May 23, 2006 - Florence Le Ber, Ludmila Mangelinck, Amedeo Napoli. To cite this version: ... ThÑme 3 â Interaction homme-machine, images, donnÑes ...
Design and Comparison of Lattices of Topological Relations for Spatial Representation and Reasoning Florence Le Ber, Ludmila Mangelinck, Amedeo Napoli
To cite this version: Florence Le Ber, Ludmila Mangelinck, Amedeo Napoli. Design and Comparison of Lattices of Topological Relations for Spatial Representation and Reasoning. [Research Report] RR-4321, INRIA. 2001, pp.57.
HAL Id: inria-00072266 https://hal.inria.fr/inria-00072266 Submitted on 23 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 destin´ee au d´epˆot et `a la diffusion de documents scientifiques de niveau recherche, publi´es ou non, ´emanant des ´etablissements d’enseignement et de recherche fran¸cais ou ´etrangers, des laboratoires publics ou priv´es.
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Design and comparison of lattices of topological relations for spatial representation and reasoning Florence Le Ber — Ludmila Mangelinck — Amedeo Napoli
N° 4321 Novembre 2001
N 0249-6399
ISRN INRIA/RR--4321--FR+ENG
THÈME 3
apport de recherche
!"#$% &' ($ ) !# * +%* !# ), - !# . # * /1032547698:;6=6@?A6;4CB9DEjz
v
Po;ig>|_!ik_7lu[]_7iklu[]_eW;a9*bd>o+;_(^-]ih_z;]b;
vjzy;_7{ qnp#gh[7(gk+ot]
Wtottx oty;Z,nxl7[vjznx{¢ihik_7_(
Pj+o;ghinxotgeP
]{,ih_v{jt_7{he9_7gk|{jto;e eotgkik[]nxyt_ nxevvjz{h_9jzoz
]£¤
]ikj+o;ghj;ghnlul[ _7{gho1oz£{h
vihjz_7ghxjznjzgh9nxotihev_7{7
]¥$ih_Z,{_7[ve9nx{1gkj+jzgk
]npo;
]eiko;jzj;evlu|[qik[v_7j;j;{{>o;We]_(nxe]_7ey ¡|]_(t_7po;
P_|-£¦oti${h
vjzghnjz]ik_7j;{o;e]npevy nxesgk[]_|o;^`jtnpesot£"jzytiknl]pgh]iujzjzeP|]{hl7jz
W_>jzevjtp§{hnx{7¥Z,[]_>ik_(
Wotihg gk|]jtotih_7
W_X{klotnpike9xnpotghWy;ik_7onx{ l7|jzv¨vzl(iuik_7{_(g-|¢j+¥ghgk[]Z,npo;_*[]ev_$^`{(¥#luoz[v¬]ghoto;nx+n]lj+i_7gk{|npo;^snpe©5jt_(ozik|_(£_Xe9gk£¦g#[]oti_*j+{gh
]
Pghihnj+l_gh_{n{_7jze99otg-ik£_(ghik
]ot_7ik
W{h_7_7ot{hjzx_(otiue9luy;gk[ nxjzl7ghjz¡ nx;ototihe ik_7ª'xjtjzevghjt|nxevotik|)ev_7{7jtghw7[v{hnxotev_evl(y;nppe]v_(y|]e]np_7e]ikyn¯jtgkE[ ®!£¦ghjziu[vjzxot_7^`n{h{"_X_ ¡ j+j+otghgghikgknª«nxll(__7ot{({ £ w jnxt^`ih_
]x|_(n^`{hl(_(ve9{kgk{jz_gh|¢nxotw¤egho;ozyt£_(otgh[]ev_7_ i ot¡£gknpgh[][°_j@j+gghgk[]nxl(o;_7ih{o;]ytnp[±gh[v{npe=gkvjt|e§©o;jtev|±_7lglrLotv^`jt
v{h_7jt|ihnih{h_7ot
]e²ik_7ot{h£_(e9gh[vgkjz_ghnx£¦oto;¡ e]i`{h§xjz{gkg_(gk^nxl(_7wv{7j;¥±{ Z,[]_7p_ j;{X{h
vj+gknxjtvj+ghghnl_rLvj;{_|-ik_7j;{o;e]nxe]y ¡ n¯gk[s¡ gho;
Po;po;ytnl(jt]ih_7xjzghnxotev{Enpesgk[]n{${h§{gk_(^³jzik_gh[]_7eq|_(gkjznx¡ x_7|¢¥ ´¶l(otµ9^`·5
]¸k¹ guºj+gk+np»#o;te" wikj;Z{otgk
W_(i,otxnxot^`y;jtnxl7ytjz_v{(ikw_(o;j+gk_7npo;levgrL{7vw;jtj+{h_7ghgh|qnlih__7rL
]vihj;_{{__7|qe9gklj+gkjtnp{ko;{hen¯¨P{hl7§j+{gkgknpo;_(^se"w}{ ®!jtpo;nx{lo;e]e]_lmghnxotew9ik_(j+gknpo;e
¼EĽ]žÆÇ¿ÈJÉÀÂÁ@Ê+Ë+À¦Ã#ÌuËC¿"ÍÀÂÎÁ ÉXÏ+ÌuÐ"ÑÒ À¦Ã#¿"Á ÉfÓÑÔÌ ¿ ÎÕmÖØ×mË ½ ×mÐÙÐ3ÌuÖØËÉ Ú ½]¾¿ÀÂÁ'Û¢Ã#¿Ü
Unité de recherche INRIA Lorraine LORIA, Technopôle de Nancy-Brabois, Campus scientifique,
* *u( (%* # ( ! * ' * 'q , - !# ( * > " _( |]g _ pih_¶_7xiujzjzghnnx {hototeve]{e] gh_7ot_`^`
Wiu_(otjze9x
]otg`y;
W{hnot9
vih]jzg _ghn
v{!jzih_~g-{9_7vj=e;jzgk~x_-npghgk~vj+gke]|n¯_s£~(¥ ;jz_(
]x ot
]_
]ikgo
Wgklu_=~([]_ _ jz =
]o;
v|]ihihnx_7yto{nxluev[]¨Pjt_¶evp_-{ {
P|jto;_q
]]
]ihi]_nxlx_¶jotev{ikev]_(
]jziqnik{h~7{k {hjz_(ghePe9nxlxgknx_sjz{kj+gh| nxgkotnp oto;e@ike±y;|]jz|_Aev_nx{k_7gkj+ih{hgk_7
vnpnpo;jtxxevl(nx_{{ {h|]
v_!jzl(gh_ njzghx_7iujC{C|jt_,np5
v_(jCg,§x{h_jtytl(_j;{||]ih_1jtevgh[v{~(p_otik|n ;o;v^s_ jz|nxe]__{,jtihyt_7xikjzotghe]nxoto;ev^`{$n9gkot]
W_;ot¥ x "ot_,ytn iu9jz]
]_7
W{ot|]ihjtgev|]{,~7lp_!ik9npg]| _(¢ jze]Wo;otviu|-{e]xj1otP^`{,oz
]ghnxx+j#j+"gko;npevo;{(e ¥ ototvv{{
]|]iknx{k~7l{h_(e9gkotgho;evev{,{$_(9gvlj+o;gk^Aih_
Pgkjzihik_7otnpxevxnx{{x|_7_E{ikl(_(jt
vj+jtghnxl(otn¯gkeP~7{5{gho;|
P_o;l(p_7o;{,ytngk;ihv_7np_7x{7pnw{,|_(o;ee9g^s|j+_(gk&np\7%!ih{h_ot|e9_!g|ik_(_
]{"ikgk~7ih{h_7_(npxe9pngu{j+|]ghnx_$ote®!jz_gxot|n{(_ ¥ iu
Wjzotnv{hotiXe]je]_7l^`jt_({ke9{npg7¨P¥l(¬jzghnxevnxotjtesp_7|^A__7{e9ghg7ikwvvevlghot]vik{>_7{$|]~7{l
vikjznxtghnotjzePx_7{{E|v nx^Ajzev
v{¤xjtx_1e;gul7j+jtgk|npo;ik_>e*| _( g]eq {hgk§np{xngk{h\(jz^`ghnx_>ote=|_| ik ]_(
ve=ih~|{_ _7e;l(_7guj+{,gkgknpiho;_7eAnpx|xnx_{ l(ote]ePjzn{h{kjzevl(_7{$
vjzio;_gu{(¥ '®!jtº po;nx {7¸ w l(( jt x¶l(] |_!_(ik_(j+gkj+npgho;nxevot{eP{(ghwotnx
W^sotjzxotyty;_n{9]ikj;_{{(gkwW_(l]ijtw}{k{ihnp_7¨P
]l7ihj+~gh{nx_7ote9e)gkj+ qgknp
vo;jzeihgh|nx_ i1l(|]ot_ e]ghePikjz_(nnx{hxp{knjz{(evw l( _7o;{$ih
vik_7jz{hi
Po;o;ev|]_jtgu{evl_ |_
a
5 -s*E# gk_7Z,[]e}[v_9_>nxikik{_(otgkote]vik^`|y;§Ajt_(e]e9ozn!g£57jw;+x|jtgk_7evnpo;
P|Ae _7vevoz{|£_nxe]£Ùnxjt{Ey-ihjz^`o;gEe
]jzluevik[v_7|¢jz{hw}_(evgke9yt[]gE_7_{Xoz£Wgkozik¨v£¢jtiugkev{[]{gE_1£¦o;nx^`jtihyt^s
Piko;jznxl(ghi]gunxot¯jzgkevev]{l(ik__tozwt£npe _;jz¥ jtyPevyt¥|]ik_({kote]l(e]jto;jz
P^Aik_ytn_7jtl(^A{7evwC|_7npe9esghgX[]o;oz_ ik£¢|]jt£Ù_(¯jtigkih_(gh^ iuoj+gk_(vnpe9evo;ghev|_7_({ihiu
voz{ih£gknjz{gheP_[]{(| _ w ^`ot£o;|Pnp¨Pjzl(xn¯jzgughj+nxghotnxe¶t_ otjt£Xevjz| ytik9nlv]jzpe9gh]gkn¯iugujzj+ghnx
]tiu_ jtlm9gk]nxl(__7{#{gknpo;"Jlevik{ ot
]ik_(
vy9npe]jzyiu|
]nxe]jzyqevgk{7[]wP_q_(gknxlte9¥ gh$_7¥1ih
]Z,ik[]_ngu{1j+gk{npgho;Pe'|§ot£p_
]jtih|]_{{_7ghe9o*g jsjzeve}|)]^
vWj;_({ig
vjzikePj;|Nlmghnvl{h__t{w¤otgke²[]_gh[]
v_*ih_{|gknxihlvghlnxotgh]e²ik_ot£ot£>jzevxjt|Nev|)P{v_*{h_tnpe©wghgh[v[]__*le]o;_evjz|i npgh£¦nx]otghev]{ ik_tghw¤[vjzgk[]g-_[vjCnp e ;%v_`]gh_(o«ePlP_7_q{-£¦oz]£¯¨Pghp[]x_7_|)jzy;gko@ihnlik]_7pj;ghluv[)ikjtj gk|][]_7_{hnp( ike]_7l_|ghjzvijtjz£¦pevx§t|vghw#v{hl7ihgh_jz[v
W_7ot{h_t£#_wW_jz9gkev]lt|_7¥'{vgh&¶nx{hot_ o;ePihjz{ _7evo+jz|*tik_(_sjziy;wxnpihnpe]ng!lª;vl(_7ot¯|'gk]]gkih|ot_ ytPot_(_-egh[]
Pgh_7o9[vi {h_{hnxeNnxv]jtpgh_ {h[vnx{,_qgho otjz£vy;gkevih[]o;|_e]_(otiu
]{^`ikgk_7jzn{hl(eP_({!|*e9ikggh_7[]ot{h_7_Avjz{h
]iu_(luikik[]_7+{h_j+_({gke9npo;jzg1evW{{(otgk¥ j+g`gk_ jzjzytePiknp| r +ikl(_7]jzj;ghpgh{nxot]o;eviuevjz{!{ o;xe«jt[}ev§!^s|]x{kjtjzl(ev
Pjz|]{(
Ww{k_ l(jtjtjz_(
PikePnx_jzjtxjz¤§}ev
]{hjtn[]{(p§otwgh{hgkotnx[v{y;j+nxikg {#jtoz
]nx{1£][v^sl({ jtjtjzihnpevike np|)_nx|*^`{kj+ot
Pgkeo;_(ixghpgunp[vjzgh_ _`evl(vnx_X^`jtnx{hjte n{>ytgk_oz[]{(£_¥s¨vjtZ,_7ytx[]ik|otn{!e]nxe o;nx{!9^`]o;nxnxl7e]ih{¢nx_s_7ih{1oz_{£$jz_evghjz[]|¶iu_`lu{h[]
v£¦_7vjz{"evghe]n|]jzo jz"^`o;j;_7v|]e;{jCgu_7§jzi{r ¡ ¡ ) * _5ote9gkjtnpe]_{!,+.-/10L¥#¬votigh[Pj+g¤
]]ik
Po9{_;wCgh[]_>jtytikote]o;^`nxl7{"ik_7{h_7jziulu[]_7ik{jzik_$
vjtigknxl(]jzikp§!nxe;gk_(ik_7{gh_| nx_7e=e}9gknx[]ik_`ote]ih^`_7x_(jze9ghnxgot¥±ev{hZ,[][]nx
=_7§NW_ghg ik¡ §N_(gk_(o)e'|]jznx{kevl|]o+{k;l(_(jti`
P_Ajzevjz|&ev|@£¦ot£Ùikjz^sik^`jzxnpn ev7_y{hjz§}eP{|]gh_7{h^sl7jz{
Wjt_ev
v|¶j+ghgkgh[]_(_(iknxevi {-lo;gh[Pevj+{h_gq9jz]ik_(_*ePl
v_7jz{1ihghotne@l]gh[]jz_i gkgk{ghp[v_7ikj+^`vg#l_(ghghe9[v]g7_,ikw_7{£Ù{ghjtikozihv^`£¤lxghnxjte]]evysik|¶_X{ot§v£v{{hghx_tjt_7w 2^ev¡ | $ []P)n* {lu_[=_5ihjz_7otikte9_ _gkjzxjtnpe]np{"e]ª;gk__7[]{!|*_ , gk+.o+tot}ik{hª}
Pw np_3evly_(npev¨Pozol £v4ghg!l([]ot1 _$^ +£Ù+;vjz1 npikev03^`¥ jznpgh( e]nxotyty!evik{hot{>§}e]oz{o;gh£¤^A_7£Ù^jtnl(l¥ {gho; ikikjt_7{#{hev_7|]"Jjt{{ko;ikl(lunpjt3[]wW
P_7ih_$ik_7{
vpnxjtj+_{kgh£{hghw5]_({ik^`_(evg_{r _%npnxgh{[g ikjz_(g y9jz{h_(iut|s_7ghikoAjtgk{k[]l(_jzx_(_7e}{1}jznpikevot|@ev^Ajzik_7_ e9g7t¥ _7ih§v{_(£¦]¡ #£¦oti1ytxotvjt|njzy;e]o;{h_7{>jtev|£¦o;ih_l(jt{gk{ote=jtytiknxl(]¯gk]ik_ ¡ jzev|}rLv{h_>^sjz
v{Xvjt{h_7|Ao;e {hjzgh_(xxn¯gk_>np^sjtyt_7{Xjzik_>t_7ih§-v{_(£¦]]£¦o;iXjzev|v{hl7jz
W_jzevjtp§{hnx{7¥ 5o ¡ _7t_7i WW_7_,l7^`jzvot{hik__ot7_ £"6 ghl[vnx__(e99gEv{jtve9lugh[Anpg
]§`ikjtoevl_7|s{k{h£¦iknpe]_y19]^ _7evvl{g¤§`npoteP£"lxghv[]|__,{_gh[v|]_jzgk_jv%w9
Pjt_7eigkjznx{h]_,ghozot£v^sgkjz[]gh_nlik_7
]{hik_7ojzliu_lu{h[]{h_7npevik{y jznxW{ote]_7g_7|£Ùjz_ik|¢^`¥¤npZevoy {h{h§§{{gkgk_(_(^s^ {Xgh[Pjtevj+g|slotjzevv|qx|sv[v{h_(_tx¥
qZ,jz[9y;Piho;{(e]w}otnpg$^`n{n{¡gu{otghihoAgh[ _ ¡ %[]
]nxxxot_npg$gho-jzvev{|_ r3v( {hc¤_^`^s_jtgk
v[]{Eo£¦|]o;{$iXgho-jzev]|v]{hnxl7x|jz
Wj_1ª}jze]ePo jz¡ x§}p_{hn|{(yt¥_(Z,r3P[]jt_({hik_7_| r £¦l(o;xj;ih_;{h{hw¢np£¦gh§9[vnx_se]9y xjtev81|] :{kl(
jz
W_ _`%}gk
vikj+j;ghlmghgh_7_ih|Nev{ote²|]_gh¨v[]e]_*_|'^s9jz§=
v{ gh[]) _ #_ jt3ytik_(oti>e]jzo;eP^A;| nl(&={1jtik_7e]{hyt_7_7jzpiunxevlu[]luª¶_7ik1{1+[v+jC-1t0L=¥ _AW[ j;(o|];jze]
_gk_7l(|@otik£¦ihot_(i r }W{h
Wnx_(potEjzev|]y;|]_(_t{se]¥ otghgh(o©nxe]j@(oyqt?gkev}[]_ np_`xxnxjt{ xjtyt^sev_*|}jtghrL|_7vih_{hik_-npozghl(£otjzikikgh§.j;_7A {ytgkot¡ _(iki []§tnikw5lu_(_;[°y;¥ yPnpo;n¥ { evl{7{ikwvot
]n3
v¥
P_;{7¥@o9w¢{^`l_o;|±_7e]j;ghe]|oN_o lmWgh__@{(|NwW_£¦{o;%}_(ih
vgk_p{-{o;gn¯ozgkw¢£_79|±
]nxxn x}%jt§²_(yt_t{ ghw5[v¡ _(_=gknplzgh£Ù[N¥AjzikZ,gk^`[][]_(__`iu{`{kjtjz|]oz^`jt£!_
ghgh[v_j+nx| {r _7jze9ePgh|]npgh{hnxl7_7jz{
Wjz_1eP|*
Pj+j`ggk{h_(_ikg>ev{7otw]£l(9jzvxxjz_7x|@npgkj+!gknp :;B_ 7{
v jz DghnjzC2¢,ikB._(
j+E ugkwPnpo;jzevik_ {P|_(_g{hl(ih_7nx_(¡We*_7| gh[]¡ _np{gh_![¶_7j-e;gkpn¯ngk{npg>_{(oz¥ £jtytiknxl(]¯gk]iujz¢{
Pj+ghnjz ¡ lmghr3Pjt{h_7|«ª9evo ¡ p_|yt_Aih_7
]ik_7{h_(e9gkjzghnxote«{h§{r v ¬ h i ; o ^ z j ' e x n A ^ v
p 7 _ A ^ 7 _ 9 e k g + j k g p n ; o ) e P
; o p n 9 e g z o , £ } p n _ w z j ' e t o ] 7 _ ¡ gk1_(jz^
Ww,otxotHn i*
IGF!J( 1 +{h+t§} {03gh¥¤_7cf^eP|w_(_!_9|¢]w]np
v_ %
P
]_x| otnp¡ghnxe]n¯gky`[ jzl(xevj;|}{hrL{hvnp¨P{h_l(jz^sghnxotjze±
v{^A£¦o;_(igh[]xjtoev|]|]{q{kl([vjzjt
W{`_Wjz_(ev_7jte°p§v{h{hnx{,_7| ^sjC) 1§ jzW
W_ otxlnEo;,ev+.{h+;nx|}9r w _7jtihev_|K|)(ojtt{ ev_7jt{eNlnpo;evih{ikgk_7jt{hev
Wlot_ev|@ljtgh{ko{npnx¨Pevl({jzgughjznxevotl(e'_7{!
]ikgkot[v]j+xg _(^[PjCw t¡ _-[]gh_(o¶ik_sW_ xjtlev|]jt{k{kl({npjt¨v
P_7_ |'^`jtl7ol|o;_7ikx|{ nxe]l(otyikihgh_o¶{
WjzoteveP|v|={hl7gkjzo@
Wl_Ajt^`{k{o_|}{(r w _7nx^`x{7
]¥¤x¬]§9o;nxe]i>ys{o;gkp[v}j+nxg1e]y-ª9ev{hvo lu[p_jA|ytl(_!xj;ot{he¶{hnp¨Pjtl(ytjzikghnxnxl(ot]e ¯gk
]]ikiuotjzv¢p_(_7e9^*gkn¯w}gknpgk_[]{_!jzxePjt|ev|]ot{ke¶l(jt{
P
P_ j+gh^`njzo}|]ih_(_7x{,jzgh[vnxjCottev_1{gh^-o`vW{_ gikP_(_
vih_(_ev{l(_7o}e;|]gk_7_7|¢|¢¥w ¡ 3_{n|_7{7w9^A_(gh[]o|]{£¦o;i$_%}ghiujtlmgknpevy ik_(ytnxoteP{¤£¦ikot^³gh[v_1jzev|r3v{h_^sjt
v{,jzev|`£¦o;ilu[]_7luª}nxe]y-{h
vj+gknxjtPik_r
¿¿ ËL M NPO1Q
' 7 . 7E : DE
j;j+{Xgknpj o;evv{Ejt{ho;nxe`{X£¦ghot[]i_{j _1l(ihx_7j;yt{h{hnxotn¯¨Wevl({Ej+[vgknpjCo;tes_
]Wik_(o}_7l(eq_7{k|{(_w ¨Pe][]_7o;| {h_) &=y;jto;e]jtyt]_7nx{$pnxevgko-luªKlo; 7^`
vjzJ7ik,_,++.gh[]/ _ 0L¥ikZ,_(yt[vnx_7ot{heP_>{X^`jzeP_gh|`[vgho}[]|v_1{$ihjt_7ihx_>jzghPnxot{_ev| { _gk[]%}_ghiujtjzlmevgk|]_7|A{kl(£¦jtik
Pot_!^ ^`j o|jz_(eP|}{7r3¥ P{_>^sjt
q]ev|]_(i,¡ {gkv|§Agho gh[]_ _(e9ghnpghnx_7{jzeP|`gh[]_ ik_(j+ghnxoteP{Xjt{k{ho}l(nxjzgh_| ¡ npgh[ gkik[]_(
v_(§ihcf_e-{jz_7otike;_]guigkj+[]jzgk_
]npo;
v^`e@pno;l(oz{jz£$gghghnxluoto;[Pe"
Pjzo;wiughpjto;[vlmyt_gkn_(l(l(ikjzxj;nx{{hghik{hn_(n¯l>¨Wj+_7l(gkpj+_7npgko;^`npevo;_({!ee9P
]gk{,_iko}l(otjtl(£v_7gh{k{[v{"_A_ngk{x[]^sjt_(ev§'jt|]npe]{kl(l(jzx§jze'
Wv_ Wj;_ ^A{_|o|_7|ot{k_7lexik{7gknp ¥ W[] '_7_,|'{_
vjz[PjzePghjC|«ntjz_1;^sih£¦jto}_7e]xl(jzvnpgh
v{hnx]_7ot|*xevjz{7ghotw+_e{|@nxevgho;[]le __ gkik[]_(
v_qih_P{jt_7{he;nx{-guj+ozgk£npo;j e¡{h§}_({xgh,_7|^ _¨vozev£_7gh|)[]_!gk[]gk_(oto;
Wihot_(xghotny;l(nxjzl7Xjz£¦5ikihjt_7^`xjz_ gh¡ nxototevik{ªWgk¥«[vj+g_( x§}npe]y@oteNgk[]nx{-£¦iujz^`_ ¡ otikª5w ¡ _ e]_7_7|²j |_¨Pe]_7{
]ihnx^`n¯gknp;_7{,gkoqlo;^`
]gh_ ih_7xjzghnxotev{o;eikj;{gk_(i>nx^sjzyt_{ Eghoql(ot^`
]gk_ 9o;i,ghoqlu[]_luª j ih_7xjzghnxote W_g ¡ _(_(e*g ¡ o`ih_7ytnxotev{ @jzeP| ^`_jzev{gko`gh_7{g>np£ []o;x|]{7¥ npe9gk_(ytiuj+gk_7{,jzx¢gk[]_ih_7xjzghnxotev{v{h_7|*nxeqgk[]_jzev|]{kl(jt
P_!^`o|_({7w jzxpo ¡ {$gko {gkotik_ ev_ ¡ nxe£¦o;ih^sj+gknpo;e"w jzxpo ¡ {"ih_jt{hote]nxe]y,oteik_(j+gknpo;ev{¢jzev|l(ot^`
Wo;{hn¯gknpo;eoz£}ih_7xjzghnxotev!{ 5gho>ik_7j;{o;e1o;eih_7xjzghnxotev{5^`_jzev{ gho |_|vl(_ ev_ ¡ ih_7xjzghnxotev{$£¦ikot^%jtpik_7j;|§ lo;^`
]gh_|qo;e]_7{7¥ l(jte@W_A^sjtevjzy;_7|=}§=jte)G F{h§{gk_(^w"jzeP|=gk[9P{(w5gk[]_sjz
]
]xnl(j+gknpo;e@^-v{gW_`po ¡ rf{!n (_|¶nxe gh_7ih^s{ot£^`_(^`otik§q{h
vjtl(_t¥ ( Pnxe jt{h) _7>| l7jtlevotot|e iu_7|pjNnxe]jty-xjzevghg| oAgknxl(gh_'[]ot_[]{{e'gh_!ikv,e]+.lm_7gk+;_7],|]ik0{7_tw gh#¥ oN¡ _ "}|P[PiujlujC[ t_!j²nx|e_7£¦ik_(_({hiknp
]y;_(ikePe]_7l_7{h_7|*_({Ae9jAguo;j+ihe&gh_7nx
]otike ik_(_7j+{h[v_(gkj;npe9o;{ gkevjzW{(gh¥$_(nxot_7e e «ot_jz£xikgh[v_7[vjCjt_!;|]_gh§©otv
Wv]ot{hnpx_7potgs| y;£¦nxot£¦l7o;jzviqWiAih__7%j+xghjzjtghgh^`nnxlot
]_evp{(_{ w nxj;ev{hl({hpovl|]nj+npe]gknpye]yg ¡ {ho¶_gk{ j+gozgk£$nxl(o;_7{_7Pljtgk{h{ _7|'"¦gh[]ot_e) &gk%.[] _q¡ 7 ®! `jzxozot£Xn{ gk[]lo;_qe]l(e]ot_evlml(ghnx_(ot
eguw"{ $gh[Pgho=j+g {h_n{ gu{voz{h_7£,|«j+ghgkgho=iknpl]ik]_7ghj+_7gk{ _ "Â gh[v :@_ :
m w } § $ ) * gko;3,[ve`j+jzghgik[]][v_1jCg>np;^s_EjzjtePghyto1|;_tP¥&¶_,Z,o;ik[]e+_7_l(jzot|]iuyt|n¯ev5_(n _(g!7_ik7_(1|!e9+9gXotze-}j+w jzghe ghnjClnxt^s_7_({$jz§[vy;jCjz_$;evl(_|jtPe E_7Wik_(np_e _{j;_7gk{hCp{h_7jto§@plPn,j+j++.ghgk+t__7|s}| w'ghjz °o ev|`
]npxikpnxot_s^`
W1
]_(+xih_(+9gh^`nx,_703_({¥,e9ghcfgh[ve_jz|sggh[vnxl7e`nxjz{ e-gh¡ []P_jC_,§;£¦ikw]ljto;ih^A_7^Axjz_
vghnxoto;gh_evih|ª { ot£o;Z,]i>[]_ jz
]
vo;pihnl(ª*jzgh
]nxikot_7e"{h¥_(e9gh_|[]_(ik_-{h[]o {1{_7t_(iujze]_ jtev|¶otiknxytnxevjzj;{
W_7lgk{npe@gh[]_-^`jtevjzy;_(^`_(¡e9got£ {ikh
v_(
vjzihgh_njz{#_7e;ih¡gu_7j+xjzgkghnpo;nxoteAevjt{7evwP|Aik_(ihy9_jzjtiu{h|otnxe]e]nxyse]y!ih_7
]
]]ikik_7¡
P{h_(o9e9{gk_jz{(ghwtnxghot[]e"_>wWghih[]__7jt¡ ot{hotik§ e]nxoze]£"y ®!jtjzevx|=otn{¤nx^`j+
]ghpgh_7n^`l_7_({Ee9[vgkjtjz{XghnxPote@_7_(j;es{_(
W^`_7l
]gkx{7o+¥!§t_¬v| oti1ghnp[]gh[ _ {gkhotv
Wl7lot_7xot{k{y;nxjtl7evjz|ik[v_(j;j+{gknpjzo;xevxo {7¡ w5_|]|q_(
Wgk_(oqev]|vnxe]npy|=ot|e@npWgh_7[]ih_ _7e9g1jC§j+ggkgk[]nxl(_`_7{Po;
]]iho+ev}|]njt|ihnx§e]yqot£$|npjqW_7iuihjt_7{e9gh_7gi1
Piko;_(npy;e9npguo;{e=otn£E{ 9l(nxot_ ev¡ {hno;|e¶_(¡ ikgh_7[]|¢_ ¥ ¡ &=otik_(o+t_7i7w}npgn{>otev_oz£gh[]_ ]e]n ;v_ ¡ o;ihª{,ik_(x§}npe]yso;egh[]_A®!jzxotn{xjzggknxl(_!gh[]_7otik§tw]gk[vj+g1nx{P{vjtpx§ j;) ® {h{hoo|lnxnej+gkjt_7ev| | ¡ &¶npghnx[){k{k£¦jzo;otihv^sn¤jt, E+l+toteP(w l"}_(np
]^`g o;jze*evjtjtevp§|{hnx{ jz) °
Wotnpxxn¤x_s, +., +++1+90L, ¥ 03w#¬#otnpi!ePjz£¦xo;pi§;w5ª}l(e]xj;o ¡{h{hpnp_¨P|l(ytjz_sghnxot|en{krLlvo+jtt{h_7_7ih|§¶ik
v_7j;]{iho;
We]o;nx{he]_7y { nW{EozPgk[°{_|`l£¦jtot{ki{npnp¨Pe]l(£¦jz_(ghiknxihotnxe]e&y oz{h£1
vj+_7e9gknxghjtnpghvnxik_7_({sj+jzgkePnpo;|&ev{Eik_(jzePj+gk| npo;{ev
P{7j+¥ ghnjz( We]{gkozihgkP[]lm_(ghisvihe]_ot{Eghnozl£_jtjzyt]ikx_¶nxl(]jtp{hgh
P]_iulmjzgs]_7nx{Ae9ghgknp[vghnxj+_7gs{7w;gknx[]e}nt{ otx}o;npevihªy jPtp{x_!o ¡ ^s{jzj
v{79wvWjt_7pnpl(gkjtjzvgh{hnxt__1gk[]j;_ { ¡ lu[]_7o;p¢{h_(jte{,jnp^`9
]vxjz_(e9^`gh_7npgke;jzgughj+nxgktnp_ o;eqjz
]£¦
]iujzik^`o;j;_ lu[`otghikoAª5w;gh[vn3¥ _ _t¥$jtGevjzFx§ {n{X{h§ot{£gk_(jz^sev{7|vw{h
]l7ihjzo+
W}_n|ot_7e{x¡ Wjtozevgk|}[ r ik_7j;{o;e]nxe]yqjzeP|«l(ot^`
]guj+ghnxote@£Ùjtl(npxn¯gknp_{(¥AZ,[]n{lote9gkikj;{gu{ ¡ ¡ npgh['_ %n{gknpe]y ¡ otikª}{1nxe@gk[]_s|ot^sjznxe@ot£ À¦Ã#¿"ÀÂÁ
;o9{h
ve]vjzxjt§tghp¥nnpgkjzjzcfvevgh_7nx|e9t_7gh_ _7npgh|¢{hnx
v_7w5{,j+o;gk]jznxevjti1E|s{h§ikgh_7{[]jtgk_7_({hnp^otiev9nple]votyPjz^-xw n¯]gu¡ j+nxe][]gknp_7n;lu{1_>[){ih§}^s_7^ xjzjzWnxghe]nxototpx§«evnl {$£¦ojzjzevlevv|| { e}
]ot]iheNo+^`}ik_7n_7|ihj;n_7l({{Ejto;"ihe]_ghnp{ev_]luy*p[]gkjte]{XPn gh9o;[P]j+_7gg{>jt9£¦ihotv_1ijzx_7iknpj;gk_7j+{j;§-gk{npo;;ghe]o-_snxe]ihih_y_7jtxjzjz|sghWnxjzototePev| g{ vy;_(evo;|yt_(iuiujz{
]gkjz[]ePnl>| nx£¦eo;£¦i,o;ihjt^sytikj+otgke]npo;o;e*^`{hnx§{gk{{7gk¥#_(^sZ,{7[v¥ nx{,ik_7{h_7jtiklu[ ¡ otikª l(jteW_evjzgh]iujzxp§s_%}gh_(eP|_7|qgho`gk[]_|_7{hnpy;eot£ l(j+otghe9ghghZ,nl_[]_%}{-ng { otozjt£>£ighgkoto;nx]l(
Ppi _o;po;|yto;_7n{kihl(ª©ljtik$nxjtPevik__(|°{`j+ot|gk]np_o;i{hevl(¡{(ihnx¥NotPik_cLªN{`gsotghn{`[ve&_@{ghgk[]{ih
Pv_=j+lghgh|]n_(jzik¨v>_7e]|&ghnp[]ghjtnx_7ot{-ote°ik£¦npot_jzx{sePxo |²ot¡ e gk{ [] s_¶gk[][]lnluot_*[°^`¨v
vnpiugq{jtg`ihnxn{
v{hotjzve©ihjtg`{hot_7np£|e9ghggkik[]ho_=[]|_'v|l(np{W_7__7{-liho;gh_7ev[]e;| _g
Pjtevjzih|°gE£¦
]o;ih]_ih{gh_7[ e9gk{¤
Pjzo;ih]gk¡ iE{*
]|ik_7ot{k
Wlo;ik{hnpWn¯gk_«npo;ghe []£¦_'o;iX+ljzo;iknp^`o;v
]{qgh
Wnxe]o;y{k{hgknpot]
Wnxxotn¯gkxnpot_y;{qnxl7gkjz[vj+ikg¶_([vj+ghjCnx;¡ot_@eP{Wot_(es_7e iujt_ {%gh_(
]i¤xotnxik^s_7|°jzy;£¦_7ot{izgh][v]_nxghx|][]npnxe]iu|y nx^`j+gh
]ghnxl_(_^`{$_(jte9evgk|qjzghj-nxotlesotot^`£W
vgkjt[]ih_>n{hikot_(esj+ozgknp£o;ghev[]{¤_jz{_ ev|Axjzgkg[]gknx_(l(nx_7iX{7P¥{Z,_[v£¦o;_>i¤¨]gh£Â[vgk[_1l
vjtjti{kg{hn¯
]¨Pikl7_7j+{hgk_(npe9o;gke-{ot{£¢o;{h^`
v_jzgh_(nxjz_(v^`{gh_7ike;vgulm{,gk]jzWik_7ot{7¥#gZ,gh[][]__ {hn %9_gkl[¶o;ev
vljzxihvg|y;_;np¥ ;_7{jte¶_(+jzxvjzghnxote=jzeP|¶{o;^A_
P_7ik{h
P_lmgknp;_7{>ot£¤gh[]_-
]ik_7{h_(e9g>ih_{_jziulu[ ¡ o;ihª5¥¬#npevjtpx§ ¡ ( ! gkcfe*[]_(gk^[]_ w][P{_jClmtgk_ npo;npeve {h¡
]nx_!ih_
]|*ih_ot{]_7ie9g,¡ ikot_7ik{hªW_7¥jtiklu[ ¡ o;ihª{$gh[vjzgjzik_!ih_7xjzgh_7|qgho`o;]i ¡ o;ihª jtev|gh[vjzg7w£¦o;i>{o;^`_ ot£
! #"$ %'&)(*" +, ! - &
h£¦{ o;_ihg ^sA-/.jz{$
evjzC2| ik_?evgh o;_(
Pnxyt o;[}po;Pyto;nihl([vjzo91xxo0§ | n_Am{9¥!]PZnxjt+o;{hjz
P_7x|¶o;_(pe9o;o;g$yte¶np§¶£gh[]o;l(jte]_e@_?ot£¦jzot
Wik{_(^ oe=Pl({h_s_jtgesA |_(Pev¨v_!oze]ghl_nxo;ot| e;e«gk¡ npjze}npevgh][«|=o;vgh|][]{h_p_A§-¨ve]e]gh_iuozjz{>gkevnpgko;{[]e@£¦_Aototike]^`£$ozl_7gko;|npo;e;ev"¦gkn3np{¥ e}_tot]¥ £npg?§ l(npgh p[o9g {¡ e]_|oo [gkvototikxv_1${7¥npe9Zghoto
Wghot[vxot_Ay;ot§ gh[]l(jt_7eqi! gk£¦[]ot_(i enpePW{_gujzvev{l(__t|wghjtose@lu[v_(y;jzyqiujtnl{ gh_7_ih9n!](_nxC£¦jtotpik_7^`e9g1{7¥gko*jvjzx¤]gn{ e]ozg!_9]nx+jzx_(¡ e9g1gko*j ogk;[]ihnx_A_(cfe9_(e gue9j+gh;ghnpPghnxotnxjz_7esx{7n¯gu¥ ikj+_(ghZ,nxj+t[]gk__Anpo;ihvev_7jt{7
]¥#{hihn_Zl {ot_7ot
We9e9otgkgkj+xototgkxy;npoto;nxytl7evnjzl({¤]jtotik£_(_7{e;j+
vgkgkj;npn¯go;l§¶_;evwt{Xngk{ jtotihyt
W_1_7ote]]xot_(npePytiujznjzl(xikpjt§A§vjtikj_(evih| j+_7gkytnxnpevnxo;ot|eve"_7{X¥
Pjt_7ihev_>_7|yto;_(nx
]e9ot
Wg,evo;{1oz{h£¢_7ihgk_7|A[]
]gh_1ikoA_7o;{h|ih_(nxne9_({g1gue9jzgu
Wevj+otghl(ihnx_1otghnxesjzotePevot| {£ ot) 2 £nx{_(
P)jt1l_++t|1a _0L¥gk_(ik^Anxe]_|N}§'l(otevl(ih_(gh_ o;_7lgk{7wEjzev|Njtih_ evozgAl(otev{hn|_(ik_7|Nj;{ {h_gk{-oz£{h
vjzghnjzX
Wotnxe9gk{ Wjte«_(y;j np ev%}e] 7nxot npev^s yjzghot1n£$l 0qzvnx+{,j;gk{[«j _-ghl(£¦[]_(ot_7e9i!otghik]gk§sotik
W§¶ozot£"jtxotgk{ []y;jz§_ e' jtjzevp P|«gh4_(36ikyt5ev_(.o;jzgh^`nx
t__ghihik_7gk§¶xoqjzghozgknx£$ot[]e"ih_A_7¥#{hytcL_nxgotg ev¡ gh{ [vj;_(iu{Xotj+nxikghe9§[vgh_(ik)i o} |]gh_7v[v{he]ljt_nxe«_ |q¡ ot}{h£X§ ª9
Wn¤ "ot1nx_+;e;{9guev{(snp¥_ 1¡ &¶+t{a]ª}_7 n5ih0L_7j+¥otg,xcLotg!ghyt[]nx§_{ |]jte9_¨vghnpe]rL{h_§}{^Agh[v^`_>_(ihgh_7ikxnxjzl ghjznxotev8e |7 gkikjt ev {np mghw;nxt£¦ot_i 9 % P ,0$:w ¡ [vnxlu[sn{Ej!
vjtigknxjtotiu|_(iE{hnpePl_npgXnx{Eih7_ %v_ %nxt_tw ; = ; B ; H
¿¿ ËL M NPO1Q
@
@
@A7
D7 !E?7 F ?G D7 !E?7 H FI7 H
' 7 . 7E : DE /
ik _(j+ "}gk np_7 o;t e@_7e=ik^`_(ih_7j+_7jtxgkjzevnpo;gh{Cnxe°ot9 ev% ^A{1_l( jzjteve¶{ :P9 _`% |
_ G¨PB e]_70 | P£¦ik ot8 ^%0$ :gh¥ P[v nxZ,{ [v
]@_ iknp ^`. Knpghnx 7 t _ C !ik 9ih_(_7j+ xjz gkghnpo;nx ote e« :"Ù^A¥{h_(__AZ,jzZev[]jt{C_']9 pih%K_X_7^s,$mjz¥! 7nxe] PZ,npev[]:y²_ B7ih0$_77:xjz¥q gh nxZ,ot []ev _{ ik_(
vih_{_7e;g,+jziknpo;v{,l(j;{_{,oz£gk[]_'?o+t_(ikjz
A1jtev| ?nxevlxv{hnpo;e A e]otghnxotev{7¥ 7 E 7 $H @A7 4H $H @A7 H !E 7 E 7 7 E 7 E 77
E?7 DH' E 7 H ?
)2 2 kgZ#[]jz_vpv_>{hv jz¢&¶xot_7y;ih_7nxl7otjzxot¢ytlno;l(e]jte]z_ik_(lmghj+nxtgh_nxot{(eP¥ {H"Ù{h_(_ np_7«1 ++ta}w jzi (n¤1 ++./10 $¥#Z,[]_{§}^-Po;x#{ E¶jzev| *ih_7
]ih_{_7e9g evnp£ozghgh[]nx ot_7e §jzik){hªt [v_xjzjtik[vih_ª;jt_-j`{-1x
Pjz+o;gh-vnp_7e9+iAgw ¥
v ih( xo;jt
Pih
Wª;o9ot_`{nx_e9,|'g>+-9nxgh{>o«, 03j ¥£¦ot7_Z ik(^`¡ ikozosjtrfp|ikn!(_nx_(^Aqytnx_7ghotev[]eP{h_{npo;«
vevjtjzjzi¢evghr{h| ¡
vj+[vgkotnxjzxjtik_ "_!ih_({k_7xjz_(xjz^`n|gh_(nxotghe9ose²gwvWPjt_ {l7nxlle]oto;y«iue]|e]ghnx[]_e]_2lmyAgh?_ghl(|osote]npgkev{_7^slm gk jznpo; ghe[ A r _7^sj+ghnl(jt¢^`_7jzevnpe]yP¥¤Z,[]_ xjtihª;_ {$gh[]_7otik§snx{>|]_¨ve]_|*9§ gh[]_!£¦o;pxo ¡ npevyAj %}nxot^s!{ ; * ; B ; B
@
@ F @ ; H @ DH' DH' F
CG
_7p§}nxe]yNote±gk[]_=lo;e]e]_7 l gh nxot 8e 9 % ik_( Dj+gh#nxotew P jz ik0$ªt_:7[vj;7 {s | _ ¨v ev _79|±% ¨v ;_*ik:_( j+ gknp 7o; 'ev {! PI ! 0$ : 9 % nxe9gh _7ih _ { gknp e]'yPjt_evl(| jzP={_E{h[vnpgjzik^s_-jtjªt _7
W{9 ot% j>nxe;|g @np¶WB_7jt ih 7ev_7 | ev 7l _$ P _( g ¡ C _7_( e 0$':j>¥Ojt
PevZ,o;| np[]e9=_g#{hjtgk[vev[]jt| _(iho;_Ajih§&ikjq_(y;vik_(npjto;y;{he"np_7o;w7|±e"gh[v¥o;jte&Z,e][]ªgk[]nx{¢{!_7gh{ho|_¶npgh5[]ik_(_(_$ik_(j+ihe9_7ghghxnxjzotnj+ghePgknx{`otnpo;evnxe {{ jt0$p:x%w o ¡ $'{,7gk[] _- | _(¨v9 e]% npghnx =ote= ot£gh [].ik 7_( _A jt|] | npghnx Pot2ePjz ik0$_(:j+'w gk&npo;ev$'!{ 7 #" 9 % B 9 K% > &%. 7 P : . 70 : 7 P B 5 0$/. : Wl7"J{jzot_7xv_-p_ev| Z#|]jzjzC2]ik § x 7_ $W npe9$¥ gko¬#ghnx[]ev_Xjz1x
]0+x§]¥ ikgh_([]x§1n{1{h_|]gn¯rL5v_(j;ik{_(_e9|1ghnevj+ozgknpgho;nxote=ePn{¢{ozv£}{hgh_7[v|¶_Egh^`o*_(npike9_(ghotikxoot|y;§vl( P_ gk[]gh_ o;
P o;pjzo;ikytªtn_#l( jt{W"gk[]e]_(ozo;gknpiho;§1evnx{ {"gh"¦nx[]e;_7gkih_(_(ik£¦npoto;iki7_ w "}_7t_7ikjt5gh[]_7otiknp_{[vjCt_ gk[]_(e¶W_(_7e¶
]iho;
Po9{_|£¦otigkot
Wotxotytnl(jt¢ih_7xjzghnxotev{ ) >jtev|_(xH 7 J7,++9+¢w 2 np_7), ++;1a 03¥ Z,[]_7{h_gh[]_7otiknp_{sjzik_¶yt_7e]_(iujzxp§)£¦o;ih^sjtp!n (_|©nxe ¨viu{g o;ik|_7ispo;ytnlz¥ Z,[]_=|]n¯5_(ik_(evl(_7{ g?kWnxnp_e;o;g gkev¡ _({7ik_(¥ev_7jze¬]#o;gh
vi[]jt_ npiePg gh{A []gujz_7e]otevozikl(gknp_tnp_o;w {>e ) jz>ikjt_ []evjt_(|ikP_7_7o;pj; { 7g> ) gh [vot_ J7[v,e}=e +.]+; 7^ z j1W0,_(i1J7|, _oz+.¨P£¤+te]ika _7_(0E{ j+|j*gh_(nx¨votgke]eP[]_7{(_({!wWo;ihjzj § evgh|*¡[]_7gkn¯gk[]ot[°ik_ § 7nxe9*ghn¯_(ikgkik_([©
]j+ik, gh_/qnxguotj+ePihgh_7{!nxxotjznpeevghnxl(ototp£#evP{1gk|[]npnxev_ evy¶likx_(vgh[]|}j+_ rr nx|]e]_y'¨ve]ih__7|qxjzgh}nx§ otevj`{-{hv_g,j;{oz_£#|²j %ote©npo;¡ ^`gh[]{7_ w|?h_(lo;
We9_(;eP_|%)npev[}yA]o;peqAgke][]ot_ghnx|ot_7(e {h )nxih_(| *,
]+.ik-0ot/2
W1#_(ih3¤gh4w nx_7/2{56oz-£/217gh¡ []3_w{h_(
vgkj+lzgk¥ nxjt
