• Aucun résultat trouvé

Local Illumination in Deformed Space Fabrice Neyret

N/A
N/A
Protected

Academic year: 2022

Partager "Local Illumination in Deformed Space Fabrice Neyret"

Copied!
14
0
0

Texte intégral

(1)

HAL Id: inria-00073835

https://hal.inria.fr/inria-00073835

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.

Local Illumination in Deformed Space

Fabrice Neyret

To cite this version:

Fabrice Neyret. Local Illumination in Deformed Space. [Research Report] RR-2856, INRIA. 1996.

�inria-00073835�

(2)

ISSN 0249-6399

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Local Illumination in Deformed Space

Fabrice Neyret

N ˚ 2856

Avril 1995

TH ` EME 3

(3)
(4)

,.-0/213547698:6<;=1>6 ?:@

ABDC

EF)EHGJILKNM7OPEQSRUTVOPWYXZM

B

X F)F)EV[5FR\T

B

WYM]E ^

WYF:R\_ E`>^7a]X M]McbEE`>^]TXZM]MdR\WY`P`eRUM]TE`

f

QgXUhiEVOkj<lmM<OPWYF

n

RUo]odX QPOa]EQgEVT

B

EQPT

B

EpM"q:rZs t uJI vwxQgWzy{| | tJI {>r}o0RU_ZE`

~)2€V‚>ƒd„U … AB

EQgE†RUQgE‡O‰ˆŠX‹ˆRlx`)XZŒQeRl7[5OPQeRUTVWYM]_‹`go0RUTEV[Ža]EVŒX QgF)EaXZ‘mhiETVOP`>’9TX F)o]“mOgWzM]_9O B E

QgE`P“”y•OPWYM]_9X ‘mhiETVO‡RUM]a–QPEM”a]EQPWYM]_W•O>^ŠX Q—a”WzQgETVOPy•l˜QgEM]a]EQgWzM]_™O

B

E‡X ‘mhiEVTVOWzM–W•OP`šWzM”W•OPW›R\yœ`Po0RUTE†‘<l

T“]QPwxWYM]_‡QeRlx`>

AB

Wz`*y›R\`POžRUo]o]QgX<RUT

B

WY`"R\a]wZRUM<OeR\_ EX “]`žŒ›XZQ—RUyzy.M]X Mm[5EVŸmo]yzWYTW•O"QgEo]QgE`gEM<OSR\OPWYXZM]`*O

B

R\O

XZŒYOgEM`

B

XZ“”yza–XUO

B

EQ ˆWz`gE‡‘dEŒ5RUTEVOPWz¡Eap¢N£j]¤ž^.WzF)o]yYWzTW•OžŒ›“]M]TVOgWzXZM”`e¥e^XZQ—Œ›XZQ:yRUQP_ Ea0R\OSRU‘0R\`gE`ŒX Q

ˆ B WzT

B

OgX7XF:RUM<l‹TX F)odXZM”EM<OP`š`

B

XZ“”yza˜‘dE:OgQSRUM]`PŒ›XZQgF)Ea¦¢§o0RUQ OgWzTyzE` lm` OgEF)`^w X yz“”F)EV`>^TX F)o]yYEVŸ

_ EXZF)EVOgQ l0¥S

¨

E"a]E>RUy

B

EQPEˆW•O

B

QeRl:T>RU`POPWzM”_)WzM†R`POPQP“”TVOP“]QgEa†`PodR\TE)¢§w X>ŸmEVyY`^0TXZF)o”yzEVŸ_ EXZF)EVOPQPlWzMw<XZyY“m[

F)EVOPQgWzTOPEVŸ7Og“]QgEV`>^m_ZEX F)EVOPQPlWzM)_ QPWYa]`V¥S^<Œ›X7T“]`gWzM”_*X M)O

B

E&yzXxTRUydWYyzyz“”F)WzM0R\OPWzX MžEVwZRUyz“dR>OgWzX M^xE`godETWRUyzyzl

WzM:O

B

E"R\M”Wz`gXUOgQPX o]WYTT>RU`PE 

¨

E"RUo]o]yzlW•O+OPX—O

B

EEyzyYWzo]`gX Wza0RUydQgEV©”ETVOSRUM]TE*F)Xxa]Eyda]EVw<EyzX odEaŒ›XZQœw<XZyY“m[

F)EVOPQgWzT&OPEVŸ7OP“”QPE`WzMª¬«œEVl]| t>­‰

®‡¯x°²±P³*´

‚Zµ=€U…

w<XZyY“]F)EVOPQgWzTœOPEVŸ7Og“]QgE`^0`PodR\TEa]EVŒ›X QPF:R\OPWYXZM^mTX F)o]yzEVŸ)_ZEX F)EVOPQPl

¶›·"¸

¹ ºN»>¼

¸

¹œ½D¾zºN¿NÀÁ

Â7ÃZÄeÅ\Æ5ǬȠÉVÊË=ÉiÌ\ƧɠÍNÎÏǬÐ\Æ5ǬÄ\ÊÑÒÆÔÓV͎ͧÕ7Ö×e×gØØØÙYÆ5ÚÈ Û<ÊǬÐ\ƧǬÄUÊÑÒÆN×SÜ5Ì>ÐVÍ5ÇÞÝ×gÆ5ɠ܎ɠÄVÆ5ÈNÓZ×gÐ\ÉiÌ\ƧɠÍ

Unit´e de recherche INRIA Rocquencourt

Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France)

T´el´ephone : (33 1) 39 63 55 11 – T´el´ecopie : (33 1) 39 63 53 30

(5)

¯ € ¯ …

K‰y]EVŸxWY` OgEŠa”E“mŸžŒ5RTX M]`#a]E+T>RUyzT“]yYEVQ.EMy›R\M]TEQ.a]EœQSRl<XZMyYE+QPEM]a”“aXZ‘mhiEVOP`cRl7RUM<O#`P“”‘]W•O

“]M”EacbEVŒ›XZQgF:R\OPWzX M`PodR>OPW›R\yYE2’#EM‡TX M]`POPQg“]Wz`eRUM<OyXZ‘mhiEVOœQmbE`P“”y•OSRUM<ORVw RUM<OaEM‡T>RUyzT“]yYEQyzEQgEM]a”“^]XZ“

EM:QPEM]adR\M7OŠa]WYQPETVOgEF)EM<OcyXZ‘mhiEVOŠadR\M”`c`gXZM:E`PodR\TE&o”QPX o]QgEEeO+EMTX “]Qg‘0RUM<O+yzE`cQeRl X M]`>#£cEVO OgEa]EQP[

M]W

C

EQPE"RUo]o]QgXxT

B

EžE` ORw R\M7OSRU_ZE“]`gEžodX “]QOPX “mOPE`&yYE`&QgEVo”QmbE`gEM<OeR>OgWzX M]`œM”XZM][5EVŸmo]yzWYTW•OPE`x“]W=a]EVwxQeRUWzEM<O

RU“mOPQgEF)EM<OEVOPQPE*Œ5R\TEVOPWY`mbEE`—¢N£j”¤ž^]Œ›XZM”TVOPWzX M]`&WzFo]yzWzTWzOPE`V¥S^xX “†odXZ“”QœyYE`œ_ QgXZ`g`gE`œ‘dR\`gE`&a]Ea]X M]MŠbEE`

odX “]Q=yzE`7“”EyzyzE`=Wzy7Œ§RU“]a”QSRUW•O=OPQeRUM]`PŒX QgF)EQOPQgX o"a”EcTX F)odXZ`eRUM<OPE`Š¢§`Plx`PO

C

EF)E`Ïa]EcodR\QPOPWYT“]yzE`>^\w X yz“]F)E`>^

_=bEXZF˜bEVOgQPWYE&TXZF)o”yzEVŸxE\¥S

«œX “]`—OPQeR\W•OgXZM”`—WYTWŠa”“˜yRUM]TEQša]EQSRl<XZMEME`go0RUTE` OPQg“]TVOg“]QmbE9¢§w X>ŸmEVyY`>^c_ÏbEX F˜bEVOPQgWzE:TVX F)o]yYEVŸxE

EM OPEVŸxOP“]QgE w<XZyY“]F)W7“]E ^*_=bEXZFbEVOgQPWYEOPQgWebEE EMH_ZQgWzyzyYE\¥S^*EMk`gE TXZM]TEM7OPQeR\M7O‹`P“”Q yibEew RUyz“0R\OPWYXZMka”E

yWzyYyz“]F)WYM0R>OgWzX MyYX7T>R\yYE ^ EM—o0R\QPOPWYT“]yzWYEQadR\M]`.yzE+T>RU`a”EyÞR\M”Wz`gXUOPQgX o]WzE =«œX “]`.yÞR\o]o”yzWx“]X M]`.RU“F)Xxa

C

EyzE

a]EQmbEV©”ETVOSRUM]TEEyzyYWzo]`gXza0RUy aŠbEVw EyYXZo]oŠbEodXZ“”QyzE`OPEVŸ7OP“”QPE`œw<XZyY“]F)Wx“]E`+a0RUM]`*ª¬«œEVl]| t>­‰

\€

±

„

¯ …

OgEVŸ7OP“”QPE`œw X yz“”F)Wx“]E`^xacbEVŒX QgF:R>OgWzX M`go0R\OPWRUyzE ^]_=bEXZF˜bEVOgQPWYE&TXZF)o”yzEVŸxE

(6)

G

(

=!.%‡c2ž

j7odR\TEa]EVŒ›X QPF:R\OPWYXZM F)EVO

B

X7a]`RUQgE9“]`gEa OgXF)Xxa]Ey&X ‘mh‰EVOg` ‘<l a]EVŒ›X QPF)WYM]_ `gWzF)o]yYEX M]E` ª¬j

f

s u7^

)

ET>|+* ­‰^”X QœOPX)a]EVŒ›XZQgF X ‘mh‰ETVOg`RUyzX M]_šO

B

EOPWYF)E—ª¬£-,<|x{V­N

AB

WY`œWY`_ZEM]EQeRUy•l‡a]X M]E*‘7lOPQeR\M]`PŒ›X QPF)WYM]_

w<EQ OgWzTE`"ŒX QžŒ5RUTEeOg`X Q"TX M<OgQPX ycodX WzM7OP`"Œ›XZQodR>OgT

B

E`¢§odR>OgT

B

E`T>RUM˜RUyz`gX†‘dE)a]WzQgETVOPyzl9OPQeRUM]`PŒX QgF)Ea

WzM7OPX

B

WY_

B

EQ—a]E_ QgEEo0R>OgT

B

E`V¥S j7X”^cO

B

Wz`šWz`M]XZOšˆŠEyzy&R\adR\omOgEa˜OgX™XZO

B

EQ)QPEo]QgE`gEM<OSR\OPWYXZM”`^cXZŒOPEM

“]`gEa WzM†QeRl7[5OPQeR\TWYM]_]^²`P“”T

B

R\`"£j”¤pXZQWzF)o”yzWzTWzO+Œ“”M]TVOPWzX M]`—¢

B

X>ˆ+EVw EQ>^ O B

E`gE"QgEo]QgE`gEVM7OSR\OPWzX M]`T>R\M

‘dEŒ5R\TEVOPWY¡Ead¥S/.0“]QPO

B

EQgF)X QPE ^<EVw EM‡ˆœW•O

B

Œ5R\TEVOg`^0`PX F)E&o]QgX ‘]yzEF)`#XxTT“]Q+ˆœWzO BB

WY_

B

a]EVŒ›X QPF:R\OPWYXZM]`>^

‘dET>RU“]`gE+OPQeRUM]` Œ›X QgF)Ea*Œ5RUTEVOP`#`POSRl"Œ5RUTEVOP`¢§M]EVw<EQPO

B

EyzE`g`>^ `gX F)EcF)EVO

B

X7a]`#R\QgEœR\‘”yzE+OgX`g“]‘da]WzwxWY`PEcO B E

Œ5R\TEVOg`&a]“]QgWzM”_žO

B

Ea”EVŒX QgF:R>OPWYXZM ¥S10‡X QPEX>w<EQ^”O

B

Wz`T>RUM‡‘dETX ` Ogy•lŒ›X Q

B

“”_ZE"QPEo”QPE`gEM<OeR>OPWYXZM”`^]`g“]T

B

RU`w<X yz“]F)EVOgQPWYTa0R\OSRm^do0R\QPOPWYTyzE`Plx`POPEF)`X QTXZF)o”yzEVŸQgEVo EVOPW•OPWzw E"_ZEX F)EVOPQPl<^]Œ›XZQœˆ

B

WzT B O B

E*Mx“]F‘dEQ

XZŒTXZF)o XZM]EM7OP`šT>R\M‘dE

B

Wz_

B

EQšO

B

RUMO

B

E‡Mx“]F‘dEQ—XUŒwxWz`gWz‘”yzE:o]W•ŸmEyz`> vM]a32”M0RUyzy•l<^cQgEV©”ETVOSRUM]TE

`godETW42”T>R\OPWYXZM]`š¢5‘]“]F)o F:RUo]o”WzM]_”^²R\M]WY`gXUOPQgX o<l0¥&RUQPE—‘<lxodR\`g`gEa^ÏR\`M]X QgF:R\yY`&RUQgEQgEVTX F)o]“]OPEa†Œ›QPX F

O B

EQPE`g“]yzOPWzM]_—_ZEX F)EVOPQPl<

v `PX yz“mOgWzX M‹Wz`"OPXRVw<X Wza‹E5 ETVOgW•w E_ EXZFEeOgQPWYTOgQSRUM]`PŒ›XZQgF:R\OPWzX M^2‘<l™OPQeRUM]` Œ›X QgF)WzM]_‡QeRlx`žQeR>O

B

EQ

O B

R\M`go0RUTE ^DO

B

“]`a]X WzM”_O

B

EšQgEM]a]EQgWzM]_WYM O B

E—WYM]W•OgWRUyX ‘mh‰ETVOž`PodR\TE —vyRU`^²ˆŠE

B

Rw<E—M]XZOŒ›XZ“”M]a

RUM<l WzF)o]yYEVFEVM7OSR\OPWzX M^.RU`Œ5RUQ)RU`š`PX y•wmWzM]_†O

B

E‡_ EXZF)EVOgQ lx[5QeRl‹WzM7OPEQP`gETVOPWYXZM ˆW•O

B

M]XZM][5yYWzM]E>RUQQeRVlm`

Wz`—M]XZO—E>R\`Pl<

¨ B

EM–a0R\OSR™R\QgE`POPQg“]TVOP“”QPEaWzM `PodR\TE™¢›w<X yz“]F)E:WzM w X>ŸmEyz`V¥*XZQ—T>R\M˜‘dE`POPQg“]TVOP“”QPEa

¢§E _]HˆœWzO

B R _ QgWza–ˆ

B

WzT

B

`PX QPOP`:O

B

E9Œ5R\TEVOP`V¥S^O

B

E™QSRlT>R\M¦‘dE Œ›X yzyzX>ˆ+Ea `POPEo ‘<l`POPEo R\`yzWYM]E

a]QeRˆœWzM”_"R\yY_ZX QgW•O

B

F)`a]XWzMšo]WzŸxEyz`>£ŠXZM”TVEQgM]WYM]_

B

“”a]_ EœadR>OSRU‘0RU`gEV`>^7X M]E

B

RU`.OPX*M”XUOgEO

B

R>OcTX F)o]yYEVŸ

QgEodEVOPW•OgW•w<E`œ_ EXZF)EVOgQPWYE`RUQPE"` OgWzyzyXZŒOPEM

B

WzEQeR\QgT

B

WY¡Ea‡XZQ`gXZQPOPEa‡ˆœW•O

B

_ZQgWza”`^”ˆ

B

WYT

B

RUQPE“”`PEa‡ŒX QR

yzX M]_‡OPWzF)EOPX‡X omOPWYF)Wz¡EQeRl7[5OPQeR\TWzM”_]^=XZQT>RUM RUyz`gX‘dE)QgEo]QPE`gEM<OgEa‘<l w<XZyY“]F)EVOPQgWzT"OPEVŸxOP“]QgE`>

¨ E

o]QgX odXZ`gEWYM`PETVOPWYXZM‹r‡R`PWYF)o]yzE"QSRl7[ŽT>RU` OgWzM]_‡FEeO

B

X7a9Œ›XZQ`g“]T

B

R` OgQP“”TeOg“]QgEa9`go0RUTE ^DO

B

E—_ EM]EQeR\y

T>RU`PE‘dEWYM]_žw<EQ la]W46)T“]yzO

KNM}`PETVOgWzX M}Gx^ˆ+E˜Œ›XxT“]`‹X MHO

B

E–o]QgX ‘]yzEF XZŒ:yzXxT>R\yšWzyYyz“]F)WYM0R\OPWzX M^72”Qg` O™ˆœW•O B O B E

fB

X M]_

F)Xxa]EyŽ^.O

B

EMˆœWzO

B

RUM]Wz`gXZOPQgXZo7l<–KNOšWY`—a”W46)TV“”y•OOgX`PodETWzŒYl ˆ B R>O)T>R\M

B

RUo]odEMOPX R Œ›“]yzy )98n

.

¢§‘”W•[Ža]WzQgETVOPWzX M0RUyQPEV©”ETVOeR\M”TVE Œ“”M]TVOPWzX Md¥šR\ŒOPEQ)O

B

E†a]EVŒ›XZQgF:R\OPWzX M˜XZŒ*RUM“]M]a”EQPyzlxWzM”_9`g“]QPŒ5R\TEˆ

B

EM

RUM]Wz`gXZOPQgXZo7lWz`:M]XZO:T>RU“]`gEVa¦‘<lF)WzTQgXZ[5_ EXZF)EVOgQ l<;:O

B

EQ ˆWz`gE ^cO

B

E9a]EVŒ›X QPF:R\OPWYXZM–XZŒO

B

Wz`F)WYTQPXZ[

_ EXZF)EVOgQ l9T>RUM ‘dE)TXZF)o”“mOPEa

¨ B

EM‹T>RU“]`gEVa ‘<l‹F)WYTQPXZ[5_ EX F)EVOPQPl ^ )98n

. T>RUM ‘ E)QPEo]QgE`gEM<OPEa

‘7l9M]X QPF:RUyz`&QgEo0RUQPOPW•OPWYXZM™Œ›“]M”TVOPWzX M^=XZQ‘7lR:`

B

RUodE—o”QPXxa]“]TWzM”_:O

B

WY`*M]X QPFR\y=a]WY` OPQgWY‘]“mOPWYXZMD^=R\TVOPWYM]_

yzW=<ZE">TQPlx`POSRUyzyzWY¡>R>OgWzX Mz

AB

“]`>^dˆŠE"`P“”o]odX `PEa†OgX

B

Rw Ež`g“]T

B

RQgEo]QgE`PEM7OSR>OgWzX M†OPX:EVM”TX7a]EO

B

EžyzXxT>R\y

QgEV©”ETVOSRUM]TEª

f

..|$?7^d£90 jms&@m^%.”X “0| r>­‰

KNMž`gETVOPWzX M*”^ˆ+EŠR\o”o]y•lO

B

E`gE#TX M]`gWza]EQeR>OgWzX M]`OgXw X yz“”F)EeOgQPWYT=OPEVŸxOP“]QgE`=QPEM]a”EQPWYM]_”’ O B Wz`DF)EVO

B

X7aD^

WzM7OPQgX7a”“]TEa‡‘<lAR>hiW•lxRžWYM‹ªABAs |­‰^mWY`EVŸ7OgEM]a]WYM]_)WzMª«EVl]| t>­OPXšO

B

E`gTXZodE"XUŒ2QgEodEVOPW•OgW•w<ETX F)o]yYEVŸ

_ EXZF)EVOgQ lF)Xxa]EyzWYM]_”^cXZM¦R‹F“”y•OPWY`PT>RUyzE:ˆœRVlˆ

B

WzT

B

o]QgEVw EM7OP`R\yYWRU`PWYM]_ R\M”aa]ETQgE>R\`gE`TXZ`PO v

w<XZyY“]F)EVOPQgWzT`eRUF)o]yzE—` OgXZQgE`—Ra”EVM”`PWzONlRUM]a˜RyYX7T>RUycQgEV©”ETVOSRUM]TEWYM™w X>ŸmEVyY`>^=`POPQg“]TVOP“”QPEaWYM‹XxTeOgQPEE 

AB

E"QgEodE>R\OPEaRUM]a™a]EVŒ›X QPF)Ea†TXZo”WzE`>^²T>RUyzyYEVa C'DEF

^²ˆ

B

WYT

B

R\QgEF:RUo]odEa†XZM™R`g“]QPŒ5R\TE ^ÏR\QgE"O

B

“]`

R‡`go0R\TE)a”EVŒX QgF:R>OgWzX M‹XUŒ+O

B

EQgEVŒ›EQPEM”TEšw X yz“]F)E KNM O B

Wz`*`gETVOPWYXZM^=ˆ+EšŒ›X7T“]`X MO

B

EQgEV©”ETVOSRUM]TE

TX F)o]“mOeR>OPWYXZMWYMO

B

Ea]EVŒ›X QPF)Ea`go0RUTEZ^mˆW•O

B

RUM‡EyzyYWzo]`gX Wza0RUydQgEV©”ETVOSRUM]TE*F)Xxa]EyŽ

GHG

ÐJILKNMONP

(7)

*

}! &%

vk`go0RUTE*a]EVŒ›X QPF:R\OPWYXZM OPQeR\M”` Œ›X QPF)`&R—odX WzM<OWYM<OPX*¢¥S^0O

B

E>X dRUM]a >` ]`g“]‘]`gTQPWYomOP`

QgEVŒ›EVQgWzM”_&OgXO

B

EX ‘mhiETVO.`go0RUTERUM]ažOPXO

B

E`gTEM]E`go0RUTE  AB

EX o]odX `PWzOPEŠOPQeR\M”` Œ›X QPF:R\OPWzX MžWz`2_ EM]EQeR\yYy•l

a]W6šT“”y•OOgXXZ‘mOeR\WYMEVŸxo]yYWzTW•Ogy•l‹¢§E _]šWzM<w<EQg`PEOPQgWzT“]‘]WYTo0R\OPT

B

¥e—v ‘dX “]M”a]WzM”_:‘ XŸ9T>RUM‘dEa”E 20M]Ea

RUQPX “]M”a‡O

B

E*X ‘mhiEVTVO*R\M]aa]EVŒ›XZQgF)Ea†R\OO

B

Ež`eR\F)EOPWzF)E ^]`gX—O

B

R\O&O

B

E*OPQeR\M”` Œ›X QPF:R\OPWYXZMžhi“]`POM”EEa†OPX

‘dEœ‘]WhiETVOPW•w<EWYM]`gWza]EcO

B

WY`#‘dXŸ²^<WzMX QPa”EQ2OgX‘dETX F)o0R\OPWY‘]yzEcˆœW•O

B

QPEM”a]EQgWzM]_WzMX ‘mhiEVTVOc`go0RUTE #j7“]T B R

QgEM]a]EQgWzM”_Wz`a”XZM”E*‘<lWzM7OPEQP`gETVOPWYM]_—O

B

Ea]EVŒ›X QPF)Ea‘dX “]M]a”WzM]_š‘dX>Ÿ ^0TXZM7w EQPOPWzM”_šO

B

E`gEWzM7OPEQg`PETVOPWYXZM

odX WzM7OP`2WzM"O

B

EX ‘mh‰ETVO#`go0R\TE ^ZO

B

EMšRUT

B

WYEVwxWzM”_&O

B

E+QPEM]a”EQPWYM]_ˆœWzO

B

T“]QPw EaQeRlx`2WYM"O

B

E+X ‘mh‰ETVO#`go0R\TE 

¨

EXZ“]OPyzWzM”EWYMO

B

Wz`œ`PETVOPWYXZM

B

X>ˆ OPX—QSRl7[ŽT>RU` OˆœWzO

B

T“]QPw EaQeRlx`>

AB

E ,<RUTXZ‘”WRUM)F:R>OgQPWzŸXZŒ O B

Eœa”WzQgETVOOPQeRUM]`PŒX QgF:R>OgWzX MT>R\M)‘dETX F)o]“mOgEVaR\OcRUM<lšodXZWYM<O^mRUM]a

O B E ,<R\TX ‘]WRUM

! XUŒ0O

B

E+QPEVw<EQP`gEcOPQSRUM]`PŒ›XZQgF:R\OPWzX M*WY`DO

B

E+WzM7w EQg`gEcXZŒ”O

B

EŠŒX QgF)EQ=F:R>OPQgW•Ÿ²v˜w<ETVOPX Q

" R\OO

B

EodX WzM7O# Wz`OgQSRUM]`PŒ›XZQgF)Ea ‘7l$kWYM<OPX

" %&¢ ¥('

"  AB

ET“”Q w<Ea QeRVl EVŸmo]QgEV`g`gWzX M

Wz`

B

RUQgaOPX)_ EVOR\M]aOPX)“”`PE ^”ˆ

B

WYyzEO

B

E"WzM7OPEQg`PETVOPWYXZM”`œXZŒ2O

B

E*“]M”a]EVŒ›XZQgF)Ea‡QeRlˆœWzO B O B

E"a]EVŒX QgF)Ea

Œ5R\TE`XZŒ#O

B

E‘dXZ“”M]a]WYM]_‘dX>ŸWz`E>R\`gWzEQOPX_ EVO—¢§WzOWY`Ro]QgXZ‘]yYEF XUŒcWYM<OPEQg`gETVOPWzX M9‘dEVO‰ˆŠEEM™` OgQSRUWz_

B O

QeRlx`RUM]a†`P“”Q Œ5RUTE`^²`PEEªAR>hPs r>­5¥S^²R\M”aF)XZOPWYXZM9RUyzX M]_šO

B

EžQeRl‡TRUM ‘dE"a]X M]Ež“]`gWzM]_šO

B E ,<R\TX ‘]WRUM

AB

Wz`#`g“]_ _ZE`POP`«œEVˆOPX Mm[ŽyzW< E&Mx“]F)EQPWYT>R\y”`PT

B

EF)E`.OPX*WYM<OPEQg`gETeOŠO

B

E_ZEX F)EVOPQPl<^ ‘”“mOŠX M]ET>R\M:o]QgEa]WzTVO

RUM)WzF)odX QPOSR\M7O.TX `PO+R\a”a]Ea)OgXO

B

E“]`g“0R\y0WzM7OPEQg`PETVOgWzX M)TXZ`PO

¨

Eo]QgXZodX `gE

B

EQPER`gWzF)o”yzE+M7“”F)EQPWYTRUy

`gT

B

EF)E*R\adR\omOgEaOPXš`POPQP“”TVOP“]QgEa`PodR\TE 

v 2”Qg` O‹o”QPX ‘]yYEVF WY`™OPX QgEVw EQg`gE˜O

B

EOPQeR\M]`PŒ›XZQgF:R\OPWzX M)^)WŽE LOPX 2”M]a* <7M”X>ˆœWzM]_+

¢§QgE`godETVOPW•w<Ey•l M”XUOgEa-, RUM]a+. WzM O B E Œ›XZyYyzX>ˆœWzM”_ o]`gE“]a”XU[ŽTX7a]E\¥e/,œ`PWYM]_–O

B

E–RUo]o]QgX>ŸxWzF:R\OPWYXZM

1032\¢%465&k¥ 781032U¢k¥94 0:2

¢k¥;5< O B

EMžW•OgEQSR\OPWYM]_&_ W•w<EV`#Rœ`PWYF)o]yzEcRUyz_ XZQgW•O B F ŒX Q

>=@?BADCE

’

F+GIH@JLKMJLKNJOKQP

R<S&SUT VQW

GYXZH[F\P

] V G V ^ VQW

_a`cb] V

b[d<e Tgfih&j elkme!ng_ h

_ok<pgq

G

_ok<p

H q HDF3P<P

]FmG _ok<pgq

J[]

V

F GrF>s!]F

u v

w J .D −1

object space

ray

x y

z

D

scene space

ray

u v

tË Gtvu

(8)

t

AB

Eco]QgX ‘]yzEF Wz`=M]X>ˆ OPX&TQgXZ`g`ÏO

B

E+X ‘mhiEVTVO.`PodR\TER\M]a"OgX&WzM<OgEQP`gETVO=O

B

EŠ_ZEX F)EVOPQPl<ÏK‰M"`POPQg“]TVOP“”QPEa

`go0RUTE ^O

B

EQeRl‹TQPX `g`PE`TEyYyz`"ˆ

B

EQgEadR>OeR†Wz`ž`POPX QPEaD™v yzWzM”Ea]QeRˆœWzM”_yYW< E)F)EVO

B

Xxa TX M]`gWz`POP`žWzM

o0RUQg`PWYM]_šO

B

E"TEyYyz`>^0‘7l 2”M”a]WzM”_šO

B

EžWzM7OPEQg`PETVOPWYXZM9‘dEVONˆŠEEM†O

B

EžQSRl9R\M]a O B

Ež_ZQgWYa‡ˆ

B

WzT

B

`gEo0R\QeR\OPE`

TEyzyY`

AœB

Wz`+yzE>RUa]`+OgXžO

B

Eo”QPX ‘]yYEF}XZŒ2a]EVOPEQgF)WzM”WzM]_"O

B

EWzM7OPEQg`PETVOPWYXZM‘dEVO‰ˆŠEEMO

B

EQeRVlRUM]aR`PyYWzTE

o0RUQeR\yYyzEyÏOPXRUM™R\ŸxWY`&a]WzQgETVOPWzX M^²a]E2”M]Ea™‘<lO

B

EžWzM]a”EVŸ+XUŒcWzOP`&TX M]`POSRUM<OTXZF)odX M]EM7O^RUM]a ‘<lO B E

w RUyz“]EœXZŒ=O

B

Wz`TX F)odXZM”EM<O

AœB

EQSRlWY`a]E2”M”Ea‡‘<l)O

B

EXZQgWz_ WzM. ?—R\M”aO

B

Ea”WzQgETeOgWzX M 8 

AB

Wz`_ W•w<E`+O

B

E"RUyz_ X QPWzO B F

''& F 'oA C E ’

V G V@W

R<S&SUT

F+G _9k@p XZH V P

_a`cb

F _

^ bDd&e

Tgf hj eUk+eln:_

h

_ok<pgq

G

_ok<p

H q HDF3P<P

]FmG _ok<pgq

J

]mGMH

^ F

_

P!]!F

_

S _a`

]F _

G W

V G V

s] J

F+GiF s] JD]!F

v&M)WzF)o”QPX>w<EF)EM<OTX M]`gWz`POP`#WYM)WzM]WzOPWRUyzWz¡WYM]_#,ž¢ ¬tš¬t¬t<¥.R\OcO

B

E&‘dE_ZWYM]M]WYM]_XUŒ

''& F '

^<O

B

EM

M]XZO+OPXžWzM”W•OPW›R\yzWY¡E , WYM

>=@?



AœB

“]`>^<O

B

E`POSRUQ OgWzM]_žodX WzM7OŠWz`cO

B

EyRU`POcTXZF)o]“]OPEa,"^<ˆ

B

WYT

B

WzF)o”QPX>w<E`

O B

E)TXZM7w EQg_ EVM”TEQSR\OPE  AB

Wz`*T>RUM RUyz`gX†‘dE)a]X M]EšŒ›XZQ

''& F '

WYM]W•OPW›R\yYWz`eR>OgWzX M^OPX <ZEEo OB E)QSRl

TX

B

EQgEM]TE v&M]XZO

B

EQšWzF)o”QPX>w<EF)EM<O"WY`—M”XUO—OPXQPEV[ŽEVw R\yY“0R\OPE¢ŽRUM]aOPXWzM7w<EVQg`gE\¥,9WzM =Q?

^“]`gWzM]_

O B

E—y›R\`POw R\yY“]EšTVX F)o]“]OPEa9WYM

'& F'

 A

X‡`eRw E—O

B

E)Mx“]F‘dEQXUŒ+`gyzWzTEWYM<OPEQg`gETVOPWzX M]`>^DXZM”E)T>R\M

“]`gE

B

WYEQSRUQPT

B

WzT>RUy`go0RUTE:`POPQg“]TVOg“]QSR\OPWYXZMD^cWzM˜X Qga]EQOgX`P“”‘da]W•wmWza]E:O

B

E‡`go0RUTE‡XZM”y•l‹ˆ

B

EQgE:O

B

EQgE‡Wz`

F:R\OPEQgWRUyŽ^]RUM]aOPX x“]WzT <7y•l‡TQgXZ`g`EF)omO‰l‡RUQPE>RU`+vk`gWzF)o]yYE&X M]E*WY`œXxTVOPQgEE"QgEo]QgE`gEVM7OSR\OPWzX M‹ªÞjmRUF:|?­‰^

ˆ B WzT

B

RUyzyzX>ˆ+EV`OPXš“]`gEQgXZ“”_

B

TEyzyY`WzMEF)omO‰lRUQPE>RU`RUM]aOgX—`go]yzWzOcO

B

EF QgET“]Qg`gW•w<EVyzlšWYM 2”yzyYEa:X M]E`>

£cX M<w<EQg_ZEM]TE

B

RU`OPX‘dE#_ “0RUQSRUM<OgEVEaD^ R>O=yzE>R\`POD‘<lTyzWYo]o]WYM]_,OPXL<ZEEo"W•ODWzMO

B

E#XZ‘mhiETVO2‘dX “]M]a]WYM]_

‘dX>Ÿ  AB

E†TXZFo]yzEVOPE9RUyz_ XZQgW•O B F ˆ B

WzT

B

OgQSRUTN<7``g“]TTE`g`PWzw E†_ QPWYaWzM<OgEQP`gETVOPWYXZM]`WY`R™yYW•O OgyzE F)X QgE

TX F)o]yzWYT>R>OPEaO

B

RUM:Œ›XZQœyzWzM”Eœa”QSRˆœWYM]_]

A

X_ XžŒ›QgXZF R"_ QPWYaWYM<OPEQg`gETVOPWzX M)OPXO

B

EM]EVŸ7OXZM”ERUyzX M]_"O B E

QeRl<^7O

B

E&o]QgXZ‘”yzEF WY`#OPXT

B

X7X `gEO

B

EM]EVŸ7O`gyzWYTEOgX"QgE>RUT

B

v&M)E`POPWYF:R>OgWzX M)T>R\M:‘dE&_ZXZO‘<l:RU`P`g“]F)WYM]_

O B

EœQeRlžOPX*‘dE`POPQeR\WY_

B

O.WYM]`gWza]E&R&TEyYyŽ’ÏWzŒ O B

E` OgEVo`PWY¡E‘dEVONˆ+EEM)`PyYWzTE`#Wz`œ{Z^7O

B

ET“]QgQPEM7OcodX WzM<O#Wz`"^

RUM]a—O

B

EQeRl"a”WzQgETeOgWzX M—WY`! #"$&%('g@') ‡^ZO

B

EM—O

B

Ea]WY` OeR\M”TVE`.‘dEVONˆ+EEM*RUM]a—O

B

EWYM<OgEVQg`gETVOPWzX M]`.XUŒ

O B E"`POPQeRUWz_

B

OœQeRlˆœW•O B O B

E*‘dX “]M]a”WzM]_)`gyzWYTE`œWY`&_ZWzw EM†‘<l$+-,/./01325436

798

4

R\M”a 2 0

+:,/.013254;6

798

4 

AB

E"`PF:RUyzyYE` O

odX `gW•OPW•w<E*X M]Ež_ W•w<E`RUME`POPWYF:R>OgWzX MXZŒ.O

B

EžQgERUy=WzM7OPEQg`PETVOPWYXZM o XZWzM7O^²RUM]a XZŒO

B

Ež`PyYWzTE*a]WYQgEVTVOgWzX M†OPX

“]`gE 

<

‹+* >‡‡2

vŒOPEQ

B

RVwmWzM]_QgE>RUT

B

EaHRodX WzM7O†X MpR\M X ‘mh‰ETVO>^*O

B E yYX7T>RUy"WYyzyz“”F)WzM0R\OPWYXZMTX F)o]“mOeR>OgWzX M T>RUM]M]XZO

‘dEa]X M]EWzM O B

EX ‘mh‰ETVOTXxXZQga]WYM0R\OPE` lm` OgEF WYM]`POPE>R\aXUŒO

B

E`PTEM”E:TXxXZQga]WYM0R\OPE` lm`POPEF ˆW•O

B

X “mO

F)Xxa]W420TR\OPWYXZM”`’šWzyzyY“]F)WzM0R\OPWYXZM™“]`gE`M]X QgF:R\y#WYMmŒ›XZQgF:R\OPWzX M^2‘]“mOžO

B

E:OPQeR\M]`PŒ›X QPF:R\OPWzX M‹XZŒRM]X QPFR\y

w<ETVOPXZQ>= XZŒ‡O

B

E¦XZ‘mhiEVOX M R odX WzM<Or Wz` M]XpyzX M]_ZEQ M]X QgF:R\yšOgX O B

E¦a]EVŒ›XZQgF)Ea X ‘mhiETVO’

GHG

ÐJILKNMONP

(9)

u

% 1

6 ¢¢[ ¥P¥ '% ¢[ ¥S£cX M]`gE 7“]EM7OPy•l<^=O

B E fB

X M]_†WzyYyz“]F)WYM0R\OPWzX M9F)Xxa]Ey

ˆ B WzT

B

“”`PE`&a”XUOo]QgX7a]“”TVOP`‘dEVO‰ˆŠEEM9O

B

EyYX7T>RUy=M]XZQgF:RUy=RUM]a9w ETVOPX Qg`15‡RUM]a WYM‡O

B

E`gTEM]E`go0RUTE

T>RUM]M]XZO‘dEEVw R\yY“0R\OPEa˜a]WYQPETVOgy•l™WYMO

B

EX ‘mhiEVTVOš`PodR\TE ^“”`PWYM]_O

B

E:yzX7T>RUycM”XZQgF:RUyX ‘mOSRUWzM”Ea WYMO

B

Wz`

`go0RUTE"R\M]a‡OPQeR\M”` Œ›X QPF)WYM]_"O

B

E"XUO

B

EQw<ETVOPX Qg`

A

X—TX F)o]“mOgEO B E

fB

X M]_šF)X7a”Ey²ŒQgX F XZ‘mhiETVO`go0RUTE

a0R\OSRm^7X M]E

B

RU`#EW•O

B

EQ#OPX"a]EVŒ›XZQgFJO

B

EM]EWz_

B

Og‘dXZ“”Q

B

XxX7a:XUŒ RUM]a)QgEV[5EVw R\yY“0R\OPEO

B

EœM”XZQgF:RUyŽ^ZEW•O

B

EQ

OPX™F)X7a”W•Œl9O

B

Ea]XZO—o]QgX7a”“]TVO—`gX O B

R>OšW•O_ZWzw E`žO

B

E‡`eR\FE)QPE`g“]y•OšRU`žO

B

ETRUM]X M]WYTRUya”XUO—o”QPXxa]“]TVO

WzM9O

B

E—`gTEM]E`go0RUTE  AB

EVM9O B E

fB

X M]_F)Xxa]Ey2T>RUM‘dEEVw R\yY“0R>OgEa—v&M”Wz`gXUOgQPX o]WzTžQgEV©”ETVOSRUM]TEšˆœWYyzy

‘dEžEVw R\yY“0R\OPEa R\`ˆŠEyYy2R\ŒOPEQ

B

RwxWYM]_a”E>R\yzOˆœWzO B O B

E—`SRUF)E*o”QPX ‘]yzEF Œ›XZQO

B

EM”XZQgF:RUyz`QPEodR\QPOPWzOPWzX M

Œ›“]M]TVOgWzX M‡WzM7OPE_ZQeR\OPWzX M

J (M) −1

L d

d

L N

N ray

ray shade−ray

shade−ray

scene space texture space

M M

y x

u v

z

w

EVO '

2 'O

B

ET>RUM]X M]WzT>RUy a”XUOo]QgX7a”“]TVOXUŒ ' 2

RUM]a 'U^]RUM]a'+O

B

E “]TyzWYa]WRUMM”XZQgF XZŒ ' 

¤&W•w<EM†R*w<ETVOPX Q

" R\M]a‡O

B

EM”XZQgF:R\y = X M$ WzM:O

B

EXZ‘mhiETVO&`PodR\TE ^mˆ+E

B

Rw<E

= "

! " =

032a'@'

"

! "* 0:2$#('= "

AB

WY`_ZWzw E`O

B

E—M”XZQgF:RUy2WzM™`PTEM”E—`go0RUTE 2

='&

0:2$# ')= )(*o 032$#')= > j7X ='&

"

+ " = )(*o 0:2$# ')=

"

, ˆ B

EQgE = )RUM]a ='&

RUQgE

O B

EM]X QPF:RUyDXZŒ#O

B

E"X ‘mhiETVO*‘dEVŒX QgERUM]a‹R>ŒOgEVQO

B

Eža]EVŒ›XZQgF:R\OPWzX M^dˆ

B

WzT

B

a”E2”M]E`O

B

EF)Xxa]W2”Ea‡a]XZO

o]QgXxa]“]TVO! = " *vM XUO

B

EQˆRl†OPX`SRl†O

B

E—`SRUF)EO

B

WzM”_:WY`&OgX:TX M<w<EQPOO

B

EyYX7T>RUy2M]X QPFR\y

= WzM7OPX =

&

WzM]`POPE>RUa‡XZŒ @')=

‘dEVŒX QgE*a]X WzM”_O

B

ET>R\M”XZM]WYT>R\yÏa]XZOo”QPXxa]“]TVOœXZŒ!= RUM]a9R"w<ETVOPXZQ

"

WzM

O B

E`PTEM]E`go0RUTE 

AB

E

fB

X M]_yzX7T>RUy.WzyzyY“]F)WzMdR>OPWYXZMF)X7a]Ey

%-/.10

++

=

2)4

-

4365

0

¢1 =

87

,

R\OžR:odX WzM<O

Wz`žM]X>ˆÔXZ‘mOeR\WYM]Ea ŒQgX F O B

E)wmWz`gWz‘]WYyzWzONl EVŸxo]QgE`g`PWYXZM”`' $9

.

" =

5:ÔRUM]a ' $96;r" =

<

QgEyR\OPEa)OgXyzWY_

B

ORUM]aXZ‘”`PEQPw<EQŠa”WzQgETVOPWzX M]`=R\M”a 50^<O

B

Ea]XZOo]QgX7a”“]TVO‘dEWzM]_"O

B

ET>RUM]X M]WzT>RUy X QŠO B E

F)Xxa]W420EVa:X M]Ea]EodEM]a”WzM]_šXZM:O

B

E`PodR\TEˆ

B

EQPEM]X QPFR\yD« WY`+OSR<ZEMD’

>

?"

-/.10

++

'' $9 ; ¢&= ¥('Y{

1@

0

BA*C

6 4 - 4365

0

'z¢D@

0

1E

1?F 6?GH@

0

$I

1?F 6

J . G ; J6 ¥, 'Y{

1@

0

BA*C

6

¢›O

B

EŒ›“]M”TVOPWzX M†{

10

$K . 6

wZRUyz“”E

{W•Œ9L% 5šWz`ŠOgQP“”E ^”Eyz`gEB?<¥S

Mt

ÑONPǬÜ#ÚVОÍ5Ó\ɜ͎ÄeÐ6QeÉPÐV͊Õ6R¬ÄeÐ\ÉÇÞОÍ5Ó\ÉÚVÅSÉPÈiÍc܎Õ\ÄeÈPÉLTm܎Ú͎Ó>ÄeÍUWVXP)Y4NP[Z\^]T]Í5Ó\É Ð,N_\a`6bNPœÇ¬Ü#ÚVО͎Ó>É

͎ÄeÐ6QVÉ ÐVÍÏÕ6R¬ÄeÐ\É2ÇÞÐÍ5Ó\É.܎ȠɠÐ\É=܎Õ\ÄeÈ ÉÊ

u

ÜcU`ed

Mgf

bVXP)Y4N_cZh\iUVcPY4NPiZh\]T`*d

M?f

bVcP#ǬÜÚeƧ͎Ó>ÚLQeÚVÐ\ÄBR7Í5ÚjN_BTUÅZÉPǬÐ6Q

͎ÓDk>ÜDÍ5Ó\É.Ð\ÚeÆ5ÝÄBR<ÇÞÐÍ5Ó\É2܎ÈPÉ Ð\É2܎Õ\ÄeÈ ÉÊ

lBm

\ npoeq

rnpoeq r

Ê"sǬÜcÍ5Ó\ÉǬÐLtVÉPƧ܎ÉÚeÑÏÆ§ÚLk6QeÓ\Ð\ɠ܎ÜPÊvu

nxwgyLy

ÄVÐ6z%uh_|{B}4~ÄVƧÉ͎Ó\Éz\Çk\܎ÉÄeÐ6zšÜŽÕZÉPÈ1k6R¬ÄeÆ.ƧÉ1€UÉ Èi͎ǬÚeÐ

È Ú>É$È Ç¬ÉPÐeÍPÊ

tË Gtvu

(10)

@

.0XZQRUM]Wz`gXZOPQPX o]WYT2QgEV©”ETVOSRUM]TE ^UO

B

E#yzX7T>RUy<WzyYyz“]F)WYM0R>OgWzX M&R\O2RodX WzM7O=R\TTX QPa”WzM]_œOPXœO

B

E#_ W•w<EMM]X QPFR\y

QgEo0RUQ OgWzX MŒ›“]M]TVOgWzXZM Wz`:EVwZRUyz“dR>OgEVa ‘7l–WYM<OPE_ QeR>OgWzM]_ O B E yzXxT>R\y fB

X M]_ F)X7a”Ey&XZM OB

E™M]X QPFR\y

a]WY` OgQPWY‘]“mOgWzX MX MO

B

Ež¤RU“]`g`gWRUM:`go

B

EQPE ’

>

?"

xK

1?F . ;

6@ 0 1E

1?F 6 2

4

1?F 6

@ 0

1E

1?F 6 2

4

1?F 6

v¦M]XZQgF:RUymWz`cR\`g`gX7TWR\OPEašOPX"R`P“”Q Œ5RUTEEyzEF)EM7O 5 9 B

RVwmWzM]_R\MRUo]o0RUQgEVM7Oc`g“]QPŒ§RUTE5 9l'' $9

.

XZQ ?WzŒdO B E

M]X QgF:R\yÏWz`&M]XZO&OPX>ˆœR\Qga]`O

B

EX ‘]`gEQ w<EQ^²RUM]a

B

R\`R)a]Wz`POPQgWz‘”“mOPWYXZM ¢&= ¥S^DR\yYyDO

B

Wz`ˆŠEWY_

B

OPEM]WzM”_šO B E

yzXxT>R\y fB

X M]_QgEV©”ETVOSRUM]TE  AB

EWzM7OPE_ QSRUy WY`+M]XZQgF:RUyzWz¡Eaš`gXžO

B

R\O+O

B

E“]M”a]EQPyzlxWYM]_—R\o”o0R\QgEM<O`P“”Q Œ5RUTE

Wz`*{Z

normal distribution shape supporting the normal distribution

. .

. . . . . .

. . . .

apparent shape

d

¨ B

E"RU`g`P“]FEO

B

R\O&«¦WY`a]E2”M”Ea‡‘<lRž`

B

R\odE ^mO

B

EM]X QPF:RUyda]WY` OgQPWY‘]“mOPWYXZM:‘dEWzM”_žO

B

EM”XZQgF:R\yY`#XUŒ

O B E`

B

R\odEˆ

B

WzT B OB

“]`a”E2”M]E"R <7WYM]aXUŒ >TQPlx`POSRUyzyYWz¡>R\OPWzX Mz

AB

EMWzyzyY“]F)WzMdR>OgWzXZMšT>RUM‡‘dEˆœQgW•OPOPEM

>

?"

! #" $

xK

1?F 1&%#6 . ;

6@ 0 1E

1|F 1'% 6;6 2

4

.(

#"

@ 0 pE

1|F 1'% 6;6 2

4

.(

AB

Wz`WYM<OPE_ QeR\y²T>R\M‘dEˆœQgW•O OPEMa”WzQgETeOgy•lX MO

B

E"R\o]odR\QgEM<Or

8

`g“]QPŒ5R\TE ’

>

?"

*)+ , -!. $

$K/

1?F 1'%

10 23

6 . ;

6 .

)+ , -!.

. ^

ˆ B WzT

B

T>RUM‡‘dE"RUo]o]QgX>ŸxWzF:R\OPEa:‘<l™{(% ' 4 K6587

%:9 ¢&=¢

1<;=>6

¥ 5 c¥

AB

E*RUM]WY`PXZOPQgX o]WzTWzyzyY“]F)WzMdR>OgWzXZMšTX F)o]“mOeR>OPWYXZM`gT

B

EF)EWz`ŠO

B

“]`>’

?

EVwZRUyz“dR>OPWYM]_—O

B

E"RUo]o0RUQgEM<Oœ`g“]QPŒ5R\TEXUŒO

B

E`

B

RUodEF)Xxa]EyzWYM]_"O

B

EQgEV©”ETVOSRUM]TE ^

?

R>OœE>RUT

B

`eRUF)o]yzEX MO

B

WY``g“]QPŒ5R\TE ^”T>RUyzT“]y›R>OgWzM]_)« X MO

B

E`

B

R\odE

? EVwZRUyz“dR>OPWYM]_ ' $9

. ' $9;^.WzM XZ‘mhiETVO—X Qž`PTEM]E`go0RUTE ^2ˆ

B

WzT

B

_ W•w<E`žO B E

fB

X M]_ WYyzyz“”F)WzM0R\OPWYXZMD^

O B

R\OœWz`œT“]F“]y›R>OgEVaOPX 2”M0RUyzyzl_ZWzw E`

>

?"ϝ

GHG

ÐJILKNMONP

(11)

s ( Ï%* †&c=*+

AB

E&QPEV©0ETVOSR\M”TEF)X7a]Ey”ˆŠEa]E`PTQgWz‘ EVa:WzM™ª«œEVl”|Zt\­ EM]TX7a”E`+O

B

EM]X QgF:R\y0QgEo0R\QPOPWYXZMŒ›“]M]TVOPWYXZM ‘<l

RUM EyzyzWYo]`gXZWYa‡`POPX QPEa†WzMw<XŸmEyz`WzMO

B

EžQgEVŒEQgEM]TEž`go0RUTVE ^²WzM9R\a”a]W•OPWYXZMOPX‡Rša”EVM”`PWzONl<

AB

WY`&F)X7a”EyDWz`

TX F)o0RUTVO^ ‘”“mOc_ EM]EQgWzTEM]X “]_

B

WzMžO

B

E`PTX odEXUŒdw<X yz“]F)EVOgQPWYTcOgEVŸ7OP“”QPE`>^<ˆ

B

EQPEWzO.EM”TX7a]E`Š`P“”‘m[5w X>ŸxEy

_ EXZF)EVOgQPWYTwZRUQgWR\OPWzX M]`>

AB

EWzM]WzOPWRUy=`PodR\TEWY`a”EeŒ›X QgF)Ea ‘<l†O

B

EOPQSRUM]`PŒ›XZQgF:R\OPWzX M$pWYM<OPX:O

B

E`gTEVM”E`go0RUTVE *v`P`g“]F)WYM]_

yzWYM]E>RUQ"a”EVŒX QgF:R>OgWzX M R\Ow X>ŸmEyŠ`gWz¡E‡R\QgX “]M]a O B

Ew<X>ŸxEy+TEM<OgEQ

0

¢›O

B

EyzX7T>RUy+a]EVŒ›XZQgF:R\OPWzX M‹‘dEWYM]_

a]EVOgEQPF)WYM]Ea‘<lO

B

E,<R\TX ‘]WRUM ¢

0

¥P¥S^2O

B

EQgEV©”ETVOSRUM]TET>R\M `POPWYyzyc‘dE)EM”TX7a]Ea˜‘7l R\M EyYyzWzo”`PX Wza

WzMO

B

Ež`PTEM]Ež`go0RUTE jxXšOPXTX F)o]“]OPEO

B

E"WYyzyY“]F)WzM0R\OPWYXZMD^mˆŠE*T

B

XZ`gE"OPX:TVX M7w EQPO&O

B

EžyYX7T>RUyÏEyYyzWzo”`PX Wza

a]E20M]Ea WzM–O

B E WzM]WzOPWRUy&`go0RUTE ^œWzM7OPX O B

E™`gTVEM”E `PodR\TE  AœB

E o]QgX ‘]yzEF Wz`)O

B

“]`:OgX˜EVwZRUyz“dR>OgE†O B E

QgE`P“”y•OPWYM]_EyzyzWYo]`gXZWYa WzM™XZQga]EQOPX_ZEVOžW•OP`M]X QgF:R\yY`^DR\M”a9O

B

ER\o”o0R\QgEM<O*EyYyzWzo”`PEOPX‡‘dEš`eR\F)o]yYEaKNM

O B

ET>R\`gEXZŒ#w<XZyY“]F)EVOPQgWzTOgEVŸ7OP“”QPE`>^²O

B E >¬TQ lm` OeR\yYyzWz¡>R\OPWzX M R\yY`PX:EM]TX7a”E`O

B

E)R\M”Wz`gXUOPQgX o]WzT"X7TTyz“”`PWYXZM

¢ŽRžw<XŸmEyDWz`+M”XUORž`g“]QPŒ5R\TEEyzEF)EM7Oe¥S^m`PXO

B

R\ORUMRUa]a]W•OgWzX M0RUyM]XZQgF:RUyzWz`eR\OPWzX M

B

RU`œOPX‘dEa]X M]E 

v&MEyYyzWzo”`PX WzažWz`.T

B

RUQeR\TVOPEQgWz¡Ea‘7lšR‘0RU`gWz` RUM]ažO

B

QPEEœyzEM]_ZO B 0

^Z`gX&O

B

ERU`P`gX7TW›R>OgEa x“0RUa]QSR\OPWYT

Œ›XZQgF% # ' ' {Wz` # ' 0

' WYMšO

B

EWzM”W•OPW›R\y0`PodR\TE ^<ˆW•O

B

a]WRU_ XZM0RUyd`g“]T

B

RU`

00

a 0 ^

M”XZQgF:R\yN^mRUM]a$ RžodXZWYM<OœX MO

B

EEyzyzWYo]`gXZWYa†¢›O

B

E*X QPWY_ZWYM‘dEWzM”_O

B

EEyzyzWYo]`gXZWYa)TEM<OPEQV¥S

£cX M<w<EQPOPWzM]_šO

B

EžEyzyzWYo]`gXZWYa‡WzM‡O

B

Ež`gTEVM”E*`go0RUTE"WY`œE x“]W•w RUyzEM7O&OPX)‘0RUTN<<[ŽTX M<w<EQ O"R—odX WzM<O1&XZM

O B

EQPE`g“]yzOPWzM]_—EyzyzWYo]`gXZWYa)WzM<OgXO

B

EWzM]WzOPWRUy `go0RUTE ’

#

'6' k{¢›ˆW•O

B

odX `PWzOPW•w<E\¥ / 0:2 ' ' ' {m #

!

' # ' 0 ' '

v&TTX QPa”WzM]_šOPXšO

B

Ežo]QgEVwxWzX “]``gETVOPWzX M^0ˆŠE

B

Rw E"OPX20M]aO

B

E—RUo]o0RUQgEVM7O&`

B

R\odE ^²RUM]aO

B

EžM]X QPF:RUy

TX QPQgE`godXZM”a]WzM”_OPX:RodX WzM7Oœ`eR\F)o]yYEaXZMO

B

Wz``P“”Q Œ5RUTEZ

AB

EžRUo]odR\QgEM<O&EyzyYWzo]`gEWY`+O

B

E*o]QgXUhiETVOPWYXZM†XUŒ

O B

EEyzyYWzo]`gXZWYa"ŒX yzyYXˆWzM]_O

B

EX ‘]`gEQ w<EQa”WzQgETVOPWzX M650ÏKŽOg` 7“0RUa]QeR\OPWzTŒX QgFpWz`[&>#5&5

#

"(U5

#

#50

WY_ZEM<w RUyz“]E`¢4

7

¥#RUM]aEWz_ EM<w<ETVOPX QP`+a]EVOgEQPF)WYM]ER‘ XZ“]M”a]WzM”_"‘dX>Ÿ)XUŒÏO

B

EEyzyYWzo]`gE ¤&Wzw EM9¢

¥.XZM

O B

EžRUo]o0RUQPEM7OœEyzyYWzo]`gE`P“”Q Œ5RUTE ^ž`gX—O

B

R\Ož¢

7¥ Wz`œXZM‡O

B

E*EyYyzWzo”`PX Wza:Wz`X ‘mOeR\WYM]Ea‡Œ›QgXZF O B E

`gETXZM”a‡XZQga]EQœE 7“0R\OPWYXZM

'5 ##5 4 rQ'z¢'5 # [Q4

'5 # 7

¥\4¢

'#[@4

'7 # 7 4 r

'7 #[ –{\¥B ?

]¢›[!

[

¥#T>RUM‘dE&X ‘mOSRUWzM”EaR\OcO

B

E&`SRUF)EœOPWzF)E ^<`gX

B

RUy•ŒDXZŒO

B

EEyzyzWYo]`gEM]EEaOPX‘dE`eR\F)o”yzEa=v&yzy”O B E

OPEQgF)` ' #

2 ' R\QgEXZŒ2TXZ“”QP`gEo]QgEV[5TX F)o]“]OPEa

vJM]X QPFR\yOgX)O

B

EžEVyYyzWYo]`PX Wza R>O1T>RUM†O

B

EF ‘dEžXZ‘mOeR\WYM]Ea ‘<l = " %

#" % J

^0ˆ

B

WzT

B

_ W•w<E`O B E

WzyYyz“]F)WYM0R\OPWzX M X MO

B

Wz`žodXZWYM<O—R\TTX QPa”WzM]_†OgX‡O B E

fB

XZM”_F)Xxa]EyŽ$ T>RUM ‘dEa]WzQgETVOPy•lEVŸ7OPQeRUTVOPEa

‘7l% ' [34

'

7

4&Q' 5”^2Rw<XZWYa]WzM”_ F:R>OgQPWzŸ9o]QgX7a”“]TVO

AB

E:WzyzyY“]F)WzMdR>OgWzXZM™TX F)o]“mOSR\OPWYXZM `gT

B

EF)E

a]EVOeR\WYyzyzEaWzM:O

B

Eo]QgEVwxWzX “]`œ`PETVOPWYXZMT>R\M‡O

B

EM‡‘dEEVw R\yY“0R>OgEa

v&M‡R\a]a”W•OPWYXZMdR\ydM”XZQgF:R\yYWz`eR>OgWzX M

B

RU`ŠOPXž‘dE&a]X M]E&WYMšO

B

E`PTX odE&XZŒw X yz“]FEeOgQPWYT+OPEVŸxOP“]QgE`>^xWzM:XZQga]EQ

OPX&OPQPE>R\O=ˆœW•O B O B

Ec`eR\F)EˆŠEWY_

B

O=O

B

EŠa]W45 EQgEM<O=`

B

R\odE`>^\ˆ

B

WYT

B

R\yY`PXEM]TXxa]E+RUM]Wz`gXZOPQgXZo”WzT#X7TT“”y•OSR\OPWzX M

AB

Wz`+M]X QPFR\yzWY`SR\OPWYXZM)WY`_ W•w<EVM‘7lO

B

EF)E>R\M‡R\o”o0RUQPEM7Oœ`g“]QPŒ§RUTEXUŒ=O

B

EEyzyzWYo]`gXZWYa

¨

E"R\o”o]QgXŸmWzF:R\OPE

W•O‘7l:“”`PWYM]_žO

B

E"R\o]odR\QgEM<O`P“”Q Œ5RUTEWzM:O

B

EO

B

QPEE"R\ŸxWY`a]WYQPETVOPWYXZM”`’

'

7)(O(ZG<'Y¢|

2

6 4W6B+*4W

2

,*U¥S

¨

W•O B.-

) #

' # ') 032 ' ' ^]ˆ

B

WzT BB

RU`&EWz_ EM<w R\yY“]E`

{6(

0 ˆ B

EM$$

>

50^

'

7/(O(ZG<'01x 32Z¢

-

¥1(l54251e¢

-

¥30m¢§EVŸ]RUTVOcXZM”y•lW•ŒdO

B

Ea]EVŒ›XZQgF:R>OgWzX MWz`cRQPWY_ZWYa

F)XZOPWzX Md¥e

tË Gtvu

(12)

|

Ïe

AB

E 2”_ “]QgE ` B

X>ˆœ`ROPEVŸmEyXUŒw<XZyY“]F)EVOPQgWzT‡OPEVŸ7OP“”QPE™‘dEVŒ›XZQgE‹R\M]a R\ŒYOgEQO

B E OgQPWYyzWzM”E>R\Q)a”Wz`POPX Q OPWYXZMD

AB

E‡©0X7X QWY`)`PyYWz_

B

OPyzlRUM]WY`PXZOPQgXZo”WzT  :&M]E†TRUM`gEEX M–O B E `Po

B

EQgE‡O

B

R>OO

B

E†OPQeRUM]`PŒX QgF:R>OgWzX M˜XUŒ

O B

E"WYyzyz“”F)WzM0R\OPWYXZM:E5 ETVOP`ž¢§`godET“]y›R\Q>^da]W45 “”`PER\M”a`

B

RUa]X>ˆœ`V¥+a]X)M]XZO`gWYF)o]y•l)Œ›X yzyzX>ˆ O B

Ež_ZEX F)EVOPQgWzT

a]EVŒ›X QPF:R\OPWYXZMRU`RžOPEVŸ7Og“]QgEˆ+X “]yzaa]X”

AB

ET“]‘dEWz`

B

EQPEOPXšWzyYyz“]`POPQeR>OgE*£œj]¤ ¢NR\yzO

B

X “]_

B

£j]¤HRUM]a

WzFo]yzWzTWzOcTXZM”` OgQP“”TeOgWzX M]`RUQgEw<X>ŸxEyYWz¡Ea^]“]`gWzM”_žw X yz“”F)EVOPQgWzTOPEVŸxOP“]QgE`QPEo]QgE`gEM<OSR\OPWYXZM ¥S

ž Ï

¨ E B

Rw E.o]QgX odXZ`gEa"R_Z“]WYa]EyzWYM]E=OPXQeRl7[5OPQeR\TE.`PodR\TEV[Ža]EVŒ›XZQgF)Ea*X ‘mhiETVOP`=WzM&O

B

EWzQÏWzM]WzOPWRUyZ`go0RUTE ^ˆ

B

WzT

B

WzFo]QPX>w<E`2TX F)o]“mOSR\OPWYXZMWYMO

B

ET>RU`PEXZŒ

B

“”_ZEadR>OeR\‘0RU`gE`^]R\M]aRUyzyzX>ˆœ`.M]X Mm[ŽEVŸxo]yYWzTW•O#QgEo]QgE`PEM7OSR>OgWzX M]`

XZŒYOgEM“”`PEaWYM:QeRl7[5OPQeR\TWYM]_”

AB

E*QgEe©0ETVOSRUM]TE*TX F)o]“mOeR>OPWYXZMWzMO

B

E*`gWzF)o”yzER\M]a9RUM]Wz`gXZOPQgXZo”WzTT>R\`gE`

B

RU`œ‘dEEM†o]QgE`gEVM7OPEacv

`gWzF)o]yYER\M]WY`PXZOPQgX o]WzTQPEV©0ETVOSR\M”TE*F)X7a”EyŽ^7“]`eRU‘]yzEŒ›XZQœw<XZyz“”F)EVOPQgWzTOPEVŸxOP“]QgE`>^

B

R\`‘dEEMa]E`gTQgWz‘dEa

v `gWzF)o”yzE*T“”Q w<Ea9QeRlT>RU` OgWzM]_

B

RU`"RUyz`gX:‘ EEVM™o]QgX odXZ`gEa Œ›X Q` OgQP“”TVOP“]QgEa9`go0RUTE "KNO

B

R\`OPX‘dE

Œ›“]yYy•la]E`gTQPWY‘dEaWzM:O

B

E_ EM]EQeR\yÏT>R\`gE 

GHG

ÐJILKNMONP

(13)

{?

œ !&‡+

É È ŠÊ

ɠȉÓ>ݜÄeÐ\Ð7ÊÕ\ÄeÈPÉcz\ÉiѕÚeÆ5ÝÄeÍ5ǬÚVÐÝÚz\É1R¬ÜdÜk\Æ?tÉiÌÊ

¼2ÀZ»>¾Y¹‰º À º

T M! "$#‰ÖO&%')(+O'MP6T*&UÊ

+,

!- ÄVÅ>ǬÐ\É

+

Ú>Û)k\ÇRR¬ÄVƛÍdÄVÐz/.dǬÉPƧÆ5É

,

ÄVÐ>È0É Ð\ÉVÊ

u

Ð>ÇÞÝÄS͎É1zcÑÒÆ5É ÉiÙYÑÒÚVÆ§Ý z\ÉiѕÚeÆ5ÝÄeÍ5ǬÚVÐ7Ö

u

ЊÇÞÐe͎ɠÆ5ÄeÈ Í5ÇtÉDÄVÐ\ǬÝÄS͎ǬÚVÐ

͎ɠȉÓ>Ð\ǬÛk>ÉÊ

t

Ð21Ó\ÚeݜÄeÜ39ÊÉ1z\É Æ5Å É Æ|QTZÉ1z\Ç͎ÚeÆ1T4

¼=ÀZ»\¾Y¹56 Àiº

¶87'9

:

·<;>=?A@BCD=

N¹‰¹FE"G'HeºÁ

T

tÚBRk\ÝÉJKO)T>Õ\ÄLQeÉ Ü KIJ(+K'PT

,

k6RÌK*!eÊ

+L M%J

ƧǬÄVÐ

+

ÄeÅ\Æ5ÄBRTDË=É1R¬ÜŽÚVÐ

L

Ä&M TDÄeÐ6z

G

É Å É È È ÄNÕ>Æ5ǬÐ6QeݜÉiÌVÉPÆiÊ

Çz\ǬƧÉPÈiÍ5ÇÞÚeÐ\ÄBRÆ5É$€UÉ Èi͎ǬÚVÐ)Ñk>Ð\Èi͎ǬÚVÐ>ܜѕƧÚVÝ

Ük\ƧÑÒÄVȠɆÅk\ÝÕ ÝœÄeÕ\ÜPÊ

tÐ L ÄLk\ƧÉPÉ Ð

+

ÊDÍ5ÚVÐ\ÉLT*É1z\ÇÍ5ÚVÆ$TO

¼=ÀZ»>¾¹*P À º

¶Q7'9

>

·<;>=?R@S!T

=

‰¹N¹FE"GUHSº›Á

TBtÚBRk\ÝÉJK'& V#xT\Õ\ÄLQeÉPÜHK%IJ(+K'M!BT

,

kR¬ÌK*M%>Ê

ÃUÚLkUKJ

u

R¬ÄVǬÐ*ÃUÚLk\ƧÐ\ǬɠƠʜË=ÚeÆ5ÝÄLRez\ǬÜ5Í5Æ5ǬÅ6k>Í5ǬÚVÐ"Ñk\Ð\ÈiÍ5ÇÞÚeÐ\ÜÄVÐ6zžÝ k6RÍ5ÇÞÕR¬ÉŠÜk\ƛѕÄeÈPÉ ÜPÊ

6 ÀV º

9

GZ¾¹*"W*$N¹

@BX

Y

-ZPº- À

G\[

F]

9

]^]»¼_"G¾"

G

T\Õ\ÄLQeÉ Ü O(+O KT

L

ÄPÌK*K>Ê

`

ÄBSMKJ

,

ÄVÝÉ ÜD12Ê

`

ÄBSÇÌÄ\Ê

G

ÄPÌ͎ƧÄVȠǬÐ6Q—Õ\ÄVƧÄVÝÉi͎Æ5ǬÈÕ\ÄeÍ5ȉÓ>ÉPÜPÊ

t

Ð

¼=ÀZ»>¾¹a6 ÀV º

¶87'9

>

·<;>=?b@SX

=

‰¹N¹FE"GUHSº›Á

TBtÚBRk\ÝÉ_ PU VI#xT\Õ\ÄLQeÉPÜHK O(+K O6T

,

kR¬ÌK*MK>Ê

``

M&&

,

ÄVÝÉ Ü<1Ê

`

ÄBS›ÇÌVÄ+ÄVÐzc1ǬÝÚeÍ5ÓVÌ5d0Ê

`

Ä ÌÊ

G

ÉPÐz\É Æ5ǬÐ6QŠÑk\ÆØDÇ͎Ó͎Ó\ƧɠÉXz\ǬÝÉ Ð\܎ǬÚVÐ\ÄBR\͎É*M>Í k\ƧÉPÜPÊ

tÐ , É1 Æ5ÉiÌ

dxÄeÐ\ÉLT]É1z\ÇÍ5ÚVÆ1T>4

¼2ÀZ»>¾¹*c6 À º

¶87'9

>

·<;>=?e@S$BK=

N¹‰¹FE"G'HeºÁ

TtÚBRk\ÝÉ-KJI! VI#xT”Õ>ÄLQeÉPÜ1K%$-(KNMB]T

,

k6RÌK M\Ê

Ë=ÉiÌUOJHÃUÄVÅ\ƧǬÈPÉ Ë=ÉiÌ\ƧÉiÍPÊ

u

QVÉ Ð\É Æ5ÄBRÄVÐzŠÝ k6R͎Ǭ܎ȠÄLR¬É”ÝœÉiÍ5Ó\Úz2ѕÚeÆetVÚLRk>ݜÉi͎ƧǬȔ͎É*MÍk\ƧɠÜPÊ

 À º

9

GZ¾¹*"W*$N¹

@Bf

=

‰¹N¹FE"GUHSº

TBtVÚLRk\ÝÉO]B]! ]$#xT\Õ\ÄBQVÉ Ü]L]B](D]L]B]T

L

Ä Ìg*O>Ê

.dÃB]&h.dǬÉPƧÆ5É_.”ÚBk6R¬Ç¬Ð*ÄVÐ6z

u

R¬ÄVǬÐÃUÚBk\Æ5Ð>ÇÞÉ ÆiÊ

u

ݜÚ)z\É1RxÑÒÚVÆ.ÄeÐ\Ǭ܎ÚeÍ5Æ5ÚeÕ\ǬȊƧÉ$€UÉ È Í5ǬÚVÐ7Ê

t

Ð"ÃUÚeÆ5É Ü5Í

ÄeÜFiVÉiÍ5Í1T7É1z\Ç͎ÚeÆ1T

¼2ÀU»\¾Y¹D6 ÀV º

¶87U9

:

·;=j?k@Bl/=

‰¹N¹)E&"GUHSº›Á

TBtÚBRk\ÝœÉ KU V#xT>Õ\ÄBQVÉ Ü K%JI(KNMKT

u

kQLk\Ü5Í:*B]UÊ

ÄVÝmB]&on=ÄVÐ>ÄVÐPÄVÝÉiÍPÊqp

¹ º)^H&GPGE

;

G]rSº-•º W 7

À$¾VV]

p

¾V

7

¾"‰»UP¾•»$޹iº Ê u

z6z\Ǭ܎ÚeÐ>ÙV3žÉ ÜR¬É ÌDT

G

É ÄLz\ǬÐQT

L

ÄV܎܎ÄeȉÓDk>܎ɠ͎ͧÜpTB]UÊ

$. MP 1Ó\ÚeݜÄeÜs3 ÊtÉ1z\É Æ5Å É Æ|QÄVÐz\È ÚeÍ5Í

G

Ê.]ÄVƧƧÌÊ2ÃUÆ5É ÉiÙzѕÚeÆ5Ý z>É ÑÒÚVƧݜÄS͎ǬÚeЍÚSÑd܎ÚLR¬Çz QVÉ ÚVÝÉi͎ƧǬÈÝÚ)z\É1R¬ÜPÊ

2Äpt>Çz +

Êu teÄVÐ\ܔÄVÐ6z

G

k\܎܎É1RR , Ê u

͎Ó\Ä Ì)TÉpz>Ç͎ÚVƧÜpTv

¼=ÀZ»\¾Y¹w6 À º

¶87'9

>

·<;>=?x@Syw=

N¹‰¹FE"G'HeºÁ

T

tÚBRk\ÝÉJK8]6T>Õ\ÄLQeÉ Ü>'O$-(PB]T

u

kQLk\Ü5Í:*M PUÊ

tË Gtvu

(14)

Unit´e de recherche INRIA Lorraine, Technopˆole de Nancy-Brabois, Campus scientifique, 615 rue du Jardin Botanique, BP 101, 54600 VILLERS L ` ES NANCY

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 46 avenue F´elix Viallet, 38031 GRENOBLE Cedex 1

Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902 SOPHIA-ANTIPOLIS Cedex

Editeur ´

INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France)

ISSN 0249-6399

Références

Documents relatifs

Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP

Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP