Flattening of 3D data
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Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Flattening of 3D data Robert Acar — Brent W. Seales. N° 5048 Décembre 2003. ISSN 0249-6399. ISRN INRIA/RR--5048--FR+ENG. THÈME 3. apport de recherche.
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(19) 24)13 576 )83 5 9 ) 3 [ SUy DLN?`D^BD]lSOlD^ :PcLlLNDJ`SJB\`¡ D8DD _\|~¤$³oTRLbD LN?_PcL[8 SLN?BTR`L@UTV]b]§Tc \VDJBDONPRUSLKV[` DQZ?BT"TV]bDkLb?BDk:PgLbLNDJBSUJB\{pBPRJBDkLbTyqDoLN?BD 2 5 6 pBmPcJBD&SLN]lDá Pc 43 5&5 43 LN?BD pBObTgfhDQLbSTRJB]TR$ ' 5&5 ' TVJLb?BD 2 5 6 pBPRJBDc >@?BDPR\RTVObSLN?BC SU²LN?BDJy D > |Vjd±DOl¨TVOlC[ SUJLb?BD 2 5 6 pBPRJBDc[P xkDmPR`J_P/LNObSPRJB\RBmPgLNSUTVJTc 3 5 5 3 EI¥L QTVJ`]bSU]lLN]eTc rLbObSPRJB\VUD] 5 PRU 5 5 §Lb?BD@D^B\RD]eTR_Lb?BS]LbObSPRJB\V"X mPgLNSUTVJ² 7ESJBJ`T8QBTVB] PRyBB]lDoTc²JBTRLNPcLNSUTVJ²[MS ±fhTRSJB] LN?`D RDOhLNSUQD] "! PRJB#^ $b[ Q/PRU Lb?BDD^B\VD fhTVSUJBSUJB\ ' !PRJB(^ '%$ 5 ]bTLb?_Pc L S] LN?BDp`ObTcfhDQLNSUTVJTR TVJWLb?BD 2 5 6 pBPRJBDRkIKJWLN?BD.]NPRCEDC PRJBJ`DO[q^BDJ`TRLNDyM '& LN?BPcLkLbObSPRJB\VUD ?_P/"SJB\WpBObTcfhDQLbSTV(J )& 5 ObDp`ObD]lDJMLN] P LNObSPRJB\RBmPgLNSUTVJ TR§Lb?BD ]bBOh;PRQD ^_PgLZP`© D SU§`]bDLN?BD]bDD^B\RD] PRJB^LNOlSmPcJB\VUD]ESJLb?BDcPRObSPcLNSUTVJ_Pc ¨TVObCHBPcLNSUTVJ²[±PRJB^ D(ObD\MPROb*^ 43 5 5 43 PR]&¡¢PRUCETV]lLZ¤kLN?BD HDObTRLb? SLNDObPcLND TR TVBO _JBPR]bTVU`LbSTV+J 5&5 z8jxk&D BJBDLb?BDQOlSULbDObSUTVJ ¡;TVy"fhDQLbSURD¨`JBQLbSTVJ_¤$[_TVO@DJBDOl\R > , .- /1032 ?BDOlD - 5476 89 :;89 <=6?> PRJ`^ 2@A4*76 B '& :1B) '& C=6 > 5 PRJB^ ?BDOlD 8 CED/PRJB] eBQSU^BD/PcJ&UDJB\RLb? PRJB^ B CED/PRJ`]"eBQSU^BDPRJPROlD/P`@¡¢³oTcLND§LN?BPcL LN?BD7]bpBPcLNSPR1LNObSPRJB\RBmPgLNSUTVJ.SU]pBSUDQD SU]bD§:PgL/[R]lTkLN?BPcLDPRQZ?]lp_PcLNSPR1LNOlSmPRJ`\VD7SU]P pBPRJBD§LNOlSmPcJB\VUD~¤$ 0 S]7PQTVJMLbObTVBpBPRONPRCED$LNDOK> 0D.E CED/PcJB]eLN?_PcL TRBOeQOlSULbDObSUTVJ S]p`BObDU CEDLbObSUQ$X¥pBObD]bDOh"SJB\`[ ?BDObDPR] 01F + C DPRJB]LN?BPcLTVBOQObSLNDOlSTRJSU]. LNSUULbD^ LNT~ PROb^B] pBOlD]lDOl"SUJB\PcObD/P8 F` D¨TRObD. D]lLNPROlLkLN?BDSLNDONPcLbSTRJSJ,"SUD TR C P;1SJB\Lb?BDQOlSULbDOlSTVJCESUJBSUC.BC [ D C.B]hL C(P ;RD§]lBObD§Lb?_PcLLb?BD§pBOlTVyBUDC S]± D XKp TV]bD^Ey1`£8SJ`\DJBTV`\V?{C PRJM cPRObSPRyBUD]e>@?BDOlDkSU] CETVOlDjLb?_PRJ&TRJBDj P/(LbTH^`THLN?`S]`]bT;PRO[M Dk?_P/RDkDUSUQSLND^ LNT QZ?BT"TV]bDLK T&PR^cflPRQDJMLoJBT8^`D]oPRCETVJB\ELN?BGD 43N]¡¨]NP/V[:J1BCHyqDObD^H 3 PRJB^+43> ¤ PRJB^ OlDpBPRQD&LN?BD&^BS]hLZPRJ`QDy DLK DDJLb?BDC [ ?BSUQZ?S].Lb?BDpBOlTcfhDQ$LNSUTVJTR§Lb?BD ^BSU]lLZPcJBQJD I ' 5 ' > [ByMK I ' 5 ' > 7 >7"pBSUQ/PcV"[ 43 5 43> PRObDQZ?`TV]bDJLNT;Pc²TRJ Lb?BD yqTRBJB^_PROhTReLN?BD.QTVJMVDY£ ?1BUTR 43 5 5 43 FjTV^`SJB\(LN?BD]bDLK T `£8D^²[2Lb?BD TVJB\VDJ1BSJ`DRPcObSPRyBUD]@ SU2Lb?BDJ y LD M 5 D$ L N.y DLN?BDObPcLNSUT{y DLK DDJ ÏÏ ÁZ [$ÝC\K].
(20) =?= . L. I ' 5 ' > PcJB^ I 3 5 3> opWLbT&]h8CECEDLbOlR[qLN?`D.JBD$ RPcBD]TR 3M 5 3 PROlD TVy`LNPRSJ`D ^,yMP&ObDQT"TVOb^`SJ_PgLNSU]NPcLbSTVJWQTVJB]lS]hLNSUJB\TR P QTVJ`\VObBDJBQDH¨TVUT~ D^yM P^`SPcLNSUTVJTR§ObPcLNSUT+8N © D C P~Pc]b]b`C Dc[DcÇ\BU[±Lb?_PcLLN?`D(JBD$ 43 SUU y D PcL LN?BD.TVObSU\VSUJTR LN?BD 2 5 6 pBPRJBDR[ 4 3> ?_Pc]JBT~¦QT8TVOl^BSUJ_PcLND] E 5 I ' 5 ' > C [²PRJB^ PRU2LN?BDTRLb?BDO@¨OlDDVDOlLNSUQD]o?BP~RDHJ`TVJBJBD\MPcLNSVDHPRyB]lQSU]b] 243M 5 243 . vB FkP/"SJ`\ `£8D^LN?BDSJ`SULbSmPR@\RBD]l]&SUJLN?`S]E;PR]b?`STVJ2[ DJBT~ SLNDObPcLNDBJMLNSU DS X LN?BDO P]lLNTRpBpBSUJB\QObSLNDObSUTVJS] CEDL[kTVO PQDOlLNPRSJJ1BC.y DO TRHSLNDObPcLNSUTVJB]SU] D$£8QDD^BD^²[:SJ`^BSQPcLNSUJB\EPRQ ;&TR QTVJMVDOb\VDJBQDc ©D?_P/VDB]lD^ LN?BD PcLNPRyObTR8X LNSUJBD q[ ?BSUQZ? D{?_P/RD¨TVBJB^,LbTyqD{CETVOlDObTRyBB]lLkLN?_PRJCED$LN?BT"^B] LN?_PgL.B]lD&\VObPR^BSUDJMLHSJ`¨TRObC PcLNSUTVJ² ³jTRLND LN?_PgLHLb?BD(TRy8fhDQ$LNSVD&¨BJ`QLNSUTVJ²[± ?BSUD ]bCET"TRLN?²[`S] JBTVJ`QTVJMVDY£ ¡;]bDD.PcpBpqDJB^BS £ @¤Y ®¯ « ` ²R |V@©?BDJpqDOl¨TVOlCESJB\ LN?`D SUJBSLNSPR xkDmPR`J_P/LbObSPRJB\V`mPcLbSTRJ²[ SULSU]HJBDQD]b]NPcOlV[PR] PpBOlDUSCESUJ_PROh ]hLNDp2[§LNT DY£`QS]lDWLN?`TV]bDLNObSPRJB\RD]( ?BSUQZ? SUkPcpBpqDPRO(PcL(Lb?BD yqTRBJB^_PROhV[PcJB^, ?BSUQZ?PcObDJBTcLpBObTgfhDQLbSTRJB]TR7\VDJ1BSUJBD{CEDCHyqDOb]TR PRJPcp8X pBObT/£8SUC(PgLND LNObSPRJB\RBmPgLNSUTVJ TcHLb?BD]lBOl;PcQDSULb]bDá[yB`LObPcLN?BDOPRObD @á?BPRJB\VSUJB\ ^BT~ J LN?`D]bSU^BD] BZ D"SJBQD&LN?`DLNDJ`^ LNT,y D&DTRJB\MPcLbD^PRJ`^ =] ;1SUJBJMV[ TVJBDQPRJ ^BSU]bQ/PcOb^LN?BDC B]lSJB\PWLb?BObD]b?BTVU^ TVJLN?BDPROb\RD]lL PcJB\VUDR FjDOlDR[ D]lSCEpB B]bD^PLb?BObD]b?BTVU^ TVJLN?BD&PRObDP >. D^BSU]bQ/PcOb^BD^ LN?BTV]lD(LbObSPRJB\VUD]LN?BD&PRObDPTR ?BSUQZ? PR]]lC PRUDOLb?_PRJ Lb?BDP/VDONPR\VD,PRObDP y1CETVObDLN?_PRJ TRJBDW]hLZPRJB^BPROb^ ^BD"SPcLNSUTVJ² LN?`DO QOlSULbDObSP{ SU?_P/VDLNTEy DHPc^BTVp`LbD^PR^?BT8Qc z8+ D8SUJBQD DEPRObD.JBTRLB]lSJ`\\VONPR^`SDJ1LSUJ`¨TVOlC PcLNSUTVJ²[²SLSU]JBTRLJBDQD]b]bPROlWLNT]b`C ]b´1_PROlD]{SUJ LN?BD&^B&D _J`SULbSTVJTc@LN?BDDJBDOl\R¡¨TVO[SJC PcLb?BDC PcLbSQPR LbDObCE][ D QTV`^ `]bDPRJ SJB]hLNDPR^ TRjPRJ > QObSLNDObSUTVJ:¤Y>@?BD&B]bDTc§LN?BD(]b´1_PROlD]SU] SJ`^BSQPcLND^TVJByqDQ/PRB]lD. D{PRObDHB]bSUJB\ [² ?BDOlD.LN?BDPR\RTVObSLN?BC SU] J_PcLbBONPRU PR^_PRp8LND^LbT&P{]b`C TR±]b´1_PROlD]
(21) . . . . .
(22) . !Y © D LND]lLND^Lb?BDWPc\VTRObSLN?BC TRJ PRJD$£`PRCEpBUDSUJMVTV"SJ`\zVtJBT8^`D] >@?BD]hLNDpB]PROlD SU`]lLNObPcLND^SUJ _\VBOlD](z `t" SU\zW]b?BT~ ]ELN?BDSUJBSLNSPR@xkDmPcBJ_P/LNOlSmPRJ`\VBPcLNSUTVJTR ]bp_PcLbSmPc^BPcLZP` SU\(F(]b?`T¸ ]oLN?BDHpqTV]lSULbSTRJWTRLb?BD.SUJBSLNSPR \VBD]b] SU\V]jvPRJB^t ]b?`T¸ . . . . . . ͨÎÏͨÐ.
(23) }.
(24) . LN?BD ObD]bBL{TR ObBJBJ`SJB\ ObD]lpqDQLbSURD ?BDJ 0. + PRJB^ 0 E TcLN? _\VBOlD] ]b?BT~LN?BD pBPRQDCEDJML TcqLb?BD ]bTVU`LNSUTVJ²[1C PRO ;RD^(yMLN?BD ?BTRUT~ ^BTRLb][1ObDmPgLNSVD LNT{LN?BDSUJBSLNSPR\VBD]b][:C PRO ;RD^yMLN?BD `£8D^LbObSPRJB\VBPcLbSTVJ2 >@?`D p TVSJMLTR8LN?BSU]±DY£`PRCEpBD S]CEDOlDLbTkQZ?BDQ ;LN?BD7]bTV`JB^BJBD]b]TR8LN?BD PRU\VTVOlSULb?BC JEPROb\RDO D$£`PRCEpBUD][8C PcLbmPRy Ob`JB] SJMLNTLNOlTVByBUD> D DObDjBJ_PcyBD@LbTQPRObOh{TV`LeLb?BD QTVCEpB`LNPcLNSUTVJTVJP|¸tcwM} LgX¥JBT8^`D ¡ + + ¤§D$£`PRCEpBUDR[ PRJB^ D¨TVBJ`^Lb?_PcLjSUL PR] PROlD/PR^8{QTVJ`]bSU^BDObPRyBE]bUT¸ D^(^BT~ J&TVJ PEW| LVuVu¸XKJBT"^BD§]lByBp_PcLbQZ?&TR LN?`Dj^BPcLZP`[M^`BD@LNT C(PgLNPRy ]D$£8QD]b]lSURDkCEDCETVOhObD´1BSOlDCEDJMLb] _BOlLb?BDOLbD]hLNSUJB\TR:LN?BD§CED$LN?BT"^{ TV`^ ObD´1BSUObDB]lSJB\(PRJBTcLN?BDO@?BS\R?8XKUDRD ]bQSDJ1LbS BQ.PRJB\V_Pc\VD]bBQZ?WPR] TVO _TVOhLNObPRJ²
(25) . . . v3 (e8 ). e8. x. SU\VBOlD |> . ! !E ± Q
(26) . . v7. u2 u7. u3. y. . v2. S]@Lb?BD:PcLbLbDJBSUJB\ C PRp. J`D(TVCESU]b]lSTVJ¨ObTVC LN?BD CEDLN?`T8^^BD]lQObSUy D^²[SU]?BT~ LNT LZP;cD&SUJMLNTPRQQTVBJMLSUJ`¨TVOáX C(PgLNSUTVJ&PcyqTV8L QBOlcPcLbBObDcIKJB^BDD^²[`P]lBOl;PcQDjS]lTVCEDLNOlSQ LNTHP:PcL7ObD\VSTRJ(CHB]lL ?_P/VD DVDOl1 ?BDObD HDObT PRB]b]lSmPcJQBOlcPcLbBObDc D8`QZ?WSUJ`¨TVObC PcLbSTRJQPRJyqDDCHyqD^B^BD^,SJP Ob&D BJBDCEDJMLeTcBTVBOpBOlT8QD^BBOlD§PR] ¨TVUT~ K] >\RSURDJ.Lb?BD ]lp_PcLNSPR1^_PcLNP`[gB]bD T"Q/PR"PRp`pBObT/£1X SC PcLbSTVJLNT(Lb?BDQBOlcPcLbBObDHSJ,TROb^BDOoLNT&]bD\RC DJMLLN?BD.]bp_PcLbSmPc±OlD\VSUTVJ,SUJMLNTTVJ`D.p_PROhL ?BSQZ? Q/PRJyqDE:PcLlLNDJ`D^²[ePcJB^ TVJ`D ?BSUQZ?Q/PcJBJBTRL>@?BSU]H SU PRObSU]bDc[±¨TVOSUJB]lLNPRJBQDR[ SJ PRJM]lSULb_PcLbSTVJ ?BDOlDPRJSJBSLNSPRUU :PgL.TVy"fhDQL.?_PR]HpqTVOhLNSUTVJB] ?BSUQZ?^BDRDUTVpqD^²[ ÏÏ ÁZ [$ÝC\K].
(27) w. =?= . 40 35 30 25 20 110. 190 180. 100 170. 90 160. 80 150. 70. ±S\V`ObDz >7xkDmPR`J_P/LNObSPRJB\RBmPgLNSUTVJ TR^BPcLZP 60. 140. . 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. −5. −10. −15. −20. −25. −30. −35. −40. −45 0. 21. 22. 23. SU\VBOlDHF >eIKJBSULbSmPc\VBD]l]. 5. 10. 15. 20. 25. 30. 25. 24 35. 40. . ͨÎÏͨÐ.
(28)
(29) α = 1, no convergence 1. 0. 2. 3. 4. 5. 7. 8. 9. 10. 13. 14. 15. 18. 19. 20. −5. −10 6 −15. −20 11. 12. −25. −30 16. −35. 17. −40. −45. 21. 22. 23. 24 30. 25 40. SU\VBObDv > njD]bBLo ?`DJ 0 + T¸RDO LNSUCEDR[1§PROlpBSUJB\.TVO yB`yByBUSJB\`eI¥L SU]7Lb?BDJ(TR²SUJMLNDObD]hL LbTHCET"^BSU {Lb?BD pBObTRyBDC ]bT LN?_PcL[qJ`T¸[ LN?BDH:PcLbLbDJBD^,^_PcLNP&SU]kObDpBPRQD^y1JBDPROb_PcLbLbDJBD^²[²PRJ`^,TVJBDH^BD"SU]bD] P^B_Pc7 P/LbTW]lLbTVObD&PRJB^ "SUD LN?`D&Q`OlVD^p_PROhL/[B]lSJ`\B[]NP/R[ePW\VObPRpB?BSUQ/PR B]lDO ] SJMLNDOl;PRQDR ioJBTRLb?BDOjpBBOlpqTV]lD¨TROj`]bSUJB\Q`OlcPcLN`ObDSJ`¨TRObC PcLNSUTVJS] LNT y D.PRy`DLNT \VDJ`DONPgLND ^_PcLZP]h8JMLb?BDLbSQPRESUJ "SUD TcqLbD]lLbSJ`\Lb?BS]eTROeTRLN?BDOeCEDLN?`T8^B]"Lb?BD C PcLN?BDC PcLNSUQ] TR LN?BSU]pBObTRyBDC PROlD{JBT~¦TR ^BS 2DObDJ1LbSmPcX¥\VDTVCED$LNObSUQEJ_PcLbBObDc.© D{?BP~RD(]hLZPROhLND^ TVO ; LNT{LN?BSU] DJB^2 0. 5. 10. 15. 20. 25. 35. . . H E
(30) !(! ±QP IKJ ]lDQLbSTRJ z8[j D]b?BT~ D^LN?_PcLBJ`S´1BDJBD]l]WTRHLN?BD ]bTR`LbSTRJ TRLN?`DQTVJMLNSUJ1BTVB] pBObTVy`DC PRCETVBJMLb]kLNTBJ`S´1BDJBD]l]HTR" [²SU]bTVCEDLbObSUQ{]bDU X¥C(PcpTc7PpBmPcJBD{ObD\VSTRJ [ BJB^BDOLN?BD PR]l]bBCEp`LbSTRJ Lb?_PcL (UD/P/RD] p_PROhLeTR:LN?BD@y TVBJ`^_PROl`£8D^W¡;SUJ{TRLN?`DO TVOb^B][ ]bBQZ? P( QPRJWTVJ`Uy DLb?BD.SU^BDJMLbSULK`¤$oI¥LkSU] ;1JBT~ J,Lb?_PcLjLN?BSU]kSU]oSUJB^BDD^,Lb?BD.QPR]bDHSU TVJBDB]lD]@LN?BD;PcQL@LN?BPcL@SU]bTVCEDLbOlp`ObD]lDOhVD]oT"Q/Pce¡ eBQSU^BDPRJ:¤§^BSU]lLZPcJBQDc IK]@SLjPRU]bT . ÏÏ ÁZ [$ÝC\K]. #.
(31) |~u. =?= . α = 0, converges 1. 0. 2. 3. 4. 5. 7. 8. 9. 10. 13. 14. 15. 18. 19. 20. −5. −10 6 −15. −20 11. 12. −25. −30 16. −35. 17. −40. −45. 21. 22. 23. 24 30. 25 40. SU\VBObDt > njD]bBLo ?`DJ 0 E LN?BDQ/PR]lDHSeTVJ`DHOlD´1BSUObD]oCEDObDU Lb?_PcLp`ObD]lDOhVD]UT"Q/PR PROlD/PV >@?BDHPRJB]l DOjLNBOlJB] TV`L§LbT y DJBT`[_PR]§LN?`D¨TVUT~ SJ`\ DY£`PRCEpBD]l?BT~ ]jSUJ Q/PR]lD ?BDOlD SU]@LN?BDBJ`SUL ^BSU]bQ> D$L N yqD Pj¨BJ`QLNSUTVJ^`&D _JBD^{TVJ E 5 + 5 SLN?HLb?BD p`ObTVp DOhLKLb?_PcL]bDJB^B] E PRJB^ HDObTBikJHD$£`PRCEpBUD TcB]b`QZ?P S] N B N + : N [ B + LbT E 5 yB`LSU]±JBTcL±SU^BDJ1LbSQPRUUQ PRJMObD/Pc"J1BCHyqDOexo&D _JBD7LN?BDJ [cSUJ.p TVPRO QT"TVOb^BSUJ_PcLbD][RyM > N 5 N 5 / N C QPRJ D/Pc]bSUUyqD ]bDDJ LbTWpBOlD]bDOlRDLN?BD&PRObDPWCED/PR]lBObD N
(32) N PRU]bTWDP~RD].Lb?BD yqTV`JB^_PROhTR Lb?BD BJBSLH^`S]lQ `£8D^ ¡¢PRJ`^SLN]QDJ1LbDO[PR]SLH?BPRpBp DJB]N¤$[PcJB^ SU]HJ`TRL LN?BDSU^BDJMLNSLKV JBDQ/PRJ LN?`SJ ;&TR% ,Pc]oP{]l?BD/PRO@ SLN?ONPR^BSPR²]h"C CED$LNOlR >@?`S]PRQ ;WTc `JBS´1BDJBD]l]HQPRJLN?BDJyqD{DY£"LNDJ`^BD^ LNTPcJ1WpqTRU"\VTVJBPROlD\VSUTVJ > y1Lb?BDHnjSUDC PRJBJWC(PcpBpBSUJB\(Lb?BDTVOlDC ¡¨]bDDc[qDcÇ\`[ $Ç't & ¤Y[ S]jQTVJ8¨TVObC PRUU D´1BSUcPRUDJML LNT Lb?BD,BJBSL^BSU]bQc I¥ X SU]P QTRJ`¨TVObC PRoC PRp ¨ObTVC LNT [§Lb?BDJ X X 5 Lb?BD QTVJcfh`\MPcLND.TR [²SU]P]bDU X¥C(PcpTR ?BSUQZ?SU]JBTRLkLN?BDSU^BDJ1LbSULKR[ ?BSQZ?UD/P/VD]Lb?BD yqTV`JB^_PROhTR `£8D^²[ PRJB^ ?BSUQZ?WpBOlD]bDOlRD]PROlD/P`[_]lSJ`QDSULb] VPRQTVyBSPRJ²[_pBOlT8^`BQLjTR LN?BD VPRQTVyBSPRJ TRDPRQZ? ;PRQLbTVO[BSU] TVJBDc ³oTRLbDLb?_PcL ?BDObD DHPcObDJBTRL DY£`p`SUQSLN B]bSUJB\ LN?BD.;PcQLkLb?_PcL X SU]QTVJ8¨TVObC PR;[2TVJ`ULN?_PgLSLS]P&^BS 2DTVCETVObpB?`S]lC SU\VBOlD] L&PRJB^ }?BDp "SU]b_PcS HD&Lb?BSU]H]lD XKC PRp² IKJLb?BD]l(D _\V`ObD][LN?`D(QTVJ`¨TVOlC(Pc7C PRp¨ObTVC Lb?BD 0. 5. 10. 15. 20. 25. 35. . . . ͨÎÏͨÐ.
(33) |V|.
(34) . BJBSLe^BSU]bQ§LNToLN?BD§]l´1_PRObD§ PR]eQTVCEpB`LND^EB]bSUJB\>TVyM{xkOlS]lQTVU ] 8D QZ?M PRO=HYX ?BOlS]hLNT qD WPcLNPRyLNT"TVUyqT/£¡¨]bDD $ v & ¤$ . −1. −0.8. −0.6. −0.4. −0.2. 0. 0.2. 0.4. 0.6. 0.8. 1 −1. −0.8. S\RBObDQL > jJBSULj]l´"BPRObD. −0.6. . −0.4. −0.2. 0. 0.2. 0.4. 0.6. 0.8. 1. .
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(51) Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vignes 4, rue Jacques Monod - 91893 ORSAY Cedex (France) Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France). Éditeur INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France).
(52). . ISSN 0249-6399.
(53)
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