Unfolding Of Surfaces
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Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Unfolding Of Surfaces Jean-Marie Morvan — Boris Thibert. N° 4615 Novembre 2002. ISSN 0249-6399. ISRN INRIA/RR--4615--FR+ENG. THÈME 2. apport de recherche.
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(401) 5= ! -". ÓU½'ع²rº+´¿½t×É¥À¶ÃhÊ Ãkµ+³. ÓUÅ\عÍ×7ËU¸¥À¶Ä7ÃcÄZ¾º9´¿½t×É¥À¶Ã5Ê Ãkµ³. PUVW^EgiGSx 45X [?`cG V M I. . M ^ g JW. PQV?^EgiG X 4hX [W`lG'V \M B M ^g 0PW . X ^Egi}AC[\BEYl^EGgiYiGÖglP][[\Y;OEV?G7RQ[WG,XtB FmPUG O?`lYiBG giT\PQT?~g¨_}WVWG ^_gcglYiG G' P]`P]``cYl`kYigiPQP]RUX¥RsYlRUPQb O1`lO_X G glV?PUd1[\G7YlqPU}WGPUO. C/`lpE$BERG B/glZG '[\^O1g Bq 0,YlPQB_"GB qEPUPU`;`iX'YlgiBEG'YiG{GX KsG O[WYl^_gt`l[\` R I. ÆÜÑaÆÐê.
(402) yX.
(403) . }?KsG [Wgl^_YlG `i` X'[\^EO_giq }[C/Yl^_$glRGNB5Z PQO1 `lX 'glPUd1^gG7 q
(404) PQT\OYiBE`lpEG giBE G giP]`cG G¤¥5. ACB#^_`CGNB1[}WGS[~YlgiPU[WOEVWRUGsF6G7`cB PQYlB`cYlgiPUX'YlRUb;OEG V[YiPQ}?G. PUVW^EgiG- 4hAgiP][\OEV?RQGsFmG `lB PQYlBOEG V?[\YlPU}WGIKs[\^_`i`CX'^Egi}[Yi^EglGsPUO_`iX'giPQd!G q
(405) PUO .. ÑÑ ×
(406) _Eà'ßP`ba.
(407) yY. U
(408) -,
(409) &
(410) 5= ! -". `lACG B_O1PU`cAC`5GBEYlgiYlG~PUB_[WYl[\OEgiY~VWP][\RUYiG OEBEV?G
(411) FmRQG~G qE`lF6PUB;`iX'G7PUgi`c`¡G'B,YiOEG
(412) T\T\5Y Ks¨1PQ[\O_VW^1`i^EX'`lgi`6giGGPUd1X'^EG7qgiPU}`sPQ[O;qrYi^EG [}Wgl`cG
(413) G pERQT?[B_p_YmG [\giG GWdE[?RUXtGdEB^r[WY O_}WqÖG PUO;gcYiPQYi[IG'`N `ld!FmT\TW T^ETWYiO_BEYlq_B;G[\`lgid1^Eb T?gl^E967[W O_7X'qEGZ[WT\(+gl¹b " gl% PUG `6}W!T?#OERRQTW^r(+Y~Yi &
(414) PQYiT?
(415) T#Oa<cT{¹W PQR]O,[\B_giYlT?VWBE`lGWGG Ks[W^_`i` X'^Egi}[Yl^_glGNPU`Z`kYiglP]X¥YiRQb;p!T?`lPQYlPU}WGS[YoG7[WXtBPUOYlG glPUTWg p!TWPUOY . ÓU½'ØaÒÃkå'ÃkÀ¶¸¥¼½tÅ7À¶Ã5¾+º9´¿½t×É¥À¶Ã5Ê Ãcµ+³ UÓ Å\عÍ×7ËU¸¥À¶Ä7ÃcÄZ¾º9´¿½t×É¥À¶Ã5Ê Ãkµ³ KsPU[WVW^_^E`igi` G\X' ^E4 gi}° [YlG ^_}?glG G RUTWp_[WdERUGYiglP][\OEV?RQGFmG `lBPUO_`iX'giPQd!G q PQO [,`lFmT#T\YlB `c^_gc9[?X'G
(416) PYiB `cYlgiPUX'YlRUb p1T`cPQYlPU}WG. ÆÜÑaÆÐê.
(417) yY.
(418) . }?X ^EG glgiYl}ACG [\KBEYl^EGB1gi¤'YlG hgiPU[¢o[WYhOETG VW[?RUG G;XtB~}WFmG PUg OG WYl`lYlG BBEglPUP]TWTW`¡ ghYlgi}?¨_PUG VW[Wgl^EOEYlgiVWP]X'GÖRUG G `y7FmP]`5G PU`l`c`~B;YlgiOEPUPUTWX'` YlY6X'RUbIRUqrT?G OE`l}WG G RUG Vb~RU[TWPUYip1O_PQ}?[\`iGsdEX'giRU9GWPQPQd!UO6G q;9I[?PQX¥T?O;YglGC/[~$pE`cFmglRB5G7T#X'Z T\P]`cYiG B;RQb? '`c^E^Ylglg BEB9[W0G
(419) X [GoqrYhPUT\`iG7¹X'[WgigiXtG'G B6Yi}?G
(420) TWPQORUKs^rYlG Yl[WPUgl^_TWPUTWOa`lg` B_T?AC`lGSB#^_Ks`[W ^_`iG,` B_X'^E[}Wgi}G,[Yl[^_glYlGNgiPU[WPU`oOEVWPU` RUGÖ`cYlFmgiPUX'G Yl`lRUB b; p!T?PQYl`lB(PYiPQ`k}?YiGsglP][\X¥YoYiRQG b [?XtOEBG V?PUO[YiYlPQG }?giG,PUTWgCKsp1[\T?^1PQ`lO`Y7 X'^Egi}[Yl^_glGÖPUO_`iX'giPQd!G q PQO[ `lFmT#T\YlB`l^Egc9[?X'Gs PQYlB`kYiglP]X¥YiRQbp1T`cPQYlPU}WGIKs[\^1`l` X ^Egl}[\Yl^EgiGW. ÓQÅ\Ø/²rº+´¿½t×7É¥À¶Ã¡Ê Ãkµ+³ ¿ÀÓU½t½'º9ØÉ¥Ç ÃcºaÊ ¾+¸ ³¸t½t¾+× ³µ+º9ËU½tÏkÃh·´ ¾+³Sã=½tÂ7µµÏcÂ7º9åt½i¾Âº9à PUPQVWYlB^Egi`cGYlgiy7PU X'Yl4=RUb;Agip!P][\T?OE`lPV?YiRQPQGo}?GSFmKsG7`c[WB^_`iT\` X'`cYl^EgigiPU}X'[YlRUYlb^_glOEG G V[YlPU}WGNKs[\^_`i` X ^Egi}[\Yl^EgiGZPUO_`iX'giPQd!G q;PQO
(421) [~`lFmTTWYlB`l^Egl9[WX G .
(422) I= ' ~
(423) *
(424) YiYiACBEglB_P]P][\`PU`sO_p1VWp_[\RU[WGop!gcG FmYsg7G sVW`lPUACB;}WG7B_X'`sGRUT?`cF`lT?G F6[\RUb~PUG6O{OEPUG7O?giG [\Yi`lG g^Egi[IFmRQY`cG FmT\qr¡P]T#[YlT\YiB_YiG~[\BYNgi`lG p_^E`l[W^Egc9gcRQ[?YiYN`sX'PUG?` WYiBE BEP]BEXtGBT`cT?Go[WRQglRUO_TG~TW ^_giPUFm`lOEG V;[Wq,RUpE` PQOgi[\TWgip!p_GoT?[WX'`lgcRUPYST?Yi`lPQx;T?GoOaYiG TSO_TWn pE^EglTWV?T^_B}?VWGIBEYlTSYiRUbBEYiGBE`cp!GZglG G7O_[W`cTW^_ giRPUFmYtOE`V[WTWRU[ ` YiTWTm¹YlPY7BE GN`cFmT#T\YiB`l^Egc9[?X'GZ[WO_q BEP]XtB;P]` X RQT`cGG OET?^EVWBmYiTIYiBEGN`lFmT#T\YlB;`l^Egl9[WX GZP]` 6T&Y8%
(425) -" 8% ". - ; < k V® l5® nÐY n *® o r "K0 !U&-8%P
(426) "T5 Q
(427) 819+&B "% ) @) " ) -(+ 7&B ) >G1 2 &
(428) @ ! ! &"T - ;&=R. 8 )5L J X|NFQ&
(429) @0 t 5 ,J | (+ -,J, b9!G~ L`R Z R ,jZ Rx R,ZcZ § R,Z&W § ]5R!-Z § ]5R0!-Z . . DGF. W. ÑÑ ×
(430) _Eà'ßP`ba. . . .
(431) HW. U
(432) -,
(433) &
(434) 5= ! -". A +5 ) R,Z* "T5 "T5U> ;" 5+N (+ -,J@, Rx R,jZZ "T5% "T5U> ";5+ (+ -,
(435) @, ]5R!-Z* "T5 ) &"T ,
(436) (+ -,
(437) &
(438) ".(+ ! >> 0 " !
(439) & @ *";5+ 8 & \B 8 &
(440) &=R ! ".A) ]"T5F -8%& >@0 &F ! t. WTACB_YiPUBE` GsfhYkgl T?p1TT`l`c^EPQYlglPU9TW[WO;X'G7qE` PQ giG X'YlRUb~PUFmpERQPUG `¡YlB_GoTWRURUT PQOEV
(441) TWgiTWRURU[WglbI B_PUXtB;X TWFmp_[\giG `hYlBEGN`cBET?gcYiG `cY¡p_[\YlB_` ~
(442) ® ® [|N 9r@ Q&«
(443) @ 0 tr " (50 )
(444) & Q,8
(445) P
(446) |"T5 9
(447) Q
(448) :81";"9+8&B " Q!
(449) :&FFQ " Q -!G(+ 7~ &R Q > 1 2 &
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