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[-:yLMPCEX(Mathematicsdept.),MacquarieUnivÎersityJ,XNorthRyde,Sydney,AustraliaNSW2109. > "5-:1L(- cmcsc10PostScriptXisaregisteredTJrademarkofAdob74B.1 UnsuppGortedUUincompatibilitiesC.....74B.2 ObsoleteUUkernelfeatures񍍑........75B.3 ObsoleteUUextensions&features1....76B.4 ObsoleteUUloading֍............76B.5 CompilingUUv2-diagrams.........77CCommonTErrorsz77ReferencesZ77Indexޕ78!#ListffofFigures1  !", cmsy10hpGosiitions. ҍ...............82 ExampleUUhplaceis1H............103 hob8jectis.................124 hdecoriations...............165 KernelUUlibraryhdiriectionals......176 hciricles.x.................197 SyntaxUUforcurves.q@...........228 PlainUUhframeis.c.............259 BracketUUhframeis.׍............2510 Rotations,UUscalingsand ipsO......3111 TheUU38standardMacintoshpatterns.8 .3212 impGortingUUagraphicforlabelling...3413 hpathisFύ..................3814 harrowis..................4115 PastingUUdiagram.F............4416 htwoGcellisލ................45gweL17ePhgraphisǍ.................52 jeL18ePhknot-pieceiUUconstructionset.....62eL19ePknotD~crossingswithorientationsand ePlabGelUUpositions8t..............63eL20ePknotsjoins,withorientations,labGelsePandUUshiftsj................65eL21ePExtension[implementationreplacedbyePuseUUofhdriverispGecials..........69WReKVRff׉ffB?\,UU.;*̖ross.eps)ff>;=nTPff"銍eKPrefaceeKThisreferencemanualgivesconcisedescriptionsofeKthe\moGdulesofXXY <\-pic,writtenbytheindividualau-eKthors.èPleasepdirectanyTU>'ExXnicalquestionorsug-eKgestion"forimprovement"directlytotheauthoroftheeKcompGonent<;inquestion,A@preferablybyelectronicmaileKusingtheindicatedaddress. 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TheremainingpartsdescribGetheeKthreekindsofoptions:8/': cmti10extensionsinpartIGIextendeKthekernelgraphiccapabilities,:fe}'aturesDzinpartIGIIeKprovideTspGecialinputsyntaxforparticulardiagrameKtypGes,oand#driversinpartIVmakeitpGossibletoeKexploitTtheprintingcapabilitiessuppGortedbyDVIeKdrivercprograms.F*oreachoptionitisindicatedhoweKit,shouldbGeloaded.]dTheappendicescontainanswerseKtoalltheexercises,A7asummaryofthecompatibil-eKity^withversion2,`andlistsomereasonswhyZXY A^-piceKmightUUsometimeshaltwithacrypticTU>'ExXerror.eKLicense.XY-picIisfreesoftwareIinthesensethatiteKisUUavqailableunderthefollowinglicenseconditions:"׍ǍV323232fd]%g3232%<$afd3$afd32V3232fd]%g3232󎍍pXY-pic:qGraphsUUandDiagramswithTU>'ExX ፍ Ujc M 㣲1991{1997 Kristo erUUH.Rose  |c j  1994{1997 RossUUMoGore"čeKThe.XY2-pic2packqageisfreesoftware;6youcanredis-eKtributeQitand/ormoGdifyitunderthetermsoftheeKGNUsGeneraltPublicLicenseaspublishedbytheF*reeeKSoftware=]F*oundation;EZeitherversion2oftheLicense,eKorUU(atyouroption)anylaterversion.eKTheXY D-picpackqageisdistributedinthehopGethateKitwillbGeuseful,Obutwithout\anywarr}'anty};withoutLWK3*tj??]even/theimpliedwarrantyofmer}'chantability笲or t- nessforap}'articularpurpose[.wSeeutheGNUuGeneralPublicUULicenseformoredetails.Y*oushouldhavereceivedacopyoftheGNUGen-eralXIPublicLicensealongwiththispackqage;ifnot,write{totheF*reeSoftware{Foundation,RInc.,675{MassAve,UUCambridge,MA02139,USA.InpracticethismeansthatyouarefreetouseXY -pic?foryourdoGcumentsbutifyoudistributeanypartn@ofnthenyouareobligedtoensurethatthefullsourcetextOofKXY aO-picisavqailabletothem(thefulltextofthelicenseOinthe leCOPYINGOexplainsthisinsomewhatmoreUUdetail [ٓRcmr7" 0ercmmi7^\).^ZNotationalCcon9ventions. W*eZ~givedescriptionsofthemsyntax(ofpicturesasBNF^2 Ͳrules;z,inexplana-tions`wewilluseuppGercaseletterslike b> cmmi10X)andYforhdimenisionsOandlowerOcaselikexandy(forhfactoris.#8PartffI0Nq cmbx12The KernelꨍVers.3.6bCyKristo erH.Rosehkrisrose@brics.dkiuTAfter\givinganoverview\ofthe\XY -picenvironmentin8x1,qSthispartdoGcumentthebasicconceptsof8XY -pictureconstructioninx2,includingthemaintained`graphicstate'.+Thefollowingsectionsgivethepre-cisesyntaxrulesofthemainXY-picconstructions:the\pGositionlanguageinx3,^theob8jectconstructionsinx4, Bandthepicture`decorations'inx5.SUx6presentsthekernelrepGertoireofob8jectsforuseinpictures;x7mdoGcumentstheinterfacetomXY -picoptionslikethestandardUU`feature'and`extension'options.Detailsfoftheimplementationarenotdiscussedhere3butinthecompleteTU>'ExXnicaldoGcumenta-tionUU[15 ]. q荍1TheǨX#՟YY-picffimplementationThisCsectionbrie ydiscussesthevqariousaspGectsofthe~present~}XY -pickernelimplementationofwhichtheuserUUshouldbGeaware.^Z1.1LLoading&aX1"Yv-picXY -picPiscarefultosetupitsownenvironmentinor-der0tofunctionwithalargevqarietyofformats.!XF*oreKmostUUformatsasinglelinewiththecommand<\input?xyeKinKzthepreambleofadoGcument leshouldloadthe eKkernel(see`integrationwithstandardformats'bGeloweKfor.vqariationspGossiblewithcertainformats,dinpar-eKticularUUL5ffA͉TU>'ExX[9]).eKTherestofthissectiondescribGesthingsyoumusteKconsider/ifyouneedtouse+XY c/-pictogetherwithothereKmacro%packqages,,styleoptions,,orformats.u6ThelesseKyour<|environmentdeviatesfromplainTU>'ExXtheeas-eKier:itshouldbGe. ConsulttheTU>'ExXnicaldocumenta-eKtion[15 ]fortheexactrequirementsforotherde ni-eKtionsUUtocoGexistwithUQXY U-pic.?eKPriv\racy:XY-picwillwarnabGoutcontrolsequenceseKityrede nes|thusyoucanbGesurethatthereareeKnoPcon ictsbGetweenLXY $P-pic-de nedPcontrolsequences,eKthoseofyourformat,һandothermacros,providedyoueKloadUQXY U-picUUlastandgetnowarningmessageslikeXy-pic?Warning:`[:::h'?redefined.eKIn|generalthe|XY-pickernelwillcheckallcontrol eKsequencesitrede nesexc}'eptвthat(1)generictem-eKpGorarieslike\nextarenotchecked,(2)prede nedeKfontidenti ers(seex1.3)areassumedintentionallyeKpreloaded,andFF(3)someofthemoreexoticcontroleKsequenceBnamesusedinternally(like@{-}6)areonlyeKcheckedUUtobGedi erentfrom\relax.eKCategorycoQdes: ThesituationiscomplicatedbyeKthe exibilityofTU>'ExX'sinputformat..TheculpritiseKthen`categorycoGde'conceptofTU>'ExX(cf.[6,p.37]):eKwhenaloadeda XY -picrequiresthecharacters \{}%a(theeK 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neddimen-sionIregistersetc.andyetstillbGeindependentoftheformatunderwhichitisused.OThecurrentversion(3.4)handlesplainTU>'ExX(version2and3[6]),AU>'M S-TU>'ExXd(version2.0and2.1[16 ]),ЕL5ffA͉TU>'EX(version2.09[8]and'2"[9]),AU>'M S-L5ffA͉TU>'ExX(version1.0,1.1[2],and1.2),andUUeplain(version2.6[3])^3|s.!{;xy .st9y: If}3youuseL5ffA͉TU>'ExXthenthis lemakesitpGossibletoloadXY-picasa`packqage'usingtheL5ffA͉TU>'ExX2"[9]UU\usepackagecommand: Nff2 '\usepackageUU[Rhoptioni,?...] ?{xy}4*ff2OwherethehoptioniswillbGeinterpretedasifpassedto\xyoptionUU(cf.x7). 4(Thexonlyexceptionstothisaretheoptionshav-ingthesamenamesasthosedriverpackqageoptionsofpartIV,whichappGearincf.[4,table11.2,p.317]orotheL5ffA͉TU>'ExX2" I5graphics7hbundle.Thesewillauto-maticallyBinvokeanybackendextensionrequiredtobGestl'ExX2" behaviour.}(Thismeansthat,"e.g.,[dvips]and[textures]canbGeusedasoptionsStothe\documentclasscommand, RwiththenormalUUe ect.)Theր lealsoworksasaL5ffA͉TU>'ExX2.09[8]`styleop-tion'althoughyouwillthenhavetoloadoptionswiththeUU\xyoption5ꏲmechanismUUdescribGedinx7.썍1.2Logo,version,andmessageseLoadingPXY 3T-picTprintsabannercontainingtheversionandvauthorofthekernel;ksmallprogressmessagesareprintedLwheneachma8jordivisionofthekernelhasbGeenUloaded.Anyoptionsloadedwillannouncethem-selfUUinasimilarfashion.IfzyourefertozXY -picinyourwrittentext(pleasedo 2 V8W^\) 2thenyoucanusethecommand\Xy-pic &totypGesetthe\XY -pic"logo.aTheversionoftheker-nel IistypGesetby\xyversionandthereleasedateby\xydate(asfoundinthebanner).,Bytheway*, theXY -pic"Lname[^4 _originatesfromthefactthatthe rstversionwaslittlemorethansuppGortfor(x;y[ٲ)coordi-nates8inacon gurablecoGordinatesystemwherethemain)ideawasthatallopGerationscouldbespeci edinamannerindepGendentoftheorientationoftheco-ordinates.GThis^propGertyhasbeenmaintainedexceptXeKthatnowthepackqageallowsexplicitabsoluteorien- eKtationUUaswell.@ieKMessages'thatstartwith\Xy-pic#Warning"areeKindicationsthatsomethingneedsyourattention;2aneK\Xy-pic#'ExXbGecauseoJXY N-picdoeseKnotUUknowhowtoproGceed.->eK1.3%KFontseKThevXY Lz-piczkernelimplementationmakesitsdrawingseKusingUU vespGeciallydesignedfonts:@3eKL͉ffNfd͟ fffdF*ontCYy fff\VCharacters ffN&Default۟ ffffN͟ ff͟fd\xydashfontCYy ffodashes ffN&xydash10۟ ff ͟ ff͟fd\xyatipfontCYy ffNQarrowUUtips,uppGerhalf ffN&xyatip10۟ ff͟ ff͟fd\xybtipfontCYy ffOarrowUUtips,lowerhalf ffN&xybtip10۟ ff͟ ff͟fd\xybsqlfontCYy ffMU7quarterUUcirclesfor ffN&xybsql10۟ ff͟ ffCYz ff\hoGoksUUandsquiggles ff۟ ff͟ ff͟fd\xycircfontCYy ffT&1=8UUcirclesegments ffN&xycirc10۟ ffffNeKThe# rstfourcontainvqariationsofcharactersina eKlargesnumbGerofdirections,zthelastcontains1/8cir-eKcleUUsegments.+>eKNote: ThedefaultfontsarenotpartoftheXY 8-piceKkernel~sp}'eci 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"5-:4LNoXdescriptionofaTAEMXprogramiscompletewithoutanexplanationofitsname.LWK5G*tj??gw2PictureffbasicsThebasicconceptsinvolvedwhenconstructingXY3- picturesllarepGositionsandob8jects,andhowtheycom-bineUUtoformthestateusedbythegraphicengine.Theb@generalstructureofanb'ExXusersmaysubstituteUU\begin{xy};*...\end{xy}2U \whereX]istheTU>'ExXIdimensiondistancerightXY B-picture(0?hasco-ordinates(<0mm,0mm>3h,\of(course).%ThezeropGositionofֱthe֭XY V-picturedeterminesthebGoxproducedbythe\xy...\endxy[commandtogetherwiththefourpa-rameters[Xmin ,XmaxA̲,Ymin,and[Ymax$'setsuchthatallJtheob8jectsinthepictureare`contained'inthefollowingUUrectangle::t$W3232tW32fdkMg3232Lבt L_fd\L_fd32t$W3232tWfdkMg3232eL O!cmsy7o '0;΄fdfe;hxfdfe;"fdfeW;̄fdfe;vfdfe;C fdfe;ʄfdfew;tfdfe?;gfdfe;Ȅfdfe;rfdfe;fdfe_;AƄfdfe c|TU>'ExXUUreferencepGointrhLͷt4҄fdfer)ofdfepP,Vfdfenx]阄fdfelڄfdfej#dfdfeh!^fdfegޠfdfee=LfdfecdY$fdfeaffdfe_uӨfdfe]؟fdfe\;N,fdfet5f2fd$t5foo{v UTXmin2m2fdG!T//7˟ 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.=ZU3eKThewaysthevqariousob8jectsconnectaredescribGedeKalongUUwiththeob8jects.eK2.4%KDecorations퍒eKWhenCthe\xycommandreachessomethingthatcaneKnotbGeinterpretedasacontinuationofthepGositioneKbGeingread,$thenitisexpectedtobeade}'corationc,eKi.e.,inarestrictedsetofTU>'ExXcommandswhichaddeKtotpictures.zMostsuchcommandsareprovidedbyeKtheCvqarioususerGzoptionsd(cf.x7)|onlyafewarepro-eKvidedwithinthekerneltofacilitateprogrammingofeKsuchUUoptions(andusermacros)asdescribGedinx5.eK2.5%KThe&aX1"Yv-picstate퍒eKFinally0wesummarisetheuser-accessiblepartsoftheeGXYK-pictureǦstateoftwoǦpGositionstogetherwiththeeKlastob8jectassoGciatedwitheach:thepr}'evious!,%}p,iseKthe_pGosition< P\XpR, ﮵YpR>with_theob8jectLpR,?!Rp,Dp,eKUpR,(Edgep,andthecurr}'entز,c,isthepGosition< >Xc,eKYc> 3withUUtheob8jectLc,Rc,Dc,Uc,Edgec. EeKF*urthermore,XY-pic]hasacon gurablec}'arte-eKsian:rc}'oordinatesystem 'ɲdescribGedcfbyanorigineKpGosition/< oX1t}\cmti7originm,~Yoriginm>#gand/twob}'ase vectorsLWK6c*tj??gw<Xxbase,筵Yxbase>ܲand/<,XybaseN,KYybaseN>zaccessed/bythe usualUUnotationusingparentheses:{dE(Bx,?y[) ]P=$n<#dkXorigina+8xXxbase+yXybase",#dkYorigina+8xYxbase+yYybase">This޺isexplainedinfullwhenweshowhowtosetthebaseUUinnote3dofx3. IZFinally^typGesettingaconnectionwillsetupa\placementǦstate"forreferringtopGositionsontheconnection9\thatisaccessedthroughaspGecial? po-sitionvconstruction;thisisalsodiscussedindetailinx3.ThewXY {-pic{stateֲconsistsofalltheseparameterstogether. /TheyxareinitialisedtozeroexceptforXxbasenȲ=Yybasef=1mm.The\edgesarenotdirectlyavqailablebutpGointsonthe?edgesmaybGefoundusingthedi erenthcorneriformsUUdescribGedinx3.ItTispGossibletoinsertan`initial'pieceofhposihdecoriJatthestartofeveryJXY ʱ-picturewiththedec-laration ff2 F\everyxy={}htextiUU}I\ff2This=willactasifthehtextiwastypGedliterallyrightafterGeach\xycommand,parsingtheactualcontentsasfifitfollowsthis{thusitisrecommendedthathtexti?hastheformhpGosi, .2s,<0pt>?,(0,0),andD;/0pt/"gisD;di erentfromtheoth-ers?Notes؍3a.Whendoingarithmeticwith+{and-thentheresultingxjcurrentob8jectinheritsthesizeofthehcoGordi,i.e.,theRrightargument|thiswillbGezeroUUifthehcoGordiisahvectori.̼Exercise2: How#doyousetctoanob8jectthesame{sizeasthesaved{ob8ject"ob"@butmoved<?X,ߵY8>x?gweK3b.Skewing{^using!qjustmeansthatthereference eKpGoint ofcismovedwithaslittlechangetotheeKshapGeoftheob8jectaspossible,$i.e.,theedgeofceKwillQ\remaininthesameloGcationexceptthatiteKwillgrowlargertoavoidmovingthereferenceeKpGointUUoutsidec.MteKExercise3: WhatpdoGesthehposi...!R-Ljdo?eKBug:tTheresultof! 폲isalwaysarectanglecur-eKrently*..eK3c.0A+hpGosi+c}'oversanotherifitisarectanglewitheKsizesucientlylargethattheotheris\under-eKneath".[UThe/.[opGeration/\extends"ahpositoeKcover*fanadditionalone|thereferencepGointofceKisMnotmovedMbuttheshapGeischangedtoarect-eKangleUUsuchthattheentirepob8jectiscovered.xeKBug:lnon-rectangular(ob8jectsare rst\trans-eKlated"]intoarectanglebyusingadiagonaleKthroughb@theob8jectasthediagonaloftherect-eKangle.eK3d.ThekopGerations:and::Wsettheb}'ase,3usedforeKhcoGordiinatesnhavingtheform(x,?y[)ֲ.#The: 9op-eKeration^willset<Xoriginm, /Yoriginm>to^p,a<Xxbase,eKYxbase>todcDorigin0,Kand< 'aXybaseN,YybaseN>toeK<HlfYxbase,ʵXxbase>(thisensuresthatitisausualeKsquareecoGordinatesystem). The::J4operationeKmay thenbGeusedafterwardstomakenonsqareeKbasesAbyjustsettingyb}'ase5toc֍originIԲ.7WHereeKarerWtwoexamples: rstly0;<1cm,0cm>:E䊲setstheeKcoGordinateUUsystem1IcLͷK0u2fds玍g\//JCsfdK0u OO/|eoriginj\xbase@WLybasec͟m\6(1,1)JC?KfdfeLڟ?KfdfeNq?KfdfeP?KfdfeR?KfdfeTy6?KfdfeV^͟?KfdfeXDd?KfdfeZ)?Kfdfe\?Kfdfe])?Kfdfe_?KfdfeaW?Kfdfec?Kfdfee?Kfdfegq?Kfdferˍgq*32fdfeigq*32fdfegq*32fdfegq*32fdfegq*32fdfegq*32fdfegq*32fdfegq*32fdfegq*32fdfegq*32fdfegq*32fdfegq*32fdfegq*32fdfegq*32fdfegq*32fdfegq*32fdfeeKwhile y<1cm,.5cm>;<2cm,1.5cm>:<1cm,1cm>::eKde nesLҍ;JLͷ=%?CQ ?IGG?O>?V?=6__ "/ybase j!e&bAefore)n::[>ruYoX?l:if4b_ł\)Yu6??YWF 9fdYɟ OO+\origin%xxbaseLNybaser"1{_N(1,1)YW32fdfe&Zq32fdfe\ K32fdfe]h%32fdfe^32fdfe`ٞ32fdfeax32fdfebӍ32fdfed.g32fdfeeA32fdfef32fdfeh>32fdfeiϞ32fdfej32fdfelO32fdfem]32fdfeo732fdfep`32fdfeq32fdfesŞ32fdfetp32fdfeuy32fdfeҵču32fdfe8u32fdfeu32fdfeu32fdfeu32fdfeu32fdfeu32fdfeu32fdfeu32fdfeuYeKwhere,4ineachcasetheisat0l1,4nthebasevectorseKhaveUUbGeendrawnandtheisat(1,1)F.xeKWhen5`workingwithcartesiancoGordinatestheseeKthreeUUspGecialhfactorisareparticularlyuseful:[eKff2 )򍍒\halfroottwoK0:70710678 K1K&fes2 )PpHPfeE2 \partroottwoK0:2928932218 l1l&fes2PpPfeE2\halfrootthreeK0:86602540 K1K&fes2 )PpHPfeE3zeKff2 YeKMore(canbGede nedusing\defLD(or\newcommand eKinUUL5ffA͉TU>'ExX).LWK7R*tj??ځ> ffffd TQղSyntax\ActionX-ffd m͍QոhpGosiCI]!d 3hcoGordi\c hcoGordiiJ\jd 3hpGosiUU+hcoordi\c hpGosi5+8hcoGordi"1ɟ^3aJ\jd 3hpGosiUU-hcoordi\c hpGosi58hcoGordi"1ɟ^3azJ\jd 3hpGosiUU!qǸhcoordi\c hpGosithenUUskew^3b ߵcbyhcoGordiJ\jd 3hpGosiUU.qǸhcoordi\c hpGosibutUUalsocovering^3c øhcoGordiJ\jd 3hpGosiUU,hcoordi\c hpGosithenUUc hcoGordiJ\jd 3hpGosiUU;hcoordi\c hpGosiUU,UUswappandc,c hcoGordiJ\jd 3hpGosiUU:qǸhcoordi\c hpGosiUU,UUsetbase^3d C,c hcoGordiJ\jd 3hpGosiUU::qǸhcoordi\c hpGosiUU,UUyb}'aseP c8origin',UUc hcoGordiJ\jd 3hpGosiUU*hob8jecti\c hpGosiUU,UUdrop^3f Hhob8jectiJ\jd 3hpGosiUU**hob8jecti\c hpGosiUU,UUconnect^3g Qusinghob8jectiJ\jd 3hpGosiUU?qǸhplacei\c hpGosiUU,UUc hplacei^3hJ\jd 3hpGosiUU@hstackingi\c hpGosiUU,UUdohstackingi^3oJ\jd 3hpGosiUU=hsavingi\c hpGosiUU,UUdohsavingi^3pQոhcoGordiCI]!d 3hvectori\hpGosiUUishvectoriwithzerosize J\jd 3hemptyijqc\reuseUUlastc(donothing)J\jd 3p\pJ\jd 3xjqy\axisUUintersection^3k Wwith~fe [۟gpciJ\jd 3shdigitijqs{khnumbGeri}\stack^3o QpGositionUUhdigitiorhnumbGeribelowthetopJ\jd 3"i`0hidi"\restoreUUwhatwassaved^3p ߲ashidiearlierJ\jd 3{lhpGosiUUhdecori}\theUUcresultingfrominterpretingthegroup^3lQոhvectoriCI]!d 30\zero J\jd 3\absoluteJ\jd 3\absoluteUUwithequaldimensionsJ\jd 3(lhfactoriUU, ꧸hfactoriUU)\inUUcurrentbase^3diJ\jd 3aUU( ꧸hnumbGeriUU)\angleUUincurrentbase^3eJ\jd 3hcorneri\fromUUreferencepGointtohcorneriofcJ\jd 3hcorneriUU( ꧸hfactoriUU)\TheUUhcornerimultipliedwithhfactoriJ\jd 3/lhdirectioniUUhdimeni/\vectorUUhdimeniinhdirectioni^3miQոhcorneriCI]!d 3LUUj qRUUjDUUjU\o set^3n ߲toUUleft,right,down,upsideJ\jd 3CLUUj qCRUUjCDUUjCUUUjC\o set^3n ߲toUUcenterofside,truecenterJ\jd 3LDUUj qRDUUjLUUUjRU\o set^3n ߲toUUactualleft/down,...cornerJ\jd 3EUUj qP\o set^3n ߲toUUnearest/propGortionaledgepointtopzQոhplaceiCI]!d 3<UUhplaceijq>hplacei\shave^3h (0)/(1)UUtoedgeofp/c,fڧ 0=1J\jd 3(lhfactoriUU) ꧸hplacei\fڧ hfactorizJ\jd 3hslidei\pickUUplace^3h ߲andapplyhslidei@4J\jd 3!q{ ĸhpGosi}Rhslidei\intercept^3j HwithUUlinesetupbyhpGosiandapplyhslidei@4QhslideiCI]!d 3/lhdimeniUU/\slide^3i hdimeniUUfurtheralongconnectionJ\jd 3hemptyi\noUUslideffdRFigureUU1:qǸhpGosiitions.LWK8 *tj??X3e.Anangle^ }inXYH-picisthesameasthecoGor- dinatepair( cos z,sin z) ~where mustbGeanintegerinterpretedasanumbGerofdegrees.UThustheиhvectoria(0)isthesameas(1,0)Eanda(90)asUU(0,1)F,UUetc.8T3f.T*odr}'opjanhob8jectiatcwith* meanstoactu-allyy\physicallytypGesetitinthepicturewithref-erenceUpGositionatc|howthisisdonedependsonz@thehob8jectiinquestionandisdescribGedindetailu inx4.TheintuitionwithadropisthatittypGesetssomethingat<Xc, R޵Yc> andsetstheedgeofUUcaccordingly*.3g.S8Thec}'onnectopGeration**0will rstcomputeanumbGer.ofinternalparametersdescribingthedi-rectionKfromptocandthentypGesetsaconnection lledwithcopiesofthehob8jectiasillustratedin؎x2.3.qTheexactdetailsoftheconnectionde-pGendinx4.Theintuitionwithaconnectionis6thatittypGesetssomethingconnectingpandcandUUsetsthe? ꧸hpGosioperatorupaccordingly*.3h.qUsingʱ? _willʱ\pickaplace"alongthemostrecentconnectionR@typGesetwith**:.hWhatexactlythismeans@isdeterminedbytheob8jectthatwasusedfortheconnectionandbythemoGdi ersdescribedinUUgeneraltermshere.*The\shave"moGdi ersinahplacei,5<Kand> ,changethedefaulthfactori,f,andhowitisused,byv`moving'thepGositionsthatcorrespondto(0)and(1)빲(respGectively):Theseareinitiallysetequal2topandc,)butshavingwillmovethemto}thepGointontheedgeofpandcwheretheconnectionD\leaves/enters"them,{andchangethedefaulti=f|̲asindicated.#WhenoneendhasalreadybGeenZshavedthusthensubsequentshaveswillcor-respGond toslidingtheappropriateposition(s)aTU>'ExX\jot(usuallyequalto3ptٲ)furthertowardstheˋotherendoftheconnection(andpastit).CFi-nallyAthepickU~actionwillpickthepGositionlocatedtheQsfractionfeofthewayQsfrom(0)bݲto(1)wherefڧ=0.5difUUitwasnotset(by<R,>,orexplicitly).AllǦthisisprobablybGestillustratedwithsomeexamples: eachr in gure2istypGesetbyasequenceoftheformp; c**@{.}**?0'hplacei*{\oplus}'(where]weindicatethe?hplaceiineachcase.q(W*eUUalsogiveexamplesofhslideis.)8T3i.A1Thslidei1]willmove1]thepGositionadimensionfur-ther0Halongtheconnectionatthepicked0HpGosition.F*or,straightconnections(theonlyoneskernel(XY ),-pic`provides)thisisthesameasaddingavectorXeKinMthetangentdirection,i.e.,? mL:::›/A/isMthesame eKasUU? ?:::I+/"CA/?.eK3j.eKThis2QspGecialhplacei ndsthepointwheretheeKlast connectioninterceptswiththelinefrompeKtocassetupbythehpGosi,thususuallythiswilleKhavetheform!{ hcoGordi;?hcoordi}^5 p,0forexample,eKBug:oOnlyPworksforstraightarrowsatpresent.N8eK\xy?<1cm,0cm>:H(0,0)*=0{+}="+"?;H(2,1)*=0{\times}="*"?**@{.},H(1,0)*+{A}?;(2,2)*+{B}**@{-}H?!{"+";"*"}?*{\bullet}eK\endxyeKwillUUtypGesetE69t+r\v ?GfdfetE͟"fdfer~fdfepQ$fdfenÄfdfem(՟bfdfekafdfeiYxfdfeg\?fdfef ݟ?ބfdfedD#}fdfeb}afdfe`#껄fdfe^Zfdfe]'fdfe[`ifdfeY+y7fdfeW\քfdfeV @ufdfeTCq$fdfeR|3fdfePRfdfeNfdfeM&yfdfeK_;/fdfeIy΄fdfeGп]mfdfeF A fdfeDBC$fdfeB{Jfdfe@ǟfdfe>쉟ψfdfe=%K'fdfeV VꪵAr5!B{pwfgnDlhj4hexcEah_4]` 쾕@eK3k.sThepGositionsdenotedbytheaxisointerse}'ctioneKhcoGordiinatesFxandyarethepointswheretheeKlinethroughpandcintersectswitheachaxis.eKTheUUfollowing gureillustratesthis:/_܍: originZdßF xb}'asep3S{ol4'oh4od5ϟ=o`6o\7wioX8Kot0F 77/sTFyb}'aseIVF ?LC?OVŸy?RJ?T.?IVF __rbiǷx2py[/Է}?cY,xp.'32fdfeͤ32fdfe!32fdfe32fdfe#32fdfe~?32fdfe}\32fdfe|x32fdfe{32fdfez32fdfey 32fdfexꆞ32fdfex32fdfew#32fdfev?32fdfeu\z32fdfetx32fdfetxyyfdfev@>fdfexfdfey Ȅfdfe{썄fdfe}\ Rfdfe#&fdfe!B܄fdfe&_fdfej8=Qyki՜m\32fdfe8n?32fdfeo#B32fdfep32fdfepꀞ32fdfeq32fdfer32fdfes]32fdfetx32fdfeX2fdfeYZfdfeZ^fdfe\a|fdfe]Zϟfdfe^=^Xfdfe`Ƅfdfea[ 4fdfeb^fdfed fdfee[c ~fdfefџ ^fdfeh? Zfdfei[ Ȅfdfej_6fdfelfdfem[ fdfeDeKExercise4: Given'prede nedpGointsA,Bq,C,eKandsDײ(storedasob8jects"A"3,"B"`Ѳ,"C",ands"D"),eKwritej0ahcoGordispeci cationthatwillreturntheeKpGoint=wherethelines}fe:ABand}fek`CDcross(thepointeKmarkedUUwithalargecirclehere):CWFsFsFFGsGsH(H(<AZ^i "Z^i "Zd "Zd "[^i "[^i "\n "\n "PH0 "Bkpkpkklplpm%m%opCq!tq!tql|tql|tr!tr!trֆtrֆtu!tD`f0>`f0>aW0>aW0>cf0>cf0>eu0>eu0>PjC432fdfei"32fdfehܞ32fdfef߰32fdfee32fdfedX32fdfec|,32fdfeb[32fdfea9Ԟ32fdfe`32fdfe^|32fdfe]P32fdfe\$32fdfe[32fdfeZr̞32fdfeYQ32fdfeX0t32fdfeWH32fdfeU32fdfeT32fdfeSĞ32fdfeR32fdfeQil32fdfePH@32fdfeO'32fdfeN32fdfeL伞32fdfeKÐ32fdfeJd32fdfeI832fdfeH` 32fdfeG>32fdfeF32fdfeD32fdfeC\32fdfeB032fdfeA32fdfe@w؞32fdfe{^432fdfeڍ^32fdfe_32fdfe`32fdfea32fdfebqs32fdfecO32fdfed.Y32fdfee ̞32fdfee?32fdfefɲ32fdfeg%32fdfeh32fdfeie 32fdfejC~32fdfek!32fdfeld32fdfelמ32fdfemJ32fdfen32fdfeoz032fdfepX32fdfeq732fdfer32fdfer32fdfeso32fdfet32fdfeuU32fdfevmȞ32fdfewL;32fdfeLeK3l.eKA?hpGosihdecorigr}'ouped!in{},-braces^6 ) isinter-eKpretedT3inaloGcalscopeinthesensethatanypeKand9b}'asebuiltwithinitareforgottenafterwards,eKleaving}lonlythecastheresultofthehcoGordi.eKNote:dqOnly:pandb}'asearerestored{itisnotaeKTU>'ExXUUgroup.fffy̟ J= "5-:5LTheXbracescanb "5-:6LOneXcanuse(* U`.j..*) insteadXalsohere.LWK9 *tj??)Lɠ7L͍Y GFc EDY@AcBCL΍\76c54 \01c23 6pUUiscircular: f8XcU>isa c.squaregpftext!]z[3232]32fd'g3232($]`‰'fd'fd32]z[3232]fd'g3232^533(`Ɵ5(33X{RORFER< R3Ik"R)ALR uv]R ؠ#R ßR6RouRbEG;RqRލR#ǟčR˹SROsRIAR{kRkR˟1R(.5)`ßq sfdqf?<>(.2)(.5)u?rd^rEHurU2rΩrG[Fr{yyig?`]?rddFrgD0urkUrnΨrrGZFr`cyyQY}0HL.?>>>>U  sfdU=D5ڇ.Ɵ2?<>(.7)밟+rdbrar#UƟr&xͫr*G*˕2r밟 Ѻyy3O˟?>(.7)`\ sfdŸ\,CFigureUU2:qExamplehplaceisR/)Exercise;5: WhatGe ectisachievedGbyusing theUUhcoGordiinate\{;}"?b3m.The;vector/8Z/,whereZ=Wisahdimenision,isthesamemasthevector<jZaIJcoso z,IwZaIJsinS z>where istheK{angleofthelastdirectionsetbyaconnec-tioni(i.e.,with**Sc)orsubsequentplacement(??)pGosition.[ItispGossibletogiveahdirectioniasdescribedinthenextsection( gure3,note4linparticular)that5FwillthenbGeusedtosetthevqalueof z.gItisalsopGossibletoomitthehdimeniinwhichcaseitUUissettoadefaultvqalueof.5pcUI.3n.qA hcorneri6isano setfromthecurrent<>3Xc, R޵Yc>pGositionu[toaspeci cpositionontheedgeofthecԲob8ject(thetwo-letteronesmaybGegiveninanycombination):FύK3232KE32fd8Wg3232%'Kiz$fdi$fd32K3232KEfd8Wg3232WcKiz2fdfeM"2fdfeNŸ2fdfeP2fdfeRN 2fdfeT.2fdfeUR2fdfeWyv2fdfeQ62fdfecP2fdfeuj2fdfe~2fdfe|2fdfez2fdfexҟ2fdfev2fdfet2fdfer 2fdfeq:2fdfeoT2fdfem*n2fdfek<2fdfeiN2fdfeg`2fdfeer֟2fdfec2fdfea 2fdfe_$2fdfe]>2fdfe[X2fdfeYi32fdfe'Yi32fdfeYi32fdfeYi32fdfeYi32fdfeYi32fdfe降Yi32fdfelYi32fdfeYi32fdfeYi32fdfeYi32fdfeYi32fdfeYi32fdfeYi32fdfeYi32fdfeYi32fdfeYi32fdfeYi32fdfeYi32fdfe49L=<2fd`K//l9Rh2fd`hooW6DYiҟ fdYֺ֛OOW6UYiτ fdY֛Ϻ6LDGA yE֟ yCko^yKֺ<<YORDhӹVb V\ Vhֺkk<Մ'LU߈WI)"1}荍G/1E51KϺvLܼRUh㛹r r)!rhϺyy4yN,CLG#ϟ%ODcOAIOKbS''ZCRhb:d'd[dhbSrrrUDCh̹Ej)g }ElBD H.EhֺbblՄ'UC߈Wh[x }荍j [x lv[x hϺwSM,Chb=ok}ooop}KohbSww59mPFg-dB1d=y5dK22jߟqQpWy|fdfeUuHfdfeSnfdfeRgfdfePE`qfdfeNxY* fdfeLR≄fdfeJKfdfeIDSfdfeGD= fdfeEw6}fdfeC/|fdfeA(5wfdfe@!fdfe>CqfdfeplK22667<TheD`edgepGoint'E rliesontheedgealongthelinefromN_ptothecentreoftheob8ject,Oincontrasttothe4`propGortional'pointP ѲwhichisalsoapGointon؎theedgebutcomputedinsuchawaythattheob8jectUUloGoksasmuchUU`awayfromp'aspGossible.[Finally*,ka3following( sf) suxwillmultiplytheo setUUvectorbythehfactorif.%mExercise٭6: Whatzisthedi erencebGetweenzthehpGosiitionsUUc?<jandUUc+EL?/)eKExerciseT7: WhatUUdoGesthistypeset?N8eK\xy?*=<3cm,1cm>\txt{Box}*\frm{-} H!U!R(.5)?*\frm{..}*{\bullet}\endxy𕍒eKHintز:+T\frmnisde nedbytheframeextensionandeKjusttypGesetsaframeofthekindindicatedbytheeKargument.]eKBug:EزCurrentlywonlythesingle-lettercorners(L,eKR, ID,U,C,E,andP) 7willworkforanyshapGe|theeKotherssilentlyassumethattheshapGeisrectan-eKgular.DeK3o.,jTheWstackk\isaspGecialconstructionusefulforstor-eKing,asequenceofhpGosiitionsthatareaccessibleeKusing,thespGecialhcoordiinatessln,4wherenisei-eKtherasingledigitorapGositiveintegerin{} |s:Eqs0eKisalwaysthe`top'elementofthestackandiftheeKstack hasdepthdthenthe`bGottom'elementofeKthestackhasnumbGers{ wd~1}?.RThestackissaideKtoj]bGe`empty'whenthedepthis0andthenitiseKanterrortoaccessanyofthes Bqnor`pGop'whicheKmeansremovethetopelement,%/shiftingwhatiseKins10tos0!,s2Atos1,etc.VSimilarly*,`pushc'eKmeans$toshifts0.tos1 ,-etc.,and$theninserttheeKcUUasthenews0 O.eKTheUUstackismanipulatedasfollows: eKff2  @I̸hstackingi>aAction_eKff2 * @+hcoGordi>apushUUhcoGordii @-hcoGordi>ac hcoGordi&VthenUUpGop @=hcoGordi>aloadUUstackwithhcoGordi @@hcoGordi>adoUUhcoGordi&forUUc stack @i>ainitialise @(>aenterUUnewframe @)>aleaveUUcurrentframe_eKff2eKT*oy`loadstack',(meanstoloadtheentirestackeKwithUthepGositionssetbyhcoordiwithinwhich,eKmeansUU`pushc'.LWeJ10 &Ϡ*tj??gwT*o;#`dohcoGordiforallstackelements'meansto set`ctoeachelementofthestackinturn,fromthebGottomandup,andforeachinterpretthehcoGordi.2Thus9ythe rstinterpretationhascsetto thebGottomelementofthestackandthelasthascsettos0 u.QIfthestackisempty*,thehcoGordiisUUnotinterpretedatall.These-=twoopGerationscanbecombinedtorepeataUUparticularhcoGordiforseveralpoints,likethis:N8\xy@={(0,-10),(10,3),(20,-5)}?@@{*{P}}\endxy!LwillUUtypGesete?F^P[$aPx$P.Finally*,thew3stackcanbGeforciblyclearedusing@i ,vQhowever,thisoisrarelyneededbGecauseof@( ﲲ,which^savesthestackasitis,aandthenclearsit,suchwhenithasbGeenused(andisempty),and@)isissued,thenitisrestoredasitwasatthetimeUUofthe@( O.Exercise8: HowNwouldyouchangetheexam-ple2@abGovetoconnectthepGointsasshownbGelow?TCԟgGGgL{gQ7-g)gU8MgZ qg_iڕgd$ghl|gmߟNgrWR%gwş Ig痍\dYVSxQgNEVKrEH4E#Bx %eEtvEqEm?2EjcEf}EbYE_xE$B(3p.qIt?ispGossibletode nenewhcoordiinatesontheform" @hidi"bysavingthecurrentcusingthe...=" *hidi" OhpGosiitionrRform.ȾSubsequentusesof"hidi" 1willthenreestablishthecatthetimeoftheUUsaving.Usinga"hidi"thatwasneverde nedisanerror,however,C_saving>intoanamethatwaspreviouslyde ned justreplacesthede nitionwithoutwarn-ing,;i.e.," {hidi" alwaysreferstothelastthingsavedUUwiththathidi.However,many`otherthingscanbGe`saved':ingeneralUU@RhsavingiUUhaseitheroftheforms ʍff2 9x@:"Whidi"Hm"M hidi",restores /currentHmb}'asefd@׸hcoGordi"?hidi"Hm"M hidi"6FreinterpretsIhcoGordi@@"Whidi"Hm@="X-hidi"(reloadsthisstackff2dThe rstformde nes"hidi"tobGeamacrothatrestoresUUthecurrentb}'ase[.TheseconddoGesnotdependonthestateatthetime_ofde nitionatall;itisamacrode nition.gweKY*ou~canpassparameterstosuchamacrobylet- eKtingitusecoGordinatesnamed"1"ײ,"2"ƈ,etc.,andeKthen2use="1"&,')="2"',')etc.,just2bGeforeeveryuseeKof&ittosettheactualvqaluesofthese.N Note:<0itiseKnot,pGossibletouseahcoordioftheform" )hidi"eKdirectly:qwriteUUitas{" Ohidi"} ."Q덒eKExercise9: W*ritechamacro"dbl"todoubletheeKsizeofthecurrentcob8ject,e.g.,changingitfromeKtheUUdottedtothedashedoutlineinthis gure:/{ɍYnU+*GT3232H荍3232K(32323232323232323232323232323232323232323232323232323232323232323232K3232ʍG;#㋷3232O3232323232323232323232323232323232323232323232323232s5t㋷3232O323232323232323232323232323232323232323232323232323232GT3232H荍3232K(32323232323232323232323232323232323232323232323232323232323232323232K3232V1q-32321__;[_ D______ D_D3232=Ztؾ11W ;32323232 ;32ؾL5 ;32323232 ;32321q-32321__;[_ D______ D_D3232(_XeKThe\ nalformde nesaspGecialkindofmacroeKthatshouldonlybGeusedafterthe@=vstackoper-eKation:\the+,entirecurrentstackissavedsuchthateKtheUUstackopGeration@="Lhidi"Rwillreloadit.eKNote:hThereisnodistinctionbGetweenthe`nameeKspaces'$ofhidisusedforsaved$coGordinatesandeKotherUUthings.$͍eK4Obfjects. eKOb8jectsaretheentitiesthataremanipulatedwitheKthe* ۱and**hpGosiڲoperationsabovetoactuallygeteKsomeoutputin}XY)-pictures.nKAsforhpGosiitionstheeKopGerationsareinterpretedstrictlyfromlefttoright,eKhowever,ftheactualob8jectisbuiltb}'eforeqalltheeKhmoGdi eris=takee ect.CThesyntaxofob8jectsisgiveneKin gure3withreferencestothenotesbGelow.lRe-eKmark:.Itisnever⧲allowedtoincludebraces{}.insideeKhmoGdi eris!=In'caseyouwishtodosomethingthateKrequires{...} thencheckinthismanualwhetheryoueKcanuse(* в...*)Fzinstead.^IfnotthenyouwillhavetoeKuseUUadi erentconstruction!?eKNotesEeK4a.,jAnhob8jectiisbuiltusing\object(obox;{Ahtexti}?.eK\object%6box+:isUUinitiallyde nedasN8eK\def\objectbox#1{%H\hbox{$\objectstyle{#1}$}}eK\let\objectstyle=\displaystyleeKbuta\maybGerede nedbyoptionsortheuser.eKThe\htextishouldthusbGeinthemoderequiredeKbylthe\objectboxcommand|withthedefaulteK\objectbox,Obshownj5abGoveitshouldbGeinmatheKmoGde.LWeJ11 R*tj??X ffffd T SyntaxĆActionX-ffd fd hob8jectiE%K!^GhmoGdi eriUUhob8jectiĆapplyUUhmoGdi eritohob8jecti LEj^Ghob8jectbGoxiĆbuildUUhob8jectbGoxithenapplyitshmodi erisi hob8jectbGoxiE%K!^G{gahtextiUU}ĆbuildUUdefault^4a Qob8jectLEҸj^GhlibraryUUob8jectijq@\nhdiriĆuseUUhlibraryob8jectiorhdiriectional(seex6)zLEҸj^GhTU>'ExXUUbGoxi{ ꧸htexti}Ćbuild'ExXbGoxiĆcommand,UUe.g.,\hbox_LEҸj^G\objectUUhob8jectiĆwrapUUupthehob8jectiasa nishedobjectbGox^4cLEҸj^G\compositeUU{ ꧸hcompGositeiUU}ĆbuildUUcompGositeob8jectbox^4diLEҸj^G\xyboxUU{ ꧸hpGosiUUhdecori}ĆpackqageUUentireUQXY U-pictureasob8ject^4ez hmoGdi eriE%K!^G!gahvectoriĆhob8jectiUUhasitsreferencepGointshifted^4f HbyhvectoriLEj^G!Ćhob8jectiUUhastheoriginalreferencepGointreinstatedLEҸj^GhaddUUopihsizeiĆchangeUUhob8jectisize^4gzLEҸj^GhjqiĆhob8jectiUUishidden^4h C,invisible^4i@4LEҸj^G[gahshapGeiUU]Ćhob8jectiUUisgiventhespGeci edhshapei^4jLEҸj^G[=UUhshapGei]Ćde neUUhshapGei^4k Wtoreestablishcurrentob8jectstyle LEҸj^GhdirectioniĆsetUUcurrentdirectionforthishob8jecti haddUUopiE%K!^G+jjt(-\j#=oʸj+= 5j}-=Ćgrow,UUshrink,set,growto,shrinktoi hsizeiE%K!^GhemptyiĆdefaultUUsize^4gLEҸj^GhvectoriĆsizeUUassidesofrectanglecoveringUUthehvectoriz hdirectioniE%K!^GhdiagiĆhdiagionalUUdirection^4lzLEҸj^GvUUhvectoriĆdirection^4l ofUUhvectoriLEj^Gq{RhpGosiUUhdecori}Ćdirection^4l fromUUptocafterhpGosihdecoriLEj^GhdirectioniUU:qǸhvectoriĆvectorUUrelativetohdirectioni^4mLEҸj^GhdirectioniUU_?jhdirectioniUU^Ć90^9cloGckwise/anticlockwiseUUtohdirectioni^4m hdiagiE%K!^GhemptyiĆlastUUuseddirection(notnecessarilydiagonal^4lIJ)LEҸj^Glgajm~ rv]j|/d!juĆleft,UUright,down,updiagonal^4lLEҸj^GldljrrdWjlujruĆleft/down,UU...diagonal^4l hcompGositeiE%K!^Ghob8jectiĆ rstUUob8jectisrequiredLEҸj^GhcompGositeiUU* ꧸hob8jectiĆaddUUhob8jectitocompGositeobjectbGox^4dffd 'ExXbGoxwithdimen- sionsYwR7(h+d)willhaveLc R=qRc=wD=2,Uc=;=*ZDc=(h`+d)=2,thusinitiallybGeequippedwiththeadjustment!C(seenote4f).NInpartic-ular:inlordertogetthereferencepGointonthe(centerJof)thebaselineoftheoriginalhTU>'ExXbGoxithenyoushouldusethehmoGdi eri!;utogetthereference=pGointidenticaltotheTU>'ExXreferencepGointUUusethemodi er!!LL._TU>'ExXnicalremark:xAnymacrothatexpandstosomethingxthatstartswithahbGoximaybGeusedasUUahTU>'ExXbGoxihere.r4c.T*akes{anob8jectandconstructsit,hbuildingabGox;itisthenproGcessedaccordingtothepreceedingmoGdi ers. H^This2formmakesitpossibletouseany2hob8jectiasaTU>'ExXbGox(evenoutsideof2XY -pictures)0IbGecausea nishedob8jectisalways0IalsoaUUbGox.4d.qSeveralLhob8jectiscanbGecombinedintoasingleob8jectusingthespGecialcommand\compositewith#alistofthedesiredob8jectsseparatedwith*s9astheargument.[rTheresultingbGox(andob-ject)istheleastrectangleenclosingallthein-cludedUUob8jects.4e.T*akeanentireXY:-pictureandwrapitupasabGox``asdescribedinx2.1.Makesnestingof`\XY `-picturespGossible:?+theinnerpicturewillhaveitsown$zeropGointwhichwillbGeitsreferencepointintheUUouterpicturewhenitisplacedthere.4f.Anob8jectisshifte}'duahvectoribymovingthepGointRinsideitwhichwillbGeusedastherefer-encepGoint.ASThise ectivelypushestheob8jectthesameUUamountintheoppGositedirection.zčExercise810: WhatHisthedi erencebGetweentheUUhpGosiitions0*{a}!DR0and0*!DR{a}-U=?4g.S8Ahsizeiزisapair<յWc,H>ӲofthewidthandheightofG}arectangle.H?Whengivenasahvectoritheseare}justthevectorcoGordinates,i.e.,the}hvectoristartsinthelowerleftcornerandendsintheup-pGer?rightcorner.`Thepossiblehaddopierationsthat"@canbGeperformedaredescribedinthefol-lowingUUtable.2;L͉fffd͟ ff͟fdhaddUUopi/` ff4#descriptionޟ ffff͟ ff`fd+/` ff4#growޟ ff ͟ ff`fd-/` ff4#shrinkޟ ff͟ ff`fd=/` ff4#setUUtoޟ ff͟ ffpbfd+=/` ff4#growUUtoatleastޟ ff͟ ffpbfd-=/` ff4#shrinkUUtoatmostޟ ffff38tIn\eachcasethehvectorimaybGeomittedwhichinvokes"the\defaultsize"fortheparticularhaddgweKopi:4̍L͉fffd͟ ff͟fdhaddUUopi/` ff4#defaultR ffff͟ ff`fd+/` ff4#+g k ff ͟ ff`fd-/` ff4#-g k ff͟ ff`fd=/` ff4#=R ff͟ ffpbfd+=/` ff4#+= ʟ ff͟ ffpbfd-=/` ff4#-=  ffff4GeKThekdefaultsforthe rstthreearesetwiththe eKcommands eKff2 ~.\objectmarginUUhaddopi{Rhdimeni}.\objectwidthUUhaddopi{Rhdimeni}.\objectheightUUhaddopi{Rhdimeni}eKff23eKwhere_haddopiisinterpretedinthesamewayaseKabGove.<3eKThe{defaultsfor+=8u/-=are{suchthattheresult-eKingob8jectwillbGethesmallestcontaining/largesteKcontainedUUsquare.eKExerciseL11: How3 aretheob8jectstypGesetbyeKtheWhpGosiitions\*+UR{\sum}4"and\*+DL{\sum}"eKenlarged?eKBug:XCurrentlyHchangingthesizeofacirculareKob8ject?isbuggy|itischangedasifitisarect-eKangle^andthenthechangetotheRr\parametereKa ects/thecircle.[TThisshouldbGe xedprobablyeKbyageneralisationoftheo ?QshapGetobeovqalsoreKellipsesUUwithhorizontal/verticalUUaxes.xfeK4h.AhiddenMob8jectwillbGetypesetbuthiddenfromeGXYK-picinthatitwon'ta ectthesizeoftheentireeKpictureUUasdiscussedinx2.1.eK4i.eKAnQinvisibleob8jectwillbGetreatedcompletelyeKnormalexceptthatitwon'tbGetypGeset,i.e.,XY m-eKpicUUwillbGehaveUUasifitwas.eK4j.eKSettinggtheshap}'e²ofanob8jectforcestheshapGeofeKitsedgetobGeasindicated.ThekernelprovideseKthree|shapGesthatchangetheedge,namely[.],eK[],UUand[o],correspGondingtotheoutlines#! @a ,s3232AÞ32fdFFg3232Qa/fdfI։/fd323232AáfdFFg32328$@2fdfe 2fdfe"2fdfe$(2fdfe&82fdfe(sH2fdfe*YX2fdfe,?h2fdfe.%x2fdfe0 2fdfe12fdfe3ר2fdfe52fdfe7ȟ2fdfe9؟2fdfe;o2fdfe*mELf2fdfed&V2fdfeb6 2fdfe`E2fdfe^Uo2fdfe\e"2fdfeZt՟2fdfeX2fdfeV;2fdfeT2fdfeR2fdfePT2fdfeN2fdfeL⺟2fdfeJm2fdfeI 2fdfeGӟ2fdfeE!2fdfeC192fdfeA@2fdfe?P2fdfe=`R2fdfe;p2fdfeM˞ERC;o32fdfe⍍;o32fdfe;o32fdfe;o32fdfe;o32fdfe;o32fdfe;o32fdfe8BD_;o32fdfe';o32fdfe;o32fdfe;o32fdfe;o32fdfe;o32fdfe;o32fdfe;o32fdfe;o32fdfe;o32fdfe;o32fdfe8ƟUpIֲ,UUandb@`g^Za^Zfbe"c"dO2fdfe!2fdfet2fdfe2fdfe\2fdfefП2fdfe8D2fdfe 2fdfe,2fdfe2fdfe~2fdfeO2fdfeĄELO2fdfe~2fdfe2fdfe02fdfe 2fdfe8H2fdfefԟ2fdfe`2fdfe2fdfex2fdfe!2fdfeO2fdfe{ ERhO32fdfe.O32fdfeO32fdfeO32fdfeO32fdfeO32fdfeO32fdfeO32fdfeO32fdfeO32fdfeO32fdfeO32fdfe"C EDFO32fdfetO32fdfeO32fdfeO32fdfeO32fdfeO32fdfeO32fdfeO32fdfeO32fdfeO32fdfeO32fdfeO32fdfei`EUeKwhereOthedenotesthepGointofthereference eKpGosition̠intheob8ject(the rstisapoint).קEx-eKtensionscanprovidemoreshapGes,however,alleKshapGes6settheextentdimensionsL,oRDz,D,andeKU.<3eKTheMdefaultshapGeforob8jectsis[]andforplaineKcoGordinatesUUitis[.].LWeJ134*tj??gwF*urthermoreFthehshapGeis[r],|[l],[u],andF[d], areLde nedforconvenienceLtoadjusttheob8jecttotheMindicatedsidebysettingthereferencepGointsuch ythatthereferencepGointisthesamedis-tance6afromtheoppGositeoftheindicatededgeandthe8Aob8ject[r]\hbox{Wide?text}j0Ihasrefer-encev!pGointattheinΟWideUUtextW323232fd+}/g3232捍ôfd/ąôfd32W3232fd+}/g32323:buttheob8ject[d]\hbox{Wide?text}[ŲhasreferencepGointattheoinWideUUtext֞323232fd+}/g3232捍=ôfd/ôfd32֞3232fd+}/g3232檸/.Finally*,6[c]putsthereferencepGointUUatthecenter.DNote:ExtensionszcanaddnewhshapGeiob8jecthmoGdi erisPwhicharethencalledhstyleis.p'ExXeKgrouping.荍eK4l.eKSetting~AthecurrentdirectionissimplypretendingeKfor4thetypGesettingoftheob8ject(andthefollow-eKingϔhmoGdi eris)thatsomeconnectionsetit{theeKhemptyicasejustinheritsthepreviousdirection.eKIt{uisparticularlyeasytosethdiagionaldirections:D`QQHQQOTթITթN]QJ]QMeKeL*6S")dl7}e")=ldٞAo-ӺDsGǹJN EQLAo-bZ09d]'qDŽfd]Q'qǺn3")dr{_E")=rduٞ?rrX?oSޟ?l'J T?h (?e"@?y6b枧riQ2fd`//n3ݶ,ur{_Eݶ,=ru?EvZs8 oݡl"i(e$z,??Zϧu]fd]QҧOO*6SޝIul7}eޝI=luAmI?D=ɏ?Gџ?Je"?NNa?QLz?AmI__*9l22fd`2ooHeKAlternativelyvȨhvectorisetsthedirectionasiftheeKconnectionfrom0 'tothehvectorihadbGeentypGe-eKset exceptthattheorigintisassumedzerosucheKthat pdirectionsv(jx,?y[) Fmeanthenaturalthing,eKi.e.,-isthedirectionoftheconnectionfrom(0,0)eKtoUU(Rx,?y[)ֲ.eKIncasethedirectionisnotassimple,youcaneKconstructw{/AhpGosiwhdecori}thatsetsuppandeKcԮsuchthat~fe [۟gpc7hasthedesireddirection.Note:eKthatyoumustusethe(*$...*)JformifthisistoeKappGearUUinanob8jecthmodi eri!eKExercise12: WhatXe ectisachievedXbyusingeKhmoGdi erisUUv/1pc/&*andUUv/-1pc/(@?荍eK4m.OnceutheinitialdirectionisestablishedaseithereKtheUlastoneoranabsoluteonethentheremain-eKderUUofthehdirectioniisinterpreted.eKAddingVasingle^ or_denotestheresultofrotat-eKingkthedefaultdirectionarightangleinthepGos-eKitive9andnegativedirection,ri.e.,anti-/cloGckwise,eKrespGectively*.!Note:DosnotKuse^ p^>butonly__eKtoUUreversethedirection!eKAtrailing: éhvectoriislikev éhvectoributuseseKthe\hdirectionitosetupastandardsquarebaseLWeJ14*tj??gwsuchbthat:(0,1)%and:(0,-1)*Bmeanthesameas :a(90)kandwd:a(-90))andwdas^ .Ųand_a,respGectively*.^Exercise13: WhatXe ectisachievedXbyusinghmoGdi erisUUv/1pc/:(1,0)EandUUv/-1pc/__2:?!N5DecorationshDecoriations[areactualTU>'ExXmacrosthatdecoratetheUcurrentpictureinmannersthatdepGendonthestate.gThey6areallowed6afterJ:thehpGosiitioneitherofthemouter\xy...\endxymorinside{ 1j...}꧲.FThempGossi-bilitiesUUaregivenin gure4withnotesbGelow. Mostoptionsaddtotheavqailablehdecori,xinparticularthev2&optionloadsmanymoresinceXY -picversionspriorto2.7providedmostfeaturesashdecori.Notes5a.S8Saving Iandrestoringallows`excursions'wherelotsWofthingsareaddedtothepicturewithouta ectingQtheresultingQXY -picstate,Ri.e.,c,p,andb}'ase[,%andwithoutrequiringmatching{}|s.fTheindepGendenceof{}isparticularlyusefulincon-junction2withthe\afterPOS2command,jforex-ample,UUthede nitionN8\def\ToPOS{\save\afterPOS{% \POS**{}?>*@2{>}**@{-}\restore};p,}uwillccausethecoGde\ToPOS#hpositoconstructadouble-shaftedarrowfromthecurrentob8jecttothehpGosi(computedrelativetoit)suchthat\xy*{A}?\ToPOS+<10mm,2mm>\endxyL²willtypGesettheUUpicturejA 3O9.6 ee*ame 1`e?e".Note: Saving.thiswayinfactusesthesamestateasthe{}r`grouping',_sothecoGdep1|s,{p2|s\save},.j ...Y{\restore}@will-havecU=p1bGothUUatthe...andUUattheend!nz5b.qOneverytemptingkindofTU>'ExXcommandstopGerformashdecoriisarithmeticoperationsonthe]XY`a-picastate. Thiswillworkinsimple]XY-picturesChecktheTU>'ExX-nicaldoGcumenta-tionUU[15 ]fordetailsabGoutthis!7=Macrosthatexpandtohdecoriwillalwaysdothesame,UUthough.5c.\xyecho` willturnonechoingofallinterpretedXY -picϸhpGosicharacters.6Bug:*NotcompletelyimplementedIayet.M\xyverbosewillswitchonagweKtracingnofalljXYn-piccommandsexecuted,swith eKlineenumbGers.T"\xytracingtracesevenmore:EOtheeKentire4UXY Y-pic4YstateisprintedaftereachmoGdi ca-eKtion.q\xyquietUUrestoresdefaultquietopGeration. eK5d.Ignoringn@meansthatthehpGosihdecoriisstilleKparseddtheusualwaydbutnothingistypGesetandeKtheUQXY U-picUUstateisnotchanged.eK5e.0It_;ispGossibletosave_;anintermediateformofcom-eKmandsthatgeneratepartsofanXY-picturetoeKa'$ lesuchthatsubsequenttypGesettingofthoseeKpartsissigni cantlyfaster:?thisiscalledc}'om-eKpiling}.ThezaproGduced lecontainscodetocheckeKthat[thecompiledcoGdestillcorrespondstotheeKsameʳhpGosihdecoriaswellasecientʯXY J-coGdetoeKredo^$it;bifthehpGosihdecorihaschangedthentheeKcompilationUUisredone. eKTherearetwowaystousethis.mThedirectiseKtoinventahnameiforeachdiagramandtheneKembraceitin\xycompileto{Iҡhnamei}?| {...} }o{eKthis;vdumpsthecompiledcoGdeintothe leeKhnamei.xyc.eKWhen_qmanydiagramsarecompiledtheniteKis̃easiertoadd\xycompile{?...} *around̃theeKhpGosihdecori3#tobecompiled. 1ThiswillassigneK le]namesnumbGered]consecutivelywithahpre xieKwhich]isinitiallytheexpansionof\jobname-4buteKmayUUbGesetwith ceKff2 l'#k\CompilePrefix{?hpre xi}ōeKff2LeKThishasthedisadvqantage,Zhowever,thatifaddi-eKtionalcompiledXY H-picturesareinsertedthenalleKsubsequent(pictureswillhavetobGerecompiled.eKOneK6particularsituationisprovided,though:eKwhen@usedwithinconstructionsthattypGesettheireKcontentsmorethanonce(suchasmostAU>'M S-eKL5ffA͉TU>'ExXUUequationconstructs)thenthedeclaration 덒eKff2&\CompileFixPoint{?hidi}ōeKff2LeKcan @bGeusedinsidetheenvironment @to xtheeKcountertohavethesamevqalueateverypassage. eKFinally*,Ɖwhen|many`administrativetypGesettingeKruns'dareneeded,ie.g.,readjustingdL5ffA͉TU>'ExXcrosseKreferencesandsuch,thenitmaybGeanadvqan-eKtagextonottypGesetanytXY x-picturesatallduringeKtheintermediateruns.T8ThisissuppGortedbytheeKfollowing declarationswhichforeachcompilationeKcreatesaspGecial lewiththeextension.xydcon-eKtainingUUjustthesizeofthepicture: ceKff2;1\MakeOutlines;1\OnlyOutlines;1\ShowOutlinesLWeJ15 *tj??n&o ffffd TSyntaxActionX-ffd fdhdecori< B!QhcommandiUUhdecoriꖲeitherUUthereisacommand... BjQhemptyiꖲ...orUUthereisn't.ihcommandi< B!Q\saveUUhpGosiꖲsaveUUstate^5a ,thendohpGosiBjQ\restoreꖲrestoreUUstate^5a Qsavedbymatcing\saveBjQ\POSUUhpGosiꖲinterpretUUhpGosiBjQ\afterPOSUU{ ꧸hdecoriUU}hpGosiꖲinterpretUUhpGosiandthenperformhdecoriBjQ\dropUUhob8jectiꖲdropUUhob8jectiasthehpGosi* ꧲operationBjQ\connectUUhob8jectiꖲconnectUUwithhob8jectiasthehpGosi***operationBjQ\relaxꖲdoUUnothingzBjQhTU>'ExXUUcommandsiꖲanyUUTU>'ExXcommands^5b ߲anduser-de nedmacrosthatUUneithergeneratesoutput(watchUUoutforstrayspaces!),UUnorchangesthegrouping,maybGeused$͍BjQ\xyverboseUUj q\xytracingUUj\xyquietꖲtracing^5c òcommandsBjQ\xyignoreUU{RhpGosiUUhdecori}ꖲignore^5d ۲XY-coGdeiBjQ\xycompileUU{RhpGosiUUhdecori}ꖲcompile^5e toUU lehpre xihnoi.xycBjQ\xycompileto{?hnamei}{ hpGosihdecori}ꖲcompile^5e toUU lehnamei.xycffd FigureUU4:qǸhdecoriations.ّ&o=X\NoOutlines:|ff2 +Ther rstdoGesnomore. Thesecondusesthe  leDtotypGesetsadottedframeoftheappropri-atesizeinsteadofthepicture(unlessthepicturehas5 changedandisrecompiled,lthenitistypGe-setaasalwaysaandthe.xyd. leisrecreatedforsubsequentruns).XThethirdshowstheoutlinesasddottedrectangles.ThelastswitchesoutlineproGcessingUUcompletelyo . g6KernelffobfjectlibraryInthissectionwepresentthelibr}'aryobjectsƲprovidedwiththekernellanguage|severaloptionsaddmorelibraryob8jects.MTheyfallintothreetypGes::Mostofthewekernelob8jects(includingallthoseusuallyusedwithf**BƲtofbuildconnections)aredir}'ectionals!,Dide-scribGed9inx6.1.hTheremainingkernellibraryob8jectsareUUcir}'cles'vofx6.2andtextH-ofx6.3.T!6.1LDirectionalsuTThegkernelprovidesaselectionofdir}'ectionals!:ob-jectsthatdepGendonthecurrentdirection.0TheyalltakeUUtheformʉff2 ލ^i\dirhdiriff2 dtoltypGesetaparticularhdiriectionalob8ject.AllhavetheUUstructureʉff2 ލ6^YhdiriUU q!!hvqarianti{?hmaini}ff2&oeKwith[hvqariantibGeinghemptyioroneofthecharacters 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hshorti.tex,andjxy궸hshorti.doc,wherejhshortiishoptioniEtruncatedto6(six)characterstoconformwithUUtheTWG-TDS[17 ]. \xyrequireSfisthesameexceptitisignoredifanoptionޱwiththesamenameisalreadypresent(thusdoGesUUnotcheckUUtheversionetc.).Sometimesw%somedeclarationsofanoptionorheader@ leorwhateveronlymakessenseaftersomeparticular~>otheroptionisloaded.InthatcasethecoGdeUUshouldbewrappedinthespecialcommand n[ff2 {Œ\xywithoptionUU{ ꧸hoptioniUU}{hcoGdeiUU}ff2.which1[indicatesthatifthehoptioniisalreadyloadedthen\hcoGdeishouldbeexecutednow,ސotherwiseitshould#bGesaved#andifhoptionievergetsloadedthens]hcoGdeishouldbeexecutedafterwards.Note:TheęhcoGdeishouldallowmorethanoneexecution;itJissavedJwiththecatcoGdesatthetimeofthe\xywithoptionUUcommand.Finally*, kit3ispGossibletodeclarehcodeiassomecommandstobGeexecutedbeforeeveryac-tualkexecutionof\xywithoption{?hoptioni}{ ...}꧲,andbsimilarlyhcoGdeitobeexecutedbeforeev-ery\xyoption{7>ݸhoptioni}and\xyrequire{<~ڸhoptioni}(reK(collectivelyUUcalled`requests')::eK ff2 ~9\xyeverywithoptionUU{ ꧸hoptioniUU}{hcoGdeiUU} \xyeveryrequestUU{ ꧸hoptioniUU}{hcoGdeiUU}׉ff2!rThisismostoftenusedbyanoptiontoactivqatesomehoGokUUeverytimeitisrequesteditself.|7.2Option leformatOptionUU lesmusthavethefollowingstructure:_V%%&Qhidenti cationi%%&Qhcopyright,UUetc.i/\ifx\xyloaded\undefined?\inputxy\fi\xyprovide{Rhoptioni}{ hnamei}{hversioni}% A{F@hauthori}{ hemaili}{haddressi}hbGodyUUoftheoptioni\xyendinput_UThe6argumentsto\xyprovideshouldcontainthefollowing:Ghoptioni(@Option}loadnameasusedinthe\xyoptioncommand.GYThis shouldbGesafeanddistinguish-able?foranyopGeratingsystemandisthuslim-itedhtocharacterschosenamongthelowercaseletters<(a?{z),digits(0{9),anddash(-),andalloptionspshouldbGeuniquelyidenti ablebythe rstUU6(six)charactersonly*._Vhnamei$wDescriptiveUUnamefortheoption.hversioni+jIdenti cationUUoftheversionoftheoption.hauthori)βTheUUname(s)oftheauthor(s).hemaili$wTheCelectronicmailaddress(es)oftheau-thor(s)ˉorthealiationifnoemailisavqailable.haddressi-#TheUUpGostaladdress(es)oftheauthor(s).LWeJ19>*tj??O]w\Thisinformationisusednotonlytoprintaniceban- ner'butalsoto(1)silentlyskiploadingifthesameversionwaspreloadedand(2)printanerrormessageifUUadi erentversionwaspreloaded. <The[`dummy'optiondescribGedinx21isaminimaloption usingtheabGove features.ItusesthespecialDOCMODE OformatKtoincludeitsowndoGcumentationforthisdoGcument(likeallocialXY -picoptions)butthisisUUnotarequirement. ys7.3LDriveroptionsThehdriverioptionsdescribGedinpartIVrequirespe-cialattentionbGecauseeachdrivercansuppGortseveralextensionoptions,anditissometimesdesirabletochangeA[hdriveriorevenmixthesuppGortprovidedbyseveral.^7Ahdriverioptionisloadedasotheroptionswith\xyoption{ hdriveri} C(orthroughL5ffA͉TU>'ExX2" -classorpackqageoptionsasdescribGedinx1.1).3Thespecialthing9NabGoutahdriveriisthatloadingitsimplyde-claresthenameofit,_establisheswhatextensionsitwillоsuppGort,/andselectsittemporarily*.ThusthespGecial~capabilitiesofthedriverwillonlybeexploitedintheproGducedDVI{ leifsomeoftheseextensionsare alsoloadedandifthedriverisstillselectedwhenoutputisproGduced.1SGenerally*,theorderinwhichtheoptions areloadedisimmaterial.Z(Knownexceptionsa ectxonlyinternalproGcessingandarenotvisibletothe[userintermsoflanguageandexpGectedoutput.)In(particularonedrivercanbGepreloadedinaformatandUUadi erentoneusedforaparticulardoGcument.TheUUfollowingdeclarationscontrolthis:ff2 > e\UseSingleDrivere5forcesUUonedriveronly e\MultipleDriverse5allowsUUmultipledrivers e\xyReloadDriverse5resetsUUdriverinformation>ff2?The rstcommandrestoresthedefaultbGehaviour:that:onyonehdriveriisallowed,&3i.e.,each:loadingofg}ahdriverioptioncancelstheprevious.>Thesec-ondl8allowsconsecutiveloadingofdriverssuchthatwhenloadingahdriverionlytheextensionsactuallysuppGorted>areselected,C7leavingotherextensionssup-pGorted_bypreviouslyselecteddriversuntouched._Be-ware+thatthiscanbGeusedtocreateDVI+ lesthatcannot=bGeprocessedbyanyactualDVI=driverpro-gram!The8ilastcommandissometimesrequiredtoresettheXY -picǸhdriveriinformationtoasanestate,forexample,IafterZhavingappliedoneoftheothertwointhemiddleofadoGcument,NorwhenusingsimpleformatslikeplainTU>'ExXthatdonothaveaclearlydis-tinguishedUUpreamble.w\eKAstheabGovesuggestsitsometimesmakessense eKtoloadhdriverisintheactualtextualpartofadoGc-eKument,'>however,itisrecommendedthatonlydriverseKalsoloadedinthepreamblearereloadedlater,MandeKthatmE\xyReloadDriversisusedwhenthereisdoubteKabGout.thestateofa airs. IncaseofconfusioneKthe@spGecialcommand\xyShowDriverswilllistalleKthepresentlysuppGortedandselecteddriver-extensioneKpairsUUtotheTU>'ExXlog.eKIt[isnotdiculttoaddsuppGortforadditionaleKhdriveris;*howisdescribGedintheTU>'ExXnicaldocumen-eKtation.eKMostextensionswillprintawarningwhenacapa-eKbilityisusedwhichisnotsuppGortedbythepresentlyeKloadedhdriveri.3Suchmessagesareonlyprintedonce,eKhowever,(forsomeformatstheyarerepGeatedattheeKend).e(Similarly*,whenuthesuppGortofanextensioneKthatexploitsaparticularhdriveriisusedawarn-eKingxmessagewillbGeissuedthattheDVIxJ leisnoteKpGortable.'SeKPartffIs3IeKExtensionsꨍeKThispartdoGcumentsthegraphiccapabilitiesaddedeKby2eachstandardextensionoption. _F*oreachisindi-eKcated[thedescribGedversionnumbGer,]theauthor,andeKhowUUitisloaded.eKManyoftheseareonlyfullysuppGortedwhenaeKsuitableidriveroption(describGedinpartIV)isalsoeKloaded,*however,all|addedconstructionsarealwayseKac}'cepted]޲evenUUwhennotsuppGorted. 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õfd%õfd323232롄fdn[g3232*$RbQoldTwhiteonblac9k4{͍\xy?*+<1.5pt>[F**:white]++[F**:red]\txt{text?withbackground},+!D+/d1pc/,*++[F**:black][white]\txt\bf{bold?whiteonblack}\endxyVʍNotice8thatwhenmultipleframe-moGdi ersareused,thefframesareactuallyplacedinreverseor-der,]lso(thatearlieronesareprintedontopoflaterones.T oDo: C6The frameoptionisnotquitecom-pleteyet:WsomenewframesandseveralnewbracketsshouldUUbGeadded.+9.5LUsingcurvesforframesGIfthecurveoptionisloaded,Wthencircularandellipti-cal3+framesofarbitraryradiuscanbGeconstructed,:byspGecifying\UseCurvedFramesWշ.|Thiscanbenegatedby\UseFontFramesM?p.BothofthesecommandsobGeynormal/TU>'ExXgrouping. UF*urthermore,edottedanddashed#framesnowhavearegularspacingoftheirconstituent ob8jects.PTheusualwarningsabGoutmem-ory@requirementsforlargenumbGersofcurvesapplyhereUUalso.'P]10}MoreffTipsextensionVers.3.3bCyKristo erH.Rosehkris@diku.dkiLoadTas:p\xyoption{tips}Thisextensionprovidesseveraladditionalstylesof`tips'foruse(primarily)asarrowheads,andmakesitpGossibletode necustomisedtips.ThisisusedtosuppGorttipsthatmimicthestyleoftheComputerMoGdern)fonts^82byKnuth(see[7]and[6,appGendixF])andL`oftheEulermathfontsdistributedbytheAAMS.w\eKF*ontUUselectionisdonewiththecommandeK ff2 +\SelectTipsUU{Rhfamilyi}{ Ohsizei}>@ff2{whereޱthehfamilyiandhsizeishouldbGeselectedfrom theUUfollowingtable.'WqL͉fffdͤ ff͟fdF*amily ffBj10 ff)G11 ff$12 ffffͤ ff{ fdxy ff;x//4ZK1͟+3?1͟3fd ?1͟1fd X"_]"*4Q"3fd͎Q"1fd͎Q"2fd͎f" ffx:U//ps7+3{3fd {1fd d_d*4d3fd͎d1fd͎d2fd͎d ff2//퇟+3퇟3fd 퇟1fd ܟ_ܟ*4ܟ3fd͎ܞ1fd͎ܟ2fd͎ܟ ffͤ ff{ fdcm ff;x5D xycmat10/5D xycmbt10/4ZK1͟+3?1͟3fd ?1͟1fd X"_]"*4Q"3fd͎Q"1fd͎Q"2fd͎f" ffx:U35D xycmat11/45D xycmbt11/ps7+3{3fd {1fd d_d*4d3fd͎d1fd͎d2fd͎d ff255D xycmat12/65D xycmbt12/퇟+3퇟3fd 퇟1fd ܟ_ܟ*4ܟ3fd͎ܞ1fd͎ܟ2fd͎ܟ ffͤ ff{ fdeu ff<ߟ75D xyeuat10/85D xyeubt10/4L4%9@43fd @41fd W퉟_\퉟%9P퉟3fd P퉞1fd P퉟2fd f# ffy 95D xyeuat11/:5D xyeubt11/qYv%9|v3fd |v1fd Kf_Kf%9Kf3fd Kf1fd Kf2fd e ff~;5D xyeuat12/<5D xyeubt12/{%93fd 1fd ЩC_թC%9ɩC3fd ɩC1fd ɩC2fd ݟ ffff&Onceaselectionismade,thefollowingcommandsareUUavqailable:ff2 !Y\UseTipsPAactivqateUUselectedtips!Y\NoTipsPAdeactivqate>@ff2{TheywareloGcalandthuscanbeswitchedonand/oro forindividualpicturesusingtheTU>'ExXgroupingmech-anism,UUe.g.,N8\SelectTips{cm}{10}\xy*{}?\ar?@{*{\UseTips\dir_{<<}}-*{\NoTips\dir{>}}}?(20,5)*{}\endxyvwillUUtypGesetfoXiiѾsVxs`wF33|g=^gʟ:g|TW gw7grqfgn!gifĆgdbg_寧">g[42QgVxgregardlesskofwhichtipsareusedotherwiseinthedoGc-ument.(x11 fdLineffstylesextensionZVers.3.6bCyRossMoKorehross@mpAce.mq.edu.auiLoadTas:p\xyoption{line}*Thisextensionprovidestheabilitytorequestvqari-ous?e ectsrelatedtotheappGearanceofstraightlines;e.g..qthickness,UUnon-standarddashing,andcolour. >>Thesearee ectswhicharenotnormallyavqail-ableUwithinTU>'ExX. sInsteadtheyrequireasuitable`back-end'Eboptiontoprovidethenecessary\specialcommands,thisextensionwillhaveU>no!ޜe ectU>ontheoutputunlessusedwith!aU>backendthatexplicitlysuppGortsit.5o323232fdzg3232$趍։$fd+$fd32o3232fdzg3232"KThe]extensionprovidesspGeciale ectsthatcanbeusedsHwithanysDXY H-pichob8jecti,zbyde ning[EhshapGei]moGdi ers.@The}modi cationislocaltothehob8jecticurrentlybGeingbuilt,*sowillhavenoe ectifthisob8jectUUisneveractuallyused.ffffy̟ J= "5-:8LThisXfunctionwÎasearliersupp]ZO,setUUthicknesstohdimenin[k|#hhdimeni]ZO,alsoUUsetstohdimenin[k|#h=(]ehwordi]ZO,make[(hwordi]setcurrentZO,styleUUsettingsX+n[k|#h*]ZO,reuseUUpreviousstylen[butt]ZO,buttUUcapatendsn[roundcap]ZO,roundUUcapatendsn[projcap]ZO,pro8jectingUUsquarecap.ff23:Latersettingsofthelinewidthoverrideearlierset-tings;5multiple@callsto[thicker]9~eand[thinner]compGound,but(theothervqariantssetanabsolutethickness. Theline-thicknessspGeci cationa ectsarrow-tips\aswellasthethicknessofstraightlinesandcurves.Threekindsofline-capsareavqailable;theyhxarediscussedbGelowinthesectionon`poly-lines'.$: =DtqGcmr17C<4P //O< 2fdF //O< 2fdF //O< 2fdF //O< 2fdFs\xy/r8pc/:*++\txt\huge{C}="c",0*++\txt\huge{P}="p",,"p",{\ar@*{[|(1)]}"p";"c"<20pt>},"p",{\ar@*{[|(4)]}"p";"c"<14pt>},"p",{\ar@*{[|(10)]}"p";"c"<4pt>},"p",{\ar@*{[|(20)]}"p";"c"<-16pt>}\endxyUsingxthePostScriptback-end,@thesizeofthearrow-headgrowsaestheticallywiththethicknessofthelineusedtodrawit.¹Thisgrowthvqariesasthesquare-roGot0ofthethickness;/ͳ2fdfe@!*ͳ2fdfeBSͳ2fdfeD|ͳ2fdfeEͳ2fdfeGΟͳ2fdfeIͳ2fdfeK ͳ2fdfeMIͳ2fdfeOrͳ2fdfeQͳ2fdfeSğͳ2fdfeUͳ2fdfeW{ͳ2fdfeYm?ͳ2fdfe[_hͳ2fdfe]Qͳ2fdfe_Cͳ2fdfea5ͳ2fdfec( ͳ2fdfee5ͳ2fdfeg ^ͳ2fdfehͳ2fdfejͳ2fdfelٟͳ2fdfenͳ2fdfep+ͳ2fdferTͳ2fdfe-zƍ*g32fdfe s*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfe*g32fdfeg-2fdfek-2fdfeo-2fdfes-2fdfew-2fdfe{-2fdfe-2fdfeꃟ-2fdfe-2fdfe-2fdfe-2fdfe-2fdfe -2fdfe-2fdfe-2fdfe"-2fdfe)-2fdfe0-2fdfe7-2fdfe>-2fdfeE-2fdfeL-2fdfeS-2fdfeZß-2fdfeaǟ-2fdfeh˟-2fdfeoϟ-2fdfevӟ-2fdfe}ן-2fdfe۟-2fdfeߟ-2fdfe}-2fdfe{-2fdfey-2fdfew-2fdfeu-2fdfes-2fdfeq-2fdfeo-2fdfem-2fdfek-2fdfei -2fdfeg-2fdfee-2fdfec-2fdfea-2fdfe_-2fdfe^#-2fdfe\ '-2fdfeZ+-2fdfeX/-2fdfeV3-2fdfeT&7-2fdfeR-;-2fdfeP4?-2fdfeN;C-2fdfeLBG-2fdfeJIK-2fdfeHPO-2fdfeFWS-2fdfeD^W-2fdfeBe[-2fdfe@l_-2fdfe>sc-2fdfewSٳ2fdfe@fΟٳ2fdfeBVIٳ2fdfeDEğٳ2fdfeF5?ٳ2fdfeH$ٳ2fdfeJ5ٳ2fdfeLٳ2fdfeM+ٳ2fdfeO⦟ٳ2fdfeQ!ٳ2fdfeSٳ2fdfeUٳ2fdfeWٳ2fdfeY ٳ2fdfe[ٳ2fdfe]oٳ2fdfe_^~ٳ2fdfeaMٳ2fdfec=tٳ2fdfee,ٳ2fdfegjٳ2fdfei ٳ2fdfej`ٳ2fdfel۟ٳ2fdfenVٳ2fdfepџٳ2fdferLٳ2fdfe!y6g32fdfe ׍6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfe6g32fdfeg!2fdfe̟!2fdfe1!2fdfeҖ!2fdfe!2fdfe`!2fdfeş!2fdfe*!2fdfe!2fdfe!2fdfe Y!2fdfe!2fdfe#!2fdfe&!2fdfe.!2fdfe7R!2fdfe?!2fdfeH!2fdfeP!2fdfeX!2fdfeaK!2fdfei!2fdfer!2fdfezz!2fdfeߟ!2fdfe}D!2fdfe{!2fdfey!2fdfews!2fdfeu؟!2fdfes=!2fdfeq!2fdfeo!2fdfeml!2fdfekџ!2fdfei6!2fdfeg盟!2fdfee!2fdfece!2fdfebʟ!2fdfe` /!2fdfe^!2fdfe\!2fdfeZ"^!2fdfeX*ß!2fdfeV3(!2fdfeT;!2fdfeRC!2fdfePLW!2fdfeNT!2fdfeL]!!2fdfeJe!2fdfeHm!2fdfeFvP!2fdfeD~!2fdfeB!2fdfe@!2fdfe>!2fdfe2fdfeP* 2fdfeR2fdfeT2fdfeU왟2fdfeW2fdfeYã2fdfe[(2fdfe]2fdfe_22fdfeaq2fdfec]<2fdfeeH2fdfeg4F2fdfei˟2fdfek P2fdfel՟2fdfenZ2fdfepߟ2fdferd2fdfeuBg32fdfe{Bg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeBg32fdfeg2fdfeڟ2fdfeM2fdfe2fdfe32fdfe2fdfe2fdfe2fdfe 2fdfer2fdfe!2fdfe,X2fdfe6˟2fdfeA>2fdfeK2fdfeV$2fdfe`2fdfek 2fdfeu}2fdfe}2fdfe{c2fdfey֟2fdfewI2fdfeu2fdfes/2fdfeq2fdfeo2fdfemӈ2fdfek2fdfein2fdfeg2fdfeeT2fdfedǟ2fdfeb:2fdfe`2fdfe^' 2fdfe\12fdfeZ<2fdfeXFy2fdfeVP2fdfeT[_2fdfeReҟ2fdfePpE2fdfeNz2fdfeL+2fdfeJ2fdfeH2fdfeF2fdfeD2fdfeBj2fdfe=g32fdfe녍g32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdfeg32fdferg2fdfet2fdfevq2fdfex{2fdfezg{2fdfe|S2fdfe~>2fdfe* 2fdfe2fdfe2fdfe왟2fdfe2fdfeã2fdfe(2fdfe2fdfe22fdfeq2fdfe]<2fdfeH2fdfe4F2fdfe˟2fdfe P2fdfe՟2fdfeZ2fdfeߟ2fdfed2fdfeB왟2fd0Bg0fdB왟2fd`g0fdr왟2fd0gKUAgB]P2fd+Y]P2fd+Y]P 2fd+Y=.~\xycompileto{poly}%{/r4pc/:,*[|<5pt>][thicker]\xybox{%?*+(3,2){}="X";@={p+CU,p+LU,p+LD,p+RD,p+RU,p+CU}?,{0*[miter]\xypolyline{}}?,{\xypolyline{*}},@i@),"X",*+(2.5,1.5){}="X"LWeJ28ߠ*tj??gw,@={!CU,!LU,!LD,!RD,!RU,!CU} ,{0*[gray][roundjoin]\xypolyline{}},{0*[gray]\xypolyline{*}},@i@),"X",*+(2,1){}="X",@={!CU,!LU,!LD,!RD,!RU,!CU},{0*[white]\xypolyline{*}},{0*[bevel]\xypolyline{}},@i@),"X"-(.7,0)*++\txt\LARGE{A}="a","X"+(.7,0)*++\txt\LARGE{B}="b",{\ar@{-}@*{[butt][thinner]}"a";"b"<1pc>},{\ar@{-}@*{[roundcap][thinner]}"a";"b"},{\ar@{-}@*{[projcap][thinner]}"a";"b"<-1pc>}}}NoteXbtheuseof{0*[...]\xypolyline{..}}|toapplystyle-moGdi ersBBtoapolyline.8The@={!..}-DomethodforPxloadingthestackgivesequivqalentresultstous-ing;@={p+..}3(, since\xypolylineAaignorestheedgeextentsUUofeachhpGosiinthestack. [`Noteɵalsothattheargument#1dto\xypolylinea ectsUUwhatistypGeset.qAllowableUUargumentsare: ff2 č e\xypolyline{}e5solidUUline e\xypolyline{.}e5dottedUUline e\xypolyline{-}e5dashedUUline e\xypolyline{*}e5 llUUenclosedpGolygon e\xypolyline{?}e5 lltenclosedpGolygonusinge5even-oGddUUrulefd e\xypolyline{{*}}e5useUU\dir{*}+jforUUlines e\xypolyline{}y5usingUU\dir{}[bff2EThelattercasesonehas**\dir{...}BibGeingusedtowjconnecttheverticesofthepGolyline,with{{*}}bGeingneededtoget**\dir{*}2Ѹ.'@Similarly**\dir&isusedB?whenahdriveriisnotavqailabletospGeci callysuppGortpolylines;1inparticularthetwo` ll'options* andP? uwillPresultinadottedpGolygonoutlinetheregionUUintendedtobGe lled.InfallcasesitisuptotheusertoloadthestackbGe-forecalling\xypolyline{BӾ...}꧲.mAparticularlycom-moncaseistheoutlineofanexistingXY -pichob8jecti,asPintheexampleabGove.F*uturePextensionsto\frmwill‘provideasimpli edmechanismwherebytheuserneednotcall\xypolyline?explicitlyforsuche ects.)M12 fdRotateffandScaleextension)Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.auiLoadTas:p\xyoption{rotate}bThisTextensionprovidestheabilitytorequestthatanyEob8jectbGedisplayedrotatedatanyangleaswellasUUscaledinvqariousways.Thesearee ectswhicharenotnormallyavqail-ableUwithinTU>'ExX. sInsteadtheyrequireasuitable`back-end'Eboptiontoprovidethenecessary\specialgweKcommands,thisextensionwillhaveU>noCe ectU>ontheoutputunlessusedwith#aU>backendthatexplicitlysuppGortsit.5G3232z32fdzg3232$趍.!$fdBv$fd32G3232z졄fdzg3232eKThe]extensionprovidesspGeciale ectsthatcanbeeKusedwithanyXY Y-pichob8jectibyde ning[ hshapGei]eKmoGdi ers.@The}modi cationislocaltothehob8jectieKcurrentlybGeingbuilt,*sowillhavenoe ectifthiseKob8jectUUisneveractuallyused.eKThefollowingtableliststhemoGdi ersthathaveeKsocvfarbGeende ned.!(Theycomeintwocvtypescv{eitheraeKsinglekeyword,*Forakey-characterwiththefollowingeKtextUUtreatedasasingleargument.eK >ff2  A[@]eXalign&withcurrentdirec-eXtionfd A[@U;hdirectioni]eXalignUUtohdirectioni A[@!8hnumbGeri]eXrotateUUhnumbGeridegrees A[*U;hnumbGeri]eXscaleUUbyhnumbGeri A[*U;hnumix,hnumiy·]eXscaleUUxandy.separately A[left]eXrotate yanticloGckwisebyeX90^fd A[right]eXrotateUU(cloGckwise)by90^ A[flip]eXrotateby180^;HsameaseX[*-1,-1]񍍍 A[dblsize]eXscaleUUtodoublesize A[halfsize]eXscaleUUtohalfsizeff2fThese[ chshapGei]modi ersfspecifytransformationsofzthehob8jecticurrentlybGeingbuilt.IftheobjecthasoParectangleedgethenthesizeoftherectangleistransformedtoenclosethetransformedob8ject;ϣwithaUUcircleedgetheradiusisalteredappropriately*.]:EachtsuccessivetransformationactsupGonthere-sult ofallprevious.Oneconsequenceofthisisthatthe'"orderoftheshapGemodi erscanmakeasignif-icantdi erenceinappGearance|ingeneral, dtransfor-mationsdonotcommute.0Evensuccessiverotationscan2givedi erentsizedrectanglesiftakeninthere-verseUUorder.Sometimes,9thischangeofsizeisnotdesirable.ThefollowingcommandsareprovidedtomoGdifythisbGehaviour.wff2 v_\NoResizing[v;preventsUUsizeadjustmentv_\UseResizing[v;restoresUUsizeadjustmentsff2iTheL \NoResizing@WcommandL isalsousefultohaveL attheWbGeginningofadocumentbeingtypesetusingadriverthatcannotsuppGortscalinge ects,}inpartic-ularwhenappliedtowholediagrams.ZInanycaseanunscalediversionwillresult,butnowthespacingandpGositioningwillbeappropriatetotheunscaledratherthanUUthescaledsize.LWeJ29T*tj??gwScaling]nandScaledT ext TheJhshapGeimodi er cancontaineitherasinglescalefactor,orapairin-dicatingdi erentfactorsinthex-andy[ٲ-directions.Negativevqaluesareallowed,#toobtainre ectionsintheUUcoGordinateaxes,butnotzero.hRotationOandRotatedT ext Within:\[@...]%the...\areLparsedasahdirectioniloGcally*,fIbasedonthecurrentdirection. MThevqalueofcountregis-terw\Direction>~вcontainswtheinformationtodeter-minektherequesteddirection.^$Whennohdirectioniisparsed then[@]requestsarotationtoalignwiththecurrentUUdirection. uThespGecialsequence[@!...]*ɲisprovidedtopassanangledirectlytotheback-end.FTheXY-picsizeand3shapGeofthehob8jectiwith\rectangleEdgeRthisextensionwillhaveU>noe ect KonU>theoutputunlessusedwithadvi-driverU>thatexplicitlysuppGortsit.5G3232z32fdzg3232$趍.!$fdBv$fd32G3232z졄fdzg3232#deKColoursXarespGeci edasahshapeimodi erwhicheKgivesythenameofthecolourrequested.iItisappliedeKtothewholeofthecurrenthob8jectiwhetherthisbGeeKtext,RNanQXY ь-picQline,curveorarrow-tip,RNoracompGos-eKiteob8jectsuchasamatrixorthecompletepicture.eKHoweversomeDVIdriversmaynotbGeabletosup-eKpGortUUthecolourinallofthesecases.eK >ff2 썍[ ?hcolourUUnamei]\NuseUUnamedcolourb\newxycolor{?hnamei}{ hcoGdei}\Nde neUUcolour\UseCrayolaColors\NloadUUcolournamesbff2؍BIftheDVI-driverBcannotsuppGortcolourthenare-questr?forcolouronlyproGducesawarningmessageinthe(log le.@Aftertwo(suchmessagessubsequentre-questsUUareignoredcompletely*.NamedcoloursandcolourmoQdels NewFcolournames,arecreatedwith\newxycolor<,4Ttakingtwo,ar-guments.C_Firstly2anameforthecolourisgiven,fol-lowedqbythecoGdewhichwillultimatelybGepassedtothenoutputdeviceinordertospGecifythecolour.IfthecurrentdrivercannotsuppGortcolour,!orgrayscaleshading,)thenthenewnamewillbGerecognised,butignoredUUduringtypGesetting.F*orWPostScriptdevices,XStheWXY ׺-psPostScriptdictionary|de nesopGeratorsrgbs,)tcmykGandgray*㉍A;@*B&s~2hr|0Fw l+l'&l"lU~lv(Wl槟0lV l Ʒl6slǟFlϟmlןFlߟlf矫ldlF7l l'\lٗ5llwUl'(lW/l7rl7?KlGt$lOFlWl_lggȿloʒalGwe:l8l' llӰlwՃwl租VPl~W))lyǷlu7lpǟޡllϟtlgןGflbߟ?l^glYlUGlPelL(8|lG UlC.l>xl9'l5X/Vl07)l,8?klꍍ2TlabGelUU1=/3232>򿍍3232?3232?z3232/ύ=n3232 323232323232323232323232323232323232323232323232Dn3232 32323232323232323232323232323232323232323232323232=/3232>򿍍3232?3232?z3232^1Cŵ:PzlabGelUU2P3232Qg3232C32323232323232323232323232323232323232323232C3232nHPN3232'd323232323232323232323232nfVN3232'd32323232323232323232323232P3232Qg3232C32323232323232323232323232323232323232323232C3232[B5mkȲlabGelUU3s۞3232tm3232e3232323232323232e3232~32s۞3232tm3232e3232323232323232e3232)KlabGelUU47$32323232:m32323232323232323232323232323232323232323232:[3232荍ċ}3232A@3232"l}3232A@323232$32323232:m32323232323232323232323232323232323232323232:[3232ȿYlabGelUU5Th3232̍3232X^labGelUU8}0_[83232ȍ3232?3232?z3232/ύAn3232 323232323232323232323232323232323232323232323232"fn3232 32323232323232323232323232323232323232323232323232[83232ȍ3232?3232?z3232UkspGecialUUe ect:qalignedtextj3232332325323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323253232"N֍џ3232323232323232323232323232323232323232323232323232323232323232X323232323232323232323232323232323232323232323232323232323232323232j3232332325323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323253232FigureUU10:qRotations,scalingsand ips9=ǍF*urtherecolournamesarede nedbythecommand \UseCrayolaColoursE that=loadsthecrayon'hoption,in(whichmorecoloursarede ned.Consultthe lexyps-col.doc%8vforthecoloursandtheirspGeci cationsinUUtheRGBorCMYKmoGdels.xycra9yon.tex: Thisoptionprovidesthecom-mand#toinstallde nitionsforthe68coloursrecog-nisedbynamebyT*omasRokicki'sdvips yɲdriver[11 ].This:qcommandmustbGecalledfromahdriveri- lewhichUUcanactuallysuppGortthecolours.+14}PatternffandTileextensionVers.3.4bCyRossMoKorehross@mpAce.mq.edu.auiLoadTas:p\xyoption{tile}uTThis|extensionprovidestheabilitytorequestthata lledUUregionbGetiledusingaparticularpattern.This2Pisane ectnotnormallyavqailablewithinTU>'ExX.cInstead)@itrequiresasuitablehdriverioptiontoprovideSthenecessary\special0>commands,* togetherwithDanyextracommandsneededtoimplementthee ects.qThus |UsingU>thisextensionwillhaveU>noe ectqonU>theoutputunlessusedwithaѸdvi-driverU>thatexplicitlysuppGortsit.5n323232fdzg3232$趍T$fdiD$fd32n3232fdzg3232 tAll=e ectsde nedinthetilenextensioncanbGeim-plemented*usingmostPostScripthdriveris,3#loadedasUU\xyoption{77hdriveri}?.P9atterns Patterns#arespGeci edasahshapeimodi- er,similartothewaycoloursarespGeci edbyname.Thepatternisappliedtothewholeofthecurrenthob8jecti_ѲwhetherthisbGetext,pan_XY -picline,curveoroarrow-tip,uoracompGositeob8jectsuchasamatrix=ǍeKor\thecompletepicture.However\someDVI-drivers eKmayUUnotsuppGortuseofpatternsinallcases. t>eKIfthecurrentDVI-drivercannotsuppGortpatternseKthen#arequestforonesimplyproGducesawarningeKmessage3inthelog le.]Aftertwo3suchmessagessub-eKsequentUUrequestsareignoredcompletely*.eK @ff2 ڢ [hnamei]:PuseUUnamedpatternt> \newxypattern{?hnamei}{ hdatai}:PspGecifyUUnewpatternusinghdatai \UsePatternFile{_|h lei}:PsetsUUdefault leforpatterns \LoadAllPatterns{dyh lei}:PloadUUallpatternsinh lei \LoadPattern{Ohnamei}{ h lei}:PloadUUnamedpatternfromh lei \AliasPattern{U3haliasi}{ hnamei}{h lei}:PletUUhaliasidenotepatternfromh lei.t@ff2B9[AlthoughpatterndatamaybGespeci eddirectlyus-ing\newxypatternG,$itismoreusualtoloaditfromaEh leiinwhichmanypatternsarede nedbyname,eachonaseparateline._jByconventionsuch lesal-waysendin.xyp(XY -pattern)sonoextensionshouldbGe|speci ed.Thepatternisthenrequestedusingei-ther~thenamesuppliedinthe leorbyanalias.*UOnce\UsePatternFileQGhasbGeenused,thenanullh leiar-gumentxtotheothercommandswillstill ndpatternsinnthedefault le. 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jq\Xݞ3232X32fd#mg3232늍XDXfd|ۉXfd32Xݞ3232Xfd#mg3232q\Xݞ3232X32fd#mg3232늍XDXfd|ۉXfd32Xݞ3232Xfd#mg3232I]mac26z\ jq\\323232fd#mg3232늍CXfdJXfd32\3232ꡄfd#mg3232q\\323232fd#mg3232늍CXfdJXfd32\3232ꡄfd#mg3232Imac27z\ jq\ 3232=Ş32fd#mg3232늍XfdXfd32 3232=šfd#mg3232q\ 3232=Ş32fd#mg3232늍XfdXfd32 3232=šfd#mg3232I5mac28z\ jq\ظn3232렞32fd#mg3232늍؞ՉXfdlXfd32ظn3232렡fd#mg3232q\ظn3232렞32fd#mg3232늍؞ՉXfdlXfd32ظn3232렡fd#mg3232I[mac29z\ jq\fI3232{32fd#mg3232늍LXfd'TGXfd32fI3232{fd#mg3232q\fI3232{32fd#mg3232늍LXfd'TGXfd32fI3232{fd#mg3232I6mac30z\ jq\.$3232.GV32fd#mg3232늍-XfdR"Xfd32.$3232.GVfd#mg3232q\.$3232.GV32fd#mg3232늍-XfdR"Xfd32.$3232.GVfd#mg3232I3?mac31z\ jq\X3232X132fd#mg3232늍XfXfd|Xfd32X3232X1fd#mg3232q\X3232X132fd#mg3232늍XfXfd|Xfd32X3232X1fd#mg3232I]mac327 jD7.3232.4432fd#mg3232늍-iXfdQXfd32.3232.44fd#mg3232D7.3232.4432fd#mg3232늍-iXfdQXfd32.3232.44fd#mg3232m3+mac337 jD7Xݞ3232X32fd#mg3232늍XDXfd|ۉXfd32Xݞ3232Xfd#mg3232D7Xݞ3232X32fd#mg3232늍XDXfd|ۉXfd32Xݞ3232Xfd#mg3232m]mac347 jD7\323232fd#mg3232늍CXfdJXfd32\3232ꡄfd#mg3232D7\323232fd#mg3232늍CXfdJXfd32\3232ꡄfd#mg3232mmac357 jD7 3232=Ş32fd#mg3232늍XfdXfd32 3232=šfd#mg3232D7 3232=Ş32fd#mg3232늍XfdXfd32 3232=šfd#mg3232m5mac367 jD7ظn3232렞32fd#mg3232늍؞ՉXfdlXfd32ظn3232렡fd#mg3232D7ظn3232렞32fd#mg3232늍؞ՉXfdlXfd32ظn3232렡fd#mg3232m[mac377 jD7fI3232{32fd#mg3232늍LXfd'TGXfd32fI3232{fd#mg3232D7fI3232{32fd#mg3232늍LXfd'TGXfd32fI3232{fd#mg3232m6mac384kFigureUU11:qThe38standardMacintoshpatterns.Yd\AliasPattern{bricks}{mac12}{xymacpat} \AliasPattern{bars}{mac08}{xymacpat}\xy?*+<5pc,3.1pc>{},{*[bricks]\frm{**}},*+<2.5pc>[o]{},*[bars]\frm{**}\endxyP9attern5data A\regionistiledusingcopiesofasingle+#`cell'regularlyplacedsoastoseamlesslytiletheentireregion.ThehdataiappGearingasanargu-mentto\newxypatternLGisultimatelypassedtothedvi-driver. ٍThen|simplestformofpatterndatais:[hnumihHex-datai,NwhereTthedataisa16-characterstringofHexadecimal:;digits;i.e. x0{9,stA{Fc.EachHex-digitequatesto4binarybits, sothisdatacontains64bitsrepresentingPpixelsinan88Parray*.cThehnumiisanMintegercountingthenumbGerof`0'samongthe64bits.T*akenbiasafractionof64,thisnumbGeroritscomplement,$OrepresentsǷtheaverageǷdensityof`on'pixelsaaCPostScriptopGeratormacfreq+qhasbeende-eK ned=tofacilitaterequestsfor9:375,uvia[!macfreq]7k.eKTheMnextdiagramdisplayschangestothefre-LWeJ32! *tj??gwquency*.ˍˍY lled j2patternˍ13232Lc32fd#mg3232늍Xfd/Xfd3213232Lcfd#mg3232ˍ13232Lc32fd#mg3232늍Xfd/Xfd3213232Lcfd#mg3232@9.375ˍ0@ lled j+patternˍ(3232(4232fd#mg3232늍'gXfdKXfd32(3232(42fd#mg3232ˍ(3232(4232fd#mg3232늍'gXfdKXfd32(3232(42fd#mg3232@112.5ˍi( lled jdhpatternˍ`Ϟ3232a32fd#mg3232늍`6Xfd͉Xfd32`Ϟ3232afd#mg3232ˍ`Ϟ3232a32fd#mg3232늍`6Xfd͉Xfd32`Ϟ3232afd#mg3232@hc18.75ˍn lled j7patternˍО3232О32fd#mg3232늍XfdXfd32О3232Сfd#mg3232ˍО3232О32fd#mg3232늍XfdXfd32О3232Сfd#mg3232@37.5%zY lled j2pattern:13232Lc32fd#mg3232늍Xfd/Xfd3213232Lcfd#mg3232:13232Lc32fd#mg3232늍Xfd/Xfd3213232Lcfd#mg3232<܍9.375%z0@ lled j+pattern:(3232(4232fd#mg3232늍'gXfdKXfd32(3232(42fd#mg3232:(3232(4232fd#mg3232늍'gXfdKXfd32(3232(42fd#mg3232<܍112.5%zi( lled jdhpattern:`Ϟ3232a32fd#mg3232늍`6Xfd͉Xfd32`Ϟ3232afd#mg3232:`Ϟ3232a32fd#mg3232늍`6Xfd͉Xfd32`Ϟ3232afd#mg3232<܍hc18.75%zn lled j7pattern:О3232О32fd#mg3232늍XfdXfd32О3232Сfd#mg3232:О3232О32fd#mg3232늍XfdXfd32О3232Сfd#mg3232<܍37.5VRSa9vingW,patterns: Whenstylesaresavedusing hwordi]?,-seenote4kofx4,thenthecurrentpattern(ifany)isalsosaved.Subsequentuseof[ hwordi]recovers \thepatternaswellascolourandline-stylesettings.5 This^includesanyexplicitvqariationsappliedusingUUthe\StyleEscapGe"mechanism. 荑HereVisavqariationofanearlierexample,withex-traUUe ects.%ύ_3232K32fdg32320 E/fdx/fd32_3232Kfdg3232활x323232fdfcg3232荍_fd<_fd32x3232硄fdfcg3232L΍x WV,x UTxPQ,xRSL΍V_3232VK32fd;g3232 kVE 8Rfdx 8Rfd32V_3232VKfd;g3232L΍V_3232VK32fd;g3232 kVE 8Rfdx 8Rfd32V_3232VKfd;g3232Wxe33<Ee fd33ycY>R6ff cmss12Kilroy[+Wwas/here+΍\UsePatternFile{xymacpat}\AliasPattern{bricks}{mac12}{}\LoadPattern{mac28}{}\LoadPattern{mac05}{}\xy?*=0[!macfreq-45pa][mac28][|=Bars]{},*+<12pc,4pc>{}*[bricks]\frm{**},-<3.5pc,0pt>,*+<2.65pc>[o]{},*[Bars]\frm{**},*[thicker]\frm{o},+<6pc,0pt>,*+<5pc,?2.7pc>{},*[mac05]\frm{**},*\frm{-,},*[white]\txt\Large\bf\sf{Kilroy\\was?here}\endxy,15}Imps3ortffgraphicsextensionVers.3.6bCyRossMoKorehross@mpAce.mq.edu.auiLoadTas:p\xyoption{import}This7featureprovidestheabilitytoeasyaddlabGelsand3annotationstographicspreparedoutsideTU>'ExXorL5ffA͉TU>'ExX.;AnXY 3-picgraphicsenvironmentisestablishedwhose>coGordinatesmatchthatwithinthecontentsofthetimpGortedgraphic,+;makingiteasytospecifyex-actlywherealabGelshouldbeplaced,orarrowdrawntoUUhighlightaparticularfeature.A2commandI\xyimport6wisIde nedwhichisused,in@PconjunctionwithimpGortedgraphics,{toestablisha}coGordinatesystemappropriatetotheparticulargraphics.SThis^enableshpGosiitionswithinthegraphictobGeeasilylocated, eitherforlabellingoraddingex-tra_embGellishingfeatures.ItisusedineitherofthefollowUUways: ff2 |L\xyimport(:Dwidth,?height){ hgraphici}gw*S\xyimport(5width,?height)( x-o ,y[ٲ-o ){hgraphici}eK̉ff2 ʍNormallyNthehgraphicsiwillbGeaboxcontaininga graphicͩimpGortedusingthecommandsfrompackqagessuchSasgraphics.;,epsforepsfig$/A,orusingothercommandsprovidedbytheloGcalTU>'ExXimplementa-tion.ňHoweverthehgraphicicouldbGeanybalancedTU>'ExXmaterialwhatsoGever;8provideditoccupiesnon-zeroUUsize,bGothverticallyandhorizontally*.ThewidthandheightarehnumbGerisgiveninthecoGordinategsystemforthec}'ontentsofthehgraphicsi.ThesegFarenotdimensions,butcoGordinate-lengths,us-ingA[theunitsappropriatetothepicturedisplayedA[byhgraphici.When#provided,( ӵx-o ,?y[ٲ-o ) \ givethedistancein4XcoGordinateunitsfrombottom-leftcornertowherethe)originofcoGordinatesshouldbelocated,^usuallywithinkareacoveredkbythehgraphici.UsuallythenegativesEofthesenumbGerswillgivethecoGordinateloGcationofthebottom-leftcornerofthehgraphici.QIfnoo setsaresuppliedthentheoriginispresumedtolieUUatthebGottom-leftcorner.Normally!the\xyimport5commandisusedatthebGeginningo ofan\xy..\endxy@environment.Ito isnotnecessaryCtogiveanybasissetup,Gtforthisisdeducedbyymeasuringthedimensionsofthehgraphiciandusing9thesuppliedwidth,heightando sets. Thehgraphiciitselfde nesnamedhpGosicalled"import"-ز,loGcatedi+attheoriginandhavingappropriateextentstoldescribGetheareacoveredlbythehgraphici.U Thismakesitparticularlyeasytosurroundthehgraphiciwith,aframe,aasontheleftsideof gure12,ortodrawUUaxespassingthroughtheorigin.HereisthecoGdeusedtoapplythelabellingin gureUU12:N8\def\ellipA{\resizebox{6cm}{!}{% \includegraphics{import1.eps}}}\xy\xyimport(3.7,3.7)(1.4,1.4){\ellipA}*\frm{-},!D+<2pc,-1pc>*+!U\txt{%?framedcontentsofgraphicsfile}\endxy\qquad\qquad\xy\xyimport(3.7,3.7)(1.4,1.4){\ellipA},!D+<2pc,-1pc>*+!U\txt{Rational?points?ontheellipticcurve:$x^3+y^3=7$},(1,0)*+!U{1},(-1,0)*+!U{-1},(0,1)*+!R{1},(0,-1)*+!R{-1},(2,-1)*+!RU{P},(-1,2)*+!RU{-P},(1.3333,1.6667)*+!UR{-2P},(1.6667,1.3333)*!DL{\;2P},(-.5,1.9)*++!DL{3P},(1.9,-.5)*!DL{\;-3P},(-1,2.3)*+++!D{\infty}*=0{},{\ar+(-.2,.2)},(.5,2.3)*+++!D{\infty}*=0{},{\ar+(-.2,.2)},(2.3,-1)*+++!L{\infty}*=0{},{\ar+(.2,-.2)}\endxyLWeJ33" *tj??U`촍#2>Yps: currentpoint currentpoint translate 0.65166 0.65166 scale neg exch neg exch translateffk׉ffUUimport1.eps ff-Äffeps: currentpoint currentpoint translate 1 0.65166 div 1 0.65166 div scale neg exch neg exch translateM&3232PX32fdPg3232qfdCqfd32&3232PXfdPg3232SBPframedUUcontentsofgraphics le2N>Yps: currentpoint currentpoint translate 0.65166 0.65166 scale neg exch neg exch translateffk׉ffUUimport1.eps ff-Äffeps: currentpoint currentpoint translate 1 0.65166 div 1 0.65166 div scale neg exch neg exch translateU;FRationalUUpGointsontheellipticcurve:qǵx^3S+8y[ٟ^3d=7Rm՟1CFǸ1Tҕd16.q1xB85xԵPTPLXo2Pvw2P93P;4k3P՟a1l'A__l'A?E'?k?8a14ҟ'A__4ҟ'A?7zg?:Rk?џ-ʜ1#4ú1T?f.|?џ+?rnuFigureUU12:qimpGortingagraphicforlabellingVs`This fexampleusestheL5ffA͉TU>'ExX2"زstandard graphicsJHpackqageGtoimpGortthegraphics leimport1.epsK;other;packqagescouldhavebGeenusedinstead.e.g.epsfig.-Ȳ,epsf,orthe\pictureorR\illustrationL屲commandsRinTexturesontheMacintosh. TheuonlypGossibleproblemsthatcanoccurarewhentthegraphicspackqageisloadedaftertXY -pichasbGeeng"loaded.-GenerallyitisadvisabletohavegXY "-picloadingUUafterallothermacropackqages./;16}MovieStorybs3oardextensionZVers.3.5bCyKristo erH.Rosehkrisrose@brics.dkiLoadTas:p\xyoption{movie}ThisOextensioninterpretsthe\sceneprimitiveofthemovieiclass,settingtheprogressindicatorstodummyvqalues.z#TheXfollowingassumesthatyourarefamiliarwithUUthemovie ꛲class.Theʱsizeoftheframeisdeterminedbythecom-mand _ff2 a ]\MovieSetup{width=$widthc,height=*Kheight,2ղ...}ff2(the...gindicatetheotherargumentsrequiredbythemovienclass}butsilentlyignoredbytheyXY }-picmovieextension).Note:PThisextensionstillexpGerimentalandsub-ject!tochange.,TheonlydoGcumentationisinthemovie.cls2:sourceUU le.s`eK17˯PostScriptffbackendeKVers.3.4bCyRossMoKorehross@mpAce.mq.edu.aui eKLoadTas:p\xyoption{ps}eGXYK-psisa`back-end'whichprovidesXY ]-picwiththeeKabilitytoproGduceDVIQ lesthatusePostScripteK\specialsforUUdrawingratherthantheUQXY U-picfonts. eKIn#particularthismakesitpGossibletoprintXY c#-piceKDVIKB lesKonsystemswhichdonothavetheabilityeKtoloadthespGecialfonts.aThepenaltyisthattheeKgeneratedDVI leswillonlyfunctionwithonepar-eKticularDVIldriverprogram.O-HencewheneverXY m-psiseKactivqatedUUitwillwarntheuser:#썍 ȍ7XYr -picU>W*arning:TheproGducedDVI le isU>notp}'ortable[:ItcontainsPostScript qō\specialsU>forhoneparticularidriver8G3232z32fdzg3232%谍.!%~fdBv%~fd32G3232z졄fdzg3232%eKA݈moreݫcompletediscussionoftheprosandconsofeKusingUUthisbackendUUisincludedbGelow.$eK17.1KCho`osingtheDVI-drivereKIncluding \xyoption{ps}Vhwithin thedoGcumenteKpreamble,ztells{XY -pic{ thatthePostScriptalterna-eKtiveQtothefontsshouldbGeused,RqprovidedthemeanseKtoʰdothisisalsospGeci ed.CThisisdonebyalsospeci-eKfyingxadvi-driverwhichiscapableofrecognisingandeKinterpreting\special1J&commands.a%Althoughthe leeKxyps.texis5readwhentheoptionrequestisencoun-eKtered,theUmacroscontainedthereinwillhavenoe ecteKuntilUUanappropriatedriverhasalsobGeenloaded.LWeJ34# -*tj??]WithYL5ffA͉TU>'ExX2"bGoththebackendYanddrivermay bGe,speci ed,"alongwithotheroptions,viaasingle\usepackage Mcommand,UUsee[4,page317];e.g. ƺff2 ֎ \usepackage[ps,textures,color,arrow]{xy}p,ff2TheM6rebindingsnecessarytosuppGortPostScriptarenot%e ecteduntilthe\begin{document}Ycommandisencountered.}Thismeansthatanalternativedrivermay=bGeselected,byanother\xyoption{9hdriveri}?,atanytimeuntilthe\begin{document}W붲.5yOnlythemacrosXrelevqanttolastnamedhdriveriwillactuallybGeUUinstalled. p*ThebfollowingtabledescribGesavqailablesuppGortforPostScriptOcdrivers._PleaseconsulttheindividualdriverBsectionsinpartIVfortheexactcurrentlist.F*orC#eachhdriverithereisacorrespGonding lenamedxy hdriveri.texaowhicha{de nesthenecessarymacros,as=wellasadoGcumentation lenamedxy zhdriveri.doc.ThenspGellingisalllower-case,designedntobebothde-scriptive6%anduniqueforthe1st8charactersofthe leUUnames.:ÍL͉ff fdhdriveri|ŐDescriptionff dvipsAT*omasUURokicki'sdvips dvipsAKarlUUBerry'sdvipskdvipsAThomasUUKi e'sdvipsforMacintoshtexturesABlueUUSkyResearch'sTexturesv1.7+16texturesABlueUUSkyResearch'sTexturesv1.6oztexAAndrewUUT*revorrow'sO4zTU>'ExXv1.8+17oztexAAndrewUUT*revorrow'sO4zTU>'ExXv1.7ff /p*OtherDVI-driversmayalsoworkusingoneofthese les,&iftheyuseconventionssimilartodvips,O4zTU>'ExXOporTextures.oAlternativelyitshouldnotbGetoGogdiculttowritethe lesrequired,+usingtheseasabasisindicatingthetypGeofinformationneededtodsuppGortthespeci c\special2²commands.Any-one>attemptingtodothisshouldinformtheauthorandconveyasuccessfulimplementationtohimforinclusionUUwithintheUQXY U-picdistribution.Note:In somepreviousversionsofXY-picDthePostScriptbackendDanddriverwereloaded simultaneouslybyacommandoftheform>\UsePSspecials{Uhdriveri}?.ɁF*or>backward-compatibilitythesecommandsshouldstillwork,butnowloadingthelatestversionofthegivenhdriveri. Howeverltheirfutureuseisdiscouragedinmfavouroftheoption-loadingmechanism,svia\xyoption{4hdriveri}?.NThislattermechanismismore exible,bGothinhandlingupgradesoftheactualdriverAsuppGortandinbeingextensibletosupportmoreUUgeneralformsof\special0commands.P~OnceoactivqatedthePostScriptbackendocanbGeeKturnedo andonagainatwill,5usingtheuserfollow- eKingUUcommands:eKkff2 Vf\NoPSspecialsh3cancelsUUPostScript Vf\UsePSspecials?{}h3restoresUUPostScript"Bff2 TheseobGeynormalTU>'ExXscopingrulesforenviron-ments;henceitissucienttospGecify\NoPSspecialswithinanenvironmentorgrouping.UseofPost-Script willbGerestoreduponexitingfromtheenvi-ronment.?D17.2%Whyuse?- cmcsc10PostScriptuTAtsomesitesusershavedicultyinstallingtheex-trafontsusedbyXY -pic. The.tfmv lescanalwaysbGe'installedlocallybutitmaybenecessaryforthe.pkbitmapC(fonts(orthe.mfFGMETAF9ONTfonts)tobGekinstalledglobally*,bythesystemadministrator,forprintingZtoworkcorrectly*.IfPostScriptisavqail-ableƽthenƹXY F-psallowsthislattersteptobGebypassed.Note:{withu+XY /-psu/itisstillnecessarytohaveu/the.tfmx=fontxImetric lescorrectlyinstalled,asthesecon-tainUUinformationvitalforcorrecttypGesetting.DOtherXadvqantagesobtainedfromusingTXY 4X-psarethefollowing:Circles`yandcirclesegmentscanbGesetforarbi-traryUUradii.DsolidUUlinesarestraighterandcleaner.TheArangeofpGossibleanglesofdirectionalsis greatlyUUincreased.SplineecurvesaresmoGother.1T*ruedottedanddashed kversionsarenowpGossible,usingequallyspacedUUsegmentswhicharethemselvescurved.TheRoPostScript leproGducedbyadriverfromanXY-psDVI leisingeneralsigni cantlysmallerzqthanoneproGducedbyprocessingan`or-dinary'wDVIw leusingthesamedriver.'Onerea-sonforthisisthatnofontinformationfortheXY"-picfontsisrequiredinthePostScript le;this8ifurthermoremeansthattheuseof8eXY i-picdoGesnotinitselflimitthePostScript letoaUUparticularresolution.^9The~latestversionofzXY }~-picnowenablesspGeciale ectssuchasvqariablelinethickness,İgray-leveland colour. Also,>rotationoftextand(pGor-tions1Lof)diagramsisnowsuppGortedwithsomedrivers.5SimilarlywholediagramscanbGescaledup$ordownto tagivenareaontheprintedpage.F*utureնversionswillallowtheuseofre-gions lledwithcolourand/orpatterns,aswellasUUotherattractivee ects.ffffy̟ J= "5-:9LMostjTAEMXPostScriptdrivÎersstoretheimagesofcharactersusedinthetextasbitmapsataparticularresolution.Thismeans thatXthePostScript lecanonlyb'ExXsourcecoGde,;expecting4ptherecipientDtohaveDXYĺ-pic ^l,orsenda(com-pressed)UUPostScript le.ٍThelattercommentappliesto lesinwhichanyspGe-cial`back-end'suppGortisrequired,JnotjusttoPost-Script.q]OfTcourseitcanbGeignoredwhenyouknowtheUUcon gurationavqailabletotheintendedrecipient.tiPostScript6header le: WithsomeDVI-driversit>ismoreecienttohavethePostScriptcom-mandsj?thatj;XY ?-psneedsloadedinitiallyfromasepa-rate\header" le.YOT*ousethisfacilitythefollowingcommandsUUareavqailable...F?ff2 \1L\UsePSheader?{}1L\UsePSheader?{}1L\dumpPSdict?{}1L\xyPSdefaultdict_ff2 ѠNormallyitissucienttoinvoke\UsePSheader{}Mj,whichۏinvokesthedefaultnameofxy36dict.pro,re-ferring=tothecurrentversionof=XY -pic.iTheoptionalh lenameiallowsadi erent letobGeused.Plac-ing\dumpPSdict{..}T-withinthedoGcumentpreamblecausesTthedictionarytobGewrittentothesuppliedh lenamei.See>thedoGcumentationforthespeci cdrivertoestablishwherethedictionary leshouldbGelocatedonanyparticularTU>'ExXsystem.̈Usuallyitissu-cientXtohaveacopyinthecurrentworkingdirectory*.Invoking3thecommand\dumpPSdict{}Lwillplaceacopyroftherequisite le,!lhavingthedefaultname,!linthegcurrentdirectory*.This lewillbGeusedasthedictionary/forthecurrentproGcessing,f*provideditisonthecorrectdirectorypath,sothatthedrivercanloGcateqitwhenneeded. ConsultyourlocalsystemadministratorUUifyouexpGeriencediculties.w\eK18˯TPICffbackendeKVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui eKLoadTas:p\xyoption{tpic}eKThisIoptionallowstheIXY -picfontstobGereplacedbyeKtpicg\special-Os,'kwhengusedwithadvi-drivercapa-eKble"ofsuppGortingthem..ExtracapabilitiesincludeeKsmoGotherslines,{zevenlyspaceddotted/dashedcurves,eKvqariable!line-widths,,8gray-scale llsofcircles,ellipseseKandUUpGolygonalregions. !eKUse oftpic\special/ hso ersanalternativetoeKthe6XY -pic6fonts.Howevertheyrequireadvi-drivereKthat6`iscapableofrecognizingandinterpretingthem.eKOnew6suchviewerisxdvik',KarlBerry'smoGdi cationeKto1thexdviVvieweronunix^10 bsystemsrunningX-eKwindowsoraderivqative.-dvipsk$t,KarlBerry'smoGd-eKi cationtodvips#SIalsohandlestpic\special.s,soeKxdvik'ExXimplementationprovidesasuiteof\special/commandstofacilitatethedraw-ing4oflines,nbGothon-screenandwithvqariousprintingdevices.`This"G`back-end'extensionallowsthelinesinXY -picUUdiagramstobGedrawnusingthesemethods.CNotethatthisextensiondoGesnothavetobeusedwithwem-TU>'ExX.z,BetterresultsmaybGeobtainedusingthePostScriptback-endanddvipshdriveri,sinceaoversionofdvipsisavqailableforem-TU>'ExX. UHow-ever,gin1particularforscreenpreviewingpurpGoses,itmayHbGeconvenienttousethisback-end. F*urther-more\notethatdvipsiscapableofsuppGortingem-TU>'ExX\special)s.Once0loadedusing\xyoption{emtex}X,=withanappropriate^AhdriverialsospGeci edeitheralreadyorsubsequently*,theSVfollowingcommandsareavqailabletoUUturntheem-TU>'ExXbackendUUo /on.mЉff26b\NoEMspecials`8turnsUUo em-TU>'ExXspGecials.6b\UseEMspecials`8reinstatesUUem-TU>'ExXspGecials. Cff2jOf-thecurvesde nedinthexycurve+Wextension,5onlysolidsplinecurvesaresuppGorted.0ThisisdonebytreatingdthesplineasapGolygon(poly-line)withmanysegments.6PartffIs3IICF=eatures.]ThispartdoGcumentsthenotationaddedbyeachstandard/featureoption.[TF*oreachisindicatedthedescribGed&versionnumbGer,theauthor,andhowitisloaded.The rsttwo,`all'and`dummy',describGedinxx20andy21,Baretrivialfeaturesthatneverthelessproveusefulsometimes.~Thenexttwo,P`arrow'and`2cell',describGed3inx22and23,kprovidespecialcommandsforob8jectsthat`pGoint'. Thefollowing,f`matrix'inx24,`graph'inx25,`pGoly'inx26,and`knot'inx29,areAinputymo}'desQbthatsuppGortdi erentoverallstruc-turingUUof(partsof)UQXY U-pictures.w\eK20˯AllfffeatureseKVers.3.3bCyKristo erH.Rosehkrisrose@brics.dki eKLoadTas:p\xyoption{all}čeKAsaspGecialconvenience,-thisfeatureloadsasubseteKofXY'-pic,^11 u+namelytheextensions:{curve%(cf.x8),eKframe˲(x9),b^cmtip"޲(x10),b^line(x11),b^rotate(۲(x12),eKcolorF(x13),7and thefollowingfeatures: 2matrixeK(x24),UUarrow ꛲(x22),UUandgraph(x25).'ueK21˯DummyffoptioneKVers.3.3bCyKristo erH.Rosehkrisrose@brics.dkieKLoadTas:p\xyoption{dummy}čeKThissoptionisprovidedasatemplatefornewoptions,eKitprovidesneitherfeaturesnorextensionsbutitdoGeseKcountUUhowmanytimesitisrequested.'ueK22˯ArrowffandPathfeatureeKVers.3.5bCyKristo erH.Rosehkrisrose@brics.dkieKLoadTas:p\xyoption{arrow}čeKThisafeatureprovides]XY 6a-picwiththearrowparadigmeKpresentedUUin[12 ]. eKNote:a\PATH ۲commandincompatiblychangedforeKversionUU3.3(the\arjcommandisuna ected).eKTheobasicconceptintroGducedisthep}'athc:acon-eKnection~]thatstartsP~fromc(thecurrentob8ject),endseKataspGeci edob8ject,Axandmaybesplitintosev-eKeralFse}'gmentsbGetweenintermediatespGeci edob8jectseKthatcanbGeindividuallylabelled,changestyle,haveeKbreaks,UUetc.eKx22.1y+isabGoutthe\PATH!2Gprimitive,!includingtheeKsyntax(.5)ȍhitiAYGv.!Wj#hdigitiUUj qhletteriUUj{ĸhtexti}RjhcsiappliedUUto... ffffeͤ fffd< ff3>nextUUsegmentonly͟ ff ͤ fffd> ff3>lastUUsegmentonly [ ffͤ fffd= ff3>everyUUsegment ffffe(h(whenseveralapplytothesamesegmentthey#}eKareUUinsertedinthesequence<>+L)."eKThis7isusefultodrawconnectionswitha`center eKmarker'*inparticularwitharrows,e.g.,the*`map-eKsto'[exampleexplainedbGelowcanbechangedintoeKaUU`breakto'example:qtypingN8eK\xy*+{0}\PATHH~={**\dir{-}}H~>{|>*\dir{>}}H~+{|*\dir{/}}H'(10,1)*+{1}?'(20,-2)*+{2}(30,0)*+{3}eK\endxyZeKwillUUtypGesetж0$0L1Dιb@ubscb:Jbk2i2clU_2ڟUZП(UVƟL]U3ie{|ktew`A,es2e}bGecausewhen\endxy*:isseenthentheparserknowsg"thatthenextsymbGolisneitherofthechar-acters!~'`9and!hencethatthelasthsegmentiistobGe(expected.Instead,]khowever,the(failurecon-tinuation*isinsertedandparsed,andthehpathiisUU nishedbytheinsertedmaterial.* F*ailureUUcontinuationscanbGenested:\xy?*+{0}\PATH~={**\dir{-}}~{~{(30,0)*+{3}}'(20,-2)*+{2}}?'(10,1)*+{1}\endxyxDwillUUalsotypGesettheconnecteddigits.T22d.rAUU\straightsegment"isinterpretedasfollows:1. First9.pissettotheendob8jectoftheprevi- oussegment(forthe rstsegmentthisisc justhbGeforethepathcommand)andcisset tothehpGosistartingthehsegmenti,andthe currentUUhslideiisapplied.* 2. Then7the= 3andpturning!)segment>isonethatdoGesnotgoallthen>waytothegivenhpGosibutonlyasfarasre-quired1tomakeaturntowardsit.Thecissettotheactualturnob8jectafteraturningsegmentgweKsuchthatsubsequentturningorothersegments eKwillstartfromthere,HTinparticularthelastseg-eKmentC#(whichisalwaysstraight)canbGeusedtoeK nishUUawindingline.|ߍeKWhattheturnloGokslikeisdeterminedbytheeKhturniUUform:eKhemptyieQNothing/bGetweenthe`andthehpGosi eKisinterpretedthesameasgivingjustthe eKhdiagiUUlastusedoutH-ofaturn.eKhdiagi²SpGecifyingxasinglehdiagidisthesameas eKspGecifyingceitherofthehciriclesd^ord_,de- eKpGendingonwhetherthespeci edhposihas eKits]center`abGove'or`bGelow'thelinefromp eKinUUthehdiagionaldirection.eKhciri OWhen8afullexplicithciricleisavqailable eKthenCthecorrespGondinghciricleob8jectis eKplacedsuchthatitsingoingdirectionisa eKcontinuationgofastraightconnectionfromp eKand=theoutgoingdirectionpGointssuchthat eKaUfollowingstraight(orlast)segmentwill eKconnectUUittoc(withthesameslide).eKHereUUisanexampleusingallformsofhturnis:pZ䍍,base_0ꪵAG QFrfdoo Kδabg0ꪵBC#@ #A1#fdC# cybb1ꪵC27_ADF7_BDF7_EVx7_CVx7_DC-afd%DF-_//]hT*/caEi 5m?lȟP?o[R?sd r?vׁ8?zJ?}%?/:?͟G?`t?"i?&Y?l)̋?ެ-??Q?0?ҟ4$>?6e7?; `?i 5mκ__'\dBh2fdbBhooJ'eP‍eKwasUUtypGesetbyN8eK\xy?<4pc,0pc>:(0,0)H*+\txt{base}="base"H\PATH?~={**\dir{-}?>*\dir{>}}%6`l(-1,-1)*{A}?^a%6`?(1,-1)*{B}?^b%6`_ul (1,?0)*{C}^c%6`ul^l?"base"?^d7$"base"?^eeK\endxyeKBug:fT*urns$areonlyreallyresonableforpathseKthatUUusestraightlinesliketheoneabGove.|ߍeKNote:n[AlwaysN~writeavqalidhpGosiafterahturni,eKotherwiseanyfollowing^or_labGelscancon-eKfuse?theparser.Soifyouintendthe^rxin`^reKtobGealabelthenwrite`,^rƲ,qusingadummy,eKhpGosiition.eKTheRdefaultusedforturnr}'adiusscanbGesetbytheeKopGeration ȇeKff2 C+\turnradiusUUhaddopi{Rhdimeni}|ፒeKff2b!eKthatworkslikethekernel\objectmarginetc.eKcommands;UUitdefaultsto10pt.LWeJ39( s*tj??gwExerciseT23: TypGeset?bꪵA\@\G_xA_xFfBfEmCmDNf@NfGQTNAQTNFXfBXfE_x299gxusingUUhturnis.)d22g.S9The[lastsegmentisexactlyasastraightoneex- ceptthatthe>action(ifany)isexecuted(andcleared)UUjustafterthedefaults}touseobje}'ct-mar}'ginifUUnotset.22j.arBreakingTmeansto\sliceahole"intheconnec-tion>andinserthitithere. lThisisrealizedbytypGesetting/theconnectioninquestioninsubse}'g-ments!,one}leadingtothebreakandonecontin-uing\afterthebreakasdescribGedinnotes22aandUU22d.The^FspGecialcontrolsequence\holeisprovidedtoUUmakeiteasytomakeanemptybreak.22k.VUnless|yhitiisafull- edgedhob8jecti(byusingthe*form),+itistypGesetusinga\labelboxob-ject(initiallysimilarto\objectboxofbasicXY -picUUbutusing\labelstyleforthestyle).Remark:'^Y*oucanonlyomitthe{} @~saroundsin-gleUUletters,digits,andcontrolsequences.22l.UAlabGeloisanob8jectlikeanyotherinthekXY;o-picture. UInsertinganhaliasi="?hidi" 6savesthelabGelUUob8jectas"Rhidi"forUUlaterreference.HJExerciseT24: TypGeset3vƍ[A&K33Def{4!fq%ǟxfgf]}%fRX|DfH3f>)jf4f@FlabGelZdɟnW50ҍUN5gxgweK22.2KArrowseKArrowsUarepathswithaparticularlyeasysyntaxfor eKsettingu+uparrowswithtail, stemc,andu+he}'ad}intheeKstyleof[12 ].=ThisisprovidedbyasinglehdecoriationeKthesyntaxofwhichisdescribGedin gure14(withtheeKaddedٳconventionthataraised`*'means0ormoreeKrepGetitionsUUofthepreceedingnonterminal).![eKNoteseK22m.BuildinganharrowiissimplyusingthespGec-eKi eddirectionals(using\dirofx6.1)tobuildaeKpath:the rsthtipibGecomesthearr}'owJtailoftheeKarrow,'theʸhconniectioninthemiddlebGecomeseKthe+arr}'owstemc,(andthesecondhtipibGecomeseKthe%arr}'owhChead.aIfahvqariantiisgivenbGeforetheeK{athenthatvqariant\dirisusedforallthree.>F*oreKexample,N8eK\xy\ar?@^{(->}(20,7)\endxy3eKtypGesets[u=м'0ҸyŸK5u E<}jp+jlYGjg]jcݟRj_Mß؝jZ^=jVjRBui}jM[jIAtjE7']j@ j0cQeKExerciseT25: TypGesetUUthesearrows:@4E:ꪵABHA^0:ـ8:ـ?]ـ9]ـ> :ـ: :ـ=%bـ;%bـ<$h0@ZZBO$hع4΍&C4)m̟4+U4.rޟ40g41BHA^000:ـ80:ـ?2]ـ92]ـ>8:ـ:8:ـ==bـ;=bـ<8:KS6 VVfd8VVfdHBHA^000F:ـ@F:ـGHـAHـFP:ـBP:ـEWlـCWlـDGA x JPm nF zC A0 >w h:ـ:h:ـ=mbـ;mbـ<z }tytntn XZZlh0@ZZۍl532fdfemM32fdfeneʞ32fdfeo}32fdfep 32fdfeq-32fdferN32fdfeso32fdfet32fdfev32fdfew&Ҟ32fdfex>32fdfeyW32fdfezo532fdfe{V32fdfeykBHBq^00x:ـ8x:ـ?z]ـ9z]ـ>:ـ::ـ=bـ;bـ<|;U_|;V_~9U_~9V_:KS:KS ~ 32fdfe舍~ 32fdfe~ 32fdfe~ 32fdfe~ 32fdfe~ 32fdfe~ 32fdfe~ 32fdfe~ 32fdfe~ 32fdfe~ 32fdfe 32fdfe舍32fdfe32fdfe32fdfe32fdfe32fdfe32fdfe32fdfe32fdfe32fdfe32fdfeDȟBHBq^000:ـ@:ـGـAـF:ـB:ـElـClـDpϟIJJ;J{(JܟJ$ٟ茐 "^h}{!/4.5pt/\dir{|}2e'*:(1,-.2)\dir^{>}2e'*:(1,+.2)\dir_{>}}3eKde nesUUanewarrowtipthatmakeseK\xy?(0,0)*+{A}H\ar?@{=|>}(20,3)*+{B}eK\endxy3eKtypGesetdQSslideUUarrow^22s[thehdimeniBSjR|UUhanchorihitiQSbreakUUeachsegmentathanchoriwithhitiBSjR^UUhanchorihitijq_hanchorihitiQSlabGelUUeachsegmentathanchoriwithhitiBSjR@?QSreverseUUmeaningofabGoveandbGelow^22t޸hvqarianti<B%!Rhemptyijq^j_VPj_t0jq1j2j3QShvqarianti:qplain,UUabGove,bGelow,double,ortriple޸htipi<B%!RhtipGchari*QSdirectionalUUnamedasthesequenceofhtipGcharisiBSjRhdiriQSanyUUhdiriectional^22n޸htipGchari<B%!R<[BMja^>ijp(xոj~G)Wjt | ]j%'!jד`ljW+j;/QSrecognisedUUtipcharactersBSjRhletterijqhspaceiQSmoreUUtipcharacters޸hconni<B%!Rhconnchari*QSdirectionalUUnamedasthesequenceofhconncharisiBSjRhdiriQSanyUUhdiriectional^22n޸hconnchari<B%!R-[BMja^.ijp~xոj~G=Wjt :QSrecognisedUUconnectorcharactersffd FigureUU14:qǸharrowis.U-uExerciseq26: OftenEtipsusedas`tails'have theirc/inkonthewrongsideofthepGointwheretheyareplaced. 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}ݲorhdecoristospecifyeKtheUU2-cells,givingthesamepicture.N8eK\xy?*+{A}="A",+<1cm,1.5cm>*+{B}="B",H+<2cm,0pt>*+{C}="C",H+<1cm,-1.5cm>*+{D}="D",eK"A";"B",{\uppertwocell^\alpha{}},eK"B";"C",{\twocell^\zeta_\xi{\gamma}},eK"C";?\afterPOS{\drop\compositemap{}}"D"eK\POS?"A";H\afterPOS{\drop\lowertwocell{}}"D"eK\endxyeKThe\connect/|vqariantisusuallypreferableasthiseKmaintainsthesizeoftheob8jectatc,whilethe\dropeKvqariantIleavesarectangularob8jecthavingpandconeKoppGositeUUsides.&ZeK24˯MatrixfffeatureeKVers.3.4bCyKristo erH.Rosehkrisrose@brics.dkieKLoadTas:p\xyoption{matrix}uTeKThisoptionimplements\XY -matrices",`i.e.,matriceseKwhere"itispGossibletorefertotheentryob8jectsbyeKtheirrow/columnaddress.[W*e rstdescribGethegen-eKeralformofXY-matricesinx24.1,Wtheninx24.2weeKsummariseƢthenewhcoGordiinateformsusedtorefereKtoentries.,Inx24.3weexplainwhatparameterscaneKbGe~settochangethespacingandorientationoftheeKmatrix,'andyinx24.4weexplainhowtheappGearanceeKofUUtheentriescanbGechanged.獍eK24.1X1"Y -matriceseKTheUUfundamentalcommandofthisfeatureiseK %Aff2 &)5WQ\xymatrixUUhsetupi{Rhrowsi}ljff2that$readsamatrixofentriesinthegenericTU>'ExXrow&columnDiformat,.i.e.,whererowsareseparatedLWeJ470 2*tj??]withPz\\andcontaincolumnsseparatedwith&(we discuss?inthefollowingsectionswhathsetupicanbGe).EgThusFamatrixwithmaxr}'owZrowsandmaxc}'olcolumnswhereeachentrycontainsr}'ow,ScolWisenteredas.Ez\xymatrix{5"1,1?&/$1,2?&Uq#&1,{ maxc}'ol\\5"2,1?&/$2,2?&q#&2,{ maxc}'ol\\ԍw.w.w.D:^.H.Lx.5"maxr}'ow0,1?&/$maxr}'owR#2,2?&q#&maxr}'ow4,1maxc}'olњ}1+E(TU>'ExXnicallyYthe& characterrepresentsany`alignmenttab',UUi.e.,characterwithcategorycoGde4).A.hmatrixi.canappGeareitherinan.XY -picture(ashdecori)UUor\stand-alone".TheaspGectsinwhich\xymatrix6di ersfromor-dinary΍matrixconstructions,lsuchasPlainTU>'ExX's\matrix{ ...} ?andUUL5ffA͉TU>'ExX'sarray ꛲environment,UUare|arbitraryiXY -picihdecoriationsmaybGespeci edinTeachentryandwillbGeinterpretedinastatewhereUUcisthecurrententry*,ヘthe#entirematrixisanob8jectitselfwithrefer-enceUUpGointasthetopleftentry*,anda9progressmessage\X"*nisprintedforeachmatrixwithr}'owsPCc}'ols1ϲentriesmandiXY{m-piccomplexitysizeȲ(thenumbGerofprimitiveoperationsperformed),.un-lessethedeclaration\SilentMatricesisissued.Entries?startingwitha*arespGecial(describedinUUx24.4)^12x,souse{*}jtogeta*UV.|F*orUUexample,N8\xy\xymatrix{A&B\\C&D}\drop\frm{-}\drop\cir<8pt>{}\endxywillUUtypGeset qǍ?ꪵAe*B?0%Ce%D<֞3232<32fd4g32321ȍ<=1|fdq9Љ1|fd32<֞3232<fd4g3232;8;?>n9>n>C:C=I_;I_<6 Bug:qDzMatrixUUnestingisnotsafe.Matrices3ꪵAB` O5_O_2O{o%@x=@t,S@q/G,@mb @j!}V@f@[%B O%Cf"fdfeh"fdfej"fdfel"fdfen"fdfep"fdfer"fdfet"fdfev"fdfex"fdfez"fdfe|"fdfe~"fdfe7wasUUtypGesetbyN8$$\xy\xymatrix{?A\POS[];[d]**\dir{~},$[];[dr]**\dir{-}\\?B&C\POS[];[l]**\dir{.}}\endxy$$IfAanentryoutsidetheAXY-matrixisreferencedthenUUanerrorisrepGorted.Inucaseseveralmatricesareusedinthesamedi-agram,MYandK[theyrefertoeachother,thenitisusefulto\givethematricesdi erent"hpre xi"hsetupi\suchthatttheycanrefertoeachotherusingthefollowingspGecialtcoordinateformsthatallhavethesamemean-ingexceptthetargetentryispickedfromaparticularmatrix:Wff2 ֍4{":%xhpre xirG,c"ffy̟ J=w-:12LIngeneralitisrecommendedthatenÎtriesstartwithanon-expandingtoken,i.e.,anordinary(non-active)character,{,or \relax,XforcompilationtowÎork.LWeJ481 <*tj??gwq[""hpre xi"?rG,c] q[""hpre xi"Rhhopi*UV]q[""hpre xi"Rhhopi^+ hplaceiUU]uff2InafactabsolutereferencesmustTalwaysabGegivenusing"?hpre xihrowi,hcoli",UUeveninsidethematrixitself.HereUUisanexampleusingthis:=j-ꪵABjǟ%C~%Dgm3232g_s_ A__ 8_832321ȍ΃jggsԤ (323232 32΃jEg (323232 3232gm3232g_s_ A__ 8_83232L2 qA^0g#fdfeec9fdfed9˟ fdfeb3>fdfe`֛fdfe_%Dfdfe]skՄfdfe[ӟJȄfdfeZ;ͻfdfeu qBq^0 fdfe-fdfe$˟*fdfesifdfeLfdfefdfe_CnfdfeL͟/PC^0gn$ʪfdfeeN%f fdfec&nfdfea&Єfdfe_y'82fdfe^2'Ӕfdfe\ (nfdfeZ>) Xfdfeuqџ/PDG^0Ka%"gfdfe%Ufdfe&NCfdfesh&1fdfe'zfdfe8Ÿ( fdfeo(fdfeA󍍍I3232II_Tg_ ___ _32323@$IǰI~ vƍ323232 v32$ς vƍ323232 v3232I3232II_Tg_ ___ _3232C>waswetypGeset(usingthe`frame'extensionand`arrow'feature)UUbyN8\xy \xymatrix"*"{%A?&B\\C?&D}% \POS*\frm{--} \POS-(10,3) \xymatrix{%A'?\ar@{.}["*"]&B'\ar@{.}["*"]\\C'?\ar@{.}["*"]&D'\ar@{.}["*"]}% \POS*\frm{--}\endxy 24.3%SpacingandrotationuTAnymatrixcanhaveitsspacingandorienta-tionchangedbyaddinghsetupi`switches'bGetween\xymatrix2:andUUtheopGening{R.ThedefaultspacingbGetweenentriesofmatrixischangedUUwiththeswitches Bjff2 .׍Gz@RhaddUUopihdimeniGz@ChaddUUopihdimeniGz@UUhaddopihdimeniff2thatchangerowspacing,columnspacing,andbGoth,respGectively*,h^asdindicatedbythehaddopiandhdimeni,,%where!thehdimenimaybGeomittedandcanbGeXgivenasoneofR@andCtoindicatethecurrentvqalue oftheparameterinquestion.UNote:вthereisnodefaultز.In@addition,wXY -piccanbGeinstructedtousea` xedgrid'UUforthematrixwiththeswitches Bjff2 .׍k @!Rk @!Ck @!ff2thatƦensurethattherowspacing,"columnspacing,and0bGoth,respectively*,pretending0thatall8entrieshavepxthesizeofthelargestentry(withoutmoGdify-ing)therealsizeoftheentries,]ofcourse,onlythegweKspacingo{togettheentriestor}'eallyhaveothesame eKsizeusea@*$...OhsetupidescribGedinx24.4below).eKTheUUspGecialvqariantseK ‰ff2 OYӷ@!0Yӷ@!=hdimeni ff2 pretend0xthatentrieshavezeroorhdimeniheightandwidthpaforcomputingrowandcolumnspacing;}asabGovef}insertingR orCjustafterthe!makesthisaf-fect|onlytheroworcolumnspacing,e.g.,@!R0$[meansthat9therowspacingonlyisbGetweenthecentersoftheUUrows.Finally*,]thespacingofthingsthataretypGesetcanbGeUUadjustedseparately:ff2 OGz@MhaddUUopihdimeniGz@WhaddUUopihdimeniGz@HhaddUUopihdimeniGz@LhaddUUopihdimeni ff2\willadjusttheentrymargin,entrywidth,entryheight,andlabGelseparationused(thelatterisac-tuallyUUpassedtothearrowfeature).ThespacingcanalsobGechangedforenentireTU>'ExXgroupUUbythedeclarationsff2 O\xymatrixrowsepphaddUUopi{Rhdimeni}\xymatrixcolsepphaddUUopi{Rhdimeni} ff2\TheUUdefaultspacingforbGothis2pcL.T oDo: ioptimizeproGcessingofmatriceswithcon-stantUUgrid.AnwentirematrixcanbGerotatedbyaddingaro-tationUUhsetupioftheform sff2Y:@^z͸hdirectioni ff2 Thiswillsettheorientationoftherowstohdirectioni(the defaultcorrespGondstor,vi.e.,rows areorientedleftUUtoright).ꂍ24.4%EntriesuTTheMappGearanceofasingleentrycanbemodi edbyenteringUUitas ‰ff2?@*UUhob8jectihpGosihdecori ff2\ThisFmakestheparticularentryignoretheentrymoGd-i erseandtypGesetasakernelob8jectwiththesamereferencepGointasthe(centerof)thedefaultob8jectwouldUUhavehad.Additionalob8jecthmoGdi erismaybeaddedtoanotherwiseUUordinaryentrybyusingtheforms ‰ff2?%|**[?hshapGei]RhentryiLWeJ492 V*tj??gw"**{2qhmoGdi eri*}Rhentryimff2The rstsetsthedefaulthshapGeiforob8jects (cf.`note4j),#thesecondadefaultsize(change,cf.note4g),]andthelastmakesitpGossibletoaddanyvhob8jectimoGdi erofx4,0>e.g.,forvrecenteringen-triesdafterthedefaultentryformwhichisequivqalenttoo`!Ci+<c2obje}'ctjZmar}'gin;w8>@5'(withthee ectofcen-teringbtheob8jectandaddtheobje}'ctmarginc)btoallsides.޶ExerciseT31: TypGesetUUthefollowingdiagram:ݍH՟A8Bn|=A}}//g2fdSq@=B`왟V`gVfd}ꪵB왟yA왟gfd],$ꪵAl)HBW=~E!//g!2fdjE$BQ8A7fIt*LisalsopGossibletousethese@jIhsetupis(asusualbGetweenUU\xymatrix5ꏲandUUtheleading{R): /|ff2 AύK@*[?hshapGei]K@*Y=haddUUopihsizeiff2:ݍwhichareequivqalenttochangingallentriestobGehaveasԵiftheyhadstartedwiththesimilar**T-form.T oDo:qDzAllowUU** OhaddUUopihsizeihentryiforentries.IfLthedefaultsetofentrymoGdi ersshouldbechangedJthenthefollowingdeclarationmustbGeissuedbGeforethe\xymatrix5fcommand;)&thisistheonlywaytoqactuallyswitchtheinitialdefaultcenteringandspacingUUo : Cff2 Aύ(\entrymodifiers={ OhmoGdi eri*UV}ff2 I޶Exercisewr32: HowNdidtheauthortypGesetthefol-lowingUUmatrix?1UL͍O!/.U!-,O!()U!*+R4!ꪵANk%bcӍgd]`]Z2C[!2fd-k%bA?gMn?d] ?`?]!?Z2C"?TUl왟/.r왟-,l왟()r왟*+n}2BEEl왟/.r왟-,l왟()r왟*+n3"CL͍/.-,()*+ǟꪵD*Bug: Thefvfourconstructions@*[&m...]꧲,**[j...],@*IhaddOopihsizei,ONand,**{E...}꧲,ONac}'cumulateKinre-verseor}'der.-Only"entriesstartingwithasingle*completelyoverridethemoGdi ershsetupiwitha@*ɲ-construction.Finally*, thefollowingisspGeciallysuitedfor`one-line'UUmatricesincludedintext: |ff2 Aύm@1ff2gweKwill0}inserta`mathstrut'(\vphantom(4)intoeachen- eKtryUUtomakeitscenteringappropriatefortext. eKThiswdisjustanabbreviationusingthefollowingeKdeclaration),whichwillsetuphdecorithatshouldbGeeKinserted>bGeforeeverythingelseineachentry*.<InitiallyeKitUUisemptybuteK Vff2 ;E\everyentry={ OhdecoriUU}ff2)willinserthdecori rstineachentry;S~insidethecounter\=<T89\:;UzӞ1;1~2fdfe|U2fdfez2fdfex2fdfev/2fdfet͟2fdferk2fdfep 2fdfen2fdfelE2fdfej2fdfeh2fdfef2fdfeL͍%|?>%|=<%|89%|:;왞1;2?>\=<T89\:;Uzӟ1~N{x MG{q K{jJ{cI{;imNote:When usingcompilation, 0 changesto\everyentry>.andn!\entrymodifiersWwilln!not`resultinYrecompilationevenwhentheconstructedmatrixchanges {youmayhavetoremovethe.xyc leman-ually*.'Exercisewr33: HowNdidtheauthortypGesetthefol-lowingUUdiagram?=bH3232b5z32fd)g3232 a诉fdfd32bH3232b5zfd)g3232uR:>RMr}'ootbE@++]BϹWX7dWTTWOzqWbH3232b5z32fd)g3232 a诉fdfd32bH3232b5zfd)g3232tE.Dwfd&a)B-)Co)@fd3oo32fdbH3232b5z32fd)g3232 a诉fdfd32bH3232b5zfd)g3232t#+E.+Dw!rfd!AB.SACϟAfdSA@V AA]Kfd4@SGV oFR菟A9fdb//]2fd@*bH3232b5z32fd)g3232 a诉fdfd32bH3232b5zfd)g3232t61^Hints!:ThearrowfeaturewasusedtomakethebGend-ing#arrowsandtheframeextensionfortheframesaroundUUeachcell.+lr25 fdGraphfffeatureVers.3.6bCyKristo erH.Rosehkrisrose@brics.dkiLoadTas:p\xyoption{graph}JThisoptionimplements`XY -graph',aspGecialc}'ombi-natoricy;dr}'awinglanguagesuitableNfordiagramslike ow'`charts,directedgraphs,andvqariousformsoftrees.The^baseofthelanguageisreminiscentoftheLWeJ503 o*tj??O]w\PIC[5]languagebGecauseitusesanotionofthe`cur- rent= loGcation'andisbasedon`moves'.YButthecentralconstructionisa`map'combinatorthatisbGorrowedfromUUfunctionalprogramming. `XY -graphxmakesuseoffacilitiesofthe`arrow'fea-tureUUoptionwhichisthereforerequired.FigureR?17summarisesthesyntaxofahgraphiwithnotespbGelow.+AJhgraphicanappeareitherinanlXY hp-picture(ashdecori)or\stand-alone".^13Note:Ifyoususe\xygraph{?...} ^Einsidesconstructionswhere&issigni cant(likeplainTU>'ExX's\halignorL5ffA͉TU>'EX'sarrayk%environment)thenmakesuretoaddanextralevelUUofbracesaroundit.Notesw㍍25a.S9AUUmoveistoestablishanewcurr}'entnode[.25b.rT*oHdr}'awղsomethingissimplytodrawalineorthedspGeci edharrowifromthecurrentnoGdetothespGeci edtargetnode.8Thetargetthenbecomesthe'}currentnoGde.?AllthefeaturesofarrowsasdescribGedinx22canbeused,-inparticularar-rows,canbGelabelledandsegmented,Abutwiththeuchangethathpath-pGosimeanshnodeiasex-plainedUUinnotex22e.25c.T*o.map]overalistyissimplytosavethecur-rentnoGdeandtheninterpretthehlistiwiththefollowingUUconvention: Starteachelementofthelistwiththecur- rent9noGdeassavedandpasthepreviouslist element,UUand let*Athe? hnoGdeirefertothesaved*Acurrent noGdeUUexplicitly*.25d.rThe;%&Gand;%\\DspGecial;%movesareincludedtomakeitsimpletoenter`matrix-like'thingsasgraphs{notethattheywillnotbGeautomati-callyrGaligned,however,forrGthatyoushouldusetheUU!M*escapGe.&gisthesameas[r]and\\isthesameas[r]!{y+(0,-1)-(0,0)}bwhich*usesakerneles-capGe}tomoves}tothe rstcolumninthenextrow(wherethe rstcolumnisonthey[ٲ-axisofthecurrentUUcoGordinatesystem).Note:JʲIf[youusetheform*{ U...} for[noGdesthenyoudon'thavetochangethemifyoudecidetouseUUanUQXY U-matrix.25e.TypGesetThitiandmakeitthecurrentnoGde.BAlsosavesҘhitiforlaterreferenceusing" hidi"?:lMifhitiisasimpleletter,ordigit,thenjustas"hiti"?;ifhiti5tisoftheform{ uqtext} hIor*...{text} hIthen5tas"text"2ղ.w\eKWithlthe= SadditionitispGossibletosavelexplic- eKitlyincaseseveralnoGdeshavethesametextoreKa EnoGdehasatextthatitisimpracticaltouseforeKreference. 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Hfdfe'ʟ!dfdfe%^!_fdfe.[dfdfe,ҟfdfe+ fdfe* fdfe2o~"fdfe1Njfdfe/Ɵlfdfe.[fdfe6<2Ʉfdfe4}cfdfe3Ofdfe2o~"fdfe9Kfdfe8bfdfe7cʟfdfe6<2Cfdfen <632fdfe;32fdfe:32fdfe932fdfe?fΞ32fdfe9>ߞ32fdfe=32fdfe<32fdfe A32fdfeSl@ׂ32fdfe@!b32fdfe?kB32fdfe΍C/ڞ32fdfegB{32fdfeB32fdfeA32fdfe@v32fdfe?'&32fdfewԟxA 2\l&C_y yxJʅy}y3?}yVC9y%Fy}`ꪵBMDMs?JfdJ Vfd8F 1Uogg*[~aP ٟ\PW9P՟zP`xCrڹ"pbr۟66EvciEySE}1XEj$E'CElϟ$Eo!Y!EjJF 2k/fwwj# nn4E9nrEinvsVގnY>fDmgK.:Kn2ϟ oufs]~fw5f|0 rfdʚfgU=sfjfUYTW 3_P3 Ѝ_PPL`cJPauӟPb\Pmy&!ZEv\kxbo `+ 1yyB-{#A}~䉟ލt?ԟuȟw[" 4mCܟ쵍j69kgf9dȻ9b9D!ZF S 3m!.#.%.!'.捍.\U..|{# 5DX//xnz"fdYʎ= fG?ҟjJ4tfX؟o0XKwX|XSX-Xx~7XnL" 6؟ BBi봹l0v 8W 7ğWbSSՍğ&̍b&&ƞ&@c܍\def\alphanum{\ifcase\xypolynode\or?A\or?B\orC\orD\orE\orF\orG\orH\fi}\xy/r3pc/:?{\xypolygon3{~={40}}},{\xypolygon4{~={40}~>{{--}}}},{\xypolygon5{~={40}}},{\xypolygon6{~={40}~>{{--}}}},{\xypolygon11{~={40}}},{\xypolygon50{~={40}~>.}},?+/r8pc/,{\xypolygon7{~<<{@{-}}~><{}~<>{|*@{x}}~*{\alphanum}~>>{_{\alpha_\xypolynode^{}}}}}\endxy4Use ofthe~={ɨ...} Xswitch wasdescribGedearlier.When8usingthe~:{}...} #-more8canbGedonethanjustsettingKthebase.nInfactanykernelcoGdecanbesup-plied*here.GItisproGcessedpriortoanyotherpartofthe,pGolygon.MThegraphicsstatehascatthecentreof_thepGolygon,pattheoriginofcoordinateswithinthepictureandhasbasisunchangedfromwhathaspreviouslybGeenestablished.^ThecurrentpointcwillbGenresettothecentrefollowinganycoGdeinterpretedusingUUthisswitch. A}Nfurther}simpli cationexistsforsidesandspGokeswithout8harrowis.qIfhtokiisasinglecharacterthen~> htoki, ~>{htoki}?, ~>{{htoki}} AoalluspGecifythedirec-tional.\dir{nθhtoki}?;;similarly.withthe~<ݴswitch.dOntheotherhand,compGounddirectionalsrequireallthebraces,UUe.g.q~>{{--}}1and~>{2{.}}-U=.AfterallswitcheshavebGeenprocessed, TremainingtokensRareusedtospGecifythehob8jectiforeachver-tex.SuchktokenswillbGeuseddirectlyaftera\drop,socanincludeob8jecthmoGdi erisasin gure3.Ifan9hob8jectihasalreadybGeenspeci ed,rusingthe~*switch,=then7thefollowingmessagewillbGewrittentotheUUTU>'ExXlog:썑8Xy-pic?Warning: vertexalreadyspecified,discarding?unusedtokens:gweKwith?tokensattheendindicatingwhatremainsun- eKproGcessed.]Similarlyextratokensbeforethe{ ...}eKgenerateUUamessage:+,#Xy-pic?Warning:discardingunusedtokens:0W䍒eKNestedTP9olygons6oeKWhenT\xypolygonE)|isTspGeci edwithineitheraeK~<>{e?...} 1;orF~>>{F...}switchFforanotherpGolygon,eKthen5theinnerpGolygoninheritsanamewhichin-eKcorpGorates7alsothenumber7ofthepartonwhichiteKoGccurs,"yasrgivenby\xypolynode=Q.^Thisnameisac-eKcessedousing\xypolyname=/y.InthefollowingexampleeKtheinnerpGolygonisplacedusing~<>oinordertoeas-eKily"adjustitsorientationtotheoutwarddirectionofeKtheUUspGokes.YC|?K1ߡv?>~=<v89~:;w-Rֲ1;1/R1;2}T'lmOw-RҲ1;3?N?m|?T&ɧ?_+RԲ1;4ɧ鍍loLrmuT$uT%?rm?oM?l?'dK2ߡ!丟?>)丟=<!丟89)丟:;:ןRԲ2;1"՟R2;2/Ɗ?2?5b|?8yΟɧ? ӟRԲ2;3ɧ鍍ƈ` y̟"՟Rֲ2;4 y͟?a??Ɖ?}8yl5c2/ƋG丟FfdX'd+&3!丟?>)丟=<!丟89)丟:;"՟-*3;1 ӟ*-,3;2Aƈ` y̟"՟B-.3;3 y͟6C?a3?0k?Ɖ-?:ן*-,3;41X8yϹl5c2/Ƌ/Ɗ?2h?5b?8yΟ@?) ,Xfd|?+&4v?>~=<v89~:;_+*-,4;1w-B-.4;2uT%6C?rm3?oM0k?l-?/*-,4;31XT'lmOw--*4;4?Nh?m?T&@?AloLrmuT$G丟( ^fdX~ޟ ,XfdfBeK\xypolygon4{~:{/r5pc/:}H~<>{*\frm<8pt>{o}\xypolygon4{~:{/-2pc/:}%B~*{\xypolyname\xypolynode}}}H[o]=<5pc>{\xypolynode}}eKNoticehownestedpGolygonsinheritnames"1,1"9x,eK"1,2"<,...,"4,1",...,"4,4"#forMtheirvertices.[IfeKaRhpre xiissuppliedattheoutermostlevelthentheeKnamesMbGecome:b" hpre xii;j"҈.[Specifyingahpre xieKforɮtheinnerpGolygonoverridesɮthisnamingscheme.eKTheQsamenamesmaythenbGerepeatedforeachofeKtheSinnerpGolygons,=allowingaccessafterwardsonlyeKtothelast|pGossiblyusefulasamemorysavingfea-eKture~whentheverticesarenotrequiredsubsequently*.eKF*our|zlevelsofnestinggivesaquiteacceptableeK\SierpinskiGgasket".HTheinnermosttriangleispro-eKvidedd]by\blacktriangleNHfromtheAU>'M SsymbGolfonteKmsam5<,atP5-pGointsize.BF*urtherlevelscanbGeachievedeKusing3thePostScriptbackend,J*otherwise3lineseg-eKments;#bGecometoosmalltoberenderedusing;XY #-fonts.LWeJ558 U۠*tj??gwBNTHD"xmsam5DNR`cNS[x ߍS[x UcDNS&hfdHu=Vx`1}WUu`1P0DNO7ʮNqWOj[x ߍPD[x R`ʮDNOjfdHN֍S`1}Sџ`1WV0DNUʮNqWVx[x ߍWU[x YYʮDNVxfdHN֍YV`1}Z`1Mj͛DNKЈNJLVƟ[x ߍM3[x O7ЈDNLVƟٚfdH(oOj`1}P-`1J&ƟubDNHvtb.N$H"[x ߍI[x Kb.DNH"ֳ3fdHLVƟ`1}M3`1PubDNO7b.N$Oj[x ߍPD[x R`b.DNOjֳ3fdHS`1}Sџ`1[ ͛DNYYЈNJYV[x ߍZ0[x \LЈDNYVٚfdH(o]9`1}^`1WVubDNUb.N$Vx[x ߍWU[x YYb.DNVxֳ3fdHYV`1}Z`1^jubDN\Lb.N$]9[x ߍ^ԟ[x `b.DN]9ֳ3fdH``1}awa`1F!NDNEϟ;N#E}[x ߍFrW[x Hvs;DNE}܌̈́fdHۢH!`1}I`1Ce}(DNA+aN׼B4ٟ[x ߍC[x EϟaDNB4ٟfffdH;E}`1}Fr@`1J&ş(DNHvsaN׼H![x ߍI[x KaDNH!fffdH;LVş`1}M3`1@ٟ.DN>TNU>5[x ߍ?[x A+DN>5?fdHԍB4ٟ`1}C`1<5DN:ȓN;s[x ߍTȓDN;sfdHhm>5`1}?`1Ce}DNA+ȓNB4ٟ[x ߍC[x EϟȓDNB4ٟfdHhmE}`1}Fr@`1Mi.DNKNULVş[x ߍM3[x O7DNLVş?fdHԍOi`1}P,`1J&şDNHvsȓNH![x ߍI[x KȓDNH!fdHhmLVş`1}M3`1P DNO7ȓNOi[x ߍPC[x R_ȓDNOifdHhmS `1}SП`1aCNDN`;N#`[x ߍawy[x c{;DN`܌̈́fdHۢcC`1}d`1^j(DN\MaN׼]9[x ߍ^՟[x `aDN]9fffdH;``1}awb`1e+(DNc{aN׼cC[x ߍd[x f9aDNcCfffdH;g[`1}h8`1[ .DNYYNUYW[x ߍZ1[x \MDNYW?fdHԍ]9`1}^`1WWDNUȓNVx[x ߍWU[x YYȓDNVxfdHhmYW`1}Z`1^jDN\MȓN]9[x ߍ^՟[x `ȓDN]9fdHhm``1}awb`1h.DNf9NUg[[x ߍh8[x j<ݟDNg[?fdHԍj`1}kN`1e+DNc{ȓNcC[x ߍd[x f9ȓDNcCfdHhmg[`1}h8`1k/DNj<ݟȓNj[x ߍke[x mȓDNjfdHhmn/`1}n`19CbDN7>.Nd8[x ߍ8Ɵ[x :.DN83fdHB;s`1}"4H[x ߍ5"[x 7>{DN4H̄fdH8`1}8ﯟ`1<4DN:{N>";s[x ߍT{DN;s̄fdH>4`1}?`12HhDN0U`N1Q[x ߍ2.~[x 42U`DN1QefdH:4H`1}5 `1/!B-DN-qR.NT-[x ߍ.ڟ[x 0.DN-fdHӍ1Q`1}2.g`15B-DN42.NT4H[x ߍ5"[x 7>.DN4HfdHӍ8`1}8ﯟ`1@؟hDN>TU`N>4[x ߍ?[x A*U`DN>4efdH:B4؟`1}C`1<4B-DN:.NT;s[x ߍT.DN;sfdHӍ>4`1}?`1Ce|B-DNA*.NTB4؟[x ߍC[x EΟ.DNB4؟fdHӍE|`1}Fr?`1+DN* N*[[x ߍ+m5[x -qQ DN*[ YfdH m-`1}.Ÿ`1(`[ `DN& ,N '/[x ߍ( [x *,DN'/31fdH*[`1}+m`1/! 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"CurrentlyAtheonlyroutinesimplementedwiththisfeaturearesome\quickanddirty"macrosfordrop-pingob8jectsatthepGointsofanintegerlattice.T oDo:MorensophisticatedroutineswillbGedevelopedforUUlaterversionsofUQXY U-pic,astheneedarises.MathematicallyspGeaking,let~u [bandm~v ֡bevectorspGointinginindependentdirectionswithintheplane.Then(thelatticespannedby~u and&~v ٲisthein nitesetUUofpGointsLgivenby:E&L0=b ca~u +8bG@~v };forUUa,bintegersK̻b SL:Within/jXY n-pic/nthevectorsg~u Zand~v canbGeestablished aswthecurrentcoGordinatebasisvectors.'ThefollowingmacrosUUtypGeseta nitesubsetofanabstractlattice. Sff2 \xylattice#1#2#3#4ppGointsUUinlattice\croplattice#1#2#3#4#5#6#7#8p...inUUspGeci crectangle."ff26퍖UTheparameters#1ʤ...#4areUtobGeintegersamin ,amaxA̲,obminandbmax,sothatthepGortionofthelat-ticetobGetypesetisthatcollectionofvectorsinLforgweKwhichUUaminaamax!andbminbbmaxA̲.snjApj/pCFp p popҟp>B  j,B CFB B  B oB ҟB ;ij)i CFi#i% i(oi+ҟi,8G/j&G2CFG5G7 G:oޑG=ҟ̑G>5Aj#DCFGI Lo۸OҟɸP2Sj Y[ ^oaҟb0ejhCF km posҟt-/wj/zCF /}/ /o/ҟ/*WXjWXCFWXWX WXoWXҟWXVCFYFյaXc:Zs3232;d3232P32323232323232323232323232323232323232323232Pܞ3232TZ:@ڟ 323273232323232323232323232323232323232323232323232323232XG 32327323232323232323232323232323232323232323232323232323232:Zs3232;d3232P32323232323232323232323232323232323232323232Pܞ3232ӟs^(1)ӟ//2fdSAo呵s^(2)I呺OOIhwAp4fdieK\def\latticebody{% eK\ifnum\latticeA=1?\ifnum\latticeB=-1%eK\else\drop{\circ}\fi\else\drop{\circ}\fi}eK\xy?*\xybox{0;<1.5pc,1mm>:<1mm,1.5pc>::eK,0,{\xylattice{-4}4{-3}3}H,(1,-1)="a"*{\bullet}*+<2pt>!UL{a}H,(-1,1)."a"*\frm{.}}="L"eK,{"L"+L?\ar"L"+R*+!L{s^{(1)}}}eK,{"L"+D?\ar"L"+U*+!D{s^{(2)}}}eK\endxytFeKIntheabGovecode,noticehowthebasisis rsteKestablishedAthenthe\xylattice@ZdtypGeset. 9DoingeKthiswithinan\xybox(allowsaxestobGesizedandeKplaced#appropriately*.30SincelatticepGointsaredeter-eKminedbytheir(integer)coGordinatedisplacements,eKtheycanbGerevisitedtoaddextrahob8jectisintoeKtheVoverallpicture. KMoregenerally*,ZtheoriginforeKlattice-coGordinatesgisthecurrenthposic,NwhentheeK\xylattice.commandisencountered.HEasyaccessi-eKbilityUUismaintained,asseeninthenextexample.-r+eKWhenythebasisvectorsX~u andL~v (%arenotpGerpendic-eKularnithecollectionofpGointswitha;bintheserangeseKwill lloutaskewparallelogram.SZGenerallyitisuse-eKfulTtoplotonlythosepGointslyingwithina xedrect-eKangle.]ThisisthepurpGoseof\croplatticeB,#withitseKextraparameters#5...#8vdeterminingthe`cropping'eKrectangleTwithinwhichlatticepGointswillbGetypGeset.eKOther{pGointswillnotbetypesetevenwhenaandbeKareLEwithinthespGeci edranges.VExplicitlythehor-eKizontalrangeofthecroppingrectangleisXmintoeKXmaxA̲,fwithc]Xmin#abGeingtheX-coordinateofthevec-eKtor#5|~uV,where#5WisahnumbGeri됲(notnecessarilyeKanNinteger).]SimilarlyXmaxoistheX-coGordinateofeK#6$~>u@.HTheEverticalextentsareYminIandYmaxA̲,HgivenLWeJ569 V*tj??gwby theY8-coGordinatesof#7 3~yvOVand#83~yvOVrespGectively*.\;Q(=ȸ.qȟ*,S_Bx P(3.,kȟ%%BxN.-Pf6(ִ?./V5o7ȟ!)@ aIBx Z(p c.ASV1+\[ȟ^mBxuP<~(+twV,ȟM7BxoPݳ(V(2ȟjQP<Q.Ÿ d ̸j }T332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfeT332fdfe 퍍Bn32fdfe Bn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfeBn32fdfefnfdfed"fdfec֟fdfeafdfe_>fdfe]%fdfe[1fdfeY=ZfdfeWIfdfeUTŸfdfeS`vfdfeQl*fdfeOwޟfdfeMfdfeKFfdfeIfdfeGfdfeEbfdfeCfdfeAʟfdfe?~fdfe=2fdfe;fdfe9fdfe8Nfdfe6fdfe4fdfe2'jfdfe03fdfe03{fdfe2'j{fdfe4{fdfe6{fdfe8N{fdfe9{fdfe;{fdfe=2{fdfe?~{fdfeAʟ{fdfeC{fdfeEb{fdfeG{fdfeI{fdfeKF{fdfeM{fdfeOwޟ{fdfeQl*{fdfeS`v{fdfeUTŸ{fdfeWI{fdfeY=Z{fdfe[1{fdfe]%{fdfe_>{fdfea{fdfec֟{fdfed"{fdfefn{fdfe퍍0Hg323213232E3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232E3232'0.Οڧ3232"32323232323232323232323232323232323232323232323232323232323232323232gQڧ3232"32323232323232323232323232323232323232323232323232323232323232323232320Hg323213232E3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232E3232\ ?s^(1)\ ://(Пlfd3PD6j]s^(2)Kpj]OOK>37 v̰fdFI򍍑\def\latticebody{% \ifnum\latticeA=1?\ifnum\latticeB=-1%\else?\drop{\circ}\fi\else\ifnum\latticeA=0?\ifnum\latticeB=1\else\drop{\circ}\fi\else\drop{\circ}\fi\fi}\xy?+(2,2)="o",0*\xybox{%0;<3pc,1.5mm>:<0.72pc,1.65pc>::,{"o"\croplattice{-4}4{-4}4{-2.6}{2.6}{-3}3},"o"+(0,1)="a"*{\bullet}*+!D{\alpha},"o"+(1,-1)="b"*{\bullet}*+!L{\beta},"o"+(0,-1)="c","o"+(-1,1)="d","a"."c"="e",!DR*{};"a"**\dir{.},"e",!UL*{};"c"**\dir{.},"b"."d"="f",!DL*{};"b"**\dir{.},"f",!UR*{};"d"**\dir{.},"e"."f"*\frm{.}}="L","o"."L"="L",{"L"+L?\ar"L"+R*+!L{s^{(1)}}},{"L"+D?\ar"L"+U*+!D{s^{(2)}}}\endxyfThe\latticebodyHmacro. AtTZeachlatticepGointwithinSthespGeci edrangefora;b(andwithinthecropping rectanglewhen\croplatticeHisused),;amacros)called\latticebodyI.isexpanded. BThisismeant6tobGeuser-de nable,0pt?\divide\dimen0by64H\dimen0=\latticeY\dimen0?\relaxH\ifdim?0pt>\dimen0\dimen0=-\dimen0\fiH\ifdim?10pt>\dimen0\drop{\bullet}%H\else\drop{.}\fi?\else\drop{.}\fi}eK\xy*\xybox{0;<3pc,2.57mm>:<.83pc,2.25pc>::eK,0,{\croplattice{-3}5{-5}5E{-1.3}{4.5}{-3.4}{4.4}}}="L"eK,{"L"+L?\ar"L"+!R*+!L{\sigma^{(1)}}}eK,{"L"+D?\ar"L"+!U*+!D{\sigma^{(2)}}}eK\endxy.HeK28˯Circle,ffEllipse,ArcfeatureҒeKVers.3.4bCyRossMoKorehross@mpAce.mq.edu.auieKLoadTas:p\xyoption{arc}`ˍeKThistfeatureprovidesameanstoaspGecifycirclesofeKarbitraryradius,drawnwithavqarietyoflinestyles.eKSimilarlyellipsesmaybGespeci ed,ohavingarbitraryeKma8jor/minorcaxesalignedinanydirection.+AScircu-eKlararcjoiningtwopGointscanbGeconstructedwitheKspGeci edUUtangentdirectionatoneend. ~eKAllyLthecurvesdescribGedhere|circles,NellipsesandeKsectorsQ9ofthese|areconstructedusingthecurveseKfromthexycurve0+extension. CAssuchanycom-eKments$OgiventhereconcerningmemoryrequirementseKareequallyvqalidhere,߁pGerhapsevenmoreso.#UseeKof0thexypsTPostScriptback-endishighlyrecom-eKmended.LWeJ57: *tj??gw28.1 FullCirclesHTheTxyarc PfeatureTallowsamuchwiderrangeofpGos- sibilitiesCfortypGesettingcirclesthanisavqailablewith\cir .}Firstlytheradiusisnolongerrestrictedtoa nitecollectionofsizes.ugSecondlyfancyline(curve)styles2`areavqailable,iaswithcurvedarrows.Finallythere;areavqarietyofwaysofspGecifyingthedesiredradius, DrelativetootherpartsofthepicturebGeingbuilt,UUasinthefollowingexample. D7`6Lͷ0p9pTLͷ_xcR?O ?LQY/?I S?E) w?BeMl??q?;Ǖ?8x?6#>fdfe4Jfdfe3惄fdfe2ͥfdfe1ʟo?fdfe/Ҭ!fdfe/ _fdfe. 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hchari}/twoUUstyles\knotSTYLE{>߸hcoGdei}/useUUhcoGdeiJff2LWeJ65BnT*tj??]'8Ineachcasethenewstyleappliestoallsubse- quent"knotpieces,VUexceptthatthetwostylesapplyonlytocrossings.Thelattercaseallowsuseofob-jectD^hmoGdi eris.>ThehcodeiconsistsoftwoD^groups{..}{..}6,Oeachcontainingharrowiforms,Oasin14and4notes22m,l22r.,Onlythe rstharrowiformisusedUwithhjoiniswhereasthetwoUformsareusedre-spGectively~withthetwostringsofahcrossingiintheorderUUthattheyaredrawn.)ڍPartffIV+DrivZersThis]partdescribGes`drivers'thatcustomisethepartsoftheDVI legeneratedfromXY -picturestoexploitspGecialcapabilitiesofparticularDVIVdriverprogramsthrough~TU>'ExXxs\special1command.+CThismakestheDVIg lesgnon-pGortablebutisneededforfullsupportofr2someofther.XY 2-picextensions(describGedinpartII). +Figure21attheendofthispartsummarisestheextensionsUUsuppGortedbyalldrivers.!*30}Supps3ortforSpeci cDrivers830.1 dvidrvdriver3Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.auiLoadTas:p\xyoption{dvidrv}This driverprovidessuppGortforthe\emtex"\specialpcommands,Gwhenusingoneofthestan-dard dvi-drivers:c2dvidot$ ,8dvihplj(#,8dvimsp#l&,8dviscrordvivik",zthatcomewithEbGerhardMattes'em-TU>'ExXdistribution. +SuppGortedUU\special0e ectsUUare...em-TU>'ExXUUline-drawing\special-U=s.vqariableUUline-widths#?30.2 DVIPSdriverVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui LoadTas:p\xyoption{dvips}This\driverprovidessuppGortforallextensions/whenusing2thedvipsdriverbyT*omasRokicki[11 ].fDIthasbGeenGtestedwithdvipsversion5.55aanddvipskver-sionUU5.58f. +SuppGortedUU\special0e ectsUUare...colour,EusingAdirectcolorspGecialsandPostScript.crayonUUcolours.eKeLPostScriptUUback-end.эeKeLrotated/scaledqdiagramsandtext,9usingPost- eLScript.eKeLvqariableline-widthsandpGoly-lines,MusingPost-eLScript.eKeLextraUUframesand lls,usingPostScript.eKeLpatternsUUandtiles,usingPostScript.eKeLtpicUUdrawingcommands.eKeLem-TU>'ExXUUdrawingcommands.!ڍeK30.3KDVITOPSdriveruTeKVers.3.3bCyRossMoKorehross@mpAce.mq.edu.auieKLoadTas:p\xyoption{dvitops}eKThis leprovidessuppGortforthedvitopsdriverbyeKJamesbClark.AsofSeptembGer1995,fXithasnotbeeneKfullyUUtested.eKSuppGortedUU\special0e ectsUUare...DeKeLcolour,usingdirectcolorspGecialsforgray,rgbandeLhsbcolourmoGdels;pandPostScriptcolourwithineLdiagrams;эeKeLcrayonUUcolours.eKeLPostScriptUUback-end.eKeLrotated/scaleddiagramsandtext,GWusingdvitopseLspGecials;UUhoweverthesemaynotbGenested.eKeLvqariableline-widthsandpGoly-lines,MusingPost-eLScript.eKeLextraUUframesand lls,usingPostScript.eKeLpatternsUUandtiles,usingPostScripteKeLtpicUUdrawingcommands.!ڍeK30.4KOzTeXdriveruTeKVers.3.3bCyRossMoKorehross@mpAce.mq.edu.auieKLoadTas:p\xyoption{oztex}eKThis*1driverprovidesthenecessaryinterfacetosup-eKpGort0thePostScriptback-endandotherPost-eKScriptjpe ectswhenusingtheDVIjjdriverjpofversionseK1.8+i ofO4zTU>'ExXbyAndrewT*revorrow,^15 Earlierver-eKsions,kofOzw}TKß'E-Xshouldinste}'adusethedriveroptioneK\xyoption{17oztex}?.eKE ectssuchascolour,'line-thicknessandrotatedeKorscaleddiagramsareonlypartiallysuppGortedineKthatthee ectscannotbGeappliedtoanytextorsym-eKbGolsbplacedusingfonts..ThisisduetothenatureeKofO4zTU>'ExXhdriveri, whoseoptimizationoftheplace-eKment%offont-charactersprecludestheapplicabilityofeKsuch%:e ects.aF*urthermorethePostScriptdictionaryffffy̟ J=w-:15LOzTAEMXisasharewÎareimplementationofTAEMXforMacintoshavailablefrommanybulletinb'ExX,thereisthealternativeof5usingthedvips"hdriveri,n which5doGessupportalltheUUPostScripte ectsavqailableinUQXY U-pic. Note:ٲT*o]use]XY -pice ectivelywithO4zTU>'ExXre-quires{#changingseveralmemoryparameters.0Inpar-ticularXca`Big-TU>'ExX'isneeded,Y&alongwithanincreaseinuthepool_size8ϲparameter.(Explicitinstructionsarecontainedinthe leINSTALL.,OzTeXJ/oftheXY w-picdistribution.SuppGortedUU\special0e ectsUUare...U񍍍colour, ,usingmPostScript,butnotoffont-characters.crayonUUcolours,similarlyrestricted.PostScriptUUback-end.vqariableline-widthsandpGoly-lines,MusingPost-Script.extraUUframesand lls,usingPostScript.patternsUUandtiles,usingPostScript.rotated/scaled'diagramsandtext,\recognisedbutnotUUsuppGorted."~30.5 OzTeXv1.7driverVers.3.3bCyRossMoKorehross@mpAce.mq.edu.auiLoadTas:p\xyoption{17oztex}Thisoptionprovidesthenecessaryinterfacetosup-pGort0thePostScriptback-endandotherPost-Scripte ectswhenusingtheDVI[driverofver-sion]1.7ofO4zTU>'ExXbyAndrewT*revorrow,^16L}'aterversions0ofOzw}TKß'E-Xshouldinste}'adusethedriverop-tion͊\xyoption{oztex}WZ.-Upgradingtoversion1.9+ofO4zTU>'ExXUUisrecommended. DoGesnotsupportrotations,YscalingandcolouredtextIwithindiagramsandthePostScriptdictionarymustUUbGeavqailableina lecalledglobal.ps2:.Note:ٲT*o]use]XY -pice ectivelywithO4zTU>'ExXre-quires{#changingseveralmemoryparameters.0Inpar-ticularXca`Big-TU>'ExX'isneeded,Y&alongwithanincreaseinuthepool_size8ϲparameter.(Explicitinstructionsarecontainedinthe leINSTALL.,OzTeXJ/oftheXY w-picdistribution.SuppGortedUU\special0e ectsUUare...U񍍍colour, ,usingmPostScript,butnotoffont-characters.crayonUUcolours,similarlyrestricted.PostScriptUUback-end.𖍍eKeLvqariableline-widthsandpGoly-lines,MusingPost- eLScript.эeKeLextraUUframesand lls,usingPostScript.eKeLpatternsUUandtiles,usingPostScript.eKeLrotated/scaled'diagramsandtext,\recognisedbuteLnotUUsuppGorted.#7荍eK30.6KTexturesdriver=eKVers.3.3bCyRossMoKorehross@mpAce.mq.edu.auieKLoadTas:p\xyoption{textures}eKThis;udriverprovidessuppGortforversion1.7+ofeKBlue SkyResearch'sTexturesapplicationforMac-eKintosh^17x. s/ItxincorpGoratessupportforcolourandeKallcof_XYjc-pic'sPostScripte ects. 0EarlierversionseKofTexturesshouldinsteadusethedriveroptioneK\xyoption{16textures}O . *eKNoticethatversion1.7su ersfromaprintingbugeKwhichl"maycauseaPostScripterror.$ Ak xiskludgedeKbymmakingsurethe rstpagehasbGeenshownintheeKviewerabGeforeanypageswithdiagramsaresenttotheeKprinter.eKSuppGortedUU\special0e ectsUUare...эeKeLcolour,UUbGothon-screenandwithPostScripteKeLcrayonUUcolours.eKeLPostScriptUUback-end.eKeLrotated/scaledqdiagramsandtext,9usingPost-eLScript.eKeLvqariableline-widthsandpGoly-lines,MusingPost-eLScript.eKeLextraUUframesand lls,usingPostScript.eKeLpatternsUUandtiles,usingPostScript.#7荍eK30.7KTexturesv1.6driver=eKVers.3.3bCyRossMoKorehross@mpAce.mq.edu.auieKLoadTas:p\xyoption{16textures}eKThisdriverprovidessuppGortforversions1.5bandeK1.6ofBlueSkyResearch'sTexturesapplicationforeKMacintosh^18x.ELItincorpGoratessupportforPostScripteKcolouryandtheuXY y-psPostScriptback-end.]ThiswilleKnotxworkwithversions1.7andlater; ttheserequireeKtheUUhdriverioption\xyoption{textures}g. *eKSuppGortedUU\special0e ectsUUare...эeKeLcolour,UUusingPostScripteKeLcrayonUUcolours.ffffy̟ J=w-:16LOzTAEMXisasharewÎareimplementationofTAEMXforMacintoshavailablefrommanybulletinbw-:17LMacinÎtoshXisatrademarkofAppleComputerInc.w-:18LMacinÎtoshXisatrademarkofAppleComputerInc.LWeJ67D.*tj??gwPostScriptUUback-end.\trotated/scaledqdiagramsandtext,9usingPost- Script.vqariableline-widthsandpGoly-lines,MusingPost-Script.extraUUframesand lls,usingPostScript.patternsUUandtiles,usingPostScript.%N30.8 XDVIdriverMVers.3.3bCyRossMoKorehross@mpAce.mq.edu.auiLoadTas:p\xyoption{xdvi}This4YdriverprovidessuppGortforextensionswhenus-ingV{vqariantsofthexdvidriver,VbyEricCoGoper,VBobSchei er,MarkĴEichinandothers.IthasbGeenusedsuccessfullybwithxdviBpatchlevelb20,ebyPaulV*o8jta,andUUxdvik ꛲versionUU18f,byKarlBerry*. t'SomeofthesuppGortedfeaturesassumethattheimplementationofxdvi2islinkedtoaPostScriptrenderer;Ue.g.Ghostscript\TorDisplaUTyPostScript.Ifsuch'SsuppGortisnotavqailable,0theninvokingxdviNus-ingthecommandxdvi?-hushspecialscwillsuppresswarningmessagesthatmightotherwisebGeproduced.Onew"drawbackofsuchasetupisthatmuchofthePostScriptD~isnotrendereduntilafterallofthefontcharacters,xetc.KhaveqbGeenplacedonthepage.ThustextthatwasmeanttobGeplacedontopofa lledorpatternedregionmayappGeartobeobscuredbyit.Howeverwhenprinted,5usingaPostScriptprinter,theUUcorrectplacementisobtained.SuppGortedUU\special0e ectsUUare...\tcolour,UUusingPostScript.MNot>allversionsofxdviXpsuppGortcolor\special-&s,sothereisnodirectsuppGortforcolour.aHoweverparts#/ofpicturesrenderedusingPostScriptmayappGearcoloured,duetointerpretationofcolourcommandsUUwithinthePostScript.crayonUUcolours.PostScriptUUback-end.rotated/scaledqdiagramsandtext,9usingPost-Script.vqariableline-widthsandpGoly-lines,MusingPost-Script.extraUUframesand lls,usingPostScript.patternsUUandtiles,usingPostScript.tpicUUdrawingcommands.DThefollowingTU>'ExXimplementationisalsosuppGorted,butUUcurrentlyusesthedvipsdriver.gweK30.9KCMacTeXdriverIeKVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui eKLoadTas:p\xyoption{cmactex}eKThomas+Ki e'sCMacTU>'ExXapplicationusesdvipsaseKitsUUdvi-driver.seKOtherimplementationsnotspGeci callymentionedeKhereLEmaywellworkwithoneofthenamedhdriveris,eKthough["pGerhapsnotallfeatureswillactuallybesup-eKpGorted.!䍍eK31˯ExtraufeaturesusingE-ff cmcsc10EPost-˯Scriptffdrivers/eKThiswesectionacknowledgeswethesuppGortforextrafea-eKturesUavqailablewhenusingahdriverithatsuppGortseKuseTWof\special.commandswithnativePostScript.eKExtra^macrosarerequiredtotakeadvqantageofthis;eKthese$areloadedautomaticallyinconjunctionwitheKextensionsspGeci edusingthe\xyoption6command,eKprovidedu=ahdriveriwhichsuppGortstheextension,}7aseKindicatedUUin21,hasalsobGeenspeci ed. &eKCommandsDarealsoprovidedtoturno /onuseeKofJthesefeatures.n'ExX.VeKPostScriptescap`eIeKAn|extrahshapGeimodi erkeyallowsarbitraryPost-eKScriptUUcoGdetobeappliedtothecurrenthob8jecti.eK 3ff2  [!hpGostscriptUUcodei]h۲forUUspGeciale ects [psxy]h۲storesUUcurrentloGcation.&ff2 MSNormallythehpGostscriptcodeiwillbeasimplecom-mandtoalterthePostScriptgraphicsstate:|e.g.[!1?00setrgbcolor]mpchangesq*thecolourusedtorenderpartsofthehob8jecti.`AnynumbGerofsuchhshapGei`modi ersisallowable,choweveritismoreef- cient)$tocombinethemintoasinglemoGdi er,1when-everUUpGossible.ItisveryimpGortantthatbraces{ iand}donotappGearcNexplicitlyinanyhpostscriptcodei,asthismayLWeJ68EF*tj??s3H<ϟ٘ffP͟ ffџyhdrivӍeriXLƫ!۟?HhextensioniIj ffOGframe͟ ffv8line͟ ff,rotate͟ ff‘color͟ ff tile͟ ff ps͟ ffffPfdͤ ffzfddvidrv ff[F-B ff|+ i8 ff&y- ffh-B ff[- ff fR- b  ffffPͤ ffxfddvips ffY + 7 ff|+ i8 ff+5 ff̈́+ 7 ffmv+ i8 ff -m+); ffffPͤ ffU{fddvitops ffY + 7 ff|+ i8 ff+5 ff̈́+ 7 ffmv+ i8 ff -m+); ffffPͤ ffxfdoztex ffY + 7 ff|+ i8 ff+5 ff̈́+ 7 ffmv+ i8 ff -m+); ffffPͤ ffU{fd17oztex ffY + 7 ff|+ i8 ff+5 ff̈́+ 7 ffmv+ i8 ff -m+); ffffPͤ ff}fdtextures ffY + 7 ff|+ i8 ff+5 ff̈́+ 7 ffmv+ i8 ff -m+); ffffPͤ ff ufd16textures ffY + 7 ff|+ i8 ff+5 ff̈́+ 7 ffmv+ i8 ff -m+); ffffPͤ ff5wfdxdvi ffY + 7 ff|+ i8 ff+5 ff̈́+ 7 ffmv+ i8 ff -m+); ffffPR ͍4TFigureUU21:qExtensionimplementationreplacedbyuseofhdriverispGecials.: upset9the5XY 9-pichob8jectiparsing.{sHowever9itisac- ceptable>tohave>acontrolsequencenamehere,xex-pandingNintomoreintricatePostScriptcoGde.oThiswillUUnotbGeexpandeduntilalater(safe)time. ōDue5todi erenceswithintheDVI-drivers,lsuchsimplenPostScriptcommandsneednota ecteverypartnofanhob8jecti.$Inparticularthelines, curvesandarrowheadsgeneratedbyXY -picuseadi erentmech-anism,kdescribedintheprevioussectionalsousethismechanism,soshouldworkcorrectlywithalldrivers.N8\def\colorxy(#1){%/xycolor{#1?setrgbcolor}def}...\connect[!\colorxy(1?00)]\dir{-}...kNote#howthebracesareinsertedwithintheexpan-sionK'ExXandZXY -pic,\bnotforZdrawingnewob8jectswithinPostScript. NoguaranteeIcanbGegivenofthecurrentloGcation,Eorscale,:which JmaybGedi erentwithdi erentdrivers.HoweveragoGodPostScriptprogrammerwillbGeabletoovercomesuchdicultiesanddomuchmore. eKT*oaidinthisthespGecialmodi er[psxy]%1IJisprovided eKto#recordtheloGcationwherethereferencepointofeKthe0currenthob8jectiwillbGeplaced.ItscoordinateseKareUUstoredwithkeysxyXpos&*andxyYpos"C."eK31.1KColour}eKTheincluded lexyps-c.tex'ExXgroupings.eK ؉ff2 j]\NoPScolorX'ExXgroupings. ؉ff2 jv_\NoPSframes[v;removeUUPostScriptsuppGortLWeJ69F^A*tj??gwx\UsePSframes?TreinstateUUPostScript.ff2MZWithoutPostScriptsuppGortellipsesmaybeshown as\circlesandall lledregionsmaybGerepresentedasQ\blackrectangles.eThesecommandsareprovidedprimarilyrfortestingandtrouble-shoGoting;#e.g.withhdrivericon gurationsuntestedbytheauthorsofXY ]-pic,UUwhoshouldbGenoti edofanydiculties.(ԍ31.3%Line-styles=}Theincluded lexyps-l.tex'ExXgroupings.wff2 []\NoPSlinesX'ExXgroupings.wff2 [v_\NoPSrotate[v;removeUUPostScriptsuppGortv_\UsePSrotate[v;reinstateUUPostScript.ff2CWithoutPostScriptsuppGortdiagramscanbeexpGectedtobedisplayedunrotatedandunscaled.These.commandsareprovidedprimarilyfortestingand}trouble-shoGoting;e.g.withhdrivericon gura-tionsuntestedbytheauthorsofXY s-pic,whoshouldbGeUUnoti edofpersistentdiculties.gweK31.5KPatternsandtilesuTeKTheincluded lexyps-t.tex'ExXgroupings.eK Iff2 򍍍]\NoPStilesX'ExXgroup-ings. qff2 򍍍6b\NoTPICframes`8removeUUtpicsuppGort6b\UseTPICframes`8reinstateUUtpic.kff2ǟ/AppendicesꨍAnAnswersfftoallexercisesAnsw9erktoexercise1(p.7): InthedefaultsetuptheyNarealldenotethereferencepGointoftheNXYΤ-pictureWbutthecartesiancoGordinatehposi(0,0)de-notes~mthepGointorigo thatmaybGechangedtosome-thingUUelseusingthe: ꧲opGerator.LWeJ70Gy*tj??gwAnsw9erPtoexercise2(p.7): Use;thehpGosiition <X,ߵY8>+"ob"!Ҳ.Answ9ertoexercise3(p.7): ItK rstsetscaccord-ingyKto\...".ݨThenyKitchangesctothepGointrightofc?`atthesamedistancefromtherightedgeofcasitswidth,UUwD,i.e.,`/\TheUU...,c\||31 {@#|z31 }{}*+!DR{A},(7,10)="B"?*\cir<1pt>{}*+!DR{B},(13,8)="C"?*\cir<1pt>{}*+!DL{C},(15,4)="D"?*\cir<1pt>{}*+!DL{D},%%?gotointersectionandname+circleit:{"A";"B":"C";"D",x}?="I"*\cir<3pt>{},%%?makedottedlines:"I";"A"**{}?+/1pc/;-/1pc/**@{..},"I";"D"**{}?+/1pc/;-/1pc/**@{..}%\endxy荑AUU?! O...hplaceiUUcouldalsohaveUUbGeenused.Answ9ertoexercise5(p.9): T*ocopythepvqaluetoUUc,i.e.,equivqalentto\p?".Answ9ergtoexercise6(p.10): Whenvusingthekernelconnectionsthatareallstraightthereisnodi erence,e.g.,**{}?<)Iand/**{}+E(Ldenote/exactlytheaEsamepGosition.However,dAforaEotherconnectionsitisnotnecessarilythecasethatthepGointwheretheconnectionjtentersthecurrentob8ject,odenotedby?< n,and"thepGointwherethestraightlinefrompenterstheUUob8ject,denotedby+E O,coincide.Answ9ertoexercise7(p.10): The84coGdetypesetstheUUpicture٭ꪍMBoxF +>3232+p32fdTRg3232y+Efd&Efd32+>3232+pfdTRg3232F +>3232,3232=323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232=3232y+&3232323232323232323232323232323232323232323232323232&&323232323232323232323232323232323232323232323232323232+>3232,3232=323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232=3232iO~#鏍Answ9er=toexercise8(p.11): This< doGesthejob,savingeachpGointtomakethepreviouspGointavqail-ableUUforthenextpiece:gweK\xy H@={(0,-10),(10,3),(20,-5)},Hs0="prev"?@@{;"prev";**@{-}="prev"}eK\endxy˭eKNotice dhowweclosethelineby rstsavings0^,6gtheeKlastpGointvisited, suchthatthe rstpGointwillbGeeKconnectedUUtoit.! eKAnsw9erTtoexercise9(p.11): TheUUauthorusedN8eK\xy?={.{+DL(2)}.{+UR(2)}}"dbl",H*+<3pc,2pc>{+}*\frm{.},?"dbl"*\frm{--}eK\endxyeKtoUUtypGesetthe gureintheexercise.! eKAnsw9er^toexercise10(p.13): The rsttypGe-eKsets\a"centeredaround0 andthenmovesctotheeKlowerrightcorner,2thesecondtypGesets\a"abovetheeK0npGoint&anddoesnotchangec.P Witha\+"at0 ItheyeKloGokUUlikethis:qǟ+'a:andq+a .eKAnsw9ertoexercise11(p.13): TheyfhavetheeKoutlinesx`9P6[Ԟ3232632fdn􍍞g3232,6B;fdFJljfd326[Ԟ32326fdn􍍞g3232:|+PJandiPk3232k֞32fdํg3232$kt fdp\fd32k3232k֡fdํg3232jg=+x`eKbGecause~the rstisenlargedbythepositiveo settoeKtheuppGerrightcornerandthesecondbythenegativeeKo setUUtothelowerUUleftcorner.eKAnsw9erFFtoexercise12(p.14): The rsthasnoeKe ect`sincethedirectionissettobGethatofavectoreKinthecurrentdirection,however,thesecondreverseseKtheUUcurrentdirection.eKAnsw9eretoexercise13(p.15): NoneVinbGotheKcases.eKAnsw9erTtoexercise14(p.18): OneUUwayisN8eK$$\xyH*{+};?p+(6,3)*{+}**{}?(1)H*@{-}?*!/-5pt/^\dir{-}H*^\dir{-}?*!/^-5pt/\dir{-}eK\endxy$$˭eKThus6we rstcreatethetwo+saspandcandeKconnectthemwiththedummyconnection**{} *toeKsetupHRthedirectionparameters.JThenwemove`oneKtop+ofc'with?(1)WandpGositionthefoursidesoftheeKsquareusing^ U_and_forloGcaldirectionchangesandeK/Hhdimeni/زforskewingtheresultingob8jectbymovingeKitsUUreferencepGointintheoppositedirection.LWeJ71H*tj??gwAnsw9er)toexercise15(p.18): One|wayistoadd extra"ehalfcirclesskewed"esuchthattheycreatetheil-lusionUUofashade:N8$$\xy*\cir<5pt>{}*!<-.2pt,.2pt>\cir<5pt>{dr^ul}*!<-.4pt,.4pt>\cir<5pt>{dr^ul}*!<-.6pt,.6pt>\cir<5pt>{dr^ul}\endxy$$ڍAnsw9er*\dir{>}?(.65)*{\oplus}?*!LD!/^-5pt/{x}?(.65)/12pt/*{\oplus}?*!LD!/^-5pt/{x'}?(.28)*=0{\otimes}-/40pt/*+{Q}="q"+/100pt/*+{P};"q"?**\dir{-}\endxyڍAnsw9erctoexercise18(p.21): HereisthecoGdethatUUwasusedtotypGesetthepicture:\def\ssz#1{\hbox{$_{^{#1}}$}}\xy?(0,0)*+{A};(30,-10)*+{B}="B",**\dir{-},"B"**\crv{(5,20)&(20,25)&(35,20)}?<(0)*\dir{<}="a"??>(1)*\dir{>}="h"?(.1)*\dir{<}="b"??(.9)*\dir{>}="i"?(.2)*\dir{<}="c"??(.8)*\dir{>}="j"?(.3)*\dir{<}="d"??(.7)*\dir{>}="k"?(.4)*\dir{<}="e"??(.6)*\dir{>}="l"?(.5)*\dir{|}="f","a"*!RC\txt{\ssz{(\lt)}}; "h"*!LC\txt{\ssz{\;(\gt)}},**\dir{.},"b"*!RD{\ssz{.1}}; "i"*!L{\ssz{\;.9}},**\dir{-},"c"*!RD{\ssz{.2}}; "j"*!L{\ssz{\;.8}},**\dir{-},"d"*!RD{\ssz{.3}}; "k"*!L{\ssz{\;.7}},**\dir{-},"e"*!RD{\ssz{.4}}; "l"*!LD{\ssz{.6}},**\dir{-},"f"*!D!/^-3pt/{\ssz{.5}}\endxygweKAnsw9erTtoexercise19(p.26): HereUUishow:N8eK\xy H(0,0) *++={A}?*\frm{o};H(10,7)?*++={B}*\frm{o}**\frm{.}eK\endxy!eKAnsw9ertoexercise20(p.26): The;*\cir?{}.uop-eKerationchangesctobGeroundwhereas*\frm?{o}eKdoGesUUnotchangecatall.cMeKAnsw9erTtoexercise21(p.26): HereUUishow:eK\xyH(0,0) *+++{A}?;H(10,7)?*+++{B}**\frm{.}H**\frm{^\}}?;**\frm{_\}}eK\endxyeKThetrickinthelastlineistoensurethattheref-eKerence pGointofthemergedob8jecttobebracedistheeKrightUUoneineachcase.cMeKAnsw9ertoexercise22(p.30): ThisishowtheeKauthorUUspGeci edthediagram:eK\UseCrayolaColorseK\xy\drop[*1.25]\xybox{\POSeK(0,0)*{A};(100,40)*{B}**{}H?<<*[@_][red][o]=<5pt>{\heartsuit};H?>>>*[@_][Plum][o]=<3pt>{\clubsuit}H**[|*][|.5pt][thicker]\dir{-},eK?(.1)*[left]!RD\txt{label?1}*[red]\frm{.}eK?(.2)*[!gsave?newpathExyXpos?xyYposmoveto50duprlinetoE20?setlinewidth001setrgbcolorstrokeEgrestore][psxy]{.},eK?(.2)*[@]\txt{label?2}*[red]\frm{.},eK?(.2)*[BurntOrange]{*},eK?(.3)*[halfsize]\txt{label?3}*[red]\frm{.}eK?(.375)*[flip]\txt{label?4}*[red]\frm{.}eK?(.5)*[dblsize]\txt{label?5}*[red]\frm{.}eK?(.5)*[WildStrawberry]{*},eK?(.7)*[hflip]\txt{label?6}*[red]\frm{.}eK?(.8)*[vflip]\txt{label?7}*[red]\frm{.}eK?(.9)*[right]!LD\txt{label?8}*[red]\frm{.}eK?(.5)*[@][*.66667]!/^30pt/H\txt{special?effect:alignedtext}H*[red]\frm{.}eK}\endxy!eKAnsw9ertoexercise23(p.39): HereR~iswhattheeKauthorUUdid:eK\xy?*+{A}*\cir<10pt>{}="me"H\PATH?`ul^ur,"me""me"|>*:(1,-.25)\dir{>}eK\endxyLWeJ72I'*tj??gwThe trickisgettingthearrowheadright:the: moGdi erUUtotheexplicit\dirhob8jectidoesthat.bAnsw9erTtoexercise24(p.40): TheUUauthordidN8\xy(0,0)\ar?@{-->}(30,7)^A="a"\POS(10,12)*+\txt{label}?\ar"a"\endxyAnsw9erZtoexercise25(p.40): HereistheentireXY -pictureUUoftheexercise:\xy?;<1pc,0pc>:\POS(0,0)*+{A}\ar+(-2,3)*+{A'}*\cir{}\ar?@2+(0,3)*+{A''}*\cir{}\ar?@3+(2,3)*+{A'''}*\cir{}\POS(6,0)*+{B}\ar?@1{||.>>}+(-2,3)*+{B'}*\cir{}\ar?@2{||.>>}+(0,3)*+{B''}*\cir{}\ar?@3{||.>>}+(2,3)*+{B'''}*\cir{}\endxyt#TheO rstbatchusethedefault{->}⒲spGeci cation.bAnsw9erTtoexercise26(p.40): TheUUauthorused\newdir{?>}{{}*!/-5pt/\dir{>}}Answ9erTtoexercise27(p.42): TheUUauthorused\xy\ar?@{>>*\composite{\dir{x}*\dir{+}}<<}(20,7)\endxyAnsw9erTtoexercise28(p.42): TheUUauthorused\xy?*{\circ}="b"\ar@(ur,ul)c\ar@{.>}@(dr,ul)?(20,0)*{\bullet}\endxyt#NotethatitisessentialthatthecurvingspGeci cationcomesUUafterthearrowstyle.bAnsw9erctoexercise29(p.44): HereisthecoGdeusedUUtotypGesetthep}'astingdiagramUUin gure15.\xymatrixrowsep{1.5pc}\xymatrixcolsep{3pc}\diagram&&\relax\rtwocell<0>^{f_3^{}\;\;}{\omit}&\relax\ddtwocell<0>{\omit} \drtwocell<0>^{\;\;f_4^{}}{<3>} \ddrrtwocell<\omit>{<8>}\\&&&&\relax\drtwocell<0>^{\;\;f_5^{}}{\omit}\\A?\uurrlowertwocell<-6>{\omit}\relax\uurrcompositemap<2>_{f_1^{}}^{f_2^{}}{<.5>}gwH\drtwocell<0>_{g_1^{}\;}{\omit} H&&&\relax\urtwocell<0>{\omit}H&&\relax\rtwocell<0>^{f_6^{}\;}{\omit}H&\relax\rlowertwocell<-3>_{g_4^{}}{<-1>}H\rcompositemap<6>_{f_7^{}}^{f_8^{}}{\omit}H&?B\\H&\relax\urrtwocell<0>{\omit}H\xcompositemap[-1,4]{}%E<-4.5>_{g_2^{}}^{g_3^{}}{\omit}\\eK\enddiagramj؍eKF*orthestraightarrows, vitwouldhavebGeensimplereKtoVpuse\..to Ѳprovidedxyarrow+l˲hasbGeenloaded.uIn-eKsteadD\..twocell<0>...{\omit?}:@wasDusedtoillus-eKtratetheversatilityofnudgingand\omit$~;thuseKxy2cell Y?can4 completelyhandleawiderangeofdi-eKagrams,withoutrequiringxyarrow)`.T&NotealsotheeKuseof\relax*atthestartofeachnewcell,$toavoideKprematureexpansionofacomplicatedmacro,whicheKcanUUupsetthecompilingmechanism.^eKAnsw9erctoexercise30(p.47): HereisthecoGdeeKusedUUbytheauthortosetthe rstdiagram.N8eK{\uppercurveobject{{?}}H\lowercurveobject{{\circ}}eK\xymatrixcolsep{5pc}eK\xymatrixrowsep{2pc}eK\diagramH\relax\txt{?FUn}\rtwocell<8>{!\&}H&?\relax\txt{gaMES}H\enddiagram}\eKHereUUisthecoGdeusedfortheseconddiagram.eK\xymatrixcolsep{2.5pc}eK\xymatrixrowsep{4pc}eK\diagramH\relax\txt<1.5cm>{\bf?GroundState}H\rrtwocell<12>~^{+{}~**!/-2.5pt/\dir{>}}H~_{++{}~**!/5pt/\dir{<<}}H^{<1.5>\txt{\small?continuouspower}}H_{<1.5>\txt{\small?pulsedemission}}{!}eK&?\relax\;\;N\!i\,C\!d\;\;\CircledeK&?\relax\txt<1.50cm>{\bfExcitedState}eK\enddiagram#斍eKAnsw9erTtoexercise31(p.50): TheUUauthordideK\xymatrix?@!=1pc{H**[l]?A\timesB<\ar[r]^{/A}?\ar[d]_{/B}H&?B\ar[d]^{\timesA}eK\\HA\ar[r]_{B\times}H&?**[r]B\timesAeK}LWeJ73J*tj??O]w\Answ9ertoexercise32(p.50): MoGdi ers are usedtomakeallentriesroundwithaframe{thegeneralCformisusedtoensurethatthesequenceiswell-de ned.S>FinallythematrixisrotatedtomakeitpGossibleUUtoenteritasasimplesquare:N8\entrymodifiers={=<1pc>[o][F-]}\xymatrix?@ur{A?\save[];[r]**\dir{-}, [];[dr]**\dir{-}, [];[d]?**\dir{-}\restoreL&?B\\C?&D}$Answ9erTtoexercise33(p.50): HereUUishow:\xymatrix?@W=3pc@H=1pc@R=0pc@*[F-]{%:?\save+<-4pc,1pc>*\hbox{\itroot} \ar[]L\restore\\{\bullet}L\save*{} \ar`r[dd]+/r4pc/`[dd][dd]L\restore\\{\bullet}L\save*{} \ar`r[d]+/r3pc/`[d]+/d2pc/ `[uu]+/l3pc/`[uu][uu]L\restore\\1?}$Answ9ertoexercise34(p.51): The rstAwasnamedUUtoallowreferencefromthelast:\xygraph{[]A="A1"?:@/^/[r]A :@/^/?[r]A :@/^/?"A1"}$Answ9erTtoexercise35(p.53): TheUUauthordid\SelectTips{cm}{}\objectmargin={1pt}\xygraph{?!{0;(.77,-.77):0}!~:{@{-}|@{>}}w?(:[r(.6)]{x_1}L,:[d]z:[r]y:[u(.6)]{x_2}:"x_1":"z" :@(?{"w";"z"},{"y";"z"})"z":"x_2")})Itzalsoshowsthatonec}'an?use{} sinsidedelimitedargumentspr}'ovidedBoneaddsaspacetoavoidthe{} %sbGeingUUshavedo !w\eKAnsw9erctoexercise36(p.53): HereisthecoGde eKactuallyusedtotypGesetthe\xypolygon{}eK!P6"B"{~<-\cir<5pt>{}}eK"B1"1?"B2"2"B3"3"B4"4"B5"5"B6"6"B0"eK[rrr]0?!P9"C"{~*{\xypolynode}}}\endxy$ˑeKBVfersionff2CompatibilityeKVers.3.4bCyKristo erH.Rosehkrisrose@brics.dkieKLoadTas:p\xyoption{v2}uTeKThisappGendixdescribesthespecialbackwardscom-eKpatibilitywithXY -picversion2:I diagramswrittenac-eKcordingtothe\TypGesettingdiagramswithXY-pic:eKUser'sXManual"[13 ]shouldtypGesetcorrectlywiththiseKloaded.ݲTheyNcompatibilityisavqailableeitherasaneGXYK-option<~orthroughthespGecial lesxypic.sty5andeKxypic.texdescribGedUUbelow.eKThere@areafewexceptionstothecompatibility:eKthe[featuresdescribGedinxB.1belowarenotprovidedeKbGecauseztheyarenotasusefulastheauthororiginallyeKthoughtLandthusvirtuallyneverused.-AndoneextraeKcommand[isprovidedtospGeeduptypGesettingofdoc-eKumentswithXY -picversion2diagramsbyallowingeKthenewcompilationfunctionalitywitholddiagrams.eKTheremainingsectionslistalltheobsoletecom-eKmands?andsuggestways?toachieve?thesamethingseKusingXY /-pic3.6,i.e.,withouttheuseofthisoption.eKTheyaregroupGedastowhatpartofXY -picreplaceseKthem;UUthecompilationcommandisdescribGedlast.eKNote:\version2"ismeanttocoverallpubliceKreleases%of!XY %-picin1991and1992,i.e.,version%1.40eKandr1versions2.1through2.6.\ThepublishedmanualeKcited#abGove(forversion2.6)isthereferenceincaseeKofCvqariationsbGetweenCtheseversions,FandonlythingseKdoGcumentedưinthatmanualwillbGesupportedbythiseKoption!^19iˍeKB.1/Unsupp`ortedincompatibilitieseKHere5isalistofknownincompatibilitieswithversioneK2UUevenwhenthev2*optionisloaded.NeLeMAutomatic`shortening'ofarrowtailsusing|<<eMbreaks‚wasabugandhasbGeen` xed'soitdoeseMnotQworkanymore.TPuta|<\hole)c߲breakbGeforeeMit.ffffy̟ J=w-:19LInXadditionafewoftheexp}-f(or\tipSZ)withvqariantsUUandrotation.Thek4evenoldernotationwhereanargumentinbracesto\rto5޲andtheotherswasautomati-callytakentobGea`tail'isnotsupported.UsetheUUsuppGorted|R< O...notation.rNIf‚youdonotusethesefeaturesthenyourversion2(andwdearlier)diagramsshouldtypGesetthesamewiththisEoptionloadedexceptthatsometimesthespac-ingv%withversion3isslightlydi erentfromthatofversionUU2.6whichhadsomespacingbugs.B.2$Obsoletekernelfeatures[ Thezfollowingthingsareaddedtothekernelbythisoptiong6anddescribGedhere:idioms,obsoletepositions,obsoleteconnections,andobsoleteob8jects.MF*oreachweshowthesuggestedwayofdoingthesamethingwithoutUUthisoption:Remo9vedTAU>'M S-T<8E3sXidiomsSome%idiomsfromAU>'M S-TU>'ExXarenolongerusedby3XY-pic:.Tthe 3de nitioncommands\defineand(u\redefine,=andthesizecommands\dsize,\tsize, \ssize,and \sssize. PleaseusethenBcommandsrecommendedforyourformat|forplaintTU>'ExXtheseare\def!forthe rsttwotand\displaystyle',7\textstyle;Ҳ,7\scriptstyleF7̲,7and\scriptscriptstyleDfortherest.LThev2K\optionen-suresUUthattheyareavqailableanyway*. {oV*ersionalso2usedtheAU>'M S-TU>'ExX\textandat(non-ob8ject)bGoxconstruction\Textwhichareemulated|\texṱisonlyde nedifnotalreadyde- ned,however,usingthenativeone(ofAU>'M S-TU>'ExXorAU>'M S-L5ffA͉TU>'ExXorwhatever)ifpGossible.ePleaseusethe\txtFòob8jectconstructiondescribGedinx6.3directlysinceUUitismoregeneralandmuchUUmoreecient!gweKObsoleteTstate\eKUpto}version2.6userscouldaccessthestatevqariables eK\cL,UU\cR,\cH,and\cD,whicharede ned. eKF*romv2.7to2.12userscouldusethenameseKofxthestate\dimen(qزregisters\Xmin,\Xmax,\Ymin,eKande9\Ymax;+\Xp,2\Yp\Dp,\Up,\Lp,and\Rp;+\Xc,eK\YcI\Dc,\Uc,\Lc,and\Rc;E\Xorigin,\Yorigin,eK\Xxbase,\Yxbase,\Xybase,andw\Yybase.ٛNowtheeKsamepze ectcanbGeachievedpzusinghcornerisbutv2eKde nesUUthealiases.)IeKObsoleteTpQositionmanipulationeKInuversion2manythingsweredoneusingindividualeKhdecoriӲcontrolsequencesthatarenowdoneusingeKhpGosiUUoperators.eK|ff2SoV*ersionUU2pGositioningjReplacement ff2\gohpGosij\POS;p,hpGosi \aftergo{?hdecori}hpGosiF\afterPOS{zhdecori};p,hpGosi\mergej\POS.p\relax\swapj\POS;\relax\Drop{?htexti}j\drop+{htexti}ff2)IObsoleteTconnections\TheseE^connectionsarenowimplementedusingdirec-tionals.@|ff2So2V*ersionUU2connectionjReplacementff22\nonej\connect?h\dir{} 2\solidj\connect?h\dir{-}2\Solidj\connect?h\dir2{-}2\Ssolidj\connect?h\dir3{-}2\dashedj\connect?h\dir{--}2\Dashedj\connect?h\dir2{--}2\Ddashedj\connect?h\dir3{--}2\dottedj\connect?h\dir{.}2\Dottedj\connect?h\dir2{.}2\Ddottedj\connect?h\dir3{.}2\dottedwith{?htexti}j\connect?h{yhtexti}ff2ݍNotehowthe`hidden'spGeci erh Lshouldbeusedbe-causeiversion2connectionsdidnota ectthesizeofdiagrams.LWeJ75L⮠*tj??gwObsoleteTtips TheseUUob8jectsallhaveUU\dirUI-namesUUnow: ff2 !fV*ersionUU2tipX3ReplacementPff2f\notipX3\dir{} f\stopX3\dir{rO$|w!}f\astopX3\dir^{w!||}f\bstopX3\dir_{w!||}f\tipX3\dir{>}f\atipX3\dir^{>}f\btipX3\dir_{>}f\TipX3\dir2{>}f\aTip@3\object=<5pt>:(32,-1)\dir^{>}f\bTip@3\object=<5pt>:(32,+1)\dir_{>}f\TtipX3\dir3{>}f\ahookX3\dir^{(}f\bhookX3\dir_{(}f\aturnX3\dir^{'}f\bturnX3\dir_{'}ff2 z PTheeoldercommands\pitY,b\apitS,band\bpitV,arenotUUprovided.ObsoleteTobjectconstructions The?qfollowingob8jectconstructionmacrosaremadeobsoleteUUbytheenrichedhob8jectiformat: ff2 ! ]oV*ersionUU2ob8jecti+Replacementff2 ]o\rotate(?hfactori)htipi E+\object:(thfactori,?hfactori){ htipi} ]o\holei+\object+{} ]o\squashhtipii+\object=0{ htipi} ]o\growhtipii+\object+{htipi} ]o\grow<(]hdimeni>?htipii+\object+<hdimeni>{ htipi} ]o\squarify{?htexti}i+\object+={ htexti} ]o\squarify<=Qhdimeni>{ htexti}E+\object+={ htexti}ff2Awhere~rotationisdoneinaslightlydi erentmannerinUUversion3.6(itwasneveraccurateinversion2).B.3!Obsoleteextensions&features V*ersion2hadcommutativediagramfunctionalitycorrespGondingtotheframes'J*extensionandpartsofthePmatrix&ԎandParrow!features.pTheseParethereforeloadedandsomeextrade nitionsaddedtoemulatecommandsUUthathaveUUdisappGeared.F ramesTheyversion2framecommandsareemulatedus-ing(theframeextension(aswellasthe\dotframed8# ,gweK\dashframed%*,@*\rounddashframedZzٲcommands:comm- eKunicatedUUtosomeusersbyelectronicmail):eK ff2 덍 eV*ersionUU2ob8jecte5Replacementff2 e\framede5\drop\frm{-} e\framed<6Mhdimeni>e5\drop\frm<vhdimeni>{-} e\Framede5\drop\frm{=} e\Framed<6Mhdimeni>e5\drop\frm<vhdimeni>{=} e\dotframede5\drop\frm{.} e\dashframede5\drop\frm{--} e\rounddashframede5\drop\frm{o-} e\circlede5\drop\frm{o} e\Circlede5\drop\frm{oo}ff2MatricesuTThe1\diagramhrowsi\enddiagramcommandispro-vided0~asanaliasfor\xymatrix{<޸hrowsi} centeredin)mathmoGdeand\LaTeXdiagramschangesittouse\begin#ڣ..._\end`syntax.v2\setsZaspGecialinternal`oldmatrix' agsuchthattrailing\\allthederivedcommands\dto,E\urto%6,E...;5BtheH\arrow(~commandsHofthe -releasesUUofv3isalsoprovided.Insteadofcommandslike\rrto"ACand\uldoubleyoushouldusethearrowfeaturereplacements\ar[rr](@andUU\ar@{=}[ul]=4.Theprede nedturningsolidarrows\lltou#,...,\tord$arede nedaswell;,'ExX2.09`style{option'[xypic])f. [9Thisismadesynonymouswith|loadingthisoptionbythe lesxypic.texandxypic.styUUdistributedwiththev2*option.xypic.tex/?:7qThiss le(version3.3)justloadsthev2feature.LWeJ76M*tj??gwxypic.sty:IJLoadsUUxy.sty&*andUUthev2*feature.9B.5$Compilingv2-diagramsInh3ordertomakeitpGossibletousethenewcompila- tionfeaturesevenondoGcumentswrittenwithXY -picv2,UUthefollowingcommandwasaddedinv2.12: =ff2 썍I6\diagramcompileto{iUhnameiUU} ꧲...\enddiagram5ff2\׍whichpisliketheordinarydiagramcommandexceptthebresultiscompiled(seenote5e)..Notethatcom-pilationUUisnotquitesafeinallcases! 5There\isalsothefollowingcommandthatswitchesonNautomaticGc}'ompilationofalldiagramscreatedwithUUthev2\diagram0...\enddiagramB3command: Zff2&(\CompileAllDiagramsD{3hpre xiUU}&(\NoCompileAllDiagrams&(\ReCompileAllDiagrams5ff2willapply\xycompileto{G(Yhpre xin}{ ...} 'toeachdi-agram\withnasequencenumbGer\startingfrom1.Use\CompileMatricesWU%andUU\CompilePrefixP*instead! 5If)forsomereasonadiagramdoGesnotworkwhencompiledcthenreplacethe\diagram1ʮcommandwith\diagramnocompile^c(or$!incaseyouareusingtheL5ffA͉TU>'ExXUUform,\begin{diagramnocompile}U ).(׍CdCommonffErrorsJIn_thisappGendixwedescribesomecommoncaseswhere'smallmistakesin'XY -picturesresultinTU>'ExXer-rorUUmessagesthatmayseemcryptic.9!pBo9xTexpQected.!WAhbGoxiw9assuppQosedtobehere. This4mes-sage|iscommonwhenan|XY -pichob8jectiismistypGedsuch that XY-picexpGectsbutdoesnot ndaTU>'ExXhbGoxiUUconstruction.!}LaT eXEError:Badzmathen9vironmentzdelim-iter.!Fileendedwhilescanninguseof\xycompiled.!Argumen9t(of?\codeof@hasanextraFɌ cmbsy10Fg. Theseerrorsh(canhappGenwhilereadinganincompletecom-piledpicture(suchabGeastiscreatedwhenXY-piccrashesduringcompilationduetoasyntaxerrororotherUUsuchproblem).!ڒMissingFginserted. ThishappGenswhen\endxywasUUleftout. T oTDo:qDzAlsoUUincludethemoreobscureones...gweKReferences~eL[1]AdobGeuSystemsIncorporated.uPostScriptL}'an- guageR}'eferenceManual,UUsecondedition,1990.deL[2]Americank_MathematicalSoGciety*. cAU>'M S-L雍QATKß'E-XV;ersion1.1User'sGuide,UU1.1edition,1991.eL[3]KarlMBerry*.TExp}'andedplainTKß'E-X,version2.6edi-tion,2May-1994.AvqailableforanonymousftpfromUUCT*ANinmacros/eplain/doc.eL[4]Michel^GoGossens,~F*rankMittelbach,~andAlexan-derSamarin.The1L雍QATKß'E-XComp}'anion.Addison-W*esley,UU1994.eL[5]BrianjW.Kernighan.PIC|alanguagefortypGe-settinggraphics.Softwar}'efPracticeandExperi-enc}'e,UU12(1):1{21,1982.eL[6]DonaldKE.Knuth. TheTKß'E-Xb}'ook.Addison-W*esley,UU1984.eL[7]DonaldEE.Knuth.Computer]Mo}'dernT;ypefaces,volumeAsofComputers&T;yp}'esetting.6wAddison-W*esley,UU1986.eL[8]LeslieLampGort.8L雍QATKß'E-X|AK0Do}'cumentK_Prepara-tionSystem.nAddison-W*esley,UU1986.eL[9]LeslieLampGort.8L雍QATKß'E-X|AK0Do}'cumentK_Prepara-tion#System.JAddison-W*esley,2ndxedition,1994.eK[10]P*.lNauretal.$RepGortonthealgorithmiclan-guageX)ALGOLW60.?Communic}'ationsoftheACM,3:299{314,UU1960.eK[11]T*omasRokicki.YDVIPS:JATKß'E-XDriver.Dis-tributeda withthedvipsprogramfoundonCT*ANarchives.eK[12]Kristo er 3H.Rose.HowtotypGesetprettydia-gramarrowswithTU>'ExX|designdecisionsusedinXYs-pic. InJiuUrqZlatuxskqa, ;editor,Eur}'oTKß'E-X'92|Pr}'oceedingshtofthe7thEur}'opeanhtTKß'E-XCon-fer}'ence, pages183{190,Prague,Czechoslo-vqakia,SeptembGer"1992.CzechoslovqakTU>'ExXUsersGroup.eK[13]Kristo erH.Rose.TypGesettingdiagramswithXYs-pic:KUser'sB[manual. ,(InJiuUrqZlatuxskqa,edi-tor,QEur}'oTKß'E-X '92|Proceedingsofthe7thEu-r}'opeanpTKß'E-XConfer}'ence,6pages/273{292,Prague,Czechoslovqakia,[SeptembGer1992.CzechoslovakTU>'ExXUUUsersGroup.eK[14]Kristo er[H.Rose.{XY 6-picUser'sGuide.DIKU,UniversityofCopGenhagen,Universitetsparken1,DK{2100AKbGenhavn,E3.0edition,June1995.LWeJ77N *tj??w[15]UKristo erTH.RoseandRossR.MoGore. #XY_'- Upica{completesourceswithTU>'ExXnicalcommentary*.UnotUUyetavqailable,June1995.[16]UMichaelbD.Spivqak.TheJoyofTKß'E-X|AGourmetUGuidetoT;yp}'esettingwiththeAU>'M S-TKß'E-XMacroUPackage.'AmericanMathematicalSoGciety*,R[sec-UondUUedition,1990.eK[17]TUG)W*orking)GroupTWG-TDS.Adirectory structure1forTU>'ExX lesversion0.98.`URL,May1995.AvqailablezwithURLaftp://jaspGer.ora.com/pub/twg-tds/. Index+/!,UU8 !׍&,UU48',UU38(),UU8(0),UU8(0,0),UU70(1),UU8*,UU8,38,40,41,48,49,75**,UU8,40,49+,UU8,,UU8,39-,UU8,38.,UU8.xyd,UU15/,UU37,38,42//,UU8:,UU8,12::,UU8;,UU8<,UU8,38,40<>,UU8<>(.5),UU38=,UU8,37,38,40>,UU8,38,40?,UU8,40@,UU8,38,41,49@!,UU41,49@!0,UU49@!=,UU49@!C,UU49@!R,UU49@(,UU10,41,42@),UU10@*,UU41,50@+,UU10@-,UU10@/,UU41,42@1,UU50@<,UU41,42@=,UU10@?,UU41,42@@,UU10@C,UU49@H,UU49@L,UU49/r:@M,UU49 6΍r:@R,UU49r:@W,UU49r:@`,UU41r:@i,UU10r:[.],UU13r:[=,UU12,14,30,33r:[],UU13r:[c],UU14r:[d],UU14r:[dvips],UU5r:[l],UU14r:[o],UU13r:[r],UU14r:[textures],UU5r:[u],UU14r:\\,UU48r:^,UU38{41r:_,UU38{41r:`,UU38,39r:|,UU38,41r:|<<,UU74r:~,UU38r:0,UU6,8,41r:1,UU41r:2,UU41r:3,UU41r:10,UU27r:11,UU27r:12,UU27r:a,UU8r:activeUUcharacters,4r:haddUUopi,12r:\aftergo?,UU75r:\afterPATH?,UU37r:\afterPOS?,UU15,16,39r:\ahook?,UU76r:alloGcation,UU5r:AU>'M S-L5ffA͉TU>'ExX,UU5,15r:AU>'M S-TU>'ExX,UU5r:\apit?,UU75r:\ar?,UU14,38r:array,UU51r:arrowUUhead,40/=X[arrowUUstem,40 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