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:Thecurrentimplementationisprogrammedentirely:withiniN\standardTU>'ExXando> logo10METAF9ONT",i.e.,Kusing:TU>'ExX0Pmacros(no\special.08s)andwithfontsdesigned:usingJMETAF9ONT.OptionallyspGecial`drivers'makeit:pGossibleDtoproduceDVI leswith`specials'forextra:graphicsUUcapabilities,e.g.,using&- cmcsc10PostScript.^ٓRcmr71:ff^ J= "5-:Aacmr61L'- cmcsc10PostScriptXisaregisteredTJrademarkofAdob24 9.1 F*rames_...................24 9.2 BracketsU..................26 9.3 FilledUUregionsF...............26 9.4 F*ramingUUasob8jectmoGdi erM.......26 9.5 UsingUUcurvesforframes.........2610 MoreTTipsextensionj12611 LineTst9ylesextensionif2712 RotateTandScaleextensionIgF2813 ColourTextension} 3014 P9atternTandTileextensionK30gw:15;ImpQortTgraphicsextensionN32aU:16;P9ostScriptTbackendqZ34 :f;16.1 ?ChoGosingUUtheDVI-driverxE.........34;16.2 ?WhyUUusePostScript..........34:17;TPICTbac9kendk35:18;em-T eXTbac9kend~@o36"V:I`II Features.36:19;AllTfeatures(36:20;Dumm9yToptionr336:21;Arro9wTandPathfeatureYW36;21.1 ?Paths ...................37;21.2 ?Arrowsҍ...................39:22;Tw9o-cellTfeature41;22.1 ?TypGesettingUU2-cellsinDiagrams8$.....42;22.2 ?StandardUUOptionsͷ.............42;22.3 ?Nudging..................43;22.4 ?ExtraUUOptionsc...............43;22.5 ?2-cellsUUingeneralUQXY U-picturesr.......46:23;MatrixTfeatureK47;23.1 ;XYj?-matrices................47;23.2 ?NewUUcoGordinateformats'.........47;23.3 ?SpacingUUandrotation...........48;23.4 ?Entries|...................49:24;GraphTfeature k50:25;P9olygonTfeature52:26;LatticeTandw9ebfeatureZ}55:27;Circle,TEllipseandArcfeature856;27.1 ?F*ullUUCirclesH................56;27.2 ?Ellipses..................57;27.3 ?CircularUUandEllipticalArcs84.......57:28;KnotsTandLinksfeatureW60"V:IV DriversD564:29;SuppQortTforSpeci cDriv9ersD̖64;29.1 ?dvidrvUUdriverʍ...............64;29.2 ?DVIPSUUdriverT鍍...............65;29.3 ?DVITOPSUUdriver.............65;29.4 ?OzT*eXUUdriver...............65;29.5 ?OzT*eXUUv1.7driver............65;29.6 ?T*exturesUUdriver⍍..............66;29.7 ?T*exturesUUv1.6driver...........66LWj:2!*tj??gw 29.8 XDVIUUdriverjG................66 D 29.9 CMacT*eXUUdriver.............6730 ExtraTfeaturesusingPostScriptdriv9ers D67 30.1 ColourЍ...................68 30.2 F*rames_...................68 30.3 Line-styles1l.................68 30.4 RotationsUUandscalingM..........68 30.5 PatternsUUandtiles.............6931 ExtraTfeaturesusingtpicdriv9ers--69 31.1 frames.Ѝ...................69"App`endicesbq69A Answ9ersTtoallexercisesZ69B V ersionT2Compatibilit9yY>73 B.1 UnsuppGortedUUincompatibilitiesC......73 B.2 ObsoleteUUkernelfeatures񍍑.........73 B.3 ObsoleteUUextensions&features1.....74 B.4 ObsoleteUUloading֍.............75 B.5 CompilingUUv2-diagrams..........75C CommonTErrors75ReferencesZ75Indexޕ76!$ListffofFigureso 1 hpGosiitions. ҍ................8 2 ExampleUUhplaceis1H.............10 3 hob8jectis..................12 4 hdecoriations................15 5 KernelUUlibraryhdiriectionals.......17 6 hciricles.x..................19 7 SyntaxUUforcurves.q@............22 8 PlainUUhframeis.c..............25 9 BracketUUhframeis.׍.............25 10 Rotations,UUscalingsand ipsO.......30 11 TheUU38standardMacintoshpatterns.8 ..32 12 impGortingUUagraphicforlabelling....33 13 hpathisFύ...................38 14 harrowis...................40 15 PastingUUdiagram.F.............43 16 htwoGcellisލ.................44 17 hgraphisǍ..................51 18 hknot-pieceiUUconstructionset......61 19 knotdNcrossingswithorientationsandla-  bGelUUpositions8}................62 20 knot,gjoins,4withorientations,labGelsand shifts ....................64 21 Extensionimplementationreplacedby useUUofhdriverispGecials...........68gw:Preface:Thisreferencemanualgivesconcisedescriptionsofthe :moGdules!of!XY -pic,Twrittenbytheindividualauthors.:PleasedirectanyTU>'ExXnicalquestionorsuggestionfor:improvement/directlytotheauthorofthecompGonent:inIquestion, preferablybyelectronicmailusingthe:indicatedzqaddress.CompletedoGcumentsandprinted:technicalUUdoGcumentationorsoftwareismostuseful.;The# rstpartdoGcumentstheXY 3#-pickernelwhichis:alwaysloaded.ZTheremainingpartsdescribGethethree:kindsIGofoptions:extensionshinpartIGIextendthekernel:graphiccapabilities,Ufe}'aturesinpartIGIIprovidespecial:input81syntaxforparticulardiagramtypGes,>anddrivers:in|partIVmakeitpGossibletoexploittheprintingca-:pabilities'suppGortedbyDVI driverprograms.N F*oreach:optionEitisindicatedhowitshouldbGeloaded.The:appGendices[containanswerstoalltheexercises,asum-:maryofthecompatibilitywithversion2,andlistsome:reasonsi\whyiXXY \-picmightsometimeshaltwithacryptic:TU>'ExXUUerror.ua:License.XY-picisfreesoftwareinthesensethatitis:avqailableUUunderthefollowinglicenseconditions:zƍ[u323232fd]&g3232%A܉$bfd8$bfd32[u3232fd]&g3232󎍍u XY-pic:qGraphsUUandDiagramswithTU>'ExX ፍZYc<  蒲1991{1996 Kristo erUUH.Rose vcY !1994{1996 RossUUMoGore =TheXY-picpackqageisfreesoftware;?;you 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W*e Mgivedescriptionsofthe@syntaxuofpicturesasBNF^2 prules;rinexplana-tionswewilluseuppGercaseletterslikeXȲandY<ʲforhdimenisionsUUandlowerUUcaselikexandy.forhfactoris.#8PartffI*Nq cmbx12The KernelꨍV ers.''3.3)b9yKristo erH.Rosehkrisrose@brics.dkiuTAftergivinganoverviewoftheXY &-picenvironmentinx1,thisۦpartdoGcumentthebasicconceptsofۢXY [-pictureconstructioninx2,Jincludingthemaintained`graphicstate'.^Thefollowingsectionsgivetheprecisesyntaxrules#ofthemainXY{#-picconstructions:cthepGositionlanguage-@inx3,5Dtheob8jectconstructionsinx4,andthepicture@`decorations'inx5.x6presentsthekernelrepGer-toire&ofob8jectsforuseinpictures;Rx7doGcumentstheinterfacePtoPXY -picoptionslikethestandard`feature'andUU`extension'options. DetailsoftheimplementationarenotdiscussedherebutUUinthecompleteTU>'ExXnicaldoGcumentation[15 ]. 1]TheǨX#՟YY-picffimplementationThisޱsectionbrie ydiscussesthevqariousaspGectsofthepresent8XY m<-pichaÎvechosentoannotatethesyntaxwithbriefexplanationsof[the`action'asso'ExXUU[9]).;TherestofthissectiondescribGesthingsyoumust:considerKifyouneedtouseGXY *K-pictogetherwithother:macropackqages,styleoptions,orformats.Theless:yourenvironmentdeviatesfromplainTU>'ExXtheeasier:itrshouldbGe.EConsulttheTU>'ExXnicaldocumentation[15 ]:forƱtheexactrequirementsforotherde nitionstoco-:existUUwithUQXY U-pic.~*:Priv\racy:XY-pic willwarnabGoutcontrolsequencesit:rede nes|thus2youcanbGesurethattherearenocon-: ictsbGetweenXY-pic-de nedcontrolsequences,0those:ofyourformat,Oandothermacros,providedyouload6XYj:-picUUlastandgetnowarningmessageslikez Xy-pic?Warning:`dx:::q'?redefined.:InYgeneraltheYXY ٴ-pickernelwillcheckallcontrolse- :quencesitrede nesexc}'eptthat(1)generictempGoraries:likeW\nextarenotchecked,(2)prede nedfontiden-:ti ers(seex1.3)areassumedintentionallypreloaded,:andWU(3)someofthemoreexoticcontrolsequencenames:usedinternally(like@{-})areonlycheckedtobGedif-:ferentUUfrom\relax.:CategoryJFcoQdes: Unfortunately5uthesituationis:complicatedabythe exibilityofTU>'ExX'sinputformat.:The&culpritisthe`categorycoGde'conceptofTU>'ExX:(cf.X [6,Xp.37]):w6whenloadedXXY -picrequiresthecharac-:tersE\ \{}%EP(the rstisaspace)tohaveE\theirstandard:meaningandallotherprintablecharacterstohavethe:sameNmc}'ategoryaswhenHXY -picwillbeused|in particu-:larthismeansthat(1)youshouldsurroundtheload-:ingMofMXY ͹-picwith\makeatother...c\makeatletter:whenqloadingitfromwithinaL5ffA͉TU>'ExXpackqage,kandthat:(2)M XY -picMshouldbGeloadedafter lesthatchangecat-:egory}coGdeslikethegerman.stythatmakes" active.:Some1hstylesrequirethatyouresetthecatcoGdesforev-:erydiagram,e.g.,withfrench.styyoushouldusethe:commandUU\english0bGeforeUUevery\xymatrix2:.:However,֜itispGossibleto`repair'theproblemincase:anyofthecharacters#$&'+-.<=>`CSchangecategory:coGde::~ff2 ѰLl\xyresetcatcodeskNff2zwillUUloadthe lexyrecat.tex(version3.3)todoit.TIn9tegrationRwithstandardformats This”ishan-dledbythexyidioms.texD leandtheintegrationasaL5ffA͉TU>'ExXUU[9]packqagebyxy.sty"C.xyidioms.tex: This`included leprovidessomecom-monvidiomswhosede nitiondepGendsontheusedfor-mat#suchthatXY ;#-piccanuseprede neddimensionreg-isters9Netc.andyetstillbGeindependentoftheformatLWj:40*tj??gwunder`whichitisused.Thecurrentversion(3.3)han- dleswplainTU>'ExX(version2and3[6]),AU>'M S-TU>'EX(version2.0and2.1[16 ]),RYL5ffA͉TU>'ExX(version2.09[8]and2"[9]),AU>'M S-L5ffA͉TU>'ExX̳(version1.0,1.1[2],and1.2),andeplain(versionUU2.6[3])^3|s.)xy .st9y: IfyouuseL5ffA͉TU>'ExXthenthis lemakesitpGossi-bleStoloadSXY -picasa`packqage'usingtheL5ffA͉TU>'ExX2"|β[9]\usepackageUUcommand:ff2 ɍ+e\usepackageUU[Rhoptioni,?...] ?{xy}'ExX2" (Tgraphics9&ʲbundle:8thesewillautomaticallyinvokeanybackendextensionrequiredtobGestem-ulatetheL5ffA͉TU>'ExX2" bGehaviour(thismeansthat,Te.g.,[dvips]Dzand[textures]canbGeusedasoptionstothe\documentclassUUcommandwiththenormale ect). The_ lealsoworksasaL5ffA͉TU>'ExX2.09[8]`styleoption'althoughyouwillthenhavetoloadoptionswiththe\xyoption2:mechanismUUdescribGedinx7."ۍ1.2Logo,version,andmessages*LoadingPXY 3T-picTprintsabannercontainingtheversionandUauthorofthekernel;TsmallprogressmessagesareprintedXwheneachma8jordivisionofthekernelhasbGeenloaded.AnyoptionsloadedwillannouncethemselfinaUUsimilarfashion. IfnyourefertojXYOn-picinyourwrittentext(pleasedoD[ a(^ h)D[thenyoucanusethecommand\Xy-picDOtotypGe-setɌthe\XY -pic"logo.C/TheversionofthekernelistypGe-setby\xyversionandthereleasedateby\xydate(asfoundinthebanner).nBytheway*,MtheXY -picname[^4originates fromthefactthatthe rstversionwaslittlemoreHRthansuppGortfor(x;y[ٲ)coordinatesinacon g-urablexcoGordinatesystemwherethemainideawasthatall7opGerations/ couldbespeci edinamannerindepen-dent8oftheorientationofthecoGordinates.[pThisprop-erty[hasbGeenmaintainedexceptthatnowthepackqageallowsUUexplicitabsoluteorientationaswell. Messages'thatstartwith\Xy-pic%Warning"areindicationsthatsomethingneedsyourattention;an\Xy-pic"sError"+willstopTU>'ExXbGecause'XY s+-picdoesnotknowUUhowtoproGceed. Iff^ J= "5-:3LThey`v2'featureinÎtro "5-:4LNodescriptionofaTAEMXprogramiscompletewithoutanexplanationXofitsname.gw:1.3:FontsuT:The!XY w%-pic%kernelimplementationmakesitsdrawings :usingUU vespGeciallydesignedfonts:8S/̟L͉ffNfd͟ fffdF*ontCYy fff\VCharacters ffN&Default۟ ffffN͟ ff͟fd\xydashfontCYy ffodashes ffN&xydash10۟ ff͟ 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 ffffN:TheH rstfourcontainvqariationsofcharactersinalarge:numbGerofdirections,"thelastcontains1/8circleseg-:ments.Ɂ:Note: ThedefaultfontsarenotpartoftheXY-pic:kernelsp}'eci cationc:theyjustsetastandardforwhat:drawingcapabilitiesshouldatleastbGerequiredby:anFXYkJ-picJimplementation. 3Implementationsexploit-:ingecapabilititesofparticularoutputdevicesarein:use.tHencethefontsareonlyloadedbyXY -picifthe:controlxisequencenamesareunde ned|thisisusedto:preload:?thematdi erentsizesorpreventthemfrom:bGeingUUloadedatall.Ɂ:1.4:Allo`cationsuT:One nalthingthatyoumustbGeawareofisthatXY 5-:picalloGcatesasigni cantnumbGerofdimensionregis-:ters&andsomecounters,/token&registers,andbGoxregis-:ters,inordertorepresentthestateanddocomputa-:tions.rThe^currentkernelalloGcates4counters,+ 28di-:mensions,2XCbGoxregisters,4tokenregisters,1readchan-:nel,andP1writechannel(whenrunningunderL5ffA͉TU>'ExX;:some4YotherformatsuseslightlymorebGecausestan-:dardTgenerictempGorariesareused).Optionsmayal-:loGcategfurtherregisters(currentlyloadingeverything:loads6dimen-,3toks-,1bGox-,and9count-registers:inUUadditiontothekernelones). :27Pictureffbasics:TheBbasicconceptsinvolvedBwhenconstructing>XY^B-:picturesR+arepGositionsandob8jects,Randhowtheycom-:bineUUtoformthestateusedbythegraphicengine.;TheUUgeneralstructureofanUQXY U-pictureisasfollows:: & ff2 ).>\xyUUhpGosihdecori\endxỷff2Mbuilds&nabGoxwithan&jXY n-picture(L5ffA͉TU>'ExXusersmaysub-stituteUU\begin{xy};*...\end{xy}2U xwhereXyisthe TU>'ExX)dimensiondistancerightrandYb~thedistanceupfromQthezer}'o|DpositionJ0QoftheQXY -picture(0 hasco-ordinatesU<0mm,0mm>4A:,lUofUcourse). uThezeropGositionoftheXY 6-picturedeterminesthebGoxproducedbythe\xy...\endxycommandtogetherwiththefourparam-etersXmin ,(޵XmaxA̲,Ymin,andYmax_setsuchthatalltheob8jectsinthepictureare`contained'inthefollowingrectangle:;dNg^3232g萞32fdkMg3232LבgʼnL_fdL_fd32g^3232g萡fdkMg3232L O!cmsy7#w '0B΄fdfeXBhxfdfe B"fdfeB̄fdfeBvfdfexBC fdfe@BʄfdfeBtfdfeBgfdfeBȄfdfe`Brfdfe(BfdfeBAƄfdfe b TU>'ExXUUreferencepGointeLͷg;҄fdfeeofdfec,Vfdfeb d阄fdfe`0ǟڄfdfe^X*dfdfe\!^fdfeZޠfdfeXSfdfeVY$fdfeUffdfeSD|ӨfdfeQkߟfdfeOBN,fdfegm2fd$gm_lXI_p%_u|_z ݟ_~_1_q_gmooo@} UUXmint2fdG!_+ܟ_r_V__FП__J__ağ__>_5_|_u_//ҟ UUXmaxB"$fet$tttttttuYminB*fe3tttttttttt3OOuŵYmax2where0"prin-ciple,Fe.g.,theBindicatedTU>'ExXreferencepGointhascoor-dinatesZ < Xmin ,0pt>,YwithinZ theZXY -picture.ThezeropGositiondoesnothavetobGecontainedinthepicture,but/Xmin2Xmax ^SYminYmaxqOalways/holds.QThepGossibleUUpositionsaredescribedindetailinx3. L When`an`XY -pictureisenteredinmathmo}'de!thenthereference. pGointbecomesthe\vcenter". instead,5i.e.,weuseQthepGoint<Xmin ,-\the\fontdimen22>sPasreferencepGoint.U2.2ObjectsThegsimplestformofputtingthingsintothepictureisto`drop'anobje}'ctatapGosition.bAnob8jectislikea TU>'ExXbGoxexceptthatithasageneralEdge#aroundits referencepGoint|inparticularthishastheextents(i.e.,itisalwayscontainedwithin)thedimensionsL,RDz,OU,andvDawayfromthereferencepGointineachoftheҴfourdirectionsleft, right,up,andҴdown.Ob8jectsarejBencoGdedinTU>'ExXboxesusingtheconventionthatthe(nTU>'ExXreferencepGointofanob8jectisatitsleftedge,thus shifted<< 'L,0pt>;fromthecenter|soaTU>'ExXbGoxmaybGesaidtobearectangularob8jectwithL}=0ptt.HereUUisanexample:'v Uz/3232zbϞ32fdFFg3232%'z$fdj$fd32z/3232zbϡfdFFg3232cLͷz2fdfe{2fdfe}$2fdfe42fdfeD2fdfeT2fdfezd2fdfe`t2fdfeF2fdfe,2fdfe2fdfe2fdfeğ2fdfeԟ2fdfe2fdfe2fdfeyEL72fdfeGb2fdfeW2fdfefȟ2fdfev{2fdfe.2fdfe2fdfe2fdfeG2fdfe2fdfeԭ2fdfe`2fdfe2fdfeƟ2fdfey2fdfe#,2fdfe2ߟ2fdfeB2fdfeRE2fdfea2fdfeq2fdfe^2fdfe2fdfeמER 32fdfe832fdfe32fdfe32fdfe32fdfe32fdfe32fdfe32fdfe32fdfecD˙32fdfex32fdfe32fdfe32fdfe32fdfe32fdfe32fdfe32fdfe32fdfe32fdfe32fdfe32fdfe32fdfeҟpU b bTU>'ExXUUreferencepGointx<ğ z҄fdfex=gofdfevdʟ,Vfdfet-阄fdferڄfdfepdfdfeoV!^fdfem)ޠfdfekQfdfeixY$fdfegffdfeeEӨfdfecfdfeb N,fdfe#fݍTheob8jectshownhasarectangleedgebutothersareavqailable,7eventhoughthekernelonlysuppGortsrectan-gle[andcircleedges.ItisalsopGossibletouseentireXY-picturesasob8jectswitharectangleedge,<0 YmaxN.Thecommandsforob8jectsarede-scribGedUUinx4.gw:2.3:Connections:Besides`havingtheabilitytobGedroppedataposition :inj$apicture,Wallob8jectsmaybGeusedtoc}'onnect\the:two[currentob8jectsofthestate,i.e.,pandc.IF*ormost:ob8jectsthisisdoneby` lling'thestraightlinebGetween:thecenterswithasmanycopiesaswill tbGetweenthe:ob8jects:>ϟO \cmmi5p{9({9/=)=.{9*{9- W+ W,˟c2Ӟ3232L32fdg3232":fd2ofd32Ӟ3232Lfdg3232XHgؤgw;g]%g}џ߹Rgt%gjgqgaCgW*gNbH3gD`g;ޟ>g2)g(tg.Sg Ag MU ng32325a3232Vv3232323232323232Vg3232?K׍3232323232323232323232322m׍3232323232323232323232323232325a3232Vv3232323232323232Vg3232lKKֱfdfez ֱfdfe.ɟֱfdfe㈟ֱfdfeGֱfdfeMֱfdfe˟4L:ֱfdfe)ֱfdfe3ֱfdfeMֱfdfe4R#M32fdfeM32fdfeM32fdfeM32fdfe /DM32fdfeM32fdfeM32fdfeM32fdfeM32fdfeM32fdfe[8Un!43232w3232Vv3232323232323232Vg3232?׍323232323232323232323232t׍32323232323232323232323232!43232w3232Vv3232323232323232Vg3232:ڡ\fdfeZڡ\fdfeqڡ\fdfe%؟ڡ\fdfeڗڡ\fdfeVڡ\fdfe#LAڡ\fdfe[yڡ\fdfeuhڡ\fdfeWڡ\fdfeg#ReW32fdfeW32fdfeW32fdfeW32fdfeD W32fdfeW32fdfeW32fdfeW32fdfeW32fdfeW32fdfe ߢU؍zc3232{3232Vv3232323232323232Vg3232?zI׍323232323232323232323232 ׍32323232323232323232323232zc3232{3232Vv3232323232323232Vg32328 *azIސƄfdfe{ސƄfdfe}iސƄfdfeh(ސƄfdfeސƄfdfeѦސƄfdfe|]kLڟސƄfdfeɟސƄfdfeސƄfdfeѧސƄfdfeIRύѧ32fdfeѧ32fdfeѧ32fdfeѧ32fdfe(NDxѧ32fdfeѧ32fdfeѧ32fdfeѧ32fdfeѧ32fdfeѧ32fdfeb UBjԞ3232kQ3232Vv3232323232323232Vg3232?j;׍323232323232323232323232x]׍32323232323232323232323232jԞ3232kQ3232Vv3232323232323232Vg3232qz\˷j;0fdfel@0fdfem0fdfeox0fdfeq_70fdfes0fdfelTLx*0fdfev0fdfet0fdfes0fdfesTR9s32fdfes32fdfes32fdfes32fdfepjmD⍍s32fdfes32fdfes32fdfes32fdfes32fdfes32fdfepK߾vUݴZ$3232\>3232Vv3232323232323232Vg3232?Z΋׍323232323232323232323232i;׍32323232323232323232323232Z$3232\>3232Vv3232323232323232Vg3232a 5Z΋ofdfe\Jofdfe^8 ofdfe_ȟofdfeaofdfecVFofdfe\ Lizofdfeg"iofdfeeADɶS32fdfeS32fdfeS32fdfeS32fdfeS32fdfeS32fdfeQ)JU哀;lĞ3232Nnfdfe@qhNnfdfeB&'NnfdfeCNnfdfe=fВLINnfdfeG NnfdfeENnfdfeCNnfdfeDRВRwC32fdfeC32fdfeC32fdfeC32fdfeA1D C32fdfeC32fdfeC32fdfeC32fdfeC32fdfeC32fdfeAl;댴Uꍍ+3232-3232Vv3232323232323232Vg3232?+{׍323232323232323232323232:׍32323232323232323232323232+3232-3232Vv3232323232323232Vg32322s+{=؄fdfe-J:=؄fdfe.=؄fdfe0=؄fdfe2hw=؄fdfe46=؄fdfe-L9j=؄fdfe7Y=؄fdfe6H=؄fdfe47=؄fdfe4GRፍ4732fdfe4732fdfe4732fdfe4732fdfe1sޟD騊4732fdfe4732fdfe4732fdfe4732fdfe4732fdfe4732fdfe1|UrTd3232Gፍ3232Vv3232323232323232Vg3232?˟׍323232323232323232323232*D׍32323232323232323232323232d3232Gፍ3232Vv3232323232323232Vg3232"ݷ˟-Bfdfe-BfdfeAI-Bfdfe -Bfdfe"ǟ-Bfdfe$_-BfdfeKfL*-Bfdfe(+-Bfdfe&E-Bfdfe$_-Bfdfe$חfRK$_32fdfe$_32fdfe$_32fdfe$_32fdfe!.D􍍍$_32fdfe$_32fdfe$_32fdfe$_32fdfe$_32fdfe$_32fdfe!۟kUa 33232 13232Vv3232323232323232Vg3232? ׍323232323232323232323232=׍32323232323232323232323232 33232 13232Vv3232323232323232Vg3232'ExXcommandswhichaddtopictures.:Mostsuchcommandsareprovidedbythevqarioususer:optionsJy(cf.xXx7)|onlyafewareprovidedwithinthe:kernelętofacilitateprogrammingofsuchoptions(and:userUUmacros)asdescribGedinx5.:2.5:The&aX1"Yv-picstate:Finally0wesummarisetheuser-accessiblepartsofthe6XYj:-picture#stateoftwo#pGositionstogetherwiththelast:ob8jectassoGciatedwitheach:thepr}'evious!,KJp,isthe:pGositionx< uXpR,ǵYpR>withxtheob8jectLpR,Rp,Dp,Up,:EdgepR,andthecurr}'entز,c,isthepGosition< Xc, Yc>:withUUtheob8jectLc,Rc,Dc,Uc,Edgec. 6;F*urthermore, XY-picMhasacon gurablec}'artesian:c}'oordinate#systemTdescribGedbyanoriginpGosition:<*7X+t}\cmti7originm,~Yoriginm>"qandttwob}'asezvectorsG<Xxbase,筵Yxbase>:and<سXybaseN,KYybaseN>accessedbytheusualnotationus-:ingUUparentheses:􍍟df(cx,?y[);q= <*BXorigina+8xXxbase+yXybaseC,*BYorigina+8xYxbase+yYybaseC>:Thisisexplainedinfullwhenweshowhowtosetthe:baseUUinnote3dofx3. 6;Finally typGesettingaconnectionwillsetupa\place-:mentxstate"forreferringtopGositionsontheconnection:thatXyisaccessedthroughaspGecial? positionconstruc-:tion;UUthisisalsodiscussedindetailinx3.;ThexkXY o-picxostate8ʲconsistsofalltheseparametersto-:gether.?TheyareinitialisedtozeroexceptforXxbasenȲ=:Yybasef=1mm.;The`edgesarenotdirectlyavqailablebutpGointsonthe:edges~maybGefoundusingthedi erenthcorneriforms:describGedUUinx3.LWj:6jS*tj??gw ItKispGossibletoinsertan`initial'pieceofhposi hdecori4atthestartofevery4XY -picturewiththedecla-ration~ff2 iI\everyxy={hhtextiUU}ff2ThiswillactasifthehtextiwastypGedliterallyrightaftereach\xycommand,*parsingtheactualcontentsasifitfollowsthis{thusitisrecommendedthathtextihasQtheformhpGosi,ʲsuchthatuserscancontinuewithhpGosiUUhdecori. 3LPositionsAԸhpGosiition/isaway/ofspecifyinglocationsaswellasdroppingob8jectsatthemanddecoratingthem|infactanyaspGectoftheXY t-picstatecanbechangedbyahpGosiͲbutmostwilljustchangethecoordinatesand/orshapGeUUofc. AllXpGossiblepositionsareshownin gure1withex-planatoryUUnotesbGelow.{Exercisea#1: WhichofthepGositions0 퀲,<0pt,0pt>4Cs,<0pt>?,(0,0)׹,andhe/0pt/ishedi erentfromtheothers?NotesuT3a.When}doingarithmeticwith+;and-thentheresultingxjcurrentob8jectinheritsthesizeofthehcoGordi,/i.e.,the&rightargument|thiswillbGezeroifUUthehcoGordiisahvectori.gExercise}O2: Howgdoyousetctoanob8jectthesame{sizeasthesaved{ob8ject"ob" butmoved<?X,ߵY8>x?^ 3b.UXSkewing{^using!qjustmeansthatthereferencepGointofcismovedwithaslittlechangetotheshapGeoftheob8jectaspossible,@i.e.,theedgeofcwill/remaininthesameloGcationexceptthatitwillgrowlargertoavoidmovingthereferencepGointoutsideUUc.ExerciseD3: What.doGesthehposi...!R-L>̲do?Bug:Theresultof!Sisalwaysarectanglecur-rently*.^ 3c.8A䖸hpGosic}'oversӲanotherifitisarectanglewithsizesucientlyqlargethattheotheris\underneath".The(. kopGeration(\extends"ahpositocover(anad-ditionalnone|thereferencepGointofcisnotmovedbuttheshapGeischangedtoarectanglesuchthattheUUentirepob8jectiscovered.Bug: non-rectangularob8jectsare rst\trans-lated"intoarectanglebyusingadiagonalthroughtheUUob8jectasthediagonaloftherectangle.gw:3d.?The2opGerations:and::settheb}'asePusedfor :hcoGordiinates5;havingtheform( u8x,?y[)ֲ.xThe: sop-:erationUwillset< ڵXoriginm, [Yoriginm>toUݵp,< Xxbase,:Yxbase>`toӳcroriginU,sIand< XybaseN,YybaseN>to:<*7UYxbase,ʵXxbase>(thisensuresthatitisausual:squareJ coGordinatesystem).nThe::operationmay:thenbGeusedafterwardstomakenonsqarebasesby:just.settingyb}'asetocporigin.RHere.aretwo.ex-:amples: rstly0;<1cm,0cm>:FsetsthecoGordinate:system,ZRhL̷T5c1fds玍kJ_f_bG_]_X._T5g_pJ//T1sfe T5cǍT5cT5cT5cT5cT5cT5c OO8je,j cmti9originsKxbaseI\LybaselŻvK5(1,1)T1?JfdfeUȟ?JfdfeW_?JfdfeY?Jfdfe[?Jfdfe]~$?Jfdfe_c?JfdfeaIR?Jfdfec.?Jfdfee?Jfdfef?Jfdfeh߮?JfdfejE?Jfdfelܟ?Jfdfens?Jfdfepv ?Jfdferʍpv32fdfeipv32fdfepv32fdfepv32fdfepv32fdfepv32fdfepv32fdfepv32fdfepv32fdfepv32fdfepv32fdfepv32fdfepv32fdfepv32fdfepv32fdfepv32fdfe׍:whileUU<1cm,.5cm>;<2cm,1.5cm>:<1cm,1cm>::de-: nesFzDOLͷFП%?LV ?R6G?X>?_?F6__ +ybase j*jo cmr9bAefore2 ]-ߤN cmtt9::[>{zYx].u?r"|o#khqeb6??b\F 9fe bbbb OO+eorigin%xbaseLWybase{ 1_N(1,1)b\32fdfe&c`32fdfee:32fdfefm32fdfeg32fdfei"Ȟ32fdfej}32fdfek|32fdfem3V32fdfen032fdfeo 32fdfeqC32fdfer32fdfes32fdfeuTr32fdfevL32fdfex &32fdfeye32fdfezڞ32fdfe|32fdfe}u32fdfe~h32fdfeҵč~n32fdfe8~n32fdfe~n32fdfe~n32fdfe~n32fdfe~n32fdfe~n32fdfe~n32fdfe~n32fdfez:where#ineachcasetheisat0 ,thebasevectors:haveUUbGeendrawnandtheisat(1,1)F.E~:WhenworkingwithcartesiancoGordinatesthese:threeUUspGecialhfactorisareparticularlyuseful: Aۍ:ff2 W\halfroottwoR`r0:70710678 K1K&fes2 )PpHPfeE2 \partroottwoR`r0:2928932218 l1l&fes2PpPfeE2\halfrootthreeR`r0:86602540 K1K&fes2 )PpHPfeE3E:ff2 u:More(canbGede nedusing\defLD(or\newcommand :inUUL5ffA͉TU>'ExX).:3e.#Ananglef; ZinXY%-picisthesameasthecoGordi-:natewpair( bZcosp z,sin z),where /mustbGeaninte-:ger?interpretedasanumbGerofdegrees.Thusthe:hvectori֑a(0)is֑thesameas(1,0)!anda(90)as:(0,1)*+,UUetc.:3f.:T*odr}'op@anhob8jectiatcwith*~meanstoactu-:allyY\physicallytypGesetitinthepicturewithref-:erenceXpGositionatc|howthisisdonedependson:theθhob8jectiinquestionandisdescribGedindetail:in3޸x4. bTheintuitionwithadropisthatittypGe-:setsXsomethingat<UXc, R޵Yc> 6andsetstheedgeofc:accordingly*.:3g.YThe>7c}'onnect1opGeration**hwill rstcomputeanum-:bGer zofinternalparametersdescribingthedirection:fromIptocandthentypGesetsaconnection lled:withXxcopiesofthehob8jectiasillustratedinx2.3.:The7exactdetailsoftheconnectiondepGendonthe:actuala\hob8jectiandaredescribGedingeneralinx4.:The 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.LWj:8 g*tj??gw3h.f`Using? cwill\pickaplace"alongthemostrecent connection2@typGesetwith**:. Whatexactlythismeans@isdeterminedbytheob8jectthatwasusedfortheconnectionandbythemoGdi ersdescribedinUUgeneraltermshere.{SThe\shave"moGdi ersinahplacei,< oand>,changethehdefaulthfactori,턵f,andhhowitisused,by`moving'0IthepGositionsthatcorrespondto(0) and(1)(respGectively):Theseareinitiallysetequalto #pandc,wVbutshavingwillmovethemtothepGoint@oontheedgeofpandcwheretheconnection\leaves/enters"'ExX\jot(usuallyequalto3pt?~)furthertowardstheotherenddoftheconnection(andpastit).FinallythepickiactionVcwillpickthepGositionlocatedthefrac-tion}f/oftheway}from(0)7to(1)wherefϲ= @0.5ifUUitwasnotset(by<R,>,orexplicitly).AlllthisisprobablybGestillustratedwithsomeex-amples:.:Q(0,0)*=0{+}="+"?;Q(2,1)*=0{\times}="*"?**@{.},Q(1,0)*+{A}?;(2,2)*+{B}**@{-}Q?!{"+";"*"}?*{\bullet}\endxyɋwillUUtypGesetDCK+l8ɟ?Dfdfeq"fdfeMfdfe!fdfeџfdfeT_fdfe}Ufdfe{xfdfeyٟ\<fdfex7?ۄfdfevp]#zfdfetfdfer긄fdfeqWfdfeoSefdfem'fdfeky4fdfei\ӄfdfeh6m@rfdfefo/$fdfedfdfeb೟Ofdfeaufdfe_R7fdfe],fdfe[ûy˄fdfeY}]jfdfeX5?A fdfeVn$fdfeTßGfdfeR߅fdfeQGυfdfeOQ $fdfeh8ꩵA`ޟB{4fg~|`z-hw5usq`o-irʟ쾓K3k.DThepGositionsdenotedbytheaxisinterse}'ctionhcoGordiinatesٴxandyarethepointswheretheline ff^ J= "5-:5LThe'bracescanbcI,x{n.32fdfeғ32fdfe32fdfe 32fdfe( 32fdfeD32fdfea32fdfe}32fdfe32fdfe{32fdfe32fdfeu32fdfe 32fdfe(o32fdfeD32fdfe~ai32fdfe}}32fdfe}}yxfdfeD=fdfe fdfeDŽfdfe쌄fdfea Qfdfe( &fdfeBۄfdfe_fdfes$=RytU՝v`32fdfe8wD32fdfex(.32fdfey ͞32fdfeyl32fdfez 32fdfe{32fdfe|I32fdfe}}32fdfea *fdfeb_rfdfec^fdfee Nwfdfef_fdfeg*^Ufdfei Ąfdfej` 3fdfekt^fdfem fdfen`P fdfeo ^fdfeq , ^fdfer` ̈́fdfes_<fdfeu vfdfev` fdfe>Y7:ExerciseM4: Givenprede nedpGointsA,sBq,C,:andID-(storedasob8jects"A" ,K"B" {,K"C",KandI"D"),:writej0ahcoGordispeci cationthatwillreturnthe:pGointwherethelines}fe:AB2and}fek`CDuXcross(thepoint:markedUUwithalargecirclehere):?ӍOxOxOÞOÞPxPxQ-Q-EAccX "ccX "cS "cS "dcX "dcX "e] "e] "YM !Btututtuuuuv*v*xuCz&ptz&ptzqktzqkt{&pt{&pt{ut{ut~&psDiU0>iU0>jF0>jF0>lU0>lU0>nd0>nd0>PsH#32fdfer&32fdfeq˞32fdfeo䟞32fdfens32fdfemG32fdfel32fdfek_32fdfej>Þ32fdfei32fdfegk32fdfef?32fdfee32fdfed32fdfecw32fdfebV32fdfea5c32fdfe`732fdfe^ 32fdfe]ߞ32fdfe\32fdfe[32fdfeZn[32fdfeYM/32fdfeX,32fdfeW מ32fdfeU髞32fdfeT32fdfeSS32fdfeR'32fdfeQd32fdfePCϞ32fdfeO"32fdfeNw32fdfeLK32fdfeK32fdfeJ32fdfeI|Ǟ32fdfe{g#32fdfeڍg32fdfeh 32fdfei|32fdfej32fdfekvb32fdfelT՞32fdfem3H32fdfen32fdfen.32fdfeoΡ32fdfep32fdfeq32fdferi32fdfesHm32fdfet&32fdfeuS32fdfeuƞ32fdfev932fdfew32fdfex32fdfey]32fdfez<32fdfe{x32fdfe{32fdfe|^32fdfe}ў32fdfe~D32fdfer32fdfeQ*32fdfeѩ:3l.:AhpGosihdecorigr}'ouped*in{},-braces^6 )isinter-:pretedjinaloGcalscopeinthesensethatanypand:b}'ase ȲbuiltLmwithinitareforgottenafterwards,N5leav-:ingonlythecastheresultofthehcoGordi.Note::Onlypandb}'ase'ExX:group.ʱ:Exercise S5: Whate ectisachievedbyusingthe:hcoGordiinateUU\{;}"?:3m.TheV{vector/xZ/,VwhereZ isahdimenision,isthe:same]asthevector<ZaIJcoso z,IwZaIJsinS z>ewhere ghisthe:angleofthelastdirectionsetbyaconnection(i.e.,:withUU** O)UUorsubsequentplacement(??)pGosition.ZÍ:ItispGossibletogiveahdirectioniasdescribedin:the(nextsection( gure3,note4linparticular):thatawillthenbGeusedtosetthevqalueof z.Itis:alsopGossibletoomitthehdimeniinwhichcaseit:isUUsettoadefaultvqalueof.5pcUI.:3n.?Ahcorneri8isano setfromthecurrent< 5Xc, R޵Yc>:pGositionܟ2fdfelP2fdfejc2fdfehu*2fdfefD2fdfed^2fdfebx2fdfe`32fdfe'`32fdfe`32fdfe`32fdfe`32fdfe`32fdfe降`32fdfel`32fdfe`32fdfe`32fdfe`32fdfe`32fdfe`32fdfe`32fdfe`32fdfe`32fdfe`32fdfe`32fdfe`32fdfe;̟9LDɟ2fd`Mz̟_H˟_Dʟ_Rz̟//Œ9Rb2fd`b__Š_boo^D`ҟ fe ֍`x䍍```ֺOO^U`τ feύ````Ϻ=LDNa yL yJho^yRzֺ̟<<bYORDbӹVz V| VbֺkkClϟՄ'LU߈WPB1}鍍N :1L21Rz̟ϺTlܼRUb㛹r,rП!rbϺyy;Wn,CLN%OKldOHiORz̟bS''䬟ZCRbb:dGd[dbbSrry3ΟDCn̹Eq }Es d H.Enֺbbs| Մ'UC߈Wn[x }鍍p砟[x r[x nϺ~1m,Cnb=orӜoov}KonbSww< mPM&g-dH1dDX 5dRz̞22%HpYQjPPtAjFЗj=P j3ݟ 7j*Qj< EMO[jIxjE0 jRz̟yA55:( ff^ J= "5-:6LThe'bracescanbisa psquaresUtext!iI3232j2{32fd'g3232(&i尉'fd'fd32iI3232j2{fd'g3232k533(嶟5(33ew{R\ ן}RRCRI8 R?Y"R6d/LR,v[R#۟ؠ!R%RRQ]sR3G9R} pRߟRᨵċR>QRaRj7AR kR㟪iR+/RRWeR;(.5)岟o tfewBw5U 矴?<>(.2)(.5)qtr,^srbH(r:1rSrHGrq{dyyv5W韄?<}qr.vtrb`)rmq\rp*Fsrtb0(rw8r{Sr~FGrmqcdyy]ޣ}.T:+?>>>>a tfea2Ba2a2a25$ڇ;2?<>(.7)%qtr(_r,br/ r3Sͫ~r6˕3r%qt Pyy5!OX?>(.7)~Z tfebBb,J2FigureUU2:qExamplehplaceisP/)Thex`edgepGoint'E liesontheedgealongtheline from\ptothecentreoftheob8ject,pincontrasttothe`propGortional'XpointP ;whichisalsoapGointontheedgebutcomputedinsuchawaythattheob8jectloGoksUUasmuchUU`awayfromp'aspGossible.0Finally*,a=following( :f) ɲsuxwillmultiplytheo -setUUvectorbythehfactorif.)6Exercise(6: Whatisthedi erencebGetweenthehpGosiitionsUUc?<jandUUc+EL?ExerciseT7: WhatUUdoGesthistypeset?N8\xy?*=<3cm,1cm>\txt{Box}*\frm{-}Q!U!R(.5)?*\frm{..}*{\bullet}\endxyhHintز:*\frmisde nedbytheframeextensionandjusttypGesetsaframeofthekindindicatedbytheargument.0Bug:糲CurrentlyKonlythesingle-lettercorners(L,R,2D,U,C,E,andP)willworkforanyshapGe|theotherssilentlyassumethattheshapGeisrectangu-lar.`3o.'The7stackK\isaspGecialconstructionusefulforstor-ing,asequenceofhpGosiitionsthatareaccessibleusingthespGecialhcoordiinatess Hn,4wherenisei-therasingledigitorapGositiveintegerin{}+s:os0is"alwaysthe`top'elementofthestackandifthestackԪhasdepthdthenthe`bGottom'elementofthestackhasnumbGers{dR1}?.ThestackissaidtobGe|`empty'whenthedepthis0andthenitisanerror toaccessanyofthesInor`pGop'whichmeansremoveԗthetopelement,gshiftingwhatisins1)(tos0 ,s2Q[toܞs1 \,etc.ISimilarly*,`pushܞc'meanstoshifts0Ѳtos1 ɲ,etc.,andtheninsertthecasthenews0./):TheUUstackismanipulatedasfollows: y:ff2 9ōN@hstackingiEPActionc:ff2 A.N@+hcoGordiEPpushUUhcoGordiiN@-hcoGordiEPc hcoGordi&VthenUUpGop N@=hcoGordiEPloadUUstackwithhcoGordiN@@hcoGordiEPdoUUhcoGordi&forUUc stackN@iEPinitialiseN@(EPenterUUnewframeN@)EPleaveUUcurrentframec:ff2:T*o`loadstack',meanstoloadtheentirestackwith:the;#pGositionssetbyhcoordiwithinwhich, Cmeans:`pushUUc'.a:T*o,`dohcoGordiforallstackelements'meanstoset:citoeachelementofthestackinturn,fromthe:bGottomandup,andforeachinterpretthehcoGordi.:Thusthe rstinterpretationhascsettothebGot-:tom&elementofthestackandthelasthascset:tos0-۲.{kIfthestackisempty*,thehcoGordiisnot:interpretedUUatall.:ThesetwoopGerationscanbecombinedtorepeata:particularUUhcoGordiforseveralpoints,likethis:N8:\xy*7@={(0,-10),(10,3),(20,-5)}?@@{*{P}}:\endxy!:willUUtypGeseteEg^PboEaP~#$P.ԍ:Finally*,0the'RstackcanbGeforciblyclearedusing@i L,:however,4thiskisrarelyneededbGecauseof@( Je,which:savesthestackasitis,andthenclearsit,such:whenXithasbGeenused(andisempty),JYand@)is:issued,then itisrestoredasitwasatthetimeof:theUU@( O.LW910 @*tj??gwExerciseW8: HowXwouldyouchangetheexample abGoveUUtoconnectthepointsasshownbGelow?EKS ßgW6g\ga<g)ge8Mgj qgonuڕgt)gx[|g}ΟNg\A%g Ig痍liifxcgaV^JE[w4X#UReErvE ПE}.2EzcEvEsHEo}E%>93p.f`Itj?ispGossibletode nenewhcoordiinatesontheform" hidi"bysavingthecurrentcusingthe...=" *hidi" OhpGosiitionrRform. ȾSubsequentusesof"Qhidi" willthenreestablishthecatthetimeoftheUUsaving.J[Usinga"۸hidi"thatwasneverde nedisanerror,however,osaving7rintoanamethatwaspreviouslyde nedڳjustreplacesthede nitionwithoutwarn-ing,Xi.e.,"Uhidi"alwaysreferstothelastthingsavedwithUUthathidi.However,many}otherthingscanbGe`saved':in}gen-eralUU@RhsavingiUUhaseitheroftheforms 0ff2 ܪ@:"!hidi"V"[hidi"'restores*currentb}'aseܪ@hcoGordi"?hidi"V"[hidi"RreinterpretsUUhcoGordiܪ@@"!hidi"V@="fqhidi"greloads jcurrentVstackff2[TheM rstformde nes" hidi"toMbGeamacrothatrestoresUUthecurrentb}'ase[.The\seconddoGesnotdependonthestateatthetimeIofde nitionatall;itisamacrode nition.Y*ouVcanpassparameterstosuchamacrobylettingitusecoGordinatesnamed"1"Mв,"2"[,etc.,andthenuse=="1"1,$="2"$,$etc.,just=bGeforeeveryuseofitto7settheactualvqaluesofthese.nNote:qitisnotpGossible:touseahcoordioftheform"zhidi"directly:writeUUitas{" Ohidi"} .褍ExerciseW9: W*rite^ amacro"dbl" todoublethesizeofthecurrentcob8ject,e.g.,changingitfromtheUUdottedtothedashedoutlineinthis gure:.f΍k+*Yx3232Z˥3232K(32323232323232323232323232323232323232323232323232323232323232323232K3232̍Yfߟ㋶3232O3232323232323232323232323232323232323232323232323232a2㋶3232O323232323232323232323232323232323232323232323232323232Yx3232Z˥3232K(32323232323232323232323232323232323232323232323232323232323232323232K3232TC3232C_N_ D______ D_D3232=ZxغCCO ;32323232 ;32غwD¤ ;32323232 ;3232C3232C_N_ D______ D_D3232'uThe nalformde nesaspGecialkindofmacrothatshouldonlybGeusedafterthe@=9вstackoperation:the|xentirecurrentstackissavedsuchthatthestackopGerationUU@="Lhidi"RwillUUreloadit.Note: TherezisnodistinctionbGetweenzthe`namespaces'$ofhidisusedforsaved$coGordinatesandotherUUthings.gw:47Obfjectsэ:Ob8jects xaretheentitiesthataremanipulatedwiththe :*]and&**FhpGosi&operationsabovetoactuallygetsome:outputzinvXYKz-pictures.7AsforhpGosiitionstheopera-:tionsf*areinterpretedstrictlyfromlefttoright,_how-:ever,theHactualob8jectisbuiltb}'eforeYallHthehmoGdi eris:takeme ect.Thesyntaxofob8jectsisgivenin gure3:withreferencestothenotesbGelow.Remark:6\Itis:never㘲allowed toincludebraces{} insidehmoGdi eris!:InҘcaseyouwishtodosomethingthatrequires{ ...}:thencheckinthismanualwhetheryoucanuse(* ...*):instead.+If notthenyouwillhavetouseadi erentcon-:struction!h:Notes :4a.YAnںhob8jectiisbuiltusing\object)box>5V{CuShtexti}?.:\object%box0qisUUinitiallyde nedasN8:\def\objectbox#1{%*7\hbox{$\objectstyle{#1}$}}:\let\objectstyle=\displaystyleg:butA\maybGerede nedbyoptionsortheuser.:The\htextishouldthusbGeinthemoderequired:by6the\objectboxcommand|withthedefault:\objectbox2Qshownj5abGoveitshouldbGeinmath:moGde.J^:4b.?Anhob8jectibuiltfromaTU>'ExXbGoxwithdimen-:sionswв(h+d)willhaveLc yR=fqRc=wD=2,:Uc1 =)Dc=(h+d)=2,Vthus#-initiallybGeequipped:withgMtheadjustment!CN(seenote4f)."pInparticular::in?ordertogetthereferencepGointonthe(center:of)WthebaselineoftheoriginalhTU>'ExXbGoxithen:youshouldusethehmoGdi eri! ;;O1togettherefer-:encepGointidenticaltotheTU>'ExXreferencepGointuse:theUUmoGdi er!!LL./:TU>'ExXnicalremark: xAnymacrothatexpandsto:somethinghxthatstartswithahbGoximaybGeused:asUUahTU>'ExXbGoxihere.:4c.#T*akes`anob8jectandconstructsit,cbuildingabGox;:itisthenproGcessedaccordingtothepreceeding:moGdi ers.;pThisformmakesitpossibletouseany:hob8jectiѲasaTU>'ExXbGox(evenoutsideofXY =-pictures):bGecauseUUa nishedob8jectisalwaysUUalsoabox.:4d.?Severalhob8jectiscanbGecombinedintoasingleob-:jectusingthespGecialcommand\compositewitha:list23ofthedesiredob8jectsseparatedwith*r0sasthe:argument.zThe4resultingbGox(andob8ject)isthe:leastUUrectangleenclosingalltheincludedob8jects.:4e.#T*ake^anentire^XY -pictureandwrapitupasabGox:as8describGedinx2.1."qMakesnestingof4XY 8-pictures:pGossible:̱theinnerpicturewillhaveitsownzeroLW911 ]*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!^GhemptyiĆdefaultUUdiagonal^4lLEҸj^Glgajm~ rv]j|/d!juĆleft,UUright,down,updiagonal^4lLEҸj^GldljrrdWjlujruĆleft/down,UU...diagonal^4l hcompGositeiE%K!^Ghob8jectiĆ rstUUob8jectisrequiredLEҸj^GhcompGositeiUU* ꧸hob8jectiĆaddUUhob8jectitocompGositeobjectbGox^4dffd  PofthewidthandheightofNarectangle.o^WhengivenasahvectorithesearejustcthevectorcoGordinates,i.e.,thechvectoristartsinlthelowerlleftcornerandendsintheuppGerrightcorner.]The\pGossiblehaddopierationsthatcanbepGerformedUUaredescribedinthefollowingtable.1B@,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 ffff1yIn\eachcasethehvectorimaybGeomittedwhichinvokes"the\defaultsize"fortheparticularhaddopi:ğL͉fffd͟ 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#-=  ffff1B@TheLjdefaultsforthe rstthreearesetwiththecommandsFff2 č \objectmarginUUhaddopi{Rhdimeni} \objectwidthUUhaddopi{Rhdimeni} \objectheightUUhaddopi{Rhdimeni}qbff2where{haddopiisinterpretedinthesamewayasabGove.q`The{defaultsfor+=u/-=are{suchthattheresult-ingob8jectwillbGethesmallestcontaining/largestcontainedUUsquare.ƍExercise 11: How aretheob8jectstypGesetbythehpGosiitionsy\*+UR{\sum}4"and\*+DL{\sum}"en-larged?Bug:E;Currently>changingthesizeofacircularob-jectisbuggy|itischangedasifitisarectangleandqthenthechangetotheR8parametera ectsthecircle.XjThis =shouldbGe xedprobablybyageneral-isationfoftheo ɲshapGetobeovqalsorellipseswithhorizontal/verticalUUaxes.gw:4h.?AhiddenPob8jectwillbGetypesetbuthiddenfrom 6XYj:-picinthatitwon'ta ectthesizeoftheentire:pictureUUasdiscussedinx2.1.%:4i.:AninvisibleOob8jectwillbGetreatedcompletelynor-:mal5exceptthatitwon'tbGetypGeset,i.e.,XY B-picwill:bGehaveUUasifitwas.:4j.:Settingtheshap}'e\޲ofanob8jectforcestheshapGeof:itscedgetobGeasindicated.Thekernelprovides:threeƨshapGesthatchangetheedge,"namely[.],:[],UUand[o],correspGondingtotheoutlines&Q %@e,s(3232(F32fdFFg3232Qa'/fdoNĉ/fd32(3232(FfdFFg3232A@'2fdfe)2fdfe+2fdfe-2fdfe/&2fdfe1x62fdfe3^F2fdfe5DV2fdfe7*f2fdfe9v2fdfe:2fdfe<ܖ2fdfe>¦2fdfe@2fdfeBƟ2fdfeDt֟2fdfe3[ELo2fdfem+D2fdfek:2fdfeiJ2fdfegZ]2fdfeej2fdfecyß2fdfeav2fdfe_)2fdfe]ܟ2fdfe[2fdfeYB2fdfeW2fdfeU稟2fdfeS[2fdfeR2fdfeP2fdfeN&t2fdfeL6'2fdfeJEڟ2fdfeHU2fdfeFe@2fdfeDt2fdfeVERCDt32fdfe⍍Dt32fdfeDt32fdfeDt32fdfeDt32fdfeDt32fdfeDt32fdfeAGD_Dt32fdfe'Dt32fdfeDt32fdfeDt32fdfeDt32fdfeDt32fdfeDt32fdfeDt32fdfeDt32fdfeDt32fdfeDt32fdfeAUyNIJ,UUandg@`gcIacIfbecdTz2fdfe%2fdfeb2fdfe֟2fdfeJ2fdfek2fdfe=22fdfe2fdfe2fdfe2fdfe2fdfeTv2fdfesELT|2fdfe2fdfe2fdfe 2fdfe2fdfe=82fdfekğ2fdfeP2fdfeܟ2fdfeh2fdfe%2fdfeT2fdfeERhT{32fdfe.T{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfe'2 EDET{32fdfetT{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfeT{32fdfenOEU:whereIthedenotesthepGointofthereferenceposi- :tionintheob8ject(the rstisapGoint).\PExtensions:can5providemoreshapGes,Hhowever,all5shapGesset:theUUextentdimensionsL,RDz,DG,andU.:ThedefaultshapGeforob8jectsis[]andforplain:coGordinatesUUitis[.].:F*urthermore].thehshapGeis[r],_$[l],[u],and].[d],:are,de nedforconvenience,toadjusttheob8jectto:theMindicatedsidebysettingthereferencepGoint:suchythatthereferencepGointisthesamedis-:tance6afromtheoppGositeoftheindicatededge:andpGointattheinWideUUtextt323232fd+}/g3232捍tۉôfd0ôfd32t3232fd+}/g32324߲buttheob8ject:[d]\hbox{Wide?text}`MhasLreferencepGointatthe:*inWideUUtext3232Þ32fd+}/g3232捍fôfd0}ôfd323232áfd+}/g3232e0}.@GFinally*,_[c]putsthereference:pGointUUatthecenter.:Note:ExtensionszcanaddnewhshapGeiob8ject:hmoGdi eris2@whicharethencalledhstyleis.These:will7alwaysbGeeitheroftheform[ whkeywordi]or:[*7hcharacteri hargumenti]?.Someofthesehstyleis:doUUotherthingsthansettheedgeoftheob8ject.%:4k.vWhile"typGesettinganob8ject,someoftheprop-:ertiesareconsideredpartofthe`currentob8ject:style'.>;Initiallythismeansnothingbutsomeofthe:hstyleis de nedbyextensionshavethisstatus,+e.g.,:coloursK[red]<,[blue]&say*,usingKthexycolor+ex-:tension,or~vqaryingthewidthoflinesusingxyline"l.:SuchstylesareproGcessedleft-to-rightز;forexample,*[red][green][=NEW][blue]{A}:willtypGesetablueA Nandde ne[NEW]"Ntosetthe :colour9_togreen(allprovidedthatxycolor)2hasbGeen:loaded,UUofcourse).LW913*tj??gwSa9vingcstyles: OncespGeci edforanhob8jecti, thecollectionofhstyleiscanbGeassignedaname,using[=hwordi]?.Then[ Vhwordi]bGecomesanewhstylei,}suitable$forusewiththesameorotherhob8jectsis.CUseʲasinglehwordibuiltfromordinaryletters.$If[hwordi]alreadyhadmeaningthenewde nition'willstillbGeimposed,\ZbutthefollowingtypGeUUofwarningwillbGeissued:`~Xy-pic?Warning:Redefiningstyle[hwordiԶU]ThexlatterwarningwillappGearifthede nitionoc- curswithinan\xymatrix.wThisispGerfectlynor-mal,e7bGeingb aconsequenceofthewayb thatthema-trixBcoGdeishandled.:$SimilarlythemessagemayappGear'severaltimesifthestylede nitionismadewithinUUan\ar.Thefollowingillustrateshowtoavoidthesemes-sagesMbyde ningthestylewithouttypGesettingany-thing.N8Q\setbox0=\hbox{% \xy\drop[OrangeRed][=A]{}\endxy}.QNote1:[The)currentcolourisregardedaspartoftheUUstyleforthispurpGose.NoteP2:Such~namingsareglobalinscopGe.CTheyareƽintendedtoallowaconsistentstyletobGeeasilymaintainedpbGetweenvqariouspicturesanddiagramswithinUUthesamedoGcument.If #thesamehstyleiisintendedforseveralhob8jectisoGccurringinsuccession,/the[ |P*]hmodi ericanbGe-usedonthelaterhob8jectis.PThisonlyworkswhenC[| *]precedesCanyotherhstyleimoGdi ers;IitisloGcalinscope,&recoveringthelasthstyleisusedatUUthesamelevelofTU>'ExXgrouping.24l.SettingthecurrentdirectionissimplypretendingforthetypGesettingoftheob8ject(andthefollowinghmoGdi eris)UUthatsomeconnectionsetit.ItUUisparticularlyeasytosethdiagionaldirections:Dc}Hc}OgfIgfNo}Jo}MwܟKwܟL'ExXmacrosthatdecoratethe:currentpictureinmannersthatdepGendonthestate.:TheyYareallowedYafterm#thehpGosiitioneitheroftheouter:\xy...\endxyorinside{ F...}꧲. ThepGossibilitiesare:givenUUin gure4withnotesbGelow. ;Mostqoptionsaddtotheavqailablehdecori,ainparticu-:larthev2optionloadsmanymoresinceXY #-picversions:priorUUto2.7providedmostfeaturesashdecori.2:NotestW:5a.YSavingandrestoringallows`excursions'wherelots:ofthingsareaddedtothepicturewithouta ect-:ingtheresultingXY h-picstate, i.e.,c,p,andb}'ase[,:and`withoutrequiringmatching{} #Zs.6vTheindepGen-:denceof{}#isparticularlyusefulinconjunction:withthe\afterPOSXcommand,Hforexample,the:de nitionN8:\def\ToPOS{\save\afterPOS{%j4\POS**{}?>*@2{>}**@{-}\restore};p,}`D:willccausethecoGde\ToPOS$hpositoconstructa:double-shaftedharrowfromthecurrentob8jectto:thehpGosi(computedrelativetoit)suchthat:\xy?*{A}\ToPOS+<10mm,2mm>\endxyŬwilltypGe-:setUUthepicturejA 3O8.6Ÿ ee*bne 2`e?e".LW914*tj??m6A ffffd TSyntax?ActionX-ffd fdhdecori< B!QhcommandiUUhdecori?eitherUUthereisacommand... BjQhemptyi?...orUUthereisn't.ihcommandi< B!Q\saveUUhpGosi?saveUUstate^5a ,thendohpGosiBjQ\restore?restoreUUstate^5a Qsavedbymatcing\saveBjQ\POSUUhpGosi?interpretUUhpGosiBjQ\afterPOSUU{ ꧸hdecoriUU}hpGosi?interpretUUhpGosiandthenperformhdecoriBjQ\dropUUhob8jecti?dropUUhob8jectiasthehpGosi* ꧲operationBjQ\connectUUhob8jecti?connectUUwithhob8jectiasthehpGosi***operationBjQ\relax?doUUnothingzBjQhTU>'ExXUUcommandsi?anyUUTU>'ExXcommands^5b ߲anduserde nedmacrosthat?neitherUUgeneratesoutput(watchUUoutforspaces!)?norUUchangesthegroupingmaybGeused$_BjQ\xyverbosejq\xytracingj\xyquiet ?tracing^5c òcommandsBjQ\xyignoreUU{RhpGosiUUhdecori}?ignore^5d ۲XY-coGdeiBjQ\xycompileUU{RhpGosiUUhdecori}?compile^5e toUU lehpre xihnoi.xycBjQ\xycompiletoUU{Rhnamei}{ OhpGosiUUhdecori} ?compile^5e toUU lehnamei.xycffd FigureUU4:qǸhdecoriations.gʍ6Note: Savingxthiswayinfactusesthesamestate as*the{}N`grouping',sothecoGdep1|s, x{p2|s\save},...%{\restore}>swill${havec V=p1bGothatthe...andUUattheend!5b.f`OneverytemptingkindofTU>'ExXcommandstopGer-form?ashdecoriisarithmeticopGerationsonthe;XY ?-picstate.&ThiswillworkinsimpleXY f-picturesasdescribGeduherebutbewarned:itKisnotp}'ortablebGecause7all7XY -picexecutionisindirect,=andthisisusedabyseveraloptionsinnontrivialways.+ChecktheTU>'ExX-nicaldoGcumentation[15 ]fordetailsaboutthis! Macrosthatexpandtohdecoriwillalwaysdothesame,UUthough.5c.I\xyecho_willturnonechoingofallinterpreted[XY _-picZhpGosicharacters.Bug:{QNotcompletelyimple-mentedhJyet."\xyverbosewillswitchonatracingofally1XY 5-picy5commandsexecuted,-withlinenumbGers.\xytracingktracesevenmore:theentiregXYwk-picstateUisprintedaftereachmoGdi cation.s;\xyquietrestoresUUdefaultquietopGeration.5d.f`Ignoringn@meansthatthehpGosihdecoriisstillparsedDtheusualwayDbutnothingistypGesetandtheUQXY U-picUUstateisnotchanged.5e.IIt&XispGossibletosave&Xanintermediateformofcom-mandsthatgeneratepartsofanXY-picturetoa'$ lesuchthatsubsequenttypGesettingofthoseparts%issigni cantlyfaster:Qthisiscalledc}'ompil-ing}.S*The}proGduced lecontainscodetocheck}that6:thecompiledcoGdestillcorrespondstothesame :hpGosihdecori\aswellasecient\XY -coGdetoredoit;:ifthehpGosihdecorihaschangedthenthecompila-:tionUUisredone.#:ThereZaretwoZwaystousethis.Thedirectisto:invent=ahnameiforeachdiagramandthenembrace:it9in\xycompileto{HBhnamei}?| {...} {9thisdumps:theUUcompiledcoGdeintothe lehnamei.xyc.:Whenmanydiagramsarecompiledthenitiseasier:toާadd\xycompile{?...} NaroundާthehpGosihdecori:toDbGecompiled.]Thiswillassign lenamesnum-:bGeredconsecutivelywithahpre xiwhichisini-:tiallytheexpansionof\jobname-6IbutmaybGeset:with:ff2 ,Z\CompilePrefix{?hpre xi}%:ff2+t:This|hasthedisadvqantage,however,that|ifaddi-:tionalcompiledXYs-picturesareinsertedthenall:subsequentSpictureswillhavetobGerecompiled.:OnesJparticularsituationisprovided,though:when:used(withinconstructionsthattypGesettheircon-:tentsjmorethanonce(suchasmostAU>'M S-L5ffA͉TU>'ExX:equationUUconstructs)thenthedeclaration :ff2/\CompileFixPoint{?hidi}%:ff2+t:can@bGeusedinsidetheenvironment@to xthe:counterUUtohavethesamevqalueateverypassage.#:Finally*,՘when"Xmany`administrativetypGesetting:runs'K areneeded,Me.g.,readjustingK L5ffA͉TU>'ExXcrossref-:erences~|andsuch,thenitmaybGeanadvqantagetoLW915ו*tj??gwnottypGesetanyXY -picturesatallduringtheinter- mediatedruns.ThisissuppGortedbythefollowingdeclarationswhichforeachcompilationcreatesaspGecial lewiththeextension.xydcontainingjusttheUUsizeofthepicture: 7ff2 y鍍M]\MakeOutlinesM]\OnlyOutlinesM]\ShowOutlinesM]\NoOutlinesff2эThe rstdoGesnomore.MXThesecondusesthe letotypGesets1\adottedframeoftheappropriatesizein-steaddofthepicture(unlessthepicturehaschangedandisrecompiled,&|thenitistypGesetasalwaysandthe.xyd leisrecreatedforsubsequentruns).*Thethird$showstheoutlinesasdottedrectangles.aThelastUUswitchesoutlineproGcessingcompletelyo .!yT6]Kernelffobfjectlibrary oInthissectionwepresentthelibr}'aryobjectsn providedwithqthekernellanguage|severaloptionsaddmorelibrary'ob8jects.LTheyfallintothreetypGes::0Mostofthekernel8ob8jects(includingallthoseusuallyusedwith**#tobuildconnections)aredir}'ectionals!,TdescribGedinx6.1.TheYremainingkernellibraryob8jectsarecir}'clesofUUx6.2andtextH-ofx6.3.eƍ6.1DirectionalsTheQkernelprovidesaselectionofdir}'ectionals!:Uob8jectsthatm-depGendonthecurrentdirection.NTheyalltaketheUUform pff2a\dirhdiriff2 to3typGesetaparticularhdiriectionalob8ject. AllhavetheUUstructure pff29YhdiriUU q!!hvqarianti{?hmaini}ff2 with[hvqariantibGeinghemptyioroneofthecharacters^_23UIandUUhmainisomemnemoniccoGde.  W*ewillclassifythedirectionalsprimarilyintendedforbuildingconnectionsasc}'onnectorsandthosepri-marilyƱintendedforplacementatconnectionendsorasmarkersUUastips!. Figure5showsallthehdiriectionalsde nedbythekernel(withnotesbGelow;oeachhmainitypGehasalineshowingitheavqailablehvariantis.#Noticethatonlysomevqariants[existforeachhdiri|whenanonexistingvqari-antofahdiriisrequestedthenthehemptyivqariantis!usedsilently*.+Each!isshownineitherofthetwoformsavqailableineachdirectionasapplicable:Fcon-nectingRa toaffffff33ff33ff B(typGesetby**\dir#!@hdiri)andasagw:tip*\attheendofadottedconnectionofthesamevqari- :ant(i.e.,-typGesetbythehpGosi**\dir#nhvqarianti{.}w?>:*\dir*+hdiri). X;As aspGecialcaseanentirehob8jectiisallowedasa:hdiri|xbystartingitwitha* u: \dir*%|visequivqalentto:\object.x:Notes؍:6a.YY*out[mayuse\dir{}(hfora\dummy"directional:ob8ject޳(infactthisisusedautomaticallyby**{}ާ).:Thisisusefulforauniformtreatmentofconnec-:tions,Fe.g.,makingBRthe? ġhpGosiableto ndapoint:on8thestraightlinefromptocwithoutactually:typGesettingUUanything.^:6b.?The#plainQc}'onnectorsgroupcontainsbasicdirec-:tionalsUUthatlendthemselftosimpleconnections.:By'ExXrules.)Unfortu-:natelyIrulesisthefeatureoftheDVIIformatmost:commonlyzhandledwrongbyDVImdrivers. 5There-:foreUQXY U-picUUprovidesthehdecoriations:ff2 FN\NoRulesN\UseRulesZ:ff2v:thatUUwillswitchtheuseofsucho andon.:AscanbGeseenbythelasttwocolumns,ړthese(and:most?oftheotherconnectors)alsoexistindouble:and,xtripleversionswitha2 ora3prepGendedto:thebname.=F*orconvenienceb\dir{=}+andb\dir{:}:aresynonymsfor\dir2{-}5㚲and\dir2{.}/,re-:spGectively;{similarly\dir{==}4$isasynonymfor:\dir2{--}(*.^:6c.#Thegroupofplain1tipsɲcontainsbasicob8jectsthat:areusefulasmarkersandarrowheadsmakingcon-:nections,}&*typGesetsn44i͟e44cٟ;44^ۺ44/E~:Exercise14: TypGeset}thefollowingtwo+sand:aUUtiltedsquare:QOYt+jƟv+nU׹opѼA/lX}/lX՟}o:Hintز:fthe>dashcreatedby\dir{-}+=ղhasthelength:5pt1.LW916*tj??4aJ˜Dummy^6a*C\dir{}PlainUUconnectors^6b_\dir{-}^NXJ NXJ'O1!O1&SXJ"SXJ%Vc#Vc$C{3232{E32fd 7g3232 {z fdI fd32{3232{Efd 7g3232{z?fdfeyr#fdfewjfdfeubP5fdfetZ懄fdfer9R|لfdfepXJ+fdfenwB}fdfel:?τfdfej2!fdfeh*lsfdfef"ńfdfeefdfec1/ifdfeaP Żfdfe_o\ fdfe]_fdfe[fdfeYfdfeWUfdfew ܹirΟ9Sin5iiʌAie_k]i`J/i\) iXi\dir2{-}^r r'n!n&r"r%#$CP323232fd 7g3232  fd! fd32P3232fd 7g3232lXfdfeP/:fdfeHŌfdfe@[ބfdfe80fdfe 0fdfe &(Ԅfdfe E &fdfedKxfdfeʄfdfexfdfenfdfefdfe;fdfedfdfe4tz4tB/\dir3{~}^Ľ '!&"%#$C썞323232fd 7g3232  fdÉ fd32썞3232fd 7g3232:5񤐄fdfeY-:fdfex%4fdfegfdfe؄fdfe 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Sometimes somedeclarationsofanoptionorheader leorwhateveronlymakessenseaftersomeparticularotheroptionisloaded.PInthatcasethecoGdeshouldbewrappGedUUinthespecialcommandff2 ?" E\xywithoptionUU{ ꧸hoptioniUU}{hcoGdeiUU}ff2which[indicatesthatifthehoptioniisalreadyloadedthenShcoGdeishouldbeexecutednow,otherwiseitshouldzbGesavedzandifhoptionievergetsloadedthenhcoGdei:Mshouldbeexecutedafterwards. Note:;ThehcoGdei=shouldallowmorethanoneexecution;itissavedwithC)thecatcoGdesatthetimeofthe\xywithoptioncommand. Finally*, HitispGossibletodeclaresomehcodeithatxishouldbGeexecutedbeforeeveryactualex-ecution 5of\xywithoption{?hoptioni}{ ...}꧲,andLW9183*tj?? rS8 ffffd T.DSyntaxުActionX-ffd .D\cir+hradiusiUU{ ꧸hciriUU}ުhciricleUUsegmentwithhradiusifffd fd.DhradiusiHO !l.ehemptyiުuseUURch6astheradius OWjl.ehvectoriުuseUUX7ofthehvectoriasradius.DhciriHO !l.ehemptyiުfullUUcircleofhradiusiOWjl.ehdiagiUUhorientihdiagiުpartialcirclefrom rsthdiagionalthroughtothesecondުhdiagionalUUinthehorientiationd.DhorientiHO !l.e^ުanticloGckwiseOWjl.e_ުcloGckwiseffd NFigureUU6:qǸhciricles.r(rsimilarly bGeforeevery\xyoption{>jhoptioni}Dand \xyrequire{)hoptioni}R(collectivelyUUcalled`requests'):: ff2 9%\xyeverywithoptionUU{ ꧸hoptioniUU}{hcoGdeiUU}%\xyeveryrequestUU{ ꧸hoptioniUU}{hcoGdeiUU}Aff2ThisoOismostoftenusedbyanoptiontoactivqatesomehoGokUUeverytimeitisrequesteditself.׭7.2Option leformatuTOptionUU lesmusthavethefollowingstructure: <%%!Qhidenti cationi%%!Qhcopyright,UUetc.i?\ifx\xyloaded\undefined?\inputxy\fi\xyprovide{Mhoptioni}{ hnamei}{hversioni}% <{A@hauthori}{ hemaili}{haddressi}hbGodyUUoftheoptioni\xyendinputThe6argumentsto\xyprovideshouldcontainthe following:Lhoptioni(@Option}loadnameasusedinthe\xyoptioncommand./ThisxshouldbGesafeanddistinguish-ableforanyopGeratingsystemandisthuslimitedto {characterschosenamongthelowercaseletters(a?{z),digits{(0{9),and{dash(-?),andalloptionsshouldLbGeuniquelyidenti ablebythe rst6(six)charactersUUonly*.~hnamei$wDescriptiveUUnamefortheoption.hversioni+jIdenti cationUUoftheversionoftheoption.hauthori)βTheUUname(s)oftheauthor(s).hemaili$wThemelectronicmailaddress(es)oftheau- thor(s)UUorhthealiationifnoemailisavqailable.haddressi-#TheUUpGostaladdress(es)oftheauthor(s).(r:Thisinformationisusednotonlytoprintaniceban- :nerZbutalsoto(1)silentlyskiploadingifthesame:versionwaspreloadedand(2)printanerrormessage:ifUUadi erentversionwaspreloaded. -;The[`dummy'optiondescribGedinx20isaminimal:optionusingtheabGovefeatures.>Itusesthespecial:DOCMODEZpformatKtoincludeitsowndoGcumentationfor:thiswdoGcument(likeallocialwXY -picoptions)butthis:isUUnotarequirement.:7.3:Driveroptionse:The|hdriverioptionsdescribGedinpartIVrequirespe-:cialm'ExX2" #classor:packqageCkoptionsasdescribGedinx1.1).zThespecialthing:abGoutdahdriveriisthatloadingitsimplydeclaresthe:nameofit,establisheswhatextensionsitwillsuppGort,:andQselectsittempGorarily*.Thusthespecialcapabili-:tiesofthedriverwillonlybGeexploitedintheproduced:DVI՘ leչifsomeoftheseextensionsarealsoloadedand:ifthedriverisstillselectedwhenoutputisproGduced.:Generally*,7the^orderinwhichtheoptionsareloaded:isimmaterial. X(Knownexceptionsa ectonlyinter-:nal^>proGcessingandarenotvisibletotheuserinterms:ofElanguageandexpGectedoutput.)CInparticularone:drivercanbGepreloadedinaformatandadi erentone:usedUUforaparticulardoGcument.;TheUUfollowingdeclarationscontrolthis:: Zff2 瑍e\UseSingleDriverg5forcesUUonedriveronlye\MultipleDriversg5allowsUUmultipledriverse\xyReloadDriversg5resetsUUdriverinformation/ff2kff^ J= "5-:7LThekÎernelsupp'ExXthatdonothaveaclearlydistinguishedpreamble. As@theabGove@suggestsitsometimesmakessensetoloadhdriverisintheactualtextualpartofadoGcu-ment,-however,it3isrecommendedthatonlydriversalsoloadedeinthepreamblearereloadedlater,andthat\xyReloadDriversoLisusedwhenthereisdoubtabGoutthestateofa airs.YIncaseofconfusionthespGecialcommand\xyShowDriverswilllistallthepresentlysuppGortedandselecteddriver-extensionpairstotheTU>'ExXUUlog. ItI[isnotdiculttoaddsuppGortforadditionalhdriveris;5dhowisdescribGedintheTU>'ExXnicaldocumen-tation. Mostextensionswillprintawarningwhenacapa-bilityisusedwhichisnotsuppGortedbythepresentlyloadedhdriveri.>Suchmessagesareonlyprintedonce,however,s(forgsomeformatstheyarerepGeatedattheend).T Similarly*, when#thesuppGortofanextensionthatexploitsaparticularhdriveriisusedawarningmessagewillUUbGeissuedthattheDVI leisnotportable.*ٍPartffIs3ISExtensionsmThis@partdoGcumentsthegraphiccapabilitiesaddedbyeach"standardextensionoption.g-F*oreachisindicatedthe!describGedversionnumbGer,theauthor,andhowitisUUloaded. ManyD^oftheseareonlyfullysuppGortedwhenasuit-able+driveroption(describGedinpartIV)isalsoloaded,however,allpYaddedconstructionsarealwayspYac}'ceptedevenUUwhennotsuppGorted.#ʃ8]CurveffandSplineextensionۃ/t : cmbx9Vers.3.3bCyRossMoKore1 cmsy9hross@mpAce.mq.edu.aui Loadas:\xyoption{curve}iThisJ?optionprovidesJ;XY ?-picwiththeabilitytotypGesetsplinecurvesbyconstructingcurvedconnectionsusinggw:arbitrarydirectionalob8jectsandbyencirclingobjects :similarly*.N8Warning}:'ExX'smemory;youshouldthereforelimitthelength:andanumbGerofcurvesusedonasinglepage..Memory:use islesswhencombinedwithabackendcapableof:proGducingXitsowncurves;Ze.g.,YthePostScriptback-:end).ꍍ:8.1:CurvedconnectionsuT:SimpleUUwaystospGecifycurvesinUQXY U-picareasfollows:: ff2 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؎The@={!..}/omethod:for0xloadingthestackgivesequivqalentresultstous-:ingz;@={p+..}4G_,tsincez\xypolylineCӲignoresztheedge:extentsUUofeachhpGosiinthestack. s;Noted alsothattheargument#1Hto\xypolyline@af-:fectsUUwhatistypGeset.qAllowableUUargumentsare:: ?ff2 e\xypolyline{}g5solidUUlinee\xypolyline{.}g5dottedUUlinee\xypolyline{-}g5dashedUUlinee\xypolyline{*}g5 llUUenclosedpGolygone\xypolyline{?}g5 llpenclosedpGolygonusingg5even-oGddUUrulefde\xypolyline{{*}}g5useUU\dir{*}+jforUUlinese\xypolyline{}{5usingUU\dir{}sff29ڃThelattercasesonehas**\dir{...}AtbGeingusedtoconnecttheverticesofthepGolyline,gwith{{*}}!Obeingneededtoget**\dir{*}4 IJ.fSimilarly**\dir)isusedwhen\ahdriveriisnotavqailabletospGeci callysupportpGolylines;inkparticularthetwok` ll'options* and?willresultinadottedpGolygonoutlinetheregionintendedtoUUbGe lled. In+allcasesitisuptotheusertoloadthestackbGefore[calling\xypolyline{B[ڲ...}꧲.A[particularly[com-monʰcaseistheoutlineofanexistingʬXY J-pichob8jecti,asbintheexampleabGove.SF*uturebextensionsto\frmwill‘provideasimpli edmechanismwherebytheuserneedUUnotcall\xypolyline@jexplicitlyforsuche ects.*_.12 fdRotateffandScaleextensionzVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{rotate}LThis "extensionprovidestheabilitytorequestthatanyob8jectnbGedisplayednrotatedatanyangleaswellasscaledUUinvqariousways. These{uaree ectswhicharenotnormallyavqailablewithinTU>'ExX.[Insteadtheyrequireasuitable`back-end'option toprovidethenecessary\special1`commands,or߶extrafonts,=togetherwithappropriatecommandstoLW928<4*tj??gwimplementUUthee ects.qThus$X S(UsingU>thisextensionwillhaveU>nooe ectU>ontheoutputunlessusedwithOaU>backendthatexplicitlysuppGortsit.53232۞32fdYg3232$跍$fd;$fd323232ۡfdYg3232%C The8extensionprovidesspGeciale ectsthatcanbe usedwithanyXYY-pichob8jectibyde ning[ hshapGei]moGdi ers. Themodi cationislocaltothehob8jecticurrentlyWbGeingbuilt,wsowillhavenoe ectifthisob8jectisUUneveractuallyused. : The\followingtableliststhemoGdi ersthathavesofar PbGeende ned.ҹTheycomeintwo Ptypes P{eitherasinglekeyword,K1orakey-characterwiththefollowingtextUUtreatedasasingleargument.Mff2 􍍍A[@]fXalignwithcurrentdirectionA[@;hdirectioni]fXalignUUtohdirectioniA[@!U8hnumbGeri]fXrotateUUhnumbGeridegrees:A[*;hnumbGeri]fXscaleUUbyhnumbGeriA[*;hnumix,hnumiy·]fXscaleUUxandy.separatelyA[left]fXrotateHanticloGckwiseby90^A[right]fXrotateUU(cloGckwise)by90^A[flip]fXrotateby180^;ssameasfX[*-1,-1]񍍍A[dblsize]fXscaleUUtodoublesizeA[halfsize]fXscaleUUtohalfsize:ff2 These[hshapGei]modi ersspecifytransformationsofthehob8jecticurrentlybGeingbuilt.rIftheobjecthasarectangleedgethenthesizeoftherectangleistrans-formedtoenclosethetransformedob8ject;gwithacircleedgeUUtheradiusisalteredappropriately*. EachQ8successivetransformationactsupGontheresultofallprevious.6OneconsequenceofthisisthattheorderoftheshapGemodi erscanmakeasigni cantdif-ferencezinappGearance|ingeneral,transformationsdonotݧcommute. Evensuccessiverotationscangivedif-ferentUUsizedrectanglesiftakeninthereverseorder. : Sometimes}thischangeofsizeisnotdesirable.h>ThefollowingcommandsareprovidedtomoGdifythisbe-haviour. ۆff2 􍍍6_\NoResizing]6;preventsUUsizeadjustment6_\UseResizing]6;restoresUUsizeadjustmentsff2 u :The, \NoResizingBcommand, isalsousefultohave, atthe7bGeginningofadocumentbeingtypesetusingadriverthatcannotsuppGortscalinge ects, tinpartic-ularÓwhenappliedtowholediagrams.Inanycaseanunscaledversionwillresult,butnowthespacingandpGositioningwillbeappropriatetotheunscaledratherthanUUthescaledsize.gw:ScalingXandScaledT ext ThehshapGeimodi ercan :containVeitherasinglescalefactor,orapairindicating:di erent6factorsinthex-andy[ٲ-directions.Negative:vqaluesareallowed,toobtainre ectionsinthecoGordi-:nateUUaxes,butnotzero.%ߍ:Rotation0pandRotatedT ext Within*[@...](Bthe:...sareABparsedasahdirectioniloGcally*,xybasedonthecur-:rentqdirection.HThevqalueofcountregister\Direction:contains.theinformationtodeterminetherequested:direction.uWhennohdirectioniisparsedthen[@]{re-:questsUUarotationtoalignwiththecurrentdirection.9;ThespGecialsequence[@!...]._isprovidedtopass:anOPangledirectlytotheback-end. _TheOLXYP-picsize:and%shapGeofthehob8jectiwith\rectangleEdgeO~isun-:changed,eventhoughtheprintedformmayappGearro-:tated.@This(isafeaturethatmustbGeimplementedspGe-:ciallyLbytheback-end.F*orexample,JusingthePost-:Scriptback-end,![@!45]% willshowtheob8jectrotated:by45^insideabGoxofthesizeoftheunrotatedob8ject.;T opDo:`oProvide2exampleofrepGeated,9namedtrans-:formation.%ߍ:Re ections Re ections?canbGespeci edbyacom-:binationofrotationanda ip|either[hflip].or:[vflip] %.:Shear۰transformations T oDo:=Provide|@thestruc-:tureCtosuppGortthese;;'thenimplementitinPost-:Script.:Example Thevdiagramin gure10illustratesmany:ofdthee ectsdescribGedabovedaswellassomeadditional:onesUUde nedbythecolor ꛲androtate&*extensions.:Exercise22: SuggestEthecoGdeusedbytheauthor:toUUtypGeset10.9;TheH3actualcoGdeisgiveninthesolutiontotheexer-:cise.>#UseitasatestofthecapabilitiesofyourDVI-:driver.TheOlabGelsshould tsnuglyinsidetheaccom-:panyingUUrectangles,rotatedand ippGedappropriately*.;Bug: EThis> gurealsousescolours,\altersline-:thicknessandincludessomePostScriptdrawing.:Theg coloursmayprintasshadesofgray*,kywiththeline:fromAtoBbGeingthickerthannormal.Thewider:bandslopingdownwardsmayhavedi erentwidthand:lengthjaccordingtotheDVI-driverjused;u`thisdepGends:on$thecoGordinatesystemusedbythedriver,}when:`raw'UUPostScriptcoGdeisincluded.LW929M*tj??Ǎ>*㉍,$AH`/*B2s~>퀟r|Fl Fl|NlVȿl\^ʒalfe:lMlabGelUU8}0_''3232)3232?3232?z3232/ύ'Ǝn3232 323232323232323232323232323232323232323232323232.눟n3232 32323232323232323232323232323232323232323232323232''3232)3232?3232?z3232UZspGecialUUe ect:qalignedtext=Y3232s"32325323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323253232"N֍#3232323232323232323232323232323232323232323232323232323232323232wG323232323232323232323232323232323232323232323232323232323232323232=Y3232s"32325323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323253232;FigureUU10:qRotations,scalingsand ips9=Ǎ13wlColourffextensionVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{color}uTThis "extensionprovidestheabilitytorequestthatany ob8jectUUbGedisplayedUUinaparticularcolour. Itrequiresasuitable`driver'optiontoprovidethenecessary\special3k޲commandstoimplementtheef-fects.qThus S(UsingU>thisextensionwillhaveU>noEe ectU>ontheoutputunlessusedwitha֨dvi-driverU>thatexplicitlysuppGortsit.53232۞32fdYg3232$跍$fd;$fd323232ۡfdYg3232!f ColoursarespGeci edasahshapeimodi erwhichgivesthenameofthecolourrequested.$Itisappliedtoc/thewholeofthecurrenthob8jectiwhetherthisbGetext,?Xan9XY -pic9line,curveorarrow-tip,?XoracompGositeob8ject*Dsuchasamatrixorthecompletepicture.clHow-ever2someDVI2driversmaynotbGeabletosupportthecolourUUinallofthesecases. Zff2 0ٍ[ ?hcolourUUnamei]\NuseUUnamedcolouru\newxycolor{?hnamei}{ hcoGdei}\Nde neUUcolour\UseCrayolaColors\NloadUUcolournameswff2IftheDVI-drivercannotsuppGortcolourthenarequestforr2colouronlyproGducesawarningmessageinthelog le.AftertwosuchmessagessubsequentrequestsareignoredUUcompletely*.Named4coloursandcolourmoQdels Newcolournames%arecreatedwith\newxycolor=寲,Ytakingtwo%ar-guments.!=Firstly:|anameforthecolourisgiven,sfol-lowedbythecoGdewhichwillultimatelybGepassedtotheWoutputdeviceinordertospGecifythecolour.IfthecurrentdrivercannotsuppGortcolour,0orgrayscaleshading,thenthenewnamewillbGerecognised,butignoredUUduringtypGesetting.=Ǎ;F*orPostScriptdevices,3theXY -psPostScript :dictionaryde nesopGeratorsrgb,Icmykcandgray2cor-:respGonding)tothestandardRGBandCMYKcolour:moGdels#andgrayscaleshadings.0Coloursandshades:aredescribGedas:rgbrgborc]myk3cmykors:gray.,Uwhere"theparametersarenumbGers"intherange:0ޅr;g[;b;c;m;y;kP;sޅ1.hTheopGeratorslinktothe:built-incolourmoGdelsor,inthecaseofcmykforear-:lierversionsofPostScript,giveasimpleemulation:inUUtermsoftheRGBmoGdel.:Sa9vingS:colourandstyles Whenkstylesaresaved:using[=0hwordi]?,see,thenthecurrentcoloursetting:(ifany)issavedalso.zSubsequentuseof[햸hwordi]re-:coversthecolourandaccompanyingline-stylesettings. ;F*urthercolournamesarede nedbythecommand:\UseCrayolaColoursJthat(loadsthecrayon)6option,:inwhichmorecoloursarede ned. Consultthe le:xyps-col.doc)Bfor,thecoloursandtheirspGeci cations:inUUtheRGBorCMYKmoGdels.;xycra9yon.tex: Thiszoptionprovidesthecommand:toA[installde nitionsforthe68coloursrecognisedby:namebyT*omasRokicki'sdvips맲driver[11 ].GIThiscom-:mandUmustbGecalledfromahdriveri- lewhichcanac-:tuallyUUsuppGortthecolours.2:14PPatternffandTileextensionX:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{tile}:This\extensionprovidestheabilitytorequestthata: lledUUregionbGetiledusingaparticularpattern. ;This_isane ectnotnormallyavqailablewithinTU>'ExX.:InsteaditrequiresasuitablehdriverioptiontoprovideLW930Ę*tj??gwtheQnecessary\special0commands,Qtogetherwithany extraGTcommandsneededtoimplementthee ects.Thus"'9 S(UsingU>thisextensionwillhaveU>noEe ectU>ontheoutputunlessusedwitha֨dvi-driverU>thatexplicitlysuppGortsit.53232۞32fdYg3232$跍$fd;$fd323232ۡfdYg3232"':All:e ectsde nedinthetileuextensioncanbGeimple-mentedgusingmostPostScripthdriveris,Lloadedas\xyoption{$hdriveri}?.P9atterns PatternsarespGeci edasahshapeimodi- er,PsimilartothewaycoloursarespGeci edbyname.TheP8patternisappliedtothewholeofthecurrenthob8jectiJwhetherthisbGetext,ΈanFXY 6J-picline,curveorarrow-tip,gor0acompGositeob8jectsuchasamatrixorthe|completepicture.However|someDVI-drivers|maynotUUsuppGortuseofpatternsinallcases. !ԍ IfthecurrentDVI-drivercannotsuppGortpatternsthenarequestforonesimplyproGducesawarningmes-sageginthelog le."AftertwogsuchmessagessubsequentrequestsUUareignoredcompletely*. ԉff2 83[shnamei]=useUUnamedpattern!ԍ3\newxypattern{?hnamei}{ hdatai}=spGecifyUUnewpatternusinghdatai3\UsePatternFile{c3|h lei}=setsUUdefault leforpatterns3\LoadAllPatterns{hsyh lei}=loadUUallpatternsinh lei3\LoadPattern{Sshnamei}{ h lei}=loadUUnamedpatternfromh lei3\AliasPattern{Xhaliasi}{ hnamei}{h lei}=letUUhaliasidenotepatternfromh lei.!։ff25n[AlthoughpatterndatamaybGespeci eddirectlyus-ingt\newxypatternH[,Mittismoreusualtoloaditfroma h leiinwhichmanypatternsarede nedbyname,eachGtonaseparateline.H$Byconventionsuch lesal-waysendin.xyp[(XY -pattern)sonoextensionshouldbGe/Ospeci ed.Thepatternisthenrequestedusingei-ther,hthenamesuppliedinthe leorbyanalias.d#Once\UsePatternFileR, hasl:bGeenused,qthenanullh leiar-gumentxtotheothercommandswillstill ndpatternsinZthedefault le.IThedefaultremainsine ectforthecurrentUUlevelofTU>'ExXgrouping. !ԍ F*orUUexample,thefollowingpicture"O Xl%3:<glL΍hl WVvl UThlPQvlRSusesUU` lled'framesfromtheframe ꛲feature:N8\AliasPattern{bricks}{mac12}{xymacpat} \AliasPattern{bars}{mac08}{xymacpat}gw:\xy?*+<5pc,3.1pc>{},{*[bricks]\frm{*}} *7,*+<2.5pc>[o]{},*[bars]\frm{*},*\frm{o}:\endxy騍:P9atterndata Aregionistiledusingcopiesofasin-:gleM`cell'regularlyplacedsoastoseamlesslytilethe:entireregion.TThehdataiappGearingasanargumentto:\newxypattern.hisUUultimatelypassedtothedvi-driver. ;TheKsimplestformofpatterndatais:hnumihHex-:datai,wherethedataisa16-characterstringofHex-:adecimaldigits;i.e.O0{9,[A{Fc.EachHex-digitequates:to4binarybits,Jsothisdatacontains64bitsrepresent-:ingpixelsinan8'8array*.Thehnumiisaninteger:countingc@thenumbGerof`0'samongthe64bits.T*aken:asafractionof64,thisnumbGeroritscomplement,rep-:resentsatheaveragedensityof`on'pixelswithinasingle:cellofthepattern.QDriversunabletoprovidethe ne:detailtofapatternmaysimplyusethisnumbGer,|orits:complement,4as+agray-levelorpartofacolourspGeci -:cationUUforthewholeregiontobGetiled.X獒:The lexymacpat.xypG4containsde ningdataforthe:38ŝstandardpatternsavqailablewiththeMacintoshOp-:eratingUUsystem.qFigure11displaysallthesepatterns.p:RotatingnandResizingP9atterns SomeNimplemen-:tationsuofpatternsaresucientlyversatiletoallow:extra\parameterstoa ecttheway\thepatterndatais:interpreted.uFPostScriptղisonesuchimplementation:inTIwhichitispGossibletorotatethewholepatternand:evenUUtoexpandorcontractthesizesofthebasiccell.;Duetotherasternatureofoutputdevices,wnot:allsuchrequestscanbGeguaranteedtoproGduceaes-:theticGMresultsonalldevices.mInpracticeonlyrotations:throughspGeci cangles(e.g30^,̔45^,60^)andpartic-:ularscalingratioscanbGereliablyused.{qThusthere:isnosophisticatedinterfaceprovidedbyXY <-pictoac-:cess3thesefeatures.VHowever3the`PostScriptescapGe':mechanism3doGesallowaformofaccess,:EwhenaPost-:ScriptUUhdriveriishandlingpatternrequests.;SpGecial$PostScriptoperatorspa~Bandpfsetthe:patternBangle(normally0)and`frequency'measured:inc}'ellsperinch.{Hence,whenusedasanhob8jecti-:moGdi er,e[!?30pa18.75pq]eGrotatesbIthepatternby:30^ cloGckwiseandusesasmallerpatterncell(larger:frequency).TheY2defaultfrequencyof12:5=300=(8@3):meansIthateachpixelinapatterncellcorrespGonds,on:aEdeviceofresolution300dpi,|toa3ø3Esquareofdevice:pixels;UUonsuchadevice18:75uses282UUsquares.;At*300dpiafrequencyof9:375)=300=(8ƫ4)*uses:4OE4vsquares.֌Thesematchthenaturalsizeforpixels:ona75dpiscreenandareprettyclosefor72dpiscreens.:Thoughbappropriateforscreendisplays,etheseare`toGo:chunky'A4forhighqualityprintedwork.5eDoublingthe:frequencyistoGo neforsomepatterns,hencetheinter-:mediate|vchoiceof12:5asdefault.*InorderforprintedLW931 a*tj??F˟s=ʍBŻ lled j=patternʍ:3232:32fd#ng3232닍:lRYfd^sYfd32:3232:fd#ng3232: 6k#e@?mac01ɍms lled jhM`patternɍe3Ǟ3232ef32fd#ng3232닍e.Yfd!ƉYfd32e3Ǟ3232effd#ng3232eM` 6k#e@j^mac02ȍ!s lled jpatternF|ᥞ3232מ32fd#ng3232닍 YfdϤYfd32ᥞ3232סfd#ng3232R۱> 6k#eg mac19P({Q lled jpatternF{3232³32fd#ng3232닍uYfd}Yfd323232³fd#ng3232R۰ 6k#egnmac20P(z}- lled jVpatternFz=]3232p32fd#ng3232닍#ĉYfd +\Yfd32=]3232pfd#ng3232RۯV 6k#eghJmac21P(y+ lled jpatternFy93232k32fd#ng3232닍ѠYfd38Yfd3293232kfd#ng3232Rۮҟ 6k#eg&mac22P(xB lled j=patternFx:3232:G32fd#ng3232닍:|Yfd^Yfd32:3232:Gfd#ng3232Rۭ: 6k#eg?mac23P(wm lled jh`patternFweF3232ez#32fd#ng3232닍e-XYfd4Yfd32eF3232ez#fd#ng3232R۬e` 6k#egjqmac24zXBž lled j=patternqX:3232: 32fd#ng3232닍:lUYfd^sYfd32:3232: fd#ng3232}: 6k#eI?mac25zWms lled jhMcpatternqWe3ʞ3232ef32fd#ng3232닍e1Yfd!ɉYfd32e3ʞ3232effd#ng3232}eMc 6k#eIj^mac26zV!v lled j?patternqVᦞ3232؞32fd#ng3232닍 YfdϥYfd32ᦞ3232ءfd#ng3232}? 6k#eI mac27zUR lled jpatternqU3232´32fd#ng3232닍uYfd}Yfd323232´fd#ng3232} 6k#eIomac28zT}. lled jVpatternqT=^3232p32fd#ng3232닍#ʼnYfd +]Yfd32=^3232pfd#ng3232}V 6k#eIhKmac29zS+ lled jpatternqS:3232l32fd#ng3232닍ѡYfd39Yfd32:3232lfd#ng3232}ӟ 6k#eI'mac30zRB lled j=patternqR:3232:H32fd#ng3232닍:}Yfd^Yfd32:3232:Hfd#ng3232}: 6k#eI?mac31zQm lled jh`patternqQeF3232ez$32fd#ng3232닍e-YYfd4Yfd32eF3232ez$fd#ng3232}e` 6k#eIjqmac322Bſ lled j=patternD2:3232:!32fd#ng3232닍:lVYfd^sYfd32:3232:!fd#ng32327g: 6k#ei?mac331ms lled jhMdpatternD1e3˞3232ef32fd#ng3232닍e2Yfd!ʉYfd32e3˞3232effd#ng32327feMd 6k#ehj^mac340!w lled j@patternD0᧞3232ٞ32fd#ng3232닍YfdϦYfd32᧞3232١fd#ng32327e@ 6k#eg mac35/S lled jpatternD/3232µ32fd#ng3232닍uYfd}Yfd323232µfd#ng32327d 6k#efpmac36.}/ lled jVpatternD.=_3232p32fd#ng3232닍#ƉYfd +^Yfd32=_3232pfd#ng32327cV 6k#eehLmac37-+ lled jpatternD-;3232m32fd#ng3232닍ѢYfd3:Yfd32;3232mfd#ng32327bԟ 6k#ed(mac381xFigureUU11:qThe38standardMacintoshpatterns.Tdoutput^tomatchthescreenview,@_aPostScriptop- erator8macfreq,[has8bGeende nedtofacilitaterequestsforUU9:375,via[!macfreq]77. ⍑ Thenextdiagramdisplayschangestothefrequency*.xÍʍ] lled j7patternʍ3232QO32fd#ng3232닍Yfd# Yfd323232QOfd#ng32327 6k#e@ 9.375ɍ@E lled j;patternɍ832328932fd#ng3232닍7TYfd[Yfd328323289fd#ng32328 6k#e@A12.5ȍy- lled jtVpatternȍp3232q 32fd#ng3232닍p$YfdۼYfd32p3232q fd#ng3232qV 6k#e?xh18.75Ǎ] lled j&patternǍՍ323232fd#ng3232닍YfdÌYfd32Ս3232fd#ng3232& 6k#e?x37.5%z] lled j7pattern:3232QP32fd#ng3232닍Yfd# Yfd323232QPfd#ng3232(-ٍ7 6k#e<ۍ 9.375%z@E lled j;pattern:8323289 32fd#ng3232닍7UYfd[Yfd328323289 fd#ng3232(-؍8 6k#e<ڍA12.5%zy- lled jtWpattern:p3232q 32fd#ng3232닍p%Yfd۽Yfd32p3232q fd#ng3232(-׍qW 6k#e<ٍxh18.75%z^ lled j'pattern:Վ323232fd#ng3232닍YfdÍYfd32Վ3232fd#ng3232(-֍' 6k#e<؍y37.5VFSa9vingkpatterns:I\Whenbstylesaresavedusinghwordi]?,tseenx??,thenthecurrentpattern(ifany)isalso^rsaved.Subsequentuseof[ ohwordi]recovers^rthepatternaswellascolourandline-stylesettings.̂Thisincludesa anyexplicitvqariationsappliedusingthe\StyleEscapGe"UUmechanism. HereLisavqariationofanearlierexample,Nwithextrae ects.%č}0,;eʎLύ.} WV<} UT.}PQ<}RSf}33 ff<L͍fd3232f932fd;g3232 kfJn 8Tfd} 8Tfd32fd3232f9fd;g3232g}f33<Jpf ff33ys^=R6ff cmss12Kilroyk0Fwas/here+Í\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}d:\endxy-7:15PImps3ortffgraphicsextension_:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{import}S:ThisfeatureprovidestheabilitytoeasyaddlabGels :and3annotationstographicspreparedoutsideTU>'ExXor:L5ffA͉TU>'ExX.&AnqXY Iu-picugraphicsenvironmentuisestablished:whose>coGordinatesmatchthatwithinthecontentsof:the٪impGortedgraphic,:makingiteasytospecifyex-:actlyIwherealabGelshouldbeplaced,orarrowdrawn:toUUhighlightaparticularfeature. @z;Acommand&\xyimport61is&de nedwhichisused,in:conjunctionSwithimpGortedgraphics,Ttoestablishaco-:ordinatesystemappropriatetotheparticulargraphics.:This?enableshpGosiitionswithinthegraphictobeeasily:loGcated,neitheriwforlabellingoraddingextraembellish-:ingUUfeatures.qItisusedineitherofthefollowways:: !ff2 ލ E\xyimport(=width,?height){ hgraphici} E\xyimport(=width,?height)( x-o ,y[ٲ-o ){hgraphici}@|ff2 Acommand}\xyimport9߲is}de nedwhichisused,DinconjunctionSwithimpGortedgraphics,Ttoestablishaco-ordinatesystemappropriatetotheparticulargraphics.This?enableshpGosiitionswithinthegraphictobeeasilyloGcated,neitheriwforlabellingoraddingextraembellish-ingUUfeatures.qItisusedineitherofthefollowways: !ff2 ލ E\xyimport(=width,?height){ hgraphici} E\xyimport(=width,?height)( x-o ,y[ٲ-o ){hgraphici}@|ff2LW932! s*tj??U* Z> 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 translateJ O3232 ҁ32fdUg3232/ fdtfd32 O3232 ҁfdUg3232SYɲframedUUcontentsofgraphics le> 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=tRationalUUpGointsontheellipticcurve:qǵx^3S+8y[ٟ^3d=7^ 1zǸ1+Rғ1#.s915zTPΟ UPYB l2P⟿²2P"?_3P+3P- ^1y#__y#?4'ExXimplementation.HoweverthehgraphicicouldbGeanybalancedTU>'ExXma-terialB8whatsoGever;provideditoGccupiesnon-zerosize,bGothUUverticallyandhorizontally*.D The)widthandheightarehnumbGeris)giveninthecoGordinatepsystemforthec}'ontentsofthehgraphicsi.Thesearenotdimensions,butcoGordinate-lengths,us-ing![theunitsappropriatetothepicturedisplayed![byhgraphici. Whenprovided,C( x-o ,?y[ٲ-o ) !givethedistanceincoGordinatei+unitsfrombottom-leftcornertowheretheorigin4kofcoGordinatesshouldbelocated,;usuallywithinarea*Kcoveredbythehgraphici.UsuallythenegativesofEthesenumbGersEwillgivethecoordinatelocationoftheFbGottom-leftcornerofthehgraphici.FIfnoo setsaresuppliedthentheoriginispresumedtolieatthebGottom-leftUUcorner. Normallythe\xyimport8ﻲcommandisusedatthebGeginning6)ofan\xy..\endxyB,1environment.CIt6)isnotnecessarytogiveanybasissetup,2forthisisdeducedbyb>measuringthedimensionsofthehgraphiciandusingthesuppliedwidth,R4heightando sets.ЫThehgraphiciitselfde nesnamedhpGosicalled"import"-,locatedattheoriginandhavingappropriateextentstodescribGethe~areacovered~bythehgraphici.DCThismakesitpar-ticularlyeasytosurroundthehgraphiciwithaframe,as!9ontheleftsideof gure12,+ortodrawaxespassingthroughUUtheorigin. HereOisthecoGdeusedtoapplythelabellingin g-ureUU12:s:\def\ellipA{\resizebox{6cm}{!}{% j4\includegraphics{import1.eps}}}:\xy:\xyimport(3.7,3.7)(1.4,1.4){\ellipA}*\frm{-}:,!D+<2pc,-1pc>*+!U\txt{%*7framed?contentsofgraphicsfile}\endxy:\qquad\qquad:\xy\xyimport(3.7,3.7)(1.4,1.4){\ellipA}:,!D+<2pc,-1pc>*+!U\txt{Rational?points*7on?theellipticcurve:$x^3+y^3=7$}:,(1,0)*+!U{1},(-1,0)*+!U{-1}:,(0,1)*+!R{1},(0,-1)*+!R{-1}:,(2,-1)*+!RU{P},(-1,2)*+!RU{-P}:,(1.3333,1.6667)*+!UR{-2P}:,(1.6667,1.3333)*!DL{\;2P}:,(-.5,1.9)*++!DL{3P},(1.9,-.5)*!DL{\;-3P}:,(-1,2.3)*+++!D{\infty}*=0{},{\ar+(-.2,.2)}:,(.5,2.3)*+++!D{\infty}*=0{},{\ar+(-.2,.2)}:,(2.3,-1)*+++!L{\infty}*=0{},{\ar+(.2,-.2)}:\endxyR};ThishexampleusestheL5ffA͉TU>'ExX2".standardgraphics:packqagebtoimpGortthegraphics leimport1.epsor\illustrationL~commands:inUUTexturesontheMacintosh.E;The#onlypGossibleproblemsthatcanoccurarewhen:thegraphicspackqageisloadedafterXY$-pichasbGeen:loaded.FGenerallyditisadvisabletohave`XY Td-picdloading:afterUUallothermacropackqages.LW933" ZϠ*tj??gw16wlPostScriptffbackendnVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{ps}OXY-psisa`back-end'whichprovidesXY=-picwiththe abilitytoproGduceDVI lesthatusePostScript\specials"BforUUdrawingratherthantheUQXY U-picfonts. [ Inc#particularthismakesitpGossibletoprintcXY #-picDVI les/onsystemswhichdonothavetheabilitytoloadthespGecialfonts.Thepenaltyisthatthegen-erateddDVId leswillonlyfunctionwithoneparticularDVIW*arning:TheproGducedDVI le isU>notp}'ortable[:ItcontainsPostScript qōAc\specialsU>forhoneparticularidriver83232۞32fdYg3232%豍%fd;%fd323232ۡfdYg3232%֍AvmorecompletediscussionoftheprosandconsofusingUUthisbackendUUisincludedbGelow.#216.1Cho`osingtheDVI-driverIncluding*\xyoption{ps}IX-within*thedoGcumentpream-ble,tellsdXY -picdthatthePostScriptalternativetothefontsWshouldbGeused,Xdprovidedthemeanstodothisisalso@spGeci ed.4Thisisdonebyalsospecifyingadvi-driverwhichiscapableofrecognisingandinterpret-ing \special1(commands.-Although the lexyps.texisߴreadwhentheoptionrequestisencountered,BKthemacros>containedthereinwillhavenoe ectuntilanappropriateUUdriverhasalsobGeenloaded. [ With\4L5ffA͉TU>'ExX2" bGoththebackend\4anddrivermaybGecspeci ed,alongwithotheroptions,viaasingle\usepackage-&'ExXv1.8+17oztexAAndrewUUT*revorrow'sO4zTU>'ExXv1.7ff<~;Other1\DVI-driversmayalsoworkusingoneofthese : les,VifVtheyuseconventionsVsimilartodvips!G,O4zTU>'ExX:or(Textures.?AlternativelyitshouldnotbGetoodif-: cultdEtowritethe lesrequired,husingtheseasabasis:indicating#thetypGeofinformationneededtosupport:thespGeci c\special1%commands.*JAnyoneattempting:to[edothisshouldinformtheauthorandconvey[easuc-:cessfulJimplementationtohimforinclusionwithinthe6XYj:-picUUdistribution. ;Note:In8somepreviousversionsof4XY 8-picthePost-:Scriptq;backendanddriverwereloadedsimultaneously:byƖacommandoftheform\UsePSspecials{Qihdriveri}?.:F*or backward-compatibilitythesecommandsshould:stillvwork,butnowloadingthelatestversionofthe:givenhdriveri. 5hHowevertheirfutureuseisdiscour-:agedxinfavourxoftheoption-loadingmechanism,@via:\xyoption{jhdriveri}?.\Thislattermechanismismore: exible,7bGothpinhandlingupgradesoftheactualdriver:suppGortandinbeingextensibletosupportmoregen-:eralUUformsof\special0commands.[;OnceoactivqatedthePostScriptbackendocanbGe:turnedOo andonagainatwill,ăusingtheuserfollowing:commands:: ff2  f\NoPSspecialsjV3cancelsUUPostScript f\UsePSspecials?{}jV3restoresUUPostScript ff2LThese=obGeynormalTU>'ExXscopingrulesforenvironments;hence7itissucienttospGecify\NoPSspecialsKGwithinanyenvironmentorgrouping.)UseofPostScriptwillbGeUUrestoreduponexitingfromtheenvironment.16.2%Whyuse>- cmcsc10PostScriptAtsomesitesusershavedicultyinstallingtheex-tralfontsusedbylXY -pic.The.tfmz lescanalwaysbGeinstalledSbloGcallybutitmaybenecessaryforthe.pkbitmapfonts(orthe.mfMETAF9ONTfonts)tobGein-stalledglobally*,Rbythesystemadministrator,forprint-ingjtoworkcorrectly*.]#IfPostScriptisavqailablethenXY -psUUallowsthislattersteptobGebypassed. Note:with^XY(b-psbitisstillnecessarytohavebthe.tfm]font]metric lescorrectlyinstalled,_asthesecon-tainUUinformationvitalforcorrecttypGesetting.[OtherXadvqantagesobtainedfromusingTXY4X-psarethefollowing:LW934# p*tj??gw  Circles#andcirclesegmentscanbGesetforarbitrary  radii.6  solidUUlinesarestraighterandcleaner.  TheirangeofpGossibleanglesofdirectionalsis greatlyUUincreased.  SplinecurvesaresmoGother. #1T*ruedottedand dashed0versionsarenowpGossible,g&usingequally spacedUUsegmentswhicharethemselvescurved.  The JPostScript leproGducedbyadriverfrom an\XY a`-ps`DVIB leisingeneralsigni cantlysmaller thanoneproGducedbyprocessingan`ordinary' DVI le8usingthesamedriver.3Onereasonforthis is5thatnofontinformationforthe1XY A5-picfontsis requiredinthePostScript le;=thisfurthermore meansthattheuseofXY !-picdoGesnotinitselflimit theUUPostScript letoaparticularresolution.^9  TheYlatestversionofUXY4Y-picnowenablesspGecial e ectssuchasvqariablelinethickness,gray-level and;colour.$Also,u*rotationoftextand(pGortions of)OdiagramsisnowsuppGortedwithsomedrivers. SimilarlyS"wholediagramscanbGescaledupordown to& tagivenareaontheprintedpage.%:F*uture versionswillallowtheuseofregions lledwith colourtand/orpatterns,aswellasotherattractive e ects.k SomeoftheabGoveadvqantagesaresigni cant,butthey#8comeataprice.pKnowndisadvqantagesofusingXY-psUUincludethefollowing:3  AMDVI lewithspGecialsforaparticularPost- Scriptk&drivercanonlybGepreviewedifapre- viewerisavqailablethatsuppGortsexactlythesame \special2rformat.AauseparateaPostScriptpre- viewerUUwillusuallybGerequired.6 HoweverWrecentversionsofxdvisuppGortviewing ofWIPostScriptusingeithertheGhostScriptpro- gram>Xorvia\DisplayPostScript". ,ThePost- Script{proGducedbywXY h{-pscanbeviewedthisway  DVIi lesjQcreatedusingjMXYQ-psinfactlosetheir \device-indepGendence". So3Upleasedonotdis- tribute4DVI leswithPostScriptspGecials|send eitherQtheTU>'ExXsourcecoGde,yexpectingQtherecipient to]haveYXY s]-pic >c@*^ 9,orsenda(compressed)Post- ScriptUU le.3Thelattercommentappliesto lesinwhichanyspGe-cialf`back-end'suppGortisrequired,+notjusttoPost-Script.WOfLcourseitcanbGeignoredwhenyouknowtheUUcon gurationavqailabletotheintendedrecipient.9bff^ J= "5-:9LMost%TAEMXPostScriptdrivÎersstoretheimagesofcharacters used1inthetextasbitmapsataparticularresolution.ThismeansbXthatthePostScript lecanonlybismoreecienttohavethePostScriptcom-:mandsJ?thatJ;XY ?-psneedsloadedinitiallyfromasepa-:rate \header" le.rT*ousethisfacilitythefollowing:commandsUUareavqailable...:^<ff2 4̿\UsePSheader?{}4̿\UsePSheader?{}4̿\dumpPSdict?{}4̿\xyPSdefaultdict1ff2 靍Normallyitissucienttoinvoke\UsePSheader{}Nj,whichJinvokesthedefaultnameofxy33dict.pro,re-ferring"tothecurrentversionofXY w"-pic.W-Theoptionalh lenameioOallowsadi erent letobGeused. Plac-ing<\dumpPSdict{..}VKwithin'ExXsystem.&"Usuallyitissucienttohavekacopyinthecurrentworkingdirectory*. Invok-ingEthecommand\dumpPSdict{}KTcwillplaceacopyofthe#requisite le,havingthedefaultname,inthecur-rentEdirectory*.This lewillbGeusedasthedictionaryfor^2thecurrentproGcessing,iprovideditisonthecor-rect[directorypath,5\sothatthedrivercanloGcateitwhen needed.CYConsultyourloGcalsystemadministratorifUUyouexpGeriencediculties.$%17 fdTPICffbackendVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{tpic}uTThisoptionallowstheXY -picfontstobGereplacedbytpic\special.{s,\bwhenusedwithadvi-drivercapa-ble"ofsuppGortingthem. +.ExtracapabilitiesincludesmoGother.lines,&$evenlyspaceddotted/dashedcurves,vqariable'ExXimplementationprovidesasuite8of\special3Xcommandstofacilitatethedraw-ingoflines,bGothon-screenandwithvqariousprintingdevices.[UThis`back-end'extensionallowsthelinesinXY -picUUdiagramstobGedrawnusingthesemethods. NoteIthatthisextensiondoGesnothaveItobeusedwithtem-TU>'ExX.ρBetterresultsmaybGeobtainedusingthePostScriptback-endanddvipshdriveri,Tsincea%versionofdvipsisavqailableforem-TU>'ExX.W7However,in-particularforscreenpreviewingpurpGoses,hitmaybeconvenientX,tousethisback-end.dF*urthermorenotethatdvipsUUiscapableofsuppGortingem-TU>'ExX\special)s. Onceǿloadedusing\xyoption{emtex}WǏ,Zwithanap-propriatem'ExXbackendUUo /on. [ff2 Jb\NoEMspecialsbv8turnsUUo em-TU>'ExXspGecials.b\UseEMspecialsbv8reinstatesUUem-TU>'ExXspGecials.ff2u~Of thecurvesde nedinthexycurve,extension,6onlysolidUsplinecurvesaresuppGorted.Thisisdonebytreat-ingethesplineasapGolygon(poly-line)withmanyseg-ments.gw:PartffIs3IIP:F=eatures;:ThispartdoGcumentsthenotationaddedbyeachstan- :dard\featureoption.F*oreachisindicatedthedescribGed:versionUUnumbGer,theauthor,andhowitisloaded. P;Thev rsttwo,1}`all'vand`dummy',describGedinxx19:andƮ20,6aretrivialfeaturesthatneverthelessproveuse-:ful sometimes.mThenexttwo,:Z`arrow' and`2cell',de-:scribGedM+inx21and22, providespecialcommandsfor:ob8jectsthat`pGoint'.Thefollowing,`matrix'inx23,:`graph'u]inx24,}_`pGoly'inx25,and`knot'inx28,arein-:putimo}'desӲthat'suppGortdi erentoverallstructuringof:(partsUUof)UQXY U-pictures."%:19PAllfffeatures}:Vers.3.3bCyKristo erH.Rosehkrisrose@brics.dki :Loadas:\xyoption{all} :AsaspGecialconvenience,#thisfeatureloadsasubsetof6XYj:-pic,^11 |namelyI&theextensions:kcurve!Dz(cf.x8),Kframe:(x9),qcmtip$(x10),qlinew(x11),qrotate)(x12),qcolor:(x13),*and Xthefollowingfeatures:WImatrix&(x23),arrow:(x21),UUandgraph ꛲(x24).)a:20PDummyffoption:Vers.3.3bCyKristo erH.Rosehkrisrose@brics.dki :Loadas:\xyoption{dummy} :This:optionisprovidedasatemplatefornewoptions,:itprovidesneitherfeaturesnorextensionsbutitdoGes:countUUhowmanytimesitisrequested.)a:21PArrowffandPathfeature:Vers.3.3bCyKristo erH.Rosehkrisrose@brics.dki :Loadas:\xyoption{arrow} :Thisafeatureprovides]XY 6a-picwiththearrowparadigm:presentedUUin[12 ]. P;Note:Y\PATH&b²command ff3=lastUUsegmentonly [ ffͤ fffd= ff3=everyUUsegment ffffd(whenDseveralapplytothesamesegmenttheyare insertedUUinthesequence<>+L).Thisisusefultodrawconnectionswitha`centermarker'inparticularwitharrows,e.g.,the`map-sto'[exampleexplainedbGelowcanbechangedintoaUU`breakto'example:qtypingN8\xy*+{0}\PATHQ~={**\dir{-}}Q~>{|>*\dir{>}}Q~+{|*\dir{/}}Q'(10,1)*+{1}?'(20,-2)*+{2}(30,0)*+{3}\endxyewillUUtypGeset;BOԟ0^ò1VGιbR̟bNxQbJO֟bRП{7i2sqҞUo7ȟUj(UfôL]Un n3WekkteeA,e7eßՓm22ȞNote,=however,thatVwhatgoGesinto~+{hM...} ishlabGelsiRandthusnotahposi{itisnotanactioninUUthesenseexplainedabGove.gw:21c.# SpGecifying~{hstu i}ڱwillsetthe\failurecontin- :uation"tohstu i._ThiswillbGeinsertedwhenthe:last˸hsegmentiisexpGected|itcanevenreplaceit:orUUaddmorehsegmentis,i.e.,N8:\xy?*+{0}\PATH~={**\dir{-}}j4~{'(20,-2)*+{2}?(30,0)*+{3}}'(10,1)*+{1}:\endxy:isUUequivqalentto:\xy?*+{0}\PATH~={**\dir{-}}j4'(10,1)*+{1}?'(20,-2)*+{2}(30,0)*+{3}:\endxy:typGesetting9)0U1MyιbIybEQbA)brŸi2jKUfUa(U]L]U3elkte~>A,ezşe :bGecause^when\endxy$=Visseenthentheparserknows:that!\thenextsymbGolisneitherofthecharacters:~'` !andChencethatthelasthsegmentiistobGeex-:pGected.pInstead,however,thefailurecontinuation:isZinsertedandparsed,3andthehpathiis nished:byUUtheinsertedmaterial.:F*ailureUUcontinuationscanbGenested::\xy?*+{0}\PATH~={**\dir{-}}*7~{~{(30,0)*+{3}}*7'(20,-2)*+{2}}?'(10,1)*+{1}:\endxy:willUUalsotypGesettheconnecteddigits.Gp:21d.?AUU\straightsegment"isinterpretedasfollows:#1.:First΃pissettotheendob8jectoftheprevious :segmentn(forthe rstsegmentthisiscjust:bGeforethepathcommand)andcissettothe:hpGosi-startingthehsegmenti,5|andthecurrent:hslideiUUisapplied.Gp#2.:Thenthe=sand(.5)ȍhitiAYGv.!Wj#hdigitiUUj qhletteriUUj{ĸhtexti}Rjhcsie-._^M-+_Y] -(_Tl^-%_O{-"_J-_EW-_@-_;-_6P-_1ף-_,- _'I- _#-_-_$B-_I5-^//fmD*/cjEr#m?uP?xIR?|iܟ r?o8?O?%?4(?G?Nt?"i?t&Y?q)̋?㚟-??V-0?4$>?;S7?; `?r#mκ__'\dKV2fdbKV_P_Thޟ_X΢_]4f_a*_e_KVooS,eQ85:wasUUtypGesetbyN8:\xy?<4pc,0pc>:(0,0)*7*+\txt{base}="base"*7\PATH?~={**\dir{-}?>*\dir{>}}%`l(-1,-1)*{A}?^a%`?(1,-1)*{B}?^b%`_ul (1,?0)*{C}^c%`ul^l?"base"?^dLW938' *tj??gwFP"base"?^e \endxyJBug:fT*urns$areonlyreallyresonableforpathsthatUUusestraightlinesliketheoneabGove.܍Note:AlwayswriteavqalidhpGosiafterahturni,otherwiseyanyfollowing^or_labGelscanconfusethe}parser.Soifyouintendthe^r{rin`^rotobGealabGel/thenwrite`,^r#,usingadummy,hpGosiition.Thendefaultusedforturnr}'adiusbcanbGesetbytheopGeration Cwff2 b@%\turnradiusUUhaddopi{Rhdimeni}ލff2thatworkslikethekernel\objectmarginetc.commands;UUitdefaultsto10pt.ExerciseT23: TypGeset]rӟꪵAlӟ@lӟGo}Ao}FvӟBvӟE}C}D^ko@^koGaY=AaY=FhkoBhkoEo}2;;JusingUUhturnis.21g.(The|xlastsegmentisexactlyasastraightoneex-ceptthatthe>action(ifany)isexecuted(andcleared)UUjustafterthe}(20,7)\endxy:typGesets\|Fм'0ҸʱK5~4<}jyju^Gjq]jl̟RjhR؝jc^=j_~j[Gdi}jVJjR0tjN<]jIj";:ExerciseT25: TypGesetUUthesearrows:<>K=J(ꪵA#BGA^0! 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TheDoriginfornudginglabGelsiswherethearrowcrossesthebisector._PositivenudgesmovethelabGeloutwardswhilenegativenudgesmovetowards~fe [۟gpcand:pGossibly}beyond.D@Thedefaultpositionofalabelison :theUUoutside,withedgeattheorigin.;TheoriginfornudgingtheArrowisatthemidpGoint:ofe~fe [۟gpc '@.AGpGositiveenudgemovesinthecloGckwisedirec-:tion.ThisUwillbGethedirectionofthearrowhead,unless:itUUhasbGeenreversedusing^R.;LabGels%#ona\..compositemapU areplacedrelativeto:thejTmidpGointofthecomponentarrows.Nudgesarein:units|of1pt.2Movement|isintheusualxXY |-picab}'oveand:b}'elow徲directions, suchthatapGositivenudgeisalways:outsideUUthetriangleformedbythearrowsandline~fe [۟gpc 0.>;The:uspGecialnudgevqalue<\omit>-4ղtypGesetsjustthe:Arrow,|omittingFthecurvedarrowsentirely*.Whenused:withlabGels,athenudgevqalue<\omit>)3causesthefollow-:ingUUlabGeltobeignored.ߍ:ExerciseT29: GiveUUcoGdetotypGeset gure15.:SuchKcoGdeisrelativelystraight-forward, Husing\nudg-:ing"and\omittohelppGositionthearrows,curvesand:Arrows.tItalsousesanexcursion,*asdescribGedbelow:inUUthesubsectionExtr}'aOptions3.ߍ:22.4 j:ExtraOptionsuT:Themfollowingfeaturesareusefulinnon-mathematical:applications.:1.pnoTArro9wuT:ThisMisdeterminedbyspGecialvqaluesforhtokiasthe: rst(oronly)characterinthecentrallabGel,̙asinthe:abGoveUUdescriptionofthestandardswitches.: Sff2|d '1SarrowheadsUUpGointingcloGckwise; `1SarrowheadsUUpGointinganti-cloGckwise; "1SarrowUUtipsonbGothends; !1SnoUUtipsatall.ⅉff2 육ThecentralArrowisomitted,=leavingsymmetricallyplacedJcurvedconnectionswitharrowheadsatthespGec-i edends. 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OTheactualob8jectcanbGechangedUUusing\modmapobjectG.. 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WhenNusedwiththe<\omit>*nudge,suchNexcursionsallowralabGelledArrowtobGeplacedanywherewithinanXY -picdiagram;furthermoretheArrowcanbGeorientedtoUUpGointinanydirection.,4.pF ancyTcurv9esByspGecifying\curveobjectFÈanarbitraryob8jectmaybGe'usedtoconstructthecurvedarrows.bIndeedwitha\..twocell7_di erent}ob8jectscanbGeusedwiththeup-pGer@andlower@curvesbyspGecifying\uppercurveobjectandUU\lowercurveobject\". These.spGeci cationsapplytoall2-cellssubsequentlyconstructedjWatthesamelevelofTU>'ExXgrouping.Alter-nativelyӵusinga~-switch,asinExtr}'aOptions2,allowssuchUUaspGeci cationforasingle2-cellorcurvedpart. Ob8jectssusedtoconstructcurvescanbGeoftwotypGes.Eitherfasinglehob8jectiissetonce,jwithcopiesplacedalong!'thecurve.`bAlternatively!'adirectionalob8jectcanbGe,alignedwiththetangentalongthecurve.InthiscaseUUuseaspGeci cationtakestheform: \curveobject{N?ڸhspaceri~**hob8jecti}?.HerehspacerimaybGeanyhob8jectiofnon-zerosize.TypicallyUUitisemptyspace,e.g.+Rhdimeni{} .,Exercise'30: Give/coGdetotypGesetthefollowingdi-agrams.6 j;[FUnM~]?SlH?YZϟx?_IH?e7A?k%z?qx?w?|&?^H?̘x?ПH? ?Jc MZϟ SIhY7A8_%yhekp&8v^|̘Пh 8Bh| p^^n9&qƍ gaMESgwIҍ卍Ground \State'TH99, @880a775_}p66:7$55>s55C)y44H]?Rĺ33Mj22Q,11Vw՟<<11['{00_ӟ//dEغ..i0/⳰--mmp--r;U,,w*(++{3ܺ**v)){pȺ))~|((`,''g&&+&%%ܢ̍::con9tinuousTpAower#u ee ) ee,cgg* gg6 `ii3D1pii?Y/Pjj<|JHjjH9llEY48llQX@mmOEmm[VӟooXVӟood?кqqaqqn~`rrk%  rrw`tttEtt#@uu~%auuY-wwןwwǛ%`yy3;pyy'=]pulsedTemissionQZxNlsiC td͍IVӟgf]Vӟed(IVӟ`a]Vӟbc͍MVӟ_^]Vӟ]\ MVӟXY]VӟZ[卍0*+{B}="B",*7+<2.0cm,0pt>*+{C}="C",*7+<1cm,-1.5cm>*+{D}="D",:"A";\goVia{\uppertwocell^\alpha{}}"B"{}:;\goVia{\twocell^\zeta_\xi{\gamma}}"C"{}:;\goVia{\compositemap{}}"D"{},:"A";\goVia{\lowertwocell{}}"D"{}:\endxyh!BX $ꪵA@̈́fdfe6Py+fdfe6tfdfe6r;fdfe7Ofdfe7X@㯄fdfe7V]fdfe7Wfdfe8"԰fdfe8gXԠ1fdfe8BԐfdfe8Ԁ?fdfe97vpfdfe9}afdfe9Rfdfe: Cfdfe:S\5fdfe:{'fdfe: fdfe;- xfdfe;vYfdfe;fdfe< fdfeʆfdfeL&αfdfeMΘ„fdfeM;΀IfdfeMtޟhfdfeMğP)fdfeM欟8fdfeN!!fdfeNX| fdfeNd1fdfeNLܢfdfeO4YfdfeO<ͰVfdfeOu͚fdfeOͅ"fdfeOҟofdfeP[fdfePXFafdfeP2fdfePrfdfeQZ fdfeQфfdfei&fdfei>fdfeiv „fdfeiޟIfdfeiƟ fdfej!+)fdfejZ6fdfej|B!fdfejdNfdfekLZ1fdfek>4ffdfekwsYfdfekˀVfdfekˍfdfel!ҟ˛"fdfelZ˨fdfel˷fdfel̊afdfemrfdfem>ZfdfemwBfdfem*fdfemBfdfen!!AfdfenZ1fdfenʟBfdfen̲Rfdfeocfdfeo>uVfdfeowh̆fdfeoP̘fdfeo8̫fdfep" ̽fdfep[AfdfepBfdfep؟fdfeq fdfeq>fdfeqw2fdfeqvFafdfeq^[fdfer"Fofdfer[.ͅ"fdfer͚fdferͰVfdfesYfdfes>̟ܢfdfesw1fdfes fdfes鄟!!fdfet"l8fdfet[TP)fdfetαfdfeuwܟʆfdfeuğфfdfeu鬟bfdfev"9fdfev[|1Vfdfe_+ݟ#v''KVfdfeK憟sfdfeLn JfdfeLXV&ۄfdfeL>@&fdfeL&Y+fdfeMqfdfeM;׊cfdfeMtޟעfdfeMğ׺fdfeM欟*fdfeN鋄fdfeNX|fdfeNd{fdfeNL. fdfeO4DSfdfeO<ZVfdfeOupfdfeO؅fdfeOҟؚfdfePدfdfePXKfdfePتfdfePrÄfdfeQZfdfeQۄfdfei&&fdfei> +fdfeivfdfeiޟcfdfeiƟꖄfdfej!߃fdfejZ*fdfej|ȋfdfejdڼfdfekLڰ{fdfek>4ڤ fdfekwڗSfdfekڊVfdfek}fdfel!ҟofdfelZafdfelSfdfel̊EKfdfemr6fdfem>Z'ÄfdfemwBfdfem* #fdfemjfdfen!kfdfenZ&fdfenʟțfdfen̲ٷʄfdfeo٦fdfeo>ٕVfdfeowhكfdfeoPqʄfdfeo8_fdfep" M&fdfep[:kfdfep'jfdfep؟#fdfeqfdfeq>ÄfdfeqwتfdfeqvKfdfeq^دfdfer"Fؚfdfer[.؅fdferpfdferZVfdfesDSfdfes>̟. fdfesw{fdfesfdfes鄟鋄fdfet"l*fdfet[T׺fdfet<עfdfet$׊cfdfeu qfdfeu>Y+fdfeuwܟ@&fdfeuğ&ۄfdfeu鬟 Jfdfev"sfdfev[|Vfdfe_GkR#v֐77b7`7b7P`7Pa7 dӥ 仟sRRRe؋wR,:RբRVܺ(({4jYBvP^l4jSq~tXRtZ]tA豘tB毺v~/Пfdfe/91fdfe/r뿄fdfe/ +fdfe/n(sfdfe0VFfdfe0V>dfdfe0&{fdfe07fdfe1фfdfe19ܟGfdfe1rğfdfe1˄fdfe1䔟2لfdfe2|OÄfdfe2Vdlfdfe2L/fdfe24fdfe3fdfe3:Kfdfe3rcfdfe3ҟYfdfe3亟2+fdfe4Mۄfdfe4Vigfdfe4rфfdfe4Zfdfe5B;fdfe5:*;fdfe5sfdfe5 ӄfdfe5&kfdfe6ʟ@߄fdfe6V[1fdfe6u_fdfe6Ȁkfdfe7hSfdfe7:Pfdfe7s8ܻfdfe7 ;fdfe7fdfe8(фfdfe8V֟Afdfe8Zۄfdfe8Ȧsfdfe9Yfdfe9:vfdfe9s^Kfdfe9FՏfdfe9.fdfe:fdfe:Vfdfe:5Cfdfe:̟Lلfdfe;dKfdfe;:{fdfe;sDŽfdfe;lфfdfe;Tfdfe<<{fdfeb3fdfe>WJfdfe>2ۄfdfe>fdfe?fdfe?: фfdfe?sП fdfe? 1fdfe?堟 Efdfe@ Yلfdfe@Wp nfdfe@X fdfe@@ fdfeA( fdfeA; OfdfeAs ˄fdfeAޟ #fdfeAƟ YfdfeB kfdfeBW [fdfeB~ 0'fdfeBf BфfdfeCN UWfdfeC;6 gfdfeCt yfdfeC fdfeC fdfeD֟ fdfeDW fdfeD 1fdfeDɌ 䟄fdfeEt fdfeE;\ fdfeEtD fdfeE, (fdfeE 9fdfeF JWfdfeFW ZфfdfeFʟ k'fdfeFɲ {[fdfeG kfdfeG; YfdfeGtj #fdfeGR ˄fdfeG: OfdfeH" ٱfdfeHX fdfeH fdfeH؟ fdfeI لfdfeI; $fdfeIt 3fdfeIx AfdfeI` OфfdfeJH ]fdfeJX0 kfdfeJ yۄfdfeJ fdfeK 3fdfeK;П fdfeKt fdfeK 1fdfeK憟 ?fdfeLn +fdfeLXV fdfeL> fdfeL& fdfeM {fdfeM; fdfeMtޟ !фfdfeMğ -DŽfdfeM欟 9fdfeN EKfdfeNX| PلfdfeNd \CfdfeNL gfdfeO4 rfdfeO< }fdfeOu fdfeO KfdfeOҟ fdfeP YfdfePX fdfeP ۄfdfePr fdfeQZ фfdfeQqfdfei&ڗfdfei>ՙfdfeivyfdfeiޟ5fdfeiƟτfdfej!EfdfejZfdfej|ɄfdfejdׄfdfekLfdfek>4fdfekw-fdfekfdfek fdfel!ҟIfdfelZafdfelzWfdfel̊s)fdfemrkلfdfem>ZdefdfemwB\τfdfem*UfdfemM9fdfen!E9fdfenZ=fdfenʟ4фfdfen̲,ifdfeo#݄fdfeo>/fdfeowh]fdfeoP ifdfeo8Qfdfep" fdfep[ fdfep 9fdfep؟ ڕfdfeq τfdfeq> fdfeqw لfdfeqv fdfeq^ Wfdfer"F fdfer[. Ifdfer fdfer }fdfes rfdfes>̟ gfdfesw \Afdfes Pׄfdfes鄟 EIfdfet"l 9fdfet[T -ńfdfet< !τfdfet$ fdfeu yfdfeu> fdfeuwܟ fdfeuğ fdfeu鬟 )fdfev" =fdfev[| /fdfevb fdfevJ fdfew2 1fdfew? fdfewx yلfdfew kfdfewҟ ]fdfex" Oτfdfex[ Afdfex 3fdfexp $fdfeyX ׄfdfey?@ fdfeyx( fdfey fdfey ٯfdfez"ޟ Mfdfez[Ɵ Ʉfdfez !fdfez͖ Wfdfe{~ ifdfe{?f {Yfdfe{xN k%fdfe{6 Zτfdfe{ JUfdfe|# 9fdfe|[ (fdfe|֟ fdfe|; fdfe} fdfe}? 䝄fdfe}xv /fdfe}\ fdfe}D fdfe~#, fdfe~\ fdfe~ yfdfe~ gfdfe̟ UUfdfe? Bτfdfex 0%fdfe Yfdfej ifdfe#R Wfdfe\: !fdfe" Ʉfdfe Mfdfe fdfe?؟ fdfex fdfe nfdfeꐟ Yׄfdfe#x Efdfe\` 1fdfeH fdfe0 τfdfefdfe@fdfexلfdfeПfdfe긟1fdfe#fdfe\rfdfep]/fdfeVG=fdfe>1)fdfe@&fdfeyfdfefdfeޟyfdfe#Ɵfdfe\τfdfeńfdfe|{fdfeddIfdfe@LLׄfdfey45Afdfefdfefdfe#fdfe\ҟՍfdfeIfdfe΢fdfeWfdfe@rsfdfeyZZلfdfeBAfdfe*(τfdfe$fdfe\9fdfeܹfdfeʟfdfeQfdfe@ifdfeyu]fdfej[/fdfeP@݄fdfe$8&ifdfe]  фfdfefdfe9fdfe؟9fdfe@fdfeyτfdfeiefdfevMلfdfe$^2)fdfe]FWfdfe.afdfeIfdfe fdfe@fdfey̟-fdfelfdfe뜟Ofdfe$2ׄfdfe]lɄfdfeTfdfe<Efdfe$τfdfeA 5fdfeyyfdfeܟdfdfeğFfdfe$(qfdfe] )fdfe|뽄fdfe88b7>`7>b7`7a7 > .k;The"coGdeshownisacompactwaytoplaceachain:of2-cellswithinapicture.Itillustratesastandard:techniqueforusing\afterPOS8Sto ndahpGositobe:usedforpartofapicture,thensubsequentlyreuseit.:Also)itispGossibletouse\drop!Corhdecoristospecify:theUU2-cells,givingthesamepicture.N8:\xy?*+{A}="A",+<1cm,1.5cm>*+{B}="B",*7+<2cm,0pt>*+{C}="C",*7+<1cm,-1.5cm>*+{D}="D",:"A";"B",{\uppertwocell^\alpha{}},:"B";"C",{\twocell^\zeta_\xi{\gamma}},:"C";?\afterPOS{\drop\compositemap{}}"D":\POS?"A";*7\afterPOS{\drop\lowertwocell{}}"D":\endxyh!;Theua\connect2ꪲvqariantuaisusuallypreferableasthis:maintainsthesizeoftheob8jectatc,ǖwhilethe\dropLW946/ *tj??gwvqarianteleavesarectangularob8jecthavingpandcon oppGositeUUsides.'-023wlMatrixfffeatureVers.3.3bCyKristo erH.Rosehkrisrose@brics.dki Loadas:\xyoption{matrix}|PThisboptionimplements\XY -matrices",'i.e.,matriceswhereUitispGossibletorefertotheentryob8jectsbytheir?row/columnaddress.'ExXrow&columnXformat,i.e.,whererowsareseparatedwith\\andcontaincolumnsseparatedwith&(wedis-cuss?inthefollowingsectionswhathsetupicanbGe).Thusamatrixwithmaxr}'ow#rowsandmaxc}'olcolumnswhereUUeachentrycontainsr}'ow,Scol]޲isUUenteredas03z Ӵ\xymatrix{) 1,1?&O 1,2?&u 1,maxc}'olp\\) 2,1?&O 2,2?& 2,maxc}'olp\\ԍ~^.~^.~^.d.E.hҟ.k_.) maxr}'ow0,1?&O maxr}'owr,2?& maxr}'ow,maxc}'olŁ}1[l(TU>'ExXnically3the& Hccharacterrepresentsany`alignmenttab',UUi.e.,characterwithcategorycoGde4).  AchmatrixicanappGeareitherinanXY.-picture(ashdecori)UUor\stand-alone". ThevfaspGectsinwhich\xymatrix:,di ersfromor-dinaryFmatrixconstructions,AsuchasPlainTU>'ExX's\matrix{)...} ?andUUL5ffA͉TU>'ExX'sarray ꛲environment,UUare C arbitrarytXY -pictƸhdecoriationsmaybGespeci edineachentryandwillbGeinterpretedinastatewherecUUisthecurrententry*, the9\entirematrixisanob8jectitselfwithreferencepGointUUasthetopleftentry*,and aAprogressmessage\X"isprintedforeachmatrixwithr}'owsHLc}'olsentriesandXY !-piccomplexitysizea(thenumbGerofprimi-tive#opGerationsperformed),-unlessthedeclaration\SilentMatricesUUisissued.gw;{}:\endxyB:willUUtypGesetNFշꪵAlKBFQ%Cl%DC3232C)32fd4g32321ȍCy^1|fdx1|fd32C3232C)fd4g3232B8B?D폟9D폟>J:J=P=ߟ;P=ߟ<9O:Bug:qDzMatrixUUnestingisnotsafe. J;Matrices-areoftenquiteslowtotypGesetsoasacon-:venienceallmatricescanbGesettocompile(andnot):automaticallyUUwiththedeclarations:@‰ff2 ZG,\CompileMatricesG,\NoCompileMatricesLff2\MatricesOcanbGecompiledornotindividually*,[byus-ingGtheexplicitcommands\xymatrixcompileand\xymatrixnocompileھaswellasbyencapsulatingintheUUusual\xycompileto{G.name[}{ @U...} ?(seeUUnote5e). Note::IMatrices9willonlycompilecorrectlyifallentriesstartwithanonexpandabletoken,ohi.e.,{0or\relax"CorUUsomenon-activecharacter.!N23.2%Newco`ordinateformats;ItispGossiblewithinentriestorefertoalltheentriesofthe=XY >A-matrixAusingthefollowingspGecialhcoordiinateforms: Nff2 Z "rG,c"^ݲPosition?andextentsofen-^try4LinrowrG,:columnc(top^leftUUis"1,1"F)#d[ rG,c]^ݲrrowsOsbGelow,ccolumns^rightUUofcurrententryX+[Hhhopi*UV]^ݲentryqreachedbyhhopis;^eachhhopiisoneofdulr^ݲdescribing`xone`move'`xtoa^neighbGorUUentry/X+[Hhhopi^+ hplaceiUU]^ݸhplaceionstraightlineto^non-empty7[ wϸhhopi*]ڰff2\SoKthecurrententryhasthesynonyms[0,0]z,[] ,[rl],[ud],[dudu]",etc.,ask!wellasits`absolute'name"rG,c"?. )Wff^ J=w-:12LInpgeneralitisrecommendedthatenÎtriesstartwithanon- expandingAVtokÎen,\Ui.e.,anordinary(non-activÎe)character,\U{,or\relax,XforcompilationtowÎork.LW9470 qo*tj??gw Theseformsareusefulforde ningdiagramswhere theUUentriesarerelated,e.g.,AO;ꪵABSO5SuOSO:OoTo%@k@hG4S@dO,@a9j @]V@Z+@O%BuW%CZg&"fdfe\g%"fdfe^g$"fdfe`g#"fdfebg""fdfedg!"fdfefg "fdfehg"fdfejg"fdfelg"fdfeng"fdfepg"fdferg"fdfe6ÍwasUUtypGesetbyN8$$\xy\xymatrix{QA?\POS[];[d]**\dir{~},[];[dr]**\dir{-}\\QB?&C\POS[];[l]**\dir{.}}\endxy$$ If#anentryoutsidetheXY +#-matrixisreferencedthenanUUerrorisrepGorted. Intcaseseveralmatricesareusedinthesamedia-gram,andptheyrefertoeachother,thenitisusefulto\givethematricesdi erent" hpre xi"hsetupi\suchthat;theycanrefertoeachotherusingthefollowingspGecialTcoordinateformsthatallhavethesamemean-ing\exceptthetargetentryispickedfromaparticularmatrix:dff2 ʍ8e{"=xhpre xirG,c"8e{["Buhpre xi"?rG,c]8e{["Buhpre xi"Rhhopi*UV]8e{["Buhpre xi"Rhhopi^+ hplaceiUU]@hff2 3ōInAfactabsolutereferencesmust4alwaysAbGegivenusing"?hpre xihrowi,hcoli",UUeveninsidethematrixitself. HereUUisanexampleusingthis:AnP-ꪵA:Bn!ǟ%C%Dk m3232k@_w_ A__ 8_832321ȍ΃jk'jԤ (323232 32΃jřg (323232 3232k m3232k@_w_ A__ 8_83232Pu2 qA^0k#fdfeikc9fdfeg˟ fdfef3>fdfedVfdfebDfdfe`kՄfdfe_AӟJȄfdfe];ͻfdfey- qBq^0 fdfeV-fdfe˟*fdfeifdfeBLfdfefdfeCnfdfePF͟/PC^0j$ʪfdfei N%f fdfeg*&nfdfeeG&Єfdfecey'82fdfea2'Ӕfdfe_(nfdfe]) Xfdfexџ/PDG^0a%"gfdfe.%Ufdfe&NCfdfeh&1fdfeV'zfdfeŸ( fdfeo(fdfeA󍍍M.3232MaI_W_ ___ _32323@$MGM~ vƍ323232 v32$O vƍ323232 v3232M.3232MaI_W_ ___ _3232AwaswetypGeset(usingthe`frame'extensionand`arrow'feature)UUby\xy \xymatrix"*"{%A?&B\\C?&D}% \POS*\frm{--} \POS-(10,3) \xymatrix{%A'?\ar@{.}["*"]&B'\ar@{.}["*"]\\C'?\ar@{.}["*"]&D'\ar@{.}["*"]}% \POS*\frm{--}\endxyr23.3%SpacingandrotationuTAny'matrixcanhaveitsspacingandorientationchanged[byaddingsetup`switches'bGetween\xymatrixgw:andUUtheopGening{R. z;ThedefaultspacingbGetweenentriesofmatrixis :changedUUwiththeswitches: Mff2 Kez@RhaddUUopihdimeniKez@ChaddUUopihdimeniKez@UUhaddopihdimenizff2+that|changerowspacing,ƌcolumnspacing,andbGoth,respGectively*, asindicatedbythehaddopiandhdimeni,wherethehdimenimaybGeomittedandcanbegivenas¯oneofR [andCtoindicatethecurrentvqalueoftheparameterUUinquestion.qNote:thereUUisnodefaultز. In)addition,ZXY +^-piccanbGeinstructedtousea` xedgrid'UUforthematrixwiththeswitches Mff2 n@!Rn@!Cn@!zff2+thatuensurethattherowspacing,columnspacing,andbGoth,respectively*,pretendingMthatallֲentrieshavethesizeFofthelargestentry(withoutmoGdifyingtherealsizeofBtheentries,}ofcourse,onlythespacing{togettheentriestor}'eallyBhavethesamesizeusea@* ...ohsetupidescribGedUUinx23.4below).qThespecialvqariants ʉff2]S@!0]S@!=hdimenizff2udpretendxthatentrieshavezeroorhdimeniheightandwidthPforcomputingrowandcolumnspacing;asabGoveinsertingR CCorCjustafterthe! CCmakesthisa ectonlytherowor columnspacing,e.g.,@!R0 *meansthattherowUUspacingonlyisbGetweenthecentersoftherows. z Finally*,nthetspacingofthingsthataretypGesetcanbeadjustedUUseparately: Mff2Kez@MhaddUUopihdimeniKez@WhaddUUopihdimeniKez@HhaddUUopihdimeniKez@LhaddUUopihdimenizff2+willadjusttheentrymargin,entrywidth,entryheight,andlabGelseparationused(thelatterisactuallypassedtoUUthearrowfeature). z ThespacingcanalsobGechangedforenentireTU>'ExXgroupUUbythedeclarations Mff2"Z\xymatrixrowseptphaddUUopi{Rhdimeni}"Z\xymatrixcolseptphaddUUopi{Rhdimeni}zff2+TheUUdefaultspacingforbGothis2pcL. z T oưDo:optimize'5proGcessingofmatriceswithcon-stantUUgrid.LW9481 *tj??gw AnentirematrixcanbGerotatedbyaddingarotation hsetupiUUoftheform [։ff2 G\@a͸hdirectioni}ff2pThiszwillsettheorientationoftherowstohdirectioni(theidefaultcorrespGondstor ٲ,i.e.,rowsiareorientedleftUUtoright).,23.4%EntriesuTTheappGearanceofasingleentrycanbemodi edbyenteringUUitas ͝ff2B@*UUhob8jectihpGosihdecori}ff2g7This&makestheparticularentryignoretheentrymoGd-i ers.andtypGesetasakernelob8jectwiththesameref-erencepGointasthe(centerof)thedefaultob8jectwouldhaveUUhad. Additionalob8jecthmoGdi erismaybeaddedtoanotherwiseUUordinaryentrybyusingtheforms ͝ff2B|**[?hshapGei]RhentryiB|**{ReshmoGdi eri*}Rhentryi}ff2pThe rstsetsthedefaulthshapGeiforob8jects(cf.:6note4j),3mthesecondadefaultsize(change,cf.]Anote4g),_;andthelastmakesitpGossibletoaddanyhob8jecti"moGdi erofx4,Ue.g.,for"recenteringentriesaf-terTthedefaultentryformwhichisequivqalentto`!C+< 2oMobje}'ct, mar}'gin;8>@x'(withthee ectofcenteringtheob8jectUUandaddtheobje}'ctmarginc)UUtoallsides.,ExerciseT31: TypGesetUUthefollowingdiagram:7Lr՟A8Bq|=Aa}//kA2fdV@=BdlVd9gVfea}ꪵBlyAl9gfe`$ꪵAp)HBW=E!//k,!2fdjE$BQ8A5O ItisalsopGossibletousethese@ hsetupis(asusualbGetweenUU\xymatrix5ꏲandUUtheleading{R): [։ff2OA@*[?hshapGei]OA@*]=haddUUopihsizei}ff2g7whichareequivqalenttochangingallentriestobGehaveaswiftheyhadstartedwiththesimilar**-form.أT oDo:qDzAllowUU** OhaddUUopihsizeihentryiforentries. IfthedefaultsetofentrymoGdi ersshouldbechangedJthenthefollowingdeclarationmustbGeissuedbGeforerthe\xymatrix4@ɲcommand;ithisistheonlywayrtoactuallycswitchtheinitialdefaultcenteringandspacingo :։ff2+\entrymodifiers={ OhmoGdi eri*UV}}ff2upgw:Exercise9|32: HowdidtheauthortypGesetthefollow- :ingUUmatrix?(jBL͍:^Y/.@^Y-,:^Y()@^Y*+Ő\everyentry={ OhdecoriUU}ff2qwwill'inserthdecori rstineachentry;ڌinsidethecounterregisters\Rowand\Colaresettothecurrententry'srowUUandcolumn,respGectively*.qForUUexample,N8\everyentry={{\the\Row,\the\Col}}\xymatrix?@*[F]@*[o]{?{}\POS[];[r]**\dir{..}&\\?{}\POS[];[ur]**\dir{--}}willUUtypGesetL͍X3?>`3=<X389`3:;XӞ1;152fdfe6U2fdfe~62fdfe|72fdfez8/2fdfex8͟2fdfev9k2fdfet: 2fdfer:2fdfep;E2fdfen;2fdfel<2fdfej=2fdfeL͍|?>|=<|89|:;l1;23?>`3=<X389`3:;Xӟ1{N{{ MG{tK{mJ{fI{70Note:@_When usingcompilation, rchangesto\everyentryB%xande\entrymodifiers_willenot Xqre-sult inrecompilationevenwhentheconstructedmatrixchanges{youmayhavetoremovethe.xyc leUUmanually*.Exercise9|33: HowdidtheauthortypGesetthefollow-ingUUdiagram?veG3232ey32fd)g3232 ehfdfd32eG3232eyfd)g3232y8R:B=RLr}'ooteE@++`ϹW\*6cWWSWRpWeG3232ey32fd)g3232 ehfdfd32eG3232eyfd)g3232xýEDz3f&`)B)C3oo35fdeG3232ey32fd)g3232 ehfdfd32eG3232eyfd)g3232x#+E+Dz!4e ABRACVA@YAA`hKfeVGYnFVA:e@e//`2fd@*eG3232ey32fd)g3232 ehfdfd32eG3232eyfd)g3232x61LW9492 *tj??gwHints!:The;8arrowfeaturewasusedtomakethebGending arrowsk"andtheframeextensionfortheframesaroundeachUUcell.'ѻ24wlGraphfffeatureVers.3.3bCyKristo erH.Rosehkrisrose@brics.dki Loadas:\xyoption{graph};ThisV-optionimplements`XY -graph',VcaspGecialc}'ombina-toricdr}'awinglanguagev}suitable"fordiagramslike owcharts,directedUwgraphs,andvqariousformsoftrees.}ThebasemofthelanguageisreminiscentofthePIC[5]lan-guage(bGecauseitusesanotionofthe`currentlocation'andOisbasedon`moves'.ButOthecentralconstructionisa`map'combinatorthatisbGorrowedfromfunctionalprogramming. GXY -graph\makesuseoffacilitiesofthe`arrow'featureoptionUUwhichisthereforerequired. Figure?17summarisesthesyntaxofahgraphiwithnotes\bGelow.A hgraphicanappeareitherinanXXY \-picture(ashdecori)or\stand-alone".^13 HNote:ٲIfyouuse\xygraph{?...} |insideconstructionswhere& cissig-ni cant1(likeplainTU>'ExX's\halignorL5ffA͉TU>'EX'sarrayenvironment)tthenmakesuretoaddanextralevelofbracesUUaroundit.Notes;24a.(AUUmoveistoestablishanewcurr}'entnode[.i24b.faT*odr}'aw&somethingissimplytodrawalineorthespGeci edA\harrowifromthecurrentnoGdetothespec-i edRtargetnoGde.Thetargetthenbecomesthecur-rent noGde.AllthefeaturesofarrowsasdescribGedinx21canbGeused,#inparticulararrowscanbelabGelledandsegmented,abutwiththechangethathpath-pGosimeanshnodeiasexplainedinnotex21e.24c.IT*oymapoveralistQissimplytosavethecurrentnoGdeb?andtheninterpretthehlistiwiththefollow-ingUUconvention:i Start|eachelementofthelistwiththecur-rentUnoGdeassavedandpasthepreviouslistelement,UUand4 let Athe?ThnoGdeirefertothesaved AcurrentnoGdeUUexplicitly*.24d.faThe& and\\KspGecialmovesareincludedtomakeitxsimpletoenter`matrix-like'thingsasgraphs{notethattheywillnotbGeautomaticallyaligned,however,UUforthatyoushouldusethe!M*escapGe.4& ois>jthesameas[r]<˲and\\βisthesameas[r]!{y+(0,-1)-(0,0)}mZ$whichIXusesakernelescapGe eff^ J=w-:13LInXfactL#A TAEMXuserscanuseagraphenÎvironment.gw:tomovestothe rstcolumninthenextrow(where :theNM rstcolumnisonthey[ٲ-axisofthecurrentco-:ordinateUUsystem).ፒ:Note:SIfAyouusetheform*{F;...} forAnoGdesthen:youdon'thavetochangethemifyoudecidetouse:anUQXY U-matrix.:24e.# TypGesethitiandmakeitthecurrentnoGde.PAlso:saveswٸhitiforlaterreferenceusing"ָhidi"?:ifhitiis:a9simpleletter,ordigit,thenjustas"6hiti"?;ifhiti:is>oftheform{~text} qвor*...{text} qвthen>as"text"2ղ.:Withthe= additionitispGossibletosaveexplicitly:inJcaseseveralnoGdeshavethesametextoranoGde:has~atextthatitisimpracticaltouseforreference.:Inofactusingtheformhiti=" hidi" lwillonlysave:thecnoGdeas"Ƹhidi"andcnotVas"Ƹhiti"?!$Asaspecial:convenience{""x(thus{theemptyhidi)alwaysrefers:toӟꪵAbӟA_ӟ((H㡟 2fdfeI+풄fdfeIsвfdfeIfdfeJ2fdfeJK~fdfeJdfdfeJۡKfdfeK#32fdfeKkfdfeKfdfeKfdfeLC2fdfeLĒfdfeLӡfdfeMfdfeMc2fdfeMyfdfeMhfdfeN;XfdfeNI2fdfeNˡ:fdfeO,fdfeO[fdfeO2fdfeO롟fdfeP3fdfeP{fdfePá2fdfeQ fdfeQSزfdfeQђfdfeQ㡟2fdfeR+ŒfdfeRsfdfeRfdfeS2fdfeSKfdfeSfdfeSۡfdfeT#2fdfeTkfdfeTfdfeTfdfeUC2fdfeUfdfeUӡfdfeVŒfdfeVc2fdfeVђfdfeVزfdfeW;fdfeW2fdfeWˡfdfeXfdfeX[fdfeX2fdfeX롟fdfeY3,fdfeY{:fdfeYáI2fdfeZ XfdfeZShfdfeZyfdfeZ㡟2fdfe[+fdfe[sfdfe[Ēfdfe\2fdfe\Kfdfe\fdfe\ۡfdfe]#32fdfe]kKfdfe]dfdfe]~fdfe^C2fdfe^fdfe^ӡвfdfe_풄fdfe_c 2fdfeӟꪵAӟ((l㡟 2fdfem+풄fdfemsвfdfemfdfen2fdfenK~fdfendfdfenۡKfdfeo#32fdfeokfdfeofdfeofdfepC2fdfepĒfdfepӡfdfeqfdfeqc2fdfeqyfdfeqhfdfer;XfdferI2fdferˡ:fdfes,fdfes[fdfes2fdfes롟fdfet3fdfet{fdfetá2fdfeu fdfeuSزfdfeuђfdfeu㡟2fdfev+Œfdfevsfdfevfdfew2fdfewKfdfewfdfewۡfdfex#2fdfexkfdfexfdfexfdfeyC2fdfeyfdfeyӡfdfezŒfdfezc2fdfezђfdfezزfdfe{;fdfe{2fdfe{ˡfdfe|fdfe|[fdfe|2fdfe|롟fdfe}3,fdfe}{:fdfe}áI2fdfe~ Xfdfe~Shfdfe~yfdfe~㡟2fdfe+fdfesfdfeĒfdfe2fdfeKfdfefdfeۡfdfe#32fdfekKfdfedfdfe~fdfeC2fdfefdfeӡвfdfe풄fdfec 2fdfeIӞkkc2fdfeКfdfeӡ҄fdfeڄfdfeC fdfeZfdfe.҄fdfekAfdfe#S2fdfeۡefdfev҄fdfeKZfdfefdfeڄfdfes҄fdfe+̚fdfe~㡟2fdfe~횄fdfe~S҄fdfe~  ڄfdfe}áfdfe}{-Zfdfe}3<҄fdfe|롟Lfdfe|[2fdfe|[jfdfe|x҄fdfe{ˡZfdfe{fdfe{;ڄfdfez҄fdfezfdfezc2fdfezښfdfeyӡ҄fdfeyڄfdfeyCfdfexZfdfex҄fdfexk'fdfex#32fdfewۡ?fdfewJ҄fdfewKVZfdfewafdfevlڄfdfevsw҄fdfev+fdfeu㡟2fdfeufdfeuS҄fdfeu ڄfdfetáfdfet{Zfdfet3҄fdfes롟fdfes2fdfes[fdfes҄fdferˡZfdferfdfer;ڄfdfeq ҄fdfeqfdfeqc2fdfeq$fdfepӡ+҄fdfep2ڄfdfepC9fdfeo@ZfdfeoF҄fdfeokMfdfeo#S2fdfenۡYfdfen^҄fdfenKdZfdfenifdfemnڄfdfemss҄fdfem+xfdfel㡟}2fdfelfdfelS҄fdfel ڄfdfekáfdfek{Zfdfek3҄fdfej롟fdfej2fdfej[fdfej҄fdfeiˡZfdfeifdfei;ڄfdfeh҄fdfehfdfehc2fdfehfdfegӡ҄fdfegڄfdfegCfdfefZfdfef҄fdfefkfdfef#2fdfeeۡfdfee҄fdfeeKZfdfeefdfedڄfdfeds҄fdfed+fdfec㡟2fdfecfdfecS҄fdfec ڄfdfebáfdfeb{Zfdfeb3҄fdfea롟fdfea2fdfea[fdfea҄fdfe`ˡZfdfe`fdfe`;ڄfdfe_҄fdfe_fdfe_c}2fdfe_xfdfe^ӡs҄fdfe^nڄfdfe^Cifdfe]dZfdfe]^҄fdfe]kYfdfe]#S2fdfe\ۡMfdfe\F҄fdfe\K@Zfdfe\9fdfe[2ڄfdfe[s+҄fdfe[+$fdfeZ㡟2fdfeZfdfeZS ҄fdfeZ ڄfdfeYáfdfeY{ZfdfeY3҄fdfeX롟fdfeX2fdfeX[fdfeX҄fdfeWˡZfdfeWfdfeW;ڄfdfeV҄fdfeVfdfeVc2fdfeVfdfeUӡw҄fdfeUlڄfdfeUCafdfeTVZfdfeTJ҄fdfeTk?fdfeT#32fdfeSۡ'fdfeS҄fdfeSKZfdfeSfdfeRڄfdfeRs҄fdfeR+ښfdfeQ㡟2fdfeQfdfeQS҄fdfeQ ڄfdfePáfdfeP{ZfdfeP3x҄fdfeO롟jfdfeO[2fdfeO[LfdfeO<҄fdfeNˡ-ZfdfeNfdfeN; ڄfdfeM҄fdfeM횄fdfeMc2fdfeM̚fdfeLӡ҄fdfeLڄfdfeLCfdfeKZfdfeKv҄fdfeKkefdfeK#S2fdfeJۡAfdfeJ.҄fdfeJKZfdfeJ fdfeIڄfdfeIs҄fdfeI+КfdfeH㡞2fdfe:24f.MovingDAbyaseriesofhopsbissimplymov- :inginagridasthesequenceofdulr$YL(for:down/up/left/right)gindicates.Thegridisastan-:dardu\cartesiancoGordinatesystemwith3pcunitun-:lessh,thecurrentbaseisrede nedusing[]!{h ...}:with%anappropriatehpGosiitioncontaining:Gand:::asUUdescribGedinnote3d.:T oDo:b:DescribGe6;theuseofhmoveis6;withhplaceis:in4detail...Uin4particular(1)`untilpGerpendicular:toг...'and(2)`untilinterceptswith...'canbGe:coGded...:24g.ZThisY`escapGes'intotheUXY 4Y-pickernellanguageand:interpretsOthehpGosihdecori.]ThecurrentnoGdeis:thensettotheresultingcob8jectandthegridfrom:theUUresultingb}'ase[.:Theֱe ectofthehpGosihdecoricanbecompletely:hiddenwhfromwdXYh-graphbyenteringitas{\save:hpGosiUUhdecori\restore}2:.:24h.?It>ispGossibletoinsertahmatrixiinagraphpro-:vided"the`matrix'optiondescribGedinx23hasbeen:loaded:NEitCoverwritesthenoGdewiththeresultof:\xymatrix(*hmatrixi.AfterwardsÚthegraphgridis:set3asthetopleft`square'ofthematrix,:ci.e.,with:[d] andjW[r]adjustedjWastheyworkinthetopleft:entry*.:Bug:&[dr]Oimmediatelyafterthematrixwillwork:as[expGected,Je.g.,makethecenterof"2,2"$ theLW9503 *tj??gC ffffd TWSyntaxのActionX-ffd W\xygraph{hgraphi}のtypGesetUUhgraphifffd fdWhgraphi@F!_hstepi*のinterpretUUhstepisinsequenceiWhstepi@F!_hnoGdeiのmove^24aOtoUUthehnoGdeizG=Ej_-dFharrowiUUhnoGdeihlabelsiのdraw^24b8ݲlineUUtohnoGdei,withhlabelsiG=Ej_:dFharrowiUUhnoGdeihlabelsiのdraw^24b8ݸharrowiUUtohnoGdei,withhlabelsiiG=Ej_(ghlistiUU)のmap^24c1currentUUnoGdeoverhlistiWhnoGdei@F!_[ghmoveiUU]のnewUUnoGdehmoveidUUrelativetocurrentG=Ej_&j9jtc\\のnewUUnoGdeinnextcolumn/row^24dG=Ej_"dFhidi"のpreviouslyUUsaved^24e2noGdeG=Ej_?のcurrentlyUUmappGed^24c1nodeG=Ej_hnoGdeiUUhitiのhnoGdeiUUwithhititypesetandsaved^24e2thereG=Ej_hnoGdeiUU= "*hidi"のhnoGdeiUUsaved^24e2as"Rhidi" G=Ej_hnoGdeiUU! ꧸hescapeiのaugmentUUnoGdewithmaterialinanothermodezWhmovei@F!_hhopi*のhhopis^24f޲(dulr)UUfromcurrentnoGdeG=Ej_hhopi*UVhplaceiUUhmoveiのdoUUhhopis^24f޲butuseitshplaceiandhmoveiUUagainiWhlisti@F!_hgraphiUU, ꧸hlistijqhgraphiのlistUUofsubgraphs^24cWhescapGei@F!_{ghpGosiUUhdecori}のpGerformUUhposihdecori^24gzG=Ej_MghmatrixiのinsertUUhmatrixi^24h@4G=Ej_PghpGolygoniのinsertUUhpGolygoni^24iG=Ej_EghellipseiのinsertUUhellipsei^24iG=Ej_~ghsetupiのsetupUUparameters^24jffd FigureUU17:qǸhgraphis*Dgcurrent+`noGde,3butothersmightnot,3e.g.,[rr]_will notnecessarilyplacethecurrentnoGdeontopof"1,3"P.mV24i.DItbispGossibletoinsertahpolygonioranhellipseiinagraphprovidedthepoly)ʲoptiondescribGedinx25orFthearc؃optiondescribGedinx27hasbeenloaded,respGectively:V0itljwillhavecasthecurrentnoGde,pasthepreviousone,andthethecurrentbasehastheUUhhopis[r]jand[u]asbasevectors.Note:+lattices,iknots,etc.,can2QalsobGeusedbutno1]spGecialsyntaxisusefulsincethe!{ W...} syntaxisUUadequate.24j.aThis allowssettingofsomeparametersofthegraph:q!~hsetupiUUshouldbGeoneofthefollowing: ff2 !~:{fQharrowiUU}gwincludeUUwithevery: ꧲arrow!~-{fQharrowiUU}gwincludeUUwithevery- ꧲line!~*{fQhmoGdi ersiUU}gwincludeiwitheverynon-*gwnoGdefd!~hletteri{RhgraphiUU}gwde nenewgraphescapGegw!lthletteriAff2g:These/aredestructive:&Gthepreviousvqalueislost. :Noticep|thatthedefaultforthesecondis!~-{@{-}}:whichishowordinarylinesareobtained,andfor:thethirditis!~*{+}&$whichiswhydefaultnoGdes:areUUinmathmoGdeandhaveUUthedefaultmargin.):The "lastpGossibilityisalsoavqailableasacommand):ff2 Z~\newgraphescape{h}׸hletteri}{ hgraphi}):ff2 ×:that^CmakesthespGeci edescapegeneratethe:hgraphiͲasamacro;withititispGossibletopass:argumentssWtothehgraphiusingthestandardTU>'ExX:\def?methoGd:qTheUUdeclarationcodeN8:\newgraphescape{i}#1#2{*7[]!{+0="o#2"*=<10pt>{};p!#1**{},"o#2"j4-/4pt/*!E\cir<2pt>{}j4+0;p-/:a(-30)24pt/**\dir{-}="X2"j4;p-/:a(-60)24pt/="X1"**\dir{-}j4;?(.5),="i#2",j4p-/:a(-60)24pt/**\dir{-},j4"o#2"."i#2"."X1"."X2"}}x.:isL(rathercomplicatedkernelcoGde)thatmakesthe:noGdeG3escape!i-dntypesetan`inverter'orientedLW9514 *tj??gwwith;athedcornerastheoutputwithinputnamed "i n"Mand outputnamed"o n"suchthatthegraphN8\xygraph{?[]!iR1("i1"[l]x-"i1")-[r]z}kwillUUtypGeset:x!x!x xz z {) {) c0 ʹMgSMkwПdMoMs ~Mb fec0 @c0 c0 c0 c0 sm qoqkwpqgSȟhqc0 qfdfeN#'ՄfdfeO+BfdfeOe_ fdfeO|fdfeOfdfeP(fdfePTfdfePFfdfePp%fdfeQ ʟL'fdfeQLsʄfdfeQGfdfeQidžfdfeR &fdfeRNy!LfdfeRfP|fdfeR:fdfeS fdfeSYŸjfdfeSfdfemá++hPWd;jW_B~W[ 0_Wxlinefromthecentretothe rstvertexishorizon-tal,`pGointing\totheright.Anyotherdesiredorientationgw:canٽbGeobtained,uwithanynumbGerofvertices,ubyusing :theUU~={L...} ?asUUdescribGedbelow.);TheUUgeneralformfor\xypolygon;*is...: ^ff2 Ǎs\xypolygonDhnumbGeri"?hpre xi"{ hswitchesi...}_eff2>ƍwhereu^the"[hpre xi"andu^hswitchesiareoptional.' TheirusesUUwillbGedescribedshortly*. Aڝ\xypolygon<5>establishesڿpGositionsfortheverticesofTapGolygon.AtthesametimevqariousthingsmaybGetypeset,C3accordingtothespeci edhswitchesi.Anhob8jecti5maybGedroppedateachvertex,,\spGokes"drawnltothecentreandsuccessiveverticesmaybGecon-nectedsasthepGolygon's\sides".@LabelsandbreakscanbGeUUspeci edalongthespokesandsides. _c Eachmvertexisautomaticallynamed:"1",2"2"x),2...,"?hnumbGeri" <with"0"3ascentre.f!Whenahpre xihasbGeenmygiven,names"vhpre xi0" ,...,"ոhpre xihnumbGeri"areFusedinstead. FWhilethepGolygonisbeingcon-structedk9themacro\xypolynum9VTexpandstothenumbGerof1^sides,8while\xypolynode@"expandstothenumbGer1^ofeachPvertex,#spGokeandsideatthetimeitisproGcessed.ThisYoGccursinthefollowingorder: vertex1,sp}'oke1,vertex2,esp}'oke2,side1,vertex3,sp}'oke3,side2,...,vertexn,sp}'oken,sidenD1,siden_wherethe nalsidejoinsUUthelastvertextothe rst. Themacro\xypolyname>KholdsthenameofthepGoly-gon,which ishpre xiifsupplied.EInthiscasethevqalueofi\xypolynum:isialsostoredas\\fhpre xiNUMSIDES),'ac-cessibleUUoutsidethepGolygon. AsRstatedabGove,aRpolygonwithupto12verticesis /orientedsoastohavea atbase,6&whendrawnus-ingA|astandardsquarebasis.k)ItsverticesarenumbGeredinjsanti-cloGckwiseorder,commencingwiththeoneathorizontal-rightofcentre,"orthesmallestangleabGovethis~(seeexamplebGelow).Withmorethan12verticesthenvertex"1"isloGcatedonthehorizontal,extendingtotherightfromcentre(assumingastandardsquarebasis)./Byw"providingaswitchoftheform~={7hanglei}thenڱthevertex"1"uYwillbGelocatedontheunitcircleatmhanglei^ anti-cloGckwisefrom\horizontal"|morecorrectly*,NfromMGtheX-directioninthebasistobGeusedwhen|settingthepGolygon,whichmaybGeestablishedusingUUa~:{L...} ?switch.5w-d滏 $[x oC[x ![x !j[x #)[x %˟[x (Dm[x *[x ,ձ[x BKD  2fd)?"a _:) _5 _1k _,ف _(GI _# _"ٟ _ _۠/Y`1􌍍1 `13꿟`163^`18{`1:Ĝ`1= ;`1?Uڟ`1Ay`1-1)2G"b3uq0rY rY'sh!sh&wY"wY%z⚟#z⚟$Y Y'h!h&Y"Y%⚟#⚟$|Y2fdY_ف_|Y_~Y ~Y 'h !h &Y "Y %⚟ #⚟ $n`~rw |' yY n`ٟ`1`1bG`1fY fY 'gh !gh &kY "kY %n⚟ #n⚟ $n`mٟ`1p`1rbG`1pYRfdpY _tف _yY _ZY ZY'[h![h&_Y"_Y%b⚟#b⚟$dY2fddY_hف_mY_aٟ[x $čd[x fb_[x fYH fYH'ghH!ghH&kYH"kYH%n⚟H#n⚟H$ mٟ[x $čp[x rb_[x frw1$čd'1aA1~YH ~YH'hH!hH&YH"YH%⚟H#⚟H$ ~rw1$č|'1yA1pY|fdyYH_tفH_pYH_7@rw ' Y r1S2iS3]r4iR5R6r0H1A2 0`1H2`1r3þSųџcS84Qǟ*kEl/kQ5퍍@[x 7F#[x  r6 ƍ%ќ"%p7 ̹D!d DY8ת@fdB _ _nџ r9̿Qٹz Qzȧ6o-򍍍$hIExerciseT36: GiveUUcoGdetotypGesetthese.LW9525 Π*tj??gw OneimpGortantuseofhpre xiistoallowthevertices ofJ?morethanonepGolygontobeaccessedsubsequentlywithin>>thesamepicture.,Herearesomeexamplesofthis,#incorpGorating&the~:{...} Ͳswitch&toperformsim-plerescalings.YNFirstlytheedgesofadoGdecahedronasaUUplanargraph: ߟK➍bnA չH_*} -H[湟gHXo0HU_1Hs#vpHbZvm) vie vf}vq#:H)֎rQK:H)ss:H)tϛ:H)vß:H)[#:fd)[__`_c_h_l#_JhU_1Ő)hV\ŐW݇ŐYŐZ[ݟŐf}#HjHnCuHrHvŮHz6ȘpH~˂H؟kH)UkHz?H˟(HfHmHHaH` H&K}v*MΟ*v.Pȁv2Rpv6T/v:W v>Yc!vB[84vF^NvJ`VdvNb{9vRdȑvVgIŧvZi¾>v^k럿ԕvbnк4OfdOYΎ*4_54_@4_zKǟ4_uVܟ4_pa4_km4_fx4_a04_\E4_WZ4_Ro4_M4_H4_CŮ4_>ß4_i֍1!zjZJ:Fd\iIˆxiM2}iPti#vGG iGF Fߐ F F F F_ aq fh]G !hXϟ#DhTz~$qhP-%hKܟ')#hGG(u|hfJo@fe@f}jf}f}f}㇟' V|}6%Vx$qgVs#%VoJC!صVj \Vf}@V QnN.θ`U~iEU{*UwU6$( L T ^  -Y zT@AT~iT(RTK۹T^ 5;`59,5653Y51kis[iΟKifJofjfjfef}5f}f}&K}賋U*&{U/7kU0 >к84kA8DT|80 ?{64k}66K>\xy?/l1.5pc/:,{\xypolygon5"A"{}},{\xypolygon5"B"{~:{(1.875,0):}~>{}}},{\xypolygon5"C"{~:{(-2.95,0):}~>{}}},{\xypolygon5"D"{~:{(-3.75,0):}}},{"A1"\PATH~={**@{-}}'"B1"'"C4"'"B2"},{"A2"\PATH~={**@{-}}'"B2"'"C5"'"B3"},{"A3"\PATH~={**@{-}}'"B3"'"C1"'"B4"},{"A4"\PATH~={**@{-}}'"B4"'"C2"'"B5"},{"A5"\PATH~={**@{-}}'"B5"'"C3"'"B1"},"C1";"D1"**@{-},"C2";"D2"**@{-},"C3";"D3"**@{-},"C4";"D4"**@{-},"C5";"D5"**@{-}?\endxyNextHahexagonalpyramid,arectangularbGoxandanoGctahedralMcrystalspeci edasatriangularanti-prism.Noticethowthe~:{k...} switchtisusedtocreatenon-squarebases, allowingtheillusionof3D-pGerspectiveintheUUresultingdiagrams:,؍.(/=0t(/2M(/5&(/7<(/9[؟(/;z(/=(/?c(/Y.&H'?/P&H'0&H'2&H'3,o&H'4G$&H'5aٟ&H'6kt32fdfeO@32fdfeN 32fdfeL؞32fdfeK32fdfeOI{x32fdfezD;32fdfeym32fdfex32fdfew32fdfevG32fdfev 32fdfeu>͞32fdfeth32fdfesS32fdfer32fdfeqٞ32fdfeq32fdfep9_32fdfeoc"32fdfen32fdfem32fdfeMHrZ;ߟH*HGH{HHHMfd)kd_M3d_d_(ßd_d_Sd_rd_d_Md_𔨍9999C9q99[ K dX?#DŽfd#U_@_[__W_[__n_?<q,<K=<%N<_<p<<=%fdfeufdfe[Ƅfdfefdfefdfe(Ufdfel2fdfeşMfdfehfdfe95㍃fdfe}m|fdfekfdfeݟZԄfdfeJIfdfeM9 fdfe҅(%fdfe@fdfeZ[fdfe-vfdfee䑄fdfe932fdfe!֍3p32fdfe32fdfeAޞ32fdfe32fdfePL32fdfe׃32fdfe^32fdfe32fdfem(32fdfe_32fdfe{32fdfe͞32fdfe32fdfe;32fdfer32fdfe32fdfe32fdfe.32fdfeN32fdfe<32fdfeü32fdfeJ32fdfe*32fdfe~|v32fdfeǞ32fdfe32fdfei32fdfe 32fdfe9 32fdfeQ\32fdfei32fdfe32fdfeO32fdfe32fdfeyfdfeݟNƄfdfeAЄfdfegڄfdfe, fdfemfdfeџHfdfey5{fdfe= fdfefdfea fdfeşC*fdfeO)u4fdfe>fdfeHfdfeU Rfdfe`=\fdfe%offdfe遟pfdfezfdferIfdfe67fdfeifdfeu󛢄fdfe}32fdfe=^32fdfe 32fdfe032fdfele32fdfe32fdfe㿞32fdfel32fdfe[32fdfeƞ32fdfes32fdfe 32fdfeI͞32fdfez32fdfe'32fdfeԞ32fdfe832fdfet.32fdfe۞32fdfe눞32fdfe'532fdfeb32fdfe32fdfe<32fdfe32fdfeύY32fdfeҍ32fdfe\32fdfes32fdfeў32fdfe/32fdfeM32fdfe 32fdfeI32fdfe32fdfe8Y32fdfeO32fdfe \xy/r2pc/:?="A",+(.2,1.5)="B","A",{\xypolygon6{~:{(1,-.1):(0,.33)::}Q~<>{;"B"**@{-}}}}\endxy\quad?\xy/r2pc/:{\xypolygon4"A"{~:{(0,.7)::}}},+(.7,1.1),{\xypolygon4"B"{~:{(.8,0):(0,.75)::}}},"A1";"B1"**@{.},"A2";"B2"**@{.},"A3";"B3"**@{.},"A4";"B4"**@{.}\endxy\quad?\xy/r2pc/:{\xypolygon3"A"{~:{(0,.7)::}}},+(.7,1.1),{\xypolygon3"B"{~:{(-.85,0):(-.15,.8)::}}},"A1"\PATH~={**@{.}}'"B2"'"A3"'"B1"'"A2"'"B3"'"A1"?\endxygw:V ertexb_object: Unless^the rstcharacteris~1[,\signi- :fyinga\switch",լthenthewholeofthebracedmaterial:istakenasspGecifyingthehob8jectiforeachvertex.It:willobGetypesetwithacircularedgeusing\drop[o]...5:H)Y:H)E-c񝌸IWҾHLCLHPSHSP$hHWH@E2fdE_I_M_Q_V_E-c <IW -.vLvPSLvSPuvWjvQ-c$ iyTXŐU6ŐVŐX>>ŐYŸŐ`$ iy`Yw)_ )]w)\s)['w)l <h<BNHe&ѻHa̠a(H^rRH[HK8'f^l Tl Tll՟@l7l/lx\m-lC錜x7·l4!9Ud`7 "?.?hß錜9M鸟^,7^,xl^,?Ɵ^,x^,7p^,Rʟ^,$^,hğfd^~hğS_BS_~k$^RwRRʟmRUҟR>)RRxRڍ)Ս~k$Uʟ{TllBlpNl,l}l-lҟtklv\fevhß, ȹ:nRΟ. : x? Tb? ~7?C, dX,:,ն,e,  ,:¹,h,4,hğzfd^~BH_hğH_K$͟nRR'L\RxTR8/R \CR≞&Rm1RP.+ v\fe@DK퀍DK*W::\xy/r2pc/:?{\xypolygon12{\circ}},:+/r5pc/,{\xypolygon10{~<{-}~>{}{\circ}}},:+/r5pc/,{\xypolygon8{~*{\circ}~<=}}\endxyR:Switc9hes:Theallowableswitchesaregiveninthefollowingtable:: ff2 !O6~:{+-...}[dusefulUUforrescaling.O6~*{+-hob8jecti}[dhob8jectiUUateachvertex.O6~={+-hanglei}[dalignUU rstvertex.O6~<{+-...}[ddirectionalUUfor\spGokes";O6~<<{0O*harrowi}[duseUUharrowiforspGokes;O6~<>{0O*...}[dlabGelsUU&breaksonspokes.O6~>{+-...}[ddirectionalUUfor\sides";O6~><{0O*harrowi}[duseUUharrowiforsides;O6~>>{0O*...}[dlabGelsUU&breaksonsides.\ff2(č/IUsing~<<{/=harrowi} oFor~><{harrowi} oFismostappro-priate}whenarrowheadsarerequiredonthesidesorspGokes,ˏorQwhenlabels/breaksarerequired. Hereharrowi߲isasin gure14,ځsoitcanbGeusedsimplytospGecifythestyleofdirectionaltobeused.^Thus~<<{}sets0eachspGokeasadefaultarrow,ϧpGointingoutwardsfrom&Vthecentre;6~<<{@{-}}5;suppressesthearrowhead,while޵~><{@{}}1Ruses޵anemptyarrowalongthesides.LabGelsandbreaksarespeci edwith~<>{...} wdand~>>{...}꧲,where ]the{ `Z...} use ]thenotationforahlabGeli,UUasin gure13. Whennotipsorbreaksarerequiredthentheswitchesd5~<{$,...} Nܲandd5~>{...} Nܲared5somewhatfaster,sincelessproGcessingisneeded..{\...} andh~>>{...}꧲,,buthnowusingthekernel's˸hplaceinotationof gure1.*Infactanyker-nel)coGdecanbeincludedusingtheseswitches.With~<>thecurrentpandcarethecentreandvertexre-spGectively*,whilefor~>>ۛtheyarethecurrentvertexandu[thepreviousvertex.(Theconnectionfromvertex"?hnumbGeri"Ųtovertex"1" isdonelast.)f ThepyramidabGoveuisanexampleofhowthiscanbeused.BothLW9536 Fi*tj??gw~<{...} Q:andf~<<{fharrowi} canfbGespeci edtogether, but!onlythelastwillactuallybGeused; similarlyfor~>{...} ?andUU~><{UIharrowi}?.7<C,=KeUhe~[ebe"Пke&e+"B{e07Kne4tꙋe9e>VƟeC #eGGe!ύ4N:V1 :-:*M:'Ӣ:$:!L:::vK:c:P:>J: SJ~"IG5GF D_yBAQ?w=)<2:8m7JP'\#6d\,?y\5eG\>\GΟX\㍍8Qܟ8 8T88̟8CA'\:8\0R\'l@\rS\\VCL3 %荍KeJIIHH,#̟W(!>W,t_W1/H߀W5࡮W:<œW>ğWCJxWGl%fW 3=P =P %=P =P =P =P  =P =P =P 7%(b:w"*,:+:-:/:1T:3:4: 6:JsYlF2lBVAl>ڟvl9spl5\ 04l1l,>l(aן nQlYcL8!PLt!MQ!M!M(!NKd!N!Nܟ!OE!*nS4PS>E &SG䚂SC,9/z.b꒕zz'ΟEaz#%덍%%(%2=LS( S:՟1jSSO_ zG.)z?BMGz7W zFL8% .N{%PJ%R̟%;)J>BF&JB"cGJEOΟhJH}㝉J'_+Q_/#ğW_2_6_CLsʟ s{s Vws#BsHsI /:pwܟ3}#5 #C# }# #*:w:j: ::+ wU(UU$sUU ٟU&y3U?B@kh;pZh7ȟu0h44 zh0P!~hN=7[KI"AFDKǍT֍SmRҥR8.QL8kX-#N3rkX-OkX-QCkX-R kX-DIY32fdfeTJb(32fdfeKjV32fdfeLr32fdfeEZnBfdfeG:afdfeH/UfdfeIYHfdfeBʟGfdfeCJÄfdfeD*ߡ?fdfeEZmfdfe= !!fdfe?GJ fdfe@ffdfeBʟ fdfe9'fdfe; 9fdfe!rfdfe,!pɄfdfe5N!d0fdfe4&^!}τfdfe2n!nfdfe1$~! fdfe: +fdfe8& Gfdfe7!!cfdfe5N!_fdfe>`ڟcfdfe<Ÿfdfe; fdfe: fdfeBtn"fdfeANJfdfe?lfdfe>`ڟ~fdfeFA"ȄfdfeD}bfdfeCOfdfeBtn"fdfeIJfdfeHRfdfeGhfdfeFA"Bfdfen L&32fdfeKš32fdfeJ32fdfeI32fdfeOk32fdfe9NϞ32fdfeM32fdfeL32fdfe Q32fdfeSlPr32fdfeP&R32fdfeOp232fdfe͍S4ʞ32fdfegRk32fdfeR" 32fdfeQ32fdfefzfe^CW 3o_n4ƺ ʍo_nP덍pfPPqm2PrtP}~!ZE֟\kg^ `+ 1wG.(0ԟx$;jPk" 4}JwPz89#w9tz9r.93!ZF  S 3m...&.;.卍b..sj"fdj# 5̳X//uc"fdWP̳"fdAfGDjJ4ԟtfXo0XPDwXlXג[X4Xl~7Xs;" 6 v\def\alphanum{\ifcase\xypolynode\or?A\or?B\orC\orD\orE\orF\orG\orH\fi}\xy/r3pc/:?{\xypolygon3{~={40}}},{\xypolygon4{~={40}~>{{--}}}},{\xypolygon5{~={40}}},{\xypolygon6{~={40}~>{{--}}}},{\xypolygon11{~={40}}},{\xypolygon50{~={40}~>.}},?+/r8pc/,{\xypolygon7{~<<{@{-}}~><{}Q~<>{|*@{x}}~*{\alphanum}Q~>>{_{\alpha_\xypolynode^{}}}}}\endxyN8 Useofthe~={...} 4switchwasdescribGedearlier.Whenusingthe~:{...} ImorecanbGedonethanjustsettingGthebase.InfactanykernelcoGdecanbesup-plied!here.GItisproGcessedpriortoanyotherpartofthebpGolygon.3ThegraphicsstatehascatthecentreofthepGolygon,pattheoriginofcoordinateswithinthepictureJ?andhasbasisunchangedfromwhathaspre-viouslybGeenestablished.7ThecurrentpointcwillberesettothecentrefollowinganycoGdeinterpretedusingthisUUswitch. A4'further4asimpli cationexistsforsidesandspGokeswithoutvkharrowis. Ifhtokiisasinglecharacterthen~>htoki,~>{Ϊhtoki}?,~>{{htoki}}iallspGecifythedirec-tional\dir{9htoki}?;Ksimilarlywiththe~<sPswitch.^OntheQotherhand,compGounddirectionalsrequireallthebraces,UUe.g.q~>{{--}}1and~>{2{.}}-U=. AfterallswitcheshavebGeenprocessed,NremainingtokensareusedtospGecifythehob8jectiforeachvertex.Such%tokenswillbGeuseddirectlyaftera\drope ,.socaninclude+ob8jecthmoGdi erisasin gure3.cIfanhobjectihasalreadybGeenspeci ed,Ousingthe~*nswitch,thentheUUfollowingmessagewillbGewrittentotheTU>'ExXlog:=Xy-pic?Warning: vertexalreadyspecified,$discarding?unusedtokens:with"tokensattheendindicatingwhatremainsunpro-cessed.+SimilarlybextratokensbGeforethe{_...} ~ gener-ateUUamessage:=Xy-pic?Warning:discardingunusedtokens:gw:NestedTP9olygons :When|\xypolygon9xis|spGeci edwithineithera~<>{|u...} :orN~>>{N...} 9switchNforanotherpGolygon, ithenthe:innerpGolygoninheritsanamewhichincorporates:alsothenumbGerofthepartonwhichitoccurs,~4as:givenoby\xypolynode>/.OThisnameisaccessedusing:\xypolyname .8YIn thefollowingexampletheinnerpGoly-:gonisplacedusing~<>inordertoeasilyadjustits:orientationUUtotheoutwarddirectionofthespGokes.N8CK1ߡ?>=<89:;Rֲ1;1R1;2}Ylr>RҲ1;3џ?=?r|?Yɧ?hRԲ1;4ɧ鍍uϟx;{r~Y~Y?{r?x<?uП?0iK2ߡ*駟?>2駟=<*駟892駟:;CƟRԲ2;1+ğR2;28y?;?>Q|?A~ɧ?ŸRԲ2;3ɧ鍍 w#&O)~+ğRֲ2;4)~?&P?#? x?}A~l>R;8zP騟FfdVP騟_U=_Zҟ__g_d_0i+&3*駟?>2駟=<*駟892駟:;+ğ-*3;1Ÿ*-,3;2A w#&O)~+ğB-.3;3)~6C?&P3?#0k? x-?CƟ*-,3;41XA~l>R;8z8y?;h?>Q?A~@?2u +Vfe+2 k2222C+&4?>=<89:;h*-,4;1B-.4;2~Y6C?{r3?x<0k?uП-?*-,4;31XYlr>-*4;4џ?=h?r?Y@?Auϟx;{r~YP騟( ^fdVd',__i',_Zԟ',_U?',_P骟',_͟ +VfeՍZ8:\xypolygon4{~:{/r5pc/:}*7~<>{*\frm<8pt>{o}\xypolygon4{~:{/-2pc/:}1~*{\xypolyname\xypolynode}}}*7[o]=<5pc>{\xypolynode}};NoticehownestedpGolygonsinheritnames"1,1"9x,:"1,2"*+,W...,"4,1",...,"4,4"$fortheirvertices. DTIf:ahpre xiissuppliedattheoutermostlevelthenthe:names8bGecome:c" hpre xii;j"҈.hJSpecifyingahpre xifor:theinnerpGolygonoverridesthisnamingscheme.The:sameqnamesmaythenbGerepeatedforeachoftheinner:pGolygons, allowingaccessafterwardsonlytothelast|:pGossiblyusefulasamemorysavingfeaturewhenthe:verticesUUarenotrequiredsubsequently*.;F*our,levelsofnestinggivesaquiteacceptable\Sier-:pinskigasket".'M SsymbGolfontmsam5,at:5-pGoint‚size.OF*urtherlevelscanbGeachievedusingthe:PostScriptbackend,otherwiselinesegmentsbGecome:toGoUUsmalltoberenderedusingUQXY U-fonts.Cn[&ӟC"xmsam5CNYvcNY/[x ߍZ [x \%cCNY/&hfdH[w6_Y/6_u=]Vӟ`1}^3`1W/0CNVݟʮNqWV[x ߍWre[x YvʮCNVfdHXVӟϹ_V_N֍Y/`1}Z`1^w0CN\%ʮNqW]Vӟ[x ߍ^3[x `7ɟʮCN]VӟfdH_Ϲ_]Vӟ_N֍`w`1}a:`1Te͛CNR9ЈNJS4[x ߍT[x VݟЈCNS4ٚfdHT/Цh_S4Цh_(oV`1}WrN`1QubCNOTb.N$OC[x ߍP[x R9b.CNOCֳ3fdHQր_OCր_S4`1}T`1W/ubCNVݟb.N$V[x ߍWre[x Yvb.CNVֳ3fdHXVӟր_Vր_Y/`1}Z`1a͛CN`7ɟЈNJ`w[x ߍaQ[x cmЈCN`wٚfdHbxЦh_`wЦh_(od`1}dޟ`1^wubCN\%b.N$]Vӟ[x ߍ^3[x `7ɟb.CN]Vӟֳ3fdH_ր_]Vӟր_`w`1}a:`1eHubCNcmb.N$d[x ߍd[x fb.CNdֳ3fdHecր_dր_gx`1}hU`1MBNCNK;N#Ls[x ߍMPx[x OT;CNLs܌̈́fdHN4Y_LsY_ۢOB`1}P`1JC(CNHLaN׼I[x ߍIԟ[x KaCNIfffdHJB34_I34_;Ls`1}MPa`1Q(CNOTaN׼OB[x ߍP[x R8aCNOBfffdHQ34_OB34_;S4`1}T`1F.CNE2NUEV[x ߍF0[x HLCNEV?fdHGs ͹_EV _ԍI`1}I⦅`1CVCNAȓNBQ[x ߍC.[x E2ȓCNBQfdHDf_BQf_hmEV`1}F`1JCCNHLȓNI[x ߍIԟ[x KȓCNIfdHJBf_If_hmLs`1}MPa`1Te.CNR8NUS4[x ߍT[x VܟCNS4?fdHT. ͹_S4 _ԍV`1}WrM`1QCNOTȓNOB[x ߍP[x R8ȓCNOBfdHQf_OBf_hmS4`1}T`1W.CNVܟȓNV[x ߍWrd[x YvȓCNVfdHXVҟf_Vf_hmY.`1}Z`1hdNCNf;N#gx[x ߍhU[x jY;CNgx܌̈́fdHi:Y_gxY_ۢjd`1}k'`1eH(CNcnaN׼d[x ߍd[x faCNdfffdHed34_d34_;gx`1}hU`1l (CNjYaN׼jd[x ߍk>[x mZaCNjdfffdHl34_jd34_;n:`1}o˟`1a.CN`7ʟNU`x[x ߍaR[x cnCN`x?fdHbx ͹_`x _ԍd`1}dߟ`1^xCN\&ȓN]Vԟ[x ߍ^3[x `7ʟȓCN]VԟfdH_f_]Vԟf_hm`x`1}a;`1eHCNcnȓNd[x ߍd[x fȓCNdfdHedf_df_hmgx`1}hU`1oj.CNmZNUn:[x ߍo[x qCNn:?fdHoP ͹_n: _ԍq`1}rwo`1l CNjYȓNjd[x ߍk>[x mZȓCNjdfdHlf_jdf_hmn:`1}o˟`1rPCNqȓNq[x ߍrw[x t{ȓCNqfdHs[f_qf_hmtP`1}u`1@!bCN>q_.Nd> [x ߍ?[x A.CN> 3fdH@U_> _BBQ`1}C.t`1< CN;{N>";i[x ߍq_{CN;īfdH=Q_;i_> `1}?П`1CUCNA{N>"BQ[x ߍC.[x E2{CNBQ̄fdHD_BQ_EU`1}F`19`ihCN7U`N8/ş[x ߍ9 [x ;U`CN8/ŞefdH9 s3_8/şs3_:;i`1}q_.CN;ifdH=QL̹_;iL_Ӎ> `1}?П`1FhCNE2U`NEU[x ߍF/[x HKU`CNEUefdHGss3_EUs3_:I`1}I?`1CUB-CNA.NTBQ[x ߍC.[x E2.CNBQfdHDL̹_BQL_ӍEU`1}F`1JCB-CNHK.NTI[x ߍIӟ[x K.CNIfdHJAL̹_IL_ӍLs`1}MP``12 CN0Ο N1n|[x ߍ2KV[x 4Or CN1n| YfdH3/ğ &f_1n| &f_ m4 `1}5`1/>| `CN-*,N . ؟[x ߍ.겟[x 0Ο,CN. ؟31fdH/ _. ؟_1n|`1}2K?`15ğ `CN4Or,N 4 [x ߍ5[x 7,CN4 31fdH6h_4 _8/ğ`1}9 `1+؟CN*-N~ *4[x ߍ+[x -*CN*4 ʄfdH,n|٘_*4٘_[. ؟`1}.ꛟ`1(}4CN&^NW'L[x ߍ()j[x *-^CN'LcfdH) ؟1_'L1_58*4`1}+`1/>|CN-*^NW. ؟[x ߍ.겟[x 0Ο^CN. ؟cfdH/ 1_. ؟1_581n|`1}2K?`19`hCN7N~ 8/ğ[x ߍ9 [x ;CN8/ğ ʄfdH9 ٘_8/ğ٘_[;h`1}q^^CN;hcfdH=Q1_;h1_58> `1}?ϟ`1MBCNK NLs[x ߍMPx[x OT CNLs YfdHN4 &f_Ls &f_ mOB`1}P`1JC `CNHL,N I[x ߍIԟ[x K,CNI31fdHJB_I_Ls`1}MPa`1Q `CNOT,N OB[x ߍP[x R8,CNOB31fdHQ_OB_S4`1}T`1FCNE2N~ EV[x ߍF0[x HLCNEV ʄfdHGs٘_EV٘_[I`1}I⦅`1CVCNA^NWBQ[x ߍC.[x E2^CNBQcfdHD1_BQ1_58EV`1}F`1JCCNHL^NWI[x ߍIԟ[x K^CNIcfdHJB1_I1_58Ls`1}MPa`1TeCNR8N~ S4[x ߍT[x VܟCNS4 ʄfdHT.٘_S4٘_[V`1}WrM`1QCNOT^NWOB[x ߍP[x R8^CNOBcfdHQ1_OB1_58S4`1}T`1W.CNVܟ^NWV[x ߍWrd[x Yv^CNVcfdHXVҟ1_V1_58Y.`1}Z`1v+bCNt{.NdtQ[x ߍu+[x wG.CNtQ3fdHv_tQ_Bx[`1}y8`1rQCNq{N>"q[x ߍrw[x t{{CNq̄fdHs[_q_tQ`1}u`1yCNwG{N>"x[[x ߍy8ϟ[x {<{CNx[̄fdHz=_x[_{`1}|\`1ojhCNm[U`Nn: [x ߍo[x qU`CNn: efdHoQs3_n: s3_:q`1}rwp`1l B-CNjY.NTje[x ߍk?[x m[.CNjefdHlL̹_jeL_Ӎn: `1}o̟`1rQB-CNq.NTq[x ߍrw[x t{.CNqfdHs[L̹_qL_ӍtQ`1}u`1|=hCN{[x mZ,CNjd31fdHl_jd_n:`1}o˟`1aCN`7ʟN~ `x[x ߍaR[x cnCN`x ʄfdHbx٘_`x٘_[d`1}dߟ`1^xCN\&^NW]Vԟ[x ߍ^3[x `7ʟ^CN]VԟcfdH_1_]Vԟ1_58`x`1}a;`1eHCNcn^NWd[x ߍd[x f^CNdcfdHed1_d1_58gx`1}hU`1ojCNmZN~ n:[x ߍo[x qCNn: ʄfdHoP٘_n:٘_[q`1}rwo`1l CNjY^NWjd[x ߍk>[x mZ^CNjdcfdHl1_jd1_58n:`1}o˟`1rPCNq^NWq[x ߍrw[x t{^CNqcfdHs[1_q1_58tP`1}u`1CN4 N}[x ߍZ[x ^؟ CN} YfdH?* &f_} &f_ mކ`1}I`1M `CN~,N >[x ߍ[x 4,CN>31fdHކ_>_}`1}Z`1* `CN^؟,N ކ[x ߍ`[x |,CNކ31fdHΟ_ކ_?*`1}`1|>CN{<N~ {[x ߍ|t[x ~CN{ ʄfdH}}٘_{٘_[>`1}`1yCNwH^NWx[[x ߍy8П[x {<^CNx[cfdHz>1_x[1_58{`1}|]`1MCN~^NW>[x ߍ[x 4^CN>cfdHކ1_>1_58}`1}Z`1oΟCN|N~ ?*[x ߍ[x  CN?* ʄfdHr٘_?*٘_[Ο`1}|`1*CN^؟^NWކ[x ߍ`[x |^CNކcfdHΟ1_ކ1_58?*`1}`1rCN ^NWΟ[x ߍ|[x ğ^CNΟcfdHa1_Ο1_58r`1}5`10{t:\font\msamv=msam5?at5pt:\def\blacktriangle{\hbox{\msamv\char'116}}:\def\objectstyle{\scriptscriptstyle}:\xypolygon3{~:{/r5.2pc/:}LW9547 f*tj??gwQ~>{}~<>{?\xypolygon3"a"{~:{(.5,0):} Q~>{}~<>{?\xypolygon3"b"{~:{(.5,0):}Q~>{}~<>{?\xypolygon3"c"{~:{(.5,0):}Q~>{}~<>{?\xypolygon3"d"{~:{(.5,0):}~<>{?*!/d.5pt/=0{\blacktriangle}}}}?}}}}}}}N8NoteAtheuseofnaminginthisexample;HwhenproGcess-ingthismanualitsaves13,000+wordsofmainmem-oryand10,000+stringcharactersaswellas122stringsandUU319multi-lettercontrolsequences.&26wlLatticeffandwebfeatureVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{web}uTThis\featureprovidesmacrostofacilitatetypGesettingofarrangementsofpGointswithina2-dimensionallatticeorUU\web-like"structure. CurrentlyAtheonlyroutinesimplementedwiththisfeaturetaresome\quickanddirty"macrosfordroppingob8jectsatthepGointsofanintegerlattice."T oyDo:MoresophisticatedroutineswillbGedevelopedforlaterversionsUUofUQXY U-pic,astheneedarises. MathematicallyxspGeaking,letW~uԲandC~v&bevectorspGointinginindependentdirectionswithintheplane.ThenLthelatticespannedby+~u Sband銵~v Ρisthein nitesetofUUpGointsLgivenby:L0=b ca~u +8bG@~v };forUUa,bintegersK̻b SL:WithinXY v-picthevectorsՄ~u and#~v !ӲcanbGeestablished askthecurrentcoGordinatebasisvectors.ThefollowingmacrosUUtypGeseta nitesubsetofanabstractlattice. Hff2 Oi6w\xylattice#1#2#3#4q6#pGointsUUinlattice6w\croplattice#1#2#3#4#5#6#7#8q6#...inUUspGeci crectangle.ff2~⍖~Theparameters#1...#4"are~tobGeintegersamin ,vamaxA̲,bminandbmaxA̲,CsothatthepGortionofthelatticetobGeɟtypesetisthatcollectionofvectorsinLforwhichaminaamax!andUUbminbbmaxA̲.a.Aw/v]u!6Z t$s&"r)q*/>B-,B0]B36[B6B8#B;B <0;i?)iB]iE6\iHiJ$iMiN18KQ&JT]IW6]HZG\%ޑF_̑E`25c#f]i6^lŸn&۸qɸr32u {6_~ß'~}40] 6`ğ(5-//] /6a/ş/)//6*WWWV]WU6bWTƟWS*WRWQx]{ֵaXc\u(3232]3232P32323232323232323232323232323232323232323232Pܞ3232TZ\[ 323273232323232323232323232323232323232323232323232323232z 32327323232323232323232323232323232323232323232323232323232\u(3232]3232P32323232323232323232323232323232323232323232Pܞ3232s^(1)//.2fdad$劵s^(2)k^劺OOk,Aw4fegw:\def\latticebody{% :\ifnum\latticeA=1?\ifnum\latticeB=-1%:\else\drop{\circ}\fi\else\drop{\circ}\fi}:\xy?*\xybox{0;<1.5pc,1mm>:<1mm,1.5pc>:::,0,{\xylattice{-4}4{-3}3}*7,(1,-1)="a"*{\bullet}*+<2pt>!UL{a}*7,(-1,1)."a"*\frm{.}}="L":,{"L"+L?\ar"L"+R*+!L{s^{(1)}}}:,{"L"+D?\ar"L"+U*+!D{s^{(2)}}}:\endxyN8;IntheabGovecode,noticehowthebasisis rstestab-:lishedHthenthe\xylattice:VrtypGeset.NmDoingthiswithin:an\xybox%allowsaxestobGesizedandplacedappropri-:ately*.u SinceVklatticepGointsaredeterminedbytheir(in-:teger)tcoGordinatedisplacements,||theycanberevisited:toaddextrahob8jectisintotheoverallpicture.More:generally*,ntheȜoriginforlattice-coGordinatesisthecur-:renthpGosic,Iwhenthe\xylattice=Fcommandisen-:countered.Easycaccessibilityismaintained,g#asseenin:theUUnextexample.΍;When thebasisvectors~u Wandk~v ϲarenotpGerpendic-:ular5thecollectionofpGointswitha;bintheseranges:willٟ lloutaskewparallelogram.HGenerallyitisuseful:to7plotonlythosepGointslyingwithina xedrectangle.:Thisy&isthepurpGoseof\croplatticeCy,withitsextra:parameters(#5J...#8A̲determining(the`cropping'rect-:anglewwithinwhichlatticepGointswillbGetypGeset.'Other:pGoints$willnotbetypesetevenwhenaandbarewithin:the-spGeci edranges.dExplicitlythehorizontalrangeof:the,croppingrectangleisXmin0toXmaxA̲,withXminbGe-:ingtheX-coGordinateofthevector#5 2~9u,Ewhere#5isa:hnumbGeri_"(notnecessarilyaninteger)..SimilarlyXmax:istheX-coGordinateof#6=)~ug.ZTheverticalextentsare:YminandYmaxA̲,'givenbytheY8-coGordinatesof#7&E~v:andUU#8/x~8v respGectively*.\򍍍hG=ɸ q*,W|_ ohH3" !,j%#|, N/4pf=hIִF "65 5o>!+G| bP ahJpj #>Z51+^b^t |r:hK+q~5,|M6 msݳhL5(2iXq<X  k| ̸p |[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe[?32fdfe Iɍ32fdfe Iɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfeIɍ32fdfemɎfdfekBfdfeifdfeg쪟fdfee^fdfedfdfebƟfdfe`zfdfe^'.fdfe\2fdfeZ>fdfeXJJfdfeVUfdfeTafdfeRmffdfePyfdfeNΟfdfeLfdfeJ6fdfeHfdfeFfdfeDRfdfeBfdfe@ֺfdfe>nfdfe<"fdfe:֟fdfe9fdfe7>fdfe7>{fdfe9{fdfe:֟{fdfe<"{fdfe>n{fdfe@ֺ{fdfeB{fdfeDR{fdfeF{fdfeH{fdfeJ6{fdfeL{fdfeNΟ{fdfePy{fdfeRmf{fdfeTa{fdfeVU{fdfeXJJ{fdfeZ>{fdfe\2{fdfe^'.{fdfe`z{fdfebƟ{fdfed{fdfee^{fdfeg쪟{fdfei{fdfekB{fdfemɎ{fdfe썍7&32328l3232E3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232E3232'7 ڧ3232"32323232323232323232323232323232323232323232323232323232323232323232mrڧ3232"32323232323232323232323232323232323232323232323232323232323232323232327&32328l3232E3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232E3232:C?s^(1):B://lfd3TJVjZs^(2)RjZOORs^37v̶feF:\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{%*70;<3pc,1.5mm>:<0.72pc,1.65pc>::,{"o"*7\croplattice{-4}4{-4}4{-2.6}{2.6}{-3}3}LW9558*H*tj??gwQ,"o"+(0,1)="a"*{\bullet}*+!D{\alpha} Q,"o"+(1,-1)="b"*{\bullet}*+!L{\beta}Q,"o"+(0,-1)="c","o"+(-1,1)="d"Q,"a"."c"="e",!DR*{};"a"**\dir{.}Q,"e",!UL*{};"c"**\dir{.}Q,"b"."d"="f",!DL*{};"b"**\dir{.}Q,"f",!UR*{};"d"**\dir{.}Q,"e"."f"*\frm{.}}="L","o"."L"="L"Q,{"L"+L?\ar"L"+R*+!L{s^{(1)}}}Q,{"L"+D?\ar"L"+U*+!D{s^{(2)}}}\endxy6Then\latticebodyKmacro. AtweachlatticepGointwithinthespGeci edrangefora;b(andwithinthecrop-pingrectanglewhen\croplatticeFisused),(amacrocalled ;\latticebodyERis ;expanded.XThisismeanttobGeuser-de nable,soastobGeabletoadapttoanyspeci crequirement.qItUUhasadefaultexpansiongivenby...<D\def\latticebody{\drop{\bullet}}7:TheRfollowingmacrosmaybGeusefulwhenspecifying whatUUtodoateachpGointofthelattice. iff2 i\latticebodye0expandedUUatlatticepGointsi\defaultlatticebodyy0resetsUUtodefaulti\latticeAe0a-vqalueUUoflatticepGointi\latticeBe0b-vqalueUUoflatticepGointi\latticeXe0X-coGord,UUo setinpt Os...i\latticeYe0Y8-coGord, P...fromlatticee0origin.Ӊff2gAsintheexamplespresentedabGove,_+theob8jectdroppGedZ?atthelatticepointcanbevqariedaccordingtoUUitsloGcation,oromittedaltogether. Inthe nalexamplethe\latticebodyFmacropGer-formsoDacalculationtodecidewhichlatticepGointsshouldUUbGeemphasised:ɯ1':&: D2: D1:D0:mD/:)2D.:2…&N;:Z3::&9:08:87Cn6:M35:W4:5 $IV @[,A:HVRsV]ۤ>:go=:q4<:{;:Z&@TI:d\%TH:n! 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fdfe-fdfebZfdfebȠfdfeb%Kfdfebȵvfdfebj߽4fdfeb;v2fdfeb/wfdfecfdfec&ޠޢfdfec?]RfdfecZafdfecvFfdfecLݎfdfecnK2fdfecHfdfecҠ^fdfed܃bfdfedFǠBfdfedoufdfedfdfedFۂ|fdfedD2fdfee(fdfeeN.fdfeemڎfdfeeyS҄fdfee传fdfef-ffdfefN٩fdfefms2fdfefms2fdfef*=Äfdfef ~fdfeg0;jfdfegkƠؤfdfegʠsfdfegfDfdfeh'ĄfdfehiҠ2fdfehנ׿fdfehוNfdfei<mfdfeixFRfdfei8!!fdfej"lfdfejt/ۈfdfejȟֻ2fdfekҠ֜fdfekyfdfekdrfdfel7+Kfdfel3fdfelz(qfdfem@քfdfem5fdfemk^ fdfemfdfem2fdfen2fdfenJMOfdfenWfdfenVnfdfenJ@fdfeo89Ζfdfeov$qfdfeo҄fdfeofdfep5ս)fdfepxպ"fdfepշfdfep8յfdfeqDtմPfdfeqȠճyfdfeq9ճ2fdfe@Oة\vover@}{\vunder@\vunover@ة\hover@%{\hunder@S\hunoverǍYFigureUU19:qknotcrossingswithorientationsandlabGelpositionsp28f.aThe`characters<˲,c> wand| areusedtoindicateto which3stringpGortiontheob8jectisassociated;>with| denotingpthestringwhichcrossestheother,while< kand> u]denotetheinitialand nalpGortionsofthe`crossed'UUstring.\>28g.(A-simple-labGelenclosedinbraces,forexam-ple\vcross>{x}>>,Ɂissetinmath-moGdeusingthe\labelstyle;,/at0japre-determinedplaceonthestringUpGortion,Ushiftedineitherthe`above'Uor`be-low'0directionfromthecurveatthispGoint.(F*oreachcrossingdepictedin gure19onlydefaultvqal-uesUUareusedfortheplaceandshift-direction.)28h.faIfthe rstcharacterwithinthebraces{..}1̲is*e.g.^\htwist>{*9(@hob8jecti}?,lthengageneralhobjectimay)bGeplacedasalabel.BF*urthermoreifthe rstcharacteris^u۲or_or| ,Vthentheinterpretationis,Fe.g.k\vtwist<{^8}hanchorihiti}?,asBin14toplacehitiUUasalabGelalongan\arjofthearrow ꛲feature.28i.DAsecondcharacter< /yor>spGeci esthatanarrow-headshouldappGearatthepre-determinedplaceon9thechosenstring.[tHere>odenotesanarrow-headmpGointingwiththenaturalorientation,iwhile<pGointsagainst.5/Duetothecurvqatureofthestrings,itjisusuallybGestto\UseComputerModernTipsratherUUthannormalarrow-tips.28j.aT*o9mgeneratea`hole'use\knothole4yR,rorsimply\khole!,Has8followingtoken. DThisgeneratesa`break',U inTthesenseof21j.qIndeedsucha`hole'is:usedtoseparatethetwopGortionsofthe`crossed' :string.Defaultmsizefortheholeis5pt,whichis:alterableLNvia\knotholesize{M$hdimeni}?;normally:usedUUtosetthesizeforall]޲holesinadiagram.:28k.wIfCtheresulting\khole&iseithertoGolargeorper-:hapsknon-existent,̚thiscouldbGeduetoatechnical-:ity$inthewaybreaksincurvesarehandled.F3This:problem8shouldnotoGccurwiththestandardcross-:ings,busing,arectangularbasis,butitmayoGccur:with~non-rectangularbases.Aneasy` x'istoin-:cludeganextranull-br}'eakgonthestring,.using< Cd|a,:>*7|# or||8,whichshouldplacethezero-sizedbreak:atOparametervqalue.5onthecurve.oThespGeci ca-:tionI^shouldprecedea\khole$atahigherparameter:vqalue,UUorcomeafteroneatalowerUUvalue.|:Multiplebreaks,arrow-headsandlabGelsmaybGe:spGeci edalongthetwostringsofacrossing;#sim-:plyplacetheirspGeci cationsoneafteranother;le.g.:<>j4|1>>><{x}-j|2{y}>{z}ZYwasUUusedin gure19.:TheLEonlyprovisoisthatall`breaks'alongasingle:strandmustoGccurwithincreasingorderofparam-:eterNpGosition.o[Onthe`crossed'stringthisincludes:theautomatic`hole'tocreatespacefortheother:string.Hence]pitisadvisabletousejustthe(+..):andIJ(-..)!UvqariantsIJforsmalladjustments,andto:keepUUthesecorrectlyordered.:AdjustmenthofpGositionalongthestringscanbe:achievedusingahfactori,Poasin\vover$j|)(+.1)>I*ܲ.:Allowed syntaxis( hsignihnumi)where hsigniisLW962?H*tj??gw+ or-!toincrementordecrementfromthepre- de nedvqalue.?Alsoallowableare= orhemptyitosettheparameterpGositiontohnumi,&iwhichmustlieUUbGetween0and1tohaveanymeaning.֍Arrowheads canalsobGeplacedateither,Sorboth,endsofofthestringsformingacrossing.YThisisgovernedbyapairofbGooleans,initially{FF}.8Itishchangedforallq]subsequentstringsinadiagramby\knottips{..}Iz wheretherecognisedvqaluesare{FF},ta{FT}tU,ta{TF}Nand:{TT}:,tadenoting:tips(T?)ornotZ(F?)atthestartandendofeachstring.IT*oaddʰarrowtipsatthestartofstringsinaparticularcrossing,appGendcthe2-charactercombination=< ;similarly=>8addstipsattheends,Oifnotalreadyrequested.Theϗcombinations==(and=!spGecifybGoth({TT})andnone({FF})respGectively*. These2-characterpairscanbGemixedinwithanyspGeci- cationsjforlabGelsandbreaks,oetc.DMultiplepairscompGoundҴtheire ect;?inparticular=<=>\givesthesamexXresultas== R,while=!=<isneededtochange{FT}fQintoUU{TF}UI.TheseGarebGestusedwithsinglepieces,asinthefollowingUUequation."[r`hc//0Z2fdfew;܄fdfeĄfdfebƄfdfe>„fdfe|ړfdfefdfe<-fdfe+Zfdfea+fdfeE|fdfea|fdfezbfdfe ' fdfe SPfdfe fdfe Z2fdfe ,fdfe Rfdfe jzRfdfe =:fdfe ^}_fdfe ~>Ȅfdfe fdfe ZHfdfe ֟,fdfe "fdfe JCfdfe pZ2fdfe pZ2fdfe 2ffdfe (Rfdfe ʢnnfdfe Z2fdfe ҟfdfe 4fdfe Btfdfe 0Z2fdfe BrFfdfe U1҄fdfe hrNfdfe ~Z2fdfe fdfe >fdfe ΂fdfe Z2fdfe Z2fdfe "fdfe AuBfdfe qޟ8fdfe Zfdfe /Gʄfdfe vqfdfe6fdfe#zfdfeFIfdfejpfdfe9ۄfdfeZ_2fdfe᳟Pfdfe Ɵfdfe9Zfdfeh:fdfefdfe fdfe4:fdfe5ZRfdfemwh6fdfe{Lfdfe㾟Єfdfe!fdfebQfdfeΟfdfexfdfe0Z2fdfe0Z2fdfew;fdfefdfebfdfe>fdfe|Єfdfe{Lfdfe<h6fdfe+ZRfdfea:fdfe fdfefdfezfdfe 'Zfdfe Sfdfe Pfdfe Z_2fdfe 9ۄfdfe pfdfe jfdfe =:fdfe ^}fdfe ~>qfdfe Gʄfdfe Zfdfe ֟8fdfe uBfdfec// A"fdfe qޟ,fdfe ZHfdfe /fdfe vȄfdfe6_fdfe#zfdfeFIzRfdfejRfdfe,fdfeZ2fdfe᳟fdfe ƟPfdfe9 fdfeh:bfdfea|fdfeE|fdfe4+fdfe5Zfdfemw-fdfefdfe㾟ړfdfe!„fdfebQƄfdfeΟĄfdfex܄fdfe0Z2fdfe4`iHժ8r`h0Z2fdfew;܄fdfeĄfdfebƄfdfe>„fdfe|ړfdfefdfe<-fdfe+Zfdfea+fdfeE|fdfea|fdfezbfdfe ' fdfe SPfdfe fdfe Z2fdfe ,fdfe Rfdfe jzRfdfe =:fdfe ^}_fdfe ~>Ȅfdfe fdfe ZHfdfe ֟,fdfe "fdfec// AuBfdfe qޟ8fdfe Zfdfe /Gʄfdfe vqfdfe6fdfe#zfdfeFIfdfejpfdfe9ۄfdfeZ_2fdfe᳟Pfdfe Ɵfdfe9Zfdfeh:fdfefdfe fdfe4:fdfe5ZRfdfemwh6fdfe{Lfdfe㾟Єfdfe!fdfebQfdfeΟfdfexfdfe0Z2fdfec//0Z2fdfew;fdfefdfebfdfe>fdfe|Єfdfe{Lfdfe<h6fdfe+ZRfdfea:fdfe fdfefdfezfdfe 'Zfdfe Sfdfe Pfdfe Z_2fdfe 9ۄfdfe pfdfe jfdfe =:fdfe ^}fdfe ~>qfdfe Gʄfdfe Zfdfe ֟8fdfe uBfdfe J"fdfe pZ2fdfe pZ2fdfe 2fdfe >fdfe ʢfdfe Z2fdfe ҟrNfdfe 1҄fdfe BFfdfe 0Z2fdfe Brtfdfe U4fdfe hfdfe ~Z2fdfe nnfdfe (Rfdfe ΂ffdfe Z2fdfe Z2fdfe Cfdfe A"fdfe qޟ,fdfe ZHfdfe /fdfe vȄfdfe6_fdfe#zfdfeFIzRfdfejRfdfe,fdfeZ2fdfe᳟fdfe ƟPfdfe9 fdfeh:bfdfea|fdfeE|fdfe4+fdfe5Zfdfemw-fdfefdfe㾟ړfdfe!„fdfebQƄfdfeΟĄfdfex܄fdfe0Z2fdfe4`i+=0z?r`hc//0Z2fdfexVfdfe:fdfefdfeOZ2fdfeffdfe6҄fdfe"_vfdfehZ2fdfe.fdfe蒄fdfe 3fdfe uZH2fdfe vfdfe zRfdfe 3fdfe pZ2fdfe pZ2fdfe fdfe 嚟22fdfe rJfdfe VZ_2fdfe nfdfe z2fdfe Rfdfe 0Z2fdfe fbfdfe z2fdfe 2nfdfe Z_2fdfe BBJfdfe {22fdfe fdfe Z2fdfe Z2fdfe-fdfek:RfdfevfdfeZH2fdfe-&fdfeo蒄fdfe.fdfeZ2fdfe=_vfdfe6҄fdfeNfdfeZ2fdfeXƟfdfezfdfe^fdfe0Z2fdfec//0Z2fdfexVքfdfe:Rfdfe~fdfeOZt2fdfefTFfdfe/fdfe"fdfehZ2fdfe6fdfe}҄fdfe 3Mބfdfe uZ2fdfe 濾fdfe zfdfe 3Nfdfe pZs2fdfe pZs2fdfe Qrfdfe 嚟42fdfe rrfdfe VZ2fdfe rfdfe 2fdfe Rrfdfe 0Z2fdfe fbrfdfe 2fdfe 2rfdfe Z2fdfe BBrfdfe {42fdfe Qrfdfe Zs2fdfe Zs2fdfe-Nfdfek:fdfe濾fdfeZ2fdfe-&Mބfdfeo}҄fdfe6fdfeZ2fdfe=fdfe/fdfeNTFfdfeZt2fdfeXƟ~fdfezRfdfe^քfdfe0Z2fdfe4`ia/\UseComputerModernTips?\knottips{FT}\def\Conway#1{\mathord{\nabla\Bigl[\,Q\raise5pt\xybox{0;/r1pc/:#1}\,\Bigr]}}$$\Conway\htwist?-\Conway\htwistnegQ\;=\;?-z\,\Conway\huntwist$$#ڍJoins/*28l.DTheN\joins"areusedtoconnecttheloGoseendsofcrossingstrings.Inparticular\loGops"and\caps"areforplacingonendsofhorizontalorvertical`twist'6and`cross'crossings,DleavingthecurrenthpGosi# xed.+0The\bends"joinnon-adjacentcross-ingsjofthesametypGe,2eitherhorizontalorvertical.The\xcap..,_piecesaredesignedtojoinadjacent\xover..0 pieces;OLtheymoveceitherverticallyorhorizontally*, as\appropriate.SFinallythe\xbend..piecesuallowforsmoGothjoinsof45^slopestohor-izontal_orverticalslopGes.F*orthesetheactualpo-sitioningsofthepiece,{Asee gure20,isnotentirelyobvious.FigureL20displaystheorientationonthejoins.Also|yindicatedaredefaultpGositionsforlabelsandarrow-tips;eachzpieceusesthesamecoGde,e.g.\vloop&<>1{|6>>><{x}[z|`{y}>{z}zѲ. 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IthasbGeen'testedwithdvipsversion5.55aanddvipskver-sionUU5.58f.  SuppGortedUU\special0e ectsUUare... colour,UUusingdirectcolorspGecialsandD- cmcsc10DPostScript. crayonUUcolours. DPostScriptUUback-end. rotated/scaled7diagramsandtext,usingDPost- Script. vqariable line-widthsandpGoly-lines,VusingDPost- Script. extraUUframesand lls,usingDPostScript. patternsUUandtiles,usingDPostScript. tpicUUdrawingcommands. em-TU>'ExXUUdrawingcommands.&29.3DVITOPSdriverDVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{dvitops}DThisa leprovidessuppGortforthedvitopsdriverbyJames;Clark.xxAsofSeptembGer1995,-tithasnotbeenfullyUUtested.  SuppGortedUU\special0e ectsUUare... colour,xiusingqedirectcolorspGecialsforgrayqY,rgbŲand hsbncolournmoGdels;andDPostScriptcolourwithin diagrams; crayonUUcolours. DPostScriptUUback-end. rotated/scaledlFdiagramsandtext,usingdvitops spGecials;UUhoweverthesemaynotbGenested. vqariable line-widthsandpGoly-lines,VusingDPost- Script. extraUUframesand lls,usingDPostScript. patternsUUandtiles,usingDPostScript tpicUUdrawingcommands.gw:29.4 j:OzTeXdriveruT:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{oztex}uT:ThisqdriverprovidesthenecessaryinterfacetosuppGort :theDPostScriptback-endandotherDPostScripte ects:when>"usingtheDVI=driver>"ofversions1.8+ofO4zTU>'ExXby:AndrewaT*revorrow,^15 =xEarliernversionsofOzw}TKß'E-Xshould:inste}'adusethedriveroption\xyoption{17oztex}b.;E ectssuchascolour,line-thicknessandrotatedor:scaleddiagramsareonlypartiallysuppGortedinthat:theQe ectscannotbGeappliedtoanytextorsymbGols:placed)usingfonts.^ThisisduetothenatureofO4zTU>'ExX:hdriveri,whoseoptimizationoftheplacementoffont-:characters/precludestheapplicabilityofsuche ects.:F*urthermoretheDPostScriptdictionarymustbGeavqail-:able:ina lecalledglobal.ps9orappGendedtothe:OzTeXdict.pro+*.Howeverlwithversion1.8andlater:ofkO4zTU>'ExX,2thereisthealternativeofusingthedvips:hdriveri,+which`doGessupportalltheDPostScripte ects:avqailableUUinUQXY U-pic.;Note:D(T*ouseXY z-pice ectivelywithO4zTU>'ExXrequires:changingseveralmemoryparameters.  Inparticular:agn`Big-TU>'ExX'isneeded,alongwithanincreaseinthe:pool_size+parameter.Explicit` instructionsarecon-:tained inthe leINSTALL..OzTeXLgofthe XY -picdistri-:bution.;SuppGortedUU\special0e ectsUUare...s:;colour,uusing|DPostScript,butnotoffont-characters.ݍ:;crayonUUcolours,similarlyrestricted.:;DPostScriptUUback-end.:;vqariable line-widthsandpGoly-lines,VusingDPost- ;Script.:;extraUUframesand lls,usingDPostScript.:;patternsUUandtiles,usingDPostScript.:;rotated/scaled}Tdiagramsandtext,Srecognisedbut;notUUsuppGorted.!捍:29.5 j:OzTeXv1.7driveruT:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{17oztex}uT:This4optionprovidesthenecessaryinterfacetosuppGort:theDPostScriptback-endandotherDPostScripte ects:whenj3usingtheDVIj-driverj3ofversion1.7ofO4zTU>'ExXby:AndrewT*revorrow,^16 L}'ater%{versionsofOzw}TKß'E-Xshould:inste}'adyusethedriveroption\xyoption{oztex}WI.IJUp-:gradingUUtoversion1.9+ofO4zTU>'ExXisrecommended.:o;ff^ J=w-:15LOzTAEMXisasharewÎareimplementationofTAEMXforMacintosh aÎvailablewfrommanybulletinbw-:16LOzTAEMXisasharewÎareimplementationofTAEMXforMacintoshaÎvailablewfrommanybulletinb'ExXrequireschangingseveralmemoryparameters.  Inparticularagn`Big-TU>'ExX'isneeded,alongwithanincreaseinthepool_size#parameter.Explicit` instructionsarecon-tained inthe leINSTALL..OzTeXLgofthe XY -picdistri-bution. SuppGortedUU\special0e ectsUUare...FH colour,uusing|DPostScript,butnotoffont-characters. crayonUUcolours,similarlyrestricted. DPostScriptUUback-end. vqariable line-widthsandpGoly-lines,VusingDPost-  Script. extraUUframesand lls,usingDPostScript. patternsUUandtiles,usingDPostScript. rotated/scaled}Tdiagramsandtext,Srecognisedbut notUUsuppGorted.'+29.6TexturesdriverލVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{textures}ލThis;udriverprovidessuppGortforversion1.7+ofBlue6rSkyResearch'sTexturesapplicationforMac-intosh^17x./ItxincorpGoratessupportforcolourandallcof_XYJc-pic'sDPostScripte ects. EarlierversionsofTexturesshouldinsteadusethedriveroption\xyoption{16textures}^Pɲ.  Notice'thatversion1.7su ersfromaprintingbugwhichC%maycauseaDPostScripterror.kAC! xiskludgedby!makingsurethe rstpagehasbGeenshownintheviewerZ~bGeforeanypageswithdiagramsaresenttotheprinter. SuppGortedUU\special0e ectsUUare...FH colour,UUbGothon-screenandwithDPostScript crayonUUcolours. DPostScriptUUback-end. rotated/scaled7diagramsandtext,usingDPost- Script. vqariable line-widthsandpGoly-lines,VusingDPost- Script. extraUUframesand lls,usingDPostScript. patternsUUandtiles,usingDPostScript.佉ff^ J=w-:17LMacinÎtoshXisatrademarkofAppleComputerInc.gw:29.7 j:Texturesv1.6driveruT:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{16textures}uT:This9NdriverprovidessuppGortforversions1.5band1.6of :BlueSkyResearch'sTexturesapplicationforMacin-:tosh^18x.DItincorpGoratessupportforDPostScriptcolour:andxthexXY -psDPostScriptback-end.(NThiswillnotwork:withversions1.7andlater;#theserequirethehdriveri:optionUU\xyoption{textures}g.;SuppGortedUU\special0e ectsUUare...ȃ:;colour,UUusingDPostScript!:;crayonUUcolours.:;DPostScriptUUback-end.:;rotated/scaled7diagramsandtext,usingDPost- ;Script.:;vqariable line-widthsandpGoly-lines,VusingDPost-;Script.:;extraUUframesand lls,usingDPostScript.:;patternsUUandtiles,usingDPostScript.!օ:29.8 j:XDVIdriveruT:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{xdvi}uT:This4YdriverprovidessuppGortforextensionswhenus-:ingvqariantsofthexdvi&.driver,BbyEricCoGoper,BBob:Schei er,MarksEichinandothers.`IthasbGeenused:successfullywithxdvi1patchlevel20,\byPaulV*o8jta,:andUUxdvik ꛲versionUU18f,byKarlBerry*.;Some7ofthesuppGortedfeaturesassumethattheim-:plementationwofxdvihislinkedtoaDPostScriptren-:derer;ze.g. .GhostscriptnorDisplaUTyofDPostScript.If:such suppGortisnotavqailable,.ytheninvokingxdvi us-:ingthecommandxdvi?-hushspecialsfwillsuppress:warning%^messagesthatmightotherwisebGeproduced.:OnefdrawbackofsuchasetupisthatmuchoftheDPost-:Scriptisnotrendereduntilafterallofthefontcharac-:ters,Šetc.4havebGeenplacedonthepage.Thustextthat:wasVmeanttobGeplacedontopofa lledorpatterned:regionmayappGeartobeobscuredbyit.0Howeverwhen:printed, |usingEaDPostScriptprinter, |thecorrectplace-:mentUUisobtained.;SuppGortedUU\special0e ectsUUare...ȃ:;colour,UUusingDPostScript.;Notallversionsofxdvi,suppGortcolor\special,s, 'so;thereWisnodirectsuppGortforcolour.yOHoweverWparts;of8picturesrenderedusingDPostScriptmayappGear;coloured,jdue3tointerpretationofcolourcommands;withinUUtheDPostScript.:;crayonUUcolours.:'ExXimplementationisalsosuppGorted,butUUcurrentlyusesthedvipsdriver.#Q29.9CMacTeXdriverRVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{cmactex}RThomas9Ki e'sCMacTU>'ExXapplicationusesdvipsasitsdvi-driver.A OtherimplementationsnotspGeci callymentionedhereamaywellworkwithoneofthenamedhdriveris,though;"pGerhapsnotallfeatureswillactuallybesup-pGorted.(ߍ30wlExtra efeaturesusingE-ff cmcsc10EPost-wlScriptffdriversThiswesectionacknowledgeswethesuppGortforextrafea-turesUavqailablewhenusingahdriverithatsuppGortsuseof\special0commandswithnativePostScript.Extra>macrosarerequiredtotakeadvqantageofthis;theseareloadedautomaticallyinconjunctionwithex-tensionsFspGeci edusingthe\xyoption56qcommand, Ipro-vided,ahdriveriwhichsuppGortstheextension,4asindi-catedUUin21,hasalsobGeenspeci ed. k: Commands:?arealsoprovidedtoturno /onuseofthesefeatures.8Suchswitchesareparticularlyusefulwhendevelopingcomplicateddiagrams,&orwhentheintendedoutputdevicedoGesnotsupportPostScript;e.g. `&forOuon-screendisplay*.Alternatively*,whenOuat-tempting?tousedriversforwhichnoexplicitsuppGorthasbGeenprovided,ysomefeaturesmayworkothersmaynot.|PleaseXinformtheauthorsofXXY -picofanysuc-cessesUUorfailuresofsuchattempts. This"included le(version3.3)providessuppGortforPostScript\special1ERcommandsusedbythepsbackend6extensionaswellasPostScript-basedop-tions,toproGducespeciale ectsnotavqailabledirectlywithUUTU>'ExX.gw:PostScriptescap`e̛:An|extrahshapGeimodi erkeyallowsarbitraryPost- :ScriptUUcoGdetobeappliedtothecurrenthob8jecti. .: 1ff2 I Ҿ[!RhpGostscriptUUcodei]j۲forUUspGeciale ects Ҿ[psxy]j۲storesUUcurrentloGcation..ff2ˍzNormallythehpGostscriptcodeiwillbeasimplecom-mandtoalterthePostScriptgraphicsstate:|e.g.[!1?00setrgbcolor]nUchangesבthecolourusedtorenderppartsofthehob8jecti. AnynumbGerofsuchhshapGeipmodi ersisallowable,howeveritismoree-cientasthismayupsettheXY 6-pichob8jectiparsing.'ExXandXY u-pic,notfordrawingnewob8jectswithinPostScript.DNoguar-anteetcanbGegivenofthecurrentloGcation,(version3.3)providesPostScriptsuppGortforthee ectsde nedinthecolor NextensionUUinx13. x؍ ThisP8 leisloadedanditse ectsareactivqatedau-tomaticallywhenever\xyoption{color}[sisrequestedandD4thecurrenthdriverisuppGortscoloursusingPost-Script. 8ShouldtherebGeanyneedtoturno thissuppGort,thefollowingcommandsareavqailable;0=theyobGeyUUusualTU>'ExXgroupings. 1ff2 <]\NoPScolorZ(version3.3)providesPostScriptsuppGortforthee ectsde nedintheframeextensionݩdescribGedinx9. Itimplementssomee ectsUUotherwiseunattainable. x؍ ThisP8 leisloadedanditse ectsareactivqatedau-tomaticallywhenever\xyoption{frame}[sisrequestedandm6thecurrenthdriverisuppGortsPostScripte ectsforframes.EShouldtherebGeanyneedtoturno this :suppGort,thefollowingcommandsareavqailable;0=they :obGeyUUusualTU>'ExXgroupings.: @ff2 lC6_\NoPSframes]6;removeUUPostScriptsuppGort6_\UsePSframes]6;reinstateUUPostScript.ff2MZWithoutPostScriptsuppGortellipsesmaybeshownas\circlesandall lledregionsmaybGerepresentedas1\blackrectangles. Thesecommandsareprovidedprimarily#fortestingandtrouble-shoGoting;e.g.withhdrivericon gurationsuntestedbytheauthorsofXY ]-pic,UUwhoshouldbGenoti edofanydiculties.")30.3%Line-stylesAThe included lexyps-l.tex>(version3.3)providesPostScriptdsuppGortforthee ectsde nedinthelineextensionUUdescribGedinx11. ߍ ThisSa leisloadedanditse ectsareactivqatedauto-matically whenever\xyoption{line}SisrequestedandtheecurrenthdriverisuppGortsPostScriptlinestyles.Should[therebGeanyneedtoturno thissupport,]thefollowingVcommandsareavqailable;theyobGeyusualTU>'ExXgroupings. cff2]\NoPSlinesZ(version3.3)providesPostScriptsuppGortforthee ectsde nedintherotate"CextensionUUdescribGedinx12. ߍ ThisSa leisloadedanditse ectsareactivqatedauto-maticallywhenever\xyoption{rotate}b[isrequestedLW968Eu*tj??gwandgIthecurrenthdriverisuppGortsPostScriptrota- tions.=bShouldtherebGeanyneedtoturno thissup-pGort,EtheBfollowingcommandsareavqailable;HtheyobGeyusualUUTU>'ExXgroupings.ff2 }6_\NoPSrotate]6;removeUUPostScriptsuppGort6_\UsePSrotate]6;reinstateUUPostScript.3ff2 FneWithoutPostScriptsuppGortdiagramscanbeexpGectedztobedisplayedzunrotatedandunscaled.TheseYcommandsareprovidedprimarilyfortestingandtrouble-shoGoting;e.g.withhdrivericon gurationsuntested;bytheauthorsof;XY -pic,@WwhoshouldbGenoti- edUUofpGersistentdiculties.30.5%PatternsandtilesuTThe included lexyps-t.tex>(version3.3)providesPostScriptdsuppGortforthee ectsde nedinthetileextensionUUdescribGedinx14. ThisSa leisloadedanditse ectsareactivqatedauto-matically whenever\xyoption{tile}SisrequestedandthecurrenthdriverisuppGortsPostScriptpatterns.Should[therebGeanyneedtoturno thissupport,]thefollowingVcommandsareavqailable;theyobGeyusualTU>'ExXgroupings.Wff2]\NoPStilesZ(version3.3)providestpic2 suppGortforsomeofthee ectsde nedintheframeextension.Thisv leisloadedanditse ectsareactivqatedFautomaticallywhenever\xyoption{frame}is! requestedandthecurrenthdriverisuppGortsbothtpichandframes.ShouldtherebGeanyneedtoturno 7thissuppGort,pthefollowingcommandsareavqailable;theyUUobGeyusualTU>'ExXgroupings.ff2b\NoTPICframesbv8removeUUtpicsuppGortb\UseTPICframesbv8reinstateUUtpic.3ff2l:Appendices/`:AY(Answersfftoallexercisesf:Answ9erztoexercise1(p.7): Indthedefaultsetup :theyarealldenotethereferencepGointoftheXY /-picture:butOthecartesiancoGordinatehposi(0,0)denotesthe:pGointorigothatmaybGechangedtosomethingelseus-:ingUUthe: ꧲opGerator.j̍:Answ9ertoexercise2(p.7): Use&thehpGosiition:<*7X,ߵY8>+"ob"!Ҳ.:Answ9ertoexercise3(p.7): It= rstsetscaccording:to\...".ThenitchangesctothepGointrightofcat:thesamedistancefromtherightedgeofcasitswidth,:wD,UUi.e., '6}TheUU...3A|||31 {GD|z31 }Csȵwe [% ||31 {oԟ|z31 }kȵw*:Answ9er toexercise4(p.9): The 4hcoGordi:\{"A";"B":5"C";"D",d x}oz"returnsthecrosspGoint.:HereTishowtheauthortypGesetthediagramintheex-:ercise:N8:\xy*7%*7%?setupandmarkA,B,C,andD:*7(0,0)="A" *\cir<1pt>{}*+!DR{A},*7(7,10)="B"?*\cir<1pt>{}*+!DR{B},*7(13,8)="C"?*\cir<1pt>{}*+!DL{C},*7(15,4)="D"?*\cir<1pt>{}*+!DL{D},*7%*7%?gotointersectionandname+circleit:*7{"A";"B":"C";"D",x}?="I"*\cir<3pt>{},*7%*7%?makedottedlines:*7"I";"A"**{}?+/1pc/;-/1pc/**@{..},*7"I";"D"**{}?+/1pc/;-/1pc/**@{..}*7%:\endxy:AUU?! O...hplaceiUUcouldalsohaveUUbGeenused.:Answ9er{toexercise5(p.9): T*ocopythepvqalue:toUUc,i.e.,equivqalentto\p?".:Answ9er:Xtoexercise6(p.10): Whenΐusingtheker-:nelΤconnectionsthatareallstraightthereisnodif-:ference,e.g.,**{}?<)"Ҳand6**{}+E(Zdenote6exactlythe:same8pGosition.KHowever, forotherconnectionsitisnot:necessarily#thecasethatthepGointwheretheconnec-:tion_ventersthecurrentob8ject,adenotedby?< p,aandthe:pGointcwherethestraightlinefrompenterstheob8ject,:denotedUUby+E O,coincide.LW969F *tj??gwAnsw9ertoexercise7(p.10): TheGcoGdetypesets theUUpictureՍꪍ]BoxF ;,3232;^32fdTTg3232y ;Efd+Efd32;,3232;^fdTTg3232F ;,3232<䍍3232=323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232=3232y ;%3232323232323232323232323232323232323232323232323232+%323232323232323232323232323232323232323232323232323232;,3232<䍍3232=323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232=3232yT~#Answ9eretoexercise8(p.10): This'doGesthejob,saving![eachpGointtomakethepreviouspGointavqailableforUUthenextpiece:N8\xyQ@={(0,-10),(10,3),(20,-5)},Qs0="prev"?@@{;"prev";**@{-}="prev"}\endxyNoticehowweclosethelineby rstsavings0 e,thelastpGointjvisited,suchthatthe rstpGointwillbGeconnectedtoUUit.UAnsw9erTtoexercise9(p.11): TheUUauthorused\xy?={.{+DL(2)}.{+UR(2)}}"dbl",Q*+<3pc,2pc>{+}*\frm{.},?"dbl"*\frm{--}\endxytoUUtypGesetthe gureintheexercise.UAnsw9erWctoexercise10(p.13): Them rsttypGesets\a"ycenteredaround0 andthenmovesctothelowerrightҞcorner,thesecondtypGesets\a"aboveҞthe0 9pointandldoGesnotchangec.\Witha\+"at0 lղtheylooklikethis:qǟ+'a:andq+UUa .Answ9er+Gtoexercise11(p.13): Theyvhavetheout-lines 7KDPH3232HÞ32fdng3232-HmfdXvfd32H3232Háfdng3232LH+bvand{/mP}b3232}씞32fdຍg3232%}ɉfdfd32}b3232}씡fdຍg3232|+7bGecauseEthe rstisenlargedbythepositiveo settotheUuppGerrightcornerandthesecondbythenegativeo setUUtothelowerUUleftcorner.Answ9erUotoexercise12(p.14): TheV rsthasnoe ectsincethedirectionissettobGethatofavectorinthecurrentdirection,%however,thesecondreversesthecurrentUUdirection.Answ9erjtoexercise13(p.14): NoneinbGothcases.Answ9erTtoexercise14(p.16): OneUUwayisN8$$\xyQ*{+};?p+(6,3)*{+}**{}?(1)Q*@{-}?*!/-5pt/^\dir{-}Q*^\dir{-}?*!/^-5pt/\dir{-}\endxy$$ ThusUwe rstcreatethetwo+saspandcandcon-nectǖthemwiththedummyconnection**{} tosetupthe9directionparameters.+sThenwemove`ontopofc'gw:with .?(1)Pand .pGositionthefoursidesofthesquareus- :ing^ Cand_forloGcaldirectionchangesand/hdimeni/:forskewingtheresultingob8jectbymovingitsreference:pGointUUintheoppositedirection.A:Answ9ertoexercise15(p.18): OneM wayistoadd:extraxhalfcirclesskewedxsuchthattheycreatetheillu-:sionUUofashade:N8:$$\xy*7*\cir<5pt>{}*7*!<-.2pt,.2pt>\cir<5pt>{dr^ul}*7*!<-.4pt,.4pt>\cir<5pt>{dr^ul}*7*!<-.6pt,.6pt>\cir<5pt>{dr^ul}:\endxy$$y:Answ9erKtoexercise16(p.21): ThisisthecoGde:thatUUwasactuallyused::\xy?(0,20)*[o]+{A};(60,0)*[o]+{B}="B":**\crv{}?\POS?(.4)*_+!UR{0},"B":**\crv{(30,30)}?\POS?*^+!D{1},"B":**\crv{(20,40)&(40,40)}?\POS?*^+!D{2},"B":**\crv{(10,20)&(30,20)&(50,-20)&(60,-10)}:\POS?*+^!UR{4}?\endxyy:Answ9erKtoexercise17(p.21): ThisisthecoGde:thatUUwasusedtotypGesetthepicture::\xy?(0,20)*+{A};(60,0)*+{B}:**\crv{(10,20)&(30,20)&(50,-20)&(60,-10)}*7?<*\dir{<}??>*\dir{>}*7?(.65)*{\oplus}?*!LD!/^-5pt/{x}*7?(.65)/12pt/*{\oplus}?*!LD!/^-5pt/{x'}*7?(.28)*=0{\otimes}-/40pt/*+{Q}="q"*7+/100pt/*+{P};"q"?**\dir{-}:\endxyy:Answ9er,toexercise18(p.21): HereisthecoGde:thatUUwasusedtotypGesetthepicture::\def\ssz#1{\hbox{$_{^{#1}}$}}:\xy?(0,0)*+{A};(30,-10)*+{B}="B",**\dir{-},:"B"**\crv{(5,20)&(20,25)&(35,20)}*7?<(0)*\dir{<}="a"??>(1)*\dir{>}="h"*7?(.1)*\dir{<}="b"??(.9)*\dir{>}="i"*7?(.2)*\dir{<}="c"??(.8)*\dir{>}="j"*7?(.3)*\dir{<}="d"??(.7)*\dir{>}="k"*7?(.4)*\dir{<}="e"??(.6)*\dir{>}="l"*7?(.5)*\dir{|}="f",*7"a"*!RC\txt{\ssz{(\lt)}};j4"h"*!LC\txt{\ssz{\;(\gt)}},**\dir{.},*7"b"*!RD{\ssz{.1}};j4"i"*!L{\ssz{\;.9}},**\dir{-},*7"c"*!RD{\ssz{.2}};j4"j"*!L{\ssz{\;.8}},**\dir{-},*7"d"*!RD{\ssz{.3}};LW970G6Q*tj??gw"k"*!L{\ssz{\;.7}},**\dir{-}, Q"e"*!RD{\ssz{.4}};"l"*!LD{\ssz{.6}},**\dir{-},Q"f"*!D!/^-3pt/{\ssz{.5}}\endxy!)Answ9erTtoexercise19(p.24): HereUUishow:N8\xyQ(0,0) *++={A}?*\frm{o};Q(10,7)?*++={B}*\frm{o}**\frm{.}\endxyAnsw9ertoexercise20(p.24): TheJ*\cir?{}0op-erationЬchangesctobGeroundwhereas*\frm?{o}4=doesnotUUchangecatall.zAnsw9erTtoexercise21(p.26): HereUUishow:N8\xyQ(0,0) *+++{A}?;Q(10,7)?*+++{B}**\frm{.}Q**\frm{^\}}?;**\frm{_\}}\endxym The)trickinthelastlineistoensurethattheref-erencepGointofthemergedob8jecttobebracedistherightUUoneineachcase.Answ9ertoexercise22(p.29): ThisishowtheauthorUUspGeci edthediagram:N8\UseCrayolaColors\xy\drop[*1.25]\xybox{\POS(0,0)*{A};(100,40)*{B}**{}Q?<<*[@_][red][o]=<5pt>{\heartsuit};Q?>>>*[@_][Plum][o]=<3pt>{\clubsuit}Q**[|*][|.5pt][thicker]\dir{-},?(.1)*[left]!RD\txt{label?1}*[red]\frm{.}?(.2)*[!gsave?newpathxyXpos?xyYposmoveto50duprlineto20?setlinewidth001setrgbcolorstrokegrestore][psxy]{.},?(.2)*[@]\txt{label?2}*[red]\frm{.},?(.2)*[BurntOrange]{*},?(.3)*[halfsize]\txt{label?3}*[red]\frm{.}?(.375)*[flip]\txt{label?4}*[red]\frm{.}?(.5)*[dblsize]\txt{label?5}*[red]\frm{.}?(.5)*[WildStrawberry]{*},?(.7)*[hflip]\txt{label?6}*[red]\frm{.}?(.8)*[vflip]\txt{label?7}*[red]\frm{.}?(.9)*[right]!LD\txt{label?8}*[red]\frm{.}?(.5)*[@][*.66667]!/^30pt/Q\txt{special?effect:alignedtext}Q*[red]\frm{.}}\endxygw:Answ9er9toexercise23(p.39): Here>Hiswhatthe :authorUUdid:N8:\xy?*+{A}*\cir<10pt>{}="me"*7\PATH?~={**dir{-}}j4`ul^ur,"me"?"me"|>*:(1,-.15)\dir{>}:\endxy;Thetrickisgettingthearrowheadright:the: moGd-:i erUUtotheexplicit\dirhob8jectidoGesthat.E:Answ9erTtoexercise24(p.39): TheUUauthordid:\xy(0,0)*7\ar?@{-->}(30,7)^A="a"*7\POS(10,12)*+\txt{label}?\ar"a":\endxy:Answ9eritoexercise25(p.39): Heremistheentire6XYj:-pictureUUoftheexercise::\xy?;<1pc,0pc>:*7\POS(0,0)*+{A}*7\ar+(-2,3)*+{A'}*\cir{}*7\ar?@2+(0,3)*+{A''}*\cir{}*7\ar?@3+(2,3)*+{A'''}*\cir{}*7\POS(6,0)*+{B}*7\ar?@1{||.>>}+(-2,3)*+{B'}*\cir{}*7\ar?@2{||.>>}+(0,3)*+{B''}*\cir{}*7\ar?@3{||.>>}+(2,3)*+{B'''}*\cir{}:\endxy;TheUU rstbatchusethedefault{->}spGeci cation.E:Answ9erTtoexercise26(p.40): TheUUauthorused:\newdir{?>}{{}*!/-5pt/\dir{>}}:Answ9erTtoexercise27(p.41): TheUUauthorused:\xy*7\ar?@{>>*\composite{\dir{x}*\dir{+}}<<}*7(20,7):\endxy:Answ9erTtoexercise28(p.41): TheUUauthorused:\xy?*{\circ}="b"\ar@(ur,ul)c*7\ar@{.>}@(dr,ul)?(20,0)*{\bullet}:\endxy:NotethatitisessentialthatthecurvingspGeci cation:comesUUafterthearrowstyle.E:Answ9er,toexercise29(p.43): HereisthecoGde:usedUUtotypGesetthep}'astingdiagramUUin gure15.:\xymatrixrowsep{1.5pc}:\xymatrixcolsep{3pc}:\diagramLW971HS*tj??gwQ&&\relax\rtwocell<0>^{f_3^{}\;\;}{\omit} Q&\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>}Q\drtwocell<0>_{g_1^{}\;}{\omit}Q&&&\relax\urtwocell<0>{\omit}Q&&\relax\rtwocell<0>^{f_6^{}\;}{\omit}Q&\relax\rlowertwocell<-3>_{g_4^{}}{<-1>}Q\rcompositemap<6>_{f_7^{}}^{f_8^{}}{\omit}Q&?B\\Q&\relax\urrtwocell<0>{\omit}Q\xcompositemap[-1,4]{}%<-4.5>_{g_2^{}}^{g_3^{}}{\omit}\\\enddiagramhF*orUthestraightarrows,UitwouldhavebGeensimplertouseK\..to ףprovidedKxyarrow+WhasKbGeenloaded.nInstead\..twocell<0>...{\omit?}pκwasusedtoillustratetheversatility3ofnudgingand\omit#;thusxy2cell-']cancompletelyhandleawiderangeofdiagrams,withoutrequiring}xyarrow']h.4Note}alsotheuseof\relax)atthestartofeachnewcell,toavoidprematureexpansionofaNcomplicatedmacro,,whichcanupsetthecompilingmechanism.뵍Answ9er,toexercise30(p.46): HereisthecoGdeusedUUbytheauthortosetthe rstdiagram.N8{\uppercurveobject{{?}}Q\lowercurveobject{{\circ}}\xymatrixcolsep{5pc}\xymatrixrowsep{2pc}\diagramQ\relax\txt{?FUn}\rtwocell<8>{!\&}Q&?\relax\txt{gaMES}Q\enddiagram}| HereUUisthecoGdeusedfortheseconddiagram.\xymatrixcolsep{2.5pc}\xymatrixrowsep{4pc}\diagramQ\relax\txt<1.5cm>{\bf?GroundState}Q\rrtwocell<12>~^{+{}~**!/-2.5pt/\dir{>}}Q~_{++{}~**!/5pt/\dir{<<}}Q^{<1.5>\txt{\small?continuouspower}}Q_{<1.5>\txt{\small?pulsedemission}}{!}&?\relax\;\;N\!i\,C\!d\;\;\Circled&?\relax\txt<1.50cm>{\bfExcitedState}\enddiagram!9퍑Answ9erTtoexercise31(p.49): TheUUauthordid\xymatrix?@!=1pc{Q**[l]?A\timesBgw*+\ar[r]^{/A}?\ar[d]_{/B} *7&?B\ar[d]^{\timesA}:\\*7A\ar[r]_{B\times}*7&?**[r]B\timesA:} ꍒ:Answ9ertoexercise32(p.49): MoGdi ers;pareused:tomakeallentriesroundwithaframe{thegeneral:form{isusedtoensurethatthesequenceiswell-de ned.:FinallyzthematrixisrotatedtomakeitpGossibleto:enterUUitasasimplesquare:N8:\entrymodifiers={=<1pc>[o][F-]}:\xymatrix?@ur{*7A?\save[];[r]**\dir{-},"[];[dr]**\dir{-},"[];[d]?**\dir{-}\restore1&?B\\*7C?&D}:Answ9erTtoexercise33(p.49): HereUUishow:N8:\objectheight{1pc}?\objectwidth{3pc}:\xymatrixrowsep={0pc}:\xymatrix?@*[F-]{%*7:?\save+<-4pc,1pc>*\hbox{\itroot}*+\ar[]1\restore:\\*7{\bullet}1\save*{}.\ar`r[dd]+/r4pc/`[dd][dd]1\restore:\\*7{\bullet}1\save*{}.\ar`r[d]+/r3pc/`[d]+/d2pc/j`[uu]+/l3pc/`[uu][uu]1\restore:\\*71?}:Answ9ertoexercise34(p.50): Thez rstAwas:namedUUtoallowreferencefromthelast:N8:\xygraph{*7[]A="A1"?:@/^/[r]Aj:@/^/?[r]Aj:@/^/?"A1"}:Answ9erTtoexercise35(p.52): TheUUauthordidN8:\SelectTips{cm}{}:\objectmargin={1pt}:\xygraph{?!{0;(.77,-.77):0}LW972Ic*tj??gwQ!~:{@{-}|@{>}} Qw?(:[r(.6)]{x_1},:[d]z:[r]y:[u(.6)]{x_2}:"x_1":"z":@(?{"w";"z"},{"y";"z"})"z":"x_2")} Italsoshowsthatonec}'anquse{}Psinsidedelimitedargumentslpr}'ovidedu_oneaddsaspacetoavoidthe{} вsbGeingUUshavedo !^Answ9er,toexercise36(p.52): HereisthecoGdeactuallyRusedtotypGesetthe\xypolygon=e1s,Qwithinan\xygraphP.Itillustratesthreedi erentwaystoplacetheUUnumbGers.qOtherwaysarealsopGossible.N8\def\objectstyle{\scriptscriptstyle}\xy?\xygraph{!{/r2pc/:}[]?!P3"A"{\bullet}"A1"!{+U*++!D{1}}?"A2"!{+LD*+!RU{2}}"A3"!{+RD*+!LU{3}}?"A0"[rrr]*{0}*\cir<5pt>{}!P6"B"{~<-\cir<5pt>{}}"B1"1?"B2"2"B3"3"B4"4"B5"5"B6"6"B0"[rrr]0?!P9"C"{~*{\xypolynode}}}\endxy'\$B ~Vfersionff2Compatibility[Vers.3.3bCyKristo erH.Rosehkrisrose@brics.dki Loadas:\xyoption{v2}'ThisUappGendixdescribesthespecialbackwardsUcompat-ibilitydwithdXY -picversion2:)diagramswrittenaccord-ing?tothe\TypGesettingdiagramswith;XY ?-pic:˜User'sManual"L[13 ]shouldtypGesetcorrectlywiththisloaded.The[compatibilityisavqailableeitherasanWXY i[-optionorthrough1thespGecial lesxypic.sty4Gandxypic.texde-scribGedUUbelow. _Ǎ There areafewexceptionstothecompatibility:M thefeatures?describGedinxB.1belowarenotprovidedbGe-causefXtheyarenotasusefulastheauthororiginallythoughtqqandthusvirtuallyneverused.AndoneextracommandisprovidedtospGeeduptypGesettingofdocu-mentsαwithέXY N-picversion2diagramsbyallowingthenewUUcompilationfunctionalitywitholddiagrams. Theweremainingsectionslistalltheobsoletecom-mands?andsuggestways?toachieve?thesamethingsusingl,XY 0-picl03.3,i.e.,withouttheuseofthisoption.Theyg"aregroupGedastowhatpartofgXY "-picreplacesthem;UUthecompilationcommandisdescribGedlast. Note: i\version,2"ismeanttocoverallpublicre-leasesofXY-picin1991and1992,i.e.,version1.40and9Nversions2.1through2.6.Thepublishedmanualcited?abGove(forversion2.6)isthereferenceincaseof;^vqariationsbGetween;^theseversions,tandonlythingsdoGcumentedinthatmanualwillbGesupportedbythisoption!^19 Kff^ J=w-:19LIn#additionafewoftheexpEncloseitinbraces,i.e.,}+W(or\tipK̲)withvqariants'M S-T<8E3sXidioms:Some~idiomsfromAU>'M S-TU>'ExXarenolongerusedbyzXY j~-:pic:the de nitioncommands\defineand\redefine,:andthesizecommands\dsize,ȭ\tsize,\ssize,and:\sssize.}Pleaseusethecommandsrecommendedfor:your&format|forplainTU>'ExXtheseare\def@forthe rst:twoDand\displaystyleG,H\textstyle7,H\scriptstyleBG,: ff^ @v2.7{2.12Xarealsosupp'M S-TU>'ExX\textanda(non-ob8ject)bGoxconstruction\Textwhichareemulated|\text=isDonlyde nedifnotalreadyde ned,޿however,using:thenativeone(ofAU>'M S-TU>'ExXorAU>'MS-L5ffA͉TU>'ExXorwhatever)vmifpGossible.Pleaseusethe\txtβob8jectcon-struction/describGedinx6.3directlysinceitismoregen-eralUUandmuchUUmoreecient!NObsoleteTstateuTUpto]version2.6userscouldaccessthestatevqariables\cL,UU\cR,\cH,and\cD,whicharede ned. F*rom"v2.7to2.12userscouldusethenamesoftheLstate\dimen(Lregisters\Xmin,\Xmax,\Ymin,and\Ymax;_\Xp,s\Yp\Dp,\Up,\Lp,and\Rp;_\Xc,\Yc\Dc,\Uc,\Lc,andO\Rc;\Xorigin,\Yorigin,\Xxbase,\Yxbase,\Xybase,and\Yybase.-sNowthesameef-fectrcanbGeachievedrusinghcornerisbutv2޲de nesthealiases.ObsoleteTpQositionmanipulationuTInUversion2manythingsweredoneusingindividualhdecoriFcontrolsequencesthatarenowdoneusinghpGosiopGerators.^ff2 ፍ V*ersionUU2pGositioningkReplacement4ff2 \gohpGosik\POS;p,hpGosi \aftergo{?hdecori}hpGosiG\afterPOS{|@hdecori};p,hpGosi \mergek\POS.p\relax \swapk\POS;\relax \Drop{?htexti}k\drop+{htexti}ff2rNObsoleteTconnectionsuTThesep connectionsarenowimplementedusingdirec-tionals.l؉ff2 ፍ V*ersionUU2connectionlyReplacementff2 \nonely\connect?h\dir{} \solidly\connect?h\dir{-} \Solidly\connect?h\dir2{-} \Ssolidly\connect?h\dir3{-} \dashedly\connect?h\dir{--} \Dashedly\connect?h\dir2{--} \Ddashedly\connect?h\dir3{--} \dottedly\connect?h\dir{.} \Dottedly\connect?h\dir2{.} \Ddottedly\connect?h\dir3{.} \dottedwith{?htexti}ly\connect?h{9htexti}ff2 9DNotehowthe`hidden'spGeci erh shouldbeusedbe-cause0version2connectionsdidnota ectthesizeofdiagrams.gw:ObsoleteTtips :TheseUUob8jectsallhaveUU\dirUI-namesUUnow:: ff2 !fV*ersionUU2tipY3ReplacementPff2f\notipY3\dir{} f\stopY3\dir{t$|yO!}f\astopY3\dir^{yO!|~}f\bstopY3\dir_{yO!|~}f\tipY3\dir{>}f\atipY3\dir^{>}f\btipY3\dir_{>}f\TipY3\dir2{>}f\aTipA3\object=<5pt>:(32,-1)\dir^{>}f\bTipA3\object=<5pt>:(32,+1)\dir_{>}f\TtipY3\dir3{>}f\ahookY3\dir^{(}f\bhookY3\dir_{(}f\aturnY3\dir^{'}f\bturnY3\dir_{'}ff2 z P The@oldercommands\pit@,{\apit,{and\bpit,arenotUUprovided.ObsoleteTobjectconstructions The(followingob8jectconstructionmacrosaremadeob-soleteUUbytheenrichedhob8jectiformat: ff2 ! oV*ersionUU2ob8jectkO+Replacementff2 o\rotate(?hfactori)htipi GO+\object:(vhfactori,?hfactori){ htipi} o\holekO+\object+{} o\squashhtipikO+\object=0{ htipi} o\growhtipikO+\object+{htipi} o\grow<*]hdimeni>?htipikO+\object+<hdimeni>{ htipi} o\squarify{?htexti}kO+\object+={ htexti} o\squarify{ htexti}GO+\object+=<{ hdimeni>{ htexti}ff2Awhere[rotationisdoneinaslightlydi erentmannerinversionUU3.3(itwasneveraccurateinversion2).B.3!Obsoleteextensions&features V*ersion?p2hadcommutative?pdiagramfunctionalitycor-respGonding7totheframes'extensionandpartsofthematrix"!and.arrowMfeatures.5These.arethereforeloadedandLsomeextrade nitionsaddedtoemulatecommandsthatUUhavedisappGeared.F ramesTheyversion2framecommandsareemulatedus-ing(theframeextension(aswellasthe\dotframed9 ,LW974K*tj??gw\dashframed),\rounddashframed_OͲcommandsecomm- unicatedUUtosomeusersbyelectronicmail):Iff2 lōeV*ersionUU2ob8jectg5Replacementcff2e\framedg5\drop\frm{-}e\framed<8Mhdimeni>g5\drop\frm<6hdimeni>{-}e\Framedg5\drop\frm{=}e\Framed<8Mhdimeni>g5\drop\frm<6hdimeni>{=}e\dotframedg5\drop\frm{.}e\dashframedg5\drop\frm{--}e\rounddashframedg5\drop\frm{o-}e\circledg5\drop\frm{o}e\Circledg5\drop\frm{oo}cff2'DMatricesuTTheA\diagramhrowsi\enddiagramcommandispro-vided~asanaliasfor\xymatrix{>޸hrowsi}`centeredin)mathmoGdeand\LaTeXdiagramschangesittouse\begin"...Y\endsyntax.Zv2뎲setsaspGecialinternal`oldmatrix' agsuchthattrailing\\+zareignoredanden-triesUUstartingwith* ꧲aresafe. \NoisyDiagramsزisignoredbGecausethematrixfea-tureUUalwaysoutputsprogressmessages. Finally VVtheversion2\spreaddiagramrows,\spread$diagramcolumnsqspacingYcommandsareemu-latedUUusing\xymatrixrowsepUj}and\xymatrixcolsepR(:Arro9wsuTThe5mainarrowcommandsofversion2werethe\morphismͲand\definemorphismcommandswhichnowUUhavebGeenreplacedbythe\arjcommand. v2providesdthemaswellasusesthemtode nethe&version2commands\xto,M\xline,\xdashed,\xdotted, V\xdouble,andallthederivedcommands\dto,(\urto ,(...;_the\e\arrow*8commands\eofthe -releasesUUofv3isalsoprovided. Instead?ofcommandslike\rrto oand\uldouble5cyoushouldPusethearrowfeaturereplacements\ar[rr])aand\ar@{=}[ul]9߲. TheqBprede nedturningsolidarrows\lltou$0,<...,\tord5areDde nedaswell;,'ExX2.09`style{option'[xypic]*f. 9Thisismadesynonymouswith|loadingthisoptionbythe lesxypic.texandxypic.styUUdistributedwiththev2*option.㍍xypic.tex/?:7qThiss le(version3.3)justloadsthev2feature.xypic.sty/?:7qLoadsUUxy.sty&*andUUthev2*feature.gw:B.5Compilingv2-diagrams:InordertomakeitpGossibletousethenewcompilation :featuresevenondoGcumentswrittenwithXY B-picv2,ߑthe:followingUUcommandwasaddedinv2.12::ff2 > 6\diagramcompileto{lUhnameiUU} ꧲...\enddiagramײff2(whichfisliketheordinarydiagramcommandexcepttheresult5iscompiled(seenote5e).NNotethatcompilationisUUnotquitesafeinallcases! װ Thereisalsothefollowingcommandthatswitcheson5jautomaticvc}'ompilationͲofalldiagramscreatedwiththeUUv2\diagram0...\enddiagramB3command:Nff2* (\CompileAllDiagramsD{hpre xiUU}* (\NoCompileAllDiagrams* (\ReCompileAllDiagramsײff2/awillNapply\xycompileto{Ghpre xin}{ ...} 9toNeachdia-gram withnasequencenumbGer startingfrom1.(Use\CompileMatricesWU%andUU\CompilePrefixP*instead! װ If~forsomereasonadiagramdoGesnotworkwhencompiled thenreplacethe\diagram4 commandwith\diagramnocompile_c(or$!incaseyouareusingtheL5ffA͉TU>'ExXUUform,\begin{diagramnocompile}U ).-9}CdCommonffErrorsxIn`xthisappGendixwedescribesomecommoncaseswheresmall|mistakesinxXY |-picturesresultinTU>'ExXerrormes-sagesUUthatmayseemcryptic.v!pBo9xTexpQected.!AhbGoxi7w9assuppQosedtobehere. Thismes-sage\iscommonwhenan\XY -pichob8jectiismistypGedsuchthatXY b-picexpGectsbutdoesnot ndaTU>'ExXhboxiconstruction.!LaT eX+Error:=Bad+mathen9vironment+delim-iter.!Fileendedwhilescanninguseofձ\xycompiled.!jArgumen9t"of:\codeof@hasanextraFɌ cmbsy10Fg. Theseerrorsh(canhappGenwhilereadinganincompletecom-piledpicture(suchabGeastiscreatedwhenXYd-piccrashesduringcompilationduetoasyntaxerrororotherUUsuchproblem).!]Missing@Fginserted. ThishappGenswhen\endxywasUUleftout.6q T oTDo:qDzAlsoUUincludethemoreobscureones...LW975L*tj??gwReferences [1]DAdobGeSystemsIncorporated. QPostScriptL}'an- DguageR}'eferenceManual,UUsecondedition,1990.P [2]DAmerican6MathematicalSoGciety*.ֶAU>'M S-L雍QATKß'E-XDV;ersion1.1User'sGuide,UU1.1edition,1991. [3]DKarl6Berry*.fExp}'andedplainTKß'E-X,version2.6edi-Dtion,May1994.yAvqailableforanonymousftpfromDCT*ANUUinmacros/eplain/doc. [4]DMichelQGoGossens,F*rankMittelbach,andAlexan-Dder|Samarin.TheL雍QATKß'E-XComp}'anion.Addison-DW*esley,UU1994. [5]DBrianՖW.Kernighan."PIC|alanguagefortypGe-Dsettingfgraphics.Softwar}'ePracticeandExperi-Denc}'e,UU12(1):1{21,1982. [6]DDonaldE.Knuth.The-TKß'E-Xb}'ook.Addison-W*esley,D1984. [7]DDonald,E.Knuth.ComputerZMo}'dernT;ypefaces,DvolumeAofComputers&T;yp}'esetting.A%Addison-DW*esley,UU1986. [8]DLeslie+LampGort.5L雍QATKß'E-X|A)Do}'cument)PreparationDSystem.nAddison-W*esley,UU1986. [9]DLeslie+LampGort.5L雍QATKß'E-X|A)Do}'cument)PreparationDSystem.nAddison-W*esley,UU2ndedition,1994.[10]DP*.5Nauretal.*RepGortonthealgorithmiclanguageDALGOL460.Communic}'ationsFoftheACM,I3:299{D314,UU1960.[11]DT*omasuRokicki. DVIPS:AjTKß'E-XDriver.Dis-Dtributeda withthedvipsprogramfoundonCT*ANDarchives.[12]DKristo erH.Rose.HowtotypGesetprettydia-DgramarrowswithTU>'ExX|designdecisionsusedin@XYD-pic.RIn/JiuUrqZlatuxskqa,editor,Eur}'oTKß'E-X '92|DPr}'oceedings,ofthe7thEur}'opean,TKß'E-XConfer}'ence,Dpages?183{190,z?Prague,Czechoslovqakia,z?Septem-DbGerUU1992.CzechoslovqakUUTU>'ExXUsersGroup.[13]DKristo erH.Rose.xKTypGesettingdiagramswithXY >-Dpic:yUser's.manual.9gInJiuUrqZlatuxskqa,editor,Eu-Dr}'oTKß'E-X'92|Proceedingsofthe7thEuropeanTKß'E-XDConfer}'ence,3pages273{292,Prague,Czechoslo-Dvqakia,|SeptembGerbA1992.CzechoslovqakTU>'ExXUsersDGroup.[14]DKristo erxH.Rose.XY -picAUser'sGuide.DIKU,DUniversity\ofCopGenhagen,Universitetsparken\1,DDK{2100UUKbGenhavn,3.0edition,June1995.[15]DKristo ermH.RoseandRossR.MoGore.fXY uj-piccom-DpletegsourceswithTU>'ExXnicalcommentary*.notyetDavqailable,UUJune1995.gw:[16]xvMichaelWzD.Spivqak.uTTheJoyofTKß'E-X|AGourmet xvGuideWtoT;yp}'esettingwiththeAU>'M S-TKß'E-XMacroxvPackage.American$MathematicalSoGciety*,-secondxvedition,UU1990.f:[17]xvTUG*W*orking*GroupTWG-TDS. 2AdirectoryxvstructureforTU>'ExX lesversion0.98. URL,Mayxv1995. Avqailable6withURL5ftp://jaspGer.ora.com/xvpub/twg-tds/.D:Index:!,UU8 :&,UU47:',UU38:(),UU8:(0),UU8:(0,0),UU69:(1),UU8:*,UU8,38,39,41,47,49,73:**,UU8,39,49:+,UU8:,,UU8,39:-,UU8,38:.,UU8:.xyd,UU16:/,UU37,38,41://,UU8::,UU8,12:::,UU8:;,UU8:<,UU8,37{39:<>,UU8:<>(.5),UU38:=,UU8,37{39:>,UU8,37{39:?,UU8,39:@,UU8,38,40,48:@!,UU40,48:@!0,UU48:@!=,UU48:@!C,UU48:@!R,UU48:@(,UU10,40,41:@),UU10:@*,UU40,49:@+,UU10:@-,UU10:@/,UU40,41:@1,UU49:@<,UU40,41:@=,UU10:@?,UU40,41LW976M*tj??gw@@,UU10 /@C,UU48@H,UU48@L,UU48@M,UU48@R,UU48@W,UU48@`,UU40@i,UU10[.],UU13[=,UU12,14,30,32[],UU13[c],UU13[d],UU13[dvips],UU5[l],UU13[o],UU13[r],UU13[textures],UU5[u],UU13\\,UU47^,UU38{40_,UU38{40`,UU38|,UU38,40|<<,UU73~,UU38^g0,UU6,8,401,UU402,UU403,UU4010,UU2711,UU2712,UU27a,UU8activeUUcharacters,4haddUUopi,12\aftergo?,UU74\afterPATH?,UU37\afterPOS?,UU14,15,37\ahook?,UU74alloGcation,UU5AU>'M S-L5ffA͉TU>'ExX,UU5,15AU>'M S-TU>'ExX,UU5\apit?,UU73\ar?,UU14,37array,UU50arrowUUhead,39arrowUUstem,39arrowUUtail,39\astop?,UU74\aTip?,UU74\atip?,UU74\aturn?,UU74banner,UU5gw:\bhook?,UU74 $:BNF,UU4:hbGodyUUoftheoptioni,19:\bpit?,UU73:\bstop?,UU74:\bTip?,UU74:\btip?,UU74:\bturn?,UU74rЍ:C,UU8,10:c,UU6:c,UU8:cartesianUUcoGordinatesystem,6:categoryUUcoGde,4:CD,UU8:\cD?,UU74:\cH?,UU74:hciri,UU19:\cir?,UU18,71:\Circled?,UU75:\circled?,UU75:circles,UU5:CL,UU8:\cL?,UU74:cm,UU27:\Col?,UU49:columnUUspacing,48:hcommandi,UU15:\CompileFixPoint?,UU15:\CompilePrefix?,UU15:compiling,UU15:hcompGositei,UU12:\composite?,UU11,12,18:connect,UU6:\connect?,UU15:hcoGordi,UU8:COPYING,UU4:copyright,UU3:hcorneri,UU8:CR,UU8:\cR?,UU74:CU,UU8:currentUUob8jectstyle,12,13:DG,UU6:D,UU8,10:Dc,UU6:DpR,UU6:\Dashed?,UU74:\dashed?,UU74:dashes,UU5:\dashframed?,UU75:\Dc?,UU74:\Ddashed?,UU74:\Ddotted?,UU74:hdecori,UU15:decoration,UU6LW977N*tj??gwdefaultUUentry*,49 5\define?,UU73\definemorphism?,UU75hdiagi,UU12\diagram?,UU75dimensionUUregisters,5\dir?,UU16,18,39,40hdirectioni,UU12\documentclass?,UU5\dotframed?,UU75\Dotted?,UU74\dotted?,UU74\dottedwith?,UU74\Dp?,UU74hdriveri,UU19\Drop?,UU74\drop?,UU15\dsize?,UU73\dumpPSdict?{},UU35ߍE,UU8,10Edge,UU6Edgec,UU6EdgepR,UU6\enddiagram?,UU75\endxy?,UU5,6,14entryUUheight,48entryUUmargin,48entryUUwidth,48\entrymodifiers?,UU49Error,UU5hescapGei,UU51eu,UU27\everyentry?,UU49extension,UU19extents,UU6 xedUUgrid,48fonts,UU5formats,UU4\Framed?,UU75\framed?,UU75freeUUsoftware,3french.sty,UU4\frm?,UU10,24\frm?{**},UU26\frm?{*},UU26german.sty,UU4GNUUUGeneralPublicLicense,3\go?,UU74hgraphi,UU51\grow?,UU74h,UU12\halfrootthree?,UU7\halfroottwo?,UU7\halign?,UU50gw:\hbox?,UU12 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ۍ:\spreaddiagramrows?,UU75:\squarify?,UU74:\squash?,UU74:squiggles,UU5:\ssize?,UU73:\Ssolid?,UU74:\sssize?,UU73:state,UU6:hstepi,UU51:\stop?,UU74:style,UU13:styleUUoption,5:\swap?,UU74o:TU>'ExXUUreferencepGoint,6:\Text?,UU74:\text?,UU74:\Tip?,UU74:\tip?,UU74:tips,UU5:\tsize?,UU73:\Ttip?,UU74:\turnradius?,UU39:\txt?,UU18:U,UU6:U,UU8,10:Uc,UU6:UpR,UU6:\Uc?,UU74:\Up?,UU74:\UseCrayolaColors?,UU30:\usepackage?,UU5:\UsePSheader?{},UU35:\UsePSheader?{},UU35:\UsePSspecials?{},UU34:\UseRules?,UU16:\UseSingleDriver?,UU19:\UseTips?,UU27:v,UU12:hvectori,UU8:version,UU5:Warning,UU5:warningUUmessages,4:warranty*,UU3:X,UU6:x,UU8,9:Xoriginm,UU6:Xxbase,UU6:XybaseN,UU6:Xc,UU6:XpR,UU6:XmaxA̲,UU6:Xmin ,UU6:\Xc?,UU74LW979Pg*tj??gw\xdashed?,UU75 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,UU6:\Yc?,UU74:\Ymax?,UU74:\Ymin?,UU74:\Yorigin?,UU74:\Yp?,UU74:\Yxbase?,UU74:\Yybase?,UU74N8:zeroUUpGosition,6LW980;lPFɌ cmbsy10E-ff cmcsc10D- cmcsc10C"xmsam5@-hcmbx5?f$cmbx7>- cmcsc10=R6ff cmss12 logo105D xycmbt105D xycmat10FQ xycirc105D xybsql105D xybtip105D xyatip106δ xydash10 !", cmsy10 O!cmsy7 0ncmsy5 b> cmmi10 0ercmmi7O \cmmi5K`y cmr10ٓRcmr7Zcmr5u cmex10