• Aucun résultat trouvé

An Elementary Algorithm for Reporting Intersections of Red/Blue Curve Segments

N/A
N/A
Protected

Academic year: 2023

Partager "An Elementary Algorithm for Reporting Intersections of Red/Blue Curve Segments"

Copied!
17
0
0

Texte intégral

(1)

HAL Id: inria-00072646

https://hal.inria.fr/inria-00072646

Submitted on 24 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished 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.

An Elementary Algorithm for Reporting Intersections of Red/Blue Curve Segments

Jean-Daniel Boissonnat, Antoine Vigneron

To cite this version:

Jean-Daniel Boissonnat, Antoine Vigneron. An Elementary Algorithm for Reporting Intersections of

Red/Blue Curve Segments. [Research Report] RR-3999, INRIA. 2000, pp.13. �inria-00072646�

(2)

ISSN 0249-6399 ISRN INRIA/RR--3999--FR+ENG

a p p o r t

d e r e c h e r c h e

THÈME 2

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

An Elementary Algorithm for Reporting Intersections of Red/Blue Curve Segments

Jean-Daniel Boissonnat — Antoine Vigneron

N° 3999

Septembre 2000

(3)
(4)

Unité de recherche INRIA Sophia Antipolis

2004, route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex (France)

Téléphone : 04 92 38 77 77 - International : +33 4 92 38 77 77 — Fax : 04 92 38 77 65 - International : +33 4 92 38 77 65

!,.-0/1243527698:! (

;=<?>=@ABC>=@$DE<GFHJIKDMLNLOIK@@P>RQ?SPT@'QUIKDE@$<WVCDEXK@$<GYNIK@

Z\[#]U^W_a`abdcfeUg'hi_:jik?lmhinUhi_Uj

_UonqpGjinUr'jtsu=^av$k?jwhixyr#_

z!{kG|_Uoz!{his^W_

}JpG~'~$k?{o'_:{_n[#_U{n[#_€gƒ‚m„m„m„…bd†=_U~'o_U^v'{_`m‡m‡m‡b ˆq‚‰~7pGlŠ_s

‹"ŒŽq’‘'“ŠŠ” • _Uo—–˜™pGg#š–›fv$_‰oœ0kžs_Uos:kGŸ\ #¡¢^Wk?g#k?ok?g#_.pGg#£g#k?gK¡¢hwgRo_U{s_nUohwg'l£nUr'{¤Š_

s_Ulm^W_Ugyosq¥\–§¦–˜J¨–›WpGg#ª©–«©0¦¬!­¯®°_±lmhw¤Š_²p£g#_Uœ&sœ0__U~K¡¢jwhwg#_²pGjwlŠk?{hwo['^§o[7pGo

{_U~$k?{osCo[#_ž³´hwgyo_U{s_nUohwg'l°~7pGhw{sWkGŸµs_Ulm^W_UgyosWkGŸf–.­·¶Jr'{.pGjwlŠk?{hwo['^r#s_s™k?g'jwu¸o['{__

shw^™~'ji_—~'{_KhinqpGo_sfo[7pGo:pGjwjikqœ¹ok.'_nUhi'_‰hºŸ!oœ»k¼s_Ulm^W_UgRosµhwgyo_U{s_nUoq¥hºŸ»p.~k?hwgRohisJji_OŸ½ofk?{

{hwlm[RoJok«pGg#k?o[#_U{J~$k?hwgyoq¥$pGg#…hºŸ»pW~k?hwgRohisfpGvk¾¤Š_m¥7v$_Ujikqœ¹k?{µk?g£p™s_Ulm^W_UgRoq­Z\[#_s_ao['{__

~'{_KhinqpGo_sµs__U^4okWv_:o[#_ashw^™~'ji_so~'{_KhinqpGo_sJo[7pGoji_qp?…ok.sr'vxRr7p?K{pGohinapGjwlŠk?{hwo['^Wsq­

¶Jr'{apGjwlŠk?{hwo['^hisapGjw^Wkmso—k?~'ohw^.pGj»hwgšo['his:{_so{hinUo_š^Wk='_Uj¿kGŸÀnk?^™~'r'opGohik?g*­.ÁÂosfohw^W_

nk?^™~'ji_OÃKhwou¼hisJÄWÅÅƬ"Ç·³7ÈyÉwÊmË\¬ŽÈ»pGg#±hwoÀ{_xRr'hw{_sµÄ™ÅƬŽÈ¿s~7p?n_m­

Z\[#_spG^W_™pGjwlŠk?{hwo['^Ì[7p?sµv__Ug£'_snU{hwv$_²hwg²k?r'{µ~'{_U¤Rhik?r#sµ{_U~$k?{o™ÍÏΒН­µZ\[7pGoµ{_U~$k?{o

~'{_s_Ugyo_ÑpGjiskWpGgžpGjwlŠk?{hwo['^4ŸÆk?{Ào[#_:lŠ_Ug#_U{pGjtnqp?s_:v'r'ohwospGg7pGjwu=shisÀœ0p?sÀg#k?oJnk?{{_nUoq­

҅ӊÔ$ÕÖ× ’ØŽŠ”ÚÙ k?^™~'r'opGohik?g7pGjcf_k?^W_Uo{uŠ¥}k?v'r#sog#_ss¾¥7ۃÃ#p?nUoµpG{hwo['^W_Uohinm¥*†Rœ»__U~K¡¢jwhwg#_

pGjwlŠk?{hwo['^Ws

Ü$ÝGÞÏߎà$áâ¢ãµÝGäNߎåmæçæéè:ê?äâÆë¢ÞìäíÏíÏî—ßÆï’êGêmáâÆë¢æðfåîJë¢Ý’æ»ñò’ó#ôtõö܅õ½÷°ø¾Ü$ôšó#â¢áùöæéúÂë!ûŽáJüý¾þÿNÿ øRõ

äNè?ðë¢ÝGæ*úÂë¢ÞÏáNè:ð’æƒôtæú¢ÝGæçâú¢ÝGæ ááOêçâäë¢ÞOæçáçëÆâ¢Þúéä

(5)

!(7!)ta( ,‰2 a( C!(1, ) ( ,‰ ) J2a.

 ” †=k?hwo'_UrKÅ_Ug#s_U^av'ji_sJÏpG{ns'_:nk?r'{v$_: #¡¢^Wk?g#k?ok?g#_sJ_UoKhisö|k?hwgyosJKr±~'jEpGg

– ˜ _Uoƒ–›U¥m–¹¦ – ˜ ¨À–›t_UoŽ¬ž¦ ©–¼©­¶Jg~'{es_UgRo_\r'gg#k?r'¤Š_Uj#pGjwlŠk?{hwo['^W_\~7pG{Žv7pGjEpuypGlŠ_ÀxRr'h

'eUo_U{^™hwg#_fji_s³.~7pGhw{_sÀÏpG{ns'_f– xRr'hPs_fnk?r'~_UgRoq­ Ù _UopGjwlŠk?{hwo['^W_:gr'ohwjwhis_:xRr#_µo{k?his

~'{eKhinqpGos\eUjieU^W_UgRopGhw{_sÀxyr'h#~$_U{^W_Uoo_UgyoÀ'_J'enUhi'_U{0sh'_UrKÃ"pG{ns»s_nk?r'~_UgRoq¥Ksh7r'g"~k?hwgRo

_so™K{k?hwo_ak?r™lypGr#n[#_ar'g£pGr'o{_m¥7_UoshPr'g…~k?hwgRoJ_sopGrÑ'_ssr#sq¥#sr'{q¥#k?rÑpGrž'_ssk?r#s

r'g±pG{nm­ Ù _s0o{k?his0~'{eKhinqpGosÀs_U^av'ji_UgRoUo{_µji_s»~'jwr#s\shw^™~'ji_s0~'{eKhinqpGosÀxRr'h~$_U{^W_Uoo_Ugyo

k?v'o_Ug'hw{µr'gÑpGjwlŠk?{hwo['^W_‰sk?r#s顝xRr7p?K{pGohixyr#_m­ • ÏpGjwlŠk?{hwo['^W_Cp™r'g#_ank?^™~'ji_OÃKhwoe_Ug…o_U^™~#s

'_²Ä™ÅÅƬ²Ç¹³7ÈyÉwÊmË0¬ŽÈ¥0n_žxyr'h_so.~'{_sxyr#_žk?~'ohw^.pGjJ#pGg#s.n_…^WkR']Uji_…'_žnqpGjinUr'j¢¥0_Uo.r'g#_

k=nnUr'~7pGohik?g…^WeU^Wk?hw{_'_aęÅƬŽÈ¥#n_:xRr'ht_sok?~'ohw^.pGj¢­

•

_ž^U^W_špGjwlŠk?{hwo['^W_šp´eUoeÑ'enU{hwo¼#pGg#s«r'g5{pG~'~$k?{o"~'{ene'_UgRo°ÍÏΒН­

Ù

_Ñ{pG~'~$k?{o

~'{es_UgyopGhwopGr#ssh=r'gCpGjwlŠk?{hwo['^W_\~$k?r'{Žji_»nqp?sŽlŠeUg#eU{pGjK^.pGhisƒsk?gCpGg7pGjwuKs_»g_soŽ~7p?sŽnk?{{_nUo_m­

¹× q Õ “  ” c:ek?^WeUo{hi_²pGjwlŠk?{hwo['^™hixRr#_m¥}k?v'r#so_ss_m¥{hwo['^WeUohixRr#_²_OÃ'p?nUo_m¥JjwlŠkG¡

{hwo['^W_sJ'_fv7pGjEpuypGlŠ_

(6)

3

%K:,C2a)tJ

Z\[#_r#sr7pGj#^Wk='_Uj#okapGg7pGjwu4q_ÀlŠ_k?^W_Uo{hinJpGjwlŠk?{hwo['^Ws»his!o[#_}J_qpGj7}654œÀ['hin[.his¿p?ssr'^W_

oknk?^™~'r'o_J_OÃ#p?nUojwu™œÀhwo[.{_qpGjgyr'^v_U{sfÍwˆqÎGН­ƒZ\['his»^WkR'_Uj['hi'_s¿o[#_ŸÆp?nUo¿o[7pGo»o[#_µpG{hwo[K¡

^W_UohinkGŸ{_qpGj#nk?^™~'r'o_U{s»[7p?s¿pµjwhw^™hwo_™~'{_nUhishik?g«pGg#™hwlmg#k?{_sgRr'^W_U{hinqpGjpGg#™{k?v'r#sog#_ss

hissr#_sq­ Js0pank?g#s_xyr#_Ug#n_fp—Khw{_nUo\hw^™~'ji_U^W_UgyopGohik?g…kGŸ pGg±pGjwlŠk?{hwo['^ o[7pGo»his0nk?{{_nUo0r'gK¡

'_U{!o[#_}_qpGj#}654^Wk='_Uj7'k=_s!g#k?og#_n_ssNpG{hwjwuo{pGg#sjEpGo_hwgyokpµ{k?v'r#so»pGg#17Gk?{¿_8.nUhi_Ugyo

~'{k?lm{pG^…¥pGg#…nqpGop?so{k?~'['hin—v$_U[7p¤=hik?r'{sJpG{_ank?^™^Wk?g'jwu¼k?v#s_U{¤Š_P­

:9#{so!pG~'~'{kŠp?n[™okµ{_U^W_Kuao['hisŽ~'{k?v'ji_U^hisŽokr#s_»_OÃ#p?nUopG{hwo['^W_Uohinm­!Ág‰o[#_\nk?gyo_OÃKo

kGŸ lŠ_k?^W_Uo{hin—pGjwlŠk?{hwo['^Wsq¥'^ar#n[±~'{k?lm{_ss\[7p?s0v__Ug±'k?g#_fhwg«o[#_µ{_n_UgyoÀ~7p?so:Íwˆ;'¥ˆq„'¥ˆ<'¥

ˆ=?Н­ Jg#k?o[#_U{±pG~'~'{kŠp?n[*¥ok´v$_…ŸÆk?jwjikqœ0_ [#_U{_m¥À[7p?s¼_U^W_U{lŠ_5{_n_UgRojwuŠ­?>f_nUhishik?g#s¼hwg

lŠ_k?^W_Uo{hin£pGjwlŠk?{hwo['^Ws«'_U~_Ug#5k?g¯lŠ_k?^W_Uo{hinž~'{_KhinqpGo_s«œÀ['hin[1pG{_…r#sr7pGjwjwu·pGjwlŠ_Uv'{pGhin

_OÃK~'{_sshik?g#s¾­A@#k?{_OÃ'pG^™~'ji_m¥'Ÿök?{p‰o{hw~'ji_—kGŸŽ~k?hwgRoslmhw¤Š_Ug±vRu"o[#_Uhw{nqpG{o_shEpGgžnkRk?{Khwg7pGo_s¾¥

'_nUhiKhwg'lќÀ[7pGo—his:o[#_Wk?{hi_UgRopGohik?g¸kGŸÀo[#_™o{hEpGg'lmji_.{_Kr#n_s—ok…_U¤mpGjwr7pGohwg'lCB½o[#_"shwlmg°kGŸD

pš^ar'jwohw¤mpG{hEpGo_ž~$k?jwuRg#k?^™hEpGjJkGŸ:'_Ulm{__žoœ0k'­1ÁŸ—pGg5pGjwlŠk?{hwo['^§k?g'jwu r#s_s.~'{_KhinqpGo_s"kGŸ

'_Ulm{__™`«p?sµpWŸör'g#nUohik?g£kGŸ»o[#_ahwg'~'r'o:#pGopK¥PpGg#²hºŸo[#_hwg'~'r'of#pGop¼pG{_nk='_šp?sJshw^™~'ji_

9'Ã'_…~'{_nUhishik?gÑgRr'^av$_U{sq¥nk?^™~'r'opGohik?g#s:nqpGgÑv_'k?g#_a_OÃ#p?nUojwu±r#shwg'l«o[#_—g7pGohw¤Š_‰'k?r'v'ji_

~'{_nUhishik?g±[7pG{Kœ0pG{_akGŸŽo[#_:nk?^™~'r'o_U{q­Z\[#_—'_Ulm{__:kGŸ!pGgžpGjwlŠk?{hwo['^4his\o[#_U{_OŸök?{_—{_UjEpGo_

okao[#_~'{_nUhishik?g«{_xRr'hw{_.oka{r'g¼pGg¼pGjwlŠk?{hwo['^ r#shwg'l_OÃ#p?nUo0pG{hwo['^W_Uohinm­Z\['his»^Wk?ohw¤?pGo_s

o[#_»'_shwlmgkGŸ7_8.nUhi_UgRopGjwlŠk?{hwo['^WsŽkGŸ'jik¾œ¸'_Ulm{__m­ƒ}_Kr#nUhwg'lJo[#_»'_Ulm{__0kGŸ'o[#_0pGjwlŠk?{hwo['^Ws

œÀhwjwj!{_Kr#n_Wo[#_Cgyr'^av$_U{pGg#£o[#_™nk?^™~'ji_OÃKhwouškGŸ\o[#_™'_UlŠ_Ug#_U{pGo_Wnk?g9#lmr'{pGohik?g#sq¥ ^.pFEŠ_

o[#_‰pGjwlŠk?{hwo['^Wsµ^Wk?{__Uji_U^W_UgRopG{u²pGg#…^Wk?{_lŠ_Ug#_U{pGj¢¥{_Kr#n_ao[#_‰pG^Wk?r'gyo:kGŸgyr'^W_U{hinqpGj

nk?^™~'r'opGohik?g#s¾¥œÀ['hin[1his"r#sr7pGjwjwu xRr'hwo_ÑpšjEpG{lŠ_žŸö{p?nUohik?g1kGŸ—o[#_Ñok?opGjµ_OÃ'_nUr'ohik?g1ohw^W_

_s~_nUhEpGjwjwuhºŸ^ar'jwohº¡¢~'{_nUhishik?g"nk?^™~'r'ohwg'l—hisƒhwgR¤ŠkEŠ_P¥=pGg#C~$kmsshwv'jwupGjiskf{_OŸ½{pGhwg™o[#_\r#s_\kGŸ

nk?^™~'jwhinqpGo_ž#pGop™so{r#nUor'{_sÀ{_sr'jwohwg'l™hwg±jik¾œ+s~7p?n_f{_xRr'hw{_U^W_Ugyosq­HGJk¾œ»_U¤Š_U{q¥'{_Kr#nUhwg'l

o[#_À'_Ulm{__ÀkGŸ*pGg.pGjwlŠk?{hwo['^ ^.pquhwg#nU{_qp?s_hwosƒohw^W_Ànk?^™~'ji_OÃ=hwoÂu‰hwg™o[#_À}J_qpGj#}65 ^Wk='_Uj¢­

@7k?jwjikqœÀhwg'l • hik?oop‰_Uo\pGj¢­Íwˆq‚GН¥Rœ»_µnk?g#shi'_U{»o[#_µ'_Ulm{__fkGŸ*o[#_~'{_KhinqpGo_sÀp?s\pGg¼p?'Khwohik?g7pGj

^W_qp?sr'{_kGŸo[#_‰nk?^™~'ji_OÃ=hwoÂuÑkGŸ~'{k?v'ji_U^Ws:pGg#£pGjwlŠk?{hwo['^Wsq¥PpGg#žhwgRo_Ug#Ñok"_Ujwr#nUhi#pGo_‰o[#_

{_UjEpGohik?g#s['hw~"v$_Uoœ0__Ug"ohw^W_O¡nk?^™~'ji_OÃKhwou¼pGg#.'_Ulm{__µkGŸ$o[#_~'{_KhinqpGo_sq­!}_UjEpGo_.{_s_qpG{n[

nqpGgžv_µŸÆk?r'g#¼hwgJIfgyr'o[sJs_U^™hwg7pGj*œ0k?{E£Íwˆq`?Ð pGg#±hwg…sk?^W_:{_n_UgRo~7pG~_U{sÍwˆq‡K¥=7¥#‚’Н­

Ágo['his ~7pG~$_U{q¥?œ»_\nk?g#shi'_U{Žo[#_0~'{k?v'ji_U^kGŸ#{_U~k?{ohwg'lfo[#_À³:hwgRo_U{s_nUohwg'l:~7pGhw{s!pG^Wk?g'l

ps_Uo kGŸ7¬. #¡¢^Wk?g#k?ok?g#_\nUr'{¤Š_0s_Ulm^W_Ugyosq­ ®°_\p?'K{_ssto[#_»{_17’v'jwr#_\nqp?s_m¥GœÀ[#_U{_¿o['hisŽs_Uo his

~7pG{ohwohik?g#_Whwgyok:oœ»k—sr'v#s_UokGŸg#k?g™hwgyo_U{s_nUohwg'ls_Ulm^W_UgRosq­ƒZ\['his!~'{k?v'ji_U^€nqpGg™v$_0sk?jw¤Š_

hwgÑk?~'ohw^.pGjƒÄ™ÅƬ:ÉwÊmË0¬.Ç ³7È»ohw^W_.ÍK<K¥7„K¥*ˆÐ­LGµkqœ»_U¤Š_U{µo[#_s_‰pGjwlŠk?{hwo['^Wsr#s_—~'{_KhinqpGo_sJkGŸ

['hwlm[Ñ'_Ulm{__m¥#_m­l#­ok™nk?^™~7pG{_ao[#_apGv#snUhissp?_:kGŸƒoœ0kWhwgRo_U{s_nUohik?gž~$k?hwgyosJk?{ok™jik=nqpGo_—pGg

hwgRo_U{s_nUohik?g.~$k?hwgyo»œÀhwo[W{_s~$_nUook—pf¤Š_U{ohinqpGjsjEpGv*­ƒZ\[#_s_À~'{_KhinqpGo_s[7pq¤Š_Jp:'_Ulm{__JpGg#

pGg«pGjwlŠ_Uv'{pGhinJnk?^™~'ji_OÃKhwou™o[7pGo\pG{_r#sr7pGjwjwuC['hwlm[#_U{¿o[7pGg"o[#_hwgRo_U{s_nUohik?g"~'{_KhinqpGo_MŽo['his

hisfhwg£~7pG{ohinUr'jEpG{—o[#_Cnqp?s_ŸÆk?{fjwhwg#_™s_Ulm^W_UgyosapGg#šnUhw{nUji_™s_Ulm^W_UgyosÍς’Н­‰¶Jr'{apGjwlŠk?{hwo['^Ws

ô ô&èONPQQQ

(7)

k?g'jwuÑr#s_o[#_Chwgyo_U{s_nUohik?gš~'{_KhinqpGo_WpGg#£oœ»k±k?o[#_U{—shw^™~'ji_‰~'{_KhinqpGo_s Mo[#_~'{_KhinqpGo_

o[7pGo—sk?{os:oœ0k±~k?hwgRos—vRu£pGv#snUhissp?_m¥tpGg#£o[#_™~'{_KhinqpGo_™o[7pGospuKsfhºŸÀp«~$k?hwgyo:his—v_Ujik¾œ—¥

k?g*¥Àk?{¼pGvk¾¤Š_Ñps_Ulm^W_Ugyoq­ ÁÂg ~7pG{ohinUr'jEpG{q¥œ»_²'k°g#k?o"nk?^™~'r'o_Ño[#_ÑpG{{pGg'lŠ_U^W_UgRo¼g#k?{

o[#_.o{pG~_4qk?hi#pGj0^.pG~´kGŸÀo[#_"s_Ulm^W_Ugyosq­+5²k?{_kq¤Š_U{q¥ƒo[#_.~'{_KhinqpGo_saœ0_.r#s_W'k…g#k?o‰spu

pGgRuRo['hwg'l«pGvk?r'oÀo[#_fgRr'^av$_U{k?{Ào[#_:~$kmshwohik?g#sÀkGŸŽo[#_fhwgRo_U{s_nUohik?g…~$k?hwgyosq¥pGg#¼o[#_fohw^W_

nk?^™~'ji_OÃKhwou5kGŸ—o[#_s_ÑpGjwlŠk?{hwo['^Ws¼'_U~$_Ug#'s"k?g'jwu¯k?g5o[#_žgRr'^av$_U{«kGŸ—hwgRo_U{s_nUohwg'l ~7pGhw{s

kGŸs_Ulm^W_UgRosq¥Žg#k?o—o[#_WgRr'^av$_U{‰kGŸÀhwgRo_U{s_nUohik?g´~$k?hwgyos BöKhP_U{_Ugyojwu£Ÿö{k?^ o[#_Wk?o[#_U{g#k?g

o{hw¤=hEpGj pGjwlŠk?{hwo['^WsÍÏ`K¥7„K¥);K¥)<'¥PˆOÐ2DO­

Z\[#_Cohw^W_Wnk?^™~'ji_OÃ=hwoÂuškGŸ\k?r'{apGjwlŠk?{hwo['^ his‰Ä™ÅÅƬ±Ç1³7ÈyÉwÊmË0¬ŽÈ¥PœÀ['hin[his—p«jik?l¼Ÿ¢p?nUok?{

Ÿö{k?^ k?~'ohw^.pGj*pGg#"hwo¿r#s_s0k?~'ohw^.pGjPs~7p?n_:ęÅƬŽÈ­ƒZ\['his0{_sr'jwo¿lŠ_Ug#_U{pGjwh4q_spashw^™hwjEpG{»{_sr'jwo

ŸÆk?{o[#_nqp?s_kGŸ$~#s_Ur#'kG¡s_Ulm^W_Ugyos¾¥Rh¢­_m­!s_Ulm^W_Ugyos»o[7pGohwgyo_U{s_nUo0hwg"pGo^Wkmso»k?g#_À~$k?hwgyoµÍςGН­

®°_Cji_qpG{g#_°{_n_Ugyojwu£o[7pGoaZ:­ Ù [7pGgš[7p?s—hwg#'_U~$_Ug#'_Ugyojwu°k?v'opGhwg#_p¼KhP_U{_UgyoCpGjwlŠkG¡

{hwo['^ o[7pGo.r#s_s«ps_Ulm^W_Ugyoé¡¢o{__ Í ¾Ð­ ÁÂosWohw^W_O¡nk?^™~'ji_OÃKhwou5his¼ÄWÅÅƬ£Çª³7ÈyÉwÊmË0¬ŽÈ¥

œÀ['hin[hisav_Uoo_U{o[7pGgo[#_Wohw^W_.nk?^™~'ji_OÃ=hwoÂukGŸk?r'{‰pGjwlŠk?{hwo['^ ŸÆk?{‰³°¦:ÅƬ

ÈJv'r'ohwo

r#s_sJęÅƬ.ǯ³7È¿s~7p?n_m­

‰‰

nUr'{¤Š_¼s_Ulm^W_UgRoChisa / O O ahºŸhwohiso[#_.lm{pG~'[·kGŸJpž~7pG{ohEpGjwjwu´'_9#g#_¸r'g'hw¤mpG{hEpGo_

Ÿör'g#nUohik?g B½h¢­_m­JpGgyu±¤Š_U{ohinqpGjƒjwhwg#_—hwgRo_U{s_nUosfsr#n[£pWs_Ulm^W_UgRoJhwg£pGoJ^Wkmsoµk?g#_—~$k?hwgyoDO­ • _Uo

–ª¦ –˜ ¨.–›¿v_:ps_UoÀkGŸ ¬Ñ #¡¢^Wk?g#k?ok?g#_:nUr'{¤Š_:s_Ulm^W_UgRosÀsr#n[¼o[7pGoÀg#koœ»k.s_Ulm^W_UgyosÀkGŸ

–˜ B½{_s~*­»–J› D0hwgyo_U{s_nUoq­\Z\[#_:~'{k?v'ji_U^9hisÀok.{_U~k?{oo[#_‰³«~7pGhw{sJkGŸ!s_Ulm^W_UgRosJkGŸ– o[7pGo

hwgRo_U{s_nUoq­

• _Uo¼pGg# "!v$_.oœ»k£s_Ulm^W_Ugyos™kGŸµ– pGg#ji_Uo$#¯pGg#&%…v_"oœ0k²_Ug#K~$k?hwgyos™kGŸµsk?^W_

s_Ulm^W_UgyosakGŸ–"¥*g#k?o—g#_n_ssNpG{hwjwu£kGŸ'.k?{( ! ­.  Å#PÈJpGg#*)Å#Pȵ'_Ug#k?o_™o[#_Wnk=k?{Khwg7pGo_skGŸ

# ¥*pGg#+ŠÅö tÈÀ'_Ug#k?o_s—o[#_C~k?hwgRo—kGŸ,CœÀ[#kms_WpGv#snUhissp"hisf  B½hºŸÀsr#n[p"~$k?hwgyo—_OÃKhisosDO­a®°_

nk?g#shi'_U{o[#_fŸÆk?jwjikqœÀhwg'lW~'{_KhinqpGo_s M

-  Ó Ø.½“Š‘K Ó*/ ” 1023!54¦76

-  Ó Ø.½“Š‘K Ó98 ”   Å#PÈ;:·  Å<%yÈ

-  Ó Ø.½“Š‘K Ó>= ” )Å#*È1:?)Å@ŠÅö ŽÅ#PÈÈÈ

-  Ó Ø.½“Š‘K ÓBA ” )Å@yÅö  Å#*ÈÈÈ;:?)Å@3!öÅö  Å#*ÈÈÈ

-  Ó Ø.½“Š‘K Ó9C ”ED  BF&G  Å#PÈIH ŽÅ<%ŠÈ<JŽsr#n[žo[7pGo$ŠÅö tȎ¦K !Åö tÈ

z!{_KhinqpGo_"ˆahis^.pGg##pGok?{uŠ­Àz!{_KhinqpGo_™`WpGjwjik¾œsok"sk?{oo[#_a_Ug#K~k?hwgRosq­Àz!{_KhinqpGo_™‚

o_Ujwjis—œÀ[#_Uo[#_U{pGg°_Ug#K~k?hwgRo—jwhi_s—pGv$kq¤Š_Wk?{:v$_Ujikqœ p«s_Ulm^W_UgRoq­™z!{_KhinqpGo_ =±~'{k¾¤Rhi'_s—o[#_

k?{'_U{0kGŸ*oœ0k‰s_Ulm^W_Ugyos\pGjik?g'lCp—¤Š_U{ohinqpGjjwhwg#_J~7p?sshwg'lo['{k?r'lm[¼pGg«_Ug#K~k?hwgRoq­z!{_KhinqpGo_:Î

n[#_n EKs*œÀ[#_Uo[#_U{ oœ»kJs_Ulm^W_Ugyosthwgyo_U{s_nUo œÀhwo['hwgp\¤Š_U{ohinqpGjysjEpGva'_9#g#_:vyufoœ»k_Ug#K~$k?hwgyos¾­

õ½ûŽôtõ

(8)

®°_a'kWg#k?ofs~$_nUhºŸ½u…pC~'{_nUhis_a{_U~'{_s_UgRopGohik?g²Ÿök?{Jo[#_as_Ulm^W_UgRosq¥7œÀ['hin[£^.pu…'_U~$_Ug#

k?g¼o[#_:pG~'~'jwhinqpGohik?g*­L@7k?{\_OÃ#pG^™~'ji_m¥Ko[#_µŸör'g#nUohik?g±p?sskRnUhEpGo_«ok™p‰s_Ulm^W_UgyoÀ^.pqu.v$_µlmhw¤Š_Ug

_OÃK~'jwhinUhwojwu™ok?lŠ_Uo[#_U{¿œÀhwo["o[#_hwgRo_U{¤?pGjœÀ[#_U{_hwo»his¿'_9#g#_P¥=k?{¿o[#_ÀŸör'g#nUohik?g.^.pqu™v_lmhw¤Š_Ug

hw^™~'jwhinUhwojwu£p?sµo[#_‰pGjwlŠ_Uv'{pGhin‰Ÿör'g#nUohik?gškGŸ»'_Ulm{__«o[7pGoµhwgRo_U{~k?jEpGo_sfljlmhw¤Š_Ug²~$k?hwgyos

B½hwg#nUjwr#Khwg'l²o[#_«_Ug#K~k?hwgRoskGŸo[#_"s_Ulm^W_UgyoDO­£¶Jo[#_U{{_U~'{_s_UgRopGohik?g#sWpG{_"pGjiskž~kmsshwv'ji_m­

Z\[#_.'_Ulm{__skGŸÀo[#_™~'{_KhinqpGo_s‰nUji_qpG{jwu°'_U~_Ug#´k?g°o[#_Wn[#kms_Ug{_U~'{_s_UgRopGohik?g*­…ÁÂgšo[#_

opGv'ji_\v$_Ujikqœ Bös__pGjisk™ÍςK¥KˆmˆUÐ2DO¥mo[#_À'_Ulm{__skGŸ$z!{_KhinqpGo_s»`’¡ÂÎ:pG{_\lmhw¤Š_UgCŸÆk?{!jwhwg#_Às_Ulm^W_Ugyos

{_U~'{_s_Ugyo_¼vyu«o[#_fnkRk?{Khwg7pGo_skGŸto[#_Uhw{_Ug#K~k?hwgRosq¥=ŸÆk?{0[7pGjºŸ½¡nUhw{nUji_sÀ'_9#g#_¼vyu¼n_Ugyo_U{s¾¥

{p?Khwht~'jwr#sJp‰v$kRk?ji_qpGgCB½ok.Khisohwg'lmr'his[…v$_Uoœ0__Ugžo[#_:r'~'~$_U{JpGg#±o[#_:jik¾œ»_U{fpG{n DO¥'ŸÆk?{nUhw{nUji_

s_Ulm^W_Ugyos'_9#g#_žvyu¼o['{__:~$k?hwgyos B½hwg#nUjwr#Khwg'l.o[#_:oœ»k._Ug#K~$k?hwgyosJkGŸŽo[#_as_Ulm^W_UgyoDO¥pGg#

ŸÆk?{JnUr'{¤Š_sf'_9#g#_²vyu²p™~$k?jwuRg#k?^™hEpGjƒ_xyr7pGohik?g )¼¦ƒÅö tÈ­µ¶Jv#s_U{¤Š_‰o[7pGoµo[#_a~'{_KhinqpGo_s

pG{_fk?{'_U{_¼vRu.hwg#nU{_qp?shwg'lW'_Ulm{__sÀhwg…pGjwj$o[#kms_fnqp?s_sq­AGµkqœ0_U¤Š_U{q¥'o['hisÀk?{'_U{À^.pu"v_fKhºŸ½¡

ŸÆ_U{_UgyoƒŸÆk?{ƒsk?^W_\k?o[#_U{!ou=~_s!kGŸs_Ulm^W_Ugyosq­A@#k?{ƒhwg#sopGg#n_m¥mŸök?{ƒ[7pGjºŸ½¡nUhw{nUji_s'_9#g#_Cvyuo['{__

g#k?g² #¡_OÃKo{_U^W_~k?hwgRosq¥7o[#_‰'_Ulm{__‰kGŸ¿z!{_KhinqpGo_W`™hisf`m‡WœÀ['hwji_o[#_‰'_Ulm{__kGŸ¿z!{_KhinqpGo_

‚‰hisk?g'jwu =#­

z!{_KhinqpGo_ '_Ulm{__

jwhwg#_ [7pGjºŸ nUhw{nUji_ ~k?j¢­!kGŸ

s_Ulm^W_UgRo nUhw{nUji_ s_Ulm^W_UgRo '_Ulm{__

‚‰~$k?hwgyos 

ˆ ` ` ˆq` 

` ˆ ˆ ˆ ˆ

‚ ` ` = 

=#¥ÏÎ ‚ = ˆq` 

¶Jr'{.pGjwlŠk?{hwo['^k?g'jwu´{_xRr'hw{_sC~'{_KhinqpGo_sžˆm¥Ï`£pGg#¯‚ÑœÀ['hwji_±k?o[#_U{Wg#k?gK¡¢o{hw¤=hEpGjpGjwlŠkG¡

{hwo['^WsÀÍÏ`#¥?„K¥O;K¥O<K¥KˆUÐ2Dt^.pFEŠ_\r#s_\kGŸk?r'{ 9#¤Š_\~'{_KhinqpGo_sq­ƒZ\[yr#so[#_Uua[7p¤Š_\['hwlm[#_U{¿pGjwlŠ_Uv'{pGhin

'_Ulm{__JœÀ[#_Ug.œ0_Jnk?g#shi'_U{»jwhwg#_Js_Ulm^W_Ugyosq¥=[7pGjºŸtnUhw{nUji_s0k?{»nUhw{nUji_s0'_9#g#_.vRuWo['{__~$k?hwgyos¾­

$é$

ÁÂg±o['hiss_nUohik?g*¥ › B½{_s~*­˜D0'_Ug#k?o_sµp‰v'jwr#_0B½{_s~*­!{_1DÀs_Ulm^W_Ugyoq¥'o[7pGohis›,F…–J›ÀpGg#

˜$Fž–˜?­!®°_fœÀhwjwj*~'{kq¤Š_ao[#_µŸök?jwjik¾œÀhwg'l.{_sr'jwoM

ÓR×  Ó /H " %(')' -F /01 21 O %/ I %-F" 2aęÅÅƬƒÇ

³7ÈyÉwÊmË0¬ŽÈ6 2/0 O"™Ä™ÅƬŽÈ ' 2 "IO HBO"

®°_:~'{_s_UgyoµpCg#_Uœ ~'jEpGg#_—sœ0__U~ÑpGjwlŠk?{hwo['^4ŸÆk?{o['hisÀ~'{k?v'ji_U^…­ +¤Š_U{ohinqpGjŽsœ»__U~žjwhwg#_

^Wk¾¤Š_s‰p?nU{kmss:o[#_W~'jEpGg#_CŸö{k?^ ji_OŸöo—ok±{hwlm[Roq­.®1[#_Ug°hwo—{_qp?n[#_s‰pGg¸_Ug'~k?hwgRoq¥ sk?^W_.#pGop

ô ô&èONPQQQ

(9)

so{r#nUor'{_s«pG{_žr'~#pGo_1pGg#¯hwgyo_U{s_nUohik?g#s±nqpGg v$_±{_U~k?{o_P­ \o¼pGgyu·ohw^W_m¥\œ0_Ñk?g'jwu

nk?g#shi'_U{ 2-Fs_Ulm^W_UgyosœÀ['hin[£pG{_:o[#_:s_Ulm^W_Ugyoso[7pGonU{kmssÀo[#_asœ»__U~…jwhwg#_m­

±Ó .M .×K/ "C21 ' 21 O H %'

/01 ›(" "0 /01 U˜ ' L % "O1 › -F U˜O" O

H %2 "O1 U˜

Ág o[#_²ŸÆk?jwjikqœÀhwg'l sr'v#s_nUohik?g#sq¥µœ»_°'_snU{hwv_pGg+pGjwlŠk?{hwo['^ o[7pGo…{_U~k?{os…o[#_ "

hwgRo_U{s_nUohik?g#sq­Z\[#_‰k?o[#_U{fhwgRo_U{s_nUohik?g#sapG{_‰{_U~k?{o_²vRužo[#_CspG^W_™pGjwlŠk?{hwo['^ p’Ÿ½o_U{:_OÃ=¡

n[7pGg'lmhwg'l"o[#_‰k?{hi_UgyopGohik?gškGŸ!o[#_uy¡Âp’ÃKhisk?{Jo[#_ank?jik?{sµkGŸo[#_as_Ulm^W_UgRosq­Z\[#_pGjwlŠk?{hwo['^

okCv$_:'_snU{hwv$_±hisÀo[#_U{_OŸÆk?{_apG~'~'jwhi_±ŸÆk?r'{Àohw^W_sq­

"!#$ %$&'

Z\[#_—hi'_qp™hisokW{_U~k?{oo[#_alŠkRk=¼hwgyo_U{s_nUohik?g#sJœÀ['hwji_a~'r#s['hwg'lWo[#_av'jwr#_—s_Ulm^W_Ugyosµ'kqœÀgK¡

œ\pG{'sq­‰Û¿p?n[°v'jwr#_™s_Ulm^W_Ugyo:his:sok?{_£hwgp«s_Uo)(‰Å ˜GÈ0ŸÆk?{:sk?^W_Wp?nUohw¤Š_C{_šs_Ulm^W_UgRoU˜m­

Z\[#_fs_Uo\kGŸ s_Ulm^W_UgRosÀhwg*(‰Å ˜ È!œÀhwjwj$v_J^.pGhwgyopGhwg#_žKr'{hwg'l‰o[#_fsœ0__U~*­ÁÂo0nk?g#shisos0kGŸ o[#_

v'jwr#_fs_Ulm^W_UgRosÀo[7pGoÀnqpGg'g#k?oÀv_J~'r#s[#_¼'kqœÀg±v$_nqpGr#s_µo[#_Uu«pG{_µv'jik=n EŠ_±_Uhwo[#_U{ÀvRu U˜µk?{

vRu"o[#_—jikqœ»_soJs_Ulm^W_UgRokGŸ"(CÅ U˜GÈ­

Z\[#_apGvk¾¤Š_ 7’v_Ujik¾œ+{_UjEpGohik?g#s['hw~ќÀhwo['hwgž–› B½{_s~*­–˜D0hisp‰~7pG{ohEpGjŽk?{'_U{q¥'œÀ['hin[Ñhisp

ok?opGjŽk?{'_U{œÀ[#_Ug…{_so{hinUo_žok.p?nUohw¤Š_s_Ulm^W_Ugyos¾­»®°_—œÀhwjwjt^.pGhwgyopGhwg²o[#_ak?{'_U{_žjwhisokGŸ

o[#_"p?nUohw¤Š_W{_°s_Ulm^W_UgRosahwg¸p¼v7pGjEpGg#n_s_qpG{n[o{__f|ér#so:jwhEŠ_.hwg Ù [7pGgspGjwlŠk?{hwo['^ ÍK<GÐ

ŸÆk?{À{_=¡¢v'jwr#_—s_Ulm^W_UgRosq­

@#k?{_qp?n[…v'jwr#_:s_Ulm^W_Ugyo q›¥Kœ»_—p?ssk=nUhEpGo_—p{_±s_Ulm^W_Ugyo,+ÂÅ q›OÈ­!®°_fœÀhwjwjP{_xRr'hw{_fo[7pGo

o[#_foœ»kWŸök?jwjik¾œÀhwg'l.~'{k?~$_U{ohi_s{_U^.pGhwgžspGohis97_…Kr'{hwg'lWo[#_—nk?r'{s_:kGŸƒo[#_apGjwlŠk?{hwo['^ M

-  ×-Ó ’ Ô7/ " 21 O+ q›.A & " O/ 1 .%( -/+ÂÅ q›OÈ

-F O " -O' %102 3 ')45

- 

×-Ó

’

Ô 86 %O 7H 98:+çśOÈ " F;A + 0 -F I%A"

." /01 2

@#k?{W_qp?n[5p?nUohw¤Š_…{_·s_Ulm^W_Ugyo ˜ ¥¿œ»_±'_Ug#k?o_±vRu<(CÅ ˜ ȗo[#_±s_Uo™kGŸ—pGjwjp?nUohw¤Š_¼v'jwr#_

s_Ulm^W_Ugyos ›sr#n[žo[7pGo=+çÅ ›OÈ¿¦˜G­ÀÁÂohissok?{_žhwgÑp.#pGopWso{r#nUor'{_o[7pGoµpGjwjik¾œsµr'g'hik?g*¥

^™hwg'hw^r'^ _OÃ=o{p?nUohik?g°pGg#£sr'~'~'{_sshik?gÑhwgęÅÆÉwÊmË»¬ŽÈ0ohw^W_+Bö_m­l#­—p.v'hwg#k?^™hEpGjƒ[#_qpG~DO­:Z\[#_

r'g#'_U{jwu=hwg'l£k?{'_U{hiso[#_.¤Š_U{ohinqpGj\k?{'_U{CkGŸJp?nUohw¤Š_.{_¸s_Ulm^W_Ugyos™pGjik?g'l²o[#_"sœ»__U~¸jwhwg#_m­

>µk?o_Co[7pGo:œ»_.s[7pGjwjƒg#k?o—^.pGhwgyopGhwg?+çÅ q›OÈ_OÃ=~'jwhinUhwo_UjwuŠ¥Žp?s:hwo:hisfg#k?o—nUji_qpG{—œÀ[#_Uo[#_U{—œ0_™nqpGg

'k¼hwoaœÀhwo['hwg°o[#_WspG^W_™ohw^W_Wvk?r'g#'sq­™ÁÂos:¤mpGjwr#_WnqpGgšv$_™{_Uo{hi_U¤Š_šhwg°jik?lypG{hwo['^™hin.ohw^W_

Ÿö{k?^&o[#_[#_qpG~#s;(‰Å ˜¾È­!@#k?{—pGgyu±{_²s_Ulm^W_Ugyo U˜?¥o[#_s_Uo(‰Å˜’È\spGohis 97_sJo[#_—ŸÆk?jwjikqœÀhwg'l

~'{k?~$_U{ou M

õ½ûŽôtõ

(10)

-  ×-Ó ’ Ô?= /2)2/ '/ (CÅ ˜ È " O !21 ˜ O O/ 1 2

(CÅ U˜’È IO 1%10 21 U˜ O2 0 " /01 % U˜ + +

"21 /2)2/ '/ " ' )

e r

U(er ) e b

=l(eb)

sweep line

@Žhwlmr'{_WˆOM (‰Å U˜GÈ»pGg#žp‰lŠk=k=¼hwgyo_U{s_nUohik?g

GJk¾œ»_U¤Š_U{q¥Jo[#_Ñs_Uos*(CÅ ˜ ș'k´g#k?o«[7p¤Š_špGgyu1shw^™~'ji_ž^Wk?g#k?ok?g'hinUhwoÂu5~'{k?~$_U{ouŠ­?@7k?{

_OÃ#pG^™~'ji_m¥hºŸ U˜:hisJv_Ujik¾œ !˜

¥7o[#_Ug?(‰Å ˜’È0^.pu…v$_‰_Ugyohw{_UjwuÑpGv$kq¤Š_ (‰Å3!

˜

ÈÀk?{o[#_Uuž^.pu…v$_

hwgRo_U{jEp?n_CBös__69#lmr'{_‰` DO­

e b

l(eb) e b’

l(eb’)

@ hwlmr'{_`M (‰Å ˜’ÈhisJpGvk¾¤Š_ (‰Å 3!˜ È­

? %& & &

®°_—[7p¤Š_:okWnk?g#shi'_U{ŸÆk?r'{ ERhwg#'sJkGŸƒ_U¤Š_UgRoso[7pGok=nnUr'{œÀ[#_Ug…o[#_asœ»__U~Ñjwhwg#_:{_qp?n[#_sµpGg

_Ug#K~$k?hwgyoCkGŸp…s_Ulm^W_UgRoq­žÛ¿p?n[¸_U¤Š_UgRo‰nk?{{_s~k?g#'sok…o[#_.hwg#s_U{ohik?g*¥ƒo[#_.'_Uji_Uohik?g kGŸJp

v'jwr#_k?{Jp™{_Ñs_Ulm^W_Ugyoq­0®°_aœÀhwjwjtg#kqœ¹_OÃ=~'jEpGhwgÑhwgÑ'_UopGhwj [#kqœ¹o[#_s_—_U¤Š_Ugyos:pG{_:[7pGg#Kji_P¥

pGg#…~'{kq¤Š_:o[7pGok?r'{hwgy¤mpG{hEpGgyosB½~'{k?~_U{ohi_sˆm¥#`K¥7‚ D\pG{_:^.pGhwgyopGhwg#_P­

ô ô&èONPQQQ

(11)

=8/  Ó ¾ . ‘š Ó Ø1 Ó Ó 

Z\[#_Wg#_Uœ€{_°s_Ulm^W_UgRo ˜‰hisÀ|çr#soahwg#s_U{o_šhwgo[#_WjwhisoakGŸp?nUohw¤Š_W{_°s_Ulm^W_UgRos‰pGg#°o[#_

[#_qpG~(‰Å ˜ È¿hisÀhwg'hwohEpGjwh4q_²p?spGg…_U^™~'ou±s_Uoq­0¶Jr'{hwgy¤mpG{hEpGgyosµpG{_—k?vy¤=hik?r#sjwu¼^.pGhwgyopGhwg#_P­

=88  Ó ¾ . ‘šŒ Ó  Ó Ó 

®1[#_Ug²o[#_‰sœ»__U~šjwhwg#_{_qp?n[#_s:o[#_C_Ug#K~$k?hwgyo—kGŸ0p.v'jwr#_Cs_Ulm^W_Ugyoq›O¥œ0_ 9#{soµ'_Uo_U{^™hwg#_

o[#_«{_·s_Ulm^W_UgRo

˜

o[7pGo™jwhi_sµ|çr#soCv$_Ujikqœ o[#_±_Ug#K~$k?hwgyoq­¸Á¢Ÿ q›C'kR_sCg#k?oChwgyo_U{s_nUo

˜ ¥

o[#_Ug£hwofhisµhwg#s_U{o_£hwg (‰Å ˜’È­‰¶Jo[#_U{œÀhis_m¥Pœ»_‰{_U~$k?{ofo['hisfhwgyo_U{s_nUohwg'l…~7pGhw{—pGg#²{_U~$_qpGo

o[#_‰spG^W_~'{kRn_ssJœÀhwo[²o[#_™p?nUohw¤Š_‰{_Ñs_Ulm^W_UgRofo[7pGoµhisJv$_Ujikqœ ˜ r'gRohwjƒœ»_‰{_qp?n[°p.{_

s_Ulm^W_Ugyoo[7pGo'k=_sÀhwgRo_U{s_nUo ˜‰­

e b

l(eb)

e r e

r -1

@ hwlmr'{_‚M!Ág#s_U{ohik?gÑkGŸ q›

Z\['hisƒ~'{kRn_Kr'{_ÀnqpGgCv$_¿œÀ{hwoo_Ug™hwgCo[#_»Ÿök?jwjik¾œÀhwg'l:œ0pquŠ¥ŠœÀ[#_U{_ U˜

'_Ug#k?o_s!o[#_Àp?nUohw¤Š_

{_±s_Ulm^W_Ugyoo[7pGojwhi_sÀhw^™^W_KhEpGo_Ujwu±v_Ujik¾œ U˜?­

 Ó ’ › HU˜

®1['hwji_›\hwgRo_U{s_nUos ˜

{_U~k?{oo[#_fhwgyo_U{s_nUohik?g

U˜ ˜

ÁÂg#s_U{o›\hwg(CÅU˜’È

Z\[#_hwgRo_U{s_nUohik?g#s:v$_Uoœ0__Ug ›fpGg#²o[#_{_£s_Ulm^W_UgRos:o[7pGo—pG{_‰v_Ujik¾œ¹o[#_Cji_OŸöof_Ug#=¡

~$k?hwgyo—kGŸ ›:pGg#°pGv$kq¤Š_ +çÅ ›OÈ[7pq¤Š_™v$__Ugš{_U~k?{o_P¥Po[#_U{_OŸÆk?{_™~'{k?~$_U{ou ˆChisfo{r#_CŸÆk?{ q›­

\_shi'_s¾¥KhwoÀhissohwjwj*¤mpGjwhi«Ÿök?{Ào[#_ak?o[#_U{v'jwr#_—s_Ulm^W_UgRosq­

õ½ûŽôtõ

(12)

†Rhwg#n_,+çÅGÈ!{_U^.pGhwg#s\o[#_µspG^W_Ÿök?{0_qp?n[…p?nUohw¤Š_µv'jwr#_Js_Ulm^W_UgRo m¥=~'{k?~_U{oÂu«`sohwjwj7[#k?ji's

p’Ÿöo_U{Ào[#_:hwg#s_U{ohik?gÑkGŸ q›­

@ hwg7pGjwjwuŠ¥ji_Uoµr#sJn[#_n EÑ~'{k?~_U{oÂu²‚K­ÁŸ ›hiso[#_g#_Uœ¹^™hwg'hw^ar'^ kGŸ (‰Å ˜GÈ»œÀ[#_U{_ U˜:¦

+çÅ q›OÈ¥o[#_UgškGŸ¿nk?r'{s_‰hwof'kR_sµg#k?ofnU{kmss +çśOÈ­ 5Ñk?{_k¾¤Š_U{q¥Po[#_‰k?o[#_U{fs_Ulm^W_Ugyos:kGŸ (CÅ U˜GÈ

^.pqužk?g'jwu…nU{kmss(‰Å ˜’È\k?gÑo[#_{hwlm[yofkGŸo[#_‰sœ»__U~²jwhwg#_m¥7o[#_U{_OŸÆk?{_‰o[#_Uu…nqpGgÑg#k?ofnU{kmssJhwo

v$_OŸÆk?{_o[#_C{hwlm[Roa_Ug#K~$k?hwgyoakGŸ ›µhisf{_qp?n[#_°shwg#n_ ›µjwhi_s:v$_Uoœ»__Ugo[#_s_™s_Ulm^W_UgyospGg#

˜G­!Z\[#_anqp?s_:œÀ[#_U{_q›»hisg#k?oo[#_:g#_Uœ ^™hwg'hw^r'^ kGŸ (‰Å U˜’È¿hisÀo{hw¤=hEpGj¢­

=8= "Ó × . ‘š Ó Ø  Ó Ó# 

>µkqœÌsr'~'~$kms_Ño[#_Ñsœ0__U~ jwhwg#_ž{_qp?n[#_s¼o[#_ž{hwlm[Ro…_Ug#K~k?hwgRo¼kGŸp{_ s_Ulm^W_Ugyo ˜G­

'_Ug#k?o_sJo[#_—^™hwg'hw^r'^kGŸ (CÅ U˜GÈ­\Á¢ŸhwgRo_U{s_nUos U˜ Š¥7o[#_UgÑ{_U~$k?{oo[#_ahwgyo_U{s_nUohik?g*¥

o{u²pGlypGhwgќÀhwo[ ˜ ž­w­w­Jr'gRohwjp.s_Ulm^W_UgRo ˜ ¼hisŸÆk?r'g#Ño[7pGof'k=_sJg#k?oµhwgRo_U{s_nUoš­

Z\[#_Ug hisƒ^Wk¾¤Š_CŸ½{k?^ (CÅ U˜GÈ*ok;(‰ÅU˜ 'È¥RpGg#Cœ0_ÀsopG{o¿pGlypGhwg™œÀhwo[™o[#_\g#_Uœ·^™hwg'hw^ar'^

kGŸ (‰Å ˜’È­¶Jo[#_U{œÀhis_m¥yhºŸ 'k=_s!g#k?o!hwgyo_U{s_nUo U˜m¥?œ»_shw^™~'jwu^W_U{lŠ_ (‰ÅU˜’ÈŽpGg# (CÅ U˜ ?È

o[Rr#s^.pGhwgRopGhwg'hwg'l.~'{k?~$_U{ou…‚K­

Ág±o['hispGjwlŠk?{hwo['^…¥  Ó ¾ hiso[#_:~'{kRn_Kr'{_—œ»_—'_snU{hwv$_±hwg±o[#_:~'{_U¤=hik?r#ss_nUohik?g*­

®1['hwji_&¦$Å (CÅ U˜GÈÈhwgyo_U{s_nUos ˜

{_U~k?{oo[#_fhwgyo_U{s_nUohik?g

_OÃ=o{p?nUo9Ÿ½{k?^ (CÅ U˜GÈ

 Ó ¾ ˜

(‰Å ˜ ?ȃ¦ (CÅ U˜ ?È$¨*(CÅ U˜’È

\p?¸hwgRo_U{s_nUohik?g#s™^.puv_«{_U~$k?{o_¸Kr'{hwg'l£o['his™k?~$_U{pGohik?g*¥!œ»_«^.pqu…|ér#so‰KhisnqpG{

o[#_U^&vyu¼nk?^™~7pG{hwg'l.o[#_—nk=k?{Khwg7pGo_skGŸƒo[#_:ji_OŸöo_Ug#K~k?hwgRosq­

>Jk?o_Ào[7pGo +ÂÅq›OÈ*his!g#k?or'~$#pGo_.p’Ÿöo_U{^W_U{lmhwg'l (CÅ U˜ ?È pGg#/(CÅU˜GÈthwgWk?{'_U{ok EŠ__U~

k?r'{Àohw^W_ank?^™~'ji_OÃ=hwoÂu±vk?r'g#P­

Z\[#_:hwgy¤mpG{hEpGgyosfpG{_f^.pGhwgyopGhwg#_£p?sÀhis_qp?shwjwu¼n[#_nEŠ_Ñp?sÀhwgžo[#_:~'{_U¤Rhik?r#snqp?s_m­

=8A "Ó × . ‘šŒ Ó  Ó Ó# 

• _Uo ›fv$_Co[#_Ws_Ulm^W_UgRoaok±v$_C{_U^Wkq¤Š_¸pGg# U˜™¦ +ÂÅ q›OÈ­µs:œ»_WsNpGhišv_OŸÆk?{_m¥ +çÅ q›OÈnqpGg

v$_k?v'opGhwg#_"hwg¼ÄWÅÆÉwÊmË»¬ŽÈŽohw^W_ÀŸö{k?^ o[#_^W_U{lŠ_qpGv'ji_µ[#_qpG~"#pGopso{r#nUor'{_o[7pGo0sok?{_s»o[#_

s_Uos=(‰ÅºÈ­

Á¢Ÿ ›‰hisCg#k?o™o[#_¼^™hwg'hw^ar'^ÚkGŸ)(‰Å ˜¾È¥¿œ»_C|ér#soC{_U^Wkq¤Š_…hwoq­ ¶Jo[#_U{œÀhis_m¥»œ»_žsohwjwj\{_O¡

^Wk¾¤Š_ ›aŸ½{k?^ (CÅ ˜

È¥!v'r'oCo[#_Ug·œ»_«g#__ ok£n[#_nE´œÀ[#_Uo[#_U{™o[#_«g#_Uœ ^™hwg'hw^ar'^§kGŸ

ô ô&èONPQQQ

(13)

(CÅ ˜ È»hwgRo_U{s_nUos ˜ ­\Á¢Ÿ!hwoJ'k=_sq¥7œ»_~'r#s[žhwoµ'kqœÀgyœ\pG{'sfvyu…{r'g'g'hwg'l«o[#_—~'{k=n_Kr'{_ 5*Õ

 Ó ’ Bš¥U˜ DO¥o[#_Ug²{_U~_qpGoµo[#_—œÀ[#k?ji_~'{k=n_ssœÀhwo[²o[#_g#_Uœ^™hwg'hw^r'^9r'gRohwjƒhwoJ'k=_s

g#k?oÀhwgRo_U{s_nUo ˜G¥7skCo[7pGo~'{k?~$_U{ou…‚‰{_U^.pGhwg#so{r#_m­

_OÃKo{p?nUo ›0Ÿö{k?^ (‰Å˜’È

œÀ['hwji_&¦ $Å (‰Å ˜’ÈÈ»hwg#so_U{s_nUos˜

{_U~$k?{oo['hisÀhwgRo_U{s_nUohik?g

_OÃKo{p?nUo 9Ÿö{k?^ (‰Å ˜¾È

 Ó ’ B š¥U˜ D

¶Jg#n_apGlypGhwg*¥#o['his~'{kRn_Kr'{_a^.pu¼{_U~k?{ov7p?±hwgyo_U{s_nUohik?g²œÀ['hin[²nqpGg…v$_ 9'ÃK_…vyu…p

shw^™~'ji_:o_soq­

ÁonqpGg…v$_:_qp?shwjwu¼n[#_nEŠ_…o[7pGoo[#_:hwgR¤?pG{hEpGgRosµpG{_f^.pGhwgRopGhwg#_P­

Z\[#_ank?{{_nUog#_sskGŸƒo['hispGjwlŠk?{hwo['^ Khw{_nUojwu«ŸÆk?jwjikqœsŸ½{k?^ ~'{k?~$_U{ohi_saˆ—pGg#ž‚K­

3%

5£pGhwgyopGhwg'hwg'l"o[#_:k?{'_U{_±{_±s_Ulm^W_UgRosjwhisoÀopFEŠ_sJÄWÅƬ:ÉwÊmË»¬ŽÈohw^W_m­

•

kRnqpGjwh4hwg'l«pGg…_Ug#=¡

~$k?hwgyofk?{{_U^Wk¾¤Rhwg'l¼hwoJopFEŠ_sfÄWÅÆÉwÊmË»¬ŽÈ­Z\[#_‰k?o[#_U{µ~7pG{osJkGŸo[#_CpGjwlŠk?{hwo['^ opFEŠ_CpGoµ^Wkmso

ÄWÅÆÉwÊmË»¬ŽÈ!ŸÆk?{_qp?n[Ñ_U¤Š_Ugyoµk?{{_U~$k?{o_…hwgyo_U{s_nUohik?g*¥7o[#_Ug…œ0_À|ér#soÀg#__…okW~'{kq¤Š_—o[7pGoµpGg

hwgRo_U{s_nUohik?gnqpGg'g#k?o:v$_‰{_U~k?{o_£oœÀhin_m­ • _UoU˜‰pGg# q›µv_‰oœ0k±hwgyo_U{s_nUohwg'lžs_Ulm^W_Ugyos¾­

Ÿöo_U{"{_U~$k?{ohwg'l´o[#_Uhw{¼hwgRo_U{s_nUohik?g k?g#n_m¥ +çśOÈ ˜G­ 5²k?{_kq¤Š_U{q¥~'{k?~$_U{ou `°^W_qpGg#s

o[7pGo)+ÂÅ q›OÈJnqpGg´k?g'jwu£lŠk…'k¾œÀg´o[#_WjwhisoakGŸÀ{_p?nUohw¤Š_.s_Ulm^W_Ugyosq¥ƒpGg#°œ0_Wg#_U¤Š_U{—o_soao[#_

hwgRo_U{s_nUohik?gžv$_Uoœ0__Ug q›pGg#žpCs_Ulm^W_Ugyoo[7pGojwhi_sJpGv$kq¤Š_+çÅq›OÈ­

& &3& $ & ! &'

†Rhwg#n_‰o['his:pGjwlŠk?{hwo['^hisµ_Uji_U^W_UgyopG{u²œ»_Ck?g'jwužg#__Ñok¼nk?g#shi'_U{—p™ŸÆ_Uœ¹'_UlŠ_Ug#_U{pGo_™nqp?s_s

œÀ['hin[™or'{gWk?r'o!okµv_0¤Š_U{uC_qp?su—okf[7pGg#Kji_m­ƒZ*œ0k.ERhwg#'s!kGŸ$'_UlŠ_Ug#_U{p?nUu^.pqu‰k=nnUr'{MŽ_Uhwo[#_U{

oœ»k"_Ug#K~k?hwgRos[7p¤Š_—o[#_—spG^W_—pGv$nUhisspCk?{JpGg…_Ug#K~$k?hwgyoJjwhi_sk?gÑpCnUr'{¤Š_m­

Z\[#_&9#{so0nqp?s_nqpGg«v$_sk?jw¤Š_"vyu._OÃKo_Ug#Khwg'l‰o[#_~7pG{ohEpGj$k?{'_U{0k?g¼_Ug#K~$k?hwgyosÀpGvnUhissp?_

okšpGgRu´ok?opGjk?{'_U{q­´Z\[#_±k?{'_U{Ws[#k?r'ji v_«o[#_¼spG^W_"ŸÆk?{C_qp?n[ k?g#_¼kGŸJo[#_«ŸÆk?r'{C~'jEpGg#_

sœ»__U~#sœ0_:~$_U{éŸök?{^ ŸÆk?{k?o[#_U{œÀhis_ask?^W_fhwgyo_U{s_nUohik?g#sJœ»k?r'jižg#_U¤Š_U{v_flŠk=k=P­

Á¢ŸŽpa~$k?hwgyoÀjwhi_s\k?g…ps_Ulm^W_Ugyoq¥Kœ»_0|ér#so\nk?g#shi'_U{\o[7pGo\hwo0hisÀpGv$kq¤Š_fo[#_fs_Ulm^W_UgRoKr'{hwg'l

oœ»k"sœ»__U~#spGg#…v_Ujik¾œ o[#_—s_Ulm^W_UgRoKr'{hwg'l.o[#_foœ»k.sœ»__U~#sœÀhwo[žo[#_:uy¡Âp’ÃKhis\{_U¤Š_U{s_P­

õ½ûŽôtõ

(14)

3 )ŽN2a(

cfhw¤Š_Ug1p°s_Uo"kGŸ:lŠ_Ug#_U{pGjJ 7¡¢^Wk?g#k?ok?g#_Ñs_Ulm^W_Ugyosq¥Àœ0_ž[7pq¤Š_ž~'{_s_Ugyo_ pGg1pGjwlŠk?{hwo['^ ok

{_U~$k?{oµo[#_a~7pGhw{sfkGŸ{_=¡¢v'jwr#_Cs_Ulm^W_Ugyosµo[7pGoµhwgyo_U{s_nUoq­—¶Jr'{:pGjwlŠk?{hwo['^Ìr#s_sJk?g'jwužo['{__

shw^™~'ji_—~'{_KhinqpGo_sfo[7pGo:pGjwjikqœ¹ok.'_nUhi'_‰hºŸ!oœ»k¼s_Ulm^W_UgRosµhwgyo_U{s_nUoq¥hºŸ»p.~k?hwgRohisJji_OŸ½ofk?{

{hwlm[RoJok«pGg#k?o[#_U{J~$k?hwgyoq¥$pGg#…hºŸ»pW~k?hwgRohisfpGvk¾¤Š_m¥7v$_Ujikqœ¹k?{µk?g£p™s_Ulm^W_UgRoq­Z\[#_s_ao['{__

~'{_KhinqpGo_sµs__U^4okWv_:o[#_ashw^™~'ji_so~'{_KhinqpGo_sJo[7pGoji_qp?…ok.sr'vxRr7p?K{pGohinapGjwlŠk?{hwo['^Wsq­

¶Jr'{µpGjwlŠk?{hwo['^4hispGjw^Wkmsok?~'ohw^.pGj hwg±o['hisÀ{_so{hinUo_ž^WkR'_Uj*kGŸ!nk?^™~'r'opGohik?g*­

ÁgRo_U{_sohwg'lmjwuŠ¥o[#_«ohw^W_±nk?^™~'ji_OÃKhwou´kGŸfk?r'{WpGjwlŠk?{hwo['^'_U~_Ug#'s™k?g o[#_«gyr'^v_U{WkGŸ

~7pGhw{s kGŸ'hwgyo_U{s_nUohwg'lfs_Ulm^W_Ugyos¾¥¾g#k?oŽk?g—o[#_!gyr'^v_U{ƒkGŸ'hwgyo_U{s_nUohik?g‰~$k?hwgyosq­ Ág—~7pG{ohinUr'jEpG{q¥

k?r'{pGjwlŠk?{hwo['^ œ»k?{EKs_U¤Š_Ug…hºŸƒo[#_:s_Ulm^W_UgRoshwgRo_U{s_nUohwg9#g'hwo_Ujwu±^.pGgyu¼ohw^W_sq­

®°_Wnk?g#nUjwr#'_WœÀhwo[¸sk?^W_Wk?~$_Ug°~'{k?v'ji_U^Wsq­ @ hw{soq¥ nqpGg°œ0_W{_U^Wk¾¤Š_"p±ÉwÊmË0¬¸ŸÆp?nUok?{hwg

k?r'{Àohw^W_ank?^™~'ji_OÃ=hwoÂu±{_sr'jwos

Z\[#_$:ÅƬ ³Àǚ¬:ÉwÊmË¿¬ŽÈ jik¾œ»_U{\v$k?r'g#.[#k?ji's»ŸÆk?{»lŠ_Ug#_U{pGj$nUr'{¤Š_Js_Ulm^W_Ugyosq­ÁÂo¿[7p?s0v$__Ug

~$kmsshwv'ji_‰ok¼'k¼v$_Uoo_U{fŸök?{fjwhwg#_™s_Ulm^W_UgRosWÍςGН­ Ù pGgšœ0_WpGjisk±'k¼v$_Uoo_U{JŸÆk?{—k?o[#_U{—s~$_nUhEpGj

nUr'{¤Š_™s_Ulm^W_Ugyos—sr#n[p?s:nUhw{nUji_™s_Ulm^W_Ugyos¾­™†=k?^W_C~'{_Ujwhw^™hwg7pG{u£{_sr'jwosµŸÆk?{:o['hin E£k?vK|_nUos

[7pq¤Š_:v$__Ugžk?v'opGhwg#_±vyuµhwlmg#_U{k?gÍwˆ ’Н­

Ág´o['his~7pG~$_U{q¥ƒœ»_"[7p¤Š_«{_so{hinUo_ k?r'{™pGoo_Ugyohik?g·okÑ #¡¢^Wk?g#k?ok?g#_¼s_Ulm^W_UgRosq­£Z\['his

^.pquCv_pµ{_so{hinUohik?g"œÀ[#_UgWo[#_À~$k?hwgyos!œÀhwo[«pf¤Š_U{ohinqpGj#opGg'lŠ_Ugyo\pG{_Kh8.nUr'jwo¿ok:nk?^™~'r'o_m­

Z\['hishishwg…~7pG{ohinUr'jEpG{µo[#_anqp?s_fŸök?{JnUhw{nUji_s'_9#g#_Ñvyu¼o['{__—~$k?hwgyosJœÀ[#_U{_—o[#_:~'{_KhinqpGo_

o[7pGonk?^™~7pG{_s— #¡_OÃKo{_U^W_™~$k?hwgyos:[7p?sa'_Ulm{__.`m‡¼œÀ['hwji_™o[#_ChwgRo_U{s_nUohik?g~'{_KhinqpGo_.[7p?s

'_Ulm{__.ˆq`™k?g'jwuŠ­

¹!!a)Ž!(

ÍwˆOЉÁ¤mpGg#­ ÀpGjEpGv7pGg*­ g k?~'ohw^.pGjpGjwlŠk?{hwo['^ Ÿök?{9#g#Khwg'lšs_Ulm^W_Ugyo™hwgRo_U{s_nUohik?g#sq­šÁÂg

%$ !)1' *0F/! *A/!' / E¥K~7pGlŠ_sJ`Kˆmˆ=`Kˆq„K¥tˆq„m„mÎK­

ÍÏ`’Ð#­ • ­ \_Ugyoji_UuÑpGg#²Z:­ ‰­¶Joo^.pGg'g*­JjwlŠk?{hwo['^WsJŸök?{J{_U~k?{ohwg'l±pGg#žnk?r'gRohwg'l¼lŠ_kG¡

^W_Uo{hin:hwgyo_U{s_nUohik?g#s¾­ ) ) *A/!' i¥ Ù ¡Â`O;BƄ DMK<F=y‚<F= =¥P†=_U~'o_U^av$_U{ˆq„ ?„K­

Íς’Ð?¡>C­ \k?hissk?g'g7pGo!pGg##­G†Rg#k=_UuRhwgE$­=Û 8.nUhi_UgyopGjwlŠk?{hwo['^WsŽŸÆk?{tjwhwg#_\pGg#nUr'{¤Š_0s_Ulm^W_Ugyo

hwgyo_U{s_nUohik?g r#shwg'l²{_so{hinUo_¸~'{_KhinqpGo_sq­ *A/!' / 0 H %E¥Àˆ<Béˆ DO¥

`m‡m‡m‡K­

Í=?Њ_qpGgK¡>:pGg'hi_Uj \k?hissk?g'g7pGopGg#C@'{pGg#nk…zŽ­tz!{_U~7pG{pGopK­«}k?v'r#so—~'jEpGg#_Wsœ0__U~°ŸÆk?{:hwgK¡

o_U{s_nUohwg'l.s_Ulm^W_UgRosq­ *A/!' E¥KokWpG~'~$_qpG{q­

ô ô&èONPQQQ

(15)

ÍÏΒЊ_qpGgK¡>:pGg'hi_Uj \k?hissk?g'g7pGopGg# Jgyok?hwg#_ µhwlmg#_U{k?g*­™Û!ji_U^W_UgRopG{upGjwlŠk?{hwo['^Ws—ŸÆk?{f{_O¡

~k?{ohwg'lšhwgRo_U{s_nUohik?g#s"kGŸ:nUr'{¤Š_…s_Ulm^W_UgRosq­¯}µpG~'~k?{oW'_¼{_n[#_U{n[#_£‚O;m`mÎK¥»Á >J}JÁ ‰¥

ˆq„m„m„K­

ÍK<’ЉZ:­ 5¸­ Ù [7pGg*­ shw^™~'ji_¿o{pG~$_4qk?hi™sœ0__U~™pGjwlŠk?{hwo['^ªŸÆk?{Ž{_U~k?{ohwg'lf{_17’v'jwr#_\s_Ulm^W_Ugyo

hwgyo_U{s_nUohik?g#sq­¿Ág * " *A H*A/!' O/ E¥'~7pGlŠ_s`O<m‚=`O<O;K¥tˆq„m„F=#­

Í ¾Ð‰Z:­5´­ Ù [7pGg*­}_U~$k?{ohwg'l"nUr'{¤Š_‰s_Ulm^W_UgRoJhwgRo_U{s_nUohik?g#sfr#shwg'l.{_so{hinUo_ž~'{_KhinqpGo_sq­

*A/!' O/ 0 %i¥Pˆ<B2= DO¥7`m‡m‡m‡K­

ÍK;’Ð 0_U{g7pG{ Ù [7pF4q_Ujwji_WpGg# G‰­Û¿'_Ujisv'{r'g'g#_U{q­ Jg²k?~'ohw^.pGj¿pGjwlŠk?{hwo['^̟Æk?{fhwgyo_U{s_nUohwg'l

jwhwg#_:s_Ulm^W_UgyosJhwg±o[#_:~'jEpGg#_m­ *Ñ¥#‚m„Béˆ DMwˆ=ÎF=#¥tˆq„m„m`K­

Íτ’Ð I™­ • ­ Ù jEpG{EKsk?gÑpGg#…zŽ­#®ª­7†R[#k?{q­ ~'~'jwhinqpGohik?g#sJkGŸƒ{pGg#'k?^9spG^™~'jwhwg'lWhwgžnk?^™~'r'op’¡

ohik?g7pGj*lŠ_k?^W_Uo{uŠ¥7ÁÁO­. *A/!' / E¥=)MςO; =y`Kˆm¥*ˆq„O;m„K­

Íwˆq‡’Ð @0­$J^Wk?{_m¥*zŽ­ cC­ @'{pGg#nUhikmspK¥ŽpGg#šc™­

•

hik?oopK­ €{k?v'r#so:{_Ulmhik?gpG~'~'{kŠp?n[´ok«o[#_

nk?^™~'r'opGohik?gCkGŸ'lŠ_k?^W_Uo{hin0lm{pG~'[#sq­RÁg™cC­ 0hwjEpG{Kh¢¥ŠcC­ @\­’ÁopGjwhEpGg#k'¥ ‰­¾z!hi_Uo{p?nqpG~'{hwg7pK¥

pGg#5cC­¿zr#nnUh¢¥À_Khwok?{sq¥ !% / Š¥0¤Šk?jwr'^W_ˆ= <KˆžkGŸ ' O

*A/!' E¥K~7pGlŠ_saˆ ?Έ;O<K­†R~'{hwg'lŠ_U{é¡ _U{jEpGl#¥Žˆq„m„O;K­

ÍwˆmˆOЙ¶Jjwhw¤Rhi_U{0>f_U¤=hwjwji_U{sq¥ ji_OÃ#pGg#K{p @'{k?gR¤Rhwjwji_m¥ \_U{g7pG{ 5²k?r'{{pGhwg*¥ÀpGg# 5Ñk?g'hixRr#_…Z _Uhwjº¡

jEpGr#P­¿ÛƒÃ#p?nUo~'{_KhinqpGo_sŸök?{nUhw{nUji_pG{nsJpG{{pGg'lŠ_U^W_Ugyos¾­0ÁÂg " !))' *

'0/F *A/!' / E¥K~7pGlŠ_saˆq‚m„ˆ= =¥`m‡m‡m‡K­

Íwˆq`’Ð >µk?g7pGji.Û­ Ifgyr'o[*­ / '" '%%(O¥y¤Šk?jwr'^W_!<m‡O<:kGŸ ' O *AO/ '

†R~'{hwg'lŠ_U{é¡ _U{jEpGl#¥Gµ_Uhi'_Ujwv_U{l#¥cf_U{^.pGgyuŠ¥ ˆq„m„m`K­

Íwˆq‚’Йcµhwr#s_U~'~$_ • hik?oopK¥@'{pGg#nkµz ­Gz!{_U~7pG{pGopK¥ypGg#}k?v$_U{okZŽpG^.p?sshEpK­=}k?v'r#so*~'{kqÃ=hw^™hwoÂu

xyr#_U{hi_sM Jgšhwjwjwr#so{pGohik?gkGŸ\'_Ulm{__O¡K{hw¤Š_Ug¸pGjwlŠk?{hwo['^ '_shwlmg*­ !*AO/ ' E¥

`O;BƂ DMK;O<F= ;O;m„K¥tˆq„m„O;K­

Íwˆ=?Й†RuRjw¤mpGhwg¯z!hik?g*­¯ÁÂgyo_U{¤mpGjJpG{hwo['^W_UohinOMÑpGg¯_8.nUhi_UgRo.hw^™~'ji_U^W_UgRopGohik?g pGg#¯pGg1pG~'~'jwhº¡

nqpGohik?g5ok¸nk?^™~'r'opGohik?g7pGj—lŠ_k?^W_Uo{uŠ­ªÁg O O H %IO 1 - %

!%0 . 70F / " *A1 %º¥K~7pGlŠ_sJ„m„ˆmˆq‡K¥*ˆq„m„m„K­

ÍwˆqΒР@0­KzŽ­#z!{_U~7pG{pGopWpGg#+5¸­KÁN­#†R[7pG^Wkmsq­ *AO/ ' <O O% /0 70 !+1 "' ­

†R~'{hwg'lŠ_U{é¡ _U{jEpGl#¥‚G{±_Khwohik?g*¥$¶µnUok?v_U{aˆq„m„m‡K­

Íwˆ<’Й†Ro_OŸÆpGg †=n['hw{{pK­}Jk?v'r#sog#_ss£pGg#¹~'{_nUhishik?gªhissr#_sÑhwg¹lŠ_k?^W_Uo{hin·nk?^™~'r'opGohik?g*­

Ág ?{l?¡}#KhwlŠ_U{"†Kp?nE´pGg#yk?{lŠ_J{{r'ohEpK¥_Khwok?{sq¥ " *A/!' <O %

õ½ûŽôtõ

(16)

/0 0?¥$n[7pG~'o_U{Wˆ=#¥~7pGlŠ_s:Îm„ <m‚m`K­PÛ!jis_U¤Rhi_U{—†=nUhi_Ug#n_Cz!r'v'jwhis[#_U{s f­‰­ >µk?{o[K¡

GJk?jwjEpGg#P¥ J^Wso_U{#pG^…¥7`m‡m‡m‡K­

Íwˆ ¾ÐgRok?hwg#_ µhwlmg#_U{k?g*­ jwlŠk?{hwo['^W_s²eUjieU^W_UgyopGhw{_s£~$k?r'{ž{_U~$k?{o_U{žji_sžhwgyo_U{s_nUohik?g#s

k?vK|é_Uosnk?r'{v$_sq­}µpG~'~k?{o'_ >µÛ ¹pGjwlŠk?{hwo['^™hixRr#_m¥7zƒpG{hisq¥)@'{pGg#n_m¥ ˆq„m„m„K­

Íwˆ;’Ð Ù ­»pG~*­»Z kqœ\pG{'sµ_OÃ#p?nUolŠ_k?^W_Uo{hinnk?^™~'r'opGohik?g*­ *A/!' / O70 H %E¥

Béˆ DMς=`m‚K¥*ˆq„m„ =­

Íwˆq„’Ð Ù ­)I™­»pG~*­À}Jk?v'r#solŠ_k?^W_Uo{hin‰nk?^™~'r'opGohik?g*­Ág yp?nk?vÑÛ­cfk=kRK^.pGg£pGg# Škms_U~'[

¶}k?r'{EŠ_m¥!_Khwok?{sq¥ " " *A/!' < %O/ 70m¥!n[7pG~K¡

o_U{‚mÎK¥'~7pGlŠ_s<mÎm‚<O<O;K­

Ù } Ù

z{_ss

•*• Ù ¥ \kRnqpC}µpGok?g*¥@

•

¥*ˆq„m„ =­

ô ô&èONPQQQ

(17)

Unité de recherche INRIA Sophia Antipolis

2004, route des Lucioles - B.P. 93 - 06902 Sophia Antipolis Cedex (France)

Unité de recherche INRIA Lorraine : Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - B.P. 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 - 38330 Montbonnot St Martin (France)

Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - B.P. 105 - 78153 Le Chesnay Cedex (France)

Éditeur

INRIA - Domaine de Voluceau - Rocquencourt, B.P. 105 - 78153 Le Chesnay Cedex (France)

ISSN 0249-6399

Références

Documents relatifs

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 - 38330

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 - 38330

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 - 38330

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 - 38330

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 - 38330

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 - 38330

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 - 38330

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 - 38330