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Simultaneous containment of several polygons : analysis of the contact configurations

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(1)Simultaneous containment of several polygons : analysis of the contact configurations Olivier Devillers. To cite this version: Olivier Devillers. Simultaneous containment of several polygons : analysis of the contact configurations. [Research Report] RR-1179, INRIA. 1990. �inria-00075379�. HAL Id: inria-00075379 https://hal.inria.fr/inria-00075379 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(41) “3sVTt€hv nlqVf0m m ~0hV|=‚3”†‡–•"qVtv;q<|}quf‚‘X‚L—¸~3qi•k„sVquf3m›n•fhS|=qVfa‘‘‚L— ‚ƒfa‘‘nltqufBx.‚{fvƒz;vawB‚¦r“ta‚ƒ‚$m ~3hV|=‚%|=qVi˜oŽ

(42) ‚ rLqVTf*˜<n•fEi nlfB‚\hXtvÿn•x.‚š™›?œ?

(43) ž3Ÿ1 ¡;n•f¸vwT‚°|{hVm ‚¦qr7su‚ƒfT‚ƒt€h\i~3qilk suqVf3mnlf su‚ƒfT‚ƒt†hji(~8qXilk suqVf0hji ‚{f‚‘Vn•taqVfBx.‚{f vd2‘„f3h\n•x hXfƒ˜£¢/qnLmm qufBf0hXvO™ d¢}ž

(44) ¤„z d2‘„f*ž3¥1 s‘h1‘X‚yhjilsVqut nlvwTxymvaq,|}qux.~BBva‚¦vwT‚ rLt‚{‚<m ~0hV|=‚°qVt²vq qufilk¦“3f*˜qVfT‚%m qXilBvÿnlqVfr“qutyvqSqut vawBta‚ƒ‚°~8qXilk suqVf0m{‡¨§wB‚S|=qVx.~ i•‚L— nlvÿk ˜ ‚ƒ~3‚{f*˜Bm›qufEvwT‚Q˜„nu©

(45) ‚ƒta‚ƒfTv|{hVm ‚\mŠqr|=qVf‚‘V‚L— nlvJkSqXr qŽ‚ªÿ‚j|=v€mhXfƒ˜<‚ƒf‚‘VnltqVfTx.‚ƒf vƒze~3htv np|=iphXt ilk vawB‚{kCrLqVTf*˜CqVfT‚7m qXilBvÿn•quf3m‰r“qutvawB‚7|}qufBv†hjnlfBx.‚{f‘vqrevql’†_†Z{b-«k¬„vwBta‚ƒ‚1”M|}quf‚‘V‚ —Š~3qXilk suqVf0m/n•f h su‚ƒfT‚ƒt€h\i ~

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(47) ² suqVf0mnlf¦vawB‚g~iphXfT‚‘‡³‚cªÿ3m vv†h1´ ‚n•fTv‚{t‚\m v;n•f |=qVfTv€hu|}v/|}qVf

(48) “3suBt€hv nlquf3mhf*˜¦fBqVv;nlf vwB‚g‚{fBvÿnlt‚.

(49) rLt‚{‚Cm ~0hV|=‚‘‡ovgnpmg‚\hVm k$vq1m wBq39vw0hXvrLqVtvqy~3qi•k„sVquf3m{z0nñrvawB‚rLt‚{‚ ²Jm ~3hV|=‚nLmfBqVf%‚{x.~Bvÿk„z"h |=qVf

(50) “3sVTt€hv nlqVf<qr`‘^‘–BŽÐZ}^‘žBOšj6‚ —„nLm v†m{‡@§wnpmg~0hX~8‚ƒt~Btq3‘V‚jmvw nLm~Btqu~

(51) ‚{tvÿk r“qut7vawBta‚ƒ‚¦|=qVfa² ‘„‚ —²~3qXilk suqVf3mnlf%h›~8qXilk suqVf0hji ‚ƒfa‘‘nltqufBx.‚{fv(qVtr“qutvwTt‚ƒ‚~3qXilk suqVf3mx.q3‘‘nlfBsn•f$h.t‚j|=v†hXfBsil‚‘‡ dgf%h\ilsVqVtÿn•vawBx qr|}qux.~il‚ —„nlvkO­[’#® ¯ ”’†_†Z{b-«k¬,­[’#® ° ””MnLm˜‚˜0|}‚˜²vaqy~iphV|=‚vqQ’†_ Z{b-«x¬0vawBta‚ƒ‚1” |=qVfa‘‘‚L—.~8qXilk suqVf0m{‡ 0—0hx.~il‚\mhXt‚gsn>‘„‚ƒf¦vaqym wTq1ævaw3hXv(vawnpm~Btqu~3‚ƒtavknpm/rOhjipm ‚nlf1quvwT‚ƒt(|{hVm ‚jm ’OvwTt‚{‚@fBquf°|=qVfa‘‘‚L—.~8qXilk suqVf0m/n•f$h›fTqVf |}quf‚‘V‚L—¦‚{f‚‘Vn•taqVfTx.‚ƒf‘vqutrLqVTt|}quf‚‘V‚L—¦~3qilk sVquf3m/nlf°h t‚\|=v€hfBsXil‚1”€‡.

(52)   †l=‡R‰P†?†|Š † ˆL9‡0 .   !" I # U !$#&%(' H ! UXUXI ')! HPuN0U+*/H  U ³ ‚v€hB´ ‚/n•fTv‚{t‚\m v‰nlfCvawnpm/~3h~3‚ƒt(hBŽ3qVBv(m qux.‚ ~8qXilk suqVf0hji3qŽ‚ªÿ‚j|=v†mMx.q3‘‘nlfBsn•f.vt€hf3moiphXvÿnlqVfCnlf1h ~3qi•k„sVquf3h\iý‚ƒfa‘‘nltqufBx.‚{f‘v\‡c§wT‚|†i•q‘m Bta‚qXrývwT‚@‚{f‚‘Vn•taqVfBx.‚{f vZnñi i0Ž3‚C˜ ‚ƒfBquva‚v˜OŽTk-, hXfƒ˜²vawB‚ |†i•q‘m Bta‚ŠqrvwT‚qŽ‚ªÿ‚j|=v†mUŽTk/.$0U’214365;‡}‡\‡87.”€z® ’€_ Z{b-«k¬9:0#”;npmgvawB‚.mon>±{‚qXr;, ’†_†Z{b8«x¬<.$0-”€‡§wB‚ ~3q‘mon•vÿnlqVf%qXr;‚\hV|=w1q3Ž‚ªÿ‚j|=vnLm|†w3hXt†hV|=v‚{t nV±ƒ‚˜ Ž k vwT‚vt†hXf3moiphXvÿnlqVf%qXrMvwB‚~iphXfT‚>=?0A@CBED¯w nL|=w x.q3‘V‚jm&. 0 rLtqux nlv€m;t‚}rL‚{t‚ƒf0|}‚7~

(53) q‘mon•vÿnlqVf¦vaq›nlv€m|=Btta‚ƒfTv~3q„monlv nlqVf6‡F=G06nLm|{hjiñil‚v˜ h.|=qVf

(54) “3sVTt€hv nlqVf qr .$0ýhXf*˜I‚gfBquv‚H.40 IKJ vawB‚@q3Ž

(55) ª ‚\|}v;.L0n•f vwT‚|=qVf

(56) “3suBt€hv nlqVfM=?0 ‡ýdgf°0m 3hjixh}k¦vaq.t‚{~Bta‚jm ‚{fBv h~3q‘mÿnlvÿn•qufCr“quth@m kTm va‚ƒxDqXrN7gqU Ž‚ªÿ‚j|=v€m‰npmMvaq3m ‚7hO7 ²-˜„nlx.‚{f3monlqVf3h\i m ~3hu|}‚›ŒevawB‚7|=qVf

(57) “3sVTt€hv nlqVf m ~0hV|=‚‘‡F=P3 ’2=Q+R}‡ƒ‡}‡SRT=GU”A@VB D ¯ npmh.|=qVf

(58) “3suBt€hv nlqVf qXrývwT‚|=qVx.~ il‚ƒva‚›m kTm va‚ƒx$‡ ³ ‚MfTqBH˜‚L“3fT‚/hrLt‚{‚|}quf'“3suBt†hXvÿn•qufhumh(|}quf'“3suBt†hXvÿn•qufCwB‚{t‚/vawB‚;|€ilq„m Tt‚/qrTvawB‚/q3Ž'ªÿ‚\|}v†m w0h1‘V‚gfBqn•fTv‚{t€m ‚\|}vÿn•quf zhf*˜°hŠ|}qufBv†hV|=v(|}qVf

(59) “3suBt€hv nlquf°hVmh.|=qVf

(60) “3suBt€hv nlquf wT‚ƒt‚7vwT‚@nlfva‚{t n•qut qr‰vawB‚q3Ž'ªÿ‚\|}v†m w0h‘‘‚gfTq›nlfBva‚ƒt†m ‚j|=v nlqVfIŽTBvvawB‚=n•t„Ž3qVBfƒ˜Bhtk w3h‘V‚gqVfT‚jm{‡Md7md2‘ f0hjnlx ™ d2‘ fƒž¥B  il‚ƒv(3m˜‚{fBquv‚.Œ IKJ [ ,(3^].hf*˜>Z 1_R`1b3c I2J [ . g Ife 3h]ji W 3 XY=;3 ’2= Q R}‡\‡}‡R?= U ”TRZL1. 0\ a `dR_. 0\ npmvwT‚rLt‚{‚m ~3hu|}‚ k 3 XY=;3 ’l= Q R}‡\‡}‡R?= U ”TR?=@: a WRlZ 16. m 0 I2J [ ,n a `dRM. m 0 IKJ [ . m g Ioe 3^]ji m 3^].hf*˜>Z 1_R`1b3c npmvwT‚|=qVfTv€hu|}v(m ~3hu|}‚[’ p m ˜‚{fBqVva‚7vwT‚@n•f va‚ƒt nlqutqrhŠma‚{v p ” IqJ [ ,(3\]ji W 0 3 XY= 0 R_. 0h npmvwT‚rLt‚{‚m ~3hu|}‚7qXrýqufilk qVfT‚@qŽ

(61) ªÿ‚j|=vb.$0nlf1vawB‚7‚ƒfa‘‘nltqufBx.‚{f‘v;, IKJ [ . g Ioe 3^]di W 0 g 3 XY=G0Lrs= g Rl. 0h npmvwT‚rLt‚{‚m ~3hu|}‚7qXrN.0et‚}iphv nV‘ ‚=i•k.vaqt. g u 0 g 3 XY= 0 rs= g R8= 0 @VW 0 R8= g @VW g R8= 0 rs= g @VW 0 g i npmvwT‚m ‚{vqr‰ta‚}iphXvÿnV‘ ‚ rLt‚ƒ‚|}quf'“0sVBt†hXvÿn•quf3mqr . 0 hf*˜v. g n•fs, wx0 g 3 XY=G0Lrs= g R?yj=@vWPRz=0ýhXf*˜/= g ht‚@vawB‚1 Ǔï hXf*˜{` Ǔï |=qVx.~3qufB‚{fBv†m/qr =Si npmvwT‚m ‚{vqr‰ta‚}iphXvÿnV‘ ‚ rLt‚ƒ‚|}quf'“0sVBt†hXvÿn•quf3mqr . 0‰hf*˜v. g n•f°vawB‚|}qux.~il‚ƒva‚ m kTm va‚ƒx5qXrF7q3Ž'ªÿ‚j|=v†mnlf°vawB‚7‚ƒf

(62) ‘‘nltqufBx.‚{f v;,. ³ ‚.m B~B~3q‘m ‚Cvaw3hvvwT‚.m kTm va‚ƒx npmnlfEh²œVZ\ž0Z\_†šý`‘’lb8«T^ub=’p“’p^Vž0‡>|g‚{sV‚{fB‚{t€hv‚.|ƒhum ‚jmhum|=qVfa² m vat€hjnlfTvx.qVvÿnlqVf°n•fSh²|}qutt n˜qut\z

(63) hXfƒ˜R~0hXt€h\iñi•‚=i npm x Ž3‚{v‚{‚ƒf°q3Ž'ªÿ‚j|=v€mhXt‚›t‚=ªÿ‚j|=v‚˜H’om ‚ƒ‚l•6nlsVBta‚ 5.

(64) •6n•suBta‚>5uŒ$‘qux.‚C˜ ‚ƒsu‚ƒfT‚ƒt€hv‚|ƒhum ‚jm B5 ”€‡ædgf‚L—0hu|}v ˜‚L“3f n•vÿn•quf nñiñiŽ8‚1sn>‘„‚ƒfEnlf ‘‚\|}vÿnlqVf^O‡ 5u‡ JrvwT‚%m kTm va‚ƒx ˜q‘‚jm.fBqVv@‘ ‚{t nñrLk vawnpm7wBk ~TqVvawB‚\monLm{zh$m xyhjiñi}˜‚}rLqutxyhXvÿnlqVf<qrq3Ž'ªÿ‚j|=v†m@qut‚ƒfa‘‘nltqufBx.‚{fvxyhB´ ‚\m nlv7nlfEh¦su‚ƒfT‚ƒt†hji ˜‘nLm ~3q‘mon•vÿnlqVf6‡ •0qVt@h ~3qXilk„sVqVf0hjim kTm va‚ƒx h\i i/vwT‚jm ‚ym ‚ƒv†mht‚ ’OfBquf<fB‚\|=‚jmmhXtÿn ilkS|=qVfa‘X‚ —,”(~3qXilk vaqV~8‚jm{‡ WA0 z W40 g zYuF0 g hXfƒ˜xwx0 g hXta‚qu~

(65) ‚{f¦~3qXilk suqVf0m{‡ WEnLmhXf¦qV~3‚{f¦~3qXilk vaqV~3‚gqr˜„nlx.‚ƒf0mon•quf/O7hXfƒ˜ k°npmMnlv†m Ž3quBf*˜ThXtakT‡ dgf%3m 3h\ich\k vq1|=qVx.~BTv‚{W 0 hXf*˜-W 0 g npm@vaq²3m ‚›vwT ‚  nlfa´ qBm=´‘n˜„nu©

(66) ‚{t‚{f3|}‚I’#˜‚{fBqVva‚˜ ŽT k ”m ‚{‚rLqVt‚L—0hx.~il‚ ™  ³ ¤v¥1 R’ Ò npmvwT‚›|}qux.~il‚ƒxŠ‚ƒf v€htk²m ‚ƒv(qX r ”€‡ W4 0 3 , s.0 ’T51” W  0 g 3 . g s. 0 ’2O

(67) ” §wT

(68) ‚  nlf‚´„qBm=´‘nW˜„nu©

(69) ‚{t‚{f3|=‚CqXr(v9q ~3qi•k„sVquf3m7qXr mon>±{‚I®¸hXf*˜c9ª|ƒhf Ž3‚¦|=qVx.~TBva‚v˜Rnlf<vÿn•xŠ‚ ­|’9® ¯ 9 ¯ ” hXfƒ˜1w3hum7hymonV±ƒ‚l­[’#® ¯ 9 ¯ ”†z8vawnpm npmv nlsVwTvnlf%vwT‚CqVt†m v|{hVm ‚V‡?§‰qE˜ q vawnpm{z0qufB‚.|ƒhf 0m ‚ChysV‚{fB‚{t€h\ih\ilsVqut n•vawBxvq1|}qux.~BTv‚›vawB‚›htt€hfBsu‚ƒx.‚{fBvqrvwT‚ ­|’9® 9”i nlfT‚jmgt‚{~Bta‚jm ‚{fBvÿn•fTs monlx.~il‚.|}qufBv†hV|=v€mP™ W˜ ‚vž ¤ ýhf*˜°vq1|=wBqVq‘m ‚[wnp|}w$|}‚=iñiLm2Ž3‚=ilqVfBs²vaq vawB ‚  nlf‚´„qm=´‘n˜„nu©

(70) ‚{t‚ƒf0|}‚ hf*˜Nw np|}wš˜q„‚\m@fTqVvƒ‡ •0qVth²sV‚{fB‚{t€hji/~3qXilk suqVfEhf*˜Sh%|=qVf

(71) ‘V‚ —R~3qi•k„sVquf zevawB‚Cta‚jm  i•v|ƒhf Ž

(72) ‚ |=qVx.~TBva‚v˜<n•fvÿnlx.‚­|’9® 9i•qusZ® 9”hf*˜Ew3hVmyhSmonV±{‚­|’9® 9”E™ •"qVtž 1 O‡of vawB‚$|ƒhum ‚°qXrv;q |=qVfa‘‘‚L—.~3qi•k„sVquf3mW(‚g|ƒhf hV|=wnl‚ ‘V‚ vawB‚7|=qVx.~TBv†hXvÿn•qufCn•f¦vÿn•xŠ‚C­[’# ® M9 ”MhXf*˜CvawB‚mon>±{‚ nLmhjipm q ­|’9 ®  9 ”™›?œ?

(73) ž3Ÿ1 O‡ d2‘ f0hjnlx m wBq3mm qux.‚@ta‚jm  i•v†m7Œ u 0 g 3 W 0 g [ ’W 0 sW g ” ’#Ÿ

(74) ” wx0 g  u 0 g [ ’ou 0  -u g  ” ’O‹a” wT‚ƒta‚ 1A3 a ` 3 a M3^ a 1 hf*˜ynlf°vawB‚m ~3‚j|†nLh\iý|{hVm ‚7qXrývawBt‚{‚qŽ

(75) ªÿ‚j|=v€m/nlf°h.ta‚j|=v€hfBsi•‚.Œ w 0 g 3 u 0 g [ ’ouF0 -u g 1” ’ 

(76) ” (wB‚{t‚ 18Rq`dR /@-Xd5 R?O RŸji R?1b3c a `M 3 a M3^ a 1    I æU §w npm ~3h~8‚ƒt‚jm v†h1Ž iñnLm wT‚jmm qVx.‚ta‚jm ilv†mghBŽ

(77) quBv|=qVfTv€hu|}v |}quf'“0sVBt†hXvÿn•quf3mrLqVt~3qXilk suqVf0mgx.qB‘‘nlfBs nlf1vat€hf3moiphXvÿn•quf1nlf1vawB‚@~ iphXfB‚V‡ O.

(78) ˆ;hXtvzO²maTx.xyht n>±{‚\m7m qVx.‚.|}quf3mon˜‚{t€hv nlqVf0m7h1Ž3quBvvawB‚.|}qufBv†hV|=vm ~0hV|}‚.hf*˜°‚jm v†h1Ž i npm wB‚\m7h fT‚j|=‚jmmhtk7hf*˜@m ²|€nl‚{fBv

(79) |=qVf*˜‘nlv nlqVf7qXrB|}quf3|{h1‘Vn•vÿkrLqVtehZ‘ ‚{tva‚ —qXr Wgz{nlfˆ;hXtavŸvawB‚‰‚ —„nLm va‚ƒf0|}‚/qr hP˜ qVaŽil‚ ²J|}qufBv†hV|=venLm‰~Ttq‘X‚˜@n•fCvq7~0hXtvÿnp|} iLht|ƒhum ‚jmrLqVt;vawBta‚ƒ‚ q3Ž'ªÿ‚\|}v†m ŒývawBt‚{‚g|=qVf

(80) ‘V‚ —~3qXilk ² suqVf0m n•fyhg~3qi•k„sVquf3h\i"‚{f'‘Vn•taqVfTx.‚ƒf vequt;vwTt‚ƒ‚~3qi•k„sVquf3mnlfCht‚\|}v†hXfTsXil‚‘‡§wnpmM~Ttqu~"‚{tvakgnpm rJh\ipm ‚ rLqVt;x.qut‚vaw3hXf›vawBt‚{‚ ~3qXilk„sVquf3mqut‰r“qut‰vawBt‚{‚ fTqVf.|}quf‚‘V‚ —~3qilk sVquf3mnlfChfBquf¦|=qVf

(81) ‘V‚ —‚ƒf

(82) ‘Vn•taqVf‚² x.‚{fBvƒ‡R•6nlf3h\i ilkˆ‰htv

(83) ‹?˜‚v˜ 3|=‚jm8rLtqVx9vawB‚/‚L— npm v‚{f3|=‚/Q qXr,˜ qVaŽil‚|}qufBv†hV|=v€m{zjhXf›h\i•suqVt nlvawBx9vq$“0f*˜ qufB‚g|=qVfTv€hu|}vM|=qVf'“0sVTt€hXvÿnlqVfŠnñr8nlvM‚ —„nLm v†m/qufB‚(nlfCvÿn•xŠ‚ ­[’#®¯ 9Q¯Bi•qusA9”c’€_Z{b-«x¬.­[’#®,°S9I°3i•qusA9”” rLqVtv9ql’€_ Z{b-«k¬„vwTt‚ƒ‚1”M|}quf

(84) ‘‘‚L—.~3qi•k„sVquf3m{‡ýd2‘ f0hjnlxDhXfƒ˜O¢/qnLmm qufBf0hXv ém;hjilsuqVt nlvawBxym;tBfŠnlf¦vw npm |{hVm ‚Wnlvawhv nlx.‚|=qVx.~ i•‚L— nlvkqr,­[’#® ° 9 ¯ i•qus ¯ ® 9”’€_†Z{b8«x¬B­[’#® ° 9 ° i•qus ¯ ® 9 2® °  9 BilqVs&9””†‡   . Œc‰P†‡$Œ‡  >UŒ . d7mk‚‰fBquv np|}‚˜nlf ‘‚j|=vÿn•quf:5V‡ 5;vwT‚|}quf'“0sVTt€hXvÿnlqVf.m ~3hV|=‚/w3humR˜„nlx.‚ƒf0mon•quf{O7hXfƒ˜vawB‚MrLt‚{‚ ²Jm ~3hu|}‚ npmh.~3qXilk vaqu~3‚nlf1vawnpmm ~3hu|}‚V‡.  . $! 'jv' #  */P !" I # ³ ‚$|ƒh\i i7hh{^‘žB“š \h |=qVf'“0sVTt€hXvÿnlqVfqr k9humI˜ ‚ “3fT‚v˜nlf ‘‚\|}vÿnlqVfn5u‡ 5u‡ ÿfØh,|}qufBv†hV|=vx=c3 ’2= Q Rƒ‡}‡\‡R8= U ”MvawB‚ƒta‚‚ —„nLm v(vqq3Ž‚ª ‚\|}v†m4.$0;hXf*˜:. g ’JquthXf°q3Ž'ªÿ‚\|}vhf*˜¦vwT‚@‚{f‚‘‘nltqufBx.‚{f v”Mm 0|}w vaw3hv;.A0 IKJ hXfƒ˜V. g Ioe w0h1‘X‚h.|=qVx.x.quf°~3qXnlfBvquf°vwT‚}nltŽ3qVTf*˜ThXtk„zvw nLm~3qn•fTv|=qVtat‚jm ~3quf*˜Tmvq²h ‘„‚ƒtva‚L —  qr . 0 hf*˜CvqŠhf¦‚v˜su ‚ gqXr. g nlvwTqVTv;i•q‘mm/qr‰su‚ƒfT‚ƒt€h\iñn•vÿk„‡V3|=w¦h.|=qVT~il‚C’ FR 1”enLm |{hjiñil‚v˜ ʏŽ€ZS"^ b}’•™U« ÐZ=^‘žB“š \“‡  qil‚ƒv?’ &R 1”JŽ8‚hiph1Ž3‚}iqXrMmonlx.~il‚|=qVfTv€hu|}vƒ‡§‰qn•xŠ~3q„m ‚@vaw3hvvawB‚7vt€hf3moiphXvÿnlqVf =G0eqXr . 0 il‚jh3˜Bm;vwT‚2‘ ‚ƒtav‚L —  qXr . 06qVf¦vawB‚7m T~B~3qVtav nlfBsiñnlfB‚gqXrevawB‚g‚˜su‚  qXr . g vt€hf3moiphXva‚˜EŽTkt= g z„vawB‚ |=qVf

(85) “3sVTt€hv nlqVf =P˜‚\m|}tÿn>Ž3‚\mhXf°w k„~3‚ƒt~ iLhfB‚gnlf1vwT‚|=qVf

(86) “3suBt€hv nlqVf%m ~0hV|=‚‘ ‡ $qVta‚~Bta‚j|†nLm ‚=i•k„z ‚ w0h1‘V‚7h›iñn•fT‚jht7|=qVf0m vt†hjnlf vquf°vwT‚@vq@˜‘n•x.‚{f3monlqVf0hji0‘ ‚j|=vaqVt =G0rs= g ‡$§wB‚›|=qVf v†hV|=v²Jm ~3hu|}‚Pk%npm m T~B~3qVtav‚˜ Ž k m 3|†w¦wBk„~B‚{t~iphfB‚\mg|{hjiñi•‚˜ €^‘žB“š \  ["«TZ\_8« Κ‘žBZƒb=‡ ³ ‚7|ƒhf1fTq ˜‚L“3fB‚w3hvhCm kTm v‚{x nlf°œVZ\ž0Z\_š "`‘’ «0^ub}’•O’•^‘žx.‚\hXf0m{‡  µ  © ·¤ ·¢ " © !8ºL$ « #% Z%b}[\b}“Z\™ ’ b1b}š‘’•` ’•žsu‚ƒfT‚ƒt€h\i˜‘nLm ~3q‘mon•vÿnlqVf-’ R&  ZSš‘_=_š‘ž‘œ‘Z\™›Z\ž0^ Rš   {^Vž0“š \'  ["«0Z\_8« К‘žBZ{b’•žR&  ZHO7  `V’p™›Z\žTb=’p^Vž0š "b8«3š €Z’lb@’•ž1œVZ\ž0Z\_ š  «T^ub}’•“’p^Vž:¬ ( ’_¬ Z1¬&  Z.’•žBOZ\_†b=Z \O’•^‘ž°^  *) O * 7 „["«TZ\_8« К‘žBZ{b@’lbš²b=–0Ž€b-«0š €Z›+^ ›`‘’•™›Z\žTb=’p^Vž O 7r 0—, „Z ’•ž0“Z\_†b}Zj“’•^‘ž1^  .-\O. 7  ["«0Z\_8« КVž0Z{b’ b@Z\™U«8“[.¬ / d7m²|€iphjnlx.‚˜n•f ‘‚\|}vÿnlqVfn5V‡ 5uzhm xyhjiñi@~3‚ƒtavTtŽ3hv nlqVfqrqŽ

(87) ª ‚\|=v€m |{hXfvaBtfhfBk¸m km v‚{x nlf su‚ƒfT‚ƒt€h\i0˜„npm ~

(88) q‘mon•vÿnlqVf ‡Nof1vawnpm|ƒhum ‚kRnLmvawB‚Ž

(89) quBfƒ˜BhXtak¦qr Wg‡ 

(90) ‚ƒv3mgnlf vtq'˜ 3|=‚.maqux.‚[‘ q‘|ƒhBŽBiphtkTz,‚C|{hjiñi/h%b}’•™U« ÐZx{^‘žB“š \“z6hy~3qn•fTv7qr kEilk‘nlfBs1qVf h,|}qufBv†hV|=vwk„~3‚ƒta~iphXfB‚Vzh <{^‘žBOš\MnLmh%~8qXnlf vqXr;kØilk‘nlfBsRquf  |}qVf v†hV|=vwBk„~B‚{t~iphXfT‚jm{z/h L `‘^‘–BŽ ÐZx€^‘žBOšj8nLmh  ²J|}qufBv†hV|=vm 3|=w°vw0hXvv;qywBk ~T‚ƒta~iphXfT‚jmgw0h1‘V‚@iph1Ž3‚=iLm · © ¶ ¢ 0 ¶ · © 1E3¤ 2 µ ±} 

(91) ¯ µ ¡6  · £Š5¢ 4¢8 ¹ 6 8µ 7 ¤\±qVvawB‚{tnpm ‚nlvnLmh  ob=’p™U« ÐZ{^‘žB“š \O‡ 

(92) ‚ƒvN=JŽ3‚h~3qXnlfBv

(93) qVf›vwT‚wk„~3‚ƒta~iphXfB‚;qXr0iph1Ž3‚=ik9’ FR 3”†:z Ønpm0Ž3‚{v;‚{‚ƒfvawB‚v;q‚ƒfƒ˜'²“~3qXnlfBv†'m ; hf*< ˜ ;=TqX'r (n rN=;iñn•‚\mMnlf¦ h >\š В•`‘’p“[7bКŽMvt€hu|}‚˜Šquf²vawB‚wBk„~B‚ƒta~iphXfT‚‘‡Nÿf¦quvwT‚ƒtJqut˜Tm{zVvawB‚gmoiph1Ž È @

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(95) :#F. Ÿ.

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(97) qutv nlfTs V‡‰d~

(98) qnlfv nlfCvawnpm;moiLhBŽŠnpm/h@|}qufBv†hV|}vM|=qVf

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(100) ‘V‚ — ° ‡ 

(101) ‚ƒv@3m@rLq|=3m7qVf¸|}quf v€hu|}v@wBk ~T‚ƒta~iphXfT‚jm{‡vW9npm›h²Bfnlquf<qXr|=‚}iñipm7qXrvawB‚¦htt€hfBsu‚ƒx.‚{fBvqXr |=qVfTv€hu|}vw k„~3‚ƒt~ iLhfB‚\m{‡ 

(102) ‚ƒvfBqB =PŽ3‚.h.~3qXnlfBvquf%h²|}qufBv†hV|=vwBk„~B‚{t~iphfB ‚ Ez0nñrA=7npmm vt np|=v ilk quBv†monh˜ ‚CvawB‚ ‘„h\i n˜„nlvJkRmoiph1Ž<vawB‚{. f  |ƒhfBfBquvPŽ3‚¦hyrJhu|}‚¦qr4k n•f h fB‚=nlsVw‚ŽTqVtaq„qƒ˜,qr;=‡xOr;=npm m vat np|}vÿilkCnlf3mon˜‚7vwT‚‘Vh\i n˜‘n•vÿkymoiph1Ž vwT‚ƒf²nlf$h›fB‚=nlsVw

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(104) quBfƒ˜‚˜OŽ

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(107) ‚7hP‘„‚ƒtva‚L—¦qrk;zˆ‰tqu~

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(109) uþaù añô

(110) jþaù 6béû þÿö ņðBǓïjÈ/ï LƒîjÈ ã“îƒÏñ܆ÞjÈ;Ì Å=ãOã“È ʓîuÅ=ÞjɃÍÐ`Þ _ ǓÅǓïjÈ‰Ì Å=ÞjÇJÜ†Ì Çà QURcäoÓ d)e ÈÉjTÈ VXށÈ;Ü/Ì Å=ÞjÌ܆ë}ÈeëƒÈ ã“Ç“È ß܆ÊÜ/ÞjÅ}ÞgÌ Å=Þjë=È ß(ë{È ã“Ç“È ßuӏ¿RëƒÈ ã“Ç“È ß/ÍÐÊ6Ì Å=ށë=È ßXÀ{ÍÖðTÍÎÞ@Ü/ÞjÈoLÍ _=ïjÝjÅ=Ɓã“ïjÅ{ÅjÉgǓïÈ îXÅ†Ï LƒÇ“Å=îXÈÍÐÊÜ†Þ ÍÐÞjÇ“È ã“Ê“È Ì ÇpÍÎÅ=Þ(ņð0ïXÜaÏÖð0ʓîXÜ†Ì È ÊaÓ. ‹.

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(190) quBvvawB‚.m w3h~3‚CqXrvawB‚r“ta‚ƒ‚²om ~0hV|=‚Šqr~3qilk sVquf3mgxŠq‘‘nlfTs nlf1vat€hf3moiphXvÿn•quf ‡ ˆ;hXtv„Ÿ›npm˜‚ ‘Vquv‚˜²vaq²m ‚jht€|=w ˜ qVaŽil‚›|}qufBv†hV|=v€m‰n•f°vawB‚|ƒhVm ‚7qXrMvwTt‚ƒ‚qŽ

(191) ª ‚\|}v†m{‡Aÿf%m ~3‚\|€nph\i |{hVm ‚\mMqr6vawBta‚ƒ‚g|=qVfa‘V‚ —~3qXilk suqVf0m ^V_ýqreht‚j|=v†hXfBsuiphXt;‚{f

(192) ‘‘nltqufBx.‚{fv‚~Ttq‘X‚˜vwT‚ ‚ —„nLm va‚{f3|}‚ qrhE˜qu‚Ž i•‚›|=qVfTv€hu|}vƒ‡Aÿf°vawB‚sV‚ƒfT‚ƒt†hjiM|{hVm ‚Vz

(193) hXf°‚L—0hx.~il‚qXrMfBqVf°‚{x.~BvakCrLt‚{‚ ²Jm ~3hu|}‚Pn•vawBquBv ˜ qV‚Ž il‚ ²J|}qufBv†hV|=v;nLmsXnV‘ ‚{f hXfƒ˜1m qVxŠ‚t‚jm  i•v†mh1Ž8quBv(vwB‚|=qVx.~il‚L— nlvk²hXfƒ˜²vawB‚gr“qutx qXrMm 3|=w°h rLt‚{‚m ~0hV|=‚›hXt‚m wBqBf6‡ 55.

(194) ÿf°vawB‚.|{hVm ‚›qXr;vqyqVtvawBt‚{‚.|}qVfa‘X‚L—$qŽ‚ªÿ‚j|=v†m(nlf<hy~3qi•k„sVquf3hji‚ƒfa‘‘nltqVfTx.‚{fv‚[˜ ‚v˜ 3|}‚Vz rLtqux vawB‚S‚ —„nLm va‚ƒf0|}‚%qrE˜qu‚Ž i•‚ |}qufv†hV|=vƒzhXf h\i•suqVtÿn•vawBx vq–˜ ‚ƒva‚j|=vRh ~iphu|}‚{x.‚ƒfTvQn•vawBquBv |=qXiñiñnLmonlqVf0m}wnp|=wynlx.~Ttq‘V‚\m/vawB‚@~Tt‚\|}‚˜„nlfBsChjilsVqut nlvwTxym{‡ dgfnlfBva‚{t‚jm vÿnlfBsR~BtaqŽil‚{x n•f¸vw nLm›vaqV~ np|ynpm›vq,‚jm v†h1Ž i npm wilq3;‚ƒtlŽ3quBfƒ˜

(195) ‡ 

(196) q1‚{t[Ž8qVTf*˜Bm ‚L— npm v€m‰n•f.vwT‚7|ƒhuma‚qXr

(197) vwT‚7|}qux.~BBv†hXvÿnlqVfCqrýhjiñi3vwT‚@m qilBvÿn•quf3mŽBk|}qux.~BTv nlfBsvawB‚t‚jm  i•v ÖmmonV±ƒ‚Vz ŽTBvn•f vwT‚|{hVm ‚7qXrMm ‚jht€|†wnlfBsqufilk¦qufB‚m qXilBvÿn•quf ‚˜qŠfBqVv„´ fTqnñr‰quBtB~T~

(198) ‚{t$Ž3qVTf*˜TmhXt‚ vÿn•suwBvqutfBquv\‡. M'N#&  JH N %A N ØN #  U. §wT‚hBvawBqut}qui˜iñnV´ ‚gvaq›vaw3hf‚´E•"t€hXf0|€npm‰d2‘ f0hjnlx w nL|†w¦vawB‚\mÿnpm‰n•f n•vÿnphXva‚jmvawnpmWqut´"zu‚jhf‚² |hXf n•‚=iW¢/qXnpmm qVfTf3hXvghXf*˜ $qufn  T‚ §e‚}nñiñiLh*˜²rLqVthy|{hXta‚}rLiMt‚\h˜‘n•fTsyqXrvawB‚~0hX~3‚{thf*˜u‚jhf‚² ˆnl‚ƒtta‚ $‚{t il‚ƒvrLqutm B~T~ilk‘nlfBsŠwnpm/n•fTv‚{t€hu|}vÿn>‘‚C˜ t€hnlfBs~Bta‚ƒ~3ht€hv nlqVf%m km v‚{x_˜ t€hB . † Œ . ˆ | z

(199) 0K.zWD1 +  /

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(208) K x 4.+5

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(213) Œ / ‹ K z2KMQ"(#6"ABKOzWF6+<!#&-. %V!)6u<O 66+(9+ %V!#"@)

(214) &-.( ?<)

(215)  6A1L/3!= 6ƒ 5.(#&=6"(LK &705.u.v1Q4tYPB:<8=Y0543f 0=U 8Y.e $'&s(lQS fŽ ˆw f ˆ S J  J K. 5SO.

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