aic\Yqo]bkot[]S>p¡cs_ otS>^tbdS>o,c%±ota>_%Yqocs¦plb ¨;S8^]S8Y\[-^tSneb c\YqoHSLbdS¯"o Kc%¦[ P SgceLvZS8ai[>¤ O,P S otceM^taS|McebdY\[bdo-_s[[ P SgSi´l[t^tS>Tgbd[j£c%¦b [`o v]_@¯ ¤ WZYB[ P S8o]S*[j¯ cfa>_%otS>o>ml[ P SM^t_eYqa P S>o_e^]S aic\^t^tS>a[]d£ cla>_s[]S8p_eYqpB_f[t^tSSihIdbd%S-_s´Lbk_sµot[t^`qa[tq^tS*bdo,qqb d[¤ O,P S o P c\S |q^tS>otS>Y\[tS>pbkY = b n\q^]Sg % _eYqp¢ @bkobkoto`lS>p+^tceT«_go]£lY\[ P S[]bka*TgcLpqSȤ O,P S|McebdY\[`o,plS>o`a^tbdqbdYlng[ P S*o P cLS _%^tSo][`^tMai[tP M^]S8pP bkY6¬ |lk_%Yqo>>¤ <-YlS a_%YYlce[]bkaiS[ P P _s[[ P SdSeSko,ceq[t_sbkYlS8p¯,bd[ P P [ P Sotceq^`aiS|Fc%bkP Y\["dcLa>_s[tS>p_s["[ P S ^]c\Y\= [ cs[ S+o cLS_%^tSYlS>_e^]d£¢|lk_%YM_%^>u¤ <-q^TgS[ clp§bdo bd[]P [t S+otP S>YMo]bdP []bd%SP [tc [ Sdcla_s[tb c\Y¥cs[ S+otceM^taSfP |Fc%bkY\[tRo M bdY bdneq^tS 8lmR[j¯ c plb ¨;S8^]S8Ye[|Fc%bkY\[to*dcla_s[tS>pbdY^tceY\[*cs[ S[ So c\S _@%SfMS>S>Y§qotS>p[]c6aic\Tf|ql[]Sf[ S_´lbk_s KiÕÕÈö 4 4 4 4¦Î ý (NsÍZ)Ñ 4µÚìÑÖÍÏÎ ý]CÒ M M,Òó@ÍZñÙ Ô M,Òó@ÍZñ Þ Ì@ó@Íjþ%Î K.Õ M,ñ ß°ß Ì >éiïÏêìû =.
(108) 8. #% W"P%
(109) rZ )% W. = bdneq^tS+ e M (5-ol],{C],lP\1],^_\hiRgWm^z]od[)qq] \1k[RgWm efg~0\ )],lf],^_i lPd,pq{C] \[)gV^z]8~R]"[%m] \edo~RqziRkV[R`ZiJ\1[])sX ]G] m~R] \>i)m1iRd,]"g^^z[ ^z]8\1[Rpqzd,]:k[ eg^yi q]m qzi"Yg0efgn~)q],]"gs. o][`^tMai[tM^]P S8o¤ O,P Sgace^`^]S8ot|FceYqpqbdYlnB_´lbk_s
(110) o][`^tMai[tM^]S8o_e^]Sfpq^`_@¯"Y bdY¥^tS>p¢_eYqp£%Sddc¯ ¤0<-YlSga>_%Yo]S>Sg[ P _s[-[ P S£¢_e^]S YlS>_e^]d£[ Sot_eT Se¤. =. bdneq^tSf 8M@XZY [/\ C]l]^_i l d,pq{C]"\yiR\\1[%dei ^z] m^z[^Y [m e v]"q]"g^y\1[)pqzd,]8k[Refg^_\,s . ,O P S*|MS> Lbko FceYqS[ P S-q cLclpeS>o`o]S>do o P c¯"Y^]S8ot|FS>a[]bd%S> £fbkY = b n\q^tS >U _%Yqp = b n\q^]S ; _%^tSplS8ota>^]bkMS8p+\£_otS[ cs ¬ O ota>_%ª Yqo>¤ O,P S>otS pM_s[t_+aiceTgS ^tceT [ P S pq_%[t_%M_%otS cs ? bd 7 _%^tS LlS[,c%¦[ P S ¬S8|q_%^t[tTgS8Ye[cs ²ceTf|qq[]S>^*wLaibdS>YMaiS cs S> Lbd Yqb eS>^`o]bd[j£%¤ = c\^ [ P Sq cLclp¥%S>o`otSkom°[ P STf_sbkY³^`_%Tgb ;a_s[tb c\Yqo*_%^tSplS[tS>a[]S>pµmqq[¯ P S>Y¥[ P S%S8ototSko _%^tSf[]cLc6aidceotS%m_%o*bd kqo]h [t^`_s[tS>P pbdYP [ P S^tbdn P [ P |q_%^t[*cs = P bdneq^tS ; mR[ P Spq_%P[t_|FP c%bkYeP [`o MS> c\Yln%bkYln[]c plbkot[]bkYqai[ eS>o`o]S>do*_%P ^tSfaiceYMYlS>a[]S>pbkY[ P S YlSbdn Fce^ cLclpfne^`_%| _eYqpbkY[ Sn%S>clplS>otbda"ne^`_%| ¯ bda dS>_epqo¦[tc _eYbdYMaice^`^tS>ai[^]S8otld[¦c\^±[ S*ot%SdS[t_%Fa>q^]eS>o±bdY [ P bko"_e^]S8_q¤ O,P S+_s´Lbko c% [ P Sot£lYe[ P S[tbda P Sdbdac%bkpq_s±ot[t^`qa[tq^tS+|q^tS>otS>Y\[]S8p¥bdY = bdneq^tS 8a>_%YqYlce[MSceqYqp³Mo]bkYln6y-_s>_e^]bk_%Y o otMFplbdLbdotbdceYBT P S>[ P clpR¤yTS>^tS%mq_eo[ P S pq_%[t_f|Fc%bkYe[`o"_%^tS*^]S>nelk_%^t £pqbdot[t^tbdMl[]S8pbkYqotbdpqS-S8_%a P |lk_%Yq_e^ o`a_eYRml[ P Saq^t%S bdoeS>^t£+o`T cLce[ ¤ O P P u P P P = O,P Sa_%celTfdSg|q -l[to bdYlcn¯"[to bdTg[ SSpl² S>|FS> YMpq[tbdoTgTfS _s^]bk S YlLdl£ bd^tceS>Yp+[ []P cfSaiYLc\TgqT|MFl[]S>S*^*[ c% S*pq_s_%´l[t_Bbd_%;|Motce[tbd^`Y\q[`aio [`_%qYq^tSp¢cec\Y^[ [ P S SfTgce^`cLplpqS8S^ko,c%o YlcS>¯"b n Y P Mc\b n\^ qP ^]cLS8clop n\[t^tc_e| @Pl¤¤ WZY_%a[mMP_eo,Ylc%[tbdaS>pB|q^tSLb c\qot £eml[ P SaceTf|ql[`_s[]bdceYcs[ P SYlSbdn P Fce^ P cLcLp+ne^`_%| P bdo"ceYlS*cs[ P ST c\o][S´l|FS>YMo]bd%S |q_e^][cs c\q^,TgS[ cLpµ¤ -Í N*ÔÖØ ÕÈ Í 4qÜ ÕÈö 4 tÜ ÕÖö\Î M"Ú`Õ KeÎ ÕIÚìÓ\Î ÚìýÏÎ ØÙñ `ö@Ó N NÚìÑÈÍ Ó@Íj Õ `ö8ÔÈó N `ó@Ú`ÕIÚ . Þ è°ß Þ Ë.
(111)
(112) !"#%$'&)(*+ ,%- "./(0%1. bdneq^tSf >U M =. =. bdneq^tSf ; MZlf[[%mV{C] \\1],l\:r^z]~)]"[%m ] \ed8~RqziRkViRgm0^z]:\ )],lf],^_i l d,pq{)] \i)\\1[%dei ^z]"mWs. =. ß°ß Ì>éiïÏêìû. k],lf{e\|[Rg]Hr^z]>~)]"[%m ] \ed:~)qziRkViRgmJ^z]:\ C],lf],^_il+d,pq{C] \@i)\\1[%d_e}i^z] mWs. b n\q^tSg @MZ^z]:~R]"[%m]"\e}d:~RqziRkniRgWm/^z]:\ )],lf],^_i ld,pq{C]>i)\\1[%dei ^z]"m s. % .
(113) @. #% W"P%
(114) rZ )% W. ^tSiS>^tS>YMaiS-csMneq^tS>o Y\MTFS>^,c%pq_%[t_f|McebdY\[`o YLqT MS8^cs c\^tplS8^ P cs°[ P S P ² u []bkTgS bdYotS>aceYqpqo P S>%Sko YlS>b n Fce^ cLclpn\^t_e| ceYB_%YWZYqpl£ R A\ 9 8 \L¤ 9 U 9 9 R A\ U% UeUq¤Ùs 9 R A\ 9 A% Ueq¤Ùs 9 ;; ¤ 9 U R A\ 9 % >u SÖTf_%Y K l 8%% 8 el¤Ùl ;9%;9 A 8t S P ce^`otCS K 8 A 8Uel¤ Aq9 % >\% A 8 s; Ue; q¤d >;U %\ 9 9 U% ¤Ù% ; ;9 ¤ A 9 l > >% 8 Ae 8 8 UM¤ q O _%ldSf M±w\[t_%[]bko][tbda>oce^ = bdneq^tS>o[tc 8l¤ & "> ! & S P _@%S |q^tS>otS>Y\[tS>pB_%Yce^tb nebdYq_%®[]S>a P Ylb LlS [tc_%o`o]claibk_s[tS-_eY_´lbd_%Ro][`^tqa[tq^tS*[]c_fotS[,csota>_s[t[]S>^tS>pBpq_%[t_f|McebdY\[`o¤ O,P SgbkYe[tS>^`_%a[]bdceYbko-^tS>pMqaiS8p []c[ P Sfo]S> S8ai[tb c\Y cs_o]c\q^`aiS|Fc%bkY\[¤ O,P S Tf_%bdYo][tS>|qoce^[ P Sfaic\Yqot[t^`qai[tb c\Y cs¦[ P Sg_s´lS>o _e^]S M [ P SaiceTf|qq[t_s[tb c\Y+c%°[ P SYlSbdn P Fce^ P cLclp+n\^t_e| P _eYqpBcs°[ P S n%S>clplS>otbda-n\^t_e| P mlqotbdYln¬-b v]\ot[t^`_ o,_sdn%c\^]bd[ P Tm [ P SaiceTf|qq[t_s[tb c\Y+c%°neSclplS>otbkadSeSko,_%Yqp[ P S cla_%[]bdceYcs
(115) q^`_%Yqa P bkYlnfYlclplS>o>¤ <-q^TgS[ P clpbko^t_e|lbdp _%Yqp ^]c\qqot[.¯,bd[ P ^]S8ot|FS>a[°[tc[ P S cla_%[]bdceYcsM[ P S otceM^taS|Fc%bkYe[ql[[ P $ S $LP q_sdbd[j"£ "csM[ P S,^]S8otld[]bkYln P P P P P P o`sS> S>[t_sµa>q^t%S>oplS8|MS8Yqpqo,c\YB[ S_e|q|q^tce|q^tbd_%[]S*a c%bkaiS-cs[ S ce^`plS>^ cs[ P SYlSbdn Fce^ cLcLp+P ne^`_%| ¤ P ce^`§bdY |q^tc%n\^]S8oto bdYMaikqplS _s[t[]S>Tf|l[`o[]c§TgclplS"Tgce^tS|q^]S8aibko]S> £ [ SdcLa>_s[tb c\Y¡cs-[ S q^`_%YMa bdYqn¥YlclplS8o_%Yqp _%Y _el[]c\P Tg_%[]bkaP o]S> S8aiP[]bdceYcs®_-otceP M^taS |Fc%bkY\[Mo]bkYln-[ P S"plbk_%TgS>[]S>^ª c%F[ P SYqSbdn P Mc\^ P c\clpne^`_%P | P ¤ ª P T c\^]S,P ^tceqMo][aic\P Yqo][`^tMai[]bdceY c%P µ[ S*YlSbdn Fce^ cLclp n\^t_e| bko_%dotcqYqpqS>^ aiceYMo]bkplS>^`P _s[tb c\YR¤ Y+_epq_%|l[tb eS"ce^`plS8^
(116) ce^±[ S-YlSbdn Fce^ cLclpfne^`_%| q_eo]S8pfceY [ S cla>_sµplS8Yqo]bd[j£+c%pq_%[t_f|Fc%bkYe[`o"aic\lkp|q^tceM_%ld£ S>d|R¤ ± & $i/ ' g! S*¯,bdo P [tc [ P _%Yqfz_%^`aiS 7 ceo`a,c\^ P bdo bkTg|q S8T S8Y\[t_s[tb c\Yc%.[ P S aceTf|ql[`_s[]bdceY+cs.[ P S ¢YlS>_e^]S8o][ YlSbdn P Fce^`o±c%°_g|McebdY\[ bkY_gotS[,c%U%¬pq_s[`_f|McebdY\[to>¤ "#% ,"! . s s h~ efg0i gWm/Xs s Zefg`}[)qzm s Z[)jHkp^z]"qZm] \d,q1efk ^e[Rg0[ `dpq{C] m[R| -] d^_\,s
(117) g !"#%$!'& ()$"+*, - .0/ 1$" 2 # 34/5%'&6 5&7& 98: !/ ( ; s [Re=<'<> ? s bos [ e}\\1[Rggi ^ s1@%Wi k]q] d[)gW\^zqpd^ef[)gV`rq[Rj k l}i gWi q>d,q[)\\>\1] d^ef[)g\,sA()$.CB6D FEG-%$"IHCJK BI#/5G0"6L.M+8: N $,/ GG-:8 !O'O %( '<"< s P@ RQs pqzm%efg C hs y[)p S hs ],`U]"T {%q] >i gWm
(118) s@^efgWm]l sWVn[%m],lefg~ iRgm5iRgi l \e}\J[R` -b ],lf[Rg~Ci^z] m5\1Wi k] \JY@e^z iRkkled"i ^ef[)g5^z[ lf[)g~ |[)g]VjH[Rqk[)jH],^zq sWYXZX)X[ I" G ;/5##$" G\$"^]F Y"%/-'&_.M,8"78 (.-% (x ,` ( baW]"|qpWi q ( s @ +(5 ? s Zlf[[)jH]"g^zi lhiRgmcsZ@%[]"j/i C])sd Z[)g%{C[ lfp^ef[)gE\1pq1`iRd,] \,segf()$".CB6D \JKY Bg%/5Gih jJkJZl 2 N)mon p'q5r {C[ lfpjH]81a - kWiR~R] \ha -+(` 1a - s?Rpl ( +()s @X -,
(119) ys Ze^^_iRq sX@\eg~)[)\ iRgWmtVus u+s!>i)\d,p],lLs hp ^z[)j/i^e}d>q]"d,[)g\^zqpWd^ef[)g[R`Ppg\^zqpWd^zpq] m b mi ^_i%x_ Z[Rjo| eg efg~Hi jH] m eil i%e}\i gWm0efjHklede^y\1pq1`ri)d,]"\,s4-gvX4Dg$-8"Y Bg%/5G n p;w WkWiR~R] \O -'+`:O '< x@%]"k^z],jo|]"q ( -%s 4y > ? s Zlf[[)jH]"g^zWilhiRgWm s)y {%ellLszg^z]"qziRd^ef{C]0^z]"d_ge={p] \o`}[)qHefjHklede^/jH[%m],lefg~ s|()$".CB Dg FJKY Bg%/5G\h q;p;p;} j ~.CBg$"G-D.$"tI Y;/5#" >JKY Bg%/5G r aO a)x ( >` (1(
(120) VVi qzd_ ( s
(121) Kb@ s ZiR"]lflf] G.s
(122) Um]l}\1|qpgg]"q Us ? sp ef|Wi)\ iRgWmVus@ iRq1efq"sWbhe}i jH],^z]"q CY@em%^z d_l[)\1] \^Zlefg]@ki efq %i gWmokiRqziRjH]^zq1e}d \1] iRqzdzefg~sKbG /5Y M()$".CB6D"##$"!'&ZJ Y$".L #~ ( ( %s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Þ è°ß Þ Ë.
(123) >U.
(124) !"#%$'&)(*+ ,%- "./(0%1 . Xs sI Z[RqjH]"g I hs
(125) s ],e\1]"qz\1[)g iRgWm 8s+Us+e{)] \^ s I#Y$,"DI/5#%$i$ 2 & 8;$ 7:.Gzs VVd,qzi"Y hell h],Y [)q % ( s
(126) U|] G!s
(127) P|],lLs y] d,[)g\^zqpWd^ef[Rg efg^z]"qzi)d^ef{C]m], l]" jH]"g^_\:iRgi ^z[Rje7{p] \Mi0T l i em]/m ]H\1pq1`ri)d,]"\Gm ]o`r[RqjH]olef|q])s/X x] T \1]/m] m[%d^z[Rqzi ^y]"gV\d_e],gWd,] \
(128) Zd[Rlf]8>i ^ef[RgWi lf]@%pk ], q1e],pq]8m]"\@ X ], l ] d,[)jHjpg e}d,i ^ef[)g\ u i q1e}\ s?)iRg%pWi q ( s
(129) Pel "O u+s Gs
(130) Pelf]"qz\,s4@ jH[[ ^zefg~oiRgWm/efg%^z],qk[Rli ^ef[)g0Y@ef^zJWg ef^z]>m e v]"q]"gd,] \,s gAu+sI h] d |],q1^ ]"m e^z[)q )JKYBI%/5G0J .GSgE kWi ~)] \yaO ( `%a - %s d"iRm]"jedCuPq] \\ [C\^z[Rg ( Os a _
(131) ysKaW]"q1lf] CV u+s_ iRge U>i)\dp],l 8i gWm5bos ^^_ilfeLs|@ C]l]^_i l:q] d[)gW\^zqpd^ef[)g [R`|qzi gWdzefg~ \1iRk] \,sg .SB!& %/5 j D7*+;/ G n p kWiR~R] \ (a'+` (5Oa
(132) PefgWm [{C]"g >d^z[)|]" q ( %s
(133) Ppq[R~)qziRked"\,s b>b
(134) )a> s [Rkk] )XsRb>] y[C\1] )Xs)bpWdzWiRjHk '? s;VVdb>[)gi lm CiRgWm1y s'@%^zp],^z,lf])s @ pq1`i)d]@q] d,[)g\^zqpWd^ef[Rgo`rq[Rj pg[Rq~Ci gef"] m k[Refg^_\,s g()$".CB6D LJK BI%/5Gh jJkJZl 2 N)m[n p +r {C[RlfpjH]:a WkiR~)]"\S ( `"< s?Rpl ( )a%s cb KV "O bos sc8iRqq[Rg ? s Z[ i gWm sgVe\1qzi%s+],Y5gWm%eg~C\ `rq[)j ^z]b@%kem],qy5]"|Ji lf~)[Rq1e^zjnxPX [ Y@i qzm\@im ef~Re^_i lxVn[Rqz\1] ^z]"[Rq sg Gs 8s1y[)|| ] m%ef^z[Rq 4EG-DI'& ,"#%$"M7 %$".M -%/-'&()$.CB6D#:8 n p )kiR~)]"\ "O ,` -' +y[%dz] \^z]"q : >d^z[)|],q ( "Os!@gu)
(135) duUq[%d,],] m efg~)\,s c:]"q Ca, s Us;c:]"q~)[)\e],gs+X[)k[Rlf[R ~ 0iRgm/{e\1pWile"i ^ef[)g xP`}q[)j ~)]"g]"q1ed>\efg~)p liRq1e^ef] \Z^z[od[)jo| efgWi ^z[Rq1ei l \1Wi k]jH[%m ],llfefg~sxg s6@ egiR~)i Y i/Xs Ps!c:pg ee ] m%ef^z[Rq x !#%$"!"&4$ GI$ B $"v.M$,: v8: Y$".M # %//$.CB6D#:8k*+$"b,G-DI'& ,"#%$ X .[ [ !?RiRkWi g ( Ca%ss@ kq1efg~)]"q"s iR -> a s iR i qpW\,s_ Z[)pq|]"\ d %lefgWmq]"\y],^y j ], ^_i jH[)qk[C\1]"\ k[)pq@l efj/iR~)]Gm ]8\ g^zx] T \1])sUX x] T \1]Gm ]8m[%d^z[Rqzi ^h]"gV\def]"gd,] \ g e{)]"qz\e^ ]k u Y@MQCY b>]"d,]"jo|], q ( -%s ;Q a .s i iRqp\iRgm 8s,QU],qq[)pW\^ sC b ] d,[RjHk[C\e^ef[)gd %lfefgmq1e={p]Um]Pk[Rl ] T mq]U],^ d,[Rpq|]U\Y{%p],lf],^^z])sIl ,D KI 6"#%$"6'&9 : L ( 2 _ n ,*+$-8" BI %( ()#O [{C]"j|]"q ( %s V V u4<'> ? s @vs sVe^_dz],ll vbos VussVn[)pg^ viRgm\ hs Gs!u iRki)m efje^zq1ef[)p sX ]om%e\d,q],^z]G~)]"[%m ] \edkq[R|lf]"jnsbj 2 " ] !$#()$".SB6D% # ( %x O:+` "< ( "<;s >iR siR i q1e}i gs y] d,[RgW\^zqpWd_^e[Rg/iRp ^z[)j/i ^e={p]ym ]h\^zqpd^zpq]"\Ui gWi ^z[Rje={%p] \^zp|pli efq] \CiT &l ie}m ]>m ]h\1pq1`iRd,] \Zm ]@`r[)qjH] le|q])sUX x] T \1]8m ]:m[%d_^z[)qzi ^h]"g\def]"gWd,]"\ 6aiRd,pl^ ]8 m]"\S@ def]"gWd] \m ] pjefg :VViRqz\1],ellf] saWqziRgd,] 6@ ]"k ^z]"jo|],q ( s b _@ O" s>iR"iRq1eiRg ) hs Z ] m[ ^ +i gWm ?%s @%],{p],efqzi s0g^z]"qzi)d_^e{e^ i gWm b],li gi ^zq1eiRg~)p l}i^ef[)gu`}[)q:^z]q]"d,[)g\^zqpWd^ef[)g [R`+^zp|pli qhi gWi^z[)jed"i l\^zqpWd^zpq] \,sZg 'q 7i"I DI'& /-$"+*, - 6/ 0$*SYXZX))X (XK:8"s - 8 7 ]\ -; -/57s !* _%$'& $-8"~ j!$,/5 #~ Wh[{C]"jo|],q ( "Os b _@ siR i q1eiRg 4 hs) Z ] m[ ^ iRgm ? s @%],{p],efqzi%s hp ^z[)j/i ^edq] d[)gW\^zqpd^ef[)g [R`@efqq]"~RpliRq^zp|p liRqG\^zqpWd^zpq] \8pW\efg~ ~)]"g]"qzi lef"] mVd lefgWm ]"qz\,s4] ( 2 n 'p *+ l ,D kI 6"#%$"6'&9 : M ( 2 _ n ,*+$-8" BI ( () ( a) %( s Ccbc
(136) > Vus i , ` s. c p, |lf]"q 8sc>e %efg e}\ 'Vus
(137) ys;@ ]"g^z[)g )i gWm
(138) ys'@ / ] C],l sI ZWi qzi)d^z],q1e}\i^ef[)g/[R` RbQ[Rq~CiRg\1WiRk]"\ egjH] m ed"il efj/iR~)]hiRgi l \e\ZpW\efg~G\ C]l]^z[)gef i^ef[)gs
(139) 1 g 0t$"2 GYg$ Bi$"A]\7 .M"##/"&6]\ 7I$,"GC$". %$.L Y"%/-'&g.0,8: 2 !"& ~"G-G kWi ~)] \ ( >` (.- %ss
(140) 5
(141)
(142) du CV 6?Rpg] ( %s Ka O" Xs:3 b>[Rgg],ll CXs
Documents relatifs
To test whether the vesicular pool of Atat1 promotes the acetyl- ation of -tubulin in MTs, we isolated subcellular fractions from newborn mouse cortices and then assessed
Néanmoins, la dualité des acides (Lewis et Bronsted) est un système dispendieux, dont le recyclage est une opération complexe et par conséquent difficilement applicable à
Cette mutation familiale du gène MME est une substitution d’une base guanine par une base adenine sur le chromosome 3q25.2, ce qui induit un remplacement d’un acide aminé cystéine
En ouvrant cette page avec Netscape composer, vous verrez que le cadre prévu pour accueillir le panoramique a une taille déterminée, choisie par les concepteurs des hyperpaysages
Chaque séance durera deux heures, mais dans la seconde, seule la première heure sera consacrée à l'expérimentation décrite ici ; durant la seconde, les élèves travailleront sur
A time-varying respiratory elastance model is developed with a negative elastic component (E demand ), to describe the driving pressure generated during a patient initiated
The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide
Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to
