paper.dvi

Bản ghi

1 n interactive constraint-based system for drawing graphs The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters itation Kathy Ryall, Joe Marks, and Stuart M. Shieber. n interactive constraint-based system for drawing graphs. In Proceedings of the 10th nnual Symposium on User Interface Software and Technology (UIST), Published Version itable link Terms of Use This article was downloaded from Harvard University s DSH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at nrs.harvard.edu/urn-3:hul.instrepos:dash.current.terms-ofuse#l

2 n Interactive onstraint-ased System for Drawing Graphs! "#$!%&'($)+*,-/.$!0$)$1 2 3 )4&5(4% $! )!&67./8:99;<= >@?D <E ; 9 99<< *!FHG'(JI % $)0$!$1I &'K7L M7N5OPQ RS T UWVYX#Z 9<?[ K7\]* 2 ^_`$1K70&67UW8a<9? =; >@?Db? c5db 9?4cd =E ^,ë (ffg^ &JhI G^ i hj` Rf i 7klO'mnOJR Vo0$!&'&J$)0,p7GJ$)&'`G&5(qZr_ % Ks"#$!%&'($t+* 2 ^_`$1K70&67UW8a<9? = >@?Db? c5 E; d] 9=EE (4$!&J_u&JFg&J&5GJ('I 3%]KvI &5K7L STRT &Hwyxz{r (* (4&'^}$1(o,$)&JnGf$)%&#G`(+$) _`(4&5K&5K $)~- K]\q$!0(^,! 3K ^ &'K7$!L^ (4$! J&5K 0ƒ`( d < 7K7&5(o - &J\ &Jfˆ/` 0$) '&'(/&$!&'Gf$!,$! ^Š& G )1_un $)%&g^,&j`$!ƒ&'% $)L`(q(4*7(4&'^ ('IŒ (K7$!( $!0L$!($!0Ž- &5 L`&5( &#%7GJ_L1* -v(ƒ3&5g$1!$) '&'K,GJ (4n$!n( - 0ƒ:K7n]\q$)0363K: ($)^ ƒ!& GJ`(4n$! ( $1(4-lGf$) ^ &'Gn3$1(4^ `q )! \#(Y&ŽL3(4&'Y ^ $!ƒl 1 &&HK7n]\q$)0\q$)!&#&gGJ`(4n$!(Y&G$!%&I/&5(4& - &'L&'( &5(4L )$!0nƒ` K]\q$!0~&'K7$) 3 $1((Lƒu& $)g$!q^, *\]* (s`(&_`(4&5kwq^š&š0&'&jn `K ƒu \Y&'4- LvGJ`(4n$! ($1(+-lGf$) ^ &` K`(JI KEYWORDS nƒk7n]\q$)036g`(+$) _`(4&5K,1]*L'6K7n]\q$)`0!('6 G )1_un $)%&$!&J-lGJ&'('I OVERVIEW &~K7^ $!`@^ &Jƒ`Š$) &K7&'($!0 -#L`^ G^ ƒl7&j $)&JnGf$)Ž$!(r`&o% $)&'\ -`GJ^ ƒl7&jy( TJOJRf 'k DN RfI/8# `L0 $!&J-lGJ&'( _3(&'K,`$!( % $)&'\ `]%&#ƒ %&'K L`(4&J- L $!@%&J*Ž^ * (4&J4$!0(J6šL` )$)$!%& ƒ0&'((y$)@&#&5#- L^, G^ ƒl7&'r$!&jng$!ž^,]*]\ $tv&y_$! )$)+*$! &'Gfo\q$) &HG^Šƒ`L7&'Y(H nn ) mnr DN RfIoœ &H`]%&q_`L$) ) (4*7(4&J^6 GJ )!&'KŸžnwyxz{y 7 ƒ Z ]*L &'Gf$!%& $!0n^ V K7$)nˆ6- Y$!&'Gf$!%&g0nƒ!]*L756 ` 0$! J&'(`&@$!&JnG$!W$! s^ &@GJ!!_3$!%& ^,`&J 3 $! ƒ`&'%$!l3( 0nƒ` K]\q$!0 (* (4&'^,(JI & wrxz{r (* (4&'^ $1(W G`(+$) _`(4&5K K7n]\q$!0 &'K7$)WK7&'($)0&'K (ƒ3&5g$) 3GJ )!*~ &'`_` )&@L`(4&'(s&'(4$! )*~ƒ7k7l`g&š(4^, ) /`K ^ &'K7$!L^ (4$! J&5K:K7$10n^,('I & L`(4&' $1( &5(4ƒu`($!_ )& - ª4«u f ±n²]³5ýµ y q ±n¹ºh³] /¹5»'¼] D½ +¼] f Œ¹5 +ºµ¾»f ¼]ÀÁ±n f ±n qâuµrà ¼] +Ã Ä Âh 4¼Yº»ŒÅ'À Â Ä ±nã À Æ+ vç]à ¹ ±n l h 4ÃÁ±ºhÀ»f¹]Â4ÈJ±n¹]¼q¹]»nº ±n hç]à ºh ±n h oà ¹5É)»f #±ºhÀ»f¹ ±nã f ±n²5³]à Ê+ÂËvÌv³] + À Ây±#Ê+»f¹]ÂhÀ ¼] + ±nç]ã à À ºh + ±º Ä»f¹Ž f ±n²5³5½¼] ±4µrÀ ¹] q±nã ½ f»f À ºh³] qâ4è Ç Ä ºyÀ º ²5 À #±n À à Ê4»f¹5Ê4 + h¹]â/¹]»f¹]à ¹ºh 4 ±nêdº À Å oº +Ê ³]¹5À Í Ä +Â/É)»f ± Ä ºh»f #±º À ÊŒ f ±n²]³hãá±+» Ä ºYÎ Ï5È Ð5ÈÑfÑÈÑ4Ï ÈÑ4ÒÓË Qƒ`ƒ]Ô7$!^, &Ž1]*L7-Œ&Š7K7&'('6¾`K- H(ƒu&'G$)- * $)`0 K&'G1n $)%&J!* &Š %&Jn!r% $1(4L3 0`$) 5 $! - `&ŠK7$1 0^I & GJ^ ƒl7&j#gj %&'4n(o&'(&% $!(L` 0`$) 5 $! &'šl$!&j^ &J( $!Žg(&Œ-uG`(4n$!n( &Ô7ƒ&'((4&5K $!&J^ ( -y (4$!^ ƒ!&gƒ *7($!G'¾^ K&J 6`K~GJ!GJL!&5( &ƒ3(4$)$!`( -v0nƒ`$!g'_7õ+&'g(y%$1žƒ *7($!G'3($!^L1 $)viœ"#!$)e&# K$t$)`q&'Gf$!%&$!&J-lGJ&'(Š$!Ö\q`$!GnÖ`& L`(4&',^,e&5( &'šl&5(+ `K\$)(Š- &5(4ƒu`(&6qwrxz{r $1( - L! )* $) &JnG$!%&@(*7(+&J^ $! \q`$!gn _3 L`(4&'H`KQGJ^ ƒl7&jžgj Øu&5Gf &(4 &g-v`&hk7n]\q$!0($)^@ltn&'l`(!*iœ&(4*7( &J^ÙK&5( qƒ`l`(4&h\q$! )&H&L`(4&'#KK`(Y^Š %&'(Y7K7&'( )&J&'(@G`(+$)n(JIWZr$)e&J\q$1(4&6 &L3(4&'YGJ,$)&J%&J`&`K,GJ$! L&q $)&JnGfY\q$t,& K]\q$!0 (q`&š(*7(+&j^ K]Õ+L3(+n(7K7&@ƒ3(4$)$!3($!Q &J^ ƒ7q ($1(+- *,&Ž% $)L`( L`(&J (ƒ3&5g$) `&'K~G`(4n$!n(JI UW&Q(4ƒu&'GJ$tüGJ!!*6wyxz{r $!`Gƒun &'(sgj&j- L! )*ÛGn (&JÚ(&Ž-Šž4^,GJ G`(4n$!n(J6.$1(4L`YÜg0$! '$! Ý`&'L&'(.gÜHÝ/(nˆf6v\q`$!Gn &@!$!(4&5KQ$!ÚÝy$!0L`&?Þ &,ƒ ƒ` )$1GJ$! -Œ&5Gn.gÜHÝ $!($)! )L3(+&'K_ * mnolßnroh`k 4ßn OJR 1]*L7('I àû& L`(4&' (ƒ3&5g$) `&'K.gÜHÝ/(Ž&Šƒƒ!$!&'K _* G %&J$!0`&J^á$)@ (4&J -v(ƒ$!0!$)e&- ng&5( ؾ&'G$!0& ` K&'(H$)Ús0nƒQK]\q$!0`I 8gKK7$)$!` /- ng&5(g&š$) KL`G&5K,L7^, $!G'! )*Ž ƒ&'(&j%&(4* Gf$!GqGJ&5Gf`&'((/- &qk7n]\q$)03iy&l`(&jœ^,]*!(hƒƒ!*ž- ng&k7$!&5gf )*ŽŽ ` K& _ *sk7n00$!0 $t\q$)& ^ L3(4&IY& ` K&'('6`\q$1Gn &g^ K&J!&'K (Yƒu$!Y^,((&'('6 &^Š %&'K,$!@^Š$!$!^L^ &'&J0*âG `0Ln $)`(_ *âûƒ`*7($!g' ($)^@L1 $!ã_`(4&5k ~Š0&J&' )$! J&5K - GJ& K7$)&'G&5K!0$)`^åä d æ 6\q`(&H_u& 3]%$!q$1(#&5($)!*sƒƒ&'GJ$!&'K`K$)ç`L&J3G&'K_ *s&l`(4&''i `&Š($)^@L1 $! - & ƒ *7(4$1GJ ^ 7K7&' $1($!^, &'K G $) LL`( )*6rL3(ƒ % $!K$)0 L3(4&J- Lo% $1(4L` - &'&'K7_`GneW & L3(4&'ä? 6?'b æ Iq8# )`L0 \Y&5e ^ &'Gn3$1(4^Ù- ( $!(4- * $)`0 GJ`(4n$!('6&J`&J0* ^ $!$!^Š$! '$!L0 ƒ`*7($!g'r($!^ L`!$!3`K7!&'(y %&' G`(4n$!&'K(* (4&'^,(y0G&J- L )!*6 `K ƒ` % $1K7&'(~&'(4$!!* L`K7&'(4 7Ks^Š&Jƒ- &ŽL3(4&''I è Ìv³] + Œé ê ëây³]±4å Ç 4 +¹ŽÀ ¹]Ê+»f h²»f ±º +¼²5 DÅ5À» Ä Â Ã gà ¹gºµ»qÇ ±ºhÊ ³ Âh 'Âhºh 4 qâ¾é)»f v f ±n²]³ãá±4» Ä º Î ì5è]íóë`ìr³5 Œ²] + +¹ºrÂh 'Âhºh 4 À  º ³5 /î Âlº º» ±nã ûµ@À ¹Jºh + ±nêdº À Å 3 ² +Ê+À î Ê4±º À»f¹Y±n¹]¼ #±n¹]à ² Ä ÃÁ±ºhÀ»f¹Œ»nÉ]² + ÂhÀ Âhºh +¹Jº7³5À f³5½ à +Å +Ãé ê ë`ââ Ä Ê ³o±n ºh³] + fë7ï¹o +ÃÁ±ºh 4¼Œµ»f h Èðy +¹] l ±n¹]¼oð Ä ¼]»f¹o³ ±4Å ¼] + Ê+ À Ç +¼±n¹gÀ ¹º + ±nê+ºhà Å / f ±n²]³5½ãá±+» Ä ºvÂh 'Âhºh + ºh³ ±º Ä Âh 4Âv± ¼]À ñ + +¹º  Dºr»nɹ]»f¹]² +  À Âlº +¹º ÃÁ±+» Ä ºy»f² + ±º»f hâyî òóë

3 (a) (b) (c) (d) Figure 2: User intervention is required to find a globally optimal solution. D lignment Even Spacing Sequence luster T Shape Zone Symmetry D Dwrxz{r ¾6 L`(&JY^,$!ƒL1 $)`(o&#l3(4&j- L¾o!*@- o&jô ƒ` )$!0K7&'($)0Št&J` $)%&'( _L7Œ- /ƒ % $1K7$!0sžK7% $1G&5# &Ž(4*7(4&'^ \q&j$) ``K(q$)(&J )-y$! Š)7GJ¾ƒ7$)^@L^I Ýy$!0 L`&@9Š$1(H,(4$!^ ƒ )&@&Ô^ ƒ!&i DWÝ $!0L&@9 hˆ6`\ &(4&'&Ž`&'& ` K&'('6yG&5Gf&5KQ_ *Q+\Y~&'K70&'('I &,L`(&JŽ`(ŽKK&'K ($!0!& 8#!$)0^ &J.gÜHÝ,&(&- 7K7&5(JI&(*7(+&J^ 4&J^ ƒ7(# ( $!(4- * $1(gGJ`(4n$!_ *~^ %$!0 &Ž`&'& ` K&'(¾ \ KH$!^Šƒ` )$1G$)r$! Jn!$)`&ŒL`$)`0qL`0 &%&'4$!G' G&'$!K -y&&'&7k7&'( Þ ^ &' \q$!!&6& (* G$1GsGJ`(4n$!@ƒ`$)_$)$!0Ú %&'1ƒ ƒ` % $1K7&'(Š & ƒ`l!($!%&ž- GJ& _3&J+\Y&'&J 7K7&5(g`K&'K0&'('Iq DQÝ $!0L&9 l_3ˆf6 wyxz{r `( ^ %&5K 7K7&g8âK7 \qv6 `K ` K&'( [ `K 2 Lƒ \nk('ir& `&'&Y7K7&5(/GJ` _3&q!$!0&5K 6 \ &J%&''6 K7L`& &,&5K70& _u&+\ &J&' [ `K 2 I [ *Q^,L3!)*W^ % $!0~8 *\q`&j&`&!&-y- [ hýy$!0l`&9` lg'ˆˆf6&gl`(&j _7$)`( sƒ7$!^,rn`0&j^ &' lý $!0L& 9 lk3ˆ4ˆfi `&'(& $!&JnG$!`(@7GJGL`Š( &~($!^L1 $) $!(@L$!0`6 `K!! \ &@GJ^ ƒl7&jg`k (* (4&'^Ù0&`&J# G )1_ & $! 3`K7$!0Q_u&&J 0 )_` (4 )L7$)`(W&~$)^ ƒ!$!gj$t GJ`(4n$! ($1(+-lGf$) ƒ_!&j^i p L`GnãK7% $1G&Ú$!(&5(4ƒu& GJ$! )!* L`(&- L` #$)ÛG'(&'( - %&',L`K7&'GJ`(4n$!&'K K7& ($!0`('I - (& -H.gÜHÝ/(,0&J&'&'(,Û %&'GJ`(4n$!&'K 1]*L7'6`wyxz{y \q$!!¾ ``K &Ž&5&'(4(4_!&HGJ7 `0Ln $!r6 \q`$!gnû^,]* ( $!(4- * K7$tؾ&J&J.gÜHÝ/( % * $)`0 K7&J0&'&'('I `&sl`(&j56œ\qúg!( &K7&5(4$!0 ƒ7gj&'((@š 0!_`!&J%&J &WGn$!GJ&-g.gÜHÝ/(,`K & 0((Šƒ1G&'^ &J,- ` K&'( $! `&K7$10n^ ˆ6GJ &'($! )*@0L$1K7&q&G^ ƒl7&' 3`KW^ &@( $!(4-lG*(4 )L$!`(H`K G'G&Jƒ_` )&@!]*L7n( _ *~^ %$!0 ` K&'(gK]Õ+L`(4$!0.gÜHÝ/('I# DQGJ(4&-ŒL`K7&' GJ`(4n$!&5K!]*L7n(r\q$)@^L )$!ƒ!& (!L7$!3(J65`&YL`(&J/GJ!(Šƒ % $1K7&ŽK7% $1G&H &JÔ ƒ` )&Ž )&'3 $!%&5(JI D &g&ô (&'G$! \ &#$!)!L`(4n &#`&L`(&-rwyxz{r _ *,K7& (G$!_$)`0 +* ƒ$!g'y$)&'gf$)- ^,L3(4&' (qƒu&jn(4ƒu&'g$!%&i œ & &JŠK7&'(G$!_3&o&YL`K7&'!* $)0HG`(+$) (ƒ3&5g$) 3GJ$! `K ( $!(4-lG$!~^Š&5Gn``$!(^,($)K7&n$!hI Hub Shape Figure 1: Visual Organization Features (after [9]). EXMPLE INTERTION Ý $!0L&'(= c (4` \á(`ƒ3(4(-q% $)L`(Ž$!&J^ &'K7$1 & (40&5(Œ$) &#ƒ7g&5((œ-¾k]\q$!0 0$!%&' 0nƒvI/Ý $)0L&#= K&Jƒ$1Gfn(¾&YG^ ƒ!&&o(* (4&'^ $!&J-lGJ& Þ &J¾ 30L&'(v( \!*,& G' % (&'`I

4 GaussianRandomNum Particle ParticleDistribution VirtualParallelMachine Ion Electron Plasma Grid locktimer EnergyDiagnostic Figure 3: Initial layout, with labeled nodes and edges, shown in the context of the wyxz{y interface. j`m i `O Figure Ák,O 3 5: User adds three more VOFs: and. i,oj hrf GaussianRandomNum GaussianRandomNum Particle ParticleDistribution VirtualParallelMachine lass Inheritance Particle ParticleDistribution VirtualParallelMachine Ion Plasma Grid Use Relationship Ion Electron Plasma Grid Electron locktimer locktimer EnergyDiagnostic EnergyDiagnostic uxiliary lass Figure 4: User adds an tk O ` VOF to each row. i ` Jk! " Figure Áj Tf OJRfk! " $# O 6: User adds three text labels, Ák,O 3 and three VOFs: and. Ý (4$!^ ƒ!$!gj$t+*š-¾&ô7ƒu($t$)v6 `&q&ô^ ƒ!&q$)&jngf$)šk& ƒ$1gf&'k `&J&Y$1(r_3(&'KŽ@qn(eŽ$)@\q$1GnŽ& L`(&JŒ &'^Šƒ( ~G&'& ƒ`$1gl1g!]*l7)&'k7*~&j % $!($)&'Kv63n &J 3Ö&Ô7ƒ!$)0Ú)&'3 $!%&~1]*L('IÖ&L`(&J,ƒ`!G&'( (& - 7K7&'( $) ƒ`ƒ]ô7$!^, &')*& K7&5(4$!&5KQ1]*L7L`(4$!0 (43KnK K$)&'G ^ $!ƒl1 $! &5Gn$1šL&'('I,V %&' Ž$1( (40&6u \ &J%&''6& (4*7(4&'^ $1(`&J!ƒ$)`0 Lg_ * L7^, $ GJ )!* &J7- GJ$)`0ƒ$!_$)$!`(Y-y %&J1ƒƒ$!0 ` K&'( Þ ` K&'(,G!(&H0&&Jq\q$!!v_3&Ž&Jƒu&J!!&'K - ^ &'Gns&''I VoK0&'('67K7$!&5Gf&5K L``K7$!&5Gf&5K 67!$)&540`h6GJ _u& KK7&'K _3&J+\Y&'&J 7K7&5(JI Ý $)0L& =( \#( &!]*L7 -&J $!$)$1 ` K& `KQ&5K70& ƒ`!g&j^ &'Žƒ3(&I #&  À ÂŒÂhº ±n¹]¼ ±n h¼šà ¹¼] ±+µyà ¹5 gºh»'»fã Â4È º ³5 Ä Â + Œ³ ±nâoê+»f¹jºh»fã3»å + ± Åf±n hà Dº»nÉ f ±n²]³]à Ê4±nò] h»f² + lº À +Âu»nɺh³] ¹]»J¼] +ÂÈJÀ ¹]Ê+Ã Ä ¼5À ¹] ŒÂ ³ ±n² fèjé!»f¹ºè Ç ±nê J f» Ä ¹]¼#Ê4»fûf 4ÈfÉ!»f h + f» Ä ¹]¼ Ê4»fûf 4ÈÇ»f ¼] + uê+»fã»f 4ÈJ±n¹]¼¼]À q +¹]ÂhÀ»f¹]ÂË Ìv³] + Y±n ¼] + À Å +¼É)»f Âl 5Âlº + Û¼] DÉ!± Ä Ã ºhÂÈ µr³]à Ê ³ŽÊ4±n¹ŽÇ YÂh Dº/Ç Hºh³] Ä Âh 4 4È3±n¹]¼, q»'¼5à î +¼,±ºq±n¹ ŠºhÀ q Å5ÀÁ± ±¼]ÀÁ±nûf ǻ˾±nÊ ³,¹5»'¼] À  ± Ä ºh»f #±º À Ê4±nà à gâ À Æ+ +¼Hºh»#±nÊ4Ê+»f q q»j¼ ±ºh oà ºh ÃÁ±nÇ +à À É3±¹]»J¼]  ÃÁ±nÇ +à À Â Ê ³ ±n¹5 f 4¼Èºh³] Âh 'Âhºh + ÖµrÀ à à ± Ä ºh»f #±ºhÀ ʱnà à g +¹]ÃÁ±n f o±¹]»j¼] Œºh»#±nÊ4Ê+»f ½ q»j¼ ±º gà º Âq¹5 +µ ÃÁ±nÇ +Ã1ËsÌv³] + Ê4±n² ±nç]à à À ºhÀ +Â#±n g¹]»nº#â ³]»4µr¹sÀ ¹,ºh³] î Ä h +ÂË &H03`&5K70&g_3&J+\Y&'&J &~ž%œ4$!gj )&5 $1(+$!_L7$)` `K žvo )&5Gf37K7&5(JI/&(*7(+&J^}\q$)!^,$!$!Š& 0` )$)+* GJ`(4n$! lg^ ƒ$1($)0w+\yw)$!0^ &'ŠG (4n$!( `K ƒ3^ 7K7&'& (4&'& _u&j! \ĤL`0L7 & K7&5(4$!0~ƒ GJ&'((JI ykk.gühý & 1]*L'6 & L`(&J `(4~(&J!&'G(s (& -#` K&'(ŠL`($)0 (+n`k`nk ^ L`(& &'Gn$1šL&'(Š(L`Gn( GJ )$1Gnë $)`0W@&'0$! K7n00$)`0`I & L3(4&'^,]* &'ƒƒ` )* & #^ &.gühý/(q &Š(4&J_ *~ƒ`&5(($)`0 &Šƒƒƒ`$ &HƒL`( _L4`('67 )7GJ&5K &$)0Y-r&\q$!`K7 \ $! Ý $!0L&Ž=I/ DÝy$!0L`&È 6 &ŽL`(&J`(qƒƒ!$!&'K`$) ' 8 )$!0`^Š&'.gÜHÝÛ &s(4&5g3k 6r$!K 6/3K - LÚ \#( -y7k7&5(jiœ8g(q.gühý/( &ƒ`ƒ )$!&'K Š&Ž`(G&'K7$10^6 0ƒ$1GJ7$)`K$!G' (/-3&GJ`(4n$!(Œ&qKK&'K I/ DŠ& $!^ ƒ!&j^ &J&5KW(* (4&'^63&0ƒ$1GJv.gÜHÝÖ$)`K$!G' (g& ( \qû% $1(4L` )!*Ö_*Û K*3^ $!GQ$!0!$)0$!0 ^ &'Gn`$1(4^ ` og'` _u&#&'ƒ!$!g' &5K$! (4 $!G$!^,0&'('Irœ &q&'&j- & L3(4&(43K7&5(o-r0n]*@$!`K7$1GJ&K7$)Øu&'&'.gÜHÝ/( $) &g `0 L`& Þ &0&J* &'Gfn0 )&5(o$!Ýy$!0L`&HEŠ(&J%&H( 0ƒ$1GJ $!`K7$1GJq-r& 8#!$!0^ &J#.gÜHÝ/('I

5 (gƒ3&'(ƒu&'gf$)%&6ywyxz{y $1(g~($)^ ƒ (v- ng& $!( &'y&jô^ ƒ ( Zy]\ (&'(4g GaussianRandomNum ƒ`*7($!g'œ($)^@l!$!vi DÚKK$t$)v6v\ &!( K7&'(G$!_3&Š \ &WG`(4n$!n(,`K GJ`(4n$! ($1(+-lGf$! ƒ GJ&'((,& ^,K7&Žƒƒ`&' Š&ŽL`(&J5I Particle ParticleDistribution VirtualParallelMachine lass Inheritance Use Relationship Ion Electron Plasma Grid locktimer uxiliary lass Figure 7: The finished layout. EnergyDiagnostic &Q(*7(+&J^ ($1(+ 3&'( &'(&QG`(4n$!n(,% $! & ($!^L1 $!!0$)^ K7&'(G$!_3&5K $) ^ &K7&n$!y_u&J! \ŽIH D`K7&J&5K 6 ^ %&'^Š&'-r&Ž7K7&'(,($1(+- *,& G`(4n$!n( \YL!K +* ƒ$1gj!!*,ƒ7gj&j&'k \q$!)&g&l`(&j$1(kk7$!0š^ &g.gühý/('i Ý $)0L& d ( \#(q&@(4_!&g7 `0L`$!3 g&'`(l&'(g - &'/& &'& 8 )$!0`^Š&'/.gÜHÝ/(/`]%&o_u&J&' ( $!(4 `&5K 6!0 \q$) &J& ^Š&Y.gÜHÝ/(r& L`(4&'/`( KK&'K I ÜgŽ`& $!0'6 `& L`(&J 3(KK7&5K #L_ p7`ƒu&.gühý 6r$!`K7$1GJ&5K (!$)0g0n]*sG$!nG!&I&@G&J&Jg+\Y,7K7&5(@ hke~0n]*7ˆ& s_3& %&J$1GJ!!*~)$!0&5K IÝy$!`)!*6¾&- LH7K7&'(gQ&!&-#`]%&H3K~ p7*^ ^ &*s.gühý ƒ`ƒ)$!&'ks@&j^i Üg`GJ&o0$!v6&Y(*7(+&J^â4&J^ ƒ7(rg($1(+- *H!- &YGJ (4n$!n(J6u_u 1KW3K &J\Ž6¾$!QK7&J&J^ $)`$)0~&'Gn 7K7& ( ƒ1gj&j^ &J'I Ý $!0L& b ( \#(Y`&ŽLƒuK` &5K~7K7&ƒ3(4$)$!`('I VoGn \â$!(g(+$)!y)$!0&5k 63`K~`& &J\ã.gÜHÝ/(#3]%&Ž_u&J&J ( $1(4 `&'KÚ(\ &J! I D KK7$)$!r6v`& L`(&J K`K(`&'& &Ô 1_u&J1(ŽQ&!]*L75IWr&JÔ@!_3&'!(Š& (4$!^ ƒ!*úq(4ƒu&'gj$! $! J&'K 7K7&#+* ƒu&iœ&l3(4&'o`(yƒƒ!$)&5k &J&^Š&.gÜHÝ ('6 \q$1gn \q$!! _u&&'žƒ3(4$)$! &'GnQ-o&Š&JÔ 1_u&J1('I@&!$)0 0]* 7K7&5(â&!&-Q&Ú(L_7Õ+&'G Û 2 )L3(+&J.gÜHÝ Iq& K`e 0n]*` K&'(~ & _34^ & Ö_3& $! Jn!)* )$!0&5K I &~^ $!KK)&~`&'&s7K7&5(J6Y(4`K7&'K ^ &'K7$!L^å0]*6u&s_3& &J%&J!* (4ƒ3G&5K IŽÝ $)0L& c ( \#( `& `` 1]*L7q0&'&Jn &'K _ * &- L!r(&q-/$!&Ž.gÜHÝ/(JI IMPLEMENTTION Ý^ sl`(&j!&@`$)0!&j%&j $!&J-lGJ& - K`K7$)`0s3KWK7&J!&$)`0 7K7&5(g`KW&5K70&5(J6¾`K - sƒƒ!* $)`0Ú`KÖ&'^ %$!0Ú% $)L`(.gÜHÝ/(J6Y`&J&J_ *$! K7L`GJ$)`0Š`&J\ãK7]\q$!0(JI/$1( -lgjk7&$!(^,$)$)`&'ks_* & L`K&J )* $!0(* (4&'^6\q$1Gn,$!(YG$) L`)!*@n`(!$!0ŽL`(&J G$!`( $!! \!&J%&J#GJ`(4n$!(Š3 $) &'Ö$)&5( ( $1(4- *I D~`$!(g(4&5Gf$!r6\Y&ŽK7&5(GJ$!_u&& &J1 $)`($)ƒ~_u& +\ &J&J& $!0!&J%&Jv.gÜHÝ/(`K~`&! \!&J%&JvG`(4n$! ^ &'Gn`$1(4^,('6`KÖ \ &QGJ`(4n$!(,& ( $1(4 `&'KÖ_ * Ìr³5 Âl 5Âlº + À Â/µr À ºlº +¹ À ¹ ÌvÊ4ÃÌv ȵrÀ ºh³ ºh³] ÂhÀ Ä ÃÁ±ºhÀ»f¹ µr À ºlº +¹sÀ ¹ ˾Ìv³]  À Ä ÃÁ±ºhÀ»f¹ Ä ¹]ÂÊ+»f¹JºhÀ ¹ Ä ±nã à JÈy²»fà à À ¹] ŠÉ)»f Ä Â + À ¹]² Ä º Ä ÂhÀ ¹] Šºh³] ŠÉ1±nÊ+À à À º ¼ Ä hà ¹] ÂhÊ4 h + 4¹ Ä ²¼ ±ºh 4Â4Ë ï¹~ºh³]à  #±n¹]¹] + 4È Ä Âh + ŒÀ ¹]² Ä º Ê4±n¹ŠÇ YÀ q q 4¼5ÀÁ±º +à h +Ê+ºh +¼ŠÀ ¹Žºh³] ²]³ 5ÂhÀ Ê4±nà  À Ä ÃÁ±ºhÀ»f¹Ë onstraint Formulation `&- L3K^ &Jn /) \!&J%&'yGJ`(4n$!g^ &'Gn`$1(4^ $1(&5( (&J$!)!* (4ƒ$!0Š`_3&'*7(q# e& Þ 0nƒs7K7&'( ^ %&G'GnK7$!0Û &Ö(ƒ$)`0 )$!e& - GJ&'( Gn`&'Kã &J^I 8Ö^,(( (ƒ$!0#^ 7K7&' - /0nƒ@K7]\q$!0g\ (v `n(4 ƒ`ƒ3(4&5ks_ * VoK7&'(ä d æ 6u_L7H$)W`$!(g`K ^ (+g(l_`(&'šl&' (*7(+&J^,('6¾&,(ƒ$!0s- ng&5(hgj&5(4ƒu3k~ƒ3)0$1gjy 0&J^Š&J$!Gƒƒu&J$!&'( -v&0nƒri D &wyxz{y (*7(+&J^ h(o$) ä E æ ˆf67^Š&0&J`&Jn$! -r(4ƒ`$!0ž- GJ&#$!(YL`(&'K I 2 `(4n$!n( 0nƒ``(Ž-l )$!W+\ Q^,$! GJ!((&'('6Œ(4* ng$1gg`k (&J^,$1GI p * Gf$!GgG3(+$)(Y&L`$)%&Jn( &'šl$!&j^ &J(/`&'G&5((*- YŽK7$!0n^ãŽ_3&#\ &J! - ^ &'KvI `& wyxz{y (*7(+&J^ &5(4ƒu&'G( +\YÖ(4L3GnâG`(4n$!n(Q h(4&'& Ý $!0L& ˆ N!O#" un!o N ]OJRf) %$ \ 7K7&5((4L1K ~ %&J!ƒvI $!( GJ`(4n$!s$1(~&J7- GJ&'K _ *Ûƒ1GJ$)`0 Ö(4ƒ$!0 _u& +\Y&'&JQ&5GnWƒ3$!g-o7K7&'('IŽ& (4ƒ$!0!&J`0 $!( & &5šL`$)&'KÖ^ $)`$)^@L^ K7$!(4`G& _u&+\ &J&'Û7K7&'('6q_L7 $t 1(Q`(&ƒƒu&J+* `,$)( (ƒ$!0úg`(+n & K7L`G&5( '&J\q&J (4&Gn`&'K _3&'*3K $)( &5(+!&J0vI &@(ƒ$)0 &'&J- &!* ƒƒ`)$!&'(#- ng& \q&' `&+\ 7K7&'(/ %&J!ƒv6G^Šƒ`&5(($)`0&q(4ƒ$!0`I Üg%&'1ƒƒ`$)0g$!( L`( ƒ&j%&'&'kv6_l ^ %&'^ &J ƒ`y$1(o`ƒ3&'`!$) '&'K I $!(#$!(q&ž-œ(&j%&' \ ]*7( $! \q$!gn~& (4$!^L`!$!$!( &'`K7&J&'K ƒ *7(4$1GJ _ *W0&J&')$! J$!0 &,$! - (4ƒ$!0`I N!O#"4O& OŽN ]OJRf) '$Y8 (4$!^ $)1 (ƒ$)`0ž$!(oƒ!g&5k@_u&+\ &J&' &'Gn 7K7& &'K0& ƒ3$!'i K&'( & &!*Ú_7Õ+&5Gf(@ \q$!gnw- ng&g'w_u&@ƒƒ!$)&5k 6 (4,&0r-oƒƒ!* $)0s - ng&h,s&'k70&$!(qgfl3!)* GJG^ ƒ)$1(&'ks_ * ƒƒ!* $)`0 ` )-Y&Š- ng&š&5gnq-y&š+\y7k7&5(ž `&Š&5K70& ( &J`K7ƒu$!('I $1( K7$1(((7G$1 $!_3&J+\Y&'&JÖ&W(ƒ$)`0 ( G3G&JƒL` &J`K7ƒu$!(#`K &Žƒu$!(-/ƒƒ`)$1GJ$!~- &q(ƒ$!0!&y- \ L`y^ 7K7&J K7$tؾ&Jn(g- ^ ^Š&@ƒ *7(4$1GJ )!*~-l$)7- L/^,(( (ƒ$)0s(4*7( &J^,('I 8ƒƒ!* $)0&5(4&g+\ (4* Gf$!GgG3(+$)(Y!&6&(4*7( &J^å&'7- ng&5(g&,\ &J! - ^ &'K7`&'((g- K7$10^,(JI@p7&J^, $!G GJ`(4n$!('6 &Ô7ƒ&'((4&5KQ(H.gÜHÝ/('6v&J3`GJ&@& % $!(L` - ^ 3K G^ ^@L$1GJ $)%&Žƒ3 \ &J-Œ`&@K7n]\q$)`0`I)(Šxz{y (Lƒƒu( &Ž- )! \q$)`0š.gühý/('67$)^ ƒ!&j^ &'&'K\q$) (&(#- 0&J&' )$! J&5K (ƒ$)0(q(k7&5(gj$!_3&5kú l(&j&žý $)0L& ˆ Ák O ` *l `N Rfk,+5N 3 ~ OJRf hkl n OJk `OR.-/$ & (&- 7K7&'((L1K _3& G )!$)`&'3K Ô $1( )$!0&5K IŽ8 (4ƒ$!0 \q$t &5(+@)&'0 J&J $1( Gn&'KÚ_u&+\ &J&' &'Gn ` K& 0 ðr»'»f f Â217±4µ Âhº ±ºh 4º ³]±ºÂhºh ±nà ¹Èrºh³] ±ºhÀ»»nÉ ºh³] Ê ³ ±n¹] f À ¹ à 4¹5 nº ³ º»º ³5»f À fà ¹ ±nãvã +¹] nºh³èvà ²] h»f²»f hºhà»f¹ ±nãyºh»@ºh³] Âlº h 4Âh ºh³ ±º ²]»J¼ Ä Ê+ +ÂHÀ º4Ë3! ;:6<>=.?,@&2=.?ED&?=GFIH.Jâï¹~±n¼]¼]À ºhÀ»f¹~ºh», ²] hà ¹] n½ã À f É!»f hê4 +Â4ȱnà Ã5¹]»J¼] +Â3±n ¾Â Ä Ç!Kl +Ê+ººh»Œ± fã»fç ±nã5¼ ±n q²]à ¹] ré!»f hê4 3É!»f Âhº ±nç]à à À º Ë

6 Node-Node Overlap lignment (horiz.) Symmetry (vert.) Node-Edge Overlap Equal Spacing (horiz.) Nodes Rest length Spring Legend Edge Forces Figure 8: Reduction of some sample VOFs to systems of generalized springs. `K % $)L`3Ô $1( )$!0&5K )$!&L0 &G&'$1K - &~7K7&'('I #& ` Š- ng&5(@& ƒƒ!$)&5k ` )* Q& 7K7&'('6 &s% $!4L` Ô7$1(JIW D &~GJ(& - $) '¾q%&'4$!G' 8#!$!0^ &J#.gÜHÝ 6 `& Ô7$!(q )$!0 ^Š&' $!( & &'(ƒ3&5gf$)%&~ô $1('I `&$!K G'(&sL`(&'( &, Ô7$1(g\q$1GnW`&Š` K&'(Ž&@ )&'K7*^ (4ŽGJ )(4&' )*!$)0&'K I # j` i k! *l N Rfk,+5N ` D v ORf kl n -/$ &Œ7K7&5(r(L`!K _3&Š(4ƒ`G&5Ks&'%&' )*!`0@&0$)%&J Ô7$1(JI#p ƒ3g$!0 )0 & `0` Ô7$1($1(HL`G`(4n$!&'K I 8gK]Õ4GJ&JŽƒ`$!n( -v7k7&5(y&gj`&'gf&'k \q$)~(4ƒ$!0(œ\q`(&#&5(+ )&'0 $!(s`&úgj^ ƒl7&'kâ]%&jn0&wk7$1(+n`gj& _u&+\ &J&'âK Õ4G&' 7K7&'('I i O j`o u no *l `N Rfk,+5N 3 ORf kl n -/$Ž&Š7K7&5(H(L!KQ_3& nk7&j&'k$! `&@GL`&Jg(&'šL&'`G&Š!0 &0$)%&JQÔ $1('I p ƒ$)0(q\q$)wš%&'* (4#&'(4# )&'0 `K~\q$)W(* ^ ^Š&J$!G (ƒ$!0gj`(4 '&J$)- 7K7&'(&W$! ƒ`ƒ3&' (4&5šL`&J`GJ&6vƒu($t$)%& `&J\q$!(&5ĝ&@ƒ`!G&'KQ_3&J+\Y&'&JÚK Õ4G&'#7K7&'($!~& (&'šl&'`g&h,e&j&'ƒ &J^ $)nk7&''i tj Tn DOJR#$r&Y(4&Jr-77K7&5(r(L1K_u&oG!L`(4&J&'KH0&`&J5I p ƒ$)0(\q$)öw(@&'(4!&j0 & ƒ!g&5k ƒ`$!\q$!(& ^ 0Š&Ž7K7&'('I N ¾O $Y&Ž_uL`K$)0 _u]ô - `&Ž7K7&'(q(L`!KG$! &Js7K7&'('I:&W_uL``K7$!0_u]Ô $1( &5 &'KÛ( ž(lƒ3&' 7K7&6&Q7K7& 7K7&W %&J!ƒ ^ &7K $!(sƒ ƒ )$!&'Kv6 `KW&,&'(Lt$)`0s- GJ&'(Ž& ƒƒ` )$!&'K &'šl` )!* &Ž7K7&5(#G^ ƒ$1($)0@`&ž J`&I i OJ hrf *l N Rfk,+5N ` D Œ ORf kl n -/$ `&#7K7&'(Y(4`L1K _3& (4* ^ ^ &$1G _ul7g&0$!%&jwô7$!('iqvogn7k7&$!(ƒ`$!&5k \q$t &7K7&G!(&'(4q $tn(#&ç`&5gf$! _3L7#`& $ Jn /H%&'4$!G' )$!&ŠL`0 &,G&J$!K -Y! & 7K7&'('I h8` K& ^,]*_u&yƒ`$)&'k\q$t$)(&j )-3$)-`$)/$1(/G!(&'(4 $tn(ž \q &Jç`&'G$!vI ˆ VYšL3Œ`K ƒƒ3(4$)&š- GJ&'(& &' ƒ`ƒ )$!&'K~ &7K7&5($!W&5Gn ƒ`$) ^,e&ž`&j^ (4* ^ ^ &$1GŽ_uL7`&Ž )$!&Ž-/&ç`&5Gf$!rI " i O!$ & 7K7&5( (L1K - ^ (43ƒu&6/(Ž$! &J& K7$10^I~&sL`(&J(ƒ3&5G$) `&'(\q$1gn -&s7k7&'( $!(H&,ƒ`&J5I@&, (4`ƒ3&.gÜHÝ G' _3&,&'7- ng&5kq( G^_$!` $) - 8#!$)0^ &J `K VošL`up ƒ`gj$)`0ž.gühý ( - `& Gn$)1K7&JÚ`KÚ VYšL3 p ƒ`g$!0.gühý (H- & )&J-^ (4`K~$)0^ (4Gn`$)1K7&J `Ksƒ`&'5I j`m i ` `O $o&#7k7&5(o(l1kš_3&gƒ1g&5kšk7$! )!*&5šL$ K7$!(4# G$!GJ )&I 8aG&J 7K7&Ž^,]* ƒ7$)`!!* _3& (4ƒu&'GJ$t `&5KQ_ *& L`(4&' Þ $t- & $1((4ƒu&'GJ$t `&5K 6rsƒ`^ 7K7&H hk7&'(g$!_3&5k _u&j! \ˆ $1( KK7&5K &G&'&J5I p7ƒ$!0( & ƒ1g&5k_3&j+\y&'&j `&J$!0 _3(v`&oƒu&J$)^ &&J `KŽ_u& +\Y&'&JW& G&J&J` K&Š`KW&5Gn ƒu&j$)^ &&J7K7&@\q$t &5(+q!&J0&'šL`¾ `& GJ1GL`!&'K~]%&'0&#nK$)L`('I

7 ( Zy]\Ž6\q&J& * * Þ D KK$t$)v67`&-! ) \q$!0.gühý GJ_3&ŽL`(&'KsŠ0$! _ (!L7&ŽG %&'o& `& 0$)`&'Ksƒ3(4$)$!~-/7K7&'( ¾ `N R#$ 8ã7K7& (L1K~_3&Ž!7GJ&'Kq& GJL&Jqƒu ($t$)ú&'0nk7!&'((h-\q` Ž&J - ng&'(h$!ú&,ƒ`*7($!g' ($)^@L1 $!Û^,]*Ö_3& G$!0 $t5i &Q8`Gns.gÜHÝ $1($)^ ƒ!&j^ &'&'K~_ * GJ!GJL!$!0!3- GJ&'('6 _L7q`&J~ Lƒ¾K$!0H& ƒ3(4$)$!3(y-33gn&'kž` K&'('Iy$1(/$!(/GJ GJ&Jƒ7L`! )* &'šl$!%] )&'Y@0$)% $!0Š`Gn&5K,7K7&'( $!7 $)&^ (('I 8# )`L0&Š(4*7(4&J^ GJ#^Š %& `Gn`&'K~7K7&'('63& L`(&J^,]* (+$)! ^ %&g&'^ % $!@&^ŠL`(&IŒ8 L`(4&J- L¾&5Gn $1šL&@$1(- L`(&Jg~`Gn`#+\ ` K&'(g - L4&JŽGJ (4n$!sŠ(4&5G3K.gÜHÝ I"#`K&Jq #L_ p `ƒ3&.gühý 6- &Ô ^ ƒ!&6'`& K7$!L`( - & L_Ž$1(rK7&J&J^ $)`&'KH_ *HG'1GL1 $)0 `&]%&'0&ŽK7$1(+n`GJ& _3&J+\Y&'&J&G&'&Jg7K7&`K&'Gn 7K7& )0~& ƒ3&'$!ƒ&'*isyw_7n$! (4ƒu&'GJ$t 3G K7$)L3(J6 `&sl`(&j GL1K `Gn` &G&J&JŠ7K7&~ )0W\q$) & 7K7&WÖ&Wƒu&J$!ƒ&J*I & L`(&J G'Ö`&JÛ&'($) '&& L * ^ %$!0 &J$)`&Jq- `& `Gn&5K 7K7&5(JI Ý $)3!)*6ywrxz{r Qƒ %$1K7&5(gs(4$!0!& kl JRfk kl.gühý I¾8 K7$ GJ$)$1GJ.gÜHÝ:K7 &'(Š ƒ` % $1K7&~ * G3(+$) & K7$10^~6¾_L^ &'&' )*WL0^ &Jn(& K7$!0n^ \q$)úkk7$ $!3 0ƒ$1G &J!&J^ &J(Ž$!&'K (ƒ3&5gf( - & K$!0n^ 1]*L'I&ŠK7$1G$)$1GJy.gÜHÝÖ$)^ ƒ!&j^ &J&'KQgƒ&'(&J$1( `& Ýn^ &.gühý R,O!$@`&,_3L`K7$!0W_u]ÔQ- `& (4&J -7K7&'( $!( K& ^,ngj&5kw\q$) ~K7n]\q - n^ &IŽ8(H&Š7K7&'(Hƒ`4$!GJ$ ƒ`$!0 $! Ýn^ &.gühý ^ %&6v`& - ^Š&,&Jƒu($)$!`( `KW&'($) '&'(g$tn(4&'t- GJGJnK7$!0!*IŽ&ŠL`(&JG!(g(4L`Gn ƒƒu&j$!&'(y-r&g- ^ &g(y$)(g )'6ƒ`K`K7$)`0s lk$!(4`g& KK7&'K~ &_3L`K7$!0 _u]ôs_u&- &Ž_u&J$!0 K7n]\q3ˆ6``K \q&j&'/& - n^ &$!(/K7n]\q@(/ŠL7 )$!&y `! )&5K@&'G 0!&I & u&.gühýã&jô^ ƒ!&s$!öý $!0L&? $1(@$!! )L`( &'K~L`($!0,Ýn^ &.gühý ('I onstraint Satisfaction & GJ`(4n$!- ^L1 $)Ú_3 %& &5(4L )($) ƒ`*7($!g' (* (4&'^ GJ`($!(4$!0Ú- (4&J,-7K7&'( W3KÖÚ(& - 0&'&Jn!$! J&'K (4ƒ`$!0( W, * 0$!%&' $!^ &fi K&'( & ƒu($)$!&5k GJ % (@-g+* ƒ$!g'q($) '&? <9 E c <6 3K 7K7&^,((&'(g&L$)- ^ )* (&g? - g&'(&-ogj GL`!$!vI & (4ƒ$!0ÖGJ`(4( &? I 9 <`I < - (*ngf$!ghg`(4n$!n(j6 <I E@- q(4&'^,$1gggj`(4n$!(y&j 3 2 )L3(+&J$)036q`K <I < - 2 )L`(4&'$!03I &Q(ƒ$)0 &'(4g!&J0`( &@K7&&J^Š$!&5KW_ *~&Š.gÜHÝ G %&Jn(4$!v6 (K7&'(G$)_u&'K _3 %&I& ^,0$)L`K7&-o(ƒ$!0 (q- ng& $1( ˆ _ * e& $!( &QGfL3!&J0 - `& (ƒ$)0ö ~$!^ &fi K& $1( &J&- & ë»f `¹5»nº ±ºhÀ»f¹ ±nã]âhà q²]ã À Ê+À º µ ¾»f¹5à À ¹]¼]À Ê4±º u¼] +² +¹]¼5 4¹5Ê+»f¹"! '½ ²]à À Ê+À ºhà µr³] +¹H± ¼]À Âlº À ¹]ÊDºhÀ»f¹# Ä Âlº¾Ç / #±n¼] rç +ºµ¾ 4 +¹g¼]À ñ 4 h +¹Jº¾ºhÀ q +ÂÈ fë ]Ë È#!±n¹]¼$!&%(')! Ë7«¾ 4Ê4± Ä Âh ¾¹]»J¼] +±n¹]¼Œé ê ë`âê ³ ±n¹] f v±nâl 5¹]Ê ³]»f¹]» Ä Â Ã À ¹ + ²»f¹]Âh uºh» º ³5 Ä Â + ±nÊ+ºhÀ»f¹]Â3±n¹]¼ º»rº ³] ÂhÀ Ä ÃÁ±ºhÀ»f¹È±nà ÃJºh³] ¾Ån±n À ½ ±nç]ã +ÂrÀ ¹ºh³]  À Ä ÃÁ±º À»f¹±n h /º À q /¼5 4² +¹]¼] +¹ºË (L_7Õ+&5Gfg nr- ng&+*,.-0/ * $)^ &@f6œ\q&j&@# ;+ˆ $1(&(4&JŠ-(4ƒ`$!0(@ ؾ&'G$!0 ` K& 6r3K : * ;<>=D< <E <# ˆf6 &- GJ&@%&'GH&'(Lt$)`0 - ^ &Gf$) -r(ƒ$)`0f 7K7&G 6 $!( K7&&J^ $)&5K _ *Š& &J!&J% q.gühý GJ %&'($! (Gn&J^ &I : ;#<>=4<# <? <# ˆ# $!%&'$1( (4&JLƒr6V L!&J (/^Š&J7K@$!( L`(4&5K ŽG^ ƒl& & ƒu($)$! H * 4ˆ `K ^ ^ &'L^ I * 4ˆŒ- &'Gn 7K7&G %&' $)^ & - < - #! 7K7&'(J I 4ˆ - < Þ &Jƒu&' - > K Þ - #!v7k7&5(l, * M- / 2143N59 98 : * ;<O=4<# <? <E ˆ Þ P - 9NQ ^, Ôv O ˆ Þ - q&'gns` K&R I 4ˆ - I * K 4ˆ >,S * P I * K 4ˆˆ K Þ $)-S /$1(L``Gn&'K &J H * 4ˆ - H * K 4ˆ > I * 4ˆ K &J1(& H * 4ˆ - H * K 4ˆ Þ $t-/!(+(g&j&' Lƒ¾K&Ž\(^ &H` KT 0 `&JLƒ¾K & (GJ&'&Js &Jç`&'Gqƒ3(4$)$!`( H* 4ˆ L`$) / I * 4ˆ+àU9VXWY 7Z `&~K^ ƒ$)`0 GJ`(4 P - &'Gn7K7&(L1K $1K7&5! )* _u& &@GJ$)$1GJ K^Šƒ`$)0 GJ`(4#- `g7k7&63_l- GJ^ ƒl7n $)`($!^Šƒ` )$1G$)+*6q\ &Wƒƒ`]Ô7$!^ &~`$!( _*& GJ$)$1GJ K^Šƒ`$)0G`(4/- &#(40&'(4/(ƒ$)`0H$!Š& (*7(+&J^I D ƒng$1g&6r$!(šk^š$)4&'k7!* 0(( ƒƒ`]ô7$!^ $) `(,\ e&5kšl$)& \ &J!h6&' )$!^ $)`$!0 (G$!!!$!`( $! )^ (+!G'(&'('I &s$!^š&$!`g&j^ &' K $1(Š<`I <? 6 `K (G&J&',Lƒ¾K &'( 7GJGL`o&J%&J* KT - <N[? $!^ &gl`$tn(ji/œû&' & e$!&j$1g &J`&J0*0 &'(r_3&' ) \ _$)n*g% )L&)W\Y 9Z]- <N[ <? ^_ `^t6&g($!^l1 $) (4L3(4ƒu&J`K`(o$)(&J )-v&'^ ƒ3$! )* L`$)v&Ž&JÔ #L`(4&'#G$!vI Visual Presentation [ * 0&'&Jn!$) '$)`0s& % $1(4L`Yƒƒ3&5n`GJ& -q0nƒú7k7&5(j6 &' (ƒ3&5gfn( -g0ƒ K7]\q$!0ÚGJÖ!( _u& &Ô7ƒ&'((&'K \q$)s.gühý/(ji/ýy$!`(43g&6¾ DOEa /) moj T $!sk7$10^,( GJ _3& $!^ ƒ!&j^ &J&5KW\q$)L7 KK$t$)` $)- (+L`GL&IŽ8 &JÔ 1_u&J $1(^ &J&J!*ÚW7K7&s\q$t `(4ƒ3&J_`Gne0L`K `K _unk7&''i Zr_3&'!(GJÛ`&J _3&Ú Gn`&'K 0ƒ$ G' _7Õ+&'G(ŽL3(4$!0W 2!L`(+&J$)`0~.gÜHÝ - Ž&JÔ^ ƒ!&6/(ž$! Ý $!0L& c I p $!^ $)1 )*6y~7K7& \q$)ú&j$)`&j _unk7&j56v_`gne 0L`K 6 &Ô $1( Úë $!`K - ` ` DN ¾NO 3 GJ

8 (H$!^, $!Q$!(1( $)&'0nyƒ`g-o$tn(H%$1(L` _u&sl`(&- L` Š`&J_7Õ+&'G('6 (4L3Gn( &'K0&'( sý`^ &.gühý ('I DÛƒ3$1GL156qÛ`0` &'K0& G'Ú_3&s&ؾ&'G&'KÚ_ * $)&Jƒ3!$!0W ƒ`^ 7K7& &&5K70&_3&J+\Y&'&J+\ G&'G&5K7K7&'(H`K )$!0`$)0 `& ƒ`^ 7K7& \q$)&'gn -&s$)0$)`œ7k7&'(% $! `0`¾8#!$!0^ &J#.gÜHÝ/('I DsKK7$)$!, &g0ƒ$1gj3g^ ƒ3&j(o-v&gk$!0n^ $)(&J )- `& 7K7&'('6/&'K70&'('6 `K - n^ &'( &s$)&j-lg& L`(&'(% $1(4L`¾^Š&5`( ƒ&5(4&'y@&žl`(&j `& GL&'(& -3.gÜHÝ (r3 Œ&o_u&J$!0Hƒƒ!$)&5KŽ#`&K$!0n^ &J!&J^ &J('I VoGnQ.gÜHÝÛ$!`(4`G& $1(Ž$)3K7$!G' &'K _* s0ƒ$1gj k! kl n >" DN RŠ$) &WK$!(ƒ1]* Þ &W(`ƒu&-&.gÜHÝa$!`K7$1GJ,$1( ($)^ $!!W`& _$)^,ƒ &G&'(ƒ3`K7$!0 ƒl`(_l Q- `Ž.gÜHÝY6v((4 \q $! Ý $!0L&,=I 8(H&,L`(&J ^ %&5(v&^ŠL`(&Y %&J/ƒ`4$!GJL1.gÜHÝ GJ %](J6/wrxz{r $!0!$!0(Ž ) ƒ3$1g$!ƒ` $)07K7&5(JI 2 %&'(&J!*6ƒ!G$!0`&#^ L`(&q %&' Ž7K7&q\q$! )3$)0!$)0o&.gÜHÝ $!`K7$1GJ(g- Ž.gÜHÝ $)3(+n`GJ&'($! \q`$!gn 3 7K7& ƒ`4$!gj$)ƒ`&5(ji Ý $!`!!*6ƒ`!G$!0 `& ^ L3(4&W %&J.gÜHÝ ƒl`( _L7 \q$! )$)0!$)0 )q.gühý $)`K$!G' (Š-g` ƒ`4$!gjl!.gühý +* ƒ3&ih`&'(&^ &'Gn`$1(4^,(#&'`_` )&Š L`(&J &5($)!* K&&'^ $!& `& &Ô &'`K $!^Šƒ3Gf@-qƒ`$1G L1,(& -g1]*l7šgj`(4n$!('i&~.gühýa0nƒ`$!g'(@& $!&J`K&'K (!&J!* ƒ %$1K7&q% $1(4L`- &'&'K7_`Gne L`(&Jn( Þ &'* &`'6 -ygl(&6 $!`G!L`K7&5K $! &H ``¾L7ƒLK7n]\q$!0`I (Šxz{r - &J&5K7_`GneuI [ ŠL`(&JŒ3K@(*7(+&J^ Gf$!3( &`$)^, &'KŠ( `&g1]*l7o$1(yk7$1(ƒ!]*&'k $!,`&HG' % (o&5-v&g(*7(+&j^i & ƒ *7($!G'q(4$!^L`!$! G$) L`)!* Lƒ¾K &'( &ƒ3(4$ $!Q-Œ`&@7K7&5($! &@1]*L7'Ig8# )L0 &J*W& &Jƒ&'(&J&5KŽ0nƒ`$!G'!)*65&Y- ng&5(r@g7k7&y_u&'gj^ &ƒ ƒ`&' #L`(&Jn( L0_`(4&'% $!Ž`K^,$)ƒ`L!$!vI ONLUSIONS 2 3(+$) _`(4&5K &5Gn$1šL&'( `]%&s_u&j&' L7$! )$! J&5KÖ$) L ^ &JL`(K7n]\q$!0&5K7$tn(J6 &I 03I)6 ä b 6 6? <76? =76? E æ 67_L7&'* `]%& (-l~&' Õ+ *&5K )*Û!$!^Š$)&5Kâ(L`G'G&'((~$)â`$!(!&I Üg& &5(Ö- $1(sƒƒ`&' -l$! )L&W$1( &Q0&J&' )$)+* 3K GJ^ ƒ!&ô7$t+* -g^ (4,G3(+$) _`(4&5K K7n]\q$)0 &'K7$ ( &#G`(+$)Œ%7G'_L1$!&'(y`]%& -&J _3&'&J,Gn(4&' - s0`!$t+*6 GJ %&'0&6 `KÖGfn_$! )$)+*6q_`L7s^,]* Š_u&s&5(4ƒu&'GJ$! )!* G%&J$!&JŠŠ&ؾ&'Gf$)%& ë $)3K( -K7]\q$!0 (4e7('I D KK$t$)v6oL`(&Jn( -&JÖ`]%& K7$ GL )+*sl``k7&jn(43k7$)`0, \ G3(+$) _`(4&5K (* (4&'^ \ ë ('6]`K&J&- &o \ _3&5(+ygL7$! )$! J& $)'I D ƒ`$1gl`!'6 \q&' ƒ&5(4&'&'kú\q$) L``K7&J %&' G`(4n$!&'KWK]\ $!0('6¾^ *(*7(+&J^,(g_3&'`]%&@$) \ ]*7(`& ƒ`šl& `& L`(&J5I (Šxz{r $!^ ƒ %&'(H 0&J&' G`(+$) _`(4&5K (* (4&'^,( _ * ƒ %$1K7$!0 (4ƒu&'GJ$! )$! J&5K (4&J~-G`(+$)n(J6 Ìr³5 Ä Âh»nÉ3³]À ¼]¼] +¹»fÇ!Kl +ÊDº Â/ºh»gÊ+»f¹º h»fãê4»f¹5âhºh ±nà ¹ºh½Ç]±n +¼@ÃÁ±+» Ä º ³ ±nârç 4 +¹g²]»f²»f +¼²5 DÅ5À» Ä Â Ã Ë ' + È5É!»f và ¹]Âlº ±n¹]ê+ fè]ºh³] ¼]À Â Ê Ä Âh À»f¹»nÉ ±nã À f¹] q +¹ºv»fÇ!Kl 4ÊDºhÂ Ç Ã 4À Ê ³] + ±n¹]¼~à ºh JÀ ¹ŠÎ ÓË 5±n f f 4 ±º +¼ŠÉ)»f qâ»n龺 ³5 é/ê ë~à ¹]¼]À Ê4±º»f hâo±n Âh³]»µr¹À ¹ëÀ n½ Ä h 4Âì ºh³] h» Ä f³ 5Ëï¹oº ³] v±nêdº Ä ±nã Âh 'Âhºh + Ⱥh³] và ¹]¼]À Ê4±ºh»f Â3±n ¾¼] +²]À ÊDºh +¼ µrà º ³g q»f rå5à Â Ä ±nã Â Ä Ç5º à Dº Ë ($!^Šƒ` )&W^ &5Gn`$1(^ (,- ÚL`(&J KKÛ`K K7&' )&J& G (4n$!('6o3K $!L$)$!%&^ &` K- (!% $)`0W`&WG (4n$!('IW DKK7$)$!v6/_ *Ú$)`GJƒ3$!0W`$)^, $) $) & ƒ7gj&'((j6wrxz{r ((4$1(4( & L`(4&'y$!L``K7&Jn(43K7$)`0# \,Gn$!&J%& K7&5(4$!&'Ks!]*L75I `& L`(4&-,ÛG3(+$) ( $1(4-lGf$)â(Gn&J^ & lƒ * ($1GJ ($!^L1 $)3ˆ¾` $!(y$)l$t$)%&y`kžƒ&'k7$1gfn_!&6 n &Jr` &g`#$!(_u&&j# ``K7$!0 0!_` (4)L7$)`('6$1(qK7&')$!_3&' &I ( xz{y $1(H$!&'`K7&'KW~_3&Š0 7KWH0)_`!)* ( $1(4- *$!0ÚG`(+$)n(_ * $)(&J )-+I X#&''6o$t,$1( $)&'`K7&5K ƒ` % $1K7& $)&'4-lG&,`,!! \#( WL`(&- L`GJ!!_3$! _u&+\ &J&' L`(&Jg`KWGJ^ ƒl7&j$!q(!% $)0 &1]*L7ƒ_!&J^I Ý` $1(ƒLƒu(&Hƒ`&5K7$!G_$)!$)+*67(4$!^ ƒ!$!gj$t+*6``k & GJ^ ƒu&j!)$!03 L`& - & $!^ $! &Q-l~^ &Q$!^ ƒuo3sgn$!&j% $)`00!_3uƒ7$)^,!$)+* L7^, $!G'!)*I Ý $!`!!*6/`& _`(4$1G GJ`GJ&Jƒ7ŠL`K7&'!* $)0Q& wrxz{r $)&' -lg& $!0GJ!!_3$!%&#$!&'Gf$! _3&J+\Y&'&J L3(4&' `K GJ^ ƒl7&j (!%&WÖƒ7$!^ $) 5 $)Ûƒ_!&J^6q\q$t & GJ^ ƒl7&jƒu&j- ^Š$!0 )7GJgƒ7$!^ $) 5 $)â3kû`& L`(&J &'(ƒu`($)_` G ^,]* _u&sƒƒ!$!g'_!& &'q!]*l7567k7]\q$!036`k~k7&'($!0s(e7(ji KNOWLEDGMENTS `$!(Œ\ e\(œ(lƒƒu&5k _ * `& $!`3p7G$!&J3G&Ý`L K` $!Ö n #L^@_3&'(H +Xq ;= d <? ;9 `KQ +Xq ; b?5 E ˆ `K _ * UWVoXZ &8áU $)(L_$1(4`$/Vo)&5Gf$1GXq&5(4&5nGnWZr_3 n *I REFERENES? I#Xq`!K [ &'Gne&J`K + p ^,!hi 8#`$)^, $) &$!&J-lGJ&I D [ &J3KÚZrL`&'h6Y&'K7$)'6 O Rf N+ß j " N uj7 DOJR 3 OJR ß nošoftfk `I,8KK$!( œ &5(4!&J* %ol_!$!($!0 2 `I!6Xq&'K7$!0`6UW86? ;;<`I 9I $)L`(&Jƒ`ƒ3& $ [ $1(+n6 %/&&J VYK7&5(J6 Xq_3&'4 y^ (($16`K D$1(oy! )$1(JI 8 )0$t^,(Œ- K7n]\ $)0~0nƒ``(## n &'KW_`$)_!$!0nƒ`*I N ¾j7 " hkln u #OnN,O Rf /$ OnN Rf W uákl n kln `Tf6vE 9= d & 9 96? ;;È I =`I#Ýn `I [ `K7&'_`L036/&'K7$)'I RN5 nono&k! " TN4ßs O i N Tnkj án R ` R Œk! 6 %!L^ &? <9 c - yo #" hj7ro N DOT N N uj7 DOJR i JklO ¾ OJIop ƒ$!0&''6? ;; d I E3I#VoK g&j0 )&''6 UWe Ý`$!&'K&J!h6 `K & UWe7('I 2 `(4n$! K7$!%&' K7$!0n^!]*L75IQ D RN' nono k! " T N+ß O "!"!$# # # # i `N]Tfkj án %yk1tnj` $r " j` OfTf6 ƒ`0&'(==<& == d 6 [ &J0&'v6 #\]*678#L`0L`(4? ;;=I d I %/&&'VoK7&'('I8}&JL`$1(+$!GŽ- H0nƒWK7n]\q$!0`I N " ROTnTfj T j OJR 3 hkj Š6 E98? E;&?'b <6? ; È I b I#U $!Gn3&J!&J$1Gn&'Q`Kã8`K7&J\ œû$te$!vi n]\q$!0 \q$tšgj`(4n$!('i&%rk1tfj` N ¾j7 OJRf6?? =;& d7? 6? ;;E3I c I#o*7( XŽI¾#&J`*`K p7g4hvi3l`k(vi# D&JnGf$)%& 0nƒ 1]*L7'I DRN' nono k! TWN+ß'( i *)!$ 6ƒ`0&5( dd & b E36$) )&'K 6`p 2 6 %&J^@_3&'? ;;? I

9 Iq8 )1 &J*7K7 `K &J0 &J1(4vI & L9 GJ`(4n$! _`(&'KsK7]\q$!0 &'K$t5IYy&'Gn$1GJrXq&'ƒ34? =? `6 g$!0$) p7x 2 6%Œ!Š8t`6 2 86? ;;È I ;I 2 &'* (e¾6 & UWe7('6 `KpL`@Ũ IŒp $!&J_u&J5I 8L7^ $!0 &~!]*L7Š-`&+\ eúk$!0n^,( \q$) (ƒ3&5g$) `&'KÖ% $1(4L` #0$! ' $)vi # # # R TJ kln `T N i ]Tf O T,PQ : mojr uoj kl ftf6 9 Eu l=ˆ EE& E d E36 UWGn? ;;=I? <I &J0 #&J1(vI L36H G3(+$)_`(&'KÛ0ƒ$1GJ( (*7(+&J^I N ¾j7 OJR R 7kl ft * RN' nono k! TsN4ß i " ) - 6? ;3 l=ˆ 9= d &79E=6$L!*? ; d I?? I#p&Jƒ`&J #4v6v&'K$t5I RN' nono k! " T N+ߊ O i N" Tfkj N R R Œk! " 6% )L^ &?? ;< - yon j7ro N DOfT N N ¾j7 OJR i JklO u noiop7ƒ$!0&j56? ;; b I? 97Iq8g p7gj'i@8 (L%&J*-Y0nƒ`QK7n]\q$)0~(4*7(4&'^ ('I y&'gn`$!g' Xq&'ƒ34; d]db 6,"#$!%&'($)+* - #&'\ G'(4!&6 8L`(+ )$16? ;;E3I? =I#p&J%&p $1(4&Iy D&JnG$!,&'Gn`$!šL&5(Y$!sGJ`(4n$! _`(4&5KH0&J^ &$1Gy^ 7K7&')$!0`I D RN' nono k! " TN4ß R " kl T 3 OJR ß no )! 6ƒ`0&'( d & ;96 2!0*6#8#!_3&'4n6 L&? ;;? I? È I D% p7l7&'13k I i SOJ D /$#, " 7k! uo R " kl n nn Šj `kl n kln Tf ]Tf O ŠI % 3 &'($!('6U +6? ; b =I?5d IqXq_3&'4 y^,((4$1ú`k D$1( I r )!$!('6q&'K$tn(JI RN' nono k! " T N+ß O i N Tnkj N R R Œk! " 6 %!L^ & ;E - yon j7ro N OTHN N ¾j7 OJR i klo u noji p ƒ`$!0&''6? ;;E3I?'b I [ L`G& Ig^ ( `K %ŒL 2 1K7&''I 8#$!^, $!0 K7$!&'Gf ^,$)ƒ`l!$!û$!&j-lgj&'('i D RN' nono k! " T N+ß ' i )! 6/ƒ`0&'(Ž=&? 96 % $)4(_L0r6 % 8 6 # %&'^_u&j? ;; d I