Anisotropic Diagrams: Labelle Shewchuk approach revisited
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Anisotropic Diagrams: Labelle Shewchuk approach revisited Jean-Daniel Boissonnat — Camille Wormser — Mariette Yvinec. N° 5741 Novembre 2005. N 0249-6399. ISRN INRIA/RR--5741--FR+ENG. Thème SYM. apport de recherche.
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(77) "!. ͻͿ"d`b ¬[d¸oq`{d ±×tXuwu¤t§$v¤{-vw{dHx:zb u¤v½o~vwdHm 2. dpi (x, pi ) = xt Mi x − 2pti Mi x + pti Mi pi = −2qit x ˜ − 2pti Mi x + pti Mi pi. _*`bv¤m*v¤c-{uwv¤dIm$oq`b o d +Ço*±×tXuwu¤t§Cm¢oq`b o. = −2pˆi t x ˆ + pti Mi pi. pi (x, pi ). < dpj (x, pj ). 2. vw± [bt[{u¤kÅvw±. 2. 2. 2. kˆ x − pˆi k − (kpˆi k − pti Mi pi ) < kˆ x − pˆj k − (kpˆj k − ptj Mj pj ). v¤m$3uwt:mpdI} o~t oq`L oqt v½± bt[buwkÅvw±1oq`{d8t§ dI}*t± §$vwoq`}~dImqLdH>o¢oqt v¤m q8m c(t§¢ u¤d3uw}$dI}¢dIoquw`bu» [t[± vwo~m$xv¤8m*tdH§¢x:d3z{}*vw§$ [v½uwo~dI`Xo$}qpdHo~tmp8dIo o~t rLσdIpvwb¡ (_*vw`{vyoqm*`{{d}~t²J[tXdI}qmOtXoq{`Lt[ vºoI3¹{d3±×u¤t[u»}Ct± ELtX¡ vwxˆ:o z ∈ P ¹nrLdIvw{-v¤0σoq`{d _*`{d¾{}qdIlvwσtXzbm(u¤d3c-c( Ã[v¤[dHmÅ Π(z) tXbmpoq}~zb>o~vwtXÁt[± oq`{d¾ [{vympt[oq}~t[{vyp²Jt[}~t[{tXvCnvy [}4 c ¡ % mTv¤m §¢d3u¤uw·R¨l¡{t/C§$dI»b¹:dX¹tXvwcEsboqzn`boqd*v¤{o§ st[ ·ÇnLv¤tc-§¢d3d3b}¢mqnv¤t[v¤b [[ [}4u: Icª [mqd[vw ¹¬oqR`bd*3}qt[dHc-nzb{zndHo4mJ o~o~vwtstXstXt[c-±L {znmpoqvfYlv¤{·ÇnEv¤c- d3u¤tb§ mqv¤dIt[}Ob [tXu::3Xt[d lY-[d`lYz{uw`:u8zbv¤uw u R vym¸{d3dHndI ¡ _tÅ[d3ooq`bdE [{v¤mqto~}qtX{vy ²Jt[}~t[{tXvn¡vy X}~ [c0¹Lv½o }~d3c( v¤bm$o~t3t[c-{zno~doq`bdsv¤:oqd3}4mqdI>o~vwtX t[ [±*uwXoqt[`{}~dv½o~`{LcÄt§¢v¤d3}o~{`{v¤d [[±×t[}4u¤ u¤ct§$§$vw{vw-oq`mqdIoq>`{o~dvwtX»c-¹ [{vw±×t[uy P ¿¼d0ndo4 v¤uOo~`{dTtXc-{zno~ oqv¤t[bm}qdHx:z{vw}~dI rlk"t[z{} ! -,0> !$5 ¢ 0,T 10 i. j. i. j. i. i. D. D+1. ):<;. . BOU I 'DGS DH@,BO>A B
(78) L B.FHBO>)BO@ QV FGDH@<KV A. tXc-{znoqv¤{oq`{d-tXc-{uwd3oqd- {vymqtoq}~t[bv¤²Jt[}~t[{tXvnvy X}~ [c dYn{uwvyvwoqu¤kÀvym¸bto dI [mqk ¡ /t§ dI[dI}I¹8t[z{} c-dHmp`{v¤{Á u¤[t[}~vwoq`{c t[{u¤k }qdHx:z{vw}~dImÅoqt tXcEbznoqd¼²Jt[}~t[{tXv[dI}po~v¤3dIm ¡ ¿"d¾bt§ d Yn{uy v¤ `{t§oqt 3t[c-{zno~d-oq`{dHmpd(Xd3}qoqvydHm3¹»v¤ oq`bd-o§ t[·Çnv¤c-d3bmqv¤t[b [¡ u I [mqd ¡ CdI3 [uwuZoq`b o 0·Ç²C±Ó [3d-t± R c- ¬k¼rLd mqd3dIà [mhoq`bd({}qt[dIoqv¤t["t±$ 0°b{vwoqdTmqz{rbmqdot[± R _*`{vymmpd3ov¤mt[rno4 v¤{dI [mho~`{dÅv¤:oqd3}4mqdI>o~vwtX¼t[± -{v¤u¤ [v¤[{}4dI [cÄ}mptzb± rbmpL8¢ [§$dv½o~t`0±Joq`{tnd nv¤cE·÷ndIv¤bc-mqd3vwtXb¾mqvwtX= b6× t[uFr{c(o~ v¤b{v½dH±×ÀtXu¤ [m$o~`{6@dmpdIv¤d:oquwd3dI}4c-mqdIc->o~ -vwtX ¡ t8 ± ¡ oq`{}~d3d3d3u¤u¤mt± oq`bdLt§¢d3} _*`{d3t[c-Σ{zno4 oqv¤t[t±»2o~`{d ²Jt[}~t[{tXvLXd3}qoqvydHm §$`btXPmqduy r8d3uºvym {a, b, c} tXbmpvympo~m¢t±»o~`{dh±×t[u¤uwt§$v¤{ mpoqdIbm 6p 8 t[bmqvynd3}¢oq`b}qdId mqvwoqdIm a ¹ b b c mqzb4`oq`b o σ(a), σ(b), σ(c) 3t[}~}qdHmp8t[L-oqt( soq}~v¤ [{[u¤dhvw0oq`bd }qdI[z{uy }3t[c-{u¤d Y¼nzL uJo~t¡ o~`{d(8t§ dI}nv¤ [[}4 c¹ºv ¡ d ¡ mpzb4`¼oq`L ooq`bd3v¤}dIuwuym `b ¬[d- ÀtXc-cEtX {t[{·RdIcE{okÅvw:o~d3}4mpdH>oqv¤t[ 6R 8 t[c-{zno~d¢oq`{d*`lklLdI}q{uy bd H ¹§$`{vy4`vym1oq`bd¢rbv¤mqdIoqt[} t[± σ(a) b σ(b) ¹X Lo~`{d*`:kl8d3}~{uy {d ¹1§$`{vy4`¼vym oq`bd(r{v¤mqdIoqtX}t± L ¹ b¼o~`{d3"oq`bd3v¤}vw:o~d3}4mpdH>oqv¤t[Lm D L D H §$v½o~` P ¡ |Z}~ X>o~v¤I u¤uwkX¹ D b σ(b)D [}qdσ(c) }qdI{}~dImqd3:oqdHÃrlk oq`{dIvw}-{}~tdH>oqv¤t[Lmrlk Π ¹ b c-dH 2. 5. ab. bc. ab. ab. ïï ô g ~ü¬ý
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(80) " 5 _ ]". }qdHmp8dIoqv¤[dIuwk C L v¤ R vym C ab. ab. Cbc. ¡ _*`bdh3z{}qXdIm C b ab. Cbc. 2. }~d¸tX{vy3m t± R ¹{ bÅoq`{d dIx:zb oqv¤t[Åt[± 2. (xt Ma x − 2at Ma x + at Ma a) − (xt Mb x − 2bt Mb x + bt Mb b) = 0. ¿¼d{d3{t[oqd oq`bv¤m$dHx:zb o~vwtXrlk C (x) = 0 ¡ _*`{d dIx:zb o~vwtXt[± C v¤m*tXrno~ [vw{dHmqv¤cEv¤uy }~uwk ¡ 6@98 t[c-{zno~d oq`{dv¤:oqdI}~mqdIoqv¤t[0LtXvw:o~m*t[± C b C ¡ _*`bv¤m*v¤:oqd3}4mqdI>o~vwtXvym¢oq`bdmpd3oCt±²JtX}qtX{t[v [dI}po~v¤3dIm*§$`{t:mpd uy r8d3uºvym {a, b, c} v¤oq`{d²JtX}qtX{t[v»nvy X}~ [cÄt± {a, b, c} ¡ 6Ó 80+÷"oq`{dÅnvy X}~ [ct± S 6Óv ¡ d ¡ {t[o tX{u¤kÀoq`{}~d3d(mqv½o~dIm 8>¹1mptXcEd-t[±Ooq`bd(d3u¤d3c-d3:o~m t[± C ∩ C }~d {nv¤tcEo-dI²Jbt[mq}~vwtXt[ bt[vOXd3}qoqvydHmr8dI3 [zbmqdÅoq`bd3k rLdIuwtX{³o~t¾o~`{dd3u¤u¢t± ¾3uwt:mpdI}smqv½o~d ¡ % 33t[}4nv¤{[u¤k[¹ v¤ ¹Xoq`{dhu¤vw{dH }*mpzbrbmpL [d c( ¬k-v¤Xo~d3}4mpdH>o oq`{d¸Lt§¢d3}*dIuwuymOt[±
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