• Aucun résultat trouvé

Computing Signed Permutations of Polygon

N/A
N/A
Protected

Academic year: 2021

Partager "Computing Signed Permutations of Polygon"

Copied!
15
0
0

Texte intégral

(1)Computing Signed Permutations of Polygon. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters.. Citation. Aloupis, Greg et al. “Computing Signed Permutations of Polygon.” International Journal of Computational Geometry & Applications 21.01 (2011): 87–100.. As Published. http://dx.doi.org/10.1142/s0218195911003561. Publisher. World Scientific. Version. Author's final manuscript. Citable link. http://hdl.handle.net/1721.1/73973. Terms of Use. Creative Commons Attribution-Noncommercial-Share Alike 3.0. Detailed Terms. http://creativecommons.org/licenses/by-nc-sa/3.0/.

(2) 

(3)     !"

(4) # $%'&()+* , $./021436587:9<;>=!?:@ A BC0D9<@E1GFIHE?KJL,9<@E1GM NC0D?POQSRTQ1GUWVX?:F>1ZY [JD14\+VXF(]^VXF>3<140DUWVXF

(5) A _1GF>O(`(1G?aHb140dc `eVf02Ohgij140DUWVf0D@lk /m9on>\p0D?P1GnrqsR!qt9<;

(6) @2@DVX?:FjJ A uCvXwyxz|{l}Ex €~ ‚Eƒ#„

(7) †4‡ˆ E„l b‰Z†‹Š2‡‚ŒdEŠ2„ŽŠE‰X‘“’l Eˆ„G”4•T‚–p’— !‡ˆˆ˜™–GŠEš›ƒ#œEƒ#˜jž|Ÿb #¡“Ÿ#¢b¡“Ÿ#£b¡y¤y¤y¤¡ Ÿy¥D¦Z y¡“Ÿy¥4§2¨>•©ƒ,ƒª E«ˆ„ƒ–p’ƒ,ƒ¬‹ƒ#‘–'ŠEš—˜™ƒyEƒy‰“ E‡!ŠE†‹ƒy‰“ b–p‚Š2„l˜"–p’l b–t­l®¯+°"±²P® –p’lˆ˜>ƒ#œEƒ^‡ˆˆ˜™–y¨‰pƒ#˜p³l‡‚–pˆ„"ˆ„–p’ƒšŠE‰“« b–p‚Š2„ŠEšj „ƒy•´†‹Š2‡‚ŒdEŠ2„Zµo¶!’ƒ« Eˆ„ ŠE†‹ƒy‰“ b–p‚Š2„l˜©–p’l b–

(8) •©ƒ‘Š2„l˜pˆœƒy‰

(9) b‰pƒE·

(10) ¯p®¸E®¯“¹yºb» ¹>•T’lˆ‘“’¼ˆ„DEŠ2‡‚Eƒ—ˆ„DEƒy‰p–pˆ„"–p’ƒ ŠE‰“œƒy‰IŠEš T˜p³½4‡ˆˆ˜™–y¨D²¾¯™ºb¿¹K­À|¹+Á¾²¾ÁÂÀb¿¹f•T’lˆ‘“’ˆ„DEŠ2‡‚Eƒoˆ„D–™ƒy‰“‘“’l E„2ˆ„T˜p³½Z‘“’l Eˆ„l˜ Ž¾˜p³½4‡ˆˆ˜™–p˜+”“¨4 E„lœm®pÃ#Äd®ÅP¹+Æoº“­4¹T•T’lˆ‘“’ b‰pƒ" C˜™†‹ƒ#‘yˆ E‡f‘y E˜™ƒ" E„lœÇˆ„DEŠ2‡‚Eƒ"ˆ„D–™ƒy‰™È ‘“’l E„2ˆ„Ç–P•©Š‘Š2„l˜™ƒ#‘y³–p‚Eƒ¼ƒ#œEƒ#˜yµÉʘpˆ„–p’ƒ#˜™ƒ¼†‹ƒy‰“«^³–pˆ„ŠE†‹ƒy‰“ b–p‚Š2„l˜y¨ •©ƒ—ƒª›†4‡‚ŠE‰pƒ€–p’ƒ‘Š2«t†4‡‚ƒª‚–PŒ'ŠEšX†‹ƒy‰pšŠE‰“«ˆ„^‘ƒy‰p–p Eˆ„, E‘–p‚Š2„l˜y¨l˜p³l‘“’ E˜!‘Š2„›È Eƒª‚šŒ›ˆ„¼ C2‚Eƒ#„ †‹Š2‡‚ŒdEŠ2„ÇŠE‰—ŠE½l–p Eˆ„lˆ„¼‚–p˜€«‚‰p‰pŠE‰—ˆ« bEƒEµÌËS’ƒ#„ ƒ# E‘“’ ƒ#œEƒ'ŠEš

(11) –p’ƒ2‚Eƒ#„†‹Š2‡‚ŒdEŠ2„’l E˜Ì E‡ˆ˜™Š,½‹ƒyƒ#„ E˜p˜p‚2„ƒ#œ 8ÃbÁ¯p®pÍ#²¾ÁÂÀb¿ •©ƒC˜p #Œ –p’l b–o–p’ƒ!†‹Š2‡‚ŒdEŠ2„'ˆ˜>¹+Á‚ÄE¿‹®pÃbµjÎτ–p’lˆ˜‘y E˜™ƒÊ E„DŒtƒ#œEƒÊˆ„DEŠ2‡‚Eƒ#œ'ˆ„ ‰pƒyEƒy‰“˜p E‡ ‘“’l E„Eƒ#˜©œl‚‰pƒ#‘–p‚Š2„ZµX¶!’ƒT‘Š2«t†4‡‚ƒª‚–PŒ^ŠEšZ˜™Š2«tƒT†l‰pŠE½4‡‚ƒ#«˜<b b‰“‚ƒ#˜œƒy†‹ƒ#„lœlˆ„ Š2„'•T’ƒy–p’ƒy‰

(12) ̆‹Š2‡‚ŒdEŠ2„Cˆ˜©˜p‚2„ƒ#œ'ŠE‰

(13) ³l„l˜p‚2„ƒ#œZµXÐʄ¼ Eœlœl‚–p‚Š2„l E‡l‰pƒ#˜™–™‰“ˆ‘–p‚Š2„ ˆ„"« E„DŒ"‘y E˜™ƒ#˜oˆ˜X–p’l b–†‹Š2‡‚ŒdEŠ2„l˜X‰pƒ#« Eˆ„t˜pˆ«t†4‡‚ƒ> bš–™ƒy‰ƒyEƒy‰pŒ^†‹ƒy‰“«^³–p b–p‚Š2„Zµ Ñ ÒÓ Ô

(14) Õ

(15) Ö×mØmٗÔ

(16) Ú|ÖÓ Û܋ÝyÞßKà4Ý|܋á©ÞZâdá>ãfä|ä|åæ‹ç¾âdÝ|ä|èé+ä|Ý|ä|åêçìëCà›åCêދä€æ‹é+à›ã‹çä|íeàdßIá+à›é“êîå‹ïtâ^æfä|é+í¼ÜGêyâDêîà›å àdßfð îåêä|ï›ä|é+á

(17) ãë ñòódòñôbõdö ô€÷ ø^ù!ú›ûGü›ý€ù!úþ2ÿ ^á

(18) à›å‹ä€íîï›Þê>ï›Ü‹ä|á+á|ü4â"á+îå‹ï›çäÊé+ä ›ä|é+áâdç . 

(19)        "!

(20) #$%$'&(')+*%,.-0/1#$'23/546-87 9 *%

(21) :(:;:</.:=>

(22) !%?0*% ?#@

(23) ABC+  ED0#

(24) F?  G75HIJ

(25) ?# ?@ K@ L:%$("   $;MN6!

(26) #

(27) K7 ? ?7 = O /5 :#PD0#

(28) F?  G7RQG N+ ? ?7 ? :#E7 ?. . L  K7 ?. S AUTGWVX&R:J:Y":Z/.:=>

(29) !%?Z*% ?#@\[]]YX

(30) #

(31) : :L^*%_`!@\/5=a&

(32)  $%L@8AB4 ]`[%bcd

(33) @(D+*%4e@

(34) $%?=  #

(35) JN6=> 7 $%! f

(36) g !

(37) ??# D0#

(38) F?  G73

(39) ?#

(40) hN+? ?7 _`!

(41) ??# !E7 ? i D0#

(42) F?  G:3D `7j=. h:JFN+? ?7 !

(43) !E7 #

(44)  k.

(45) îáâdæ‹æ‹çîä|èêàâÝ|à›å‹á+ä|Ý|ÜGêî ›äá+äê'àdßTêދä|á+äîåêä|ï›ä|é+á'âdå‹èmêދä,é+ä|á+܋çìê'îá"êÞZâDêtêދä|îé à›é+è‹ä|éÌîáÌîå ›ä|é“êä|è —Þ‹ä däë8æ‹é+à›ã‹çä|í%êÞZâDêtâdé+îá+ä|áÌîáÌè‹äêä|é+íîå‹îå‹ï,êދäCíîå‹îí¼Ü‹í ål܋í¼ãfä|étàdßTé+ä ›ä|é+áâdçáå‹ä|Ý|ä|á+áâdé“ëmêàá+à›é“ê'â ï›î ›ä|åsæfä|é+í¼ÜGêyâDêîà›å —Þ‹îátål܋í¼ãfä|étîá Ýbâdççä|èêދäñòódòñôbõdö   ô Ï õ

(46)  yò—àdß>êދä'æfä|é+í¼ÜGêyâDêîà›å dâdé+î¾âDêîà›åàdß>êދîáÌæ‹é+à›ã‹çä|í îå ›à›ç ›ä|áC ô 

(47) Xò 'æfä|é+í¼ÜGêyâDêîà›å‹á,÷ ý—Û  ÿ ™åêދîá^Ýbâdá+ä,âdåëîåêä|ï›ä|étâ Xä|Ýêä|èsãë âï›î ›ä|åé+ä ›ä|é+áâdçoâdçá+à,ÝyÞZâdå‹ï›ä|á ‹õdñ   !âdÝyÞSàdßÊêދä|á+äÇîåêä|é+ä|á“êîå‹ïÝ|à›í¼ã‹îåZâDêà›é+î¾âdç©æ‹é+à›ã‹çä|íáÞZâdá'îìêáé+à4àdêáîå ã‹îà›îå  ßKà›é+íÇâDêîÝ|á âdå‹èríà›çä|Ý|܋ç¾âdéÇã‹îà›çà›ïdë(÷ ø^ù!ú›ûGü—ø^ù!"ú !Gü—ý€ù!úþ4$ü #%'Û &("4ü—ý—Û  ÿ ) æfä|Ý|î *ZÝbâdççìë›ülï›ä|å‹à›íä|á€ÞZ⠛ätãfä|ä|åíà4è‹ä|çä|è âdáÊçîå‹äbâdéTà›éÊÝë4Ý|çîÝ^á+,ä +l܋ä|å‹Ý|ä|á|.ü -ދä|é+ä äbâdÝyÞrä|çä|íä|åêîåâ á+,ä +l܋ä|å‹Ý|ä îá0â /|2ö 13 54àdßCá+íÇâdççä|éÇä|çä|íä|åêáêÞZâDêâdé+äså‹ä ›ä|é á+ä|æZâdéâDêä|è æfà›æ‹Ü‹ç¾âdéíà4è‹ä|ç

(48) ßKà›é'í¼ÜGêyâDêîà›å îå ›à›ç ›ä|áCîå ›ä|é“êîå‹ï8æZâdé“êá'àd߀êދä|á+ä á+,ä +l܋ä|å‹Ý|ä|á 6™åSà›é+è‹ä|étêà8è‹äêä|é+íîå‹ä,êދäål܋í¼ãfä|é'àd߀á+܋ÝyÞ í¼ÜGêyâDêîà›å‹átå‹ä|ä|è‹ä|èSêà êéâdå‹á“ßKà›é+íà›å‹ä"ï›ä|å‹à›íä^êà,âdå‹àdêދä|é|ü‹à›å‹ä"íÇâbëÇÝ|à›íæ‹ÜGêä^êދäté+ä ›ä|é+áâdçjè‹îá“êyâdå‹Ý|ä"àdß êދä,âdá+á+à4Ý|î¾âDêä|èsæfä|é+í¼ÜGêyâDêîà›å‹á ^åsä 74êä|å‹á+îà›å àdß!êދîátíà4è‹ä|ç©îá^êàÝ|à›å‹á+îè‹ä|é"êދä è‹îé+ä|Ýêîà›åàdß>äbâdÝy8Þ /|2ö 13 54 9—Þ‹îáÌçäbâdè‹áêàêދä'á“ê܋èGë8àdß>á+îï›å‹ä|è8æfä|é+í¼ÜGêyâDêîà›å‹á ;: ä îççÜ‹á“êéâDêä€á+îï›å‹ä|èîå ›ä|é+á+îà›å‹á!î=å <©îï›Ü‹é+ä -ދîÝyÞÇÞZâdá!ãfä|ä|åÇíà4è‹î *Zä|èßKé+à›í ÷ ý€ù!úþ2ÿ . . . . >. . . . k . . . . k . (. . . . . . `. . `. . . `. . Mouse. <©îï›Ü‹é+ä "k >. Human. . k. 1. 2. 3. 4. 5. 6. 7. 8. 1. 2. 5. 4. 3. 6. 7. 8. 1. 2. 7. 6. 3. 4. 5. 8. 1. 2. 7. 3. 6. 4. 5. 8. 1. 7. 2. 3. 6. 4. 5. 8. 3. 2. 7. 1. 6. 4. 5. 8. 4. 6. 1. 7. 2. 3. 5. 8. (íà›á“ê—æZâdé+á+îíà›å‹îà›Ü‹áÊä ›à›çÜGêîà›åZâdé“ëÇá+Ý|ä|åZâdé+îà¼ßKà›éÊêދä"êéâdå‹á“ßKà›é+íÇâDêîà›å àdßoÞl܋íÇâdåîåêàíà›Ü‹á+ä"Ýyދé+à›íà›á+à›íätâdá+á+܋íîå‹ï¼êÞZâDê€êދä@? Ýyދé+à›íà›á+à›íä"ä ›à›ç ›ä|á á+à›çä|çìëãëÇîå ›ä|é+á+îà›å‹át÷ ý€ù!úþ2ÿ A!âdÝyÞã‹çà4Ý5é+ä|æ‹é+ä|á+ä|åêáâ'Ý|à›å‹á+ä|é ›ä|èçîåBDâdï›äï›é+à›Ü‹æ àdß©ï›ä|å‹ä|á DCä ›ä|é+áâdçoè‹îá“êyâdå‹Ý|ätîá,ä +lÜZâdç<êà,á+Eî 7 . . . . `. . . —Þ‹ä¼æ‹é+à›ã‹çä|í. . ?. 5. àdß!Ý|à›íæ‹ÜGêîå‹ï' Pñ+õ

(49) GôF.1Eô  G1

(50) H ô Ïõ

(51)  yò^âdçá+àÇá“êä|íá^ßKé+à›í ã‹îà›îå  I.

(52) ßKà›é+íÇâDêîÝ|á ™åêދîá—Ýbâdá+ädüfâ¼êéâdå‹á+æfà›á+îìêîà›å îå ›à›ç ›ä|áÌä7GÝyÞZâdå‹ï›îå‹ïêF-Êàè‹îá  à›îåê—á+äêá àd߀Ý|à›å‹á+ä|Ý|ÜGêî ›ä îåêä|ï›ä|é+á'îåSâæfä|é+í¼ÜGêyâDêîà›å #Êà›íæ‹ÜGêîå‹ïé+ä ›ä|é+áâdçÊè‹îá“êyâdå‹Ý|äÞZâdá ãfä|ä|å á+ދ3à -å êàãfä^ù™ÞZâdé+è ÷ #€âdæZú›úDÿ

(53) ßKà›ét܋å‹á+îï›å‹ä|è æfä|é+í¼ÜGêyâDêîà›å‹á|üã‹ÜGêßKà›é"êދä á+îï›å‹ä|è ›ä|é+á+îà›å8âçîå‹äbâdéÊêîíäâdçï›à›é+îìêދí ä 7Gîá“êáC÷ ý—Û  ÿ ;#Êà›íæ‹ÜGêîå‹ï¼êéâdå‹á+æfà  á+îìêîà›åè‹îá“êyâdå‹Ý|ä^îáÊàdßj܋Bå lå‹3à -åÝ|à›íæ‹çä 7Gîìê™ë8÷ #%Û & "Dÿ —Þ‹ä"é+äbâdè‹ä|é€íÇâbëâdçá+àCãfä îåêä|é+ä|á“êä|èîå ÷ ý€ø  üIý€ù!ú›ûGü   &  ÿ ™åmêދîá"æZâdæfä|@ é -Êä,ä 74êä|å‹èsêދäîè‹äbâdá"íä|åêîà›å‹ä|èsâdãfà ›äßKé+à›í à›å‹äè‹îíä|å‹á+îà›å êà,Fê -Êà ;™å‹á“êäbâdè8àdß>Ý|à›å‹á+îè‹ä|é+îå‹ï,æfä|é+í¼ÜGêyâDêîà›å‹áàdß>îåêä|ï›ä|é+á|Bü -ÊäCÝ|à›å‹á+îè‹ä|éæfä|é+í¼Ü  êyâDêîà›å‹átàdߏò 3lòyô -ދîÝyÞsßKà›é+í.æfà›çìë4ï›à›å‹átà›étÝyÞZâdîå‹á : ä,è‹ ä *Zå‹ä  à›æfä|éâDêîà›å‹átá+܋ÝyÞ âdáò3lò:ô TõZôüñòódòñôbõdö ôâdå‹è Pñ+õ

(54) GôF.1Eô  G1

(55) GôüIîåâdåZâdçà›ïdë êà : äCîåêé+à4è‹Ü‹Ý|ä êދä,å‹àdêîà›å‹á"àdß ô 

(56) Xò  Zò

(57) ñ  Ï õ G1

(58) Gô 1.1Dö   1

(59) Gô õ

(60)  ‹ õ 

(61) Gô —Þ‹ä|á+äÝ|à›å‹Ý|ä|æGêá ï›î ›äté+îá+ätêàâ -îè‹äéâdå‹ï›ätàdß©æ‹é+à›ã‹çä|íá€êàãfätá+à›ç ›ä|è   ÓmÚÔ

(62) Ú|Ö Ó  <©îé+á“9ê -Êä'îåêé+à4è‹Ü‹Ý|ä"êދäå‹àdêîà›åàdß>âÇ ô 

(63) Xò  .1Dö   1

(64) à›é^ ô 

(65) Xò  Zò

(66) ñ  Ï õ G1

(67) àdß>â æfà›çìë4ï›à›å ^åëæfà›çìë4ï›à›å  íÇâbëãfäCè‹ä|á+Ý|é+îãfä|èãë8âçîá“êÌàdß

(68) ä|è‹ï›ä|á 

(69)    !¢  "£ !#!#!#$  ¥D¦Z

(70)    &¥ % á+îï›å‹ä|è6æfà›çìë4ï›à›å´îá,å‹à è‹î Xä|é+ä|åêbü€ä 7GÝ|ä|æGêÇêÞZâDêÇäbâdÝyÞ ä|è‹ï›äîáÇâdçá+à âdá+á+îï›å‹ä|è6âmè‹îé+ä|Ýêîà›å —Þ‹äáâdíäދà›çè‹áßKà›  éÝyÞZâdîå‹á 8—Þ‹îáîáâmï›ä|å‹ä|éâdç(î 'bâDêîà›å àdß!êދä,å‹àdêîà›åmàdßÊæZâdé+îìê™ëêÞZâDêîát܋á+ä|è î)å ÏßTêދäè‹îé+ä|Ýêîà›å‹átàdßÊâdçç©ä|è‹ï›ä|áCâdé+ä Ý|à›å‹á+îá“êä|åê¼âdá -Êä,êé⠛ä|é+á+äâæfà›çìë4ï›à›åsà›éÝyÞZâdîå<üêދä|å êދîáæfà›çìë4ï›à›å à›éÝyÞZâdîå îá 1Dñ : ò

(71) . ™ò  A™' å <©îï›Ü‹é+ä I -Êä'îççÜ‹á“êéâDêä^á+à›íäá+îï›å‹ä|èæfà›çìë4ï›à›å‹áâdå‹èÝyÞZâdîå‹á `. . . . . . k . . k . k. %. 3. `. . . . . . `. (. R. `. <©îï›Ü‹é+ä I > <Zé+à›í çäßÂêjêà^é+îï›Þêbüdâá+îï›å‹ä|èCæfà›çìë4ï›à›å<ü2á+îï›å‹ä|èCÝyÞZâdîå<üdà›é+îä|åêä|èCæfà›çìë4ï›à›å<ü à›é+îä|åêä|èÝyÞZâdîå :îìêދà›ÜGêÌçà›á+áàdß>ï›ä|å‹ä|éâdçîìê™ë›üZá+܋æ‹æfà›á+ä'êÞZâDê$-ÊäCâdé+ä'è‹äbâdçîå‹ï -îìêÞ8âdå8à›é+îä|åêä|è æfà›çìë4ï›à›å Pñ+ õ

(72) GFô .1E ô  G1

(73) àdß©Fê -Êà ä|è‹ï›ä|+á * âdå‹è ,îå ›à›ç ›ä|áÌîåêä|é+ÝyÞZâdå‹ï›îå‹ï,êދä|îé æfà›á+îìêîà›å‹ájá+à^êÞZâDêêދäÊé+ä|á+܋çìêîå‹ïÌæfà›çìë4ï›à›å'é+ä|íÇâdîå‹áà›é+îä|åêä|è —Þ‹îáoîáîççÜ‹á“êéâDêä|èîå. a. . . -.

(74) <©îï›Ü‹é+ä - Ïß *´âdå‹è,âdé+ä!Ý|à›å‹á+ä|Ý|ÜGêî ›ädüDêދîájà›æfä|éâDêîà›åtîájè‹ä *Zå‹ä|è¼âdáoâdå ò3lò:ô Tõ à›é'æ‹ç¾âdîå‹çìë ô Tõ  ©< îï›Ü‹é+äâ Ï ê¼îáå‹àdêCè‹îÝ|܋çìê'êàá+ä|äÇêÞZâDê'ä|åêîé+äÇá+܋ãfÝyÞZâdîå‹á íÇâbëâdçá+àãfä"êéâdå‹á+æfà›á+ä|è e ô 

(75) d öò+ò3l ò!êéâdå‹á+æfà›á+îìêîà›åîå ›à›ç ›ä|á€êéâdå‹á+æfà›á+îå‹ïâdå ä|è‹ï›ä - îìêÞ´âdå ä|íæGê™ë á+܋ãfÝyÞZâdîå "å‹äíÇâbë âdçá+àêދîåB àdßêދîá¼à›æfä|éâDêîà›å âdá,â êéâdå‹á+æfà›á+îìêîà›åmãfäêFÊ- ä|ä|å êދä,á+îå‹ï›çä¼ä|è‹ï›äÇâdå‹èsà›å‹ä,àdßÊîìêáå‹ä|îï›Þlãfà›é+îå‹ïá+܋ãfÝyÞZâdîå‹á  ©< îï›Ü‹é+ä ›ã  B’ A’. A B. <©îï›Ü‹é+ä - > oéâdå‹á+æfà›á+îå‹ïêF-Êàä|è‹ï›ä|á+*. (a). âdå‹è ,. (b) A. B B. A. <©îï›Ü‹é+ä

(76)  >  â\^åä|è‹ï›äá -€âdæ  ã \eá+îå‹ï›çä™ä|è‹ï›ä"êéâdå‹á+æfà›á+îìêîà›å. ñ òódòñôbõdöoàdß"âá+܋ãfÝyÞZâdîå´ãfä|çà›å‹ï›îå‹ï8êà âmæfà›çìë4ï›à›å îå ›à›ç ›ä|á,îå ›ä|é“êîå‹ïmêދä à›é+è‹ä|é^àdß>êދä¼ä|è‹ï›ä|á"îåêދä¼á+܋ãfÝyÞZâdîå

(77) tä|à›íäêé+îÝbâdççìëÇêދîá^é+àdêyâDêä|áÌêދäCá+܋ãfÝyÞZâdîå é+îï›îè‹çìë^îåêދäÊæ‹ç¾âdå‹ä!ãëCâdå¼âdå‹ï›çä!àdß á+àÌêÞZâDêoîìêáoä|å‹è‹æfà›îåêá©âdé+äTæ‹ç¾âdÝ|ä|èCä7‹âdÝêçìë'âDê äbâdÝyÞàdêދä|é  áà›é+îï›îåZâdçIçà4ÝbâDêîà›å <Zà›é€Ü‹å‹á+îï›å‹ä|èæfà›çìë4ï›à›å‹áÊêދîá—à›æfä|éâDêîà›åâdæ‹æfäbâdé+á îè‹ä|åêîÝbâdçêà êދä ;  4ñ

(78) à›æfä|éâDêîà›å8îåêé+à4è‹Ü‹Ý|ä|èmãë %dà›á+áâdå‹è ) ÞZâdå‹å‹à›å6÷   ÿ øÌ3à -Êä ›ä|é|ü€Þ‹ä|é+ä -Êäâdçç3à -é+ä ›ä|é+áâdçá,êàmêy â däæ‹ç¾âdÝ|äà›å6âdåë á+܋ãfÝyÞZâdîå<üÊå‹àdê,à›å‹çìë . . . . k . . . .

(79) à›å æfà4Ý5däêá <Zà›étá+îï›å‹ä|è æfà›çìë4ï›à›å‹á"êދäè‹îé+ä|Ýêîà›ås  àdßÊäbâdÝyÞ ä|è‹ï›äîå ›à›ç ›ä|è îåmêދä é+ä ›ä|é+áâdç>îá"á -îìêÝyދä|è<üâdá"îá^è‹à›å‹ä¼ßKà›é^æZâdé+îìê™ë8îå ™å <©îï›Ü‹é+äþ -ÊäîççÜ‹á“êéâDêäCâ é+ä ›ä|é+áâdç‹àdßIá+܋ãfÝyÞZâdîå  !#!#!#$  % ßKà›é>â^á+îï›å‹ä|è  îå‹îìêî¾âdççìë"à›é+îä|åêä|è æfà›çìë4ï›à›å "å‹ä `. . . . . . . a. b. ei+6. ej+1. ei−1 ei. ej. ei. ei−1. ej. ej+1. ei+6. <©îï›Ü‹é+ä'þ > Cä›ä|é+á+îå‹ïÇâá+܋ãfÝyÞZâdîåàdß>â,á+îï›å‹ä|èæfà›çìë4ï›à›å. Ýbâdåá+ä|ä€êÞZâDê>ßKà›é>܋å‹á+îï›å‹ä|è,æfà›çìë4ï›à›å‹á|ü›âdå,ä|è‹ï›ä™á -€âdæ,îá>íä|é+ä|çìëCâ^êéâdå‹á+æfà›á+îìêîà›å61Dñ âCé+ä ›ä|é+áâdç<àdßjFê -ÊàÝ|à›å‹á+ä|Ý|ÜGêî ›ää|è‹ï›ä|á <Zà›éÊá+îï›å‹ä|èæfà›çìë4ï›à›å‹áTêދä|é+ä"îá€âCè‹î Xä|é+ä|å‹Ý|ä îåêދäé+ä|á+܋çìêîå‹ïè‹îé+ä|Ýêîà›åàdß©äbâdÝyÞä|è‹ï›ä !âdÝyÞsàdß!êދä¼à›æfä|éâDêîà›å‹átâdãfà ›äé+ä|á+܋çìêá"îåêދä¼áâdíä¼á+ÞZâdæfä -ދä|ås܋á+ä|è à›åsâ æfà›çìë4ï›à›å<üé+ä|ïâdé+è‹çä|á+áTàdßXêދäÌè‹îé+ä|Ýêîà›å‹á!àdß<îìêá!ä|è‹ï›ä|á A™åÇàdêދä|é -Êà›é+è‹á|ülêàCÝ|à›íæ‹ÜGêä ދ3à -(âæfà›çìë4ï›à›åÝyÞZâdå‹ï›ä|áá+ÞZâdæfädüZà›å‹ätÝbâdåîíÇâdï›îå‹äÌêÞZâDê—îìê—îá—à›é+îä|åêä|è !øÌ3à -Êä ›ä|é|ü ßKà›é©ÝyÞZâdîå‹á

(80) âdçìêä|é+åZâDêäTè‹ ä *Zå‹îìêîà›å‹á©ä 7Gîá“ê A<Zà›éoä 7‹âdíæ‹çäÊÝ|à›å‹á+îè‹ä|é©êދä€à›é+îä|åêä|èÝyÞZâdîå îå <©îï›Ü‹é+ä ! : äíÇâbë8Ýyދà4à›á+ä¼êàæfä|é“ßKà›é+í â é+ä ›ä|é+áâdç

(81) à›åmä|è‹ï›ä|á  * , îåsâDê çäbâdá“ê>Fê -Êà -€âbë4á "å‹9ä -€âbë  á+ދ3à -åà›å¼êà› æ ©îá>îè‹ä|åêîÝbâdç4ê@à -ÞZâDê!îá

(82) è‹à›å‹ä€ßKà›é>æfà›çìë  ï›à›å‹á A—Þ‹îá—îá€Ý|à›å ›ä|å‹îä|åêÌã‹ÜGêÌâdçá+àíäbâdå‹á€êÞZâDê€êދätä|å‹è‹æfà›îåêá—àdßêދätÝyÞZâdîå -îçç å‹ä ›ä|é—íà ›ä (á+ä|Ý|à›å‹è -€âbë  á+ދ3à -åâDêÊêދä"ãfàdê+êà›í !îáTêà¼æ‹é+ä|á+ä|é ›äà›é+îä|åêyâDêîà›å —Þ‹îá'íÇâbësâdçç3à - êދäÝyÞZâdîå êàßKà›é+í íà›é+ä,îåêä|é+ä|á“êîå‹ïÝ|à›å *Zï›Ü‹éâDêîà›å‹á =: äÇ܋á+ä êދäç¾âDê+êä|é€è‹ ä *Zå‹îìêîà›åîå —Þ‹ä|à›é+ä|í - !îåêދäå‹ä 74êÌá+ä|Ýêîà›å tÕ Ø8Ô

(83) ÚbÓ (Ö ,Ö Ó  ) Ý|àdê+êt÷ ) Ý|àû I ÿXÞZâdáÊá+ދ3à -åÇêÞZâDêÊæ‹é+ä|Ý|îá+ä|çìë,Fê -Êà¼æfä|é+í¼ÜGêyâDêîà›å‹áTàdßâdåÇä|è‹ï›ä^çîá“ê!ßKà›é+í à›é+îä|åêä|è Ý|à›å ›ä 7´æfà›çìë4ï›à›å‹á|üTâdå‹èSêދä|á+äÞZ⠛äíÇâ 7GîíÇâdçTâdé+äbâ HÏêîá,âdçá+à lå‹3à -å êÞZâDê'îìßTêދä,çà›å‹ï›ä|á“ê'ä|è‹ï›äàd߀âæfà›çìë4ï›à›åsÞZâdá'܋å‹îìêçä|å‹ïdêÞ<üêދîátæfà›çìë4ï›à›åsíÇâbëmãfä æfä|é+í¼ÜGêä|èêà *‹êÌîåêà,â,Ý|îé+Ý|çä"àdß>éâdè‹îÜ‹á þ÷  dú2ÿ þ . . `. R. %. `. . (. . . `. `. . . % R8. ?. `. . . . .

(84) . . (. . . .

(85) C A. B A. B C A. C B. <©îï›Ü‹é+ä ! > 9-Êà -€âbë4áêÞZâDêÌâ,é+ä›ä|é+áâdçíÇâbë ãfäè‹ä *Zå‹ä|è8à›å8âÝyÞZâdîå. <Zà›éÌêދä¼é+ä|íÇâdîå‹è‹ä|é^àdß!êދîá^á+ä|Ýêîà›å -Êäæ‹é+ä|á+ä|åê'à›Ü‹é"é+ä|á+܋çìêá"Ý|à›å‹Ý|ä|é+å‹îå‹ïæfä|é  í¼ÜGêyâDêîà›å‹á"àdßTæfà›çìë4ï›à›å‹átà›é"ÝyÞZâdîå‹á : äîíæfà›á+äCêދäé+ä|á“êé+îÝêîà›åêÞZâDêá+îíæ‹çîÝ|îìê™ë í¼Ü‹á“êãfäíÇâdîåêyâdîå‹ä|èâDêÌâdççXêîíä|á|üG܋å‹çä|á+áÌíä|åêîà›å‹ä|èàdêދä|é -îá+ä ™H å <©îï›Ü‹é+ä ‹õ -Êä,á+ދ3à - âæfà›çìë4ï›à›å -ދîÝyÞ è‹à4ä|áå‹àdêCâdè‹íîìêtâdåësä|è‹ï›ä™á -€âdæ‹á 7‹âdíæ‹çä|á!á+܋ÝyÞâdá!êދîá!à›å‹äíÇâbëãfäÌä 74êä|å‹è‹ä|è äbâdá+îçìë¼êà'Ý|é+äbâDêä^âdåë,ð ™ï›à›å -ދîÝyÞ -îççjå‹àdê"âdè‹íîìêÌä|è‹ï›ä ™á -€âdæ‹á ™å <©îï›Ü‹é+ä B/ -ÊäCá+ދ3à - âæfà›çìë4ï›à›å -ދîÝyÞè‹à4ä|á^å‹àdê âdè‹íîìê€á+îå‹ï›çä ™ä|è‹ï›ä^êéâdå‹á+æfà›á+îìêîà›å‹á|ü -îìêÞêދätä 7GÝ|ä|æGêîà›åàdß©â¼ßK ä -hä|è‹ï›ä ™á -€âdæ‹áßKà›é á+à›íä ä|è‹ï›ä|á¼êÞZâDê,âdé+äâdçíà›á“êCÝ|à›ççîå‹äbâdé —Þ‹ä|á+äêéâdå‹á+æfà›á+îìêîà›å‹áCÝbâdå‹å‹àdê,ÝyÞZâdå‹ï›ä êދätãZâdá+îÝtá+ÞZâdæfä D—Þl܋á -Êä'á+ä|ätêÞZâDêá+à›íäêîíä|á€çà4ÝbâdçXæfä|é+í¼ÜGêyâDêîà›å‹;á -îççXå‹àdêãfä á+Ü Ý|îä|åêêàÇâdÝyދîä ›äè‹ä|á+îé+ä|è8é+ä|Ý|à›å *Zï›Ü‹éâDêîà›å‹á `. R. . `. . `. `. R. . `. . <©îï›Ü‹é+ä  >. . où à›çìë4ï›à›å  âè‹à4ä|áå‹àdêâdè‹íîìê,ä|è‹ï›ä™á -€âdæ‹á (ùoà›çìë4ï›à›å  ã è‹à4ä|áÇå‹àdê âdè‹íîìê—á+îå‹ï›çä™ä|è‹ï›ä^êéâdå‹á+æfà›á+îìêîà›å‹á `. `. !.

(86)  

(87)  ô  föò .1Dö   1

(88) õ  /#ò 51

(89) Zódò" €ò A   ð ¢  ñòódòñôbõdö ô  Âöò õ 

(90) . Ïõ 

(91) .

(92) ¼ô  fö G   õ  ™òñ¼òõ ñòódòñôbõdö Ê ñ131 —Þ‹îáé+ä|á+܋çìêދà›çè‹á ßKà›éêދäsíà›é+ämé+ä|á“êé+îÝêä|èhé+ä›ä|é+áâdçà›æfä|éâDêîà›åàdß  îæGê܋é+å‹áC÷ "ý# & "Dÿ   

(93) !" ô Ïõdñ

(94) :ô‹õZò .1Dö   1

(95)

(96) /#òH 51

(97) Zódò"  € ò A #  ð ¢  ò3lò ô TõZô  Âöò õ 

(98) . Ïõ 

(99) .

(100) —ô Ïõdñ

(101) :ô‹õZò

(102) XòyôyôÊõ  ™òñ—òõ ò3lò:ô Tõ%j$ õ

(103)   ô/1

(104)  ô   ;

(105) Zò ;1Dñô  õ2ôEò& Ê ñ131(j' äê*W) ãfä â æfà›îåêîåêދä dä|é+å‹ä|çCâdå‹è -îìêދà›ÜGêçà›á+áàdß¼ï›ä|å‹ä|éâdçîìê™ë á+܋æ‹æfà›á+ä^êÞZâDêTêދä^æfà›çìë4ï›à›åîáTà›é+îä|åêä|è Ý|çà4Ý5 -îá+äR Ïßjêދä^æfà›çìë4ï›à›åîáTå‹àdêÊÝ|à›å ›ä7Xü êދä|é+ä"í¼Ü‹á“ê—ä7Gîá“ê—êF-Êàá+܋Ý|Ý|ä|á+á+î ›ä'ä|è‹ï›ä|á,-.+ / âdå‹è*-+/10 -ދîÝyÞ / ßKà›é+í âCçäßÂê€ÞZâdå‹è ê܋é+å  á+ä|ä'<©îï›Ü‹é+äû›â ) îå‹Ý|äêދäæfà›çìë4ï›à›å îáá“êyâdé ™á+ÞZâdæfä|è<ü îá¼êދäà›å‹çìë ›ä|é“êä7´îå (a). (b) k’. a b. k. <©îï›Ü‹é+äû >32. b’. a c. c. k. á+îå‹ï,ä|è‹ï›ä™á -€âdæ‹áêàÝ|à›å ›ä7GîìßÂëâá“êyâdé ™á+ÞZâdæfä|èæfà›çìë4ï›à›å . êދäÝ|à›å‹äßKà›é+íä|èãëêދäÞZâdçìß ™çîå‹ä|á4) . âdå‹è*) 0 DÏß-Êä'ä|è‹ï›ä™á -€âdæ5-.+ / âdå‹/ è6-+/10 ü.-Êä à›ãGêy/8âd7 îåêދäCÝ|à›å *Zï›Ü‹éâDêîà›å8á+ދ3à -åîå <©îï›Ü‹é+ä'ûdã . 0 —Þ‹7 ä¼å‹ä -eæfà›á+îìêîà›åàdß  á+ދà3-å âdá tí¼Ü‹á“ê'ãfäá+à›í ä -ދä|é+äÇîåsêދä,êé+î¾âdå‹ï›çä  )  =—Þ‹äÇá -€âdæ‹æfä|èSä|è‹ï›ä|á¼âdé+ä á“êîçç 4îá+îã‹çä ßKé+à›9 í )füÊâdå‹è êދäë è‹à å‹àdêîåêä|é“ßKä|é+ä-îìêÞ êދäàdêދä|é,ä|è‹ï›ä|áàdßÌêދä æfà›çìë4ï›à›å —Þl܋á"êދä¼æfà›çìë4ï›à›å8é+ä|íÇâdîå‹áÌá“êyâdé ™á+ÞZâdæfä|è <Z܋é“êދä|é+íà›é+ä¼âdåë8æfà›îåê^îå êދä dä|é+å‹ä|çXé+ä|íÇâdîå‹áTîå,êދä dä|é+å‹ä|çjâdå‹è âdåëÇæfà›îåêTîåêދä^æfà›çìë4ï›à›åÇé+ä|íÇâdîå‹á!îåêދä æfà›çìë4ï›à›å  ›ä|é“ëä|è‹ï›ä 'íÇâbë ãfä"ßKà›Ü‹å‹èà›å‹çì= ë -îìêދîåâÞZâdçìßKæ‹ç¾âdå‹ä^è‹äêä|é+íîå‹ä|èãë-./ âçîå‹ä æZ-0=< âdéâdççä|ç

(106) êà êÞZâDêæZâdá+á+ä|áêދé+à›Ü‹ï›:Þ ) Ì3à - á+܋æ‹æfà›/ á+äêÞZâD0ê¼Fê -Êàsä|è‹ï›ä|á|;ü + âdå‹è + ßKà›é+í â é+îï›ÞêÞZâdå‹èê܋é+å —Þ‹îáíäbâdå‹á êÞZâDê âdå‹è Ý|à›îå‹Ý|îè‹ämâdáá+ދ3à -å. . a. . .. .

(107) b=c a. d. k halfplane of cd. halfplane of ab. <©îï›Ü‹é+äú >. ^åëæZâdîé€àdß©ä|è‹ï›ä|áÌíÇâbë ãfäá -€âdæ‹æfä|èâDêíà›á“êà›å‹Ý|ä . R. îå <©îï›Ü‹é+äú ÏêîáÇîíæfà›á+á+îã‹çäêàSíà ›ä8êދä|á+ää|è‹ï›ä|á -îìêދîå´êދä|îéÇé+ä|á+æfä|Ýêî ›ä ÞZâdçìßKæ‹ç¾âd/ å‹ä|á—0 âdå‹èîåêà,âçäßÂêÞZâdå‹èê܋é+å-îìêދà›ÜGêà›ã‹á“êé+܋Ýêîå‹ï 4îá+îã‹îçîìê™ëßKé+à›í ) êà ä|îìêދä|é à›é —Þl܋á!à›å‹Ý|äâ"æZâdîé©àdßfä|è‹ï›ä|á

(108) ßKà›é+íîå‹ï"â"çäßÂê

(109) ÞZâdå‹èê܋é+å,âdé+ä—á -€âdæ‹æfä|è<ü êދäë -îççGå‹ä ›ä|éTßKà›é+í âçäßÂê!ÞZâdå‹è,ê܋é+å âdïâdîå —Þ‹äÌæfà›çìë4ï›à›å -îççGãfä|Ý|à›íäÝ|à›å ›ä 7 à›å‹çìë -ދä|åêދä|é+ätâdé+ätå‹àá -€âdæ‹á€êàãfä"íÇâdè‹ä"à›å琢 äßÂê€ÞZâdå‹èê܋é+å‹á ) îå‹Ý|ätâdåë æZâdîé àdßÊä|è‹ï›ä|áíÇâbëmãfäá -€âdæ‹æfä|è âDêíà›á“êà›å‹Ý|ädü   ð ^á -€âdæ‹á'á+ÜÝ|äêàÝ|à›å ›ä7GîìßÂë â á“êyâdé ™á+ÞZâdæfä|èæfà›çìë4ï›à›å $™å <©îï›Ü‹é+ä  -Êä¼á+ދ3à -eêÞZâDê^êދîá^ãfà›Ü‹å‹èîáêîï›Þê @ ›ä|é“ë ä|è‹ï›ä   I  ð + I Cí¼Ü‹á“êãfäá -€âdæ‹æfä|è -îìêÞ ä|è‹ï›ä|á    !#!#!#$  ¦Z  ßKà›é¼êދä æfà›çìë4ï›à›å êàãfä|Ý|à›íätÝ|à›å ›ä7  %. . . . . `. . (. k. . . . 5. e. e. <©îï›Ü‹é+ä k  > Ý|à›å ›ä57. . . 1. n−2. á“êyâdé ™á+ÞZâdæfä|èæfà›çìë4ï›à›å - ދîÝyÞ'é+ä,+l܋îé+ä|á  ð ¢ Xä|è‹ï›ä™á -€âdæ‹áoêàãfä|Ý|à›íä û.

(110) <Zà›é€êދätßKà›ççà3-îå‹ïCêF-Êà,êދä|à›é+ä|íá-Êäè‹àå‹àdêä|åGßKà›é+Ý|ä'á+îíæ‹çîÝ|îìê™ë;  

(111) !

(112)  ò ™ òñ

(113) 

(114) .

(115)  Zò Zòñ—õ^ô  X

(116) ò;.D1 ö   1

(117) õ  #/ ò Z òñ

(118)  ™ò ô 

(119) . Pñ+õ G

(120) ôF.E1 ô  G1G

(121) ôCô316 ‹õ $ ô¼ô‹õZ ò  ôñ1Ï õ ™ ò /,  õ

(122) õ

(123) d öò 1   Ï õ 4 òyô  ðtçà›ï

(124) ð .  Çò

(125) Zò¼õdö l ò |/ ñ+õ G l ò5  ô G1

(126) 'P ñòyò =1 l òö 1  51  Ï õ G1

(127)  Êñ131  ) îå‹Ý|ä à›å‹çìë êéâdå‹á+æfà›á+îìêîà›å‹á¼âdé+äâdççà3Ê- ä|è<ü

(128) äbâdÝyÞ ä|è‹ï›ä àdßêދäæfà›çìë4ï›à›å í¼Ü‹á“ê

(129) ÞZâ(›ä—îìêá 15 .E1 ô ™ ò©âdçá+à"æ‹é+ä|á+ä|åê!îåCêދä€æfà›çìë4ï›à›å — ދîá>æ‹é+à›æfä|é“ê™ëâdçá+à^á+ÜÝ|ä|á îìßÊ- ä"è‹àCå‹àdê€îíæfà›á+ä—êދä"é+ä|á“êé+îÝêîà›åàdßjíÇâdîåêyâdîå‹îå‹ïá+îíæ‹çîÝ|îìê™ëâDê€âdçç‹êîíä|á`

(130) ýTë  à›æ‹æfà›á+îìêä Ê- äíäbâdå´âdå ä|è‹ï›ä- îìêÞ . êދ/ ä0 á< âdíäâdå‹ï›çädü!ã‹ÜGê,à›æ‹æfà›á+îìêäè‹îé+ä|Ýêîà›å. Z< à›é,ä‹7 âdíæ‹çädü€îå ©< îï›Ü‹é+ä k;k ä|è‹ï›ä|á àdß^êދä8æfà›çìë4ï›à›å´à›å´êދäçäßÂê âdé+ä íÇâDêÝyދä|èãë,ä|è‹ï›ä|á. / 0 <  ; — ދîá!íäbâdå‹á

(131) êÞZâDê!êދäÌá+ÞZâdæfäàdßXêދîá!æfà›çìë4ï›à›å,íÇâbë ãfä€é+àdêyâDêä|èãëâdå,âdå‹ï›çäÊàdß   á+ދà3- å,à›åé+îï›Þê  - îìêÞâdæ‹æ‹é+à›æ‹é+î¾âDêäTêéâdå‹á+æfà›á+îìêîà›å‹á` d e. a. b c. e b c. a. d. a. c. d b e. c b. a. e. d. <©îï›Ü‹é+ä k;k"> 'jäßÂê > âá+îï›å‹ä|è æfà›çìë4ï›à›åSßKà›é-ދîÝyÞ ä›ä|é“ë ä|è‹ï›äîá¼íÇâDêÝyދä|è ãë âdå  à›æ‹æfà›á+îìêä3 C îï›Þê > â—æfä|é+í¼ÜGêyâDêîà›åtàdß4êދä!æfà›çìë4ï›à›å -îìêÞtêދä!áâdíä

(132) á+ÞZâdæfäTé+àdêyâDêä|è. ãëâdå8âdå‹ï›çä"àdß . 8. Ïß;-Êäêéâdå‹á+ç¾âDêää›ä|é“ësä|è‹ï›äêàêދäà›é+îï›îå  á+àêÞZâDêêދäësâdé+äè‹îé+ä|Ýêä|è â -€âbë ßKé+à›í êދä¼à›é+îï›îå #ü Ê- äà›ãGêyâdîåmâÇá+äêàdßTðSæfà›îåêá` —Þ‹äá+ÞZâdæfäàdß

(133) êދäï›î ›ä|åmæfà›çìë . ï›à›åsÝbâdå ãfä,é+àdêyâDêä|è îìßÊâdå‹è à›å‹çìëîìßÊä ›ä|é“ësá+܋ÝyÞ æfà›îåêÞZâdá'âé+ä  ä|Ýêîà›åsêދé+à›Ü‹ï›Þ êދäà›é+îï›îå —Þ‹îá,Ýbâdå6ãfäè‹äêä|é+íîå‹ä|è îå:  ðtçà›ï

Références

Documents relatifs

• Nous proposons un nouvel algorithme pour le calcul et la représentation dans l’espace de Plücker de la visibilité mutuelle de deux polygones.. Ces travaux analysent et combinent

3UHPLqUHPHQW QRWUH WUDYDLO D SRXU EXW G¶pWDEOLU V¶LO H[LVWH XQH YDOHXU VDQJXLQH GH OD phosphatémie à partir de laquelle le risque CV et/ou de mortalité augmente chez

Encoding the injective parts of the function using Janssen et al.’s [25] succinct encoding, and the bijective parts of the function using one of our permutation encodings, yields

This is mainly established by the lower and upper bounds we know on the maximum values of these parameters for grids: while it is known that the maximum oriented chromatic number of

Moreover, in order to deal with the compromise between data load due to multiple viewpoints and image quality, the Layered Depth Video (LDV) selects a certain view as reference

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des

Keywords Regular class of permutations · Signature of a permutation · Uniform random sampling · Exponential generating function · Timed automata · Boltzmann

Definition 2.25 (quasi-oscillations). The element that is flipped is called the outer point of the quasi-oscillation. We also define the auxiliary substitution point to be the