; TeX output 1999.02.25:1519! /XYdict where not{250 dict /XYdict exch def /xy{mark exch XYdict begin countdictstack /xylevel exch def xyopen xycolor mark xypatt xypattern stopped xyclose end cleartomark}def /xyg{gsave xy}def /xyf{currentfont exch xy grestore setfont}def /xycc{{xychgcol}xy}def /xyc{XYdict begin xycolstore end}def /xyx{/xyYpos exch def /xyXpos exch def}def /xyp{currentpoint xyx}def /xyd{setupDirection XYdirection 2 mul}def /xyct{currentpoint xyt 2 copy 6 2 roll}def /xyt{xyXpos xyYpos 2 copy translate}def /xyr{neg rotate xynt}def /xyrs{neg rotate 3 -1 roll sub neg 3 1 roll sub exch moveto xynt}def /xynt{neg exch neg exch translate}def /xys{scale xynt}def /xyss{scale 3 -1 roll sub neg 3 1 roll sub exch moveto xynt}def /xyi{0 0 transform grestore gsave itransform}def }if&! /XYdict where pop begin XYdict begin! /xyopen{currentdict /XYddict known{XYddict null eq{} {XYddict begin xyopen}ifelse}if}def /xyclose{countdictstack -1 xylevel 1 add{pop end}for}def /xychgcol{/xycolor exch def}def /xysetcol{xypush xychgcol}def  ! /xypush{16 dict /XYddict exch def XYddict begin}def /undef where {pop /xypop{countdictstack xylevel eq{}{end}ifelse currentdict /XYddict undef}def} {/xypop{countdictstack xylevel eq{}{end}ifelse /XYddict null def}def}ifelse /pu /xypush load def /pp /xypop load def! /xypspt{72 72.27 div dup scale}bind def /pscorrect{.85 mul}bind def /gstartxy{gsave xypspt xywidth xycap xyjoin xymiter newpath 0 0 moveto}def /xypath{gstartxy rmoveto counttomark 2 idiv -1 1{pop lineto}for}def /xystroke{stroke grestore}bind def /xyfill{closepath fill grestore}bind def /xystfil{closepath gsave fill grestore 0 setgray 0 setlinewidth xystroke}bind def /xyeofill{closepath eofill grestore}bind def ! /xypolyline{xypath xystroke}def /xypolyfill{xypath xyfill}def /xydotsep{/@ currentlinewidth 2 mul def}def /xypolydot{xypath xydotsep [xydt @] 0 setdash xystroke}def /xypolydash{xypath xydotsep [@ @] 0 setdash xystroke}def /xypolyeofill{xypath xyeofill}def /pe /xypolyeofill load def /pl /xypolyline load def /pf /xypolyfill load def /pt /xypolydot load def /pd /xypolydash load def ! /arc4pop{arcto 4{pop}repeat}bind def /xyoval{gstartxy oval closepath xystroke}def /xycircle{gstartxy circle xystroke}def /circle{dup 0 moveto 0 0 3 -1 roll 0 360 arc}def /oval{newpath 2 copy exch 5 index add 2 div exch 3 copy 10 3 roll moveto 1 index dup 5 1 roll 3 index 7 index arc4pop dup dup 4 1 roll 4 index exch 6 index arc4pop 1 index dup 8 1 roll 4 index 4 index arc4pop arc4pop closepath}def /xyellipse{gstartxy counttomark 1 gt{squarify pop pop 1}if circle xystroke}def /ov /xyoval load def /ox /xyellipse load def P! /dotit{dup currentlinewidth 6 mul div round div /@ exch def [xydt @] 0 setdash}def /elldash{dup 4 -1 roll 10 exch div dashit}def /ovdash{dup 10 dashit}def /dashit{div round 2 mul div /@ exch def [@ @] 0 setdash}def /dotcirc{gstartxy cirlen dotit circle xystroke}def /dashcirc{gstartxy cirlen dashit circle xystroke}def /dotoval{gstartxy 5 copy ovlen dotit oval xystroke}def /dashoval{gstartxy 5 copy ovlen ovdash oval xystroke}def /cirlen{dup 6.283185 mul}bind def /ovlen{3 -1 roll sub 3 1 roll sub add exch 1.716815 mul sub}def /dotellipse{gstartxy counttomark 1 gt{squarify pop pop 1}if cirlen dotit circle closepath xystroke}def /dashellipse{gstartxy counttomark 1 gt{squarify add 2 div 1} {1 exch 1 exch}ifelse cirlen elldash circle xystroke}def /ot /dotellipse load def /od /dashellipse load def /vt /dotoval load def /vd /dashoval load def R! /filloval{gstartxy oval xyfill}def /stfiloval{gstartxy oval xystfil}def /fillcircle{gstartxy circle xyfill}def /stfilcircle{gstartxy circle xystfil}def /fillellipse{gstartxy squarify pop pop 1 circle xyfill}def /stfilellipse{gstartxy squarify pop pop 1 circle xystfil}def /squarify{4 copy sub 2 div 3 1 roll sub 2 div translate add 2 div 3 1 roll add 2 div 2 copy scale 2 copy add 2 div currentlinewidth exch div setlinewidth newpath}def /fe /fillellipse load def /sfe /stfilellipse load def /fo /filloval load def /sfo /stfiloval load def /fc /fillcircle load def /sfc /stfilcircle load def ! /xywidth{.4 pscorrect setlinewidth}bind def /xydash{[] 0 setdash}bind def /xycap{1 setlinecap}bind def /xyjoin{1 setlinejoin}bind def /xymiter{10 setmiterlimit}bind def 5! /cc{dup exec xychgcol}def /lw{dup setlinewidth /@l exch def /xywidth{@l setlinewidth}bind def}def /lc{dup setlinecap /@c exch def /xycap{@c setlinecap}bind def}def /lj{dup setlinejoin /@j exch def /xyjoin{@j setlinejoin}bind def}def /ml{dup setmitrelimit /@m exch def /xymiter{@m setmitrelimit}bind def}def ! /setupDirection{dup -2048 lt{3072 add neg 1024 exch} {dup 0 lt{1024 add neg -1024}{dup 2048 lt{1024 sub -1024 exch} {3072 sub 1024}ifelse}ifelse}ifelse atan dup 180 gt{360 sub}if dup /XYdirection exch def rotate}def ! userdict begin /gray{setgray}bind def /gray@{setgray}bind def /rgb{setrgbcolor}bind def /rgb@{setrgbcolor}bind def /hsb{sethsbcolor}bind def /hsb@{sethsbcolor}bind def /setcmykcolor where{pop}{/setcmykcolor{dup 3 1 roll dup 5 1 roll exch sub 1 add 5 1 roll exch sub 1 add 4 1 roll exch sub 1 add 3 1 roll setrgbcolor}bind def}ifelse /cmyk{setcmykcolor}bind def /cmyk@{setcmykcolor}bind def /sethalftone where{/sethalftone load /tone exch def}if /xycolarray 3 array def /xycolstore{currentrgbcolor 2 -1 0 {exch xycolarray 3 1 roll put}for}def xycolstore /xycolor{0 1 2{xycolarray exch get}for setrgbcolor}def /xypatt{}def /xypattern{cleartomark}bind def end ! end end&! /XYdict where pop begin XYdict begin! /:patt {XYddict begin 14 dict begin /BGnd exch def /FGnd exch def /PaintData exch def /PatternType 1 def /PaintType 1 def /BBox[0 0 1 1]def /TilingType 1 def /XStep 1 def /YStep 1 def /PatternMtx[24 0 0 24 0 0]def /PaintProc BGnd null ne {{begin BGnd aload pop setrgbcolor 0 0 1 1 rF FGnd aload pop setrgbcolor 24 24 true PatternMtx PaintData imagemask end}} {{begin FGnd aload pop setrgbcolor 24 24 true PatternMtx PaintData imagemask end}} ifelse def currentdict PatternMtx end gsave patangle xyland{180 add}if rotate macfreq patfreq div dup neg exch scale matrix currentmatrix grestore gsave setmatrix /DeviceRGB setcolorspace makepattern grestore end}defj! /rF{gsave newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto fill grestore}bind def ! /setpatscreen{/pattstring exch store patfreq patangle xyport not{90 add}if {1 add 4 mul cvi pattstring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and}setscreen}bind def /setcolpattern{setpatscreen 64 div 1 exch sub currentrgbcolor 1 1 3{pop 1 exch sub 3 index mul 1 exch sub 3 1 roll}for setrgbcolor pop}def /setgraypattern{setpatscreen 64 div setgray}def /macfreq 9.375 def /patangle 0 def /patfreq 12.5 def! /checkland{/normland where{pop normland not}{false}ifelse /xyland exch def /por where{pop por}{/isls where{pop isls not /xyland true def} {/land where{pop land not}{true} ifelse}ifelse}ifelse /xyport exch def}def *! /setpatfreq{/patfreq exch def}def /setpatangle{/patangle exch def}def /setbackcolor{/backcolor exch def}def /setforecolor{/forecolor exch def}def [1 1 1] setbackcolor xycolarray setforecolor /bg /setbackcolor load def /fg /setforecolor load def /pa /setpatangle load def /pq /setpatfreq load def ! /xypattern{checkland counttomark dup 0 eq{pop} {dup 1 eq{pop setpatscreen} {dup 2 eq{pop setcolpattern} {dup 3 eq{pop /setcolorspace where { /.setcolorspace where{pop pop pop setcolpattern} {/.buildpattern where {pop forecolor backcolor :patt setpattern }{pop pop setcolpattern}ifelse}ifelse} {pop setcolpattern}ifelse} {5 eq{/setcolorspace where{ /.setcolorspace where{pop pop pop pop pop setcolpattern} {/.buildpattern where {pop :patt setpattern }{pop pop pop pop setcolpattern}ifelse}ifelse} {pop pop pop setcolpattern}ifelse }{}ifelse}ifelse}ifelse}ifelse}ifelse cleartomark }def /xysetpattern{/xypatt exch def}def /sp /xysetpattern load def ! end end&! /XYdict where pop begin XYdict begin! /xysize 10 def /T true def /F false def /dimendiv{65536 div}bind def /xysegl 327680 dimendiv def /xyopp{1 -1 scale}bind def /xynormwidth{26213 dimendiv pscorrect}bind def /xywidth{xynormwidth setlinewidth}bind def ! /xyfont{4096 add 64 div round 64 mul 4096 sub}def /xydt 0.01 def /xysdfont{4096 add 32 div round 32 mul 4096 sub}def /xydots{xywidth 1 setlinecap [xydt 2] 0 setdash}bind def /f /xyfont load def /fs /xysdfont load def! /xyCheckDir{dup 8 div 3 mul 3 -1 roll sub neg exch div 360 mul dup dup XYdirection sub 180 div round 180 mul XYdirection add dup 3 -1 roll sub abs 10 gt not{exch}if pop}def G! /xyrulth{26213 dimendiv pscorrect setlinewidth 0 setlinecap}bind def ! /gsavexy{gsave xypspt XYdirection rotate xywidth newpath 0 0 moveto}def /gchksavexy{gsave xypspt setupDirection xywidth newpath 0 0 moveto}def m! /xyswap{XYdirection 180 add /XYdirection exch def}def /xyline{gstartxy setupDirection rlineto xystroke}def ! /dash{exch gchksavexy xysegl XYdirection dup -90 lt{pop neg}{90 gt{neg}if}ifelse exch{neg}if 0 rlineto xystroke}def /stopper{gstartxy setupDirection 0 xysegl 2 div rmoveto 0 xysegl neg rlineto xystroke }def /d /dash load def /st /stopper load def! /solid{gstartxy xydash neg exch neg exch rlineto xystroke}def /dashed{gstartxy 2 copy dup mul exch dup mul add sqrt dup xysegl add xysegl 2 mul div round 2 mul 1 sub div [ exch dup ] 0 setdash neg exch neg exch rlineto xystroke}def /l /solid load def /dd /dashed load def! /dot{gstartxy 2 setlinecap [xydt 2] 0 setdash 1 0 rlineto xystroke}def /dotted{gstartxy 2 copy dup mul exch dup mul add sqrt dup 2 div round 1 add div 2 setlinecap [xydt 3 -1 roll] 0 setdash neg exch neg exch rlineto 0 0 rlineto xystroke}def /p /dot load def /dt /dotted load def! /cubic{gstartxy docubic} def /docubic{chkvalid {chkcubedge 8 -2 roll moveto curveto xystroke pop} {cleartomark grestore}ifelse}def /chkcubedge{2 copy 1.0 eq{0.0 eq{pop pop}{cubicedge}ifelse} {pop cubicedge}ifelse}def /bz /cubic load def! /dotcubic{gstartxy 1 setlinecap [xydt 2] 0 setdash docubic}def /dashcubic{gstartxy [5 5] 0 setdash docubic}def /bt /dotcubic load def /bd /dashcubic load def! /squine{gstartxy dosquine}def /dosquine{chkvalid {chksquedge 2 copy moveto xysq2cub curveto xystroke pop} {cleartomark grestore}ifelse}def /q /squine load defD! /chkvalid{2 copy lt{dup 1 gt{false}{true}ifelse}{false}ifelse}def ! /chksquedge{2 copy 1.0 eq{0.0 eq{pop pop}{squineedge}ifelse} {pop squineedge}ifelse}def /xysq2cub{xysq2cubit 6 1 roll xysq2cubit 6 1 roll 3 index 3 index xysq2cubit 6 1 roll xysq2cubit 6 1 roll pop pop}def /xysq2cubit{2 index 2 mul add 3 div}def ! /dotsquine{gstartxy 1 setlinecap [xydt 2] 0 setdash dosquine}def /dashsquine{gstartxy [5 5] 0 setdash dosquine}def /qt /dotsquine load def /qd /dashsquine load def! /xy4mul{8 copy 5 -1 roll mul 5 1 roll 6 -1 roll mul 6 1 roll 3 -1 roll mul exch 4 -1 roll mul 3 1 roll add 3 1 roll add exch 10 2 roll 7 -1 roll mul 7 1 roll 4 -1 roll mul 5 1 roll 4 -1 roll mul 4 1 roll mul add 3 1 roll add exch 3 -1 roll }def ! /xy44mul{4 copy 16 4 roll exch 3 1 roll 4 copy 12 4 roll xy4mul 12 4 roll xy4mul 12 -4 roll 4 copy 16 4 roll 8 4 roll xy4mul 12 4 roll xy4mul}def M! /cubicedge{10 2 roll exch 8 1 roll 3 -1 roll dup dup 9 2 roll 5 -1 roll dup dup 9 1 roll 8 3 roll 4 1 roll dup dup 5 3 roll dup dup 5 1 roll 3 -1 roll 18 -2 roll 2 copy 1 sub neg 4 1 roll 1 sub neg exch 4 1 roll xy444mul pop pop pop 13 1 roll pop pop pop 9 1 roll 10 1 roll pop 8 1 roll 7 1 roll 8 1 roll pop 5 1 roll 3 1 roll}def ! /xy444mul{4 copy 24 4 roll 12 -4 roll 16 4 roll 4 copy 16 4 roll xy44mul 20 8 roll xy44mul 12 -4 roll 4 -1 roll 7 1 roll exch 4 1 roll exch 6 -1 roll exch 4 2 roll 16 8 roll 8 4 roll 4 -1 roll 7 1 roll exch 4 1 roll exch 6 -1 roll exch 4 2 roll 8 4 roll 16 4 roll 8 4 roll 20 -4 roll exch 3 1 roll 4 copy 20 4 roll 4 copy 16 4 roll 4 copy 12 4 roll xy4mul 28 4 roll xy4mul 20 4 roll xy4mul 12 4 roll xy4mul}def ! /squineedge{8 2 roll exch 5 1 roll 3 -1 roll dup 6 2 roll 1 index exch 10 -2 roll 2 copy 1 sub neg 4 1 roll 1 sub neg exch 4 1 roll xy44mul 4 1 roll pop 5 1 roll 6 1 roll 3 -1 roll pop}def c! /xyshort{2 copy abs exch abs add xysegl .5 mul lt {pop pop grestore}{rlineto xystroke}ifelse}def s! /tipwidth{xywidth xynormwidth dup currentlinewidth exch div sqrt dup dup scale mul setlinewidth 1 setlinecap}def ! /halftip{tipwidth xysize 10 div 0 0 moveto -.25 0 3 -1 roll -2.5 mul 0 xysize 2 div neg dup .62 mul 2 div neg curveto}bind def ! /atip{gchksavexy halftip xystroke}def /btip{gchksavexy xyopp halftip xystroke}def /tip{gchksavexy gsave halftip stroke grestore xyopp halftip xystroke}def /t /tip load def /a /atip load def /b /btip load def@! /cmatip{gchksavexy halfcmtip xystroke}def /cmbtip{gchksavexy xyopp halfcmtip xystroke}def /cmtip{gchksavexy gsave halfcmtip stroke grestore xyopp halfcmtip xystroke}def /halfcmtip{tipwidth 0 0 moveto -.1333 0 .25 neg dup .125 3 -1 roll .25 curveto}bind def /ct /cmtip load def /ca /cmatip load def /cb /cmbtip load def2! /xyfscale{/xyfsize exch def}def /xyfsize{10}def /eu{-0.0551 0.0643 -0.0976 0.1386 -0.125 0.2188}def /cm{-0.105 0.0437 -0.1804 0.1380 -0.2 0.25}def /XY{-0.1753 0.0181 -0.3452 0.0708 -0.5 0.155}def /tipstart{3 -1 roll gchksavexy exch xyfscale tipwidth dup XYdict exch known{dup /xy eq{pop /XY}if}{pop /XY}ifelse XYdict exch get}def /tipend{halfxytip xystroke}def /halfxytip{1 1 6{pop xyfsize mul 6 1 roll}for 0 0 moveto curveto}def /A{tipstart D}def /B{tipstart C}def /C{xyopp D}def /D{exec tipend}def /AB{tipstart dup gsave exec halfxytip stroke grestore C}def ;! /Tip{exch gchksavexy /xyfsize{10}def tipwidth gsave dup XYdict exch known{dup /xy eq{pop /XT}if}{pop /XT}ifelse XYdict exch get dup halfTip stroke grestore xyopp halfTip xystroke}def /XT{360 32 div neg}def /Xt{-1 .31 mul 1 atan}def /ET{360 64 div 5 mul neg}def /Et{-1 .31 mul 1 atan}def /halfTip{exec rotate XY halfxytip}def /halfTtip{halfTip}def /Ttip{exch gchksavexy /xyfsize{10}def tipwidth gsave dup XYdict exch known{dup /xy eq{pop /Xt}if}{pop /Xt}ifelse XYdict exch get dup halfTtip stroke grestore xyopp halfTtip xystroke}def /tt /Tip load def /tT /Ttip load def! /halfturn{xysegl 2 div dup dup neg exch rmoveto 0 exch dup exch -180 -90 arc}bind def /aturn{gchksavexy halfturn xystroke}def /bturn{gchksavexy xyopp halfturn xystroke}def /ta /aturn load def /tb /bturn load def! /xysqll 231705 dimendiv def /squigl{gchksavexy xysqll dup neg 0 rmoveto 2 div dup dup neg dup 3 -1 roll 2 sqrt mul dup 5 1 roll 135 45 arcn dup 3 -1 roll -135 -45 arc xystroke}def /g /squigl load defk! /fullhook{0 xysegl 2 div dup -90 90 arcn}bind def /halfhook{xysegl 2 div dup 0 exch 180 90 arcn}bind def ! /ahook{gchksavexy fullhook xystroke}def /bhook{gchksavexy xyopp fullhook xystroke}def /hook{gchksavexy gsave halfhook stroke grestore xyopp halfhook xystroke}def /h /hook load def /ha /ahook load def /hb /bhook load defe! /xyqcirc{dup dup neg exch translate newpath dup neg 0 exch moveto 0 0 3 -1 roll -90 0 arc}bind def x! /circ{gstartxy 3 copy pop 2 copy cos mul 3 1 roll sin mul rmoveto 0 0 5 2 roll arc 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-6.0 -20.99991 0.0 -16.79993 0.0 1.0 q}xy$g?" {mark 0.0 -25.19989 -6.0 -20.99991 0.0 -16.79993 1.0 1.0 q}xy$g?" {mark 12.0 -25.19989 6.0 -29.39987 0.0 -25.19989 0.0 0.0 q}xy$g?" {mark 12.0 -25.19989 6.0 -29.39987 0.0 -25.19989 0.0 1.0 q}xy$g?" {mark 12.0 -25.19989 6.0 -29.39987 0.0 -25.19989 1.0 1.0 q}xy$gA" {mark 36.0 -25.19989 30.0 -29.39987 24.0 -25.19989 0.0 0.0 q}xy$gA" {mark 36.0 -25.19989 30.0 -29.39987 24.0 -25.19989 0.0 1.0 q}xy$gA" {mark 36.0 -25.19989 30.0 -29.39987 24.0 -25.19989 1.0 1.0 q}xyG@92Thecurren9timplementationisprogrammedentirely2withinj\standardTuAEXando> logo10METAF9ONT",i.e.,usingTuAEX2macros(no\special*s)andwithfon9tsdesignedusing2METAF9ONT. OptionallyspAecial`driv9ers'makeitpAossi-2ble?toproAduceD9VI2 leswith`specials'forextragraphics2capabilities,Te.g.,using'- cmcsc10PostScript.-=Aacmr61ff[ A ß-:!q% cmsy6L|{Ycmr8BRICS,XComputerScience,AarhÎusUniversity(bld. 540),NyMunkegade,DK{8000AarhusC,Denmark. [-:yLMPCEX(Mathematicsdept.),MacquarieUnivÎersityJ,XNorthRyde,Sydney,AustraliaNSW2109. > "5-:1L(- cmcsc10PostScriptXisaregisteredTJrademarkofAdob75B.1 UnsuppGortedUUincompatibilitiesC.....75B.2 ObsoleteUUkernelfeatures񍍑........75B.3 ObsoleteUUextensions&features1....76B.4 ObsoleteUUloading֍............77B.5 CompilingUUv2-diagrams.........77CCommonTErrorsz77ReferencesZ77Indexޕ78!#ListffofFigures1  !", cmsy10hpGosiitions. ҍ...............82 ExampleUUhplaceis1H............103 hob8jectis.................124 hdecoriations...............165 KernelUUlibraryhdiriectionals......176 hciricles.x.................197 SyntaxUUforcurves.q@...........228 PlainUUhframeis.c.............259 BracketUUhframeis.׍............2510 Rotations,UUscalingsand ipsO......3111 TheUU38standardMacintoshpatterns.8 .3212 impGortingUUagraphicforlabelling...3413 hpathisFύ..................3914 harrowis..................4115 PastingUUdiagram.F............4416 htwoGcellisލ................45gweL17ePhgraphisǍ.................52 jeL18ePhknot-pieceiUUconstructionset.....62eL19ePknotD~crossingswithorientationsand ePlabGelUUpositions8t..............63eL20ePknotsjoins,withorientations,labGelsePandUUshiftsj................65eL21ePExtension[implementationreplacedbyePuseUUofhdriverispGecials..........69WReK4PSfile="kris.eps" llx=0 lly=0 urx=66 ury=86 rwi=660 &Kristo erUURoseRJRossUUMoGore4PSfile="ross.eps" llx=0 lly=0 urx=62 ury=84 rwi=620 "銍eKPrefaceeKThisreferencemanualgivesconcisedescriptionsofeKthe\moGdulesofXXY <\-pic,writtenbytheindividualau-eKthors.èPleasepdirectanyTU>'ExXnicalquestionorsug-eKgestion"forimprovement"directlytotheauthoroftheeKcompGonent<;inquestion,A@preferablybyelectronicmaileKusingtheindicatedaddress. CompletedoGcumentseKandprintedtechnicaldoGcumentationorsoftwareiseKmostUUuseful. X썒eKTheyn rstpartdoGcumentstheyjXY n-pickernelwhicheKisalwaysloaded. TheremainingpartsdescribGetheeKthreekindsofoptions:8.': cmti10extensionsinpartIGIextendeKthekernelgraphiccapabilities,:fe}'aturesDzinpartIGIIeKprovideTspGecialinputsyntaxforparticulardiagrameKtypGes,oand#driversinpartIVmakeitpGossibletoeKexploitTtheprintingcapabilitiessuppGortedbyDVIeKdrivercprograms.F*oreachoptionitisindicatedhoweKit,shouldbGeloaded.]dTheappendicescontainanswerseKtoalltheexercises,A7asummaryofthecompatibil-eKity^withversion2,`andlistsomereasonswhyZXY A^-piceKmightUUsometimeshaltwithacrypticTU>'ExXerror.eKLicense.XY-picIisfreesoftwareIinthesensethatiteKisUUavqailableunderthefollowinglicenseconditions:"pps: SDict begin xyc endǍY2" {0.0 89.88191 -18.49307 -89.88191 18.49306 ov}xyUXY -pic:qGraphsUUandDiagramswithTU>'ExX ፍKc. s1991{1998 Kristo erUUH.Rose  hcEK 1994{1998 RossUUMoGore#eKThe.XY2-pic2packqageisfreesoftware;6youcanredis-eKtributeQitand/ormoGdifyitunderthetermsoftheeKGNUsGeneraltPublicLicenseaspublishedbytheF*reeeKSoftware=]F*oundation;EZeitherversion2oftheLicense,eKorUU(atyouroption)anylaterversion.eKTheXY D-picpackqageisdistributedinthehopGethateKitwillbGeuseful,Obutwithout\anywarr}'anty};withoutLWK3*tj??]even/theimpliedwarrantyofmer}'chantability笲or t- nessforap}'articularpurpose[.wSeeutheGNUuGeneralPublicUULicenseformoredetails.Y*oushouldhavereceivedacopyoftheGNUGen-eralXIPublicLicensealongwiththispackqage;ifnot,write{totheF*reeSoftware{Foundation,RInc.,675{MassAve,UUCambridge,MA02139,USA.InpracticethismeansthatyouarefreetouseXY -pic?foryourdoGcumentsbutifyoudistributeanypartn@ofnthenyouareobligedtoensurethatthefullsourcetextOofKXY aO-picisavqailabletothem(thefulltextofthelicenseOinthe le/ cmmi10X)andYforhdimenisionsOandlowerOcaselikexandy(forhfactoris.#8PartffI0Nq cmbx12The KernelꨍVers.3.7bCyKristo erH.Rosehkrisrose@brics.dkiuTAfter\givinganoverview\ofthe\XY -picenvironmentin8x1,qSthispartdoGcumentthebasicconceptsof8XY -pictureconstructioninx2,includingthemaintained`graphicstate'.+Thefollowingsectionsgivethepre-cisesyntaxrulesofthemainXY-picconstructions:the\pGositionlanguageinx3,^theob8jectconstructionsinx4, Bandthepicture`decorations'inx5.SUx6presentsthekernelrepGertoireofob8jectsforuseinpictures;x7mdoGcumentstheinterfacetomXY -picoptionslikethestandardUU`feature'and`extension'options.Detailsfoftheimplementationarenotdiscussedhere3butinthecompleteTU>'ExXnicaldoGcumenta-tionUU[15 ]. q荍1TheǨX#՟YY-picffimplementationThisCsectionbrie ydiscussesthevqariousaspGectsofthe~present~}XY -pickernelimplementationofwhichtheuserUUshouldbGeaware.^Z1.1LLoading&aX1"Yv-picXY -picPiscarefultosetupitsownenvironmentinor-der0tofunctionwithalargevqarietyofformats.!XF*oreKmostUUformatsasinglelinewiththecommand<\input?xyeKinKzthepreambleofadoGcument leshouldloadthe eKkernel(see`integrationwithstandardformats'bGeloweKfor.vqariationspGossiblewithcertainformats,dinpar-eKticularUUL5ffA͉TU>'ExX[9]).eKTherestofthissectiondescribGesthingsyoumusteKconsider/ifyouneedtouse+XY c/-pictogetherwithothereKmacro%packqages,,styleoptions,,orformats.u6ThelesseKyour<|environmentdeviatesfromplainTU>'ExXtheeas-eKier:itshouldbGe. 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cationc:\theyjustsetastandardforwhateKdrawing[capabilitiesshouldatleastbGerequiredbyaneGXYK-pic1implementation.I[ImplementationsexploitingeKcapabilitites,ofparticularoutputdevicesareinuse.eKHencec9thefontsareonlyloadedbyc5XY 9-picifthecon-eKtrolsequencenamesareunde ned|thisisusedtoeKpreloadZ?thematdi erentsizesorpreventthemfromeKbGeingUUloadedatall.eK1.4%KAllo`cationseKOne nalthingthatyoumustbGeawareofisthatXY -eKpicalloGcatesasigni cantnumbGerofdimensionregis-eKtersandsomecounters,(tokenregisters,andbGoxreg-eKisters,in\ordertorepresentthestateanddocomputa-eKtions.oTheOcurrentkernelalloGcates4counters,P28di-eKmensions,g2bGoxregisters,4tokenregisters,g1readeKchannel,Hand1writechannel(whenrunningundereKL5ffA͉TU>'ExX;Ensome={otherformatsuseslightlymorebGecauseeKstandard^generictempGorariesareused)./OptionsmayeKalloGcatefurtherregisters(currentlyloadingevery-eKthingloads-o6dimen-,cv3toks-,1bGox-,and9count-eKregistersUUinadditiontothekernelones).fff[ J= "5-:3LTheX`v2'featureinÎtro "5-:4LNoXdescriptionofaTAEMXprogramiscompletewithoutanexplanationofitsname.LWK5٧*tj??gw2PictureffbasicsThebasicconceptsinvolvedwhenconstructingXY3- picturesllarepGositionsandob8jects,andhowtheycom-bineUUtoformthestateusedbythegraphicengine.Theb@generalstructureofanb'ExXusersmaysubstituteUU\begin{xy};*...\end{xy}2U \whereX]istheTU>'ExXIdimensiondistancerightXY B-picture(0?hasco-ordinates(<0mm,0mm>3h,\of(course).%ThezeropGositionofֱthe֭XY V-picturedeterminesthebGoxproducedbythe\xy...\endxy[commandtogetherwiththefourpa-rameters[Xmin ,XmaxA̲,Ymin,and[Ymax$'setsuchthatallJtheob8jectsinthepictureare`contained'inthefollowingUUrectangle:9A|ps: SDict begin xyc endǍ1" {0.0 71.16487 -34.1348 -36.95503 42.68724 ov}xyn O!cmsy7ޟ I0ܟ" {-21.37503 8.55159 dt}xy-*TU>'ExXUUreferencepGointlnn՟" {24.0 9.60004 dt}xyn՟" {-36.98839 0.0 l}xyn՟" {-1024 10 /xy AB}xyv2 wXminׇ" {71.13152 0.0 l}xyׇ" {3072 10 /xy AB}xy: wXmaxǍܟ"$" {0.0 -34.14313 l}xyܟk" {1024 10 /xy AB}xyܟ2ݵYminǍܟR3" {0.0 42.67891 l}xyܟ" {-3072 10 /xy AB}xyܟYmax1wherezthedistancesfollowthe\upandright>0"principle,Se.g.,theSindicatedTU>'ExXreferencepGointhascoGordinatesڵ< Xmin ,0pt>+ڪwithinڵtheڱXY Z-picture.ThezeroqqpGositiondoesnothaveqqtobecontainedinthepic-ture,bbut_Xmin䂸$~Xmax^^asUUreferencepGoint.2.2ObjectsuTThesimplestformofputtingthingsintothepictureisq9to`drop'anobje}'ctdatapGosition.sAnob8jectislikeamTU>'ExXbGoxexceptthatithasageneralEdge-aroundits referencepGoint|inparticularthishastheextents(i.e.,Bitڽisalwaysڽcontainedwithin)thedimensionsL,RDz, U,andD,;awayfromthereferencepGointineachofthefourdirectionsleft,right,up,anddown.oOb-jects\ areencoGdedinTU>'ExXboxesusingtheconventiongweKthattheTU>'ExXreferencepGointofanob8jectisatitsleft eKedge,Sthus shifted< `(L,0pt>`ײfromthecenter|soaeKTU>'ExX)bGoxmaybGesaidtobearectangularob8jectwitheKL=0pt.qHereUUisanexample:&2dps: SDict begin xyc endǍ32" {0.0 42.65114 -14.23187 -28.48038 22.75652 ov}xygnn՟" {-28.48038 0.0 dt}xyz8 Lڀ" {42.65114 0.0 dt}xyv RǍ3ϟ;\" {0.0 -14.23187 dt}xyT#DǍ3ϟ>U" {0.0 22.75652 dt}xyq7U-*TU>'ExXUUreferencepGointlcBn՟" {24.0 9.60004 dt}xy"weKThe{ob8jectshownhasarectangleedgebutothersareeKavqailable@eventhoughthekernelonlysuppGortsrect-eKangleandcircleedges.AItisalsopGossibletouseentireeGXYK-pictures'asob8jectswitharectangleedge,00 astheeKreferenceY|pGoint,ZL=Xmin ,R˲=XmaxX,D!=Ymin#_,eKand>Uc=LYmax\..Thecommandsforob8jectsarede-eKscribGedUUinx4.reK2.3%KConnectionseKBesideshavingtheabilitytobGedroppedatapositioneKinOapicture,allob8jectsmaybGeusedtoc}'onnect'theeKtwoZcurrentob8jectsofthestate,,i.e.,pandc.1F*oreKmostgob8jectsthisisdoneby` lling'thestraightlineeKbGetween6thecenterswithasmanycopiesaswill teKbGetweenUUtheob8jects:>7vJps: SDict begin xyc end&8O \cmmi5p" {6.0 0 360 o}xyc4" {0.0 9.0 -4.0 -9.0 4.0 ov}xy43" {155.89508 38.97359 dd}xyˍc3232)3232Vv3232323232323232Vg3232?J׍3232323232323232323232325׍32323232323232323232323232c3232)3232Vv3232323232323232Vg323284mT}E֠" {-8.53021 0.0 dt}xy]UݳL4֠" {5.69609 0.0 dt}xyIߟUR֠3" {0.0 -5.69609 dt}xy(v.D֠xD" {0.0 8.53021 dt}xyc#U53232y3232Vv3232323232323232Vg3232?c׍323232323232323232323232׍323232323232323232323232323232y3232Vv3232323232323232Vg3232z\ڏ" {-8.53021 0.0 dt}xyEGLڏ" {5.69609 0.0 dt}xy/EGRڏ񍍒GQ3" {0.0 -5.69609 dt}xyjƟ`Dڏ񍍒GQxD" {0.0 8.53021 dt}xysiUyL3232{>ɍ3232Vv3232323232323232Vg3232?yγ׍323232323232323232323232;՟׍32323232323232323232323232yL3232{>ɍ3232Vv3232323232323232Vg3232ԟL(z[" {-8.53021 0.0 dt}xy{34L;ԟ[" {5.69609 0.0 dt}xy4R[3" {0.0 -5.69609 dt}xy D[xD" {0.0 8.53021 dt}xyßU j*3232k3232Vv3232323232323232Vg3232?j׍323232323232323232323232x~%׍32323232323232323232323232j*3232k3232Vv3232323232323232Vg3232p$;jD5n" {-8.53021 0.0 dt}xyl$$Lx~$n" {5.69609 0.0 dt}xysϟ$Rnōr3" {0.0 -5.69609 dt}xyof4DnōrxD" {0.0 8.53021 dt}xyp*=UsZl3232[i3232Vv3232323232323232Vg3232?ZSS׍323232323232323232323232hu׍32323232323232323232323232Zl3232[i3232Vv3232323232323232Vg3232aAt*Z^/" {-8.53021 0.0 dt}xy\fӟLht^/" {5.69609 0.0 dt}xycSR^/cA3" {0.0 -5.69609 dt}xy`1D^/cAxD" {0.0 8.53021 dt}xy`lcϧUݍJ<3232L3232Vv3232323232323232Vg3232?J׍323232323232323232323232Yş׍32323232323232323232323232J<3232L3232Vv3232323232323232Vg3232QğfJ՟M" {-8.53021 0.0 dt}xyL#LYğM" {5.69609 0.0 dt}xySoRMSP3" {0.0 -5.69609 dt}xyPtDMSPxD" {0.0 8.53021 dt}xyPUG:3232'ExXcommandswhichaddeKtotpictures.zMostsuchcommandsareprovidedbyeKtheCvqarioususerGzoptionsd(cf.x7)|onlyafewarepro-eKvidedwithinthekerneltofacilitateprogrammingofeKsuchUUoptions(andusermacros)asdescribGedinx5.eK2.5%KThe&aX1"Yv-picstateeKFinally0wesummarisetheuser-accessiblepartsoftheeGXYK-pictureǦstateoftwoǦpGositionstogetherwiththeeKlastob8jectassoGciatedwitheach:thepr}'evious!,%}p,iseKthe_pGosition< P\XpR, ﮵YpR>with_theob8jectLpR,?!Rp,Dp,eKUpR,(Edgep,andthecurr}'entز,c,isthepGosition< >Xc,eKYc> 3withUUtheob8jectLc,Rc,Dc,Uc,Edgec. F5eKF*urthermore,XY-pic]hasacon gurablec}'arte-eKsian:rc}'oordinatesystem 'ɲdescribGedcfbyanorigineKpGosition/< oX1t}\cmti7originm,~Yoriginm>#gand/twob}'ase vectorsLWK6M*tj??gw<Xxbase,筵Yxbase>ܲand/<,XybaseN,KYybaseN>zaccessed/bythe usualUUnotationusingparentheses:{dE(Bx,?y[) ]P=$n<#dkXorigina+8xXxbase+yXybase",#dkYorigina+8xYxbase+yYybase">This޺isexplainedinfullwhenweshowhowtosetthebaseUUinnote3dofx3. IZFinally^typGesettingaconnectionwillsetupa\placementǦstate"forreferringtopGositionsontheconnection9\thatisaccessedthroughaspGecial? po-sitionvconstruction;thisisalsodiscussedindetailinx3.ThewXY {-pic{stateֲconsistsofalltheseparameterstogether. /TheyxareinitialisedtozeroexceptforXxbasenȲ=Yybasef=1mm.The\edgesarenotdirectlyavqailablebutpGointsonthe?edgesmaybGefoundusingthedi erenthcorneriformsUUdescribGedinx3.ItTispGossibletoinsertan`initial'pieceofhposihdecoriJatthestartofeveryJXY ʱ-picturewiththedec-laration ff2 F\everyxy={}htextiUU}I\ff2This=willactasifthehtextiwastypGedliterallyrightafterGeach\xycommand,parsingtheactualcontentsasfifitfollowsthis{thusitisrecommendedthathtexti?hastheformhpGosi, .2s,<0pt>?,(0,0),andD;/0pt/"gisD;di erentfromtheoth-ers?Notes؍3a.Whendoingarithmeticwith+{and-thentheresultingxjcurrentob8jectinheritsthesizeofthehcoGordi,i.e.,theRrightargument|thiswillbGezeroUUifthehcoGordiisahvectori.̼Exercise2: How#doyousetctoanob8jectthesame{sizeasthesaved{ob8ject"ob"@butmoved<?X,ߵY8>x?gweK3b.Skewing{^using!qjustmeansthatthereference eKpGoint ofcismovedwithaslittlechangetotheeKshapGeoftheob8jectaspossible,$i.e.,theedgeofceKwillQ\remaininthesameloGcationexceptthatiteKwillgrowlargertoavoidmovingthereferenceeKpGointUUoutsidec.OeKExercise3: WhatpdoGesthehposi...!R-Ljdo?eKBug:tTheresultof! 폲isalwaysarectanglecur-eKrently*.0eK3c.0A+hpGosi+c}'oversanotherifitisarectanglewitheKsizesucientlylargethattheotheris\under-eKneath".[UThe/.[opGeration/\extends"ahpositoeKcover*fanadditionalone|thereferencepGointofceKisMnotmovedMbuttheshapGeischangedtoarect-eKangleUUsuchthattheentirepob8jectiscovered.QeKBug:lnon-rectangular(ob8jectsare rst\trans-eKlated"]intoarectanglebyusingadiagonaleKthroughb@theob8jectasthediagonaloftherect-eKangle.eK3d.ThekopGerations:and::Wsettheb}'ase,3usedforeKhcoGordiinatesnhavingtheform(x,?y[)ֲ.#The: 9op-eKeration^willset<Xoriginm, /Yoriginm>to^p,a<Xxbase,eKYxbase>todcDorigin0,Kand< 'aXybaseN,YybaseN>toeK<HlfYxbase,ʵXxbase>(thisensuresthatitisausualeKsquareecoGordinatesystem). The::J4operationeKmay thenbGeusedafterwardstomakenonsqareeKbasesAbyjustsettingyb}'ase5toc֍originIԲ.7WHereeKarerWtwoexamples: rstly0;<1cm,0cm>:E䊲setstheeKcoGordinateUUsystem1h',|ps: SDict begin xyc end,n:" {28.45274 0.0 l}xy:" {3072 10 /xy AB}xyǍp" {0.0 28.45274 l}xyp-" {-3072 10 /xy AB}xy]origin=xbase$mybase7Q@(1,1)p-" {-28.45274 0.0 dt}xyǍ:" {0.0 -28.45274 dt}xyeKwhile y<1cm,.5cm>;<2cm,1.5cm>:<1cm,1cm>::eKde nesKHe&ps: SDict begin xyc endn" {-28.45276 28.45276 dd}xy̟" {-2048 10 /xy AB}xy- ybase jbAefore H::ǍWR%" {28.45276 28.45276 l}xyWz" {4096 10 /xy AB}xyǍ;%" {0.0 14.22638 l}xy;%-" {-3072 10 /xy AB}xyMj>%origin썍Zxbasem0LybaseS9]ǁ(1,1)Ǎ;%" {-28.45276 -28.45276 dt}xyǍWR%" {0.0 -14.22638 dt}xyyeKwhere,4ineachcasetheisat0l1,4nthebasevectorseKhaveUUbGeendrawnandtheisat(1,1)F.QeKWhen5`workingwithcartesiancoGordinatestheseeKthreeUUspGecialhfactorisareparticularlyuseful:_eKff2 *ˍ\halfroottwoK0:70710678 K1K&fes2 )PpHPfeE2 \partroottwoK0:2928932218 l1l&fes2PpPfeE2\halfrootthreeK0:86602540 K1K&fes2 )PpHPfeE3SeKff2 eKMore(canbGede nedusing\defLD(or\newcommand eKinUUL5ffA͉TU>'ExX).LWK75*tj??ځ> ffffd TQղSyntax\ActionX-ffd m͍QոhpGosiCI]!d 3hcoGordi\c hcoGordiiJ\jd 3hpGosiUU+hcoordi\c hpGosi5+8hcoGordi"1ɟ^3aJ\jd 3hpGosiUU-hcoordi\c hpGosi58hcoGordi"1ɟ^3azJ\jd 3hpGosiUU!qǸhcoordi\c hpGosithenUUskew^3b ߵcbyhcoGordiJ\jd 3hpGosiUU.qǸhcoordi\c hpGosibutUUalsocovering^3c øhcoGordiJ\jd 3hpGosiUU,hcoordi\c hpGosithenUUc hcoGordiJ\jd 3hpGosiUU;hcoordi\c hpGosiUU,UUswappandc,c hcoGordiJ\jd 3hpGosiUU:qǸhcoordi\c hpGosiUU,UUsetbase^3d C,c hcoGordiJ\jd 3hpGosiUU::qǸhcoordi\c hpGosiUU,UUyb}'aseP c8origin',UUc hcoGordiJ\jd 3hpGosiUU*hob8jecti\c hpGosiUU,UUdrop^3f Hhob8jectiJ\jd 3hpGosiUU**hob8jecti\c hpGosiUU,UUconnect^3g Qusinghob8jectiJ\jd 3hpGosiUU?qǸhplacei\c hpGosiUU,UUc hplacei^3hJ\jd 3hpGosiUU@hstackingi\c hpGosiUU,UUdohstackingi^3oJ\jd 3hpGosiUU=hsavingi\c hpGosiUU,UUdohsavingi^3pQոhcoGordiCI]!d 3hvectori\hpGosiUUishvectoriwithzerosize J\jd 3hemptyijqc\reuseUUlastc(donothing)J\jd 3p\pJ\jd 3xjqy\axisUUintersection^3k Wwith~fe [۟gpciJ\jd 3shdigitijqs{khnumbGeri}\stack^3o QpGositionUUhdigitiorhnumbGeribelowthetopJ\jd 3"i`0hidi"\restoreUUwhatwassaved^3p ߲ashidiearlierJ\jd 3{lhpGosiUUhdecori}\theUUcresultingfrominterpretingthegroup^3lQոhvectoriCI]!d 30\zero J\jd 3\absoluteJ\jd 3\absoluteUUwithequaldimensionsJ\jd 3(lhfactoriUU, ꧸hfactoriUU)\inUUcurrentbase^3diJ\jd 3aUU( ꧸hnumbGeriUU)\angleUUincurrentbase^3eJ\jd 3hcorneri\fromUUreferencepGointtohcorneriofcJ\jd 3hcorneriUU( ꧸hfactoriUU)\TheUUhcornerimultipliedwithhfactoriJ\jd 3/lhdirectioniUUhdimeni/\vectorUUhdimeniinhdirectioni^3miQոhcorneriCI]!d 3LUUj qRUUjDUUjU\o set^3n ߲toUUleft,right,down,upsideJ\jd 3CLUUj qCRUUjCDUUjCUUUjC\o set^3n ߲toUUcenterofside,truecenterJ\jd 3LDUUj qRDUUjLUUUjRU\o set^3n ߲toUUactualleft/down,...cornerJ\jd 3EUUj qP\o set^3n ߲toUUnearest/propGortionaledgepointtopzQոhplaceiCI]!d 3<UUhplaceijq>hplacei\shave^3h (0)/(1)UUtoedgeofp/c,fڧ 0=1J\jd 3(lhfactoriUU) ꧸hplacei\fڧ hfactorizJ\jd 3hslidei\pickUUplace^3h ߲andapplyhslidei@4J\jd 3!q{ ĸhpGosi}Rhslidei\intercept^3j HwithUUlinesetupbyhpGosiandapplyhslidei@4QhslideiCI]!d 3/lhdimeniUU/\slide^3i hdimeniUUfurtheralongconnectionJ\jd 3hemptyi\noUUslideffdRFigureUU1:qǸhpGosiitions.LWK8 Q*tj??X3e.Anangle^ }inXYH-picisthesameasthecoGor- dinatepair( cos z,sin z) ~where mustbGeanintegerinterpretedasanumbGerofdegrees.UThustheиhvectoria(0)isthesameas(1,0)Eanda(90)asUU(0,1)F,UUetc.8T3f.T*odr}'opjanhob8jectiatcwith* meanstoactu-allyy\physicallytypGesetitinthepicturewithref-erenceUpGositionatc|howthisisdonedependsonz@thehob8jectiinquestionandisdescribGedindetailu inx4.TheintuitionwithadropisthatittypGesetssomethingat<Xc, R޵Yc> andsetstheedgeofUUcaccordingly*.3g.S8Thec}'onnectopGeration**0will rstcomputeanumbGer.ofinternalparametersdescribingthedi-rectionKfromptocandthentypGesetsaconnection lledwithcopiesofthehob8jectiasillustratedin؎x2.3.qTheexactdetailsoftheconnectionde-pGendinx4.Theintuitionwithaconnectionis6thatittypGesetssomethingconnectingpandcandUUsetsthe? ꧸hpGosioperatorupaccordingly*.3h.qUsingʱ? _willʱ\pickaplace"alongthemostrecentconnectionR@typGesetwith**:.hWhatexactlythismeans@isdeterminedbytheob8jectthatwasusedfortheconnectionandbythemoGdi ersdescribedinUUgeneraltermshere.*The\shave"moGdi ersinahplacei,5<Kand> ,changethedefaulthfactori,f,andhowitisused,byv`moving'thepGositionsthatcorrespondto(0)and(1)빲(respGectively):Theseareinitiallysetequal2topandc,)butshavingwillmovethemto}thepGointontheedgeofpandcwheretheconnectionD\leaves/enters"them,{andchangethedefaulti=f|̲asindicated.#WhenoneendhasalreadybGeenZshavedthusthensubsequentshaveswillcor-respGond toslidingtheappropriateposition(s)aTU>'ExX\jot(usuallyequalto3ptٲ)furthertowardstheˋotherendoftheconnection(andpastit).CFi-nallyAthepickU~actionwillpickthepGositionlocatedtheQsfractionfeofthewayQsfrom(0)bݲto(1)wherefڧ=0.5difUUitwasnotset(by<R,>,orexplicitly).AllǦthisisprobablybGestillustratedwithsomeexamples: eachr in gure2istypGesetbyasequenceoftheformp; c**@{.}**?0'hplacei*{\oplus}'(where]weindicatethe?hplaceiineachcase.q(W*eUUalsogiveexamplesofhslideis.)8T3i.A1Thslidei1]willmove1]thepGositionadimensionfur-ther0Halongtheconnectionatthepicked0HpGosition.F*or,straightconnections(theonlyoneskernel(XY ),-pic`provides)thisisthesameasaddingavectorXeKinMthetangentdirection,i.e.,? mL:::›/A/isMthesame eKasUU? ?:::I+/"CA/?.^eK3j.eKThis2QspGecialhplacei ndsthepointwheretheeKlast connectioninterceptswiththelinefrompeKtocassetupbythehpGosi,thususuallythiswilleKhavetheform!{ hcoGordi;?hcoordi}^5 p,0forexample,eKBug:oOnlyPworksforstraightarrowsatpresent.N8eK\xy?<1cm,0cm>:H(0,0)*=0{+}="+"?;H(2,1)*=0{\times}="*"?**@{.},H(1,0)*+{A}?;(2,2)*+{B}**@{-}H?!{"+";"*"}?*{\bullet}eK\endxy獒eKwillUUtypGesetE~=Xops: SDict begin xyc endq!+5?8Ο-" {56.90549 28.45274 dt}xy qA4ܲ$BǍ5y͂" {22.03609 44.07217 l}xy#t\ɵeK3k.sThepGositionsdenotedbytheaxisointerse}'ctioneKhcoGordiinatesFxandyarethepointswheretheeKlinethroughpandcintersectswitheachaxis.eKTheUUfollowing gureillustratesthis:/BD,sps: SDict begin xyc endE/origin-Pgxb}'aseH,g" {28.45274 14.22636 l}xyH,g" {3584 10 /xy AB}xyv yb}'ase~g" {-14.22636 14.22636 l}xy~g" {-2048 10 /xy AB}xyF_K pM|QR cYdNjxT7ǍVdꬣ" {14.21939 28.43883 dt}xyH,g" {-14.21938 -7.09927 dt}xy>oş_y?BŁǍAßV" {-7.11317 -14.22636 dt}xy+֟" {-21.33955 21.33955 dt}xyD7eKExercise4: Given'prede nedpGointsA,Bq,C,eKandsDײ(storedasob8jects"A"3,"B"`Ѳ,"C",ands"D"),eKwritej0ahcoGordispeci cationthatwillreturntheeKpGoint=wherethelines}fe:ABand}fek`CDcross(thepointeKmarkedUUwithalargecirclehere):C9ꍍ9ps: SDict begin xyc end " {1.0 0 360 o}xyǵA!j-" {1.0 0 360 o}xyT}-B2}ޯ" {1.0 0 360 o}xy5}ޯC8-Ο@;" {1.0 0 360 o}xy;-Ο@;D)R" {3.0 0 360 o}xyǍ0" {41.8074 60.08694 dt}xyǍ$X" {-25.19963 50.3934 dt}xyPeK3l.eKA?hpGosihdecorigr}'ouped!in{},-braces^6 ) isinter-eKpretedT3inaloGcalscopeinthesensethatanypeKand9b}'asebuiltwithinitareforgottenafterwards,eKleaving}lonlythecastheresultofthehcoGordi.eKNote:dqOnly:pandb}'asearerestored{itisnotaeKTU>'ExXUUgroup.fff[ J= "5-:5LTheXbracescanb "5-:6LOneXcanuse(* U`.j..*) insteadXalsohere.LWK9 dՠ*tj??9Hqɠ%U 6ps: SDict begin xyc endnC]Y " {10.0 ox}xynC]Y " {7.9 ox}xy!ǵpUUiscircular: FcU>isa CKsquareG9text!ǍQ]Y2" {0.0 20.00003 -20.00003 -20.00003 20.00003 ov}xy>]X33(e*)(33=]W" {249.99997 -101.875 dd}xy?yʟ!Ǹ]b?(0)@N" {21.65613 13.01474 l}xy@N" {3686 10 /xy AB}xyMyʞ!Ǹ#]b?(1)NN" {21.65613 13.01474 l}xyNN" {3686 10 /xy AB}xyyʟ!ǸY۾:?NȞ" {21.65613 13.01474 l}xyNȞ" {3686 10 /xy AB}xyy!/y?(.7)ޝ" {21.65613 13.01474 l}xyޝ" {3686 10 /xy AB}xyyɟǸcr?<>(.5)Ǎ]X q" {0.0 -11.11113 l}xy]X8" {1024 10 /xy AB}xyyɟǸ]Zr?<>(.2)(.5)õD" {-21.65659 -13.01524 l}xyõD" {-410 10 /xy AB}xy?yʟ!Ǹ\][?@C" {-21.65659 -13.01524 l}xy@C" {-410 10 /xy AB}xy1#'毟?>>>>Ǎ5" {0.0 -11.11113 l}xy5;h" {1024 10 /xy AB}xyyq ]']?<>(.7)" {-21.65659 -13.01524 l}xy" {-410 10 /xy AB}xyyq.]?>(.7)Ǎ]%l\" {0.0 -11.11113 l}xy]%#" {1024 10 /xy AB}xy,⍍CFigureUU2:qExamplehplaceisR39Exercise;5: WhatGe ectisachievedGbyusing theUUhcoGordiinate\{;}"?⍍3m.The;vector/8Z/,whereZ=Wisahdimenision,isthesamemasthevector<jZaIJcoso z,IwZaIJsinS z>where istheK{angleofthelastdirectionsetbyaconnec-tioni(i.e.,with**Sc)orsubsequentplacement(??)pGosition.qItispGossibletogiveahdirectioniasdescribedinthenextsection( gure3,note4linparticular)that5FwillthenbGeusedtosetthevqalueof z.gItisalsopGossibletoomitthehdimeniinwhichcaseitUUissettoadefaultvqalueof.5pcUI.3n.qA hcorneri6isano setfromthecurrent<>3Xc, R޵Yc>pGositionu[toaspeci cpositionontheedgeofthecԲob8ject(thetwo-letteronesmaybGegiveninanycombination):Ejps: SDict begin xyc endǍ;k1" {0.0 42.67891 -11.37827 -14.2263 25.61012 ov}xy9AϞc-1͟" {-12.06253 0.0 dt}xyf" {40.51512 0.0 dt}xyǍ;k `" {0.0 -9.2255 dt}xyǍ;kc" {0.0 23.45735 dt}xy͟L-1͟" {14.37505 0.0 l}xy-1͟" {3072 10 /xy AB}xywyRf" {-14.37506 0.0 l}xyf" {-1024 10 /xy AB}xy8˾ DǍ;k `" {0.0 13.94447 l}xy;k " {-3072 10 /xy AB}xy8˾UǍ;kc" {0.0 -13.94447 l}xy;k" {1024 10 /xy AB}xylLD-1͟ " {8.0713 6.55676 l}xy-1͟ " {3904 10 /xy AB}xyt{RDf " {-11.00055 3.1028 l}xyf " {-1312 10 /xy AB}xy#ПեLUǍ-1͟c" {6.40436 -11.37366 l}xy-1͟" {1600 10 /xy AB}xyr mޮRUf" {-8.94489 -5.30913 l}xyf" {-416 10 /xy AB}xyoCL-1͟" {9.63824 -4.82596 l}xy-1͟" {2560 10 /xy AB}xyt|SCRf" {-11.50836 -1.79689 l}xyf" {-864 10 /xy AB}xySϟDCI " {-8.07478 6.55676 l}xyI " {-1856 10 /xy AB}xyN3եUCǍIc" {-6.396 -11.37366 l}xyI" {448 10 /xy AB}xyXnCI" {-12.26079 -6.13039 l}xyI" {-512 10 /xy AB}xy4P-1͞[" {14.13577 2.20949 l}xy-1͞[" {3232 10 /xy AB}xyp9Aϟ" {52.22581 20.8885 dt}xy  E-1͟S" {12.9053 5.24171 l}xy-1͟S" {3488 10 /xy AB}xy7TheD`edgepGoint'E rliesontheedgealongthelinefromN_ptothecentreoftheob8ject,Oincontrasttothe4`propGortional'pointP ѲwhichisalsoapGointon؎theedgebutcomputedinsuchawaythattheob8jectUUloGoksasmuchUU`awayfromp'aspGossible.qFinally*,ka3following( sf) suxwillmultiplytheo setUUvectorbythehfactorif.$GExercise٭6: Whatzisthedi erencebGetweenzthehpGosiitionsUUc?<jandUUc+EL?39eKExerciseT7: WhatUUdoGesthistypeset?N8eK\xy?*=<3cm,1cm>\txt{Box}*\frm{-} H!U!R(.5)?*\frm{..}*{\bullet}\endxy؍eKHintز:+T\frmnisde nedbytheframeextensionandeKjusttypGesetsaframeofthekindindicatedbytheeKargument.keKBug:EزCurrentlywonlythesingle-lettercorners(L,eKR, ID,U,C,E,andP) 7willworkforanyshapGe|theeKotherssilentlyassumethattheshapGeisrectan-eKgular.@eK3o.,jTheWstackk\isaspGecialconstructionusefulforstor-eKing,asequenceofhpGosiitionsthatareaccessibleeKusing,thespGecialhcoordiinatessln,4wherenisei-eKtherasingledigitorapGositiveintegerin{} |s:Eqs0eKisalwaysthe`top'elementofthestackandiftheeKstack hasdepthdthenthe`bGottom'elementofeKthestackhasnumbGers{ wd~1}?.RThestackissaideKtoj]bGe`empty'whenthedepthis0andthenitiseKanterrortoaccessanyofthes Bqnor`pGop'whicheKmeansremovethetopelement,%/shiftingwhatiseKins10tos0!,s2Atos1,etc.VSimilarly*,`pushc'eKmeans$toshifts0.tos1 ,-etc.,and$theninserttheeKcUUasthenews0 O.eKTheUUstackismanipulatedasfollows: rOeKff2  @I̸hstackingi>aActionkeKff2 m @+hcoGordi>apushUUhcoGordii @-hcoGordi>ac hcoGordi&VthenUUpGop @=hcoGordi>aloadUUstackwithhcoGordi @@hcoGordi>adoUUhcoGordi&forUUc stack @i>ainitialise @(>aenterUUnewframe @)>aleaveUUcurrentframekeKff2 鍒eKT*oy`loadstack',(meanstoloadtheentirestackeKwithUthepGositionssetbyhcoordiwithinwhich,eKmeansUU`pushc'.LWeJ10 *tj??gwT*o;#`dohcoGordiforallstackelements'meansto set`ctoeachelementofthestackinturn,fromthebGottomandup,andforeachinterpretthehcoGordi.2Thus9ythe rstinterpretationhascsetto thebGottomelementofthestackandthelasthascsettos0 u.QIfthestackisempty*,thehcoGordiisUUnotinterpretedatall.These-=twoopGerationscanbecombinedtorepeataUUparticularhcoGordiforseveralpoints,likethis:N8\xy@={(0,-10),(10,3),(20,-5)}?@@{*{P}}\endxy!LwillUUtypGesetCӍ?Fps: SDict begin xyc endOPsޟHP8缟F`P.fFinally*,thew3stackcanbGeforciblyclearedusing@i ,vQhowever,thisoisrarelyneededbGecauseof@( ﲲ,which^savesthestackasitis,aandthenclearsit,suchwhenithasbGeenused(andisempty),and@)isissued,thenitisrestoredasitwasatthetimeUUofthe@( O.Exercise8: HowNwouldyouchangetheexam-ple2@abGovetoconnectthepGointsasshownbGelow?Cps: SDict begin xyc end" {-56.90521 -14.2263 l}xyǍsޟv" {28.4526 36.98839 l}xy8缟 ۶" {28.4526 -22.76208 l}xy$5 (3p.qIt?ispGossibletode nenewhcoordiinatesontheform" @hidi"bysavingthecurrentcusingthe...=" *hidi" OhpGosiitionrRform.ȾSubsequentusesof"hidi" 1willthenreestablishthecatthetimeoftheUUsaving.Usinga"hidi"thatwasneverde nedisanerror,however,C_saving>intoanamethatwaspreviouslyde ned justreplacesthede nitionwithoutwarn-ing,;i.e.," {hidi" alwaysreferstothelastthingsavedUUwiththathidi.However,many`otherthingscanbGe`saved':ingeneralUU@RhsavingiUUhaseitheroftheforms ʍff2 9x@:"Whidi"Hm"M hidi",restores /currentHmb}'asefd@׸hcoGordi"?hidi"Hm"M hidi"6FreinterpretsIhcoGordi@@"Whidi"Hm@="X-hidi"(reloadsthisstackff2dThe rstformde nes"hidi"tobGeamacrothatrestoresUUthecurrentb}'ase[.TheseconddoGesnotdependonthestateatthetime_ofde nitionatall;itisamacrode nition.gweKY*ou~canpassparameterstosuchamacrobylet- eKtingitusecoGordinatesnamed"1"ײ,"2"ƈ,etc.,andeKthen2use="1"&,')="2"',')etc.,just2bGeforeeveryuseeKof&ittosettheactualvqaluesofthese.N Note:<0itiseKnot,pGossibletouseahcoordioftheform" )hidi"eKdirectly:qwriteUUitas{" Ohidi"} ."Q덒eKExercise9: W*ritechamacro"dbl"todoubletheeKsizeofthecurrentcob8ject,e.g.,changingitfromeKtheUUdottedtothedashedoutlineinthis gure:/Z1ps: SDict begin xyc end'㏞!+Lr3232"3232K(32323232323232323232323232323232323232323232323232323232323232323232K3232ʍ]㋷3232O3232323232323232323232323232323232323232323232323232A㋷3232O3232323232323232323232323232323232323232323232323232323232"3232K(32323232323232323232323232323232323232323232323232323232323232323232K3232g3232" {3072 F d}xy ^" {3072 F d}xy D" {3072 F d}xy" {3072 F d}xy" {3072 F d}xy" {3072 F d}xy" {3072 F d}xy" {3072 F d}xy D" {3072 F d}xyD3232=Ztؾ" {1024 F d}xyΤ ;32" {1024 F d}xy32" {1024 F d}xy32" {1024 F d}xy32" {1024 F d}xy ;32" {1024 F d}xyؾWo" {1024 F d}xyW= ;32" {1024 F d}xy32" {1024 F d}xy32" {1024 F d}xy32" {1024 F d}xy ;32" {1024 F d}xy32g3232" {3072 F d}xy ^" {3072 F d}xy D" {3072 F d}xy" {3072 F d}xy" {3072 F d}xy" {3072 F d}xy" {3072 F d}xy" {3072 F d}xy D" {3072 F d}xyD3232(ɩ_XeKThe\ nalformde nesaspGecialkindofmacroeKthatshouldonlybGeusedafterthe@=vstackoper-eKation:\the+,entirecurrentstackissavedsuchthateKtheUUstackopGeration@="Lhidi"Rwillreloadit.eKNote:hThereisnodistinctionbGetweenthe`nameeKspaces'$ofhidisusedforsaved$coGordinatesandeKotherUUthings.$͍eK4Obfjects. eKOb8jectsaretheentitiesthataremanipulatedwitheKthe* ۱and**hpGosiڲoperationsabovetoactuallygeteKsomeoutputin}XY)-pictures.nKAsforhpGosiitionstheeKopGerationsareinterpretedstrictlyfromlefttoright,eKhowever,ftheactualob8jectisbuiltb}'eforeqalltheeKhmoGdi eris=takee ect.CThesyntaxofob8jectsisgiveneKin gure3withreferencestothenotesbGelow.lRe-eKmark:.Itisnever⧲allowedtoincludebraces{}.insideeKhmoGdi eris!=In'caseyouwishtodosomethingthateKrequires{...} thencheckinthismanualwhetheryoueKcanuse(* в...*)Fzinstead.^IfnotthenyouwillhavetoeKuseUUadi erentconstruction!?eKNotesEeK4a.,jAnhob8jectiisbuiltusing\object(obox;{Ahtexti}?.eK\object%6box+:isUUinitiallyde nedasN8eK\def\objectbox#1{%H\hbox{$\objectstyle{#1}$}}eK\let\objectstyle=\displaystyleeKbuta\maybGerede nedbyoptionsortheuser.eKThe\htextishouldthusbGeinthemoderequiredeKbylthe\objectboxcommand|withthedefaulteK\objectbox,Obshownj5abGoveitshouldbGeinmatheKmoGde.LWeJ11 à*tj??X ffffd T SyntaxĆActionX-ffd fd hob8jectiE%K!^GhmoGdi eriUUhob8jectiĆapplyUUhmoGdi eritohob8jecti LEj^Ghob8jectbGoxiĆbuildUUhob8jectbGoxithenapplyitshmodi erisi hob8jectbGoxiE%K!^G{gahtextiUU}ĆbuildUUdefault^4a Qob8jectLEҸj^GhlibraryUUob8jectijq@\nhdiriĆuseUUhlibraryob8jectiorhdiriectional(seex6)zLEҸj^GhTU>'ExXUUbGoxi{ ꧸htexti}Ćbuild'ExXbGoxiĆcommand,UUe.g.,\hbox_LEҸj^G\objectUUhob8jectiĆwrapUUupthehob8jectiasa nishedobjectbGox^4cLEҸj^G\compositeUU{ ꧸hcompGositeiUU}ĆbuildUUcompGositeob8jectbox^4diLEҸj^G\xyboxUU{ ꧸hpGosiUUhdecori}ĆpackqageUUentireUQXY U-pictureasob8ject^4ez hmoGdi eriE%K!^G!gahvectoriĆhob8jectiUUhasitsreferencepGointshifted^4f HbyhvectoriLEj^G!Ćhob8jectiUUhastheoriginalreferencepGointreinstatedLEҸj^GhaddUUopihsizeiĆchangeUUhob8jectisize^4gzLEҸj^GhjqiĆhob8jectiUUishidden^4h C,invisible^4i@4LEҸj^G[gahshapGeiUU]Ćhob8jectiUUisgiventhespGeci edhshapei^4jLEҸj^G[=UUhshapGei]Ćde neUUhshapGei^4k Wtoreestablishcurrentob8jectstyle LEҸj^GhdirectioniĆsetUUcurrentdirectionforthishob8jecti haddUUopiE%K!^G+jjt(-\j#=oʸj+= 5j}-=Ćgrow,UUshrink,set,growto,shrinktoi hsizeiE%K!^GhemptyiĆdefaultUUsize^4gLEҸj^GhvectoriĆsizeUUassidesofrectanglecoveringUUthehvectoriz hdirectioniE%K!^GhdiagiĆhdiagionalUUdirection^4lzLEҸj^GvUUhvectoriĆdirection^4l ofUUhvectoriLEj^Gq{RhpGosiUUhdecori}Ćdirection^4l fromUUptocafterhpGosihdecoriLEj^GhdirectioniUU:qǸhvectoriĆvectorUUrelativetohdirectioni^4mLEҸj^GhdirectioniUU_?jhdirectioniUU^Ć90^9cloGckwise/anticlockwiseUUtohdirectioni^4m hdiagiE%K!^GhemptyiĆlastUUuseddirection(notnecessarilydiagonal^4lIJ)LEҸj^Glgajm~ rv]j|/d!juĆleft,UUright,down,updiagonal^4lLEҸj^GldljrrdWjlujruĆleft/down,UU...diagonal^4l hcompGositeiE%K!^Ghob8jectiĆ rstUUob8jectisrequiredLEҸj^GhcompGositeiUU* ꧸hob8jectiĆaddUUhob8jectitocompGositeobjectbGox^4dffd 'ExXbGoxwithdimen- sionsYwR7(h+d)willhaveLc R=qRc=wD=2,Uc=;=*ZDc=(h`+d)=2,thusinitiallybGeequippedwiththeadjustment!C(seenote4f).NInpartic-ular:inlordertogetthereferencepGointonthe(centerJof)thebaselineoftheoriginalhTU>'ExXbGoxithenyoushouldusethehmoGdi eri!;utogetthereference=pGointidenticaltotheTU>'ExXreferencepGointUUusethemodi er!!LL._TU>'ExXnicalremark:xAnymacrothatexpandstosomethingxthatstartswithahbGoximaybGeusedasUUahTU>'ExXbGoxihere.r4c.T*akes{anob8jectandconstructsit,hbuildingabGox;itisthenproGcessedaccordingtothepreceedingmoGdi ers. H^This2formmakesitpossibletouseany2hob8jectiasaTU>'ExXbGox(evenoutsideof2XY -pictures)0IbGecausea nishedob8jectisalways0IalsoaUUbGox.4d.qSeveralLhob8jectiscanbGecombinedintoasingleob8jectusingthespGecialcommand\compositewith#alistofthedesiredob8jectsseparatedwith*s9astheargument.[rTheresultingbGox(andob-ject)istheleastrectangleenclosingallthein-cludedUUob8jects.4e.T*akeanentireXY:-pictureandwrapitupasabGox``asdescribedinx2.1.Makesnestingof`\XY `-picturespGossible:?+theinnerpicturewillhaveitsown$zeropGointwhichwillbGeitsreferencepointintheUUouterpicturewhenitisplacedthere.4f.Anob8jectisshifte}'duahvectoribymovingthepGointRinsideitwhichwillbGeusedastherefer-encepGoint.ASThise ectivelypushestheob8jectthesameUUamountintheoppGositedirection.zčExercise810: WhatHisthedi erencebGetweentheUUhpGosiitions0*{a}!DR0and0*!DR{a}-U=?4g.S8Ahsizeiزisapair<յWc,H>ӲofthewidthandheightofG}arectangle.H?Whengivenasahvectoritheseare}justthevectorcoGordinates,i.e.,the}hvectoristartsinthelowerleftcornerandendsintheup-pGer?rightcorner.`Thepossiblehaddopierationsthat"@canbGeperformedaredescribedinthefol-lowingUUtable.2;L͉fffd͟ ff͟fdhaddUUopi/` ff4#descriptionޟ ffff͟ ff`fd+/` ff4#growޟ ff ͟ ff`fd-/` ff4#shrinkޟ ff͟ ff`fd=/` ff4#setUUtoޟ ff͟ ffpbfd+=/` ff4#growUUtoatleastޟ ff͟ ffpbfd-=/` ff4#shrinkUUtoatmostޟ ffff38tIn\eachcasethehvectorimaybGeomittedwhichinvokes"the\defaultsize"fortheparticularhaddgweKopi:4̍L͉fffd͟ ff͟fdhaddUUopi/` ff4#defaultR ffff͟ ff`fd+/` ff4#+g k ff ͟ ff`fd-/` ff4#-g k ff͟ ff`fd=/` ff4#=R ff͟ ffpbfd+=/` ff4#+= ʟ ff͟ ffpbfd-=/` ff4#-=  ffff4GeKThekdefaultsforthe rstthreearesetwiththe eKcommands eKff2 ~.\objectmarginUUhaddopi{Rhdimeni}.\objectwidthUUhaddopi{Rhdimeni}.\objectheightUUhaddopi{Rhdimeni}eKff23eKwhere_haddopiisinterpretedinthesamewayaseKabGove.<3eKThe{defaultsfor+=8u/-=are{suchthattheresult-eKingob8jectwillbGethesmallestcontaining/largesteKcontainedUUsquare.eKExerciseL11: How3 aretheob8jectstypGesetbyeKtheWhpGosiitions\*+UR{\sum}4"and\*+DL{\sum}"eKenlarged?eKBug:XCurrentlyHchangingthesizeofacirculareKob8ject?isbuggy|itischangedasifitisarect-eKangle^andthenthechangetotheRr\parametereKa ects/thecircle.[TThisshouldbGe xedprobablyeKbyageneralisationoftheo ?QshapGetobeovqalsoreKellipsesUUwithhorizontal/verticalUUaxes.xfeK4h.AhiddenMob8jectwillbGetypesetbuthiddenfromeGXYK-picinthatitwon'ta ectthesizeoftheentireeKpictureUUasdiscussedinx2.1.eK4i.eKAnQinvisibleob8jectwillbGetreatedcompletelyeKnormalexceptthatitwon'tbGetypGeset,i.e.,XY m-eKpicUUwillbGehaveUUasifitwas.eK4j.eKSettinggtheshap}'e²ofanob8jectforcestheshapGeofeKitsedgetobGeasindicated.ThekernelprovideseKthree|shapGesthatchangetheedge,namely[.],eK[],UUand[o],correspGondingtotheoutlines#3! ps: SDict begin xyc endaǷa ,(*ps: SDict begin xyc endǍz2" {0.0 42.65114 -11.36993 -28.48038 19.92793 ov}xyZaǷ" {-28.48038 0.0 dt}xy C LG!" {42.65114 0.0 dt}xy.ơ RǍz ^" {0.0 -11.36993 dt}xyfDǍzs" {0.0 19.92793 dt}xyaFUpIֲ,UUandps: SDict begin xyc endaǷ" {20.0 0 360 o}xy" {-20.0 0.0 dt}xyAƞ L(" {20.0 0.0 dt}xyO RǍ" {0.0 -20.0 dt}xy  DǍ" {0.0 20.0 dt}xy梟 U#eKwhereOthedenotesthepGointofthereferenceeKpGosition̠intheob8ject(the rstisapoint).קEx-eKtensionscanprovidemoreshapGes,however,alleKshapGes6settheextentdimensionsL,oRDz,D,andeKU.<3eKTheMdefaultshapGeforob8jectsis[]andforplaineKcoGordinatesUUitis[.].LWeJ13*tj??gwF*urthermoreFthehshapGeis[r],|[l],[u],andF[d], areLde nedforconvenienceLtoadjusttheob8jecttotheMindicatedsidebysettingthereferencepGointsuch ythatthereferencepGointisthesamedis-tance6afromtheoppGositeoftheindicatededgeandthe8Aob8ject[r]\hbox{Wide?text}j0Ihasrefer-encev!pGointattheinps: SDict begin xyc endjWideUUtextǍ." {0.0 40.4173 -3.47221 -3.47168 3.47221 ov}xy!Ǹ3:buttheob8ject[d]\hbox{Wide?text}[ŲhasreferencepGointattheoinps: SDict begin xyc endWideUUtextǍ0" {0.0 21.94449 -3.47221 -21.94449 3.47221 ov}xy;!Ǹ/.Finally*,6[c]putsthereferencepGointUUatthecenter.DNote:ExtensionszcanaddnewhshapGeiob8jecthmoGdi erisPwhicharethencalledhstyleis.p'ExXeKgrouping.荍eK4l.eKSetting~AthecurrentdirectionissimplypretendingeKfor4thetypGesettingoftheob8ject(andthefollow-eKingϔhmoGdi eris)thatsomeconnectionsetit{theeKhemptyicasejustinheritsthepreviousdirection.eKIt{uisparticularlyeasytosethdiagionaldirections:C'6Sps: SDict begin xyc end6" {12.0 0 360 o}xy"dlG"=ldǍ8ڟ" {-19.40031 -19.40031 l}xy8ڟ~" {0 10 /xy AB}xy3{0dǍ6)" {0.0 -29.94444 l}xy6'" {1024 10 /xy AB}xyF"drT("=rdQ̟~" {19.40623 -19.40031 l}xyQ̟~" {2048 10 /xy AB}xyc{r`{" {30.37503 0.0 l}xy`{" {3072 10 /xy AB}xyFurT(=ruǍRe6," {20.3031 20.3031 l}xyRe" {-4096 10 /xy AB}xy3{uǍ6'" {0.0 30.84723 l}xy6" {-3072 10 /xy AB}xy޿ulG޿=lu7V" {-19.40623 19.40031 l}xy7V" {-2048 10 /xy AB}xy{l " {-30.37502 0.0 l}xy " {-1024 10 /xy AB}xyH踍eKAlternativelyvȨhvectorisetsthedirectionasiftheeKconnectionfrom0 'tothehvectorihadbGeentypGe-eKset exceptthattheorigintisassumedzerosucheKthat pdirectionsv(jx,?y[) Fmeanthenaturalthing,eKi.e.,-isthedirectionoftheconnectionfrom(0,0)eKtoUU(Rx,?y[)ֲ.eKIncasethedirectionisnotassimple,youcaneKconstructw{/AhpGosiwhdecori}thatsetsuppandeKcԮsuchthat~fe [۟gpc7hasthedesireddirection.Note:eKthatyoumustusethe(*$...*)JformifthisistoeKappGearUUinanob8jecthmodi eri!eKExercise12: WhatXe ectisachievedXbyusingeKhmoGdi erisUUv/1pc/&*andUUv/-1pc/(@?荍eK4m.OnceutheinitialdirectionisestablishedaseithereKtheUlastoneoranabsoluteonethentheremain-eKderUUofthehdirectioniisinterpreted.eKAddingVasingle^ or_denotestheresultofrotat-eKingkthedefaultdirectionarightangleinthepGos-eKitive9andnegativedirection,ri.e.,anti-/cloGckwise,eKrespGectively*.!Note:DosnotKuse^ p^>butonly__eKtoUUreversethedirection!eKAtrailing: éhvectoriislikev éhvectoributuseseKthe\hdirectionitosetupastandardsquarebaseLWeJ14헠*tj??gwsuchbthat:(0,1)%and:(0,-1)*Bmeanthesameas :a(90)kandwd:a(-90))andwdas^ .Ųand_a,respGectively*.^Exercise13: WhatXe ectisachievedXbyusinghmoGdi erisUUv/1pc/:(1,0)EandUUv/-1pc/__2:?!N5DecorationshDecoriations[areactualTU>'ExXmacrosthatdecoratetheUcurrentpictureinmannersthatdepGendonthestate.gThey6areallowed6afterJ:thehpGosiitioneitherofthemouter\xy...\endxymorinside{ 1j...}꧲.FThempGossi-bilitiesUUaregivenin gure4withnotesbGelow. Mostoptionsaddtotheavqailablehdecori,xinparticularthev2&optionloadsmanymoresinceXY -picversionspriorto2.7providedmostfeaturesashdecori.Notes5a.S8Saving Iandrestoringallows`excursions'wherelotsWofthingsareaddedtothepicturewithouta ectingQtheresultingQXY -picstate,Ri.e.,c,p,andb}'ase[,%andwithoutrequiringmatching{}|s.fTheindepGendenceof{}isparticularlyusefulincon-junction2withthe\afterPOS2command,jforex-ample,UUthede nitionN8\def\ToPOS{\save\afterPOS{% \POS**{}?>*@2{>}**@{-}\restore};p,}uwillccausethecoGde\ToPOS#hpositoconstructadouble-shaftedarrowfromthecurrentob8jecttothehpGosi(computedrelativetoit)suchthat\xy*{A}?\ToPOS+<10mm,2mm>\endxyL²willtypGesettheUUpictureps: SDict begin xyc endjA 3O9" {3277 /XT tt}xyן1" {22.24545 4.47899 l}xy".Note: Saving.thiswayinfactusesthesamestateasthe{}r`grouping',_sothecoGdep1|s,{p2|s\save},.j ...Y{\restore}@will-havecU=p1bGothUUatthe...andUUattheend!nz5b.qOneverytemptingkindofTU>'ExXcommandstopGerformashdecoriisarithmeticoperationsonthe]XY`a-picastate. Thiswillworkinsimple]XY-picturesChecktheTU>'ExX-nicaldoGcumenta-tionUU[15 ]fordetailsabGoutthis!7=Macrosthatexpandtohdecoriwillalwaysdothesame,UUthough.5c.\xyecho` willturnonechoingofallinterpretedXY -picϸhpGosicharacters.6Bug:*NotcompletelyimplementedIayet.M\xyverbosewillswitchonagweKtracingnofalljXYn-piccommandsexecuted,swith eKlineenumbGers.T"\xytracingtracesevenmore:EOtheeKentire4UXY Y-pic4YstateisprintedaftereachmoGdi ca-eKtion.q\xyquietUUrestoresdefaultquietopGeration. eK5d.Ignoringn@meansthatthehpGosihdecoriisstilleKparseddtheusualwaydbutnothingistypGesetandeKtheUQXY U-picUUstateisnotchanged.eK5e.0It_;ispGossibletosave_;anintermediateformofcom-eKmandsthatgeneratepartsofanXY-picturetoeKa'$ lesuchthatsubsequenttypGesettingofthoseeKpartsissigni cantlyfaster:?thisiscalledc}'om-eKpiling}.ThezaproGduced lecontainscodetocheckeKthat[thecompiledcoGdestillcorrespondstotheeKsameʳhpGosihdecoriaswellasecientʯXY J-coGdetoeKredo^$it;bifthehpGosihdecorihaschangedthentheeKcompilationUUisredone. eKTherearetwowaystousethis.mThedirectiseKtoinventahnameiforeachdiagramandtheneKembraceitin\xycompileto{Iҡhnamei}?| {...} }o{eKthis;vdumpsthecompiledcoGdeintothe leeKhnamei.xyc.eKWhen_qmanydiagramsarecompiledtheniteKis̃easiertoadd\xycompile{?...} *around̃theeKhpGosihdecori3#tobecompiled. 1ThiswillassigneK le]namesnumbGered]consecutivelywithahpre xieKwhich]isinitiallytheexpansionof\jobname-4buteKmayUUbGesetwith ceKff2 l'#k\CompilePrefix{?hpre xi}ōeKff2LeKThishasthedisadvqantage,Zhowever,thatifaddi-eKtionalcompiledXY H-picturesareinsertedthenalleKsubsequent(pictureswillhavetobGerecompiled.eKOneK6particularsituationisprovided,though:eKwhen@usedwithinconstructionsthattypGesettheireKcontentsmorethanonce(suchasmostAU>'M S-eKL5ffA͉TU>'ExXUUequationconstructs)thenthedeclaration 덒eKff2&\CompileFixPoint{?hidi}ōeKff2LeKcan @bGeusedinsidetheenvironment @to xtheeKcountertohavethesamevqalueateverypassage. eKFinally*,Ɖwhen|many`administrativetypGesettingeKruns'dareneeded,ie.g.,readjustingdL5ffA͉TU>'ExXcrosseKreferencesandsuch,thenitmaybGeanadvqan-eKtagextonottypGesetanytXY x-picturesatallduringeKtheintermediateruns.T8ThisissuppGortedbytheeKfollowing declarationswhichforeachcompilationeKcreatesaspGecial lewiththeextension.xydcon-eKtainingUUjustthesizeofthepicture: ceKff2;1\MakeOutlines;1\OnlyOutlines;1\ShowOutlinesLWeJ15 p*tj??n&o ffffd TSyntaxActionX-ffd fdhdecori< B!QhcommandiUUhdecoriꖲeitherUUthereisacommand... BjQhemptyiꖲ...orUUthereisn't.ihcommandi< B!Q\saveUUhpGosiꖲsaveUUstate^5a ,thendohpGosiBjQ\restoreꖲrestoreUUstate^5a Qsavedbymatcing\saveBjQ\POSUUhpGosiꖲinterpretUUhpGosiBjQ\afterPOSUU{ ꧸hdecoriUU}hpGosiꖲinterpretUUhpGosiandthenperformhdecoriBjQ\dropUUhob8jectiꖲdropUUhob8jectiasthehpGosi* ꧲operationBjQ\connectUUhob8jectiꖲconnectUUwithhob8jectiasthehpGosi***operationBjQ\relaxꖲdoUUnothingzBjQhTU>'ExXUUcommandsiꖲanyUUTU>'ExXcommands^5b ߲anduser-de nedmacrosthatUUneithergeneratesoutput(watchUUoutforstrayspaces!),UUnorchangesthegrouping,maybGeused$͍BjQ\xyverboseUUj q\xytracingUUj\xyquietꖲtracing^5c òcommandsBjQ\xyignoreUU{RhpGosiUUhdecori}ꖲignore^5d ۲XY-coGdeiBjQ\xycompileUU{RhpGosiUUhdecori}ꖲcompile^5e toUU lehpre xihnoi.xycBjQ\xycompileto{?hnamei}{ hpGosihdecori}ꖲcompile^5e toUU lehnamei.xycffd FigureUU4:qǸhdecoriations.ّ&o=X\NoOutlines:|ff2 +Ther rstdoGesnomore. Thesecondusesthe  leDtotypGesetsadottedframeoftheappropri-atesizeinsteadofthepicture(unlessthepicturehas5 changedandisrecompiled,lthenitistypGe-setaasalwaysaandthe.xyd. leisrecreatedforsubsequentruns).XThethirdshowstheoutlinesasddottedrectangles.ThelastswitchesoutlineproGcessingUUcompletelyo . g6KernelffobfjectlibraryInthissectionwepresentthelibr}'aryobjectsƲprovidedwiththekernellanguage|severaloptionsaddmorelibraryob8jects.MTheyfallintothreetypGes::Mostofthewekernelob8jects(includingallthoseusuallyusedwithf**BƲtofbuildconnections)aredir}'ectionals!,Dide-scribGed9inx6.1.hTheremainingkernellibraryob8jectsareUUcir}'cles'vofx6.2andtextH-ofx6.3.T!6.1LDirectionalsuTThegkernelprovidesaselectionofdir}'ectionals!:ob-jectsthatdepGendonthecurrentdirection.0TheyalltakeUUtheformʉff2 ލ^i\dirhdiriff2 dtoltypGesetaparticularhdiriectionalob8ject.AllhavetheUUstructureʉff2 ލ6^YhdiriUU q!!hvqarianti{?hmaini}ff2&oeKwith[hvqariantibGeinghemptyioroneofthecharacters eK^_23andUUhmainisomemnemoniccoGde.eKW*e^Bwillclassifythedirectionalsprimarilyin-eKtended forbuildingconnectionsasc}'onnectors*andeKthoseprimarilyintendedforplacementatconnectioneKendsUUorasmarkersastips!.eKFigure5showsallthehdiriectionalsde nedbyeKtheYkernelwithnotesbGelow;eachhmainitypGehasaeKlineGSshowingtheavqailablehvariantis.NoticethatonlyeKsomevqariantsexistforeachhdiri|whenanonexist-eKing vqariantofahdiriisrequestedthenthehemptyieKvqariantOisusedsilently*.CpEachisshownineitheroftheeKtwof formsavqailableineachdirectionasapplicable:eKconnectinga toaffffff33ff33ff e(typGesetby**\dir# hdiri)andeKasYatipattheendofadottedconnectionofthesameeKvqariant(i.e.,typGesetbythehpGosi**\dir"hvqarianti{.}eK?>:*\dir zhdiri).eKAsaspGecialcaseanentirehob8jectiisallowedaseKahdiribystartingitwitha*T:Qt\dir*!isequivqalenttoeK\object..eKNoteseK6a.,jY*out[mayuse\dir{}&hfora\dummy"directionaleKob8ject;u(infactthisisusedautomaticallybyeK**{}e?).5ThismisusefulforauniformtreatmentofeKconnections, :e.g.,makingthe? 3hpGosiableto ndeKapGointonthestraightlinefromptocwithouteKactuallyUUtypGesettinganything.LWeJ16$*tj??4_JDummy^6aťT\dir{} PlainUUconnectors^6b^o\dir{-}^A[ps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy20" {40.75183 12.7346 dt}xy20" {40.75183 12.7346 l}xyJ\dir2{-}^ps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy29џѺ" {40.75183 12.7346 dt}xy2ҏh" {40.75183 12.7346 dt}xy29џѺ" {40.75183 12.7346 l}xy2ҏh" {40.75183 12.7346 l}xy6d>\dir3{-}^xps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy1qb" {40.75183 12.7346 dt}xy3" {40.75183 12.7346 dt}xy20" {40.75183 12.7346 dt}xy1qb" {40.75183 12.7346 l}xy3" {40.75183 12.7346 l}xy20" {40.75183 12.7346 l}xyFo\dir{.}^A[ps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy20" {40.75183 12.7346 dt}xy20" {40.75183 12.7346 dt}xyJ\dir2{.}^ps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy29џѺ" {40.75183 12.7346 dt}xy2ҏh" {40.75183 12.7346 dt}xy29џѺ" {40.75183 12.7346 dt}xy2ҏh" {40.75183 12.7346 dt}xy6d>\dir3{.}^xps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy1qb" {40.75183 12.7346 dt}xy3" {40.75183 12.7346 dt}xy20" {40.75183 12.7346 dt}xy1qb" {40.75183 12.7346 dt}xy3" {40.75183 12.7346 dt}xy20" {40.75183 12.7346 dt}xyo\dir{~}^A[ps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy20" {40.75183 12.7346 dt}xy+~X " {3392 g}xy%8 " {3392 g}xy%$ " {3392 g}xyF2( " {3392 g}xyfn- " {3392 g}xyJ\dir2{~}^ps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy29џѺ" {40.75183 12.7346 dt}xy2ҏh" {40.75183 12.7346 dt}xy+gn " {3392 g}xy$ΟlN " {3392 g}xy q. " {3392 g}xyFv " {3392 g}xy.z " {3392 g}xy,jB " {3392 g}xy%=" " {3392 g}xy] " {3392 g}xy~ " {3392 g}xyZ " {3392 g}xy6d>\dir3{~}^xps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy1qb" {40.75183 12.7346 dt}xy3" {40.75183 12.7346 dt}xy20" {40.75183 12.7346 dt}xy+u " {3392 g}xy$c " {3392 g}xyC " {3392 g}xyY# " {3392 g}xy " {3392 g}xy,UW- " {3392 g}xy%u " {3392 g}xyϟ " {3392 g}xy " {3392 g}xyG " {3392 g}xy+~X " {3392 g}xy%8 " {3392 g}xy%$ " {3392 g}xyF2( " {3392 g}xyfn- " {3392 g}xy/\dir{--}^A[ps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy20" {40.75183 12.7346 dt}xy20" {40.75183 12.7346 dd}xy \dir2{--}^ps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy29џѺ" {40.75183 12.7346 dt}xy2ҏh" {40.75183 12.7346 dt}xy29џѺ" {40.75183 12.7346 dd}xy2ҏh" {40.75183 12.7346 dd}xy1$A\dir3{--}^xps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy1qb" {40.75183 12.7346 dt}xy3" {40.75183 12.7346 dt}xy20" {40.75183 12.7346 dt}xy1qb" {40.75183 12.7346 dd}xy3" {40.75183 12.7346 dd}xy20" {40.75183 12.7346 dd}xy/\dir{~~}^A[ps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy20" {40.75183 12.7346 dt}xy/ " {3392 g}xy%$ " {3392 g}xy ?4d9 " {3392 g}xy \dir2{~~}^ps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy29џѺ" {40.75183 12.7346 dt}xy2ҏh" {40.75183 12.7346 dt}xy.ȟ1 " {3392 g}xyq/ " {3392 g}xy HO " {3392 g}xy/D " {3392 g}xy] " {3392 g}xy w # " {3392 g}xy1$A\dir3{~~}^xps: SDict begin xyc end" {5.0 0 360 o}xy20"" {0.0 5.05 -5.05 -5.05 5.05 ov}xy1qb" {40.75183 12.7346 dt}xy3" {40.75183 12.7346 dt}xy20" {40.75183 12.7346 dt}xy.۟~$ " {3392 g}xyD " {3392 g}xy [d " {3392 g}xy/|I " {3392 g}xy͟ " {3392 g}xy  " {3392 g}xy/ " {3392 g}xy%$ " {3392 g}xy ?4d9 " {3392 g}xy,+PlainUUtips^6c\dir{>}񄍑%ps: SDict begin xyc end" {3392 10 /xy AB}xy" {22.76208 7.11314 dt}xyMV\dir^{>}񄍒ps: SDict begin xyc end" {3392 10 /xy A}xy" {22.76208 7.11314 dt}xy\dir_{>}񄍒&xps: SDict begin xyc end" {3392 10 /xy B}xy" {22.76208 7.11314 dt}xy "N\dir2{>}1@Zps: SDict begin xyc end" {3392 /XT tt}xyݞʙ" {20.37592 6.3673 dt}xyG" {20.37592 6.3673 dt}xyj\dir3{>}pps: SDict begin xyc end[}" {-704 F d}xy" {3392 /Xt tT}xys " {19.7078 6.15846 dt}xyM" {19.7078 6.15846 dt}xy2f" {19.7078 6.15846 dt}xy \dir{<}񄍑%ps: SDict begin xyc end" {-704 10 /xy AB}xy" {22.76208 7.11314 dt}xyMV\dir^{<}񄍒ps: SDict begin xyc end" {-704 10 /xy B}xy" {22.76208 7.11314 dt}xy\dir_{<}񄍒&xps: SDict begin xyc end" {-704 10 /xy A}xy" {22.76208 7.11314 dt}xy "N\dir2{<}1@Zps: SDict begin xyc end" {-704 /XT tt}xyݞʙ" {20.37592 6.3673 dt}xyG" {20.37592 6.3673 dt}xyj\dir3{<}pps: SDict begin xyc end" {3392 F d}xy" {-704 /Xt tT}xy&P" {19.56209 6.11316 dt}xy(" {19.56209 6.11316 dt}xy" {19.56209 6.11316 dt}xy\dir{|}񄍑%ps: SDict begin xyc end " {3392 st}xy" {22.76208 7.11314 dt}xyMV\dir^{|}񄍒ps: SDict begin xyc endEL:H" {-2752 F d}xy" {22.76208 7.11314 dt}xy\dir_{|}񄍒&xps: SDict begin xyc end" {1344 F d}xy" {22.76208 7.11314 dt}xy "N\dir2{|}񄍒@Zps: SDict begin xyc endv " {3392 st}xywW " {3392 st}xyv " {22.76208 7.11314 dt}xywW" {22.76208 7.11314 dt}xyj\dir3{|}񄍒pps: SDict begin xyc end*YQ " {3392 st}xy[ן " {3392 st}xy*YQ" {22.76208 7.11314 dt}xy[ן" {22.76208 7.11314 dt}xy" {22.76208 7.11314 dt}xy\dir{(}񄍑%ps: SDict begin xyc end " {3392 h}xy" {22.76208 7.11314 dt}xyMV\dir^{(}񄍒ps: SDict begin xyc end " {3392 ha}xy" {22.76208 7.11314 dt}xy\dir_{(}񄍒&xps: SDict begin xyc end " {3392 hb}xy" {22.76208 7.11314 dt}xy\dir{)}񄍑%ps: SDict begin xyc end " {-704 h}xy" {22.76208 7.11314 dt}xyMV\dir^{)}񄍒ps: SDict begin xyc end " {-704 hb}xy" {22.76208 7.11314 dt}xy\dir_{)}񄍒&xps: SDict begin xyc end " {-704 ha}xy" {22.76208 7.11314 dt}xyMV\dir^{`}񄍒ps: SDict begin xyc end " {3392 ta}xy" {22.76208 7.11314 dt}xy\dir_{`}񄍒&xps: SDict begin xyc end " {3392 tb}xy" {22.76208 7.11314 dt}xyMV\dir^{'}񄍒ps: SDict begin xyc end " {-704 tb}xy" {22.76208 7.11314 dt}xy\dir_{'}񄍒&xps: SDict begin xyc end " {-704 ta}xy" {22.76208 7.11314 dt}xy$-ConstructedUUtips^6da\dir{>>}񄍑&7ps: SDict begin xyc end " {3392 10 /xy AB}xy" {3392 10 /xy AB}xy" {22.76208 7.11314 dt}xyKО\dir^{>>}񄍒Zps: SDict begin xyc end " {3392 10 /xy A}xy" {3392 10 /xy A}xy" {22.76208 7.11314 dt}xyI\dir_{>>}񄍒ps: SDict begin xyc end " {3392 10 /xy B}xy" {3392 10 /xy B}xy" {22.76208 7.11314 dt}xy -\dir2{>>}1BCps: SDict begin xyc end " {3392 /XT tt}xy" {3392 /XT tt}xyө" {20.26208 6.3319 dt}xywW" {20.26208 6.3319 dt}xyj\\dir3{>>}r[ps: SDict begin xyc end Sc" {-704 F d}xy " {3392 /Xt tT}xy[}" {-704 F d}xy" {3392 /Xt tT}xy&P" {19.56209 6.11316 dt}xy(" {19.56209 6.11316 dt}xy" {19.56209 6.11316 dt}xya\dir{<<}񄍑&7ps: SDict begin xyc end " {-704 10 /xy AB}xy" {-704 10 /xy AB}xy" {22.76208 7.11314 dt}xyKО\dir^{<<}񄍒Zps: SDict begin xyc end " {-704 10 /xy B}xy" {-704 10 /xy B}xy" {22.76208 7.11314 dt}xyI\dir_{<<}񄍒ps: SDict begin xyc end " {-704 10 /xy A}xy" {-704 10 /xy A}xy" {22.76208 7.11314 dt}xy -\dir2{<<}1BCps: SDict begin xyc end " {-704 /XT tt}xy" {-704 /XT tt}xyө" {20.26208 6.3319 dt}xywW" {20.26208 6.3319 dt}xyj\\dir3{<<}r[ps: SDict begin xyc end " {3392 F d}xy " {-704 /Xt tT}xy" {3392 F d}xy" {-704 /Xt tT}xy&P" {19.56209 6.11316 dt}xy(" {19.56209 6.11316 dt}xy" {19.56209 6.11316 dt}xya\dir{||}񄍑&7ps: SDict begin xyc endi " {3392 st}xy " {3392 st}xy" {22.76208 7.11314 dt}xyKО\dir^{||}񄍒Zps: SDict begin xyc end\" {-2752 F d}xyEL:H" {-2752 F d}xy" {22.76208 7.11314 dt}xyI\dir_{||}񄍒ps: SDict begin xyc endi" {1344 F d}xy" {1344 F d}xy" {22.76208 7.11314 dt}xy -\dir2{||}񄍒BCps: SDict begin xyc end h " {3392 st}xyv " {3392 st}xy&ȟ " {3392 st}xywW " {3392 st}xyv " {22.76208 7.11314 dt}xywW" {22.76208 7.11314 dt}xyj\\dir3{||}񄍒r[ps: SDict begin xyc endA " {3392 st}xy*YQ " {3392 st}xys(n " {3392 st}xy[ן " {3392 st}xy*YQ" {22.76208 7.11314 dt}xy[ן" {22.76208 7.11314 dt}xy" {22.76208 7.11314 dt}xya\dir{|-}񄍑&7ps: SDict begin xyc end " {3392 st}xy" {3392 F d}xy" {22.76208 7.11314 dt}xyKО\dir^{|-}񄍒Zps: SDict begin xyc endEL:H" {-2752 F d}xy" {3392 F d}xy" {22.76208 7.11314 dt}xyI\dir_{|-}񄍒ps: SDict begin xyc end" {1344 F d}xy" {3392 F d}xy" {22.76208 7.11314 dt}xy -\dir2{|-}񄍒BCps: SDict begin xyc endv " {3392 st}xyv " {3392 F d}xywW " {3392 st}xywW" {3392 F d}xyv " {22.76208 7.11314 dt}xywW" {22.76208 7.11314 dt}xyj\\dir3{|-}񄍒r[ps: SDict begin xyc end*YQ " {3392 st}xy*YQ" {3392 F d}xy[ן " {3392 st}xy[ן" {3392 F d}xy " {3392 st}xy" {3392 F d}xy*YQ" {22.76208 7.11314 dt}xy[ן" {22.76208 7.11314 dt}xy" {22.76208 7.11314 dt}xya\dir{>|}񄍑&7ps: SDict begin xyc end " {3392 st}xy" {3392 10 /xy AB}xy" {22.76208 7.11314 dt}xyKО\dir{>>|}񄍒Zps: SDict begin xyc end " {3392 st}xy " {3392 10 /xy AB}xy" {3392 10 /xy AB}xy" {22.76208 7.11314 dt}xyF\dir{|<}񄍒ps: SDict begin xyc end " {-704 st}xy" {-704 10 /xy AB}xy" {22.76208 7.11314 dt}xy -\dir{|<<}񄍒BCps: SDict begin xyc end " {-704 st}xy " {-704 10 /xy AB}xy" {-704 10 /xy AB}xy" {22.76208 7.11314 dt}xytܙ\dir{*}񄍒r[ps: SDict begin xyc endKͷ" {22.76208 7.11314 dt}xy\dir{+}񄍑&7ps: SDict begin xyc end " {3392 st}xy`:" {3392 F d}xy" {22.76208 7.11314 dt}xyVP\dir{x}񄍒Zps: SDict begin xyc end" {-3608 st}xy՟5<" {-3608 F d}xy" {22.76208 7.11314 dt}xyC\dir{/}񄍒ps: SDict begin xyc end " {3084 st}xy" {22.76208 7.11314 dt}xym\dir{//}񄍒BCps: SDict begin xyc end " {3084 st}xy " {3084 st}xy" {22.76208 7.11314 dt}xytܙ\dir{o}񄍒r[ps: SDict begin xyc endKͷ" {22.76208 7.11314 dt}xy",]FigureUU5:qKernellibraryhdiriectionalsLWeJ179ݠ*tj??gw6b.qThe=plain;c}'onnectors^groupcontainsbasicdirec- tionalsGthatlendthemselftosimpleconnections.ƍBy defaultXY a -picwilltypGesethorizontalandver-tical\dir{-},9˲connectionsusingTU>'ExXrules.Un-fortunatelyDrulesisthefeatureoftheDVI formatmostcommonlyhandledwrongbyDVIdrivers.ThereforeUQXY U-picUUprovidesthehdecoriations ,ff2 GG\NoRulesG\UseRules卑ff2񍍑thatUUwillswitchtheuseofsucho andon.AsvcanbGeseenbythelasttwocolumns,*these(andmostoftheotherconnectors)alsoex-istyindoubleandtripleversionswitha2or1ra3prepGendedtothename. F*orconve-nience\dir{=}-and\dir{:}aresynonymsfor\dir2{-}#and0\dir2{.}.0,grespGectively;tsimilarly\dir{==}"VisUUasynonymfor\dir2{--}2:.6c.Thegroupofplaintipscontainsbasicob8jectsthatm}&*typGesetsK>ps: SDict begin xyc end"sޟB" {3379 10 /xy AB}xy" {3379 10 /xy AB}xyR" {3379 10 /xy AB}xya9" {3379 10 /xy AB}xy ƟZ" {3379 10 /xy AB}xy " {3379 10 /xy AB}xy,$bExerciseq14: TypGesetZ thefollowingtwo+sandaUUtiltedsquare:*RSps: SDict begin xyc end!+R+" {3584 F d}xy2HcF" {-2560 F d}xyp" {-2560 F d}xya" {3584 F d}xyHintز:thePdashcreatedby\dir{-})_hasthelength5pte(here).6d.qTheseoDtipsarecombinationsoftheplaintipsprovidedD/forconvenience(andoptimisedforef- ciency). New,onescanbGeconstructedusing\compositeUUandbydeclarationsoftheform ff2 G \newdirUUhdiri{RhcompGositei}卑ff2ƍwhich,~de nes\dirhdiriasthehcompGositei(seenoteUU4dforthedetails).6.2LCirclesegmentscVCircleֱhob8jectisareroundandtypGesetasegmentofthe'circlecenteredatthereferencepGoint.D ThesyntaxoflcirclesisdescribGedin gure6withexplanationsbGelow.gweKTheJ'defaultistogenerateafullu#cir}'cle withthe eKspGeci edUUradius,e.g.,ۋd\xy*\cir<4pt>{}\endxyoZtypGesets#\ps: SDict begin xyc end" {4.0 0 360 o}xy"\xy*{M}*\cir{}\endxy| o|8\ps: SDict begin xyc endjMeU" {5.39583 0 360 o}xy ʪ"eKAlltheothercirclesegmentsaresubsetsofthisandeKhaveUUtheshapGethatthefullcircleoutlines.eKPartialcir}'clesegmentsawithF@horientiationaretheeKpart~>ofthefullcirclethatstartswithatangentvec-eKtorvinthedirectionofthe rsthdiagional(seenote4l)eKand`endswithatangentvectorinthedirectionoftheeKother?hdiagionalafteracloGckwise(for_<)oranticloGck-eKwiseUU(for^R)turn,e.g.,,ičd:\xy*\cir<4pt>{l^r}\endxyyztypGesetsC\ps: SDict begin xyc end" {4.0 90 270 o}xy":\xy*\cir<4pt>{l_r}\endxy,g|C\ps: SDict begin xyc end" {4.0 90 270 o}xy"\xy*\cir<4pt>{dl^u}\endxy,g|C\ps: SDict begin xyc end" {4.0 135 360 o}xy"\xy*\cir<4pt>{dl_u}\endxy,g|C\ps: SDict begin xyc end" {4.0 -180 -45 o}xy"\xy*+{M}*\cir{dr_ur}\endxy,g|0\ps: SDict begin xyc endjMeU" {8.39583 135 405 o}xyʪ"eKIfthesamehdiagiisgiventwicethennothingistypGe-eKset,UUe.g.,ičd>\xy*\cir<4pt>{u^u}\endxyxtypGesets\ps: SDict begin xyc end"eKSpGecialߔcareistakentosetupthehdiagionaldefaults:eLeMAfterP^ ѲthePdefaultisthediagonal90^βanticloGck- eMwiseUUfromtheonebGeforethe^R.]eLeMAfter\_ Zthe\defaultisthediagonal90^&@cloGckwiseeMfromUUtheonebGeforethe_R.eKTheVnhdiagibGefore^ ٲor_isrequiredfor\cirhob8jectsi.@eKExercise"c15: TypGesetvthefollowingshadedcircleeKwithUUradius5ptL:Ops: SDict begin xyc end" {5.0 0 360 o}xy33" {5.0 -135 45 o}xyff-" {5.0 -135 45 o}xy;a" {5.0 -135 45 o}xy C@eK6.3%KTextuTeKT*extȪinpicturesissuppGortedthroughthehob8jectieKconstructioneK*ff2 %3:\txtUUhwidthihstylei{Rhtexti}Éff2čthatGbuildsanob8jectcontaininghtextitypGesettohwidthiusinghstylei;inhtexti\\xcanbGeusedasanexplicitxlinebreak;alllineswillbGecentered.0hstyleishould:eitherbGeafontcommandorsomeotherstu todoforeachlineofthehtextiandhwidthishouldbGeUUeither<Rhdimeni>orUUhemptyi. ΍7 X#՟YY'M-picffoptionsNote:L5ffA͉TU>'ExX2" 2usersshouldalsoconsultthepara-graphUUon\xy*.sty"inx1.1.LWeJ18v*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(r7.1LLoadingx/XY -picisprovidedwithagrowingnumbGerofoptions suppGortingŞspecialiseddrawingtasksaswellasexoticoutputxdeviceswithspGecialgraphicfeatures.C1Theseshould0xallbGeloadedusingthisuniforminterfaceinordertoensurethattheXY -picenvironmentisprop-erlyUUsetupwhilereadingtheoption. n[ff2 {<\xyoptionUU{ ꧸hoptioniUU}<\xyrequireUU{ ꧸hoptioniUU}ff2\xyoptionC'willcausetheloadingofanC#XY '-picoption lewhichcanhaveoneofseveralnames.[Thesearetriedvinsequence:Ixy4Choptioni.tex,xy>hoptioni.doc,xy hshorti.tex,andjxy궸hshorti.doc,wherejhshortiishoptioniEtruncatedto6(six)characterstoconformwithUUtheTWG-TDS[17 ]. \xyrequireSfisthesameexceptitisignoredifanoptionޱwiththesamenameisalreadypresent(thusdoGesUUnotcheckUUtheversionetc.).Sometimesw%somedeclarationsofanoptionorheader@ leorwhateveronlymakessenseaftersomeparticular~>otheroptionisloaded.InthatcasethecoGdeUUshouldbewrappedinthespecialcommand n[ff2 {Œ\xywithoptionUU{ ꧸hoptioniUU}{hcoGdeiUU}ff2.which1[indicatesthatifthehoptioniisalreadyloadedthen\hcoGdeishouldbeexecutednow,ސotherwiseitshould#bGesaved#andifhoptionievergetsloadedthens]hcoGdeishouldbeexecutedafterwards.Note:TheęhcoGdeishouldallowmorethanoneexecution;itJissavedJwiththecatcoGdesatthetimeofthe\xywithoptionUUcommand.Finally*, kit3ispGossibletodeclarehcodeiassomecommandstobGeexecutedbeforeeveryac-tualkexecutionof\xywithoption{?hoptioni}{ ...}꧲,andbsimilarlyhcoGdeitobeexecutedbeforeev-ery\xyoption{7>ݸhoptioni}and\xyrequire{<~ڸhoptioni}(reK(collectivelyUUcalled`requests')::eK ff2 ~9\xyeverywithoptionUU{ ꧸hoptioniUU}{hcoGdeiUU} \xyeveryrequestUU{ ꧸hoptioniUU}{hcoGdeiUU}׉ff2!rThisismostoftenusedbyanoptiontoactivqatesomehoGokUUeverytimeitisrequesteditself.|7.2Option leformatOptionUU lesmusthavethefollowingstructure:_V%%&Qhidenti cationi%%&Qhcopyright,UUetc.i/\ifx\xyloaded\undefined?\inputxy\fi\xyprovide{Rhoptioni}{ hnamei}{hversioni}% A{F@hauthori}{ hemaili}{haddressi}hbGodyUUoftheoptioni\xyendinput_UThe6argumentsto\xyprovideshouldcontainthefollowing:Ghoptioni(@Option}loadnameasusedinthe\xyoptioncommand.GYThis shouldbGesafeanddistinguish-able?foranyopGeratingsystemandisthuslim-itedhtocharacterschosenamongthelowercaseletters<(a?{z),digits(0{9),anddash(-),andalloptionspshouldbGeuniquelyidenti ablebythe rstUU6(six)charactersonly*._Vhnamei$wDescriptiveUUnamefortheoption.hversioni+jIdenti cationUUoftheversionoftheoption.hauthori)βTheUUname(s)oftheauthor(s).hemaili$wTheCelectronicmailaddress(es)oftheau-thor(s)ˉorthealiationifnoemailisavqailable.haddressi-#TheUUpGostaladdress(es)oftheauthor(s).LWeJ19*tj??O]w\Thisinformationisusednotonlytoprintaniceban- ner'butalsoto(1)silentlyskiploadingifthesameversionwaspreloadedand(2)printanerrormessageifUUadi erentversionwaspreloaded. <The[`dummy'optiondescribGedinx22isaminimaloption usingtheabGove features.ItusesthespecialDOCMODE OformatKtoincludeitsowndoGcumentationforthisdoGcument(likeallocialXY -picoptions)butthisisUUnotarequirement. ys7.3LDriveroptionsThehdriverioptionsdescribGedinpartIVrequirespe-cialattentionbGecauseeachdrivercansuppGortseveralextensionoptions,anditissometimesdesirabletochangeA[hdriveriorevenmixthesuppGortprovidedbyseveral.^7Ahdriverioptionisloadedasotheroptionswith\xyoption{ hdriveri} C(orthroughL5ffA͉TU>'ExX2" -classorpackqageoptionsasdescribGedinx1.1).3Thespecialthing9NabGoutahdriveriisthatloadingitsimplyde-claresthenameofit,_establisheswhatextensionsitwillоsuppGort,/andselectsittemporarily*.ThusthespGecial~capabilitiesofthedriverwillonlybeexploitedintheproGducedDVI{ leifsomeoftheseextensionsare alsoloadedandifthedriverisstillselectedwhenoutputisproGduced.1SGenerally*,theorderinwhichtheoptions areloadedisimmaterial.Z(Knownexceptionsa ectxonlyinternalproGcessingandarenotvisibletothe[userintermsoflanguageandexpGectedoutput.)In(particularonedrivercanbGepreloadedinaformatandUUadi erentoneusedforaparticulardoGcument.TheUUfollowingdeclarationscontrolthis:ff2 > e\UseSingleDrivere5forcesUUonedriveronly e\MultipleDriverse5allowsUUmultipledrivers e\xyReloadDriverse5resetsUUdriverinformation>ff2?The rstcommandrestoresthedefaultbGehaviour:that:onyonehdriveriisallowed,&3i.e.,each:loadingofg}ahdriverioptioncancelstheprevious.>Thesec-ondl8allowsconsecutiveloadingofdriverssuchthatwhenloadingahdriverionlytheextensionsactuallysuppGorted>areselected,C7leavingotherextensionssup-pGorted_bypreviouslyselecteddriversuntouched._Be-ware+thatthiscanbGeusedtocreateDVI+ lesthatcannot=bGeprocessedbyanyactualDVI=driverpro-gram!The8ilastcommandissometimesrequiredtoresettheXY -picǸhdriveriinformationtoasanestate,forexample,IafterZhavingappliedoneoftheothertwointhemiddleofadoGcument,NorwhenusingsimpleformatslikeplainTU>'ExXthatdonothaveaclearlydis-tinguishedUUpreamble.w\eKAstheabGovesuggestsitsometimesmakessense eKtoloadhdriverisintheactualtextualpartofadoGc-eKument,'>however,itisrecommendedthatonlydriverseKalsoloadedinthepreamblearereloadedlater,MandeKthatmE\xyReloadDriversisusedwhenthereisdoubteKabGout.thestateofa airs. IncaseofconfusioneKthe@spGecialcommand\xyShowDriverswilllistalleKthepresentlysuppGortedandselecteddriver-extensioneKpairsUUtotheTU>'ExXlog.eKIt[isnotdiculttoaddsuppGortforadditionaleKhdriveris;*howisdescribGedintheTU>'ExXnicaldocumen-eKtation.eKMostextensionswillprintawarningwhenacapa-eKbilityisusedwhichisnotsuppGortedbythepresentlyeKloadedhdriveri.3Suchmessagesareonlyprintedonce,eKhowever,(forsomeformatstheyarerepGeatedattheeKend).e(Similarly*,whenuthesuppGortofanextensioneKthatexploitsaparticularhdriveriisusedawarn-eKingxmessagewillbGeissuedthattheDVIxJ leisnoteKpGortable.'SeKPartffIs3IeKExtensionsꨍeKThispartdoGcumentsthegraphiccapabilitiesaddedeKby2eachstandardextensionoption. _F*oreachisindi-eKcated[thedescribGedversionnumbGer,]theauthor,andeKhowUUitisloaded.eKManyoftheseareonlyfullysuppGortedwhenaeKsuitableidriveroption(describGedinpartIV)isalsoeKloaded,*however,all|addedconstructionsarealwayseKac}'cepted]޲evenUUwhennotsuppGorted. 卍eK8CurveffandSplineextensioneKVers.3.7bCyRossMoKorehross@mpAce.mq.edu.auieKLoadTas:p\xyoption{curve}uTeKThisxoptionprovidestXY x-picwiththeabilitytotypGe-eKsetsplinecurvesbyconstructingcurvedconnectionseKusingarbitrarydirectionalob8jectsandbyencirclingeKob8jectsT$similarly*. n4Warning}:oeUsingcurvescanbGeeKquite;astrainonTU>'ExX'smemory;youshouldthere-eKfore7!limitthelengthandnumbGer7!ofcurvesusedonaeKsingle;page.i9MemoryuseislesswhencombinedwitheKabackendcapableofproGducingitsowncurves;ye.g.,eKtheUUPostScriptbackend).sWeK8.1%KCurvedconnectionseKSimpleLjwaystospGecifycurvesinDŽXY G-picareasfollows:eK 1Ήff2 r**\crv{4]hpGoslisti}b'curvedUUconnectionff[ J= "5-:7LTheXkÎernelsuppܲ.,Asusual,+thecurrentpandcareusedasthestartand nishoftheconnection,respGec-tively*./Within`xhpGoslistithehposiitionsareseparatedbysQ&N.&qAsfullsQdescriptionofthesyntaxfor\crv斲isgiveninUU gure7. ܠ]iqps: SDict begin xyc end$Al qBlK" {157.31973 -52.38376 l}xyC Ӳ0I" {mark 170.71564 0.0 85.35782 85.35782 0.0 56.90521 0.03763 0.96143 q}xyY 1^" {mark 0.0 56.90521 56.90521 113.81042 113.81042 113.81042 170.71564 0.0 0.02762 0.9809 bz}xyY)52[" {mark 0.0 56.90521 28.4526 56.90521 56.90521 56.90521 80.61572 37.93681 0.07915 1.0 bz}xya" {mark 80.61572 37.93681 104.32622 18.9684 123.29463 -18.96841 139.89198 -30.82367 0.0 1.0 bz}xyb" {mark 139.89198 -30.82367 156.48933 -42.67891 170.71564 -28.4526 170.71564 0.0 0.0 0.92177 bz}xyo؟/49If##hpGoslistiisemptyastraightconnectioniscom-puted.When_thelengthofhpGoslistiisoneortwo_thenthe;ucurveisuniquelydeterminedasasingle-segmentBGezierquadraticorcubicspline.4ThetangentsatpandcarealongthelinesconnectingwiththeadjacentcontrolݚpGoint.IWiththreeormorehpGosiitionsacubicB-spliney\constructionisused.BGeziercubicsegmentsareUUcalculatedfromthegivencontrolpGoints.TheUUpreviouspicturewastypGesetusing:N8\xy?(0,20)*+{A};(60,0)*+{B}**\crv{}**\crv{(30,30)}**\crv{(20,40)&(40,40)}**\crv{(10,20)&(30,20)&(50,-20)&(60,-10)}\endxyexcept܌forthelabGels,whichdenotethenumbGerofen-triesinthehpGoslisti.T(ExtendingthiscodetoincludetheUUlabGelsissetbelowasanexercise).TheTJ?G-opGeratorTJofx3(note3h)isusedto ndar-bitraryUUhplaceisalongacurveintheusualway*."r ExerciseF16: Extend_thecoGdegivenforthecurvesinC8thepreviouspicturesoastoaddthelabGelsgivingtheUUnumbGerofcontrolpGoints.Using ? S˲will setthecurrentdirectiontobGetan-gentialatthathplacei,andonecanhslideispGeci eddistances["alongthecurvefromafoundhplaceiusingtheUU?R.../꧸hdimeni/notation:gwVdڍps: SDict begin xyc end$Al qB[" {mark 0.0 56.90521 28.4526 56.90521 56.90521 56.90521 80.61572 37.93681 0.07915 1.0 bz}xya" {mark 80.61572 37.93681 104.32622 18.9684 123.29463 -18.96841 139.89198 -30.82367 0.0 1.0 bz}xyb" {mark 139.89198 -30.82367 156.48933 -42.67891 170.71564 -28.4526 170.71564 0.0 0.0 0.92177 bz}xy ļo" {-1028 10 /xy AB}xy5Ɵ E" {-3154 10 /xy AB}xy>5<lx"Z1x^0Gy $]ݟTQ|wP/Ec" {-74.46059 39.55128 l}xyGeKExercise17: SuggestMcoGdetoproducesomething eKliketheabGovepicture; thesplinecurveisthesameaseKinthepreviouspicture.GHints!:3 Thelineis140ptlongeKandtouches0:28ofthewayfromAtoB+andthexeKisUU0.65ofthewayUUfromAtoBq. 퍒eKTheypGositionsinhposlistispecifyc}'ontrolpointseKwhich3Tdeterminetheinitialand naldirectionsofeKthe>curve|leavingpandarrivingatc|andhowtheeKcurvebGehavesinbGetween,usingstandardsplinecon-eKstructions. [Ingeneral,acontrolpGointsneednotlieeKupGonUUtheactualcurve.eKArnaturalsplineparametervqariesintheintervaleK[0;1]jmonotonicallyalongthecurvefromptoc.H$ThiseKis?usedtospGecifyhplaceisalongthecurve,)`]" {84.69392 -28.44571 dt}xy ϟ ȳ:1fO=:9d" {80.58003 -14.57037 l}xyyß̅z:2cӈG:8aԫ" {67.61139 -6.14874 l}xy#5p:3\k/:7Z`uœB" {48.47273 -1.81963 l}xy/г:4O :6O " {25.25992 -0.22748 l}xy?򟸝:5AZeKExerciseW:18: W*ritecoGdetoproduceapicturesucheKas"theoneabGove.`(Hintز:XSave"thelocationsofplaceseKalongthecurveforlaterusewithstraightconnec-eKtions.)eKT*o@havethesamehpGosioccuringasamultipleeKcontrolۦpGointsimplyuseadelimiter,whichleavestheeKhpGosi?eunchanged.jwThus\curve{'PhpGosi&} _usesacubiceKspline,UUwhereas\curve{(@hpGosi}Risquadratic.eKRepGeatinguthesamecontrolpointthreetimesineKsuccessionYresultsinstraightsegmentstothatcon-eKtrolUpGoint.UsingthedefaultstylesthisisanexpGen-eKsive8waytogetstraightlines,qbutitallowsforextraeKe ectsUUwithotherstyles.LWeJ21*tj??dݛܑ ffffd TŲSyntaxoActionX-ffd \curvehmoGdi eri{?hcurve-ob8jectihposlisti}oconstructUUcurvedconnectionfffd fdŸhmoGdi eriJwP !`hemptyiozeroUUormoremoGdi erspossible;defaultis~C Q"@j`~e̸hcurve-optioniUUhmoGdi eriosetUUhcurve-optionizhcurve-optioniJwP !`piE!joaPwj~WljLZmjvc 1j(CoshowQonly^8d4۲controlpGoints(p?=pGoints),Pjoinedbylineso(l?=lines),UUorcurveonly(c=curve)aQ"@j`pcnjtpCv߸jQPchjPCoshowUUcontrolpGoints^8f Handcurve^8eiQ"@j`lcnjtlCv߸jQLchjLCoshowUUlinesjoining^8g QcontrolpGointsandcurve^8eQ"@j`cCoplotMcurvetwice,OwithandwithoutspGeci edformattingŸhcurve-ob8jectiJwP !`hemptyiouseUUtheappropriatedefaultstyleQ"@j`~*k/ɸhob8jectiUUhcurve-objectiospGecifyUUthe\drop"ob8ject^8a Qandmaybemore^8czQ"@j`~**poƸhob8jectiUUhcurve-objectiospGecifyUU\connect"ob8ject^8b ߲andmaybemore^8cŸhpGoslistiJwP !`hemptyijqhpGosiUUhdelimihposlistiolistUUofpGositionsforcontrolpointsQ"@j`~@qsj{L:~@!hdelimiUUhpGoslistioaddUUthecurrentstack^8h ߲tothecontrolpGointsŸhdelimiJwP !`&oallowableUUdelimiterffd uFigureUU7:qSyntaxforcurves."eݛNotesuT8a.S8TheM\drop"ob8jectissetonce,then\droppGed" manyTtimesatappropriatelyspacedplacesalongthecurve.eIfdirectional,Athedirectionfromptocmisused.DefaultbGehaviouristohavetinydotsspacedsucientlycloselyastogivetheappGear-ance8ofasmoGothcurve.[qSpecifyingalargersizefor!the\drop"ob8jectisaway!ofgettingadottedcurveUU(seetheexampleinthenextnote).8b.qThe\connect"ob8jectisalsodroppGedateachplacefalongthecurve.mHowever,jiffnon-empty*,thisZob8jectusesthetangentdirectionateachplace.*Thisallowsadirectionalob8jecttobGespec-i ed,whose@Rorientationwillalwaysmatchthetangent.wT*oadjustthespacingofsuchob8jects,use)\anempty\drop"ob8jectofnon-zerosizeasshownUUhere:* ۍqyps: SDict begin xyc end qA:OB ;:g۟_Y:B:]؟:ҟ$: ~q:$RBu:( :+D:/?q:2uX:6` 짙:9Q:=A:Atޟٜ:Ea&`x:Ea&`x:IvXJ:Ml:R:;:VN :[@2:` :dZ:i՚|:n29:qlP:svO:vDL:y*%:{Ɖ:~eV:П :y:Pm"::6: :JT:5*:] " {1769 10 /xy AB}xytɟA#" {2065 10 /xy AB}xy ~" {2340 10 /xy AB}xy)en" {2542 10 /xy AB}xy3MП"" {2697 10 /xy AB}xy=e$" {2820 10 /xy AB}xyH.&3" {2922 10 /xy AB}xyR+&" {3008 10 /xy AB}xy]&" {3083 10 /xy AB}xyg+&" {3150 10 /xy AB}xyr $" {3213 10 /xy AB}xy{["" {3273 10 /xy AB}xy g" {3334 10 /xy AB}xy" {3400 10 /xy AB}xyBUӍ\xy?(0,0)*+{A};(50,-10)*+{B}**\crv{~*=<4pt>{.}?(10,10)&(20,0)&(40,15)}**\crv{~*=<8pt>{}~**!/-5pt/\dir{>}(10,-20)&(40,-15)}?\endxyFWhen##thereisno\connect"ob8jectthenthetan-gentcalculationsarenotcarriedout,resultinginݛeKakosavingoftimeandmemory;v|thisisthedefault eKbGehaviour. xeK8c.0The\drop"and\connect"ob8jectscanbGespec-eKi edasmanytimesasdesired. ROnlythelasteKspGeci cationofeachtypGewillactuallyhaveanyeKe ect.~(ThisYmakesiteasytoexpGerimentwitheKdi erentUUstyles.)eK8d.Complicated diagramshavingseveralsplineeKcurvesT,cantakequitealongtimetoproGcessandeKmaykusealotofTU>'ExX'smemory*.'AkconvenienteKdevice,espGeciallyRwhiledevelopingapicture,iseKto showonlytheloGcationofthecontrolpGointsoreKtojointhecontrolpGointswithlines,asastylizedeKapproximationxtothesplinecurve.1Thehcurve-eKoptionis]~p2and]~lare]providedforthispurpGose.eKUppGercaseDversions~P and~LdothesamethingeKbutRuseanyhcurve-ob8jectisthatmaybGespeci-eK ed, whereasthelowercaseversionsuseplainde-eKfaults:Nysmallîcrossfor~pC,Dstraightlinefor~l.eKSimilarly~Cand~csetthesplinecurveusinganyeKspGeci edXThcurve-optionisorasa(default)plaineKcurve.eK8e.0Useof~p 4, ~l U, etc.{.}(10,-10)&(20,15)&(40,15)}?\endxy*r8g.S8WithlinesconnectingcontrolpGointsthedefault\drop"ob8jectisempty*,9whilethe\connect"ob-jectis\dir{-}+ٲforsimplestraightlines.NIfnon-empty*,the٫\drop"ob8jectisplacedateachcon-trolpGoint._The\connect"ob8jectmaybGeusedtospGecifyUUafancylinestyle.@@uqyps: SDict begin xyc end qA:OB;-: Ǎ^Bњ qC2x qD?" {mark 12.0 36.0 39.60059 19.19824 48.0 -12.0 1.0 0.10547 q}xyzM" {-1791 10 /xy AB}xyC" {mark 12.0 36.0 39.60059 19.19824 48.0 -12.0 0.10547 0.86841 q}xy?" {mark 12.0 36.0 39.60059 19.19824 48.0 -12.0 1.0 0.86847 q}xy;" {46.20659 32.87268 l}xy!>q[xps: SDict begin xyc end qA>^Bњ qC2x qD;" {46.20659 32.87268 l}xy?" {mark 12.0 36.0 39.60059 19.19824 48.0 -12.0 1.0 0.10547 q}xyzM" {-1791 10 /xy AB}xyC" {mark 12.0 36.0 39.60059 19.19824 48.0 -12.0 0.10547 0.86841 q}xy?" {mark 12.0 36.0 39.60059 19.19824 48.0 -12.0 1.0 0.86847 q}xy!>q"񛍍\xy*+{A}="A";p+/r5pc/+(0,15)*+{B}="B",p+<1pc,3pc>*+{C}="C"gwH,"A"+<4pc,-1pc>*+{D}="D",{\ar@/_/"C"} H,?!{"A";"B"**@{-}}*++{\oplus}eK\endxy?\quad\xyH*+{A}="A";p+/r5pc/+(0,15)*+{B}="B",H,p+<1pc,3pc>*+{C}="C"H,"A"+<4pc,-1pc>*+{D}="D","A";"B"**@{-}H,?!{"D",{\ar@/_/"C"}}*++{\oplus}eK\endxyN8eKWhenxthelineseparatestheend-pGointsofacurveeKan7intersectioncanalwaysbGefound.gIfthereismoreeKthan onethenthatoGccurringearliestalongthecurveeKisUUtheonefound.eKIfthelinedoGesnotseparatetheend-pointstheneKthere)imaybGenointersectionwiththecurve.c#IfthereeKis(onetheneitherthelineistangentialornecessarilyeKtherewillalsobGeatleastoneotherintersection.:AeKmessageZdperhaps?nocurveintersection,ormany.eKisZwrittentothelog- le,butasearchforaninter- eKsectionPxwillstillbGeperformedanda\sensible"placeeKfoundonthecurve. &GIntheusualcaseofasingleeKquadraticorcubicsegment,׋theplacenearestthelineeKisUUfoundandthetangentdirectionisestablished.eKThe[followingexamplesshowthis,]WandshowhoweKtoUUgettheplaceonthelinenearesttothecurve.;3ps: SDict begin xyc end .f qADJ^B qCP qD fA" {mark 60.0 42.67891 59.18091 -19.26114 0.0 0.0 1.0 0.05884 q}xyHȟ_Y" {-3143 10 /xy AB}xy fE" {mark 60.0 42.67891 59.18091 -19.26114 0.0 0.0 0.05884 0.94629 q}xy fA" {mark 60.0 42.67891 59.18091 -19.26114 0.0 0.0 1.0 0.94635 q}xyMO5" {63.79028 14.72511 l}xy/ϟ5" {-3728 st}xy-T" {-3728 F d}xyǍ/ϟ" {-5.12988 23.44629 l}xy-xWWG XQps: SDict begin xyc end .f qADJ^B qC\ qD fA" {mark 60.0 42.67891 76.68945 -43.62149 0.0 0.0 1.0 0.04517 q}xyJџ`" {-2906 10 /xy AB}xy fE" {mark 60.0 42.67891 76.68945 -43.62149 0.0 0.0 0.04517 0.96167 q}xy fA" {mark 60.0 42.67891 76.68945 -43.62149 0.0 0.0 1.0 0.96173 q}xyYD" {75.79028 25.26807 l}xy% /ԍeK\xy?*+{A}="A";p+/r5pc/+(0,15)*+{B}="B",H,p-<.5pc,2pc>*+{C}="C","A"+<6pc,-.5pc>H,*+{D}="D","A",{\ar@/_25pt/"B"}H,?!{"C";"D"**@{-}}*\dir{x}="E"H,+/_2pc/="F";"E"**@{-},?!{"C";"D"}H,*{\otimes}\endxy\qquad\xyH*+{A}="A";p+/r5pc/+(0,15)*+{B}="B",H,p-<.5pc,2pc>*+{C}="C"H,"A"+<7pc,.5pc>*+{D}="D","A"H,{\ar@/_40pt/"B"},?!{"C";"D"**@{-}}H,*{\otimes}\endxyeKSometimes%TU>'ExXwillrunshortofmemorywhenmanyeKcurvesareusedwithoutabackendwithspGecialsup-eKpGortforcurves./Inthatcasethefollowingcommands,eKthatUUobGeynormalTU>'ExXgroupings,maybehelpful:eK ff2 ލ2s\SloppyCurves2s\splinetolerance{hdimeni}x|ff2L+allowNadjustmentofthetoleranceusedtotypGesetcurves.0The x rstsetstoleranceto.8pt,9afterwhichLWeJ23*tj??gw\splinetolerance{0pt}W"resets8Htotheoriginalde- faultUUof necurves._e8.2LCirclesandEllipses8HereAwedescribGethemeanstoaspecifycirclesofarbi-traryVradius,Vdrawnwitharbitrarylinestyles.uMWhenlarge-sized$ob8jectsareusedtheyareregularlyspacedaroundtthecircle.z%SimilarlyellipsesmaybGespeci- ed,butMonlythosehavingma8jor/minoraxesalignedinc)thestandarddirections;spacingofob8jectsisnolonger(regular,]butisbunchedtowardthenarrowerends. BSuchUUacircleorellipseisspGeci edusing... Pff2 6\xycirclef%nhvectori{?hstylei}Bff2#wherethecompGonentsofthehvectorideterminethelengths+oftheaxisfortheellipse;Cthusgivingacir-clerwhenequal.ThehstyleicanbGeanyhconni,Nasin14thatworkswithcurvedarrows|manydo.*_Al-ternatively2BhstyleicanbGeanyhob8jecti,9FwhichwillbGeplacedequally-spacedabGoutthecircleatasepara-tiontosnugly tthehob8jectis.}},*\xycircle<15pt,10pt>{};*\xycircle<10pt>{{.}}\endxy!8.3QuadraticSplines8QuadraticBGeziersplines,asdistinctfromcubicBGezierUsplines,areconstructedfromparabGolicarcs,using>`controlpGoints'todeterminethetangentswheresuccessiveUUarcsarejoined.V*ariousu`implementationsofsuchcurvesexist.The^oneadoptedhereisconsistentwiththexfigdrawingKutilityandtpicimplementations. TRThesehave=}thepropGertyofbeginningandendingwithgweKstraightDsegments,GhalfthelengthtothecorrespGond- eKinga adjacentcontrol-pGoint. F*urthermorethemid-eKpGoint/between/successivecontrol-pGointsliesontheeKspline,withVthelinejoiningthecontrol-pGointsVbeingeKtangentUUthere. ˍeKSuchGcurvesarespGeci ed,eitherasahdecorioraseKanUUhob8jecti,using...eKff2 /J\qspline{zhstylei}͉ff2!]Gwherethestartandendofthecurveareatpandc)?respGectively*.cThecontrol-pGointsaretakenfromthecurrent!stack,U#see3o.׶IfthisstackisemptythenastraightUUlineisconstructed.ThedOfollowingexamplecomparesthequadraticsplinek4withthegentlercurvingB-splinehavingthesameUUcontrolpGoints,using\crvsF.ATꍍ$ps: SDict begin xyc endǵP'շ+K+oշ+(֡ǵC7玟" {11.58334 11.58334 l}xy玟74" {mark 132.0 54.0 114.0 72.0 96.0 54.0 0.0 1.0 q}xy玟75" {mark 168.0 54.0 150.0 36.0 132.0 54.0 0.0 1.0 q}xy玟75" {mark 204.0 72.0 186.0 72.0 168.0 54.0 0.0 1.0 q}xyy(7" {3072 F d}xy[7" {3072 F d}xyg7" {3072 F d}xy玟7C" {mark 78.0 36.0 114.0 72.0 132.0 54.0 150.0 54.0 0.0657 1.0 bt}xyE" {mark 150.0 54.0 168.0 54.0 186.0 72.0 222.0 72.0 0.0 0.93372 bt}xy}΍\xy?/r1.5pc/:,+<5pc,3pc>*+{P};p@(,+(2,2)*{+}@+,?+(2,-2)*{+}@+,+(2,2)*{+}@+,?+(2,0)*+{C}="C",*\qspline{},"C",**\crvs{.},@i?@)\endxy/덍9LFframeandBracketextensionVers.3.7bCyKristo erH.Rosehkrisrose@brics.dkiLoadTas:p\xyoption{frame}ԍTheframe#mWextensionprovidesavqarietyofwaystoputsUUframesinUQXY U-pictures.TheUUframesareUQXY U-pichob8jectisontheformff2 /O\frm{RhframeiUU}͉ff2tobGeusedinhposiitions:!Droppingaframewith*?...\frm{꛸hframei}willframethecob8ject;connect-ingwith** [...\frm{꛲...hframei}willframetheresultofUUc.?p.Below2wedistinguishbGetween`ordinary'frames,`brackets'and` lls';JlastwepresenthowsomeframescanǔbGeaddedtootherob8jectsusingobjectmoGdi erhshapGeis.#9.1FramesԍFigure8showsthepGossibleframesandtheapplicablehmoGdi erisUUwithreferencetothenotesbelow.LWeJ24?*tj??ὃ0rd1ps: SDict begin xyc endyMϲF*ramedUUwith ZN\frm{} CXEframe^9a?HF*ramedUUwith p\frm{.} RNframe^9bMگ3232"3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232$=݌3232ȍ32323232323232323232323232323232323232323232323232323232323232324݌3232ȍ323232323232323232323232323232323232323232323232323232323232323232گ3232"3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232􍷍F*ramedUUwith J\frm<44pt>{.}㍍[pframe^9bǍ66" {19.02281 37.12471 -19.02281 -37.1247 19.02281 vt}xy%MϲF*ramedUUwith WdO\frm{-} RXB~frame^9b.diD2" {0.0 30.86118 -18.32835 -30.86116 18.32834 ov}xyVJ63232L3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232$=J݌3232ȍ3232323232323232323232323232323232323232323232323232323232323232݌3232ȍ323232323232323232323232323232323232323232323232323232323232323232J63232L3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232$THF*ramedUUwith P\frm<8pt>{-}㍍Nframe^9b.dн2" {8.0 34.49973 -19.02281 -34.49973 19.02281 ov}xy763232o`32328'3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323283232&΍<32323232323232323232323232323232323232323232323232323232323232323232P<3232323232323232323232323232323232323232323232323232323232323232323232763232o`32328'3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323283232$TF*ramedUUwith J\frm<44pt>{-}㍍[pframe^9b.d66" {19.02281 37.12471 -19.02281 -37.1247 19.02281 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Ҟ3232S+3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232$=9݌3232ȍ3232323232323232323232323232323232323232323232323232323232323232NW݌3232ȍ323232323232323232323232323232323232323232323232323232323232323232 Ҟ3232S+3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232V'7F*ramedUUwith  ܂\frm{_)} aW vframe^9gq"*|314}L5pg3232-3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232$XBΟ32323232323232323232323232323232323232323232323232323232323232323232=3232323232323232323232323232323232323232323232323232323232323232323232g3232-3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232V6T^ yF*ramedUUwith d\frm{^)} Chframe^9g[ yLDz314{LDZ3232\:93232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232$: ZG3232b3232323232323232323232323232323232323232323232323232323232323232e3232b323232323232323232323232323232323232323232323232323232323232323232Z3232\:93232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232V6TF*ramedUUwith •r\frm{(} Cõhframe^9gK+8+4 >>>>>>>3:LDY3232F3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232$: 3232b3232323232323232323232323232323232323232323232323232323232323232ޟ3232b323232323232323232323232323232323232323232323232323232323232323232Y3232F3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232V6T%kF*ramedUUwith \frm{)} Cframe^9gKJl9Jl4 >>>>>>>3;LD Ҟ3232S+3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232$: 93232b3232323232323232323232323232323232323232323232323232323232323232NW3232b323232323232323232323232323232323232323232323232323232323232323232 Ҟ3232S+3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232w FigureUU9:qBrackethframeis.LWeJ256k*tj??gwNotesuT9a.S8The+%\frm{})8frame+%isadummyusefulfornot puttingaframeonsomething,^e.g.,inmacrosthatUUtakeahframeiargument.*9b.qR}'ectangularNframesinclude\frm{.})v,\frm{-}),\frm{=}L,\frm{--}/ٲ,\frm{==},and!\frm{o-}/!.They}allmakerectangularframesthatessentiallytraceUUthebGorderofarectangle-shapedob8ject.PThehframeis\frm{-}*뷲and\frm{=}allowanop-tional\c}'ornerradius.thatroundsthecornersofthe@framewithquartercirclesofthespGeci edra-dius.h>This}isnotallowed}fortheotherframes|theى\frm{o-}3frameىalwaysgivesroundedcor-ners#ofthesamesizeastheuseddashes(when\xydashfont4sis{thedefaultonethentheseare5pteinUUradius).7Exercise[;19: HowdoyouthinktheauthortypGesetUUthefollowing?(0_JY5ps: SDict begin xyc end qAn " {6.75 ox}xy(Ÿ!Bߍ#3" {7.0434 ox}xyg3232􍍑32326323232323232323232323232323232323232323232323232323232323232323232326w3232!򍍐Ο3232}32323232323232323232323232323232323232323232323232323232*>3232}3232323232323232323232323232323232323232323232323232323232g3232􍍑32326323232323232323232323232323232323232323232323232323232323232323232326w3232ꎦ9c.Theframe\frm{,}0=putsashade,Y/builtfromrules,intothepicturebGeneaththe(assumedrect-angular)nob8ject,_therebygivingtheillusionof`lifting'Jgit;\frm<hdimeni>{,}J[makesthisshadehdimeniUUdeep.P\frm{-,}"VcombinesUUa\frm{-}+jwitha\frm{,}(@.9d.qCircles؁donewith\frm{o},phave؁radiusas(R+L)=2|andwith\frm<shdimeni>{o}|vhave|radiusas٥thehdimeni;\frm{oo}4uZmakesadoublecir-clewiththeoutermostcirclebGeingthesameasthatUUof\frm{o}(@.7Exercise820: WhatHisthedi erencebGetween*\cir{}YandUU*\frm{o}-U=?9e.EllipsesZspGeci edusing\frm{e})uYhaveZaxislengths(R+4L)=2Wand(UO+DG)=2,Vwhilethosewith\frm< hdimen,dimeni>{e}usethegivenlengthsfortheaxes.h\frm{ee}6۲makesadoubleellipsewithdoutermostellipsebGeingthesameasthatof\frm{e}L.PWithoutspGecialsupporttorendertheellipses,either~viaahdriveriorusingthearcfeature,theellipse {willbGedrawnasacircleofradiusapprox-imatelytheaverageofthema8jorandminoraxes.ꎍT o=Do:sAllow+hframevqariantislikethoseusedfordirectionals,i.e.,\frm2{-}/VshouldbGethesameas\frm{=}L.qAddUU\frm{o,}0andUUmorebrackets.gweK9.2%KBrackets@eKTheqhpGossiblebracketsqhareshownin gure9withnotes eKbGelow."\eKNoteseK9f.eKBr}'aces_arejjustthestandardplainTU>'ExXlargeeKbracesrinsertedcorrectlyinnXY r-picpictureswitheKthe`nib'alignedwiththereferencepGointoftheeKob8jectUUtheybrace.(}eKExercise[;21: HowdoyouthinktheauthoreKtypGesetUUthefollowing?2B2gps: SDict begin xyc end  qA%(Ÿ!BLhg3232&썍3232@~3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232@o3232,)Οt3232323232323232323232323232323232323232323232323232323232323232323232323232323232326>t32323232323232323232323232323232323232323232323232323232323232323232323232323232323232g3232&썍3232@~3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232@o3232Lhz31} Lh|31 ~{ |31 3{)sޟ z31 }VBeK9g.,jPar}'enthesisarelikebracesexcepttheyhavenoeKnibBandthusdonotdepGendonwheretherefer-eKenceUUpGointofcis.eKBug:.ThebracketsabGoverequirethatthecom-eKputermoGderncmexfontisloadedinTU>'ExXfontpGosi-eKtionUU3.$\eK9.3%KFilledregionseKIn -additiontotheabGove -thereisaspecialframethateK\ lls" )theinsideofthecurrentob8jectwithink:M1\frmeK{*}and\frm?{**};Cvthelatterisintendedforem-eKphasizing?+and\thus\strokes"theoutline,usingtheeKthinnestblacklineavqailableontheprinterorout-eKput8qdevice;)furthermoreitmoitstheactual llingeKinߕcasethiswouldobscurefurthertexttypGesetoneKtop.SomeԨalterationtotheshapGeispossible,}usingeK*\frm{*}0%.Hencerectangular,Vovqal,circulareKandw!ellipticalshapGescanbespeci edfor lling.,TheeKfollowingUUexamplesillustratethisineachcase:.捍Lˉffxfdhob8jecti4\frm{*}ex\frm{**}x\frm<6pt>{*}ffx \sps: SDict begin xyc endg32321A3232J֍32323232323232323232323232323232323232323232JĞ3232Ο{3232M3232323232323232{3232M323232323232323232g32321A3232J֍32323232323232323232323232323232323232323232JĞ32328ps: SDict begin xyc endg32321A3232J֍32323232323232323232323232323232323232323232JĞ3232Ο{3232M3232323232323232{3232M323232323232323232g32321A3232J֍32323232323232323232323232323232323232323232JĞ32320" {0.0 15.00003 -6.99998 -15.00002 6.99997 fo}xykxps: SDict begin xyc endg32321A3232J֍32323232323232323232323232323232323232323232JĞ3232Ο{3232M3232323232323232{3232M323232323232323232g32321A3232J֍32323232323232323232323232323232323232323232JĞ32321" {0.0 15.00003 -6.99998 -15.00002 6.99997 sfo}xyps: SDict begin xyc endg32321A3232J֍32323232323232323232323232323232323232323232JĞ3232Ο{3232M3232323232323232{3232M323232323232323232g32321A3232J֍32323232323232323232323232323232323232323232JĞ32320" {6.0 15.00003 -6.99998 -15.00002 6.99997 fo}xy\sps: SDict begin xyc end͍*" {6.99997 6.99997 15.00002 15.00002 ot}xy8ps: SDict begin xyc end͍*" {6.99997 6.99997 15.00002 15.00002 ot}xy*" {6.99997 6.99998 15.00002 15.00003 fe}xykxps: SDict begin xyc end͍*" {6.99997 6.99997 15.00002 15.00002 ot}xy+" {6.99997 6.99998 15.00002 15.00003 sfe}xyps: SDict begin xyc end͍*" {6.99997 6.99997 15.00002 15.00002 ot}xy " {6.0 fc}xy fgffx- ōeKHowever,F( llingB]non-rectangularshapGeswillresultineKarectangleunlessadriverisusedthatsuppGortsar-eKbitraryt lling.WithsomedriverstheabGove llswilleKthusUUallbGeidentical,asrectangular.LWeJ26X*tj??O]w\9.4LFramingasobjectmo`di erGInƮaddition,6framesmaybGeaccessedusingthespecial [F hframei]ob8jectmoGdi erhshapeisthatwilladdthedesired5ٸhframeitothecurrentob8ject.gHTheframeap-propriatetotheedgeoftheob8jectwillbGechosen(presentlyUUeitherrectangularorelliptical). If?shapGemodi ersneedtobeappliedtothehframeiHalonethentheycanbGeincludedusing: vasseparator. êThusK[F-:red]46~willKmakearedframe(providedthecolorextensionisactive,_ ofcourse).Additionallyfthevqariantofframesusing< hdimeni>canUUbGeaccessedbyspecifying[R...:< *hdimeni>] .Herearesomesimpleexamplesusingthisfeature.ꍍRps: SDict begin xyc end7`-ps: SDict begin {pu {1. 0. 0. rgb}cc}xyg endcolor push rgb 1. 0. 0.3" {0.0 53.84734 -11.19444 -53.84732 11.19444 sfo}xyps: SDict begin { pp}xyf end color pop-ps: SDict begin {pu {1. 1. 1. rgb}cc}xyg endcolor push rgb 1. 1. 1.1" {0.0 47.84734 -5.19444 -47.84732 5.19444 sfo}xyps: SDict begin { pp}xyf end color poptextUUwithbackgroundcolor push rgb 1. 1. 1.-ps: SDict begin {pu {0. 0. 0. rgb}cc}xyg endcolor push rgb 0. 0. 0.1Ǎ1" {0.0 55.67334 -9.47223 -55.67334 9.47221 sfo}xyps: SDict begin { pp}xyf end color pop-ps: SDict begin {pu {1. 1. 1. rgb}cc}xyg endSbQoldTwhiteonblac9kps: SDict begin { pp}xyf end color pop4\xy?*+<1.5pt>[F**:white]++[F**:red]\txt{text?withbackground},+!D+/d1pc/,*++[F**:black][white]\txt\bf{bold?whiteonblack}\endxyVʍNotice8thatwhenmultipleframe-moGdi ersareused,thefframesareactuallyplacedinreverseor-der,]lso(thatearlieronesareprintedontopoflaterones.T oDo: C6The frameoptionisnotquitecom-pleteyet:WsomenewframesandseveralnewbracketsshouldUUbGeadded.+9.5LUsingcurvesforframesGIfthecurveoptionisloaded,Wthencircularandellipti-cal3+framesofarbitraryradiuscanbGeconstructed,:byspGecifying\UseCurvedFramesWշ.|Thiscanbenegatedby\UseFontFramesM?p.BothofthesecommandsobGeynormal/TU>'ExXgrouping. UF*urthermore,edottedanddashed#framesnowhavearegularspacingoftheirconstituent ob8jects.PTheusualwarningsabGoutmem-ory@requirementsforlargenumbGersofcurvesapplyhereUUalso.'P]10}MoreffTipsextensionVers.3.3bCyKristo erH.Rosehkris@diku.dkiLoadTas:p\xyoption{tips}Thisextensionprovidesseveraladditionalstylesof`tips'foruse(primarily)asarrowheads,andmakesitpGossibletode necustomisedtips.ThisisusedtosuppGorttipsthatmimicthestyleoftheComputerMoGdern)fonts^82byKnuth(see[7]and[6,appGendixF])andL`oftheEulermathfontsdistributedbytheAAMS.w\eKF*ontUUselectionisdonewiththecommandeK sff2 k+\SelectTipsUU{Rhfamilyi}{ Ohsizei}? ff2 whereޱthehfamilyiandhsizeishouldbGeselectedfrom theUUfollowingtable.'{qL͉fffdͤ ff͟fdF*amily ffBj10 ff)G11 ff$12 ffffͤ ff{ fdxy ff/xps: SDict begin xyc end " {3072 10 /xy AB}xy8!Ǹ?1ps: SDict begin xyc end " {3072 /XT tt}xy " {9.5 0.0 l}xy " {9.5 0.0 l}xyQ"ps: SDict begin xyc end" {-1024 F d}xy " {3072 /Xt tT}xy͟" {8.8 0.0 l}xy͞" {8.8 0.0 l}xy͟" {8.8 0.0 l}xyf" ffl:Ups: SDict begin xyc end " {3072 10 /xy AB}xy8!{ps: SDict begin xyc end " {3072 /XT tt}xy " {9.5 0.0 l}xy " {9.5 0.0 l}xydps: SDict begin xyc end" {-1024 F d}xy " {3072 /Xt tT}xy͟" {8.8 0.0 l}xy͞" {8.8 0.0 l}xy͟" {8.8 0.0 l}xyd ff2ps: SDict begin xyc end " {3072 10 /xy AB}xy8!ps: SDict begin xyc end " {3072 /XT tt}xy " {9.5 0.0 l}xy " {9.5 0.0 l}xyps: SDict begin xyc end" {-1024 F d}xy " {3072 /Xt tT}xy͟" {8.8 0.0 l}xy͞" {8.8 0.0 l}xy͟" {8.8 0.0 l}xyܟ ffͤ ff{ fdcm ff/xps: SDict begin xyc end " {3072 10 /cm AB}xy8!Ǹ?1ps: SDict begin xyc end " {3072 /XT tt}xy " {9.5 0.0 l}xy " {9.5 0.0 l}xyQ"ps: SDict begin xyc end" {-1024 F d}xy " {3072 /Xt tT}xy͟" {8.8 0.0 l}xy͞" {8.8 0.0 l}xy͟" {8.8 0.0 l}xyf" ffl:Ups: SDict begin xyc end " {3072 11 /cm AB}xy8!{ps: SDict begin xyc end " {3072 /XT tt}xy " {9.5 0.0 l}xy " {9.5 0.0 l}xydps: SDict begin xyc end" {-1024 F d}xy " {3072 /Xt tT}xy͟" {8.8 0.0 l}xy͞" {8.8 0.0 l}xy͟" {8.8 0.0 l}xyd ff2ps: SDict begin xyc end " {3072 12 /cm AB}xy8!ps: SDict begin xyc end " {3072 /XT tt}xy " {9.5 0.0 l}xy " {9.5 0.0 l}xyps: SDict begin xyc end" {-1024 F d}xy " {3072 /Xt tT}xy͟" {8.8 0.0 l}xy͞" {8.8 0.0 l}xy͟" {8.8 0.0 l}xyܟ ffͤ ff{ fdeu ff0ps: SDict begin xyc end " {3072 10 /eu AB}xy8!Ǹ@4ps: SDict begin xyc end " {3072 /ET tt}xy " {10.5 0.0 l}xy " {10.5 0.0 l}xyPps: SDict begin xyc end" {-1024 F d}xy " {3072 /ET tT}xy " {9.6 0.0 l}xy " {9.6 0.0 l}xy " {9.6 0.0 l}xyf# ffm ps: SDict begin xyc end " {3072 11 /eu AB}xy8!|vps: SDict begin xyc end " {3072 /ET tt}xy " {10.5 0.0 l}xy " {10.5 0.0 l}xyKfps: SDict begin xyc end" {-1024 F d}xy " {3072 /ET tT}xy " {9.6 0.0 l}xy " {9.6 0.0 l}xy " {9.6 0.0 l}xye ff~ps: SDict begin xyc end " {3072 12 /eu AB}xy8!ps: SDict begin xyc end " {3072 /ET tt}xy " {10.5 0.0 l}xy " {10.5 0.0 l}xyɩCps: SDict begin xyc end" {-1024 F d}xy " {3072 /ET tT}xy " {9.6 0.0 l}xy " {9.6 0.0 l}xy " {9.6 0.0 l}xyݟ ffff&tOnceaselectionismade,thefollowingcommandsareUUavqailable:ff2 k!Y\UseTipsPAactivqateUUselectedtips!Y\NoTipsPAdeactivqate? ff2 TheywareloGcalandthuscanbeswitchedonand/oro forindividualpicturesusingtheTU>'ExXgroupingmech-anism,UUe.g.,N8\SelectTips{cm}{10}\xy*{}?\ar?@{*{\UseTips\dir_{<<}}-*{\NoTips\dir{>}}}?(20,5)*{}\endxy?willUUtypGesetGVxps: SDict begin xyc end%" {-768 10 /cm A}xy" {-768 10 /cm A}xy" {0.0 0.0 l}xy8缟g" {3328 10 /xy AB}xy8缟g" {56.90521 14.2263 l}xy8缟g" {0.0 0.0 l}xyregardlesskofwhichtipsareusedotherwiseinthedoGc-ument.(411 fdLineffstylesextension\gVers.3.6bCyRossMoKorehross@mpAce.mq.edu.auiLoadTas:p\xyoption{line}ꠍThisextensionprovidestheabilitytorequestvqari-ous?e ectsrelatedtotheappGearanceofstraightlines;e.g..qthickness,UUnon-standarddashing,andcolour. ?Thesearee ectswhicharenotnormallyavqail-ableUwithinTU>'ExX. sInsteadtheyrequireasuitable`back-end'Eboptiontoprovidethenecessary\specialcommands,thisextensionwillhaveU>no  e ectU>ontheoutputunlessusedwith ‡aU>backendthatexplicitlysuppGortsit.Ǎ^0" {0.0 94.93971 -18.4445 -94.93971 18.4445 ov}xy"mThe]extensionprovidesspGeciale ectsthatcanbeusedsHwithanysDXY H-pichob8jecti,zbyde ning[EhshapGei]moGdi ers.@The}modi cationislocaltothehob8jecticurrentlybGeingbuilt,*sowillhavenoe ectifthisob8jectUUisneveractuallyused.ffff[ J= "5-:8LThisXfunctionwÎasearliersupp]ZO,setUUthicknesstohdimenin[k|#hhdimeni]ZO,alsoUUsetstohdimenin[k|#h=(]ehwordi]ZO,make[(hwordi]setcurrentZO,styleUUsettingsX+n[k|#h*]ZO,reuseUUpreviousstylen[butt]ZO,buttUUcapatendsn[roundcap]ZO,roundUUcapatendsn[projcap]ZO,pro8jectingUUsquarecap.ff23:Latersettingsofthelinewidthoverrideearlierset-tings;5multiple@callsto[thicker]9~eand[thinner]compGound,but(theothervqariantssetanabsolutethickness. Theline-thicknessspGeci cationa ectsarrow-tips\aswellasthethicknessofstraightlinesandcurves.Threekindsofline-capsareavqailable;theyhxarediscussedbGelowinthesectionon`poly-lines'.$s64ps: SDict begin xyc endves=DtqGcmr17CvP (ps: SDict begin {pu 0.39998 lw}xyg end " {0.0 0.0 l}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 0.39998 lw}xyg endS" {3072 10 /xy AB}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 0.39998 lw}xyg endS" {70.56253 0.0 l}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 0.39998 lw}xyg endS" {0.0 0.0 l}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 1.59991 lw}xyg end " {0.0 0.0 l}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 1.59991 lw}xyg endS" {3072 10 /xy AB}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 1.59991 lw}xyg endS" {70.56253 0.0 l}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 1.59991 lw}xyg endS" {0.0 0.0 l}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 3.99979 lw}xyg end " {0.0 0.0 l}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 3.99979 lw}xyg endS" {3072 10 /xy AB}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 3.99979 lw}xyg endS" {70.56253 0.0 l}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 3.99979 lw}xyg endS" {0.0 0.0 l}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 7.99957 lw}xyg end " {0.0 0.0 l}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 7.99957 lw}xyg endS" {3072 10 /xy AB}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 7.99957 lw}xyg endS" {70.56253 0.0 l}xyps: SDict begin { pp}xyf end(ps: SDict begin {pu 7.99957 lw}xyg endS" {0.0 0.0 l}xyps: SDict begin { pp}xyf end:\xy/r8pc/:*++\txt\huge{C}="c",0*++\txt\huge{P}="p",,"p",{\ar@*{[|(1)]}"p";"c"<20pt>},"p",{\ar@*{[|(4)]}"p";"c"<14pt>},"p",{\ar@*{[|(10)]}"p";"c"<4pt>},"p",{\ar@*{[|(20)]}"p";"c"<-16pt>}\endxyUsingxthePostScriptback-end,@thesizeofthearrow-headgrowsaestheticallywiththethicknessofthelineusedtodrawit.¹Thisgrowthvqariesasthesquare-roGot0ofthethickness;][thicker]\xybox{%?*+(3,2){}="X";@={p+CU,p+LU,p+LD,p+RD,p+RU,p+CU}?,{0*[miter]\xypolyline{}}?,{\xypolyline{*}},@i@),"X",*+(2.5,1.5){}="X"LWeJ28*tj??gw,@={!CU,!LU,!LD,!RD,!RU,!CU} ,{0*[gray][roundjoin]\xypolyline{}},{0*[gray]\xypolyline{*}},@i@),"X",*+(2,1){}="X",@={!CU,!LU,!LD,!RD,!RU,!CU},{0*[white]\xypolyline{*}},{0*[bevel]\xypolyline{}},@i@),"X"-(.7,0)*++\txt\LARGE{A}="a","X"+(.7,0)*++\txt\LARGE{B}="b",{\ar@{-}@*{[butt][thinner]}"a";"b"<1pc>},{\ar@{-}@*{[roundcap][thinner]}"a";"b"},{\ar@{-}@*{[projcap][thinner]}"a";"b"<-1pc>}}}NoteXbtheuseof{0*[...]\xypolyline{..}}|toapplystyle-moGdi ersBBtoapolyline.8The@={!..}-DomethodforPxloadingthestackgivesequivqalentresultstous-ing;@={p+..}3(, since\xypolylineAaignorestheedgeextentsUUofeachhpGosiinthestack. [`Noteɵalsothattheargument#1dto\xypolylinea ectsUUwhatistypGeset.qAllowableUUargumentsare: ff2 č e\xypolyline{}e5solidUUline e\xypolyline{.}e5dottedUUline e\xypolyline{-}e5dashedUUline e\xypolyline{*}e5 llUUenclosedpGolygon e\xypolyline{?}e5 lltenclosedpGolygonusinge5even-oGddUUrulefd e\xypolyline{{*}}e5useUU\dir{*}+jforUUlines e\xypolyline{}y5usingUU\dir{}[bff2EThelattercasesonehas**\dir{...}BibGeingusedtowjconnecttheverticesofthepGolyline,with{{*}}bGeingneededtoget**\dir{*}2Ѹ.'@Similarly**\dir&isusedB?whenahdriveriisnotavqailabletospGeci callysuppGortpolylines;1inparticularthetwo` ll'options* andP? uwillPresultinadottedpGolygonoutlinetheregionUUintendedtobGe lled.InfallcasesitisuptotheusertoloadthestackbGe-forecalling\xypolyline{BӾ...}꧲.mAparticularlycom-moncaseistheoutlineofanexistingXY -pichob8jecti,asPintheexampleabGove.F*uturePextensionsto\frmwill‘provideasimpli edmechanismwherebytheuserneednotcall\xypolyline?explicitlyforsuche ects.)M12 fdRotateffandScaleextension)Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.auiLoadTas:p\xyoption{rotate}bThisTextensionprovidestheabilitytorequestthatanyEob8jectbGedisplayedrotatedatanyangleaswellasUUscaledinvqariousways.Thesearee ectswhicharenotnormallyavqail-ableUwithinTU>'ExX. sInsteadtheyrequireasuitable`back-end'Eboptiontoprovidethenecessary\specialgweKcommands,thisextensionwillhaveU>no  e ectU>ontheoutputunlessusedwith ‡aU>backendthatexplicitlysuppGortsit.Ǎ^0" {0.0 94.93971 -18.4445 -94.93971 18.4445 ov}xy njeKThe]extensionprovidesspGeciale ectsthatcanbeeKusedwithanyXY Y-pichob8jectibyde ning[ hshapGei]eKmoGdi ers.@The}modi cationislocaltothehob8jectieKcurrentlybGeingbuilt,*sowillhavenoe ectifthiseKob8jectUUisneveractuallyused.eKThefollowingtableliststhemoGdi ersthathaveeKsocvfarbGeende ned.!(Theycomeintwocvtypescv{eitheraeKsinglekeyword,*Forakey-characterwiththefollowingeKtextUUtreatedasasingleargument.eK >ff2  A[@]eXalign&withcurrentdirec-eXtionfd A[@U;hdirectioni]eXalignUUtohdirectioni A[@!8hnumbGeri]eXrotateUUhnumbGeridegrees A[*U;hnumbGeri]eXscaleUUbyhnumbGeri A[*U;hnumix,hnumiy·]eXscaleUUxandy.separately A[left]eXrotate yanticloGckwisebyeX90^fd A[right]eXrotateUU(cloGckwise)by90^ A[flip]eXrotateby180^;HsameaseX[*-1,-1]񍍍 A[dblsize]eXscaleUUtodoublesize A[halfsize]eXscaleUUtohalfsizeff2fThese[ chshapGei]modi ersfspecifytransformationsofzthehob8jecticurrentlybGeingbuilt.IftheobjecthasoParectangleedgethenthesizeoftherectangleistransformedtoenclosethetransformedob8ject;ϣwithaUUcircleedgetheradiusisalteredappropriately*.]:EachtsuccessivetransformationactsupGonthere-sult ofallprevious.Oneconsequenceofthisisthatthe'"orderoftheshapGemodi erscanmakeasignif-icantdi erenceinappGearance|ingeneral, dtransfor-mationsdonotcommute.0Evensuccessiverotationscan2givedi erentsizedrectanglesiftakeninthere-verseUUorder.Sometimes,9thischangeofsizeisnotdesirable.ThefollowingcommandsareprovidedtomoGdifythisbGehaviour.wff2 v_\NoResizing[v;preventsUUsizeadjustmentv_\UseResizing[v;restoresUUsizeadjustmentsff2iTheL \NoResizing@WcommandL isalsousefultohaveL attheWbGeginningofadocumentbeingtypesetusingadriverthatcannotsuppGortscalinge ects,}inpartic-ularwhenappliedtowholediagrams.ZInanycaseanunscalediversionwillresult,butnowthespacingandpGositioningwillbeappropriatetotheunscaledratherthanUUthescaledsize.LWeJ294*tj??gwScaling]nandScaledT ext TheJhshapGeimodi er cancontaineitherasinglescalefactor,orapairin-dicatingdi erentfactorsinthex-andy[ٲ-directions.Negativevqaluesareallowed,#toobtainre ectionsintheUUcoGordinateaxes,butnotzero.hRotationOandRotatedT ext Within:\[@...]%the...\areLparsedasahdirectioniloGcally*,fIbasedonthecurrentdirection. MThevqalueofcountregis-terw\Direction>~вcontainswtheinformationtodeter-minektherequesteddirection.^$Whennohdirectioniisparsed then[@]requestsarotationtoalignwiththecurrentUUdirection. uThespGecialsequence[@!...]*ɲisprovidedtopassanangledirectlytotheback-end.FTheXY-picsizeand3shapGeofthehob8jectiwith\rectangleEdgeRthisextensionwillhaveU>noe ect onU>theoutputunlessusedwithaIdvi-driverU>thatexplicitlysuppGortsit.Ǎ^0" {0.0 94.93971 -18.4445 -94.93971 18.4445 ov}xy#+eKColoursXarespGeci edasahshapeimodi erwhicheKgivesythenameofthecolourrequested.iItisappliedeKtothewholeofthecurrenthob8jectiwhetherthisbGeeKtext,RNanQXY ь-picQline,curveorarrow-tip,RNoracompGos-eKiteob8jectsuchasamatrixorthecompletepicture.eKHoweversomeDVIdriversmaynotbGeabletosup-eKpGortUUthecolourinallofthesecases.eK >ff2 썍[ ?hcolourUUnamei]\NuseUUnamedcolourb\newxycolor{?hnamei}{ hcoGdei}\Nde neUUcolour\UseCrayolaColors\NloadUUcolournamesbff2؍BIftheDVI-driverBcannotsuppGortcolourthenare-questr?forcolouronlyproGducesawarningmessageinthe(log le.@Aftertwo(suchmessagessubsequentre-questsUUareignoredcompletely*.NamedcoloursandcolourmoQdels NewFcolournames,arecreatedwith\newxycolor<,4Ttakingtwo,ar-guments.C_Firstly2anameforthecolourisgiven,fol-lowedqbythecoGdewhichwillultimatelybGepassedtothenoutputdeviceinordertospGecifythecolour.IfthecurrentdrivercannotsuppGortcolour,!orgrayscaleshading,)thenthenewnamewillbGerecognised,butignoredUUduringtypGesetting.F*orWPostScriptdevices,XStheWXY ׺-psPostScriptdictionary|de nesopGeratorsrgbs,)tcmykGandgrayLw.ps: SDict begin xyc endps: SDict begin xyp end킟1ps: SDict begin {pu xyct 1.25 1.25 xyss }xyg endjA;2Bcolor push rgb 1. 0. 0.-ps: SDict begin {pu {1. 0. 0. rgb}cc}xyg end^ps: SDict begin xyp end10ps: SDict begin {pu xyct 1434 xyd xyrs }xyg end~ps: SDict begin { pp}xyf endps: SDict begin { pp}xyf end color popcolor push Plum %ps: SDict begin {pu {Plum}cc}xyg endp ps: SDict begin xyp end។0ps: SDict begin {pu xyct 1434 xyd xyrs }xyg end|ps: SDict begin { pp}xyf endps: SDict begin { pp}xyf end color pop$ps: SDict begin {pu 1.0 lw}xyg end" {264.68797 105.79758 l}xyps: SDict begin { pp}xyf end"ps: SDict begin xyp endP"1ps: SDict begin {pu xyct -3072 xyd xyrs }xyg endx䍍labGelUU1*ps: SDict begin { pp}xyf endcolor push rgb 1. 0. 0.xʍS32323232?3232?z3232/ύ9n3232 323232323232323232323232323232323232323232323232!^n3232 32323232323232323232323232323232323232323232323232S32323232?3232?z3232 color popps: SDict begin {pu gsave newpath xyXpos xyYpos moveto 50 dup rlineto 20 setlinewidth 0 0 1 setrgbcolor stroke grestore}xyg end<5!ps: SDict begin xyp end:ѓo:ps: SDict begin { pp}xyf end<5!ps: SDict begin xyp end-ʟ0ps: SDict begin {pu xyct 3481 xyd xyrs }xyg endx䍍labGelUU2*ps: SDict begin { pp}xyf endcolor push rgb 1. 0. 0.41-J3232.3232C32323232323232323232323232323232323232323232C3232nH-0kN3232'd323232323232323232323232KN3232'd32323232323232323232323232-J3232.3232C32323232323232323232323232323232323232323232C3232 color popcolor push BurntOrange ,ps: SDict begin {pu {BurntOrange}cc}xyg end8QhŸps: SDict begin { pp}xyf end color popW o-ps: SDict begin xyp endHw--ps: SDict begin {pu xyct .5 .5 xyss }xyg endx䍍labGelUU3*ps: SDict begin { pp}xyf endcolor push rgb 1. 0. 0.q4O+3232Q 䍍3232e3232323232323232e3232~32O+3232Q 䍍3232e3232323232323232e3232 color popk-d!ps: SDict begin xyp end\ !-ps: SDict begin {pu xyct -1 -1 xyss }xyg endx䍍labGelUU4*ps: SDict begin { pp}xyf endcolor push rgb 1. 0. 0.Ѩ\~t3232]卍3232:m32323232323232323232323232323232323232323232:[3232荍\d۟}3232A@3232y¼}3232A@323232\~t3232]卍3232:m32323232323232323232323232323232323232323232:[3232 color popǷps: SDict begin xyp end~$Ƿ+ps: SDict begin {pu xyct 2 2 xyss }xyg endx䍍labGelUU5*ps: SDict begin { pp}xyf endcolor push rgb 1. 0. 0. ou3232p3232ߟps: SDict begin xyp endΩ,ps: SDict begin {pu xyct 1 -1 xyss }xyg endx䍍labGelUU7*ps: SDict begin { pp}xyf endcolor push rgb 1. 0. 0. Ώ3232`3232:m32323232323232323232323232323232323232323232:\3232荍vV}3232A@32328}3232A@323232Ώ3232`3232:m32323232323232323232323232323232323232323232:\3232 color pop6ps: SDict begin xyp end60ps: SDict begin {pu xyct 1024 xyd xyrs }xyg endx䍍labGelUU8*ps: SDict begin { pp}xyf endcolor push rgb 1. 0. 0.{3232;3232?3232?z3232/ύn3232 323232323232323232323232323232323232323232323232n3232 323232323232323232323232323232323232323232323232323232;3232?3232?z3232 color popqps: SDict begin xyp enda,,q5ps: SDict begin {pu xyct .66667 .66667 xyss }xyg end6$ps: SDict begin xyp endt0ps: SDict begin {pu xyct 3481 xyd xyrs }xyg endspGecialUUe ect:qalignedtextr*ps: SDict begin { pp}xyf endr*ps: SDict begin { pp}xyf endcolor push rgb 1. 0. 0.U"sX3232t32325323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323253232"N֍s?!3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232sX3232t32325323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323253232 color pop$Qps: SDict begin { pp}xyf endFigureUU10:qRotations,scalingsand ips=_F*urtherecolournamesarede nedbythecommand \UseCrayolaColoursE that=loadsthecrayon'hoption,in(whichmorecoloursarede ned.Consultthe lexyps-col.doc%8vforthecoloursandtheirspGeci cationsinUUtheRGBorCMYKmoGdels.ɍxycra9yon.tex: Thisoptionprovidesthecom-mand#toinstallde nitionsforthe68coloursrecog-nisedbynamebyT*omasRokicki'sdvips yɲdriver[11 ].This:qcommandmustbGecalledfromahdriveri- lewhichUUcanactuallysuppGortthecolours.+14}PatternffandTileextensionVers.3.4bCyRossMoKorehross@mpAce.mq.edu.auiLoadTas:p\xyoption{tile}uTThis|extensionprovidestheabilitytorequestthata lledUUregionbGetiledusingaparticularpattern.This2Pisane ectnotnormallyavqailablewithinTU>'ExX.cInstead)@itrequiresasuitablehdriverioptiontoprovideSthenecessary\special0>commands,* togetherwithDanyextracommandsneededtoimplementthee ects.qThuskV!ps: SDict begin xyc end !ˍ [UsingU>thisextensionwillhaveU>noe ect onU>theoutputunlessusedwithaIdvi-driverU>thatexplicitlysuppGortsit.Ǎ^0" {0.0 94.93971 -18.4445 -94.93971 18.4445 ov}xy All=e ectsde nedinthetilenextensioncanbGeim-plemented*usingmostPostScripthdriveris,3#loadedasUU\xyoption{77hdriveri}?.P9atterns Patterns#arespGeci edasahshapeimodi- er,similartothewaycoloursarespGeci edbyname.Thepatternisappliedtothewholeofthecurrenthob8jecti_ѲwhetherthisbGetext,pan_XY -picline,curveoroarrow-tip,uoracompGositeob8jectsuchasamatrix=_eKor\thecompletepicture.However\someDVI-drivers eKmayUUnotsuppGortuseofpatternsinallcases. v:eKIfthecurrentDVI-drivercannotsuppGortpatternseKthen#arequestforonesimplyproGducesawarningeKmessage3inthelog le.]Aftertwo3suchmessagessub-eKsequentUUrequestsareignoredcompletely*.eK Dff2 ܞ [hnamei]:PuseUUnamedpatternv: \newxypattern{?hnamei}{ hdatai}:PspGecifyUUnewpatternusinghdatai \UsePatternFile{_|h lei}:PsetsUUdefault leforpatterns \LoadAllPatterns{dyh lei}:PloadUUallpatternsinh lei \LoadPattern{Ohnamei}{ h lei}:PloadUUnamedpatternfromh lei \AliasPattern{U3haliasi}{ hnamei}{h lei}:PletUUhaliasidenotepatternfromh lei.v<ff2<9[AlthoughpatterndatamaybGespeci eddirectlyus-ing\newxypatternG,$itismoreusualtoloaditfromaEh leiinwhichmanypatternsarede nedbyname,eachonaseparateline._jByconventionsuch lesal-waysendin.xyp(XY -pattern)sonoextensionshouldbGe|speci ed.Thepatternisthenrequestedusingei-ther~thenamesuppliedinthe leorbyanalias.*UOnce\UsePatternFileQGhasbGeenused,thenanullh leiar-gumentxtotheothercommandswillstill ndpatternsinnthedefault le. Thedefaultremainsine ectfortheUUcurrentlevelofTU>'ExXgrouping. v:F*orUUexample,thefollowingpicture"Tps: SDict begin xyc endjps: SDict begin {pu {42 }sp}xyg end+" {0.0 30.0 -18.60004 -30.0 18.60004 sfo}xyps: SDict begin { pp}xyf endjps: SDict begin {pu {48 <8888888888888888> <888888888888888888888888888888888888888888888888> }sp}xyg end" {15.0 15.0 15.0 15.0 sfe}xyps: SDict begin { pp}xyf end#usesUU` lled'framesfromtheframe ꛲feature:LWeJ31  *tj??FПQn.ps: SDict begin xyc end jǍ22" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xy }sp}xyg end*3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endmac01L˟ jU[2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {08 }sp}xyg endU[3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endHmac02L˟ j 2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {16 }sp}xyg end 3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf ends0mac03L˟ jl2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {32 }sp}xyg endl3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endގmac04L˟ jeG2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {16 <55FF55FF55FF55FF> }sp}xyg endeG3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endȌimac05L˟ j"2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {32 }sp}xyg end"3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf end:Dmac06L˟ j*2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {16 }sp}xyg end*3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endmac07L˟ jUn2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {48 <8888888888888888> <888888888888888888888888888888888888888888888888> }sp}xyg endUn3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endHmac08' j*ۍ*2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {40 }sp}xyg end*ۍ*3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf end?m܍mac09' j*ۍU[2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {56 <8010022001084004> <808080101010020202202020010101080808404040040404> }sp}xyg end*ۍU[3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf end?m܍Hmac10' j*ۍ 2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {36 }sp}xyg end*ۍ 3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf end?m܍s0mac11' j*ۍl2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {42 }sp}xyg end*ۍl3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf end?m܍ގmac12' j*ۍeG2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {63 <8000000000000000> <808080000000000000000000000000000000000000000000> }sp}xyg end*ۍeG3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf end?m܍Ȍimac13' j*ۍ"2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {58 <8040200002040800> <808080404040202020000000020202040404080808000000> }sp}xyg end*ۍ"3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf end?m܍:Dmac14' j*ۍ*2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {49 <8244394482010101> <828282444444393939444444828282010101010101010101> }sp}xyg end*ۍ*3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf end?m܍mac15' j*ۍUn2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {34 }sp}xyg end*ۍUn3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf end?m܍Hmac16R jU[*2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {48 <55A04040550A0404> <555555A0A0A04040404040405555550A0A0A040404040404> }sp}xyg endU[*3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endjmac17R jU[U[2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {50 <2050888888880502> <202020505050888888888888888888888888050505020202> }sp}xyg endU[U[3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endjHmac18R jU[ 2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {31 }sp}xyg endU[ 3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endjs0mac19R jU[l2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {64 <0000000000000000> }sp}xyg endU[l3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endjގmac20R jU[eG2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {60 <8000080080000800> }sp}xyg endU[eG3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endjȌimac21R jU["2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {56 <8800220088002200> }sp}xyg endU["3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endj:Dmac22R jU[*2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {48 <8822882288228822> }sp}xyg endU[*3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endjmac23R jU[Un2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {48 }sp}xyg endU[Un3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endjHmac24}V\ j *2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {32 }sp}xyg end *3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endɒmac25}V\ j U[2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {48 <1122448811224488> <111111222222444444888888111111222222444444888888> }sp}xyg end U[3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endɒHmac26}V\ j 2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {48 }sp}xyg end 3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endɒs0mac27}V\ j l2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {56 <0102040810204080> <010101020202040404080808101010202020404040808080> }sp}xyg end l3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endɒގmac28}V\ j eG2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {56 }sp}xyg end eG3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endɒȌimac29}V\ j "2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {49 }sp}xyg end "3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endɒ:Dmac30}V\ j *2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {51 <081C22C180010204> <0808081C1C1C222222C1C1C1808080010101020202040404> }sp}xyg end *3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endɒmac31}V\ j Un2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {50 <881422418800AA00> <888888141414222222414141888888000000AAAAAA000000> }sp}xyg end Un3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endɒHmac327 jl*2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {58 <40A00000040A0000> <404040A0A0A00000000000000404040A0A0A000000000000> }sp}xyg endl*3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endwmmac337 jlU[2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {51 <038448300C020101> <0303038484844848483030300C0C0C020202010101010101> }sp}xyg endlU[3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endwmHmac347 jl 2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {46 <8080413E080814E3> <8080808080804141413E3E3E080808080808141414E3E3E3> }sp}xyg endl 3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endwms0mac357 jll2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {44 <102054AAFF020408> <101010202020545454AAAAAAFFFFFF020202040404080808> }sp}xyg endll3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endwmގmac367 jleG2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {26 <77898F8F7798F8F8> <7777778989898F8F8F8F8F8F777777989898F8F8F8F8F8F8> }sp}xyg endleG3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endwmȌimac377 jl"2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyjps: SDict begin {pu {48 <0008142A552A1408> <0000000808081414142A2A2A5555552A2A2A141414080808> }sp}xyg endl"3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endwm:Dmac38 kFigureUU11:qThe38standardMacintoshpatterns.Yd\AliasPattern{bricks}{mac12}{xymacpat} \AliasPattern{bars}{mac08}{xymacpat}\xy?*+<5pc,3.1pc>{},{*[bricks]\frm{**}},*+<2.5pc>[o]{},*[bars]\frm{**}\endxyP9attern5data 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end.^9.375Lˍh lled jblpatternqϞ2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyrps: SDict begin {pu 12.5 pq{48 <0008142A552A1408> <0000000808081414142A2A2A5555552A2A2A141414080808> }sp}xyg endqϞ3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endi12.5Lˍr lled j;patternm2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xysps: SDict begin {pu 18.75 pq{48 <0008142A552A1408> <0000000808081414142A2A2A5555552A2A2A141414080808> }sp}xyg endm3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf end.18.75LˍA lled jԵ pattern<2" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xyrps: SDict begin {pu 37.5 pq{48 <0008142A552A1408> <0000000808081414142A2A2A5555552A2A2A141414080808> }sp}xyg end<3" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: SDict begin { pp}xyf endf\37.5'/# lled j)pattern*ۍ82" {0.0 17.91483 -11.95003 -17.91483 11.95003 ov}xysps: SDict begin {pu 9.375 pq{34 }sp}xyg end*ۍ83" {0.0 17.91483 -11.95003 -17.91483 11.95003 sfo}xyps: 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\UsePatternFile{xymacpat}\AliasPattern{bricks}{mac12}{}\LoadPattern{mac28}{}\LoadPattern{mac05}{}\xy?*=0[!macfreq-45pa][mac28][|=Bars]{},*+<12pc,4pc>{}*[bricks]\frm{**},-<3.5pc,0pt>,*+<2.65pc>[o]{},*[Bars]\frm{**},*[thicker]\frm{o},+<6pc,0pt>,*+<5pc,?2.7pc>{},*[mac05]\frm{**},*\frm{-,},*[white]\txt\Large\bf\sf{Kilroy\\was?here}\endxy,15}Imps3ortffgraphicsextensionVers.3.6bCyRossMoKorehross@mpAce.mq.edu.auiLoadTas:p\xyoption{import}This7featureprovidestheabilitytoeasyaddlabGelsand3annotationstographicspreparedoutsideTU>'ExXorL5ffA͉TU>'ExX.;AnXY 3-picgraphicsenvironmentisestablishedwhose>coGordinatesmatchthatwithinthecontentsofthetimpGortedgraphic,+;makingiteasytospecifyex-actlywherealabGelshouldbeplaced,orarrowdrawntoUUhighlightaparticularfeature.A2commandI\xyimport6wisIde nedwhichisused,in@PconjunctionwithimpGortedgraphics,{toestablisha}coGordinatesystemappropriatetotheparticulargraphics.SThis^enableshpGosiitionswithinthegraphictobGeeasilylocated, eitherforlabellingoraddingex-tra_embGellishingfeatures.ItisusedineitherofthefollowUUways: ff2 |L\xyimport(:Dwidth,?height){ hgraphici}gw*S\xyimport(5width,?height)( x-o ,y[ٲ-o ){hgraphici}eK̉ff2 ʍNormallyNthehgraphicsiwillbGeaboxcontaininga graphicͩimpGortedusingthecommandsfrompackqagessuchSasgraphics.;,epsforepsfig$/A,orusingothercommandsprovidedbytheloGcalTU>'ExXimplementa-tion.ňHoweverthehgraphicicouldbGeanybalancedTU>'ExXmaterialwhatsoGever;8provideditoccupiesnon-zeroUUsize,bGothverticallyandhorizontally*.ThewidthandheightarehnumbGerisgiveninthecoGordinategsystemforthec}'ontentsofthehgraphicsi.ThesegFarenotdimensions,butcoGordinate-lengths,us-ingA[theunitsappropriatetothepicturedisplayedA[byhgraphici.When#provided,( ӵx-o ,?y[ٲ-o ) \ 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Thehgraphiciitselfde nesnamedhpGosicalled"import"-ز,loGcatedi+attheoriginandhavingappropriateextentstoldescribGetheareacoveredlbythehgraphici.U Thismakesitparticularlyeasytosurroundthehgraphiciwith,aframe,aasontheleftsideof gure12,ortodrawUUaxespassingthroughtheorigin.HereisthecoGdeusedtoapplythelabellingin gureUU12:N8\def\ellipA{\resizebox{6cm}{!}{% \includegraphics{import1.eps}}}\xy\xyimport(3.7,3.7)(1.4,1.4){\ellipA}*\frm{-},!D+<2pc,-1pc>*+!U\txt{%?framedcontentsofgraphicsfile}\endxy\qquad\qquad\xy\xyimport(3.7,3.7)(1.4,1.4){\ellipA},!D+<2pc,-1pc>*+!U\txt{Rational?points?ontheellipticcurve:$x^3+y^3=7$},(1,0)*+!U{1},(-1,0)*+!U{-1},(0,1)*+!R{1},(0,-1)*+!R{-1},(2,-1)*+!RU{P},(-1,2)*+!RU{-P},(1.3333,1.6667)*+!UR{-2P},(1.6667,1.3333)*!DL{\;2P},(-.5,1.9)*++!DL{3P},(1.9,-.5)*!DL{\;-3P},(-1,2.3)*+++!D{\infty}*=0{},{\ar+(-.2,.2)},(.5,2.3)*+++!D{\infty}*=0{},{\ar+(-.2,.2)},(2.3,-1)*+++!L{\infty}*=0{},{\ar+(.2,-.2)}\endxyLWeJ33"*tj??U`퍍#2ps: SDict begin xyc end>9Yps: currentpoint currentpoint translate 0.65166 0.65166 scale neg exch neg exch translate:PSfile="import1.eps" llx=0 lly=0 urx=261 ury=261 rwi=2610 eps: currentpoint currentpoint translate 1 0.65166 div 1 0.65166 div scale neg exch neg exch translateǍ@3" {0.0 106.19545 -64.5175 -64.51749 106.19543 ov}xyT -UframedUUcontentsofgraphics leFps: SDict begin xyc endE>9Yps: currentpoint currentpoint translate 0.65166 0.65166 scale neg exch neg exch translate:PSfile="import1.eps" llx=0 lly=0 urx=261 ury=261 rwi=2610 eps: currentpoint currentpoint translate 1 0.65166 div 1 0.65166 div scale neg exch neg exch translateU]RationalUUpGointsontheellipticcurve:qǵx^3S+8y[ٟ^3d=71"V1Nҷ+1G.1T5P#T0P|۸2Pg2PEO3PM23P#K1(@" {-0.00902 0.00902 l}xyLI" {-2048 10 /xy AB}xyLI" {-9.22758 9.22758 l}xyLI" {-0.00902 0.00902 l}xyhϟK1m쀟" {-0.00902 0.00902 l}xydI" {-2048 10 /xy AB}xydI" {-9.22758 9.22758 l}xydI" {-0.00902 0.00902 l}xy-c1ڟ+ǖ" {0.00902 -0.00902 l}xy5Ο4" {2048 10 /xy AB}xy5Ο4" {9.22758 -9.22758 l}xy5Ο4" {0.00902 -0.00902 l}xyrA5uFigureUU12:qimpGortingagraphicforlabellingVs`This fexampleusestheL5ffA͉TU>'ExX2"زstandard graphicsJHpackqageGtoimpGortthegraphics leimport1.epsK;other;packqagescouldhavebGeenusedinstead.e.g.epsfig.-Ȳ,epsf,orthe\pictureorR\illustrationL屲commandsRinTexturesontheMacintosh. TheuonlypGossibleproblemsthatcanoccurarewhentthegraphicspackqageisloadedaftertXY -pichasbGeeng"loaded.-GenerallyitisadvisabletohavegXY "-picloadingUUafterallothermacropackqages./;16}MovieStorybs3oardextensionZVers.3.5bCyKristo erH.Rosehkrisrose@brics.dkiLoadTas:p\xyoption{movie}ThisOextensioninterpretsthe\sceneprimitiveofthemovieiclass,settingtheprogressindicatorstodummyvqalues.z#TheXfollowingassumesthatyourarefamiliarwithUUthemovie ꛲class.Theʱsizeoftheframeisdeterminedbythecom-mand _ff2 a ]\MovieSetup{width=$widthc,height=*Kheight,2ղ...}ff2(the...gindicatetheotherargumentsrequiredbythemovienclass}butsilentlyignoredbytheyXY }-picmovieextension).Note:PThisextensionstillexpGerimentalandsub-ject!tochange.,TheonlydoGcumentationisinthemovie.cls2:sourceUU le.s`eK17˯PostScriptffbackendeKVers.3.7bCyRossMoKorehross@mpAce.mq.edu.aui eKLoadTas:p\xyoption{ps}eGXYK-psisa`back-end'whichprovidesXY ]-picwiththeeKabilitytoproGduceDVIQ lesthatusePostScripteK\specialsforUUdrawingratherthantheUQXY U-picfonts. eKIn#particularthismakesitpGossibletoprintXY c#-piceKDVIKB lesKonsystemswhichdonothavetheabilityeKtoloadthespGecialfonts.aThepenaltyisthattheeKgeneratedDVI leswillonlyfunctionwithonepar-eKticularDVIldriverprogram.O-HencewheneverXY m-psiseKactivqatedUUitwillwarntheuser:#%aSps: SDict begin xyc end 7XY-picU>W*arning:TheproGducedDVI le uisU>notp}'ortable[:ItcontainsPostScript qō R\specialsU>forhoneparticularidriverǍ^2" {0.0 94.93971 -18.94446 -94.93971 18.94446 ov}xy%zeKA݈moreݫcompletediscussionoftheprosandconsofeKusingUUthisbackendUUisincludedbGelow.$eK17.1KCho`osingtheDVI-drivereKIncluding \xyoption{ps}Vhwithin thedoGcumenteKpreamble,ztells{XY -pic{ thatthePostScriptalterna-eKtiveQtothefontsshouldbGeused,RqprovidedthemeanseKtoʰdothisisalsospGeci ed.CThisisdonebyalsospeci-eKfyingxadvi-driverwhichiscapableofrecognisingandeKinterpreting\special1J&commands.a%Althoughthe leeKxyps.texis5readwhentheoptionrequestisencoun-eKtered,theUmacroscontainedthereinwillhavenoe ecteKuntilUUanappropriatedriverhasalsobGeenloaded.LWeJ34#*tj??]WithYL5ffA͉TU>'ExX2"bGoththebackendYanddrivermay bGe,speci ed,"alongwithotheroptions,viaasingle\usepackage Mcommand,UUsee[4,page317];e.g. ƺff2 ֎ \usepackage[ps,textures,color,arrow]{xy}p,ff2TheM6rebindingsnecessarytosuppGortPostScriptarenot%e ecteduntilthe\begin{document}Ycommandisencountered.}Thismeansthatanalternativedrivermay=bGeselected,byanother\xyoption{9hdriveri}?,atanytimeuntilthe\begin{document}W붲.5yOnlythemacrosXrelevqanttolastnamedhdriveriwillactuallybGeUUinstalled. p*ThebfollowingtabledescribGesavqailablesuppGortforPostScriptOcdrivers._PleaseconsulttheindividualdriverBsectionsinpartIVfortheexactcurrentlist.F*orC#eachhdriverithereisacorrespGonding lenamedxy hdriveri.texaowhicha{de nesthenecessarymacros,as=wellasadoGcumentation lenamedxy zhdriveri.doc.ThenspGellingisalllower-case,designedntobebothde-scriptive6%anduniqueforthe1st8charactersofthe leUUnames.:ÍL͉ff fdhdriveri|ŐDescriptionff dvipsAT*omasUURokicki'sdvips dvipsAKarlUUBerry'sdvipskdvipsAThomasUUKi e'sdvipsforMacintoshtexturesABlueUUSkyResearch'sTexturesv1.7+16texturesABlueUUSkyResearch'sTexturesv1.6oztexAAndrewUUT*revorrow'sO4zTU>'ExXv1.8+17oztexAAndrewUUT*revorrow'sO4zTU>'ExXv1.7ff /p*OtherDVI-driversmayalsoworkusingoneofthese les,&iftheyuseconventionssimilartodvips,O4zTU>'ExXOporTextures.oAlternativelyitshouldnotbGetoGogdiculttowritethe lesrequired,+usingtheseasabasisindicatingthetypGeofinformationneededtodsuppGortthespeci c\special2²commands.Any-one>attemptingtodothisshouldinformtheauthorandconveyasuccessfulimplementationtohimforinclusionUUwithintheUQXY U-picdistribution.Note:In somepreviousversionsofXY-picDthePostScriptbackendDanddriverwereloaded simultaneouslybyacommandoftheform>\UsePSspecials{Uhdriveri}?.ɁF*or>backward-compatibilitythesecommandsshouldstillwork,butnowloadingthelatestversionofthegivenhdriveri. Howeverltheirfutureuseisdiscouragedinmfavouroftheoption-loadingmechanism,svia\xyoption{4hdriveri}?.NThislattermechanismismore exible,bGothinhandlingupgradesoftheactualdriverAsuppGortandinbeingextensibletosupportmoreUUgeneralformsof\special0commands.P~OnceoactivqatedthePostScriptbackendocanbGeeKturnedo andonagainatwill,5usingtheuserfollow- eKingUUcommands:eKkff2 Vf\NoPSspecialsh3cancelsUUPostScript Vf\UsePSspecials?{}h3restoresUUPostScript"Bff2 TheseobGeynormalTU>'ExXscopingrulesforenviron-ments;henceitissucienttospGecify\NoPSspecialswithinanenvironmentorgrouping.UseofPost-Script willbGerestoreduponexitingfromtheenvi-ronment.?D17.2%Whyuse?- cmcsc10PostScriptuTAtsomesitesusershavedicultyinstallingtheex-trafontsusedbyXY -pic. The.tfmv lescanalwaysbGe'installedlocallybutitmaybenecessaryforthe.pkbitmapC(fonts(orthe.mfFGMETAF9ONTfonts)tobGekinstalledglobally*,bythesystemadministrator,forprintingZtoworkcorrectly*.IfPostScriptisavqail-ableƽthenƹXY F-psallowsthislattersteptobGebypassed.Note:{withu+XY /-psu/itisstillnecessarytohaveu/the.tfmx=fontxImetric lescorrectlyinstalled,asthesecon-tainUUinformationvitalforcorrecttypGesetting.DOtherXadvqantagesobtainedfromusingTXY 4X-psarethefollowing:Circles`yandcirclesegmentscanbGesetforarbi-traryUUradii.DsolidUUlinesarestraighterandcleaner.TheArangeofpGossibleanglesofdirectionalsis greatlyUUincreased.SplineecurvesaresmoGother.1T*ruedottedanddashed kversionsarenowpGossible,usingequallyspacedUUsegmentswhicharethemselvescurved.TheRoPostScript leproGducedbyadriverfromanXY-psDVI leisingeneralsigni cantlysmallerzqthanoneproGducedbyprocessingan`or-dinary'wDVIw leusingthesamedriver.'Onerea-sonforthisisthatnofontinformationfortheXY"-picfontsisrequiredinthePostScript le;this8ifurthermoremeansthattheuseof8eXY i-picdoGesnotinitselflimitthePostScript letoaUUparticularresolution.^9The~latestversionofzXY }~-picnowenablesspGeciale ectssuchasvqariablelinethickness,İgray-leveland colour. Also,>rotationoftextand(pGor-tions1Lof)diagramsisnowsuppGortedwithsomedrivers.5SimilarlywholediagramscanbGescaledup$ordownto tagivenareaontheprintedpage.F*utureնversionswillallowtheuseofre-gions lledwithcolourand/orpatterns,aswellasUUotherattractivee ects.ffff[ J= "5-:9LMostjTAEMXPostScriptdrivÎersstoretheimagesofcharactersusedinthetextasbitmapsataparticularresolution.Thismeans thatXthePostScript lecanonlyb'ExXsourcecoGde,;expecting4ptherecipientDtohaveDXYĺ-pic ^l,orsenda(com-pressed)UUPostScript le.ٍThelattercommentappliesto lesinwhichanyspGe-cial`back-end'suppGortisrequired,JnotjusttoPost-Script.q]OfTcourseitcanbGeignoredwhenyouknowtheUUcon gurationavqailabletotheintendedrecipient.tiPostScript6header le: WithsomeDVI-driversit>ismoreecienttohavethePostScriptcom-mandsj?thatj;XY ?-psneedsloadedinitiallyfromasepa-rate\header" le.YOT*ousethisfacilitythefollowingcommandsUUareavqailable...F?ff2 \1L\UsePSheader?{}1L\UsePSheader?{}1L\dumpPSdict?{}1L\xyPSdefaultdict_ff2 ѠNormallyitissucienttoinvoke\UsePSheader{}Mj,whichۏinvokesthedefaultnameofxy37dict.pro,re-ferring=tothecurrentversionof=XY -pic.iTheoptionalh lenameiallowsadi erent letobGeused.Plac-ing\dumpPSdict{..}T-withinthedoGcumentpreamblecausesTthedictionarytobGewrittentothesuppliedh lenamei.See>thedoGcumentationforthespeci cdrivertoestablishwherethedictionary leshouldbGelocatedonanyparticularTU>'ExXsystem.̈Usuallyitissu-cientXtohaveacopyinthecurrentworkingdirectory*.Invoking3thecommand\dumpPSdict{}Lwillplaceacopyroftherequisite le,!lhavingthedefaultname,!linthegcurrentdirectory*.This lewillbGeusedasthedictionary/forthecurrentproGcessing,f*provideditisonthecorrectdirectorypath,sothatthedrivercanloGcateqitwhenneeded. ConsultyourlocalsystemadministratorUUifyouexpGeriencediculties.w\eK18˯TPICffbackendeKVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui eKLoadTas:p\xyoption{tpic}eKThisIoptionallowstheIXY -picfontstobGereplacedbyeKtpicg\special-Os,'kwhengusedwithadvi-drivercapa-eKble"ofsuppGortingthem..ExtracapabilitiesincludeeKsmoGotherslines,{zevenlyspaceddotted/dashedcurves,eKvqariable!line-widths,,8gray-scale llsofcircles,ellipseseKandUUpGolygonalregions. !eKUse oftpic\special/ hso ersanalternativetoeKthe6XY -pic6fonts.Howevertheyrequireadvi-drivereKthat6`iscapableofrecognizingandinterpretingthem.eKOnew6suchviewerisxdvik',KarlBerry'smoGdi cationeKto1thexdviVvieweronunix^10 bsystemsrunningX-eKwindowsoraderivqative.-dvipsk$t,KarlBerry'smoGd-eKi cationtodvips#SIalsohandlestpic\special.s,soeKxdvik'ExXimplementationprovidesasuiteof\special/commandstofacilitatethedraw-ing4oflines,nbGothon-screenandwithvqariousprintingdevices.`This"G`back-end'extensionallowsthelinesinXY -picUUdiagramstobGedrawnusingthesemethods.NotethatthisextensiondoGesnothavetobeusedwithwem-TU>'ExX.z,BetterresultsmaybGeobtainedusingthePostScriptback-endanddvipshdriveri,sinceaoversionofdvipsisavqailableforem-TU>'ExX. UHow-ever,gin1particularforscreenpreviewingpurpGoses,itmayHbGeconvenienttousethisback-end. F*urther-more\notethatdvipsiscapableofsuppGortingem-TU>'ExX\special)s.Once0loadedusing\xyoption{emtex}X,=withanappropriate^AhdriverialsospGeci edeitheralreadyorsubsequently*,theSVfollowingcommandsareavqailabletoUUturntheem-TU>'ExXbackendUUo /on. ff2 s6b\NoEMspecials`8turnsUUo em-TU>'ExXspGecials.6b\UseEMspecials`8reinstatesUUem-TU>'ExXspGecials.ff2*MOf-thecurvesde nedinthexycurve+Wextension,5onlysolidsplinecurvesaresuppGorted.0ThisisdonebytreatingdthesplineasapGolygon(poly-line)withmanysegments.&20 fdNecula'sffextensionsVers.0.0bCyGeorgeC.Neculahnecula@cs.cm9u.eduiLoadTas:p\xyoption{necula}uTThisoptioncontainstwoextensionsoftheXY-pickernel: AwayXtoexpandTU>'ExXmacrosinob8jecthmoGdi eris,qandawaytospecifyarbitrarypolygonsasUUthehshapGeiofanob8ject.R20.1%ExpansionThe spGecialsyntaxe|hmacrosi| IisintroGducedinanob8jectu͸hmoGdi erisandhcoordiinates./ItexpandsthegivenITU>'ExXhmacrosi(with\edef>:)bGeforereinterpre-tationUUasahmoGdi eriofhcoordi,respectively*.ThiscoGdemaybecomepartoftheXY -pickernelatUUacertainpGoint.R20.2%Polygonshap`esAUUpGolygonhshapeiisspeci edas ff2 sE[P:hpGosi,?...,꧸hposi]ff2w\eKwhereD[P:p1|s, p...,꧵pnq~] denotesDtheshapGeobtainedby eKtrackingtheedgewitheachpi0apGositionrelativetoeKthe@ob8jectreferencepGoint.@hvectoris@andhcorneriseKcanL*bGeuseddirectly;O8otherwiseuse-pNtogettherel-eKativeUUpGosition. CeKNote:qDzDoUUnotuse{}*or[]inthehpGosiitions.eKBug:8The algorithmassumesthatthereference eKpGointUUisalwaysinsidethepGolygon.eKItUUispGossibletoframepolygonsisalsopossible.eKBug: pThisTzcoGdeshouldbemergedwiththeeK`frame'UUand`pGoly'options.eKThe:{exampleattheendofx??hԲillustratestheex-eKtensions.+veKPartffIs3IICeKF=eatures덒eKThispartdoGcumentsthenotationaddedbyeacheKstandard/featureoption.[TF*oreachisindicatedtheeKdescribGed&versionnumbGer,theauthor,andhowitiseKloaded.eKThe rsttwo,`all'and`dummy',describGedinxx21eKandy22,BaretrivialfeaturesthatneverthelessproveeKusefulsometimes.~Thenexttwo,P`arrow'and`2cell',eKdescribGed3inx23and24,kprovidespecialcommandseKforob8jectsthat`pGoint'. Thefollowing,f`matrix'eKinx25,`graph'inx26,`pGoly'inx27,and`knot'inx30,eKareAinputymo}'desQbthatsuppGortdi erentoverallstruc-eKturingUUof(partsof)UQXY U-pictures.%eK21˯AllfffeaturesKeKVers.3.3bCyKristo erH.Rosehkrisrose@brics.dkieKLoadTas:p\xyoption{all}HeKAsaspGecialconvenience,-thisfeatureloadsasubseteKofXY'-pic,^11 u+namelytheextensions:{curve%(cf.x8),eKframe˲(x9),b^cmtip"޲(x10),b^line(x11),b^rotate(۲(x12),eKcolorF(x13),7and thefollowingfeatures: 2matrixeK(x25),UUarrow ꛲(x23),UUandgraph(x26).,eK22˯DummyffoptioneKVers.3.3bCyKristo erH.Rosehkrisrose@brics.dkieKLoadTas:p\xyoption{dummy}HeKThissoptionisprovidedasatemplatefornewoptions,eKitprovidesneitherfeaturesnorextensionsbutitdoGeseKcountUUhowmanytimesitisrequested.ffff[ J=w-:11LTheXname`all'hinÎtsatthefactthatthesewerealltheavailableoptionsatthetime`all'wasadded.LWeJ37&*tj??gw23}ArrowffandPathfeature3Vers.3.5bCyKristo erH.Rosehkrisrose@brics.dki LoadTas:p\xyoption{arrow}@Thisafeatureprovides]XY 6a-picwiththearrowparadigmpresentedUUin[12 ]. YNote:a\PATH ۲commandincompatiblychangedforversionUU3.3(the\arjcommandisuna ected).TheobasicconceptintroGducedisthep}'athc:acon-nection~]thatstartsP~fromc(thecurrentob8ject),endsataspGeci edob8ject,Axandmaybesplitintosev-eralFse}'gmentsbGetweenintermediatespGeci edob8jectsthatcanbGeindividuallylabelled,changestyle,havebreaks,UUetc.x23.1y+isabGoutthe\PATH!2Gprimitive,!includingthesyntaxappliedUUto... ffffeͤ fffd< ff3>nextUUsegmentonly͟ ff ͤ fffd> ff3>lastUUsegmentonly [ ffͤ fffd= ff3>everyUUsegment ffffe)K(whenseveralapplytothesamesegmenttheyareUUinsertedinthesequence<>+L).gweKThis7isusefultodrawconnectionswitha`center eKmarker'*inparticularwitharrows,e.g.,the*`map-eKsto'[exampleexplainedbGelowcanbechangedintoeKaUU`breakto'example:qtypingN8eK\xy*+{0}\PATHH~={**\dir{-}}H~>{|>*\dir{>}}H~+{|*\dir{/}}H'(10,1)*+{1}?'(20,-2)*+{2}(30,0)*+{3}eK\endxy܍eKwillUUtypGesetx-$ps: SDict begin xyc endګ0sޟH1sޟU" {17.45259 1.74956 l}xy5 " {2867 st}xy;缟q28缟" {17.45259 -5.24867 l}xy0-͟ " {2380 st}xyX[ګ3U[" {17.45259 3.48837 l}xyLz* " {2963 st}xyU[" {3277 10 /xy AB}xyjeKNote,khowever,thatgwhatgoGesinto~+{y^...} iseKhlabGelsiiandthusnotahposi{itisnotanactioneKinUUthesenseexplainedabGove.]HeK23c.1SpGecifyingp ~{ hstu i}willp setthe\failurecontin-eKuation"tohstu i.D`ThiswillbGeinsertedwhentheeKlast˸hsegmentiisexpGected|itcanevenreplaceiteKorUUaddmorehsegmentis,i.e.,eK\xy?*+{0}\PATH~={**\dir{-}}E~{'(20,-2)*+{2}?(30,0)*+{3}}'(10,1)*+{1}eK\endxy܍eKisUUequivqalenttoeK\xy?*+{0}\PATH~={**\dir{-}}E'(10,1)*+{1}?'(20,-2)*+{2}(30,0)*+{3}eK\endxy܍eKtypGesettingx-$ps: SDict begin xyc endګ0sޟH1sޟU" {17.45259 1.74956 l}xy;缟q28缟" {17.45259 -5.24867 l}xyX[ګ3U[" {17.45259 3.48837 l}xyjeKbGecausewhen\endxy*:isseenthentheparsereKknowsg"thatthenextsymbGolisneitherofthechar-eKacters!~'`9and!hencethatthelasthsegmentiistoeKbGe(expected.Instead,]khowever,the(failurecon-eKtinuation*isinsertedandparsed,andthehpathieKisUU nishedbytheinsertedmaterial.eKF*ailureUUcontinuationscanbGenested:eK\xy?*+{0}\PATH~={**\dir{-}}H~{~{(30,0)*+{3}}H'(20,-2)*+{2}}?'(10,1)*+{1}eK\endxy܍eKwillUUalsotypGesettheconnecteddigits.]HeK23d.AUU\straightsegment"isinterpretedasfollows:-1. eKFirst9.pissettotheendob8jectoftheprevi-  eKoussegment(forthe rstsegmentthisisc eKjusthbGeforethepathcommand)andcisset eKtothehpGosistartingthehsegmenti,andthe eKcurrentUUhslideiisapplied.LWeJ38'*tj??}X ffffd TSyntax(.5)ȍhitiAYGv.!Wj#hdigitiUUj qhletteriUUj{ĸhtexti}Rjhcsipturning!)segment>isonethatdoGesnotgoallthen>waytothegivenhpGosibutonlyasfarasre-quired1tomakeaturntowardsit.Thecissettotheactualturnob8jectafteraturningsegmentsuchthatsubsequentturningorothersegments#}eKwillstartfromthere,HTinparticularthelastseg- eKmentC#(whichisalwaysstraight)canbGeusedtoeK nishUUawindingline.|eKWhattheturnloGokslikeisdeterminedbytheeKhturniUUform:JeKhemptyieQNothing/bGetweenthe`andthehpGosi eKisinterpretedthesameasgivingjustthe eKhdiagiUUlastusedoutH-ofaturn.JeKhdiagi²SpGecifyingxasinglehdiagidisthesameas eKspGecifyingceitherofthehciriclesd^ord_,de- eKpGendingonwhetherthespeci edhposihas eKits]center`abGove'or`bGelow'thelinefromp eKinUUthehdiagionaldirection.eKhciri OWhen8afullexplicithciricleisavqailable eKthenCthecorrespGondinghciricleob8jectis eKplacedsuchthatitsingoingdirectionisa eKcontinuationgofastraightconnectionfromp eKand=theoutgoingdirectionpGointssuchthatLWeJ39(+A*tj??gw aUfollowingstraight(orlast)segmentwill connectUUittoc(withthesameslide).ѶHereUUisanexampleusingallformsofhturnis:EQps: SDict begin xyc end*Gbase1 qA G" {10.0 90 180 o}xy G" {-25.52777 -0.00195 l}xy G" {-1024 10 /xy AB}xyȟa_1 qB #" {10.0 -180 -90 o}xyǍ&" {-0.00098 -27.99805 l}xy#" {1024 10 /xy AB}xy@b_њ qCß7&" {10.0 -135 90 o}xyß-&" {158.14458 -0.00145 l}xyß-&" {3072 10 /xy AB}xy[џ*c_" {10.0 45 90 o}xyf" {-62.14403 62.1436 l}xyf" {-2048 10 /xy AB}xy~p'~hd@8" {-31.38518 0.0 l}xy@8" {-1024 10 /xy AB}xyGUeP2dwasUUtypGesetbyN8\xy?<4pc,0pc>:(0,0)*+\txt{base}="base"\PATH?~={**\dir{-}?>*\dir{>}}L`l(-1,-1)*{A}?^aL`?(1,-1)*{B}?^bL`_ul (1,?0)*{C}^cL`ul^l?"base"?^d9"base"?^e\endxy7Bug:fT*urns$areonlyreallyresonableforpathsthatUUusestraightlinesliketheoneabGove.ۍNote:n[AlwaysN~writeavqalidhpGosiafterahturni,otherwiseanyfollowing^or_labGelscancon-fuse?theparser.Soifyouintendthe^rxin`^rtobGealabelthenwrite`,^rƲ,qusingadummy,hpGosiition.TheRdefaultusedforturnr}'adiusscanbGesetbytheopGeration rff2 O?\turnradiusUUhaddopi{Rhdimeni}ݍff2~ thatworkslikethekernel\objectmarginetc.commands;UUitdefaultsto10pt.#ExerciseT23: TypGesetENfps: SDict begin xyc enddd qA$d" {10.0 0 360 o}xy " {10.0 45 315 o}xy2" {3686 10 /xy AB}xy usingUUhturnis.Ѷ23g.S9The[lastsegmentisexactlyasastraightoneex-ceptthatthe>action(ifany)isexecuted(andcleared)UUjustafterthedefaults}touseobje}'ct-eKmar}'ginifUUnotset.HeK23j.:BreakingTmeansto\sliceahole"intheconnec-eKtion>andinserthitithere. lThisisrealizedbyeKtypGesetting/theconnectioninquestioninsubse}'g-eKments!,one}leadingtothebreakandonecontin-eKuing\afterthebreakasdescribGedinnotes23aeKandUU23d.eKThe^FspGecialcontrolsequence\holeisprovidedeKtoUUmakeiteasytomakeanemptybreak.HeK23k.sUnless|yhitiisafull- edgedhob8jecti(byusingeKthe*form),+itistypGesetusinga\labelboxob-eKject(initiallysimilarto\objectboxofbasicXY -eKpicUUbutusing\labelstyleforthestyle).eKRemark:'^Y*oucanonlyomitthe{} @~saroundsin-eKgleUUletters,digits,andcontrolsequences.HeK23l.AlabGeloisanob8jectlikeanyotherinthekXY;o-eKpicture. UInsertinganhaliasi="?hidi" 6savestheeKlabGelUUob8jectas"Rhidi"forUUlaterreference.(]IeKExerciseT24: TypGeset;72ps: SDict begin xyc end" {0.0 0.0 dd}xy&CmAU[" {3311 10 /xy AB}xyU[" {85.35782 19.91682 dd}xyU[" {0.0 0.0 dd}xy 2labGelǍ |T@" {0.02669 0.0 l}xy%" {1722 10 /xy AB}xyǍ%B" {4.74312 -6.92917 l}xyǍ%B" {0.02669 0.0 l}xyJ$$7eK23.2KArrowseKArrowsUarepathswithaparticularlyeasysyntaxforeKsettingu+uparrowswithtail, stemc,andu+he}'ad}intheeKstyleof[12 ].=ThisisprovidedbyasinglehdecoriationeKthesyntaxofwhichisdescribGedin gure14(withtheeKaddedٳconventionthataraised`*'means0ormoreeKrepGetitionsUUofthepreceedingnonterminal).LWeJ40)@Ѡ*tj??uN ffffd T޲SyntaxQSActionX-ffd \arUUharrowihpathiQSmakeUUharrowialonghpathifffd fdharrowi<B%!Rhformi*QSharrowiUUhasthehformis޸hformi<B%!R@UUhvqariantiQSuseUUhvqariantiofarrowiBSjR@UUhvqarianti{ ꧸htipi}QSbuildarrow^23mUusinghvqariantiofastandardstemand QShtipiUUforthehead͍BSjR@UUhvqarianti{ ꧸htipihconnihtipi}QSbuild'arrow^23mѲusinghvqariantiofhtipi,0hconni,htipi'as QSarrowUUtail,stem,andhead(inthatorder)dBSjR@UUhconnchariQSchangeUUstemtotheindicatedhconnchari BSjR@!QSdashUUthearrowstembydoublingitBSjR@/UUhdirectionihdisti/QScurve^23oOarrowUUthehdistiancetowardsUUhdirectioniBSjR@(UUhdirectioni, ꧸hdirectioni)QScurveUUto twithin-outdirections^23pBSjR@`UU{ ꧸hcontrolUUpGointlisti}QScurveUUsetup^23qwithexplicitcontrolpGointsBSjR@[`JhshapGeiUU]QSaddUU[RhshapGei]toUUob8jecthmodi eris^23rforallob8jectsBSjR@*UU{ ꧸hmoGdi eri*UV}QSaddUUob8jecthmoGdi eris^23rforallobjectsBSjR@<UUhdimeni>QSslideUUarrow^23s[thehdimeniBSjR|UUhanchorihitiQSbreakUUeachsegmentathanchoriwithhitiBSjR^UUhanchorihitijq_hanchorihitiQSlabGelUUeachsegmentathanchoriwithhitiBSjR@?QSreverseUUmeaningofabGoveandbGelow^23t޸hvqarianti<B%!Rhemptyijq^j_VPj_t0jq1j2j3QShvqarianti:qplain,UUabGove,bGelow,double,ortriple޸htipi<B%!RhtipGchari*QSdirectionalUUnamedasthesequenceofhtipGcharisiBSjRhdiriQSanyUUhdiriectional^23n޸htipGchari<B%!R<[BMja^>ijp(xոj~G)Wjt | ]j%'!jד`ljW+j;/QSrecognisedUUtipcharactersBSjRhletterijqhspaceiQSmoreUUtipcharacters޸hconni<B%!Rhconnchari*QSdirectionalUUnamedasthesequenceofhconncharisiBSjRhdiriQSanyUUhdiriectional^23n޸hconnchari<B%!R-[BMja^.ijp~xոj~G=Wjt :QSrecognisedUUconnectorcharactersffd FigureUU14:qǸharrowis.U-uNotes23m.BuildinganharrowiissimplyusingthespGec- i eddirectionals(using\dirofx6.1)tobuildapath:the rsthtipibGecomesthearr}'owJtailofthearrow,'theʸhconniectioninthemiddlebGecomesthe+arr}'owstemc,(andthesecondhtipibGecomesthe%arr}'owhChead.aIfahvqariantiisgivenbGeforethe{thenthatvqariant\dirisusedforallthree.>F*orexample,N8\xy\ar?@^{(->}(20,7)\endxyl鍑typGesets%hCps: SDict begin xyc end " {3430 ha}xy" {0.0 0.02223 l}xy8缟" {3430 10 /xy A}xy8缟" {56.90521 19.91682 l}xy8缟" {0.0 0.02223 l}xy-ueKExerciseT25: TypGesetUUthesearrows:}{!/4.5pt/\dir{|}2e'*:(1,-.2)\dir^{>}2e'*:(1,+.2)\dir_{>}}eKde nesUUanewarrowtipthatmakeseK\xy?(0,0)*+{A}H\ar?@{=|>}(20,3)*+{B}LWeJ41*W*tj??gw\endxy;ݍtypGeset(J<Fps: SDict begin xyc end qA;HB \Y" {0.01512 0.0 l}xy g" {0.01512 0.0 l}xy6c " {3226 st}xy:ռ" {3029 10 /xy A}xy:ռ" {3449 10 /xy B}xy6;q" {40.88872 6.12706 l}xy6 zO" {40.88872 6.12706 l}xywNotice?thatthefactthatthedirectionalusesonly htipGchari3charactersmeansthatitblendsnatu-rallyUUwiththeexistingtips.$Exerciseq26: OftenEtipsusedas`tails'havetheirc/inkonthewrongsideofthepGointwheretheyareplaced. UF*ortunatelyspaceisalsoahtipGchari~sowecande ne\dir{?>}0togenerateaUU`tail'arrow.qDothissuchthatN8\xy?(0,0)*+{A}="a",(20,3)*+{B}="b"\ar?@{>->} "a";"b"<2pt>\ar?@{>->}"a";"b"<-2pt>\endxytypGesets(J<Fps: SDict begin xyc end qA;HB 0" {3226 10 /xy AB}xy 4П" {0.01512 0.0 l}xy8M-" {3226 10 /xy AB}xy8M-" {43.1118 6.4614 l}xy8M-" {0.01584 0.0 l}xyGi4" {3226 10 /xy AB}xy8밟!" {3226 10 /xy AB}xy8밟!" {40.64171 6.08992 l}xy8밟!" {0.01584 0.0 l}xywJ23n.rSpGecifying[ahdiriasahtipiorhconnimeansthat}\dirhdiriisusedforthathtipiorhconni.F*orUUexample,N8\xy\ar?@{<^{|}>}(20,7)\endxytypGesets,Cps: SDict begin xyc end" {-666 10 /xy AB}xy8缟" {3430 10 /xy AB}xy7Gq" {-2714 F d}xy3)=" {-2714 F d}xy0*|" {-2714 F d}xy,3a" {-2714 F d}xy) " {-2714 F d}xy%=7" {-2714 F d}xy!ŸuQ" {-2714 F d}xybG" {-2714 F d}xy̟" {-2714 F d}xyEQ0A" {-2714 F d}xy֟n" {-2714 F d}xy([" {-2714 F d}xy 1" {-2714 F d}xy e)" {-2714 F d}xy|g" {-2714 F d}xyo!" {-2714 F d}xy_q" {-2714 F d}xywWhenusingthisyoumustspGecifya{}}^dummyhdiriectionalxinordertoignoreoneofthetail,stem,UUortipcompGonents,e.g.,N8\xy\ar?@{{}{+}>}(20,7)\endxytypGesets,Cps: SDict begin xyc end8缟" {3430 10 /xy AB}xy8缟T " {3430 st}xy6~`" {3430 F d}xy3f " {3430 st}xy1^(Z" {3430 F d}xy.X " {3430 st}xy,1ҟ(" {3430 F d}xy)b' " {3430 st}xy'|" {3430 F d}xy$6dL " {3430 st}xy!&X" {3430 F d}xy  " {3430 st}xyП" {3430 F d}xyݸ " {3430 st}xyzc" {3430 F d}xybb " {3430 st}xyT$2" {3430 F d}xy 1D " {3430 st}xy 'ΟP" {3430 F d}xy X " {3430 st}xyx" {3430 F d}xy,` " {3430 st}xy"" {3430 F d}xy ~ " {3430 st}xy̟m" {3430 F d}xywInparticular*hob8jectiisahdirisoanyhobjectican&bGeusedforeitherofthetail,stem,or&headcompGonent:N8\xy\ar?@{*{x}*{y}*{z}}(20,7)\endxytypGesetsE@QFps: SDict begin xyc endx97.z3ß촊y.-y(e[y"Ƣy̪y?ҲyFغy ~ןy#ywNote:}A[#* introGduces[ganhob8jectiwhereasthedirectionalUU`ps: SDict begin xyc end33n'istypGesetbythehdiri{*}L.gweKExerciseT27: TypGeset"|@ps: SDict begin xyc end)o" {3430 10 /xy AB}xy" {3430 10 /xy AB}xy;j" {-666 10 /xy AB}xy8缟" {-666 10 /xy AB}xy8缟T" {-3572 st}xy7Ʉ" {-3572 F d}xy8缟T " {3430 st}xy6~`" {3430 F d}xy3f" {-3572 st}xy2.~" {-3572 F d}xy3f " {3430 st}xy1^(Z" {3430 F d}xy.X" {-3572 st}xy-p؟<" {-3572 F d}xy.X " {3430 st}xy,1ҟ(" {3430 F d}xy)b'" {-3572 st}xy(Dc" {-3572 F d}xy)b' " {3430 st}xy'|" {3430 F d}xy$6dL" {-3572 st}xy#,2" {-3572 F d}xy$6dL " {3430 st}xy!&X" {3430 F d}xy  " {-3572 st}xy֟v" {-3572 F d}xy  " {3430 st}xyП" {3430 F d}xyݸ" {-3572 st}xy4" {-3572 F d}xyݸ " {3430 st}xyzc" {3430 F d}xybb" {-3572 st}xy*" {-3572 F d}xybb " {3430 st}xyT$2" {3430 F d}xy 1D" {-3572 st}xyfԟm" {-3572 F d}xy 1D " {3430 st}xy 'ΟP" {3430 F d}xy X" {-3572 st}xy :~{}="a"e?,?(20,-10)*\cir<2pt>{}="b"H\POS"a"?\ar@/^1ex/"b"|\uparrowH\POS"a"?\ar@/_1ex/"b"|\downarroweK%H\POS?(20,10)*\cir<2pt>{}="a"e?,?(40,-10)*\cir<2pt>{}="b"H\POS"a"?\ar@/u1ex/"b"|uH\POS"a"?\ar@/d1ex/"b"|deK\endxy(7eK`UUdefaultsto.5pcifomitted.eKThisisreallyjustashorthandforcurvingusingeKthe moregeneralformdescribGednext:ܻ@/\d`/ J̲iseKthe*sameas@`{{**{}??+/B*d2`/}}whichmakeseKthe6a(quadratic)curvepassthroughthepGointde-eK nedUUbythehpGosi**{}??+/-U=d`/?.eK23p.Using B@(d2|s, pd2|s)whered1|s;d2oaresimpleeKhdirectionis@(asdescribGedinnote4lexceptitiseKnot]pGossibletouse() Ws)willtypesetthearroweKcurved/suchthatitleavesthesourceindirectioneKd1ȲandUUentersthetargetfromdirectiond2|s.|eKExerciseT28: TypGeset(9@ps: SDict begin xyc end :Zګ ZN" {mark 0.0 0.0 25.45587 25.45587 -25.45587 25.45587 0.0 0.0 1.0 0.03003 bz}xy hQ" {1919 10 /xy AB}xy ZR" {mark 0.0 0.0 25.45587 25.45587 -25.45587 25.45587 0.0 0.0 0.03003 0.96997 bz}xy ZN" {mark 0.0 0.0 25.45587 25.45587 -25.45587 25.45587 0.0 0.0 1.0 0.97003 bz}xyC"ګ ZS" {mark 0.0 0.0 25.45587 -25.45587 31.44934 25.45587 56.90521 0.0 1.0 0.03223 bt}xyC=iF" {2190 10 /xy AB}xy ZV" {mark 0.0 0.0 25.45587 -25.45587 31.44934 25.45587 56.90521 0.0 0.03223 0.9679 bt}xy ZR" {mark 0.0 0.0 25.45587 -25.45587 31.44934 25.45587 56.90521 0.0 1.0 0.9679 bt}xyAeKT oXTDo:Uimplement?thisecientlyandpropGerlyeKgetUUridoftheno-() Orestriction!eK23q.sThej? nalcurveformisthemostgeneralone:eK@`{%Bhcontrol@pGointlistsi} setsthecontrolpGointseKexplicitlytotheonesinthehcontrolpGointlistsieK(wheretheyshouldbGeseparatedby, ). SeetheLWeJ42+te*tj??gwcurveextensiondescribGedinx8forthewaythe controlpGointsareused;ÙwhenthecontrolpGointslistisparsedpisthesourceandcthetargetoftheUUarrow.23r.=@[ݲ...] AвandW)@*{ ...}formationsW)de newhatob-jectָhmoGdi erisshouldbeusedwhenbuildingob-jectsthatarepartofthearrow.Thisismostlyuseful2ginconjunctionwithextensionsthatde neadditional[ ľhshapGei]modi ers,Лe.g.,ifa[red]hmoGdi eri3#changesthecolourofanob8jecttoredthen@[red]%}:willmaketheentirearrowred;sim-ilarly ifitisdesiredtomakeandentirearrowinvisibleUUthen@*{i} ꛲canbGeused.23s.D@3willslide(eachsegmentof)thearrowthedimensionUUDrasexplainedinnote23h.23t.6@?reverseRthemeaningof`abGove'and`bGelow'forUUthisparticulararrow.AllMthefeaturesofhpathisdescribGedaboveMareavqailableUUforarrows.+鍍24}Two-cellfffeature3Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.auiLoadTas:p\xyoption{2cell}lThisʲfeatureisdesignedtofacilitatethetypGesettingof'curvedarrows,\^eithersinglyorinpairs,togetherwithklabGelsoneachpartandbetween. Thekintendedmathematical-usageisfortypGesettingcategorical\2-cell"" {1024 F d}xy*>" {1024 F d}xy," {1024 F d}xy*" {1024 F d}xy+>" {1024 /XT tt}xy/  =" {mark 73.7934 0.0 36.8967 -35.0 0.0 0.0 0.09146 0.9046 q}xyIΟ V" {3855 10 /xy AB}xy)NJ9h," {1024 F d}xy*" {1024 F d}xy,>" {1024 F d}xy*>" {1024 F d}xy+ " {1024 /XT tt}xy/3 " {0.0 0.0 l}xy}gI" {3072 10 /xy AB}xyI" {59.99998 0.0 l}xyI" {0.0 0.0 l}xyLjB3DeK\diagram eKA\ruppertwocell^f{\alpha}E\rlowertwocell_h{\beta}E\rto_(.35)g?&B\\eK\enddiagramzueKThese categoricaldiagramsfrequentlyhaveaeKmatrix-likelayout,paswithcommutativediagrams.eKT*oJ@facilitatethistherearecontrolsequencesoftheeKform:S\rtwocell}2.GG " {384 F d}xy!=7 " {384 F d}xy?H" {384 /XT tt}xyـ1vj" {36.0 -23.50845 l}xyȞ9"ff5ـ1vj" {2404 10 /xy AB}xyـ1vj" {2404 10 /xy AB}xy6TA- " {32.02 28.3348 l}xyQf1- " {3978 10 /xy AB}xy[ " {45.97998 16.06087 l}xy@{ʟA̴f2[ " {3430 10 /xy AB}xy24ȟ w" {1632 F d}xy0|" {1632 F d}xy3{1" {1632 F d}xy1R7" {1632 F d}xy6s '" {1632 /XT tt}xyG" {mark 87.75 0.0 59.18994 -51.50423 0.0 -51.41666 0.05789 0.97046 q}xy\2|" {-3676 10 /xy AB}xy1M " {35.99998 -21.57999 l}xy1M " {2458 10 /xy AB}xyoEg11M " {2458 10 /xy AB}xy" {36.0 23.5026 l}xy" {3740 10 /xy AB}xy" {3740 10 /xy AB}xy3j" {36.0 0.0 l}xyu/f63j" {3072 10 /xy AB}xy3j" {3072 10 /xy AB}xyS" {mark 301.7934 -51.41666 278.7717 -66.41666 255.75 -51.41666 0.06516 0.84705 q}xy->7M" {3515 10 /xy AB}xy@lg4)ij" {1024 F d}xy)ij" {1024 F d}xy+j" {1024 F d}xy+j" {1024 F d}xy3ij" {1024 /XT tt}xyj" {20.71896 27.0 l}xy +Y"f7j" {-3858 10 /xy AB}xy/؟-" {18.10269 -23.58334 l}xy)?"f8/؟-" {1810 10 /xy AB}xy06TB4e*" {78.0 25.45963 l}xy4e*" {3406 10 /xy AB}xy4e*" {3406 10 /xy AB}xytW[" {84.47443 -8.23247 l}xy[lXݴg2tW[" {2972 10 /xy AB}xyـ4j" {77.52557 34.6003 l}xyVJyѴg3ـ4j" {3529 10 /xy AB}xyIQFigureUU15:qPastingdiagram.m獍NormallythelabGelisbalancedtext,TsetinTU>'ExX's mathjqmoGde,with\twocellstyleMsettingthestyle.TheUUdefaultde nitionisgivenby... M8\def\twocellstyle{\scriptstyle}This canbGealteredusing\def@inversionsofTU>'ExX or \redefine7}in L5ffA͉TU>'ExX.HoweverlabGelsarenotre-stricted0tobGeingsimplytextboxes.Any0e ectob-tainableϕusingtheϑXY O-pickernellanguagecanbGesetwithinan\xybox&βandusedasalabGel.Alternativelyif +the rstcharacterinthelabGelis* XSthenthelabelissetOasanKXY O-pichob8jecti,asifwith\dropItwor*m+in-thekernellanguage.5Thecurrentdirec-tion6istangentialtothecurvedarrows.gExtrabracesareGneededtogeta* ϗasthelabGel,Jasin^{{{*}}}0or_{{}*} . M8ThepGositionofalabelnormaltothetangentialdirectionPcanalsobGealteredbynudging(seebelow).AlthoughitispGossibletospecifymultiplelabels,.onlytheeQlastusageofeachof^ and_isactuallyset,iPpre-viousUUspGeci cationsbeingignored.SimilarlyfalabGelforthecentralArrowmustbGegiven,afterWstheotherlabGels,byenclosingitwithinbracesn{...}.Annemptygroup{}]2givesanemptylabGel;ethis isnecessarytoavoid misinterpretationofsubsequenttokens.9 AsabGoveifthe rstcharacteris*thenDthelabGelissetasan@XY ]D-pichob8jecti,GthecurrentdirectionUUbGeingalongtheArrow.卍24.2 StandardOptions Theb?orientationofthecentralArrowmaybGereversed,turned4intoanequality*,-oromittedaltogether.dIneach0casealabGelmaystillbGespeci ed,gsoine ecttheUUArrowmaybGereplacedbyanythingatall.Thesee ectsarespGeci edbythe rsttokeninthecentralUlabGel,Uwhichthushastheform:{ WĸhtokihlabGeli}whereUUhtokimaybGeoneof... Չff28d-_IhArrowUUpGointscloGckwise-^IhArrowUUpGointsanti-cloGckwise-=IhnoUUtip,denotesequality#) \omitIhnoUUArrowatall.3ff2 eKWhen0noneoftheseoGccursthenthedefaultof_ uis eKassumed.bIfthelabGelitselfstartswithoneoftheseeKcharactersZthenspGecify_ dexplicitly*,orenclosethela-eKbGel{withinagroup{...}+l.48SeeExtr}'a Options1,foreKmore*vqaluesofhtoki.vGAlsonotethat* QhasaspGecialeKrole\xwhenusedasthe rstcharacter; however\xitiseKconsideredUUtobGepartofthehlabeli,seeabove.eK24.3KNudgingqԍeKPositionsofalllabGelsmaybGeadjusted,˧ascantheeKamount4ofcurvqatureforthecurvedarrows.fThewayeKthisisdoneisbyspGecifyinga\nudge"factorhnumieKatlthebGeginningofthelabel.8 Herehnumiisanum-eKbGer+whichspeci estheactualpositionofthelabelineKunitsJvof\xydashl@5Ѳ(thelengthofasingledash,Lnor-eKmallyA5pt)exceptwith\..compositemapQ,xseebGelow.eKMovementgisconstrainedtothepGerpendiculargbisec-eKtorQoftheline~fe [۟gcp g.flWhennudgingthelabGelfortheeKcentralaArrowitisthewholeArrowwhichismoved,eKalongUUwithitslabGel.eKCurvqatureQofthearrowsthemselvesisalteredbyeKa#nudgeoftheform\..twocell8߸hnumi....ݿThesep-eKarationofthearrows,alongthebisector,issettoeKbGehnumi\xydashl@/?.dWhenhnumiiszero,thatiseK\..twocell<0>...5e,;the5resultisasinglestraightar-eKrow,itsmid-pGointbGeingtheoriginfornudginglabGels.eKAnegativevqalueforhnumiisalsoacceptable;WPbuteKcheckD_theorientationontheArrowandwhichof^eKandUU_ ꧲correspGondUUtowhichcomponent.eKTheoriginfornudginglabGelsiswherethearroweKcrosseskthebisector. PositiveknudgesmovethelabGeleKoutwardswhilenegativenudgesmovetowards~fe [۟gpcandeKpGossiblybeyond.HThedefaultpositionofalabelisoneKtheUUoutside,withedgeattheorigin.eKTheKoriginfornudgingtheArrowisatthemid-eKpGointN-of~fe [۟gpc .odAN+positivenudgemovesinthecloGckwiseeKdirection.#Thisk.willbGethedirectionofthearrowhead,eKunlessUUithasbGeenreversedusing^R.XeKLabGels&ona\..compositemapU areplacedrelativeeKtopthemidpGointofthecomponentarrows.ßNudgeseKareinunitsof1pt.tMovementisintheusualXY +-picLWeJ44-t*tj??2*;G$ ffffd T^SyntaxzActionX-ffd fd^htwoGcelli8v)>!NAh2-cellihswitchesihArrowiztypGesetUUh2-celliwiththehswitchesiandhArrowi^h2-celli8v)>!NA\..twocellztypGesetUUtwocurvedarrows ? ָjNA\..uppertwocellztypGesetUUuppercurvedarrowonly? ָjNA\..lowertwocellztypGesetUUlowercurvedarrowonly? ָjNA\..compositemapzuseUUconsecutivestraightarrows^hArrowi8v)>!NA{T1>htokihtexti}zspGeci esUUorientationandlabel? ָjNA{T1>hnudgeihtexti}zadjustUUpGosition,usedefaultorientation? ָjNA{T1>htexti}zuseUUdefaultpGositionandorientation? ָjNA{T1>htoki*hob8jecti}zuseUUhob8jectiasthelabGel? ָjNA{T1>hnudgei*hob8jecti} ꧸j{G*hobjecti}^htoki8v)>!NA^Zj`Z_ljrs=zorientedUUanti-/cloGckwise/equality? ָjNA\omitznoUUArrow,defaultiscloGckwise? ָjNA`Zj`Z'ljrs"~j!znoUUArrow;tipsontwocurvedarrowsas:zanti-/cloGckwise/double-headed/noned^hswitchesi8v)>!NAhswitchihswitchesizlistUUofoptionalmoGdi cations^hswitchi8v)>!NAhemptyizuseUUdefaults? ָjNA^WhlabGelizplaceUUhlabGeliontheupperarrow? ָjNA_WhlabGelizplaceUUhlabGelionthelowerUUarrow? ָjNAhnudgeizsetUUthecurvqature,basedonhnudgeivalue? ָjNA\omitzdoUUnotsetthecurvedarrows? ָjRF!zplaceUU\modmapobjectJꃲmidwayUUalongarrows? ָjNA~WhwhatiUU{ ꧸hob8jectiUU}zuseUUhob8jectiinplacespGeci edbyhwhati^hwhati8v)>!NAhemptyizsetUUcurvesusingthespGeci edhob8jecti? jNA^Zj`Z_zuseUUhob8jectiwithuppGer/lowerUUcurve? ָjNA`Zj`Z'zuseUUhob8jectiforarrowhead/tail^hlabGeli8v)>!NAhtextijqhnudgeiUUhtextizsetUUhtexti,displacedbyhnudgei? jNA*hob8jectijqhnudgei*hobjectizsetUUhob8jecti,displacedbyhnudgei^hnudgei8v)>!NAhnumbGeri>zuse6hnumbGeriinanappropriateway*,ne.g.,topGositionzob8jectUUorlabGelalonga xedaxisX+? ָjNA<\omit>zdoUUnottypGesettheob8ject/labelffd uFigureUU16:qǸhtwoGcellisLWeJ45. *tj??gwab}'ove}eandbelowdirections,suchthatapGositivenudge is?alwaysoutsidethetriangleformedbythearrowsandUUline~fe [۟gpc 0.鍑ThespGecialnudgevqalue<\omit>)typGesetsjusttheArrow,omittingwhthecurvedarrowsentirely*.Whenused withlabGels,thenudgevqalue<\omit>*causesthefollowingUUlabGeltobeignored.IExerciseT29: GiveUUcoGdetotypGeset gure15.SuchcoGdeisrelativelystraight-forward,Dusing\nudg-ing"G%and\omit";tohelppGositionthearrows,curvesandArrows.Italsousesanexcursion,"asdescribGedbGelowUUinthesubsectionExtr}'aOptions3.I24.4 ExtraOptionsuTTheBfollowingfeaturesareusefulinnon-mathematicalapplications.1.pnoTArro9wuTThisisdeterminedbyspGecialvqaluesforhtokiasthe rstE(oronly)characterinthecentrallabGel,asintheabGoveUUdescriptionofthestandardswitches. >,ff2w􍍍d'-ӫarrowheadsUUpGointingcloGckwise;`-ӫarrowheadsUUpGointinganti-cloGckwise;"-ӫarrowUUtipsonbGothends;!-ӫnoUUtipsatall.Zff2 ơTheh#centralArrowisomitted,lleavingsymmetricallyplaced,{curvedconnectionswitharrowheadsatthespGeci edends.~xAlabelcanbeplacedwheretheAr-rowUUwouldhavebGeen.If^aspGecialarrowheadisspeci edusing~'{..}(seeExtraOptions2,)@bGelow)thenthiswillbeusedinsteadUUofthestandard\dir{>}(@.50P$ps: SDict begin xyc endx㍍Clouds?" {mark 96.61116 0.0 48.30557 50.0 0.0 0.0 0.06955 0.93109 q}xy-c6precipitationkџ" {2153 10 /xy AB}xy@" {mark 96.61116 0.0 48.30557 -50.0 0.0 0.0 0.06955 0.93109 q}xy/6evap,rorationyP" {-1943 10 /xy AB}xy9J@f$cmbx7@HA-hcmbx5A2J@Ojc?_{\hbox{\tinyevaporation}}?^{\hbox{\tinyprecipitation}}{'{\mathbf{H_2?O}}}&\relax\txt{Oceans}\\\enddiagramgwt0ps: SDict begin xyc endx㍍cMathematicsj>" {mark 98.65282 0.0 49.3264 17.5 0.0 0.0 0.19681 0.80505 q}xy93theorybj" {2854 10 /xy AB}xy&Rw" {-802 10 /xy AB}xyj?" {mark 98.65282 0.0 49.3264 -17.5 0.0 0.0 0.19681 0.80505 q}xy2exp,rerimenӍtbj~6" {3290 10 /xy AB}xy&R0" {-1246 10 /xy AB}xyeXPhysics"87eK\xymatrixcolsep{5pc} eK\diagrameK\relax\txt{\llap{Math}ematics?}\rtwocelleK_{\hbox{\tiny?experiment}}eK^{\hbox{\tiny?theory}}{"}eK&?\relax\txt{Physics}\\eK\enddiagram(ٍeK2.pChangingTTipsandMoQduleMapsuTeKThefollowingcommandsareprovidedforspGecifyingeKthe}\twocelltail{J?ڸhob8jecti}\dir{}\arrowobject{J?ڸhob8jecti}x\dir{=>}\curveobject{J?ڸhob8jecti}\uppercurveobject{d˸hob8jecti}8{}\lowercurveobject{d˸hob8jecti}8{}ffxC8eKThese22commandssettheob8jecttobGeusedforalleKsubsequent2-cellsatthesamelevelofTU>'ExXgrouping.eK\curveobject#1spGeci es bothoftheupper-andlower-eKcurve+ob8jects.vHF*orsomeofthesethereisalsoawayeKto;Uchangetheob8jectforthecurrent2-cellonly*.iThiseKrequiresa~-hswitchiwhichisdescribGedbelow,excepteKforx7the\..curveobjectNpDtypGes,qwhichx7arediscussedineKExtr}'aOptions4.[eKTheseDe ectsarespGeci edbyplacingswitchesaf-eKterthe\..twocell:zcontrolsequence,e.g.\rtwocelleKswitcheslab}'els!...oe. EachĻswitchiseitherasin-eKgle3tokenhtoki,*ora~ 0htokiwithasingleargument:eK~Hhtoki{?ar}'g}}"z.NHPossibilities+arelistedinthefollowingeKtable,inG$which{..}of~^ x8, ~_and~{..} 0misgiveninExtr}'a>COp-tions4.LWeJ46/쥠*tj??gwTheg$defaultmoGdulemapindicatorplacesasin- gleMdashcrossingthearrowatright-angles,loGcatedroughlylmidwayalongtheactualprintedpGortionofthearrow,whethercurvedorstraight.Thistakesinto\accountthesizesoftheob8jectsbGeingconnected,thereby;#givinganaestheticresultwhenthesesizesdif-fermarkedly*.*Thisalsoworkswith\..compositemapwhereanindicatorisplacedoneacharrow.Theac-tualUUob8jectcanbGechangedusing\modmapobjectG..㍑AnyUofthestandardQXY WU-pictipsmaybGeusedforarrow-heads.ZjThis>}}%5givesdouble-headedarrows.8Similarly~`{..}"ڲcanbGeusedtoplaceanarrow-tail.\NormallytheLarrow-tailis,Nsoisnotplaced;butifanon-emptytail:hasbGeenspeci edthenitwillbeplaced,t5using\drop .Nopguaranteeiso eredforthedesiredresultbGeingDobtainedwhenanarrow-tailismixedwiththefeaturesUUofExtr}'aOptions1. LL ?7+6zps: SDict begin xyc endjP?" {mark 73.25867 0.0 36.62933 20.0 0.0 0.0 0.09427 0.91327 q}xy'ɽ 'X|EMGğ" {2615 10 /xy AB}xyI\j" {2615 10 /xy AB}xy " {3528 st}xy@" {mark 73.25867 0.0 36.62933 -20.0 0.0 0.0 0.09427 0.91327 q}xy'ɽ  %BeմM,r 0ncmsy50Gğ^v" {3529 10 /xy AB}xyI\*" {3529 10 /xy AB}xy j " {2616 st}xy*" {0.0 10.0 l}xy," {0.0 10.0 l}xy$1fLjS,\modmapobject{\objectbox{\otimes}}\xymatrixcolsep{5pc}\diagramP\rtwocell~!~'{\dir{>>}}~`{\dir{|}}^{<1.5>M}_{<1.5>M'}{=f}?&S\\\enddiagram83.pExcursionsRSyntaxlfor\xcompositemapPYand\x..twocell@typGesisaalittledi erenttowhatmightbGeexpectedfromthatUUfor\xtoUI,\xline"C,etc.qF*orexample, ĉff2 'W\xtwocell[\W9hhopi]{ hdisplacei}...LNff2=AconnectstothehpGosidisplacedbyhdisplaceifromtherelativexcellloGcationspeci edbyhhopi.*~Thedisplace-mentzcanbGeanystringofvqalidvXY z-piccommands, buttheysmustbGeenclosedwithinagroup{...}d.& WhentheRcellloGcationisthetarget,Sanullgrouping{}mustbGeUUgiven.Whenusedwiththe<\omit>+nudge,fsuchexcur-sionsallowalabGelledArrowtobGeplacedanywherewithinLanHXY 'ExXgroup-eKing.*Alternatively!usinga~ -switch,asinExtr}'aOp-eKtions;2,ZallowssuchaspGeci cationforasingle2-celleKorUUcurvedpart.eKOb8jects~usedtoconstructcurvescanbGeoftwoeKtypGes.7Either/asinglehob8jectiissetonce,jwithcopieseKplaced|alongthecurve.Alternatively|adirectionaleKob8ject\canbGealignedwiththetangentalongtheeKcurve.XIn thiscaseuseaspGeci cationtakestheform:eK\curveobject{4$hspaceri~**hob8jecti}?.eKHerehspacerimaybGeanyhob8jectiofnon-zerosize.eKTypicallyUUitisemptyspace,e.g.+Rhdimeni{} . eKExercise30: GivecoGdetotypGesetthefollowingdi-eKagrams..\unRps: SDict begin xyc endjUUFUnY?㓟H?#˟x?)H?/=?5w?;x?Ax?Gg!?MU[H?SCx?Y1͟H?_ ?گ ˟ h#=8)wh/5x;g!8AU[GCM1͟hS 8Y?h^w :Xn9&qƍ_@gaMES0PKhNps: SDict begin xyc end卍Ground  >State-5H" {3687 10 /xy AB}xy1-@" {3636 10 /xy AB}xy6ߟ" {3585 10 /xy AB}xy;cݟ}p" {3534 10 /xy AB}xy@$" {3482 10 /xy AB}xyD" {3431 10 /xy AB}xyIy" {3380 10 /xy AB}xyN>R" {3328 10 /xy AB}xyRj" {3277 10 /xy AB}xyWe," {3226 10 /xy AB}xy\YS<<" {3175 10 /xy AB}xya" {3123 10 /xy AB}xyeO" {3072 10 /xy AB}xyje%E" {3021 10 /xy AB}xyo⳰" {2969 10 /xy AB}xysp" {2918 10 /xy AB}xyxeU" {2867 10 /xy AB}xy} (" {2816 10 /xy AB}xy" {2764 10 /xy AB}xyX%" {2713 10 /xy AB}xyp" {2662 10 /xy AB}xyi~|" {2610 10 /xy AB}xyA," {2559 10 /xy AB}xyg" {2508 10 /xy AB}xy&" {2457 10 /xy AB}xyܢˍ@con9tinuousTpAower)W " {-1639 10 /xy AB}xy&§ " {-1639 10 /xy AB}xy2c" {-1537 10 /xy AB}xy/ " {-1537 10 /xy AB}xy;?`" {-1434 10 /xy AB}xy9%p" {-1434 10 /xy AB}xyE;/P" {-1332 10 /xy AB}xyB^JH" {-1332 10 /xy AB}xyN" {-1229 10 /xy AB}xyKן48" {-1229 10 /xy AB}xyWcX@" {-1127 10 /xy AB}xyTß" {-1127 10 /xy AB}xya8O" {-1024 10 /xy AB}xy^8O" {-1024 10 /xy AB}xyj" {-921 10 /xy AB}xyg" {-921 10 /xy AB}xysg~`" {-819 10 /xy AB}xyq " {-819 10 /xy AB}xy}d#`" {-716 10 /xy AB}xyzE" {-716 10 /xy AB}xyΟ@" {-614 10 /xy AB}xya" {-614 10 /xy AB}xy;;-" {-511 10 /xy AB}xyS" {-511 10 /xy AB}xy%`" {-409 10 /xy AB}xyp" {-409 10 /xy AB}xy'CpulsedTemissionW< xNlsiC td͍c8N" {20.54083 ox}xy͍c8N" {18.44083 ox}xy卍Excited StateU捍eK24.5K2-cellsingeneral&aX1"Yv-pictures;eKTwo-cellscanalsobGesetdirectlywithinanyXY--eKpicture,without0thematrixfeature,usingeithereK\droporUU\connect-U=.N8eK\def\myPOS#1{\POS}\def\goVia#1{%E\afterPOS{\connect#1\myPOS}}eK\xyH*+{A}="A",+<1cm,1.5cm>*+{B}="B",H+<2.0cm,0pt>*+{C}="C",H+<1cm,-1.5cm>*+{D}="D",eK"A";\goVia{\uppertwocell^\alpha{}}"B"{}eK;\goVia{\twocell^\zeta_\xi{\gamma}}"C"{}eK;\goVia{\compositemap{}}"D"{},eK"A";\goVia{\lowertwocell{}}"D"{}eK\endxyLWeJ470*tj??]A腍hps: SDict begin xyc end I% qA'q^B`vu^C|x qD %I" {mark 28.45274 42.67912 -15.03572 40.54427 0.0 0.0 0.08237 0.91406 q}xyt $r6Ӛw" {3217 10 /xy AB}xyP>" {2400 F d}xy8L" {2400 F d}xyhHV" {2400 F d}xyO3d" {2400 F d}xy ޟ;" {2400 /XT tt}xy %R" {mark 85.35825 42.67912 56.90549 60.17912 28.45274 42.67912 0.12375 0.87823 q}xyE]v 5V" {2605 10 /xy AB}xy %R" {mark 85.35825 42.67912 56.90549 25.17912 28.45274 42.67912 0.12375 0.87823 q}xyFs]v ֲ" {3540 10 /xy AB}xyH" {1024 F d}xyF" {1024 F d}xyHr" {1024 F d}xyFr" {1024 F d}xyG" {1024 /XT tt}xyK+z ?Οް" {21.92403 -8.92139 l}xy?Οް" {2655 10 /xy AB}xyǍ휟V" {-0.32108 -24.52527 l}xy휟7" {1011 10 /xy AB}xys* G" {-352 F d}xyrtI" {-352 F d}xyq_" {-352 F d}xyoa" {-352 F d}xynptx" {-352 /XT tt}xy %?" {mark 113.81099 0.0 56.90549 -35.0 0.0 0.0 0.0593 0.9361 q}xyyҶ" {3620 10 /xy AB}xyH`" {1024 F d}xyF`" {1024 F d}xyH" {1024 F d}xyF" {1024 F d}xyG `" {1024 /XT tt}xy.RThecoGdeshownisacompactwaytoplaceachain of2-cellswithinapicture.Itillustratesastandardtechniqueforusing\afterPOS6to ndahpGositobeusedSforpartofapicture,thensubsequentlyreuseit.AlsoitispGossibletouse\drop }ݲorhdecoristospecifytheUU2-cells,givingthesamepicture.N8\xy?*+{A}="A",+<1cm,1.5cm>*+{B}="B",+<2cm,0pt>*+{C}="C",+<1cm,-1.5cm>*+{D}="D","A";"B",{\uppertwocell^\alpha{}},"B";"C",{\twocell^\zeta_\xi{\gamma}},"C";?\afterPOS{\drop\compositemap{}}"D"\POS?"A";\afterPOS{\drop\lowertwocell{}}"D"\endxyThe\connect/|vqariantisusuallypreferableasthismaintainsthesizeoftheob8jectatc,whilethe\dropvqariantIleavesarectangularob8jecthavingpandconoppGositeUUsides.&⍍25}MatrixfffeatureVers.3.4bCyKristo erH.Rosehkrisrose@brics.dkiLoadTas:p\xyoption{matrix}uTThisoptionimplements\XY -matrices",`i.e.,matriceswhere"itispGossibletorefertotheentryob8jectsbytheirrow/columnaddress.[W*e rstdescribGethegen-eralformofXY-matricesinx25.1,Wtheninx25.2wesummariseƢthenewhcoGordiinateformsusedtorefertoentries.,Inx25.3weexplainwhatparameterscanbGe~settochangethespacingandorientationofthematrix,'andyinx25.4weexplainhowtheappGearanceofUUtheentriescanbGechanged.떍25.1zX1"Y-matricesTheUUfundamentalcommandofthisfeatureis Bff2 PÍ5WQ\xymatrixUUhsetupi{Rhrowsi}aff2that$readsamatrixofentriesinthegenericTU>'ExXrow&columnDiformat,.i.e.,whererowsareseparatedwithPz\\andcontaincolumnsseparatedwith&(weeKdiscuss?inthefollowingsectionswhathsetupican eKbGe).EgThusFamatrixwithmaxr}'owZrowsandmaxc}'oleKcolumnswhereeachentrycontainsr}'ow,ScolWisenteredeKas/o:z\xymatrix{T1,1?&-V1,2?&SonX1,y|Rmaxc}'ols\\T2,1?&-V2,2?&nX2,y|Rmaxc}'ols\\ԍc.c.c.B.E.Iڪ.Tmaxr}'owb,1?&-Vmaxr}'owOd,2?&nXmaxr}'owsf,cmaxc}'ol}1:eK(TU>'ExXnicallyYthe& characterrepresentsany`alignmenteKtab',UUi.e.,characterwithcategorycoGde4). MeKA.hmatrixi.canappGeareitherinan.XY -picture(aseKhdecori)UUor\stand-alone".eKTheaspGectsinwhich\xymatrix6di ersfromor-eKdinary΍matrixconstructions,lsuchasPlainTU>'ExX'seK\matrix{ e3...} ?andUUL5ffA͉TU>'ExX'sarray ꛲environment,UUareeLeMarbitraryiXY -picihdecoriationsmaybGespeci edeMinTeachentryandwillbGeinterpretedinastateeMwhereUUcisthecurrententry*,6eLeMthe#entirematrixisanob8jectitselfwithrefer-eMenceUUpGointasthetopleftentry*,andeLeMa9progressmessage\X"*nisprintedforeachmatrixwithr}'owsPCeMc}'ols entriesmandiXY{m-piccomplexitysizeȲ(theeMnumbGerofprimitiveoperationsperformed),.un-eMlessethedeclaration\SilentMatricesisissued.eLeMEntries?startingwitha*arespGecial(describedeMinUUx25.4)^12x,souse{*}jtogeta*UV.eKF*orUUexample,N8eK\xyH\xymatrix{A&B\\C&D}H\drop\frm{-}H\drop\cir<8pt>{}eK\endxyeKwillUUtypGeset89ps: SDict begin xyc end@ qA** qB%C)f%DǍ/" {0.0 45.50868 -43.2643 -6.91075 6.40233 ov}xy" {8.0 0 360 o}xy7/eKBug:qDzMatrixUUnestingisnotsafe. MeKMatrices'ExXgroupUUbythedeclarationsff2 O\xymatrixrowsepphaddUUopi{Rhdimeni}\xymatrixcolsepphaddUUopi{Rhdimeni} ff2\TheUUdefaultspacingforbGothis2pcL.T oDo: ioptimizeproGcessingofmatriceswithcon-stantUUgrid.AnwentirematrixcanbGerotatedbyaddingaro-tationUUhsetupioftheform sff2Y:@^z͸hdirectioni ff2 Thiswillsettheorientationoftherowstohdirectioni(the defaultcorrespGondstor,vi.e.,rows areorientedleftUUtoright).ꂍ25.4%EntriesuTTheMappGearanceofasingleentrycanbemodi edbyenteringUUitas ‰ff2?@*UUhob8jectihpGosihdecori ff2\ThisFmakestheparticularentryignoretheentrymoGd-i erseandtypGesetasakernelob8jectwiththesamereferencepGointasthe(centerof)thedefaultob8jectwouldUUhavehad.Additionalob8jecthmoGdi erismaybeaddedtoanotherwiseUUordinaryentrybyusingtheforms ‰ff2?%|**[?hshapGei]Rhentryigw **{0JhmoGdi eri*}RhentryieKmff2The rstsetsthedefaulthshapGeiforob8jects (cf.`note4j),#thesecondadefaultsize(change,cf.note4g),]andthelastmakesitpGossibletoaddanyvhob8jectimoGdi erofx4,0>e.g.,forvrecenteringen-triesdafterthedefaultentryformwhichisequivqalenttoo`!Ci+<c2obje}'ctjZmar}'gin;w8>@5'(withthee ectofcen-teringbtheob8jectandaddtheobje}'ctmarginc)btoallsides.޶ExerciseT31: TypGesetUUthefollowingdiagram:Eps: SDict begin xyc endǵA8B!" {0.0 0.0 l}xy("Ǵ=A7" {3072 10 /xy AB}xy7" {22.12329 0.0 l}xy7" {0.0 0.0 l}xyǍğT" {0.0 0.0 l}xy ~ԟa=Bğ7" {1024 10 /xy AB}xyǍğV" {0.0 -22.75003 l}xyǍğV" {0.0 0.0 l}xy: qBǍ>ğj" {0.0 0.0 l}xyAğaA>ğs" {1024 10 /xy AB}xyǍ>ğ*" {0.0 -22.75003 l}xyǍ>ğ*" {0.0 0.0 l}xy9ğ% qA!ş!" {0.0 0.0 l}xy&)jPBW=8$p!" {3072 10 /xy AB}xy8$p!" {22.41667 0.0 l}xy8$p!" {0.0 0.0 l}xy;$p$ǵBQ8A7It*LisalsopGossibletousethese@jIhsetupis(asusualbGetweenUU\xymatrix5ꏲandUUtheleading{R): /|ff2 AύK@*[?hshapGei]K@*Y=haddUUopihsizeiff2:ݍwhichareequivqalenttochangingallentriestobGehaveasԵiftheyhadstartedwiththesimilar**T-form.T oDo:qDzAllowUU** OhaddUUopihsizeihentryiforentries.IfLthedefaultsetofentrymoGdi ersshouldbechangedJthenthefollowingdeclarationmustbGeissuedbGeforethe\xymatrix5fcommand;)&thisistheonlywaytoqactuallyswitchtheinitialdefaultcenteringandspacingUUo : Cff2 Aύ(\entrymodifiers={ OhmoGdi eri*UV}ff2 I޶Exercisewr32: HowNdidtheauthortypGesetthefol-lowingUUmatrix?1O!ps: SDict begin xyc endn" {6.0 6.0 6.0 6.0 ox}xy@ qAǍZE" {20.48529 20.48529 l}xy9" {45.94116 0.0 l}xyZ\!" {20.48529 -20.48529 l}xyv"x" {6.0 6.0 6.0 6.0 ox}xy\Bg "x" {6.0 6.0 6.0 6.0 ox}xy Cn?" {6.0 6.0 6.0 6.0 ox}xy; qD*UBug: Thefvfourconstructions@*[&m...]꧲,**[j...],@*IhaddOopihsizei,ONand,**{E...}꧲,ONac}'cumulateKinre-verseor}'der.-Only"entriesstartingwithasingle*completelyoverridethemoGdi ershsetupiwitha@*ɲ-construction.Finally*, thefollowingisspGeciallysuitedfor`one-line'UUmatricesincludedintext: |ff2 Aύm@1ff2LWeJ503]:*tj??O]w\will0}inserta`mathstrut'(\vphantom(4)intoeachen- tryUUtomakeitscenteringappropriatefortext. %Thiswdisjustanabbreviationusingthefollowingdeclaration),whichwillsetuphdecorithatshouldbGeinserted>bGeforeeverythingelseineachentry*.<InitiallyitUUisemptybut ff2 V;E\everyentry={ OhdecoriUU}%ff2䍲willinserthdecori rstineachentry;S~insidethecounter.andn!\entrymodifiersWwilln!not`resultinYrecompilationevenwhentheconstructedmatrixchanges {youmayhavetoremovethe.xyc leman-ually*.LjExercisewr33: HowNdidtheauthortypGesetthefol-lowingUUdiagram?1>Rps: SDict begin xyc endǍ8^ " {0.0 21.0 -9.0 -21.0 9.0 ov}xy6:r}'ootT" {0.0 -0.04689 l}xy#^g" {2816 10 /xy AB}xy#^g" {18.63063 -4.68634 l}xy#^g" {0.0 -0.04688 l}xyǍ8^ " {0.0 21.0 -9.0 -21.0 9.0 ov}xy5ގڪ^^" {10.0 0 90 o}xy8^" {0.0 0.00098 l}xy^^" {38.0 0.00098 l}xy^^)" {10.0 -90 0 o}xyǍh^," {-0.00195 -16.00098 l}xyM^3" {-1024 10 /xy AB}xyM^3" {-16.99805 0.0 l}xyM^3" {0.0 0.0 l}xy!Ǎ8^ " {0.0 21.0 -9.0 -21.0 9.0 ov}xy5ގ#ڪR^+G" {10.0 0 90 o}xy8^!G" {0.0 -0.00195 l}xyR^!G" {26.0 -0.00195 l}xyR^ϟA" {10.0 -90 0 o}xyǍ\^ϟD" {0.00098 -21.99805 l}xy^AG" {10.0 -180 -90 o}xy^KG" {-52.00098 0.00195 l}xy^O" {10.0 90 180 o}xyǍ^O " {-0.00098 57.99805 l}xy#^" {3072 10 /xy AB}xy#^" {5.00098 0.0 l}xy#^" {0.0 0.0 l}xy3Ǎ8^ " {0.0 21.0 -9.0 -21.0 9.0 ov}xy5ގ6ڪ1]rHints!:ThearrowfeaturewasusedtomakethebGend-ing#arrowsandtheframeextensionfortheframesaroundUUeachcell.(&26 fdGraphfffeature-Vers.3.7bCyKristo erH.Rosehkrisrose@brics.dkiLoadTas:p\xyoption{graph}Thisoptionimplements`XY -graph',aspGecialc}'ombi-natoricy;dr}'awinglanguagesuitableNfordiagramslike ow'`charts,directedgraphs,andvqariousformsoftrees.The^baseofthelanguageisreminiscentofthew\eKPIC[5]languagebGecauseitusesanotionofthe`cur- eKrent= loGcation'andisbasedon`moves'.YButthecentraleKconstructionisa`map'combinatorthatisbGorrowedeKfromUUfunctionalprogramming. `eGXYK-graphxmakesuseoffacilitiesofthe`arrow'fea-eKtureUUoptionofx23,whichisthereforerequired.eKFigureR?17summarisesthesyntaxofahgraphiwitheKnotespbGelow.+AJhgraphicanappeareitherinanlXY hp-eKpicture(ashdecori)or\stand-alone".^13Note:IfeKyoususe\xygraph{?...} ^Einsidesconstructionswhere&eKissigni cant(likeplainTU>'ExX's\halignorL5ffA͉TU>'EX'seKarrayk%environment)thenmakesuretoaddanextraeKlevelUUofbracesaroundit.eKNotesw㍍eK26a.,kAUUmoveistoestablishanewcurr}'entnode[.eK26b.T*oHdr}'awղsomethingissimplytodrawalineoreKthedspGeci edharrowifromthecurrentnoGdetotheeKspGeci edtargetnode.8ThetargetthenbecomeseKthe'}currentnoGde.?AllthefeaturesofarrowsaseKdescribGedinx23canbeused,-inparticularar-eKrows,canbGelabelledandsegmented,AbutwitheKtheuchangethathpath-pGosimeanshnodeiasex-eKplainedUUinnotex23e.eK26c.1T*o.map]overalistyissimplytosavethecur-eKrentnoGdeandtheninterpretthehlistiwiththeeKfollowingUUconvention:eJ eKStarteachelementofthelistwiththecur- eKrent9noGdeassavedandpasthepreviouslist eKelement,UUandeJ eKlet*Athe? hnoGdeirefertothesaved*Acurrent eKnoGdeUUexplicitly*.eK26d.The;%&Gand;%\\DspGecial;%movesareincludedtoeKmakeitsimpletoenter`matrix-like'thingsaseKgraphs{notethattheywillnotbGeautomati-eKcallyrGaligned,however,forrGthatyoushoulduseeKtheUU!M*escapGe.eK&@ɲisthesameas[r]and\\isthesameaseK[r]!{y+(0,-1)-(0,0)}`which*usesakerneles-eKcapGe}tomoves}tothe rstcolumninthenextroweK(wherethe rstcolumnisonthey[ٲ-axisoftheeKcurrentUUcoGordinatesystem).eKNote:JʲIf[youusetheform*{ U...} for[noGdestheneKyoudon'thavetochangethemifyoudecidetoeKuseUUanUQXY U-matrix.eK26e.1TypGesetThitiandmakeitthecurrentnoGde.BAlsoeKsavesҘhitiforlaterreferenceusing" hidi"?:lMifhitieKisasimpleletter,ordigit,thenjustas"hiti"?;ifeKhiti5tisoftheform{ uqtext} hIor*...{text} hIthen5taseK"Htext"2ղ.ffff[ J=w-:13LInXfactL#A TAEMXuserscanuseagraphenÎvironment.LWeJ514t̠*tj??gC ffffd TWSyntaxのActionX-ffd W\xygraph{hgraphi}のtypGesetUUhgraphifffd fdWhgraphi@F!_hstepi*のinterpretUUhstepisinsequenceiWhstepi@F!_hnoGdeiのmove^26aOtoUUthehnoGdeizG=Ej_-dFharrowiUUhnoGdeihlabelsiのdraw^26b8ݲlineUUtohnoGdei,withhlabelsiG=Ej_:dFharrowiUUhnoGdeihlabelsiのdraw^26b8ݸharrowiUUtohnoGdei,withhlabelsiiG=Ej_(ghlistiUU)のmap^26c1currentUUnoGdeoverhlistiWhnoGdei@F!_[ghmoveiUU]のnewUUnoGdehmoveidUUrelativetocurrentG=Ej_&j9jtc\\のnewUUnoGdeinnextcolumn/row^26dG=Ej_"dFhidi"のpreviouslyUUsaved^26e2noGdeG=Ej_?のcurrentlyUUmappGed^26c1nodeG=Ej_hnoGdeiUUhitiのhnoGdeiUUwithhititypesetandsaved^26e2thereG=Ej_hnoGdeiUU= "*hidi"のhnoGdeiUUsaved^26e2as"Rhidi" G=Ej_hnoGdeiUU! ꧸hescapeiのaugmentUUnoGdewithmaterialinanothermodezWhmovei@F!_hhopi*のhhopis^26f޲(dulr)UUfromcurrentnoGdeG=Ej_hhopi*UVhplaceiUUhmoveiのdoUUhhopis^26f޲butuseitshplaceiandhmoveiUUagainiWhlisti@F!_hgraphiUU, ꧸hlistijqhgraphiのlistUUofsubgraphs^26cWhescapGei@F!_{ghpGosiUUhdecori}のpGerformUUhposihdecori^26gzG=Ej_MghmatrixiのinsertUUhmatrixi^26h@4G=Ej_PghpGolygoniのinsertUUhpGolygoni^26iG=Ej_EghellipseiのinsertUUhellipsei^26iG=Ej_~ghsetupiのsetupUUparameters^26jffd FigureUU17:qǸhgraphis*DgWithlthe= SadditionitispGossibletosavelexplic- itlyincaseseveralnoGdeshavethesametextora EnoGdehasatextthatitisimpracticaltouseforreference. Inlfactusingtheformhiti=" hidi"iwillonly:_saveWthenoGdeas"߸hidi"andWnotJas"߸hiti"?!LAsaspGecialconvenience""^(thustheemptyhidi)al-wayskreferstothelastcompletednoGde,gsoadding=""afteranoGdemerelymeansitshouldnotŲbesavedUUunderitspropGername. &Exercise*34: HowdidtheauthortypGesetthis?H4ps: SDict begin xyc end qA' qA2" {mark 36.0 0.0 18.0 12.0 0.0 0.0 1.0 0.1875 q}xy$" {2645 10 /xy AB}xy5" {mark 36.0 0.0 18.0 12.0 0.0 0.0 0.1875 0.8125 q}xy3" {mark 36.0 0.0 18.0 12.0 0.0 0.0 1.0 0.81256 q}xyK qA3" {mark 72.0 0.0 54.0 12.0 36.0 0.0 1.0 0.1875 q}xyH" {2645 10 /xy AB}xy6" {mark 72.0 0.0 54.0 12.0 36.0 0.0 0.1875 0.8125 q}xy4" {mark 72.0 0.0 54.0 12.0 36.0 0.0 1.0 0.81256 q}xy4" {mark 0.0 0.0 36.0 -12.0 72.0 0.0 1.0 0.09375 q}xy " {-1301 10 /xy AB}xy8" {mark 0.0 0.0 36.0 -12.0 72.0 0.0 0.09375 0.90625 q}xy4" {mark 0.0 0.0 36.0 -12.0 72.0 0.0 1.0 0.90625 q}xyؐ26f.arMovingdAbyaseriesofhops6bissimplymov- inginagridasthesequenceofdulr"(fordown/up/left/right)indicates. mLThegridisastandardcartesiancoGordinatesystemwith3pcunitEunlessthecurrentbaseisrede nedusing[]!{ ...} CwithÜanappropriatehpGosiitioncontain-ingUU: ꧲andUU::*asUUdescribGedinnote3d.geKT o-Do:DescribGeKtheuseofhmoveisKwithhplaceis eKin4detail...Uin4particular(1)`untilpGerpendiculareKto<...'iand(2)`untilinterceptswith...'icanbGeeKcoGded...eK26g.,kThis{`escapGes'intothewXY,{-pickernellanguageeKandinterpretsthehpGosihdecori. ThecurrenteKnoGdeisthensettotheresultingcob8jectandtheeKgridUUfromtheresultingb}'ase[. eKThee ectofthehpGosihdecoricanbecompletelyeKhiddenwhfromwdXY h-graphbyenteringitas{\saveeKhpGosiUUhdecori\restore}2:.eK26h.ItΣispGossibletoinsertahmatrixiinagrapheKprovidedơthe`matrix'optiondescribGedinx25haseKbGeenloaded:itoverwritesthenodewiththere-eKsult[&of\xymatrix1 hmatrixi.cAfterwardsthegrapheKgrid}issetasthetopleft`square'ofthematrix,eKi.e.,with[d]Sand[r]adjustedastheyworkineKtheUUtopleftentry*. eKBug:Y|[dr]"immediatelyI/afterthematrixwilleKwork5asexpGected,<$e.g.,make5thecenterof"2,2"eKthercurrentnoGde,*butothersmightnot,*e.g.,[rr]LWeJ525m*tj??gwwillnotnecessarilyplacethecurrentnoGdeontop ofUU"1,3"F.:26i.UItDispGossibletoinsertahpolygonioranhellipseiinagraphprovidedthepoly+optiondescribGedinx27orthearcoptiondescribGedinx29hasbGeen_ loaded,respectively:^itwillhavecasthecurrentjnoGde,opasthepreviousone,andthethecurrentMbasehasthehhopis[r][and[u]asbasevectors.ZNote:)lattices,knots,etc.,canzalsobGeusedbutnoQ]spGecialsyntaxisusefulsincethe!{ W...} <syntaxisUUadequate.26j.arThis allowssettingofsomeparametersofthegraph:q!~hsetupiUUshouldbGeoneofthefollowing:y*ff2 !~:{bharrowiUU}[(includeywithevery: arrow!~-{bharrowiUU}[(includeUUwithevery- ꧲line!~*{bhmoGdi ersiUU}[(includewitheverynon-*[(noGdefd!~ hletteri{RhgraphiUU}[(de neUnewgraphescapGe[(!`hhletteriff2 TheseNAaredestructive:n=thepreviousvqalueislost;thewhdefaultisestablishedbythesequence!~:{}!~-{@{-}})p!~*{+}N0вmakingr:$creatersimplear-rows,;- plain4lines,;andformattingdefaultnoGdesinUUmathmoGdewiththedefaultob8jectmargin.ZTheαlastpGossibilityisalsoavqailableasacom-mand*ff2 \newgraphescape{?hletteri}{ hgraphi}\ff2 that3makesthespGeci edescapegeneratethehgraphir#asamacro;withititispGossibletopassargumentssWtothehgraphiusingthestandardTU>'ExX\def bmethoGd:qTheUUdeclarationcodeN8\newgraphescape{i}#1#2{[]!{+0="o#2"*=<10pt>{};p!#1**{},"o#2" -/4pt/*!E\cir<2pt>{} +0;p-/:a(-30)24pt/**\dir{-}="X2" ;p-/:a(-60)24pt/="X1"**\dir{-} ;?(.5),="i#2", p-/:a(-60)24pt/**\dir{-}, "o#2"."i#2"."X1"."X2"}}kis(rathercomplicatedkernelcoGde)thatmakestheonoGdeescape!i͵dntypesetan`inverter'oori-ented ewiththedcornerastheoutputwithinputnamed"il n" , andoutputnamed"on" , suchthattheUUgraph\xygraph{?[]!iR1("i1"[l]x-"i1")-[r]z}kwillUUtypGeset)Ops: SDict begin xyc end@Ǝ" {2.0 0 360 o}xy)ێއ" {-20.91797 11.7627 l}xyǍ)ێ <" {0.0 -24.0 l}xy>ΟG" {20.91504 11.7627 l}xyx އ" {0.0 0.0 l}xy)ێއ" {30.14236 0.0 l}xy)ێއ" {0.0 0.0 l}xyd:zBƎ" {0.0 0.0 l}xya:" {30.45485 0.0 l}xya:" {0.0 0.0 l}xylTheUU nalexerciseillustratesmuchUUoftheabGove.gweKExerciseT35: TypGesetˍ+.ps: SDict begin xyc end1v?w@x18Wx" {0.01625 -0.01009 l}xy=}" {2048 10 /cm AB}xy= " {5.17448 -5.1714 l}xyA \}" {4.42525 -4.42143 l}xyA \}" {0.01625 -0.00862 l}xy%?zǍ2'" {0.0 0.0 l}xy'P }" {0 10 /cm AB}xyǍ'P %" {-10.70717 -10.70717 l}xyǍП@" {-10.70744 -10.70744 l}xyǍП@" {0.0 0.0 l}xy26@y" {0.02708 -0.02092 l}xy'Pٟ'6H" {2048 10 /cm AB}xy'TQ'9" {10.7238 -10.72072 l}xy11q" {10.24297 -10.24652 l}xy11q" {0.01997 -0.02708 l}xy@%x2Ǎ8Ό3<" {0.0 0.0 l}xy=}," {4096 10 /cm AB}xyǍ=}/" {4.68524 4.68524 l}xyǍAş*" {4.41328 4.41328 l}xyǍAş*" {0.0 0.0 l}xyǍE"" {0.0 0.0 l}xyEZ#" {-3072 10 /cm AB}xyǍE\" {0.0 7.1853 l}xyǍE" {0.0 7.18529 l}xyǍE" {0.0 0.0 l}xy? " {0.0 -0.00002 l}xy/˟" {-768 10 /cm AB}xy/˟" {-16.07542 -4.01888 l}xyCw@" {-18.63101 -4.65776 l}xyCw@" {0.0 -0.00002 l}xy5-h" {mark -27.72015 -27.72015 -53.17603 -53.17603 -53.17603 -2.26428 -27.72015 -27.72015 1.0 0.04785 bz}xy]-Z#" {-3072 10 /cm AB}xy5-h" {mark -27.72015 -27.72015 -53.17603 -53.17603 -53.17603 -2.26428 -27.72015 -27.72015 0.04785 0.5 bz}xy5-h" {mark -27.72015 -27.72015 -53.17603 -53.17603 -53.17603 -2.26428 -27.72015 -27.72015 0.5 0.95215 bz}xy5-h" {mark -27.72015 -27.72015 -53.17603 -53.17603 -53.17603 -2.26428 -27.72015 -27.72015 1.0 0.95209 bz}xyCG;" {0.0 -0.04333 l}xy/ʟh" {2816 10 /cm AB}xy/," {18.63637 -4.68288 l}xy?"" {16.08089 -4.04648 l}xy?"" {0.0 -0.04332 l}xyGJ3eK27˯Polygonfffeature0eKVers.3.7bCyRossMoKorehross@mpAce.mq.edu.aui eKLoadTas:p\xyoption{poly}XeKThisxfeatureprovidesameansforspGecifyingtheloca-eKtionsPXofverticesforregularpGolygons,QWwithanynum-eKbGer (F3)ofsides.PolygonscanbeeasilydrawneKand/orthevertexpGositionsusedtoconstuctcom-eKplexn graphicswithinannXY -picture.$Manynon-regulareKpGolygonscanbespeci edbysettinganon-squareba-eKsis.KeKAUUpGolygonismosteasilyspeci edusing...eKff2 *I\xypolygon9hnumbGeri{}{UwithUUhnumbGerisides;\xypolygon9hnumbGeri{?htoki}VhtokiUUatvertices;\xypolygon9hnumbGeri{?hob8jecti}UWwithUUageneralhob8jectiateachvertex;Kff2ˍHereXhnumbGeriisasequenceofdigits,givingthenum-bGerYofsides.Ifusedwithinan\xy...\endxy%envi-ronmentthenthepGolygonwillbecentredonc,/7thecurrenthpGosi.Howeveran\xypolygon<canbGeusedoutsider`suchanenvironment,yas\stand-alone"pGoly-gon;6thewholepicturemustbGespeci edwithinthe\xypolygon77command. 卑In\xypolygon=establishespGositionsforthever-ticesEofapGolygon.ٗAtthesametimevqariousthingsmaybGetypGeset,accordingtothespeci edhswitchesi.Anhob8jectimaybGedroppedateachvertex,\spGokes"drawn4ZtothecentreandsuccessiveverticesmaybGeqgconnectedasthepolygon's\sides".LabelsandbreaksUUcanbGespeci edalongthespokesandsides. :sEachvertexisautomaticallynamed:8"1","2"ʲ,...,k" %hhnumbGeri" ;˲with"0"ascentre.e2Whenahpre xi+hasbGeengiven,names" (hpre xi0" ,...,"hpre xihnumbGeri"are usedinstead.3YWhilethepoly-gonisbGeingconstructedthemacro\xypolynum80f0" {5.0 0 360 o}xy~0" {5.0 0 360 o}xyy0" {14.0 0.0 l}xyr0" {5.0 0 360 o}xyǍo" {7.09766 12.06885 l}xyǍtX" {-7.09888 12.06885 l}xyZ0" {5.0 0 360 o}xyǍ\X" {-7.09888 12.06885 l}xy_0" {-14.0 0.0 l}xyN0" {5.0 0 360 o}xyS0" {-14.0 0.0 l}xyǍPX" {-7.09888 -12.07007 l}xyZ0j" {5.0 0 360 o}xyǍ\Xmh" {-7.09888 -12.07007 l}xyǍWmh" {7.09766 -12.07007 l}xyr0j" {5.0 0 360 o}xyǍomh" {7.09766 -12.07007 l}xym0j" {14.0 0.0 l}xyǍ{[" {7.09766 12.06885 l}xy||p>91p|puY2X|puY3L|p>94X|p5p|p6|p>90Y1۱2Ǎ⯟W" {-3.66629 6.14029 l}xy|p>93G{" {-6.64185 2.32056 l}xy ۱4(EH" {-6.63339 -2.31851 l}xyПY5Ǎҿf" {-3.66629 -6.14142 l}xy >96ǍTv" {1.14905 -7.09518 l}xyG˹7i՟->" {5.4451 -4.53683 l}xy؟˹8Ÿ/G" {7.00592 0.0 l}xyEP >99h " {5.4451 4.53568 l}xyǍԞ^" {1.14905 7.09406 l}xy$@4QExerciseT36: GiveUUcoGdetotypGesetthese.OneSaimpGortantuseofhpre xiistoallowthever-tices'"ofmorethanonepGolygontobeaccessedsub-sequently[withinthesamepicture.Herearesomeexamplesofthis,incorpGoratingthe~:{v...} OswitchtopGerformsimplerescalings.}FirstlytheedgesofadoGdecahedronUUasaplanargraph:gwF9ps: SDict begin xyc end@2$" {17.1189 -12.43762 l}xyQP1" {17.1189 12.43762 l}xyǍJƦp" {-6.53879 20.12476 l}xy5" {-21.16022 0.0 l}xyǍ/" {-6.53879 -20.12476 l}xy@2$!" {-64.19586 46.64108 l}xy" {-64.19586 -46.64108 l}xyǍ=6" {24.52046 -75.46783 l}xyg 4=" {79.3508 0.0 l}xyǍdH$" {24.52046 75.46783 l}xy " {-14.97903 -4.86708 l}xyǍ *" {0.88666 -32.52951 l}xy@2$a" {31.21127 9.20897 l}xy@2$a" {0.0 0.0 l}xyǍ@2$!" {0.0 -15.75 l}xy_h:(F" {31.21127 -9.20897 l}xyǍ`K6 m" {0.88666 32.52951 l}xyǍ`K6 m" {0.0 0.0 l}xy`K6" {14.97903 -4.86708 l}xyǍrQL" {18.40276 26.83846 l}xyTS" {-30.663 10.89546 l}xyTS" {0.0 0.0 l}xyǍT" {9.25758 12.74208 l}xyǍ@2$j" {-19.83769 25.79549 l}xyǍ,[" {-19.83769 -25.79549 l}xyǍ,[" {0.0 0.0 l}xyǍ,[" {-9.25758 12.74208 l}xy 9" {-30.663 -10.89546 l}xyǍ  m" {18.40276 -26.83846 l}xyǍ  m" {0.0 0.0 l}xydH" {13.69518 4.44992 l}xyǍ@2$" {0.0 14.40005 l}xy" {-13.69518 4.44992 l}xyǍ=6" {-8.46413 -11.64995 l}xyǍg 6" {8.46413 -11.64995 l}xyF3'eK\xy?/l1.5pc/:,{\xypolygon5"A"{}}, eK{\xypolygon5"B"{~:{(1.875,0):}~>{}}},eK{\xypolygon5"C"{~:{(-2.95,0):}~>{}}},eK{\xypolygon5"D"{~:{(-3.75,0):}}},eK{"A1"\PATH~={**@{-}}'"B1"'"C4"'"B2"},eK{"A2"\PATH~={**@{-}}'"B2"'"C5"'"B3"},eK{"A3"\PATH~={**@{-}}'"B3"'"C1"'"B4"},eK{"A4"\PATH~={**@{-}}'"B4"'"C2"'"B5"},eK{"A5"\PATH~={**@{-}}'"B5"'"C3"'"B1"},eK"C1";"D1"**@{-},"C2";"D2"**@{-},eK"C3";"D3"**@{-},"C4";"D4"**@{-},eK"C5";"D5"**@{-}?\endxyN8eKNextahexagonalpyramid,MarectangularbGoxandeKan9moGctahedralcrystalspeci edasatriangularanti-eKprism. Notice*Whowthe~:{N...} switch*WisusedtoeKcreateWnon-squarebases,allowingtheillusionof3D-eKpGerspectiveUUintheresultingdiagrams:1w-ps: SDict begin xyc endǍȟ" {-19.20007 38.40015 l}xyǍȟ" {-7.88599 30.3411 l}xy$" {-11.31409 8.05905 l}xyǍȟ" {16.11401 27.94095 l}xy " {-24.0 2.40015 l}xyǍȟ" {28.79993 33.59985 l}xy;W" {-12.68591 -5.6589 l}xyǍȟ" {17.48584 41.6589 l}xy PhJu" {11.31409 -8.05905 l}xyǍȟ" {-6.51416 44.05905 l}xy#Ph" {24.0 -2.40015 l}xy07" {12.68591 5.6589 l}xy9ps: SDict begin xyc end" {-33.94116 0.0 l}xyǍ " {0.0 -23.7587 l}xy! " {33.94116 0.0 l}xyǍ!" {0.0 23.7587 l}xy1 " {-27.15302 0.0 l}xyǍ1@" {0.0 -20.36475 l}xy/X֟j" {27.15302 0.0 l}xyǍ/X֟j" {0.0 20.36475 l}xyǍ/X֟j" {13.40585 24.70317 dt}xyǍ1j" {20.194 24.70317 dt}xyǍ1@" {20.194 28.09712 dt}xyǍ/X֟@" {13.40585 28.09712 dt}xys!ps: SDict begin xyc endǍfd" {-20.78467 -25.19989 l}xy)+" {41.56934 0.0 l}xyǍ38" {-20.78467 25.19989 l}xyǍ5ğp" {13.07726 24.48026 l}xyc8\" {-35.33417 0.0 l}xyǍ(" {22.25691 -24.48026 l}xy5ğ\" {32.93707 17.7603 dt}xyǍ)fd" {-12.1524 -42.96019 dt}xyǍ(" {-0.92485 18.47993 dt}xy+" {-40.64449 -18.47993 dt}xyǍc8p" {18.38757 42.96019 dt}xyǍ38" {2.3971 -17.7603 dt}xyǍ38" {0.0 0.0 dt}xyFeK\xy/r2pc/:?="A",+(.2,1.5)="B","A",eK{\xypolygon6{~:{(1,-.1):(0,.33)::}H~<>{;"B"**@{-}}}}\endxyeK\quad?\xy/r2pc/:eK{\xypolygon4"A"{~:{(0,.7)::}}},+(.7,1.1),eK{\xypolygon4"B"{~:{(.8,0):(0,.75)::}}},eK"A1";"B1"**@{.},"A2";"B2"**@{.},eK"A3";"B3"**@{.},"A4";"B4"**@{.}eK\endxy\quad?\xy/r2pc/:eK{\xypolygon3"A"{~:{(0,.7)::}}},+(.7,1.1),eK{\xypolygon3"B"{~:{(-.85,0):(-.15,.8)::}}}eK,"A1"\PATH~={**@{.}}'"B2"'"A3"'"B1"eK'"A2"'"B3"'"A1"?\endxy7 eKV ertexobject: Unless"{the rstcharacteris~bx,,sig-eKnifying.*a\switch",5thenthewholeofthebracedma-eKterial~istakenasspGecifyingthehob8jectiforeachver-eKtex. [ItwillbGetypesetwithacircularedgeusingeK\drop[o]...%*,exceptpwhenthereisjustasingletokeneKhtoki.$InthiscaseitisdroppGedas\drop=0{-htoki}?,LWeJ547ߠ*tj??gwhavingzerosize.SAnob8jectcanalsobGedroppedat eachvertexusingtheswitch~*{...}꧲,inwhichcaseitfwillbGecircular,k=withthecurrentobje}'ctmargin+?ap-plied.Thegnextexampleillustratesthreedi erentwaysofUUspGecifyinga\circ ꛲atthevertices.'% :ps: SDict begin xyc end+P{% 3Ǎ(' " {-6.21167 10.75891 l}xy؟d؟s" {-10.75891 6.21167 l}xyxxxs" {-12.42334 0.0 l}xy0360O" {-10.75891 -6.21167 l}xy{Ǎ" {-6.21167 -10.75891 l}xyǍ60" {0.0 -12.42334 l}xy0#Ǎ60x" {6.21167 -10.75891 l}xyxx Sxo" {10.75891 -6.21167 l}xy؟ Sd؟o" {12.42334 0.0 l}xy% #(' ?" {10.75891 6.21167 l}xy+PǍ.]P60" {6.21167 10.75891 l}xyǍ.]P" {0.0 12.42334 l}xyhګh" {21.50002 0.0 l}xydHSdAb" {17.47108 12.70857 l}xyXHkǍYQ " {6.74707 20.68346 l}xyIDkǍLoWQ " {-6.74733 20.68346 l}xy=DSAb" {-17.47137 12.70857 l}xy8ګ=" {-21.50002 0.0 l}xy=D A W@" {-17.47137 -12.70888 l}xyIDǍLoW " {-6.74733 -20.68373 l}xyXHǍY " {6.74707 -20.68373 l}xydH dA W@" {17.47108 -12.70888 l}xyk" {17.11246 7.12903 l}xyɟm" {17.11246 7.12903 l}xycApu " {7.20389 17.29674 l}xyP " {7.20389 17.29674 l}xy(&?" {-5.40839 5.40839 l}xyhc  " {-7.20453 17.29674 l}xyAx{ " {-7.20453 17.29674 l}xyu" {-7.36374 0.0 l}xyv`k}[m" {-17.11313 7.12903 l}xy~r " {-17.11313 7.12903 l}xyǍ|̞" {-5.40839 -5.40839 l}xyv` ~r"" {-17.11313 -7.1297 l}xy}c" {-17.11313 -7.1297 l}xyǍy`]" {0.0 -7.92471 l}xyhsL!" {-7.20453 -17.29738 l}xyAx %L!" {-7.20453 -17.29738 l}xy5*" {5.40839 -5.40839 l}xyApPL!" {7.20389 -17.29738 l}xyuL!" {7.20389 -17.29738 l}xy7" {7.36374 0.0 l}xy " {17.11246 -7.1297 l}xy#*" {17.11246 -7.1297 l}xyǍ ~" {5.40839 5.40839 l}xyǍZ " {0.0 7.92471 l}xy.U\xy/r2pc/:?{\xypolygon12{\circ}},+/r5pc/,{\xypolygon10{~<{-}~>{}{\circ}}},+/r5pc/,{\xypolygon8{~*{\circ}~<=}}\endxy"⍑Switc9hesThefallowableswitchesaregiveninthefollowingta-ble: u'ff2 6$6~:{)O-...}Y]dusefulUUforrescaling.6~*{)O-hob8jecti}Y]dhob8jectiUUateachvertex.6~={)O-hanglei}Y]dalignUU rstvertex.6~<{)O-...}Y]ddirectionalUUfor\spGokes";6~<<{.*harrowi}Y]duseUUharrowiforspGokes;6~<>{.*...}Y]dlabGels.&breaksonspokes.6~>{)O-...}Y]ddirectionalUUfor\sides";6~><{.*harrowi}Y]duseUUharrowiforsides;6~>>{.*...}Y]dlabGelsUU&breaksonsides.‰ff2@Using~<<{@harrowi} or~><{harrowi} ismostap-propriateVwhenarrowheadsarerequiredonthesidesorspGokes,orwhenlabels/breaksarerequired.Hereharrowi,isasin gure14,4RsoitcanbGeusedsimplytospGecifyDthestyleofdirectionaltobeused.Thus~<<{}setseachspGokeasadefaultarrow,WpGointingoutwardsfrom,]thecentre;~<<{@{-}}:#suppressesthearrow-head,,while"~><{@{}}0,uses"anemptyarrowalongthesides.wLabGelsWWandbreaksarespeci edwith~<>{WK...}anda~>>{U...}꧲,+whereathe{2^...} useathenotationforahlabGeli,UUasin gure13.WhenTnotipsorbreaksarerequiredthentheswitches9~<{...} $1and9~>{...} $1are9somewhatfaster,sincelessproGcessingisneeded..LabelscanstillbespGeci edAGwith~<>{A;...} +andAG~>>{...}꧲,|CbutAGnowus-ingthekernel'shplaceinotationof gure1.xInfactanykernelcoGdecanbeincludedusingtheseswitches.With ~<> the currentpandcarethecentreandvertexirespGectively*,whilefor~>>5theyarethecur-rent,vertexandthepreviousvertex.H(Theconnectionfrom^vertex" [hnumbGeri"to^vertex"1"Bisdonelast.)The#8pyramidabGoveisanexampleofhowthiscanbGeused.5sBoth~<{V...} 5and~<<{harrowi}֋canbGespeci- edDtogether,HbutonlythelastwillactuallybGeused;similarlyUUfor~>{L...} ?andUU~><{UIharrowi}?.gw9Սps: SDict begin xyc end|Q" {-61.40643 -10.82813 l}xyǍ*- #s" {40.08032 -47.76581 l}xyǍ?" {21.32611 58.59393 l}xy Ƞ " {-50.71838 4.43628 dd}xyǍX$" {-4.43628 -50.71838 dd}xy;؟5" {50.71838 -4.43628 dd}xyǍ?" {4.43628 50.71838 dd}xyp@" {-41.06415 10.23706 l}xyǍ H" {-22.40167 -36.21039 l}xyǍ7 "X" {27.17908 -32.09875 l}xyBt@" {39.23877 15.85327 l}xyǍ?" {-2.95203 42.21881 l}xyl-" {-33.82855 12.31183 dd}xy|Q" {-27.57788 -23.13995 dd}xyǍX$" {6.25177 -35.45398 dd}xy*- !" {33.82855 -12.31183 dd}xyE " {27.57788 23.13995 dd}xyǍ?" {-6.25177 35.45398 dd}xy.LAw" {-16.88763 11.23517 l}xyTܟ" {-20.28296 0.323 l}xy T" {-17.23645 -10.69574 l}xyǍ`TO" {-8.71875 -18.31586 l}xyǍo4" {2.5686 -20.12201 l}xyǍ4" {13.03912 -15.53906 l}xy#Z!" {19.37 -6.02216 l}xy68" {19.55127 5.40582 l}xyǍDny " {13.52472 15.11664 l}xyǍG|q" {3.20471 20.03137 l}xyǍ?" {-8.13263 18.58282 l}xyǍd\" {-2.15167 -3.9776 dt}xyǍ," {-1.63367 -4.2138 dt}xyǍ h" {-1.09424 -4.38794 dt}xyǍ0" {-0.51581 -4.16711 dt}xyǍ H" {0.03625 -5.16357 dt}xyǍ<" {0.57404 -4.15997 dt}xyǍԟ \" {1.15466 -4.37091 dt}xyǍu8" {1.69409 -4.19238 dt}xyǍ0" {2.20496 -3.94519 dt}xyǍX̟$" {2.68286 -3.64032 dt}xyǍ vj" {3.11792 -3.27338 dt}xyC" {3.50244 -2.857 dt}xy,L" {3.83423 -2.39612 dt}xy2?" {4.10449 -1.89679 dt}xy6 " {4.30884 -1.36615 dt}xy!a" {4.44781 -0.81683 dt}xy$-!" {4.51318 -0.25214 dt}xy(П!P" {4.51099 0.31586 dt}xy- p" {4.43463 0.8778 dt}xy1i\" {4.29016 1.42767 dt}xy5|" {4.07648 1.95282 dt}xy9I" {3.79962 2.4483 dt}xyo" {-0.16469 0.10196 l}xy'h 10/ܑt" {-1517 10 /xy AB}xyܑt" {-16.15808 7.77766 l}xy0/ܑt" {0.0 0.10434 l}xyc]Cҟu" {-0.0231 0.01688 l}xyuh " {-918 st}xys\۟m" {-918 F d}xyuf" {-14.08449 11.23125 l}xylW" {-8.86914 7.07527 l}xyli" {-0.10252 0.0 l}xy}Iܦ" {-0.1691 -0.08382 l}xymh 2m6Q-" {-531 10 /xy AB}xymcQ-" {-16.09448 -7.74976 l}xym6Q-" {0.0 -0.1187 l}xy\~ -DŸ" {-0.00381 0.0 l}xyr`B% " {368 st}xyq  " {368 F d}xyr_ş%" {-17.55064 -4.00534 l}xygڟ," {-10.73396 -2.44933 l}xyg," {0.0 -0.04765 l}xyǍfX܍" {-0.1564 -0.7139 l}xyX3 3b+U" {790 10 /xy AB}xyǍb+# " {-4.33328 -18.98584 l}xyǍb+" {-0.0926 0.0 l}xypSf!{ɵEǍ뫞j" {-0.00417 -0.00552 l}xy|f s " {1394 st}xy{< O" {1394 F d}xyǍ|ݟ8a" {-7.812 -16.22023 l}xyǍw" {-5.01506 -10.41331 l}xyǍwd" {-0.03564 0.0 l}xyǍe Z" {0.09442 -0.13022 l}xy^v 4p" {1841 10 /xy AB}xyǍp7|M" {11.2363 -14.08214 l}xyǍpM" {0.0 -0.13625 l}xy!{ɵFǍR" {0.03584 -0.02078 l}xy s " {2702 st}xydӟ " {2702 F d}xyǍ:U" {7.82784 -16.22786 l}xyǍL" {5.05788 -10.47966 l}xyǍL" {0.09018 0.0 l}xy{H" {0.0 0.0 l}xy_$ 5" {3072 10 /xy AB}xy" {17.35074 0.0 l}xy" {0.0 0.0 l}xyJ -G﷟" {0.01164 -0.02464 l}xyy6% " {3729 st}xyb%Q" {3729 F d}xyzM" {17.55457 -4.01767 l}xyL\" {10.83063 -2.48772 l}xyL\F" {0.10112 0.0 l}xyǍ{<" {0.04866 0.06432 l}xyH 6 " {-3889 10 /xy AB}xyǍ $" {11.28554 14.15651 l}xyǍ $" {0.0 0.08182 l}xyǍПO" {-0.1798 0.71436 l}xy 7ry)" {-2838 10 /xy AB}xyǍr]" {-4.29924 18.8393 l}xyǍrb" {-0.07738 0.0 l}xyANeK\def\alphanum{\ifcase\xypolynode\or?A eK\or?B\orC\orD\orE\orF\orG\orH\fi}eK\xy/r3pc/:?{\xypolygon3{~={40}}},eK{\xypolygon4{~={40}~>{{--}}}},eK{\xypolygon5{~={40}}},eK{\xypolygon6{~={40}~>{{--}}}},eK{\xypolygon11{~={40}}},eK{\xypolygon50{~={40}~>.}},?+/r8pc/,eK{\xypolygon7{~<<{@{-}}~><{}H~<>{|*@{x}}~*{\alphanum}H~>>{_{\alpha_\xypolynode^{}}}}}eK\endxyJeKUse ofthe~={ɨ...} Xswitch wasdescribGedearlier.eKWhen8usingthe~:{}...} #-more8canbGedonethanjusteKsettingKthebase.nInfactanykernelcoGdecanbesup-eKplied*here.GItisproGcessedpriortoanyotherpartofeKthe,pGolygon.MThegraphicsstatehascatthecentreeKof_thepGolygon,pattheoriginofcoordinateswithineKthepictureandhasbasisunchangedfromwhathaseKpreviouslybGeenestablished.^ThecurrentpointcwilleKbGenresettothecentrefollowinganycoGdeinterpretedeKusingUUthisswitch. yeKA}Nfurther}simpli cationexistsforsidesandspGokeseKwithout8harrowis.qIfhtokiisasinglecharactertheneK~>Ehtoki, ~>{htoki}?, ~>{{htoki}} AoalluspGecifythedirec-eKtional.\dir{nθhtoki}?;;similarly.withthe~<ݴswitch.dOneKtheotherhand,compGounddirectionalsrequirealltheeKbraces,UUe.g.q~>{{--}}1and~>{2{.}}-U=.keKAfterallswitcheshavebGeenprocessed, TremainingeKtokensRareusedtospGecifythehob8jectiforeachver-eKtex.SuchktokenswillbGeuseddirectlyaftera\drop,eKsocanincludeob8jecthmoGdi erisasin gure3.IfeKan9hob8jectihasalreadybGeenspeci ed,rusingthe~*eKswitch,=then7thefollowingmessagewillbGewrittentoeKtheUUTU>'ExXlog:]#Xy-pic?Warning: vertexalreadyspecified, discarding?unusedtokens:䍒eKwith?tokensattheendindicatingwhatremainsun-eKproGcessed.]Similarlyextratokensbeforethe{ ...}eKgenerateUUamessage:#Xy-pic?Warning:discardingunusedtokens:LWeJ558 *tj??gwNestedTP9olygons WhenT\xypolygonE)|isTspGeci edwithineithera ~<>{ ...} 1;orF~>>{F...}switchFforanotherpGolygon,then5theinnerpGolygoninheritsanamewhichin-corpGorates7alsothenumber7ofthepartonwhichitoGccurs,"yasrgivenby\xypolynode=Q.^Thisnameisac-cessedousing\xypolyname=/y.InthefollowingexampletheinnerpGolygonisplacedusing~<>oinordertoeas-ily"adjustitsorientationtotheoutwarddirectionoftheUUspGokes.Nq ҡps: SDict begin xyc endt=m1hw= " {8.0 ox}xyoZt1;1\t1;2Ǎ1mt" {12.23581 12.23581 l}xyoZt1;3|k" {-12.23581 12.23581 l}xyWXt1;4Ǎd ϱ" {-12.23581 -12.23581 l}xyq1kR" {12.23581 -12.23581 l}xym2h"8 " {8.0 ox}xy3t2;1t2;2(k" {-12.23581 12.23581 l}xyt2;3Ǎϱ" {-12.23581 -12.23581 l}xyt2;4WR" {12.23581 -12.23581 l}xyǍ4Wt" {12.23581 12.23581 l}xy@84" {-24.8529 0.0 l}xy+G3'"8 " {8.0 ox}xyN3;1*N3;2Ǎ$Z" {-12.23581 -12.23581 l}xyBN3;3W:-#" {12.23581 -12.23581 l}xy3*N3;4Ǎ4W0N" {12.23581 12.23581 l}xy(" {-12.23581 12.23581 l}xyǍ"8 m," {0.0 -24.8529 l}xyt=+G4'w= " {8.0 ox}xyWX*N4;1oZBN4;2q1k:-#" {12.23581 -12.23581 l}xy\*N4;3Ǎ1m0N" {12.23581 12.23581 l}xyoZN4;4|" {-12.23581 12.23581 l}xyǍd $Z" {-12.23581 -12.23581 l}xyY=(" {24.8529 0.0 l}xyǍw=" {0.0 24.8529 l}xy[\xypolygon4{~:{/r5pc/:}~<>{*\frm<8pt>{o}\xypolygon4{~:{/-2pc/:}L~*{\xypolyname\xypolynode}}}[o]=<5pc>{\xypolynode}}NoticehownestedpGolygonsinheritnames"1,1"9x,"1,2" ,...,"4,1",...,"4,4"#forMtheirvertices.[IfaRhpre xiissuppliedattheoutermostlevelthenthenamesMbGecome:b" hpre xii;j"҈.[Specifyingahpre xiforɮtheinnerpGolygonoverridesɮthisnamingscheme.TheQsamenamesmaythenbGerepeatedforeachoftheSinnerpGolygons,=allowingaccessafterwardsonlytothelast|pGossiblyusefulasamemorysavingfea-ture~whentheverticesarenotrequiredsubsequently*.F*our|zlevelsofnestinggivesaquiteacceptable\SierpinskiGgasket".HTheinnermosttriangleispro-videdd]by\blacktriangleNHfromtheAU>'M SsymbGolfontmsam5 ,atP5-pGointsize.BF*urtherlevelscanbGeachievedusing3thePostScriptbackend,J*otherwise3lineseg-ments;#bGecometoosmalltoberenderedusing;XY #-fonts.CL nnps: SDict begin xyc end3D ^D"xmsam5DN2)*NǍ2s6" {-3.3775 -5.84999 l}xy5*N9j" {6.755 0.0 l}xyǍ6 D" {-3.3775 5.84999 l}xy0yN.NNǍ/HL" {-3.3775 -5.84999 l}xy2)N6 D" {6.755 0.0 l}xyǍ2s6" {-3.3775 5.84999 l}xy7:N5NǍ6 DL" {-3.3775 -5.84999 l}xy8:N<ˌ" {6.755 0.0 l}xyǍ9js6" {-3.3775 5.84999 l}xy-ͽN+hЪ\NǍ+X&h" {-3.3775 -5.84999 l}xy.NЪ\N2/" {6.755 0.0 l}xyǍ/HL" {-3.3775 5.84999 l}xy)Xӗ)N(փNǍ(" {-3.3775 -5.84999 l}xy+hփN/H֡" {6.755 0.0 l}xyǍ+X&h" {-3.3775 5.84999 l}xy0yӗ)N.NփNǍ/H" {-3.3775 -5.84999 l}xy2)փN6 D֡" {6.755 0.0 l}xyǍ2&h" {-3.3775 5.84999 l}xy:ͽN8:Ъ\NǍ9j&h" {-3.3775 -5.84999 l}xy{}~<>{?\xypolygon3"a"{~:{(.5,0):}H~>{}~<>{?\xypolygon3"b"{~:{(.5,0):}H~>{}~<>{?\xypolygon3"c"{~:{(.5,0):}H~>{}~<>{?\xypolygon3"d"{~:{(.5,0):}eK~<>{?*!/d.5pt/=0\hbox{\blacktriangle}}eK}}?}}}}}}}N8eKNotetheuseofnaminginthisexample;xwhenpro-eKcessingxthismanualitsaves13,000+wordsofmaineKmemoryand10,000+stringcharactersaswellas122eKstringsUUand319multi-lettercontrolsequences.%xeK28˯LatticeffandwebfeatureeKVers.3.3bCyRossMoKorehross@mpAce.mq.edu.auieKLoadTas:p\xyoption{web}uTeKThisfeatureprovidesmacrostofacilitatetypGesettingeKof7arrangementsofpGointswithina2-dimensionallat-eKticeUUor\web-like"UUstructure.eKCurrentlyAtheonlyroutinesimplementedwiththiseKfeaturearesome\quickanddirty"macrosfordrop-eKpingob8jectsatthepGointsofanintegerlattice.T oeKDo:MorensophisticatedroutineswillbGedevelopedeKforUUlaterversionsofUQXY U-pic,astheneedarises.eKMathematicallyspGeaking,let~u [bandm~v ֡bevectorseKpGointinginindependentdirectionswithintheplane.eKThen(thelatticespannedby~u and&~v ٲisthein niteeKsetUUofpGointsLgivenby:55L0=b ca~u +8bG@~v };forUUa,bintegersK̻b SL:eKWithin/jXY n-pic/nthevectorsg~u Zand~v canbGeestablished eKaswthecurrentcoGordinatebasisvectors.'ThefollowingeKmacrosUUtypGeseta nitesubsetofanabstractlattice.eK .ff2 d\xylattice#1#2#3#4ppGointsUUinlattice\croplattice#1#2#3#4#5#6#7#8p...inUUspGeci crectangle.qff2&ȍUTheparameters#1ʤ...#4areUtobGeintegersamin ,amaxA̲,obminandbmax,sothatthepGortionofthelat-ticetobGetypesetisthatcollectionofvectorsinLforwhichUUaminaamax!andbminbbmaxA̲.^-5ps: SDict begin xyc endA<7c/<7Ɵ<7) <7 a<79<7R<7>cc,cƟc)cac 9c#Rc$;q&c)q)Ɵq,)q/aq29q5Rϋq688c&;Ɵ>)AaD9޳GR̳H5ګJc#ګMƟګP)ګSaګV9ګYRګZ3H\c!Hb)HeaHh9HkRHl0)nc)qƟ )t))wa)z9)}R)~-QcQƟ Q)QaQ9QRQ*ycyƟy)yay9yRy_ƟHc0Ɵaz*C3232E䍍3232P32323232323232323232323232323232323232323232Pܞ3232TZCZ 323273232323232323232323232323232323232323232323232323232b0ǟ 32327323232323232323232323232323232323232323232323232323232C3232E䍍3232P32323232323232323232323232323232323232323232Pܞ3232SHs^(1)" {0.0 0.0 l}xyS" {3072 10 /xy AB}xyS" {166.07158 0.0 l}xyS" {0.0 0.0 l}xyKRXs^(2)ǍS )Cp" {0.0 0.0 l}xyS )X" {-3072 10 /xy AB}xyǍS )e" {0.0 135.20653 l}xyǍS )e" {0.0 0.0 l}xyLWeJ569+j*tj??gw\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},(1,-1)="a"*{\bullet}*+<2pt>!UL{a},(-1,1)."a"*\frm{.}}="L",{"L"+L?\ar"L"+R*+!L{s^{(1)}}},{"L"+D?\ar"L"+U*+!D{s^{(2)}}}\endxyN8IntheabGovecode,noticehowthebasisis rstestablishedAthenthe\xylattice@ZdtypGeset. 9Doingthiswithinan\xybox(allowsaxestobGesizedandplaced#appropriately*.30SincelatticepGointsaredeter-minedbytheir(integer)coGordinatedisplacements,theycanbGerevisitedtoaddextrahob8jectisintotheVoverallpicture. KMoregenerally*,Ztheoriginforlattice-coGordinatesgisthecurrenthposic,Nwhenthe\xylatticecommandisencountered.HEasyaccessi-bilityUUismaintained,asseeninthenextexample.ύWhenythebasisvectorsX~u andL~v (%arenotpGerpendic-ularnithecollectionofpGointswitha;bintheserangeswill lloutaskewparallelogram.SZGenerallyitisuse-fulTtoplotonlythosepGointslyingwithina xedrect-angle.]ThisisthepurpGoseof\croplatticeB,#withitsextraparameters#5...#8vdeterminingthe`cropping'rectangleTwithinwhichlatticepGointswillbGetypGeset.Other{pGointswillnotbetypesetevenwhenaandbareLEwithinthespGeci edranges.VExplicitlythehor-izontalrangeofthecroppingrectangleisXmintoXmaxA̲,fwithc]Xmin#abGeingtheX-coordinateofthevec-tor#5|~uV,where#5WisahnumbGeri됲(notnecessarilyanNinteger).]SimilarlyXmaxoistheX-coGordinateof#6Jո~>u@.HTheEverticalextentsareYminIandYmaxA̲,Hgivenby theY8-coGordinatesof#7 3~yvOVand#83~yvOVrespGectively*.\l)(ps: SDict begin xyc endaX_ 0˒*N uПR$aX-0N2%& .uП<7o?-HaXeQ0 A. 5I!RuП ([+`laXґu0e. 1M#m[aXM;. -;uПn6naX. (1c^c% vuП {П Bf=r" {0.0 39.59985 dt}xyBTП" {0.0 -39.59985 dt}xyxПz" {54.71997 0.0 dt}xyB=jI" {-54.71997 0.0 dt}xy%B3232Ce,3232E3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232E3232'Bڧ3232"32323232323232323232323232323232323232323232323232323232323232323232xڧ3232"3232323232323232323232323232323232323232323232323232323232323232323232B3232Ce,3232E3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232E32323Pas^(1)" {0.0 0.0 l}xy3P" {3072 10 /xy AB}xy3P" {187.20044 0.0 l}xy3P" {0.0 0.0 l}xyUf$s^(2)Ǎ]5 " {0.0 0.0 l}xy]$" {-3072 10 /xy AB}xyǍ]]" {0.0 118.79956 l}xyǍ]]" {0.0 0.0 l}xyFX\def\latticebody{%\ifnum\latticeA=1?\ifnum\latticeB=-1%\else?\drop{\circ}\fi\else\ifnum\latticeA=0?\ifnum\latticeB=1\else\drop{\circ}\fi\else\drop{\circ}\fi\fi}\xy?+(2,2)="o",0*\xybox{%0;<3pc,1.5mm>:<0.72pc,1.65pc>::,{"o"\croplattice{-4}4{-4}4{-2.6}{2.6}{-3}3}gwH,"o"+(0,1)="a"*{\bullet}*+!D{\alpha} H,"o"+(1,-1)="b"*{\bullet}*+!L{\beta}H,"o"+(0,-1)="c","o"+(-1,1)="d"H,"a"."c"="e",!DR*{};"a"**\dir{.}H,"e",!UL*{};"c"**\dir{.}H,"b"."d"="f",!DL*{};"b"**\dir{.}H,"f",!UR*{};"d"**\dir{.}H,"e"."f"*\frm{.}}="L","o"."L"="L"H,{"L"+L?\ar"L"+R*+!L{s^{(1)}}}H,{"L"+D?\ar"L"+U*+!D{s^{(2)}}}eK\endxyEeKThe\latticebodyHmacro. AtTZeachlatticepGointeKwithinSthespGeci edrangefora;b(andwithintheeKcropping rectanglewhen\croplatticeHisused),;aeKmacros)called\latticebodyI.isexpanded. BThisiseKmeant6tobGeuser-de nable,0pt?\divide\dimen0by64\dimen0=\latticeY\dimen0?\relax\ifdim?0pt>\dimen0\dimen0=-\dimen0\fi\ifdim?10pt>\dimen0\drop{\bullet}%\else\drop{.}\fi?\else\drop{.}\fi}\xy*\xybox{0;<3pc,2.57mm>:<.83pc,2.25pc>::,0,{\croplattice{-3}5{-5}5 {-1.3}{4.5}{-3.4}{4.4}}}="L",{"L"+L?\ar"L"+!R*+!L{\sigma^{(1)}}},{"L"+D?\ar"L"+!U*+!D{\sigma^{(2)}}}\endxy+y29}Circle,ffEllipse,ArcfeatureVers.3.4bCyRossMoKorehross@mpAce.mq.edu.auiLoadTas:p\xyoption{arc}΍ThistfeatureprovidesameanstoaspGecifycirclesofarbitraryradius,drawnwithavqarietyoflinestyles.SimilarlyellipsesmaybGespeci ed,ohavingarbitraryma8jor/minorcaxesalignedinanydirection.+AScircu-lararcjoiningtwopGointscanbGeconstructedwithspGeci edUUtangentdirectionatoneend. sAllyLthecurvesdescribGedhere|circles,NellipsesandsectorsQ9ofthese|areconstructedusingthecurvesfromthexycurve0+extension. 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30a.S9Several_familiesofcrossingareprovided.Q ThosehavingBnamesas\v..."uand\h...aredesignedtostackrespGectivelyverticallyandhorizontally*.MoreVpreciselythecurrenthpGosistartsatthetop-leftcornerand nishesateitherthebGottom-leftorQtop-right.4Saythatacrossingiseithera`verti-calIIcrossing'or`horizontalcrossing'respGectively*.Thisx[certainlyappliestothe\..cross..?pand\..twist...2families,@/see7 gure19inwhichthestringsb@enterandleavethesquareallwithverticaltangentsorallwithhorizontaltangents.HIndeedallmQcrossingsareeitherverticalorhorizontal,with $eKthe nalletterindicatingwhichforthe\xover.. eKfamilies.neKF*urthermorethereisanaturalorientation#foreKeachWcrossing,Waswellasalongeachstrand.w ThiseKcorrespGonds$totheorderinwhichinkisap-eKplied'totheprintedpage,\[followingthenaturaleKparametrizationmofeachstrandasacurvedcon-eKnection~orarrow. 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and>denotetheinitialand nalUUpGortionsofthe`crossed'string.30g.S9A6 simple6labGelenclosedinbraces,forexam-ple\vcross>{x}=GŲ,issetinmath-moGdeusingthe\labelstyle/K,@atapre-determinedplaceonthestringppGortion,shiftedineitherthe`above'por`be-low'|directionfromthecurveatthispGoint.=(F*oreach?crossingdepictedin gure19onlydefaultvqalueseareusedfortheplaceandshift-direction.)30h.rIfUthe rstcharacterwithinthebraces{..}is* ;e.g. %\htwist>{*=hob8jecti}?,Jthenageneralhob8jectimaybGeplacedasalabel.F*urthermoreif)the rstcharacteris^ Oor_or| &,thenthein-terpretation>mis,Ce.g.j$\vtwist<{^8hanchorihiti}?,asinwm14toplacehitiasalabGelalongan\arѲofthearrow!_feature.30i.UAsecondcharacter< 'or>spGeci esthatanar-rowheadkshouldappGearatthepre-determinedplace3onthechosenstring. Here>denotesan%arrowheadpGointingwiththenaturalorien-tation,Nwhile<F/pGointsagainst. Duetothecurvqatureofthestrings,+itisusuallybGestto\UseComputerModernTipsodratherYthannormalarrow-tips.30j.arT*oBAgeneratea`hole'use\knothole3&,}{orsimply\khole ,as_Hfollowingtoken. Thisgeneratesa`break',inthesenseof23j.0AIndeedsucha`hole'isusedtoseparatethetwopGortionsofthe`crossed'string.DefaultUsizefortheholeis5pt,whichisal-terable2via\knotholesize{Nhdimeni}?; normallyusedUUtosetthesizeforall]޲holesinadiagram.30k.VIftheresulting\khole)yȲiseithertoGolargeorpGerhapssnon-existent,thiscouldbeduetoatech-nicalityC#inthewaybreaksincurvesarehandled.ThisproblemshouldnotoGccurwiththestandardcrossings,P usingarectangularbasis,butitmayoGccur#withnon-rectangularbases.K1Aneasy` x'is,toincludeanextranull-br}'eak,onthestring,using<Ξ|,>|or|Ξ|,whichshouldplacethezero-sizedbreakatparametervqalue.5onthecurve.The2TspGeci cationshouldprecedea\khole'䖲atahigherGparametervqalue,orcomeafteroneatalowerUUvqalue.\aMultiple*breaks,`arrow-headsandlabGelsmaybGespGeci ed4alongthetwo4stringsofacrossing;?sim-plye^placetheirspGeci cationsoneafteranother;e.g.q<>|1>>><{x}8|>1{y}>{z}fFwasUUusedin gure19.Theonlyprovisoisthatall`breaks'alongasin-gleYstrandmustoGccurwithincreasingorderofgweKparameter?pGosition.Onthe`crossed'stringthis eKincludestheautomatic`hole'tocreatespaceforeKtheotherstring.PHenceitisadvisabletousejusteKthe=(+..)"and=(-..)vqariants=forsmalladjust-eKments,UUandtokeepthesecorrectlyordered.֍eKAdjustmenthofpGositionalongthestringscanbeeKachievedKusingahfactori,asin\vover#L9|(6(+.1)>H $.eKAllowed_syntaxis(\hsignihnumi)where_hsigniiseK+orv- tovincrementordecrementfromthepre-eKde nedvqalue.O]Alsoallowableare= 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ZeK32˯Supps3ortforSpeci cDriverseK32.1KdvidrvdriveruTeKVers.3.3bCyRossMoKorehross@mpAce.mq.edu.auieKLoadTas:p\xyoption{dvidrv}eKThis driverprovidessuppGortforthe\emtex"eK\specialIJcommands,Gwhenusingoneofthestan-eKdard dvi-drivers:c2dvidot$ ,8dvihplj(#,8dvimsp#l&,8dviscreKordvivik",zthatcomewithEbGerhardMattes'em-TU>'ExXeKdistribution.eKSuppGortedUU\special0e ectsUUare... ceKeLem-TU>'ExXUUline-drawing\special-U=s.*eKeLvqariableUUline-widthseK32.2KDVIPSdrivereKVers.3.3bCyRossMoKorehross@mpAce.mq.edu.auieKLoadTas:p\xyoption{dvips}eKThis\driverprovidessuppGortforallextensions/wheneKusing2thedvipsdriverbyT*omasRokicki[11 ].fDIthaseKbGeenGtestedwithdvipsversion5.55aanddvipskver-eKsionUU5.58f.eKSuppGortedUU\special0e ectsUUare... ceKeLcolour,EusingAdirectcolorspGecialsandPostScript.*eKeLcrayonUUcolours.eKeLPostScriptUUback-end.eKeLrotated/scaledqdiagramsandtext,9usingPost- eLScript.eKeLvqariableline-widthsandpGoly-lines,MusingPost-eLScript.LWeJ66C N*tj??XextraUUframesand 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ff-y+); ffffQͤ ffzfddvidrv ff[F-B ff|+ i8 ff&y- ffh-B fff^- b  ffffQͤ ffU{fddvitops ffY + 7 ff|+ i8 ff+5 ff̈́+ 7 ff-y+); ffffQͤ ffxfdoztex ffY + 7 ff|+ i8 ff+5 ff̈́+ 7 ff-y+); ffffQͤ ffU{fd17oztex ffY + 7 ff|+ i8 ff+5 ff̈́+ 7 ff-y+); ffffQͤ ff}fdtextures ffY + 7 ff|+ i8 ff+5 ff̈́+ 7 ff-y+); ffffQͤ ff ufd16textures ffY + 7 ff|+ i8 ff+5 ff̈́+ 7 ff-y+); ffffQͤ ff5wfdxdvi ffY + 7 ff|+ i8 ff+5 ff̈́+ 7 ff-y+); ffffQR ͍4TFigureUU21:qExtensionimplementationreplacedbyuseofhdriverispGecials.: 32.9 CMacTeXdriverVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui LoadTas:p\xyoption{cmactex}Thomas+Ki e'sCMacTU>'ExXapplicationusesdvipsasitsUUdvi-driver.OtherimplementationsnotspGeci callymentionedhereLEmaywellworkwithoneofthenamedhdriveris,though["pGerhapsnotallfeatureswillactuallybesup-pGorted.5g33}ExtraufeaturesusingE-ff 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NoguaranteeIcanbGegivenofthecurrentloGcation,Eorscale,:which JmaybGedi erentwithdi erentdrivers.HoweveragoGodPostScriptprogrammerwillbGeabletoovercomesuchdicultiesanddomuchmore.T*oaidinthisthespGecialmodi er[psxy]%1IJisprovidedto#recordtheloGcationwherethereferencepointofthe0currenthob8jectiwillbGeplaced.ItscoordinatesareUUstoredwithkeysxyXpos&*andxyYpos"C.#ȍ33.1%ColourTheincluded lexyps-c.texThis leisloadedanditse ectsareactivqatedautomaticallywhenever\xyoption{color}aisre-questediandthecurrenthdriverisuppGortscoloursus-ingPostScript.kShouldtherebGeanyneedtoturno ZthissuppGort,thefollowingcommandsareavqail-able;UUtheyobGeyusualTU>'ExXgroupings. ff2]\NoPScolorXff2m_WithoutPostScriptsuppGortsomedriversmaystillbGeabletoprovidesomesupportforcolours.aThesecommands%arenotguaranteedtoworkadequatelywithalldrivers./ Theyareprovidedprimarilyfortest-ingandtrouble-shoGoting;He.g.withhdrivericon gu-rationsuntestedbytheauthorsofXY X-pic,whoshouldbGeUUnoti edofanydiculties.#ȍ33.2%FramesTheincluded lexyps-f.texThis leisloadedanditse ectsareactivqatedautomaticallywhenever\xyoption{frame}aisre-quested andthecurrenthdriverisuppGortsPost-Scriptne ectsforframes.ShouldtherebGeanyneedgweKtoH#turno thissuppGort,Jthefollowingcommandsare eKavqailable;UUtheyobGeyusualTU>'ExXgroupings.eK (ff2 荍v_\NoPSframes[v;removeUUPostScriptsuppGortv_\UsePSframes[v;reinstateUUPostScript.ff2]MZWithoutPostScriptsuppGortellipsesmaybeshownas\circlesandall lledregionsmaybGerepresentedasQ\blackrectangles.eThesecommandsareprovidedprimarilyrfortestingandtrouble-shoGoting;#e.g.withhdrivericon gurationsuntestedbytheauthorsofXY ]-pic,UUwhoshouldbGenoti edofanydiculties.!133.3%Line-stylesuTTheincluded lexyps-l.tex'ExXgroupings.ff2 荍]\NoPSlinesX'ExXgroupings.ff2 荍v_\NoPSrotate[v;removeUUPostScriptsuppGortv_\UsePSrotate[v;reinstateUUPostScript.ff2]CWithoutPostScriptsuppGortdiagramscanbeexpGectedtobedisplayedunrotatedandunscaled.These.commandsareprovidedprimarilyfortestingand}trouble-shoGoting;e.g.withhdrivericon gura-tionsuntestedbytheauthorsofXY s-pic,whoshouldbGeUUnoti edofpersistentdiculties.LWeJ70G Mˠ*tj??gw33.5 PatternsandtilesuTTheincluded lexyps-t.tex'ExXgroupings. Iff2 򍍍]\NoPStilesX'ExXgroup-ings. qff2 򍍍6b\NoTPICframes`8removeUUtpicsuppGort6b\UseTPICframes`8reinstateUUtpic.kff2ǟ/AppendicesꨍAnAnswersfftoallexercisesAnsw9erktoexercise1(p.7): InthedefaultsetuptheyNarealldenotethereferencepGointoftheNXYΤ-pictureWbutthecartesiancoGordinatehposi(0,0)de-notes~mthepGointorigo thatmaybGechangedtosome-thingUUelseusingthe: ꧲opGerator.gweKAnsw9erPtoexercise2(p.7): Use;thehpGosiition eK<HX,ߵY8>+"ob"!Ҳ.##eKAnsw9ertoexercise3(p.7): ItK rstsetscaccord-eKingyKto\...".ݨThenyKitchangesctothepGointrightofeKc?`atthesamedistancefromtherightedgeofcasitseKwidth,UUwD,i.e.,č*|ps: SDict begin xyc endTheUU...C|31 {1ǟCz31 }:3wK㏞!Ǹ'D|31 {<VDz31 }83w39eKAnsw9er Ktoexercise4(p.9): ThehcoGordieK\{"A";"B":3X"C";"D",bx}m$"sreturnsthecrosspGoint.eKHere`ishowtheauthortypGesetthediagramintheeKexercise:N8eK\xyH%H%?setupandmarkA,B,C,andD:H(0,0)="A" *\cir<1pt>{}*+!DR{A},H(7,10)="B"?*\cir<1pt>{}*+!DR{B},H(13,8)="C"?*\cir<1pt>{}*+!DL{C},H(15,4)="D"?*\cir<1pt>{}*+!DL{D},H%H%?gotointersectionandname+circleit:H{"A";"B":"C";"D",x}?="I"*\cir<3pt>{},H%H%?makedottedlines:H"I";"A"**{}?+/1pc/;-/1pc/**@{..},H"I";"D"**{}?+/1pc/;-/1pc/**@{..}H%eK\endxyeKAUU?! O...hplaceiUUcouldalsohaveUUbGeenused.eKAnsw9ertoexercise5(p.9): T*ocopythepvqalueeKtoUUc,i.e.,equivqalentto\p?".eKAnsw9ergtoexercise6(p.10): WhenvusingtheeKkernelconnectionsthatareallstraightthereisnoeKdi erence,e.g.,**{}?<)Iand/**{}+E(Ldenote/exactlyeKtheaEsamepGosition.However,dAforaEotherconnectionsiteKisnotnecessarilythecasethatthepGointwheretheeKconnectionjtentersthecurrentob8ject,odenotedby?< n,eKand"thepGointwherethestraightlinefrompenterseKtheUUob8ject,denotedby+E O,coincide.eKAnsw9ertoexercise7(p.10): The84coGdetypesetseKtheUUpicture&|) ps: SDict begin xyc end q"#/BoxǍ*2" {0.0 42.67914 -14.22638 -42.67912 14.22636 ov}xygԍg3232$3232=323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232=3232yΟ&3232323232323232323232323232323232323232323232323232U[&323232323232323232323232323232323232323232323232323232g3232$3232=323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232=3232=ɟ񠸸LWeJ71H e֠*tj??gwAnsw9er=toexercise8(p.11): This< doGesthejob, savingeachpGointtomakethepreviouspGointavqail-ableUUforthenextpiece:N8\xy@={(0,-10),(10,3),(20,-5)},s0="prev"?@@{;"prev";**@{-}="prev"}\endxy=Notice dhowweclosethelineby rstsavings0^,6gthelastpGointvisited, suchthatthe rstpGointwillbGeconnectedUUtoit.Answ9erTtoexercise9(p.11): TheUUauthorused\xy?={.{+DL(2)}.{+UR(2)}}"dbl",*+<3pc,2pc>{+}*\frm{.},?"dbl"*\frm{--}\endxy=toUUtypGesetthe gureintheexercise.Answ9er^toexercise10(p.13): The rsttypGe-sets\a"centeredaround0 andthenmovesctothelowerrightcorner,2thesecondtypGesets\a"abovethe0'a:andqps: SDict begin xyc ende+a .Answ9ertoexercise11(p.13): Theyfhavetheoutlines n8;ps: SDict begin xyc endëPǍ-" {0.0 7.9167 -7.50009 -7.91669 7.50009 ov}xy!Dz+Rqandl ps: SDict begin xyc endrëPǍ," {0.0 2.6389 -2.50003 -2.6389 2.50003 ov}xy!Dz+bGecause~the rstisenlargedbythepositiveo settotheuppGerrightcornerandthesecondbythenegativeo setUUtothelowerUUleftcorner.Answ9erFFtoexercise12(p.14): The rsthasnoe ect`sincethedirectionissettobGethatofavectorinthecurrentdirection,however,thesecondreversestheUUcurrentdirection.Answ9eretoexercise13(p.15): NoneVinbGothcases.Answ9erTtoexercise14(p.18): OneUUwayisN8$$\xy*{+};?p+(6,3)*{+}**{}?(1)*@{-}?*!/-5pt/^\dir{-}*^\dir{-}?*!/^-5pt/\dir{-}\endxy$$=Thus6we rstcreatethetwo+saspandcandconnectthemwiththedummyconnection**{} *tosetupHRthedirectionparameters.JThenwemove`ontop+ofc'with?(1)WandpGositionthefoursidesofthesquareusing^ U_and_forloGcaldirectionchangesand/hdimeni/زforskewingtheresultingob8jectbymovingitsUUreferencepGointintheoppositedirection.gweKAnsw9er)toexercise15(p.18): One|wayistoadd eKextra"ehalfcirclesskewed"esuchthattheycreatetheil-eKlusionUUofashade:N8eK$$\xyH*\cir<5pt>{}H*!<-.2pt,.2pt>\cir<5pt>{dr^ul}H*!<-.4pt,.4pt>\cir<5pt>{dr^ul}H*!<-.6pt,.6pt>\cir<5pt>{dr^ul}eK\endxy$$ڍeKAnsw9er*\dir{>}H?(.65)*{\oplus}?*!LD!/^-5pt/{x}H?(.65)/12pt/*{\oplus}?*!LD!/^-5pt/{x'}H?(.28)*=0{\otimes}-/40pt/*+{Q}="q"H+/100pt/*+{P};"q"?**\dir{-}eK\endxyڍeKAnsw9erctoexercise18(p.21): HereisthecoGdeeKthatUUwasusedtotypGesetthepicture:eK\def\ssz#1{\hbox{$_{^{#1}}$}}eK\xy?(0,0)*+{A};(30,-10)*+{B}="B",**\dir{-},eK"B"**\crv{(5,20)&(20,25)&(35,20)}H?<(0)*\dir{<}="a"??>(1)*\dir{>}="h"H?(.1)*\dir{<}="b"??(.9)*\dir{>}="i"H?(.2)*\dir{<}="c"??(.8)*\dir{>}="j"H?(.3)*\dir{<}="d"??(.7)*\dir{>}="k"H?(.4)*\dir{<}="e"??(.6)*\dir{>}="l"H?(.5)*\dir{|}="f",H"a"*!RC\txt{\ssz{(\lt)}};E"h"*!LC\txt{\ssz{\;(\gt)}},**\dir{.},H"b"*!RD{\ssz{.1}};E"i"*!L{\ssz{\;.9}},**\dir{-},H"c"*!RD{\ssz{.2}};E"j"*!L{\ssz{\;.8}},**\dir{-},H"d"*!RD{\ssz{.3}};E"k"*!L{\ssz{\;.7}},**\dir{-},H"e"*!RD{\ssz{.4}};E"l"*!LD{\ssz{.6}},**\dir{-},H"f"*!D!/^-3pt/{\ssz{.5}}eK\endxyLWeJ72I A*tj??gwAnsw9erTtoexercise19(p.26): HereUUishow:N8\xy (0,0) *++={A}?*\frm{o};(10,7)?*++={B}*\frm{o}**\frm{.}\endxy!Answ9ertoexercise20(p.26): The;*\cir?{}.uop-erationchangesctobGeroundwhereas*\frm?{o}doGesUUnotchangecatall.cMAnsw9erTtoexercise21(p.26): HereUUishow:\xy(0,0) *+++{A}?;(10,7)?*+++{B}**\frm{.}**\frm{^\}}?;**\frm{_\}}\endxyThetrickinthelastlineistoensurethattheref-erence pGointofthemergedob8jecttobebracedistherightUUoneineachcase.cMAnsw9ertoexercise22(p.30): ThisishowtheauthorUUspGeci edthediagram:\UseCrayolaColors\xy\drop[*1.25]\xybox{\POS(0,0)*{A};(100,40)*{B}**{}?<<*[@_][red][o]=<5pt>{\heartsuit};?>>>*[@_][Plum][o]=<3pt>{\clubsuit}**[|*][|.5pt][thicker]\dir{-},?(.1)*[left]!RD\txt{label?1}*[red]\frm{.}?(.2)*[!gsave?newpath xyXpos?xyYposmoveto50duprlineto 20?setlinewidth001setrgbcolorstroke grestore][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/\txt{special?effect:alignedtext}*[red]\frm{.}}\endxy!Answ9ertoexercise23(p.40): HereR~iswhattheauthorUUdid:\xy?*+{A}*\cir<10pt>{}="me"\PATH?`ul^ur,"me""me"|>*:(1,-.25)\dir{>}\endxygweKThe trickisgettingthearrowheadright:the: eKmoGdi erUUtotheexplicit\dirhob8jectidoesthat.beKAnsw9erTtoexercise24(p.40): TheUUauthordidN8eK\xy(0,0)H\ar?@{-->}(30,7)^A="a"H\POS(10,12)*+\txt{label}?\ar"a"eK\endxyeKAnsw9erZtoexercise25(p.41): HereistheentireeGXYK-pictureUUoftheexercise:eK\xy?;<1pc,0pc>:H\POS(0,0)*+{A}H\ar+(-2,3)*+{A'}*\cir{}H\ar?@2+(0,3)*+{A''}*\cir{}H\ar?@3+(2,3)*+{A'''}*\cir{}H\POS(6,0)*+{B}H\ar?@1{||.>>}+(-2,3)*+{B'}*\cir{}H\ar?@2{||.>>}+(0,3)*+{B''}*\cir{}H\ar?@3{||.>>}+(2,3)*+{B'''}*\cir{}eK\endxyt#eKTheO rstbatchusethedefault{->}⒲spGeci cation.beKAnsw9erTtoexercise26(p.42): TheUUauthorusedeK\newdir{?>}{{}*!/-5pt/\dir{>}}eKAnsw9erTtoexercise27(p.42): TheUUauthorusedeK\xyH\ar?@{>>*\composite{\dir{x}*\dir{+}}<<}H(20,7)eK\endxyeKAnsw9erTtoexercise28(p.42): TheUUauthorusedeK\xy?*{\circ}="b"\ar@(ur,ul)cH\ar@{.>}@(dr,ul)?(20,0)*{\bullet}eK\endxyt#eKNotethatitisessentialthatthecurvingspGeci cationeKcomesUUafterthearrowstyle.beKAnsw9erctoexercise29(p.46): HereisthecoGdeeKusedUUtotypGesetthep}'astingdiagramUUin gure15.eK\xymatrixrowsep{1.5pc}eK\xymatrixcolsep{3pc}eK\diagramH&&\relax\rtwocell<0>^{f_3^{}\;\;}{\omit}H&\relax\ddtwocell<0>{\omit}E\drtwocell<0>^{\;\;f_4^{}}{<3>}E\ddrrtwocell<\omit>{<8>}\\eK&&&&\relax\drtwocell<0>^{\;\;f_5^{}}{\omit}\\eKA?\uurrlowertwocell<-6>{\omit}\relaxeK\uurrcompositemap<2>_{f_1^{}}^{f_2^{}}{<.5>}LWeJ73J *tj??gw\drtwocell<0>_{g_1^{}\;}{\omit} &&&\relax\urtwocell<0>{\omit}&&\relax\rtwocell<0>^{f_6^{}\;}{\omit}&\relax\rlowertwocell<-3>_{g_4^{}}{<-1>}\rcompositemap<6>_{f_7^{}}^{f_8^{}}{\omit}&?B\\&\relax\urrtwocell<0>{\omit}\xcompositemap[-1,4]{}% <-4.5>_{g_2^{}}^{g_3^{}}{\omit}\\\enddiagramj؍F*orthestraightarrows, vitwouldhavebGeensimplertoVpuse\..to Ѳprovidedxyarrow+l˲hasbGeenloaded.uIn-steadD\..twocell<0>...{\omit?}:@wasDusedtoillus-tratetheversatilityofnudgingand\omit$~;thusxy2cell can4 completelyhandleawiderangeofdi-agrams,withoutrequiringxyarrow)`.T&Notealsotheuseof\relax*atthestartofeachnewcell,$toavoidprematureexpansionofacomplicatedmacro,whichcanUUupsetthecompilingmechanism.^Answ9erctoexercise30(p.47): HereisthecoGdeusedUUbytheauthortosetthe rstdiagram.N8{\uppercurveobject{{?}}\lowercurveobject{{\circ}}\xymatrixcolsep{5pc}\xymatrixrowsep{2pc}\diagram\relax\txt{?FUn}\rtwocell<8>{!\&}&?\relax\txt{gaMES}\enddiagram}\HereUUisthecoGdeusedfortheseconddiagram.\xymatrixcolsep{2.5pc}\xymatrixrowsep{4pc}\diagram\relax\txt<1.5cm>{\bf?GroundState}\rrtwocell<12>~^{+{}~**!/-2.5pt/\dir{>}}~_{++{}~**!/5pt/\dir{<<}}^{<1.5>\txt{\small?continuouspower}}_{<1.5>\txt{\small?pulsedemission}}{!}&?\relax\;\;N\!i\,C\!d\;\;\Circled&?\relax\txt<1.50cm>{\bfExcitedState}\enddiagram#斍Answ9erTtoexercise31(p.50): TheUUauthordid\xymatrix?@!=1pc{**[l]?A\timesB \ar[r]^{/A}?\ar[d]_{/B}&?B\ar[d]^{\timesA}\\A\ar[r]_{B\times}&?**[r]B\timesA}gweKAnsw9ertoexercise32(p.50): MoGdi ers are eKusedtomakeallentriesroundwithaframe{theeKgeneralCformisusedtoensurethatthesequenceiseKwell-de ned.S>FinallythematrixisrotatedtomakeiteKpGossibleUUtoenteritasasimplesquare:N8eK\entrymodifiers={=<1pc>[o][F-]}eK\xymatrix?@ur{HA?\save[];[r]**\dir{-}, e3[];[dr]**\dir{-}, e3[];[d]?**\dir{-}\restore%B&?B\\HC?&D})ZeKAnsw9erTtoexercise33(p.51): HereUUishow:eK\xymatrix?@W=3pc@H=1pc@R=0pc@*[F-]{%H:?\save+<-4pc,1pc>*\hbox{\itroot}<\ar[]%B\restoreeK\\H{\bullet}%B\save*{}e?\ar`r[dd]+/r4pc/`[dd][dd]%B\restoreeK\\H{\bullet}%B\save*{}e?\ar`r[d]+/r3pc/`[d]+/d2pc/-`[uu]+/l3pc/`[uu][uu]%B\restoreeK\\H1?})ZeKAnsw9ertoexercise34(p.52): The rstAwaseKnamedUUtoallowreferencefromthelast:eK\xygraph{H[]A="A1"?:@/^/[r]A-:@/^/?[r]A-:@/^/?"A1"})ZeKAnsw9erTtoexercise35(p.53): TheUUauthordideK\SelectTips{cm}{}eK\objectmargin={1pt}eK\xygraph{?!{0;(.77,-.77):0}H!~:{@{-}|@{>}}Hw?(:[r(.6)]{x_1}%B,:[d]z:[r]y:[u(.6)]{x_2}:"x_1":"z"e?:@(?{"w";"z"},{"y";"z"})"z":"x_2")}meKItzalsoshowsthatonec}'an?use{} sinsidedelimitedeKargumentspr}'ovidedBoneaddsaspacetoavoidthe{} %seKbGeingUUshavedo !LWeJ74K c*tj??O]w\Answ9erctoexercise36(p.54): HereisthecoGde actuallyusedtotypGesetthe\xypolygon{}!P6"B"{~<-\cir<5pt>{}}"B1"1?"B2"2"B3"3"B4"4"B5"5"B6"6"B0"[rrr]0?!P9"C"{~*{\xypolynode}}}\endxy$ˑBCVfersionff2CompatibilityVers.3.4bCyKristo erH.Rosehkrisrose@brics.dkiLoadTas:p\xyoption{v2}uTThisappGendixdescribesthespecialbackwardscom-patibilitywithXY -picversion2:I diagramswrittenac-cordingtothe\TypGesettingdiagramswithXY-pic:User'sXManual"[13 ]shouldtypGesetcorrectlywiththisloaded.ݲTheyNcompatibilityisavqailableeitherasanXY -option<~orthroughthespGecial lesxypic.sty5andxypic.tex!SdescribGedUUbelow.There@areafewexceptionstothecompatibility:the[featuresdescribGedinxB.1belowarenotprovidedbGecauseztheyarenotasusefulastheauthororiginallythoughtLandthusvirtuallyneverused.-Andoneextracommand[isprovidedtospGeeduptypGesettingofdoc-umentswithXY -picversion2diagramsbyallowingthenewcompilationfunctionalitywitholddiagrams.Theremainingsectionslistalltheobsoletecom-mands?andsuggestways?toachieve?thesamethingsusingXY /-pic3.7,i.e.,withouttheuseofthisoption.TheyaregroupGedastowhatpartofXY -picreplacesthem;UUthecompilationcommandisdescribGedlast.Note:\version2"ismeanttocoverallpublicreleases%of!XY %-picin1991and1992,i.e.,version%1.40andr1versions2.1through2.6.\Thepublishedmanualcited#abGove(forversion2.6)isthereferenceincaseofCvqariationsbGetweenCtheseversions,FandonlythingsdoGcumentedưinthatmanualwillbGesupportedbythisoption!^19iˍB.1$Unsupp`ortedincompatibilitiesHere5isalistofknownincompatibilitieswithversion2UUevenwhenthev2*optionisloaded.NAutomatic`shortening'ofarrowtailsusing|<<breaks‚wasabugandhasbGeen` xed'soitdoesnotQworkanymore.TPuta|<\hole)c߲breakbGeforeit.w\eLeMTheversion2.6*pGositionoperatorisnotavqail- eMable.STheversion2.6constructiont0|s; pt1|s*(mx,?y[)eMshould\bGereplacedbytheratherlongbutequiv-eMalentUUconstructionOdeM{Ot0';p+/r/:,t1'=E"1";p+/u/,x;(0,0);:E"1";p+/r/,y;(0,0);::,(lx,?y[)}eMIn_Wmostcasest0|s; pt1|s**{}?(#ax)?,pGossiblywithaeMtrailingUU+/^:::"C/'U@,UUsucesinstead.JeLeMUsingt0|s; pt1|s:(mx,?y[) ͲasthetargetofanarroweMcommanddoGesnotwork.JEncloseitinbraces,eMi.e.,UUwrite 7={DqVt0'; t1':(x,?y[)}]EeLeMThe tolder\pit,7\apit,and t\bpitcommandseMareSfnotde ned.kUse\dir{>}-f(or\tipSZ)witheMvqariantsUUandrotation.eLeMThek4evenoldernotationwhereanargumentineMbracesto\rto5޲andtheotherswasautomati-eMcallytakentobGea`tail'isnotsupported.UseeMtheUUsuppGorted|R< O...notation.7eKIf‚youdonotusethesefeaturesthenyourversion2eK(andwdearlier)diagramsshouldtypGesetthesamewitheKthisEoptionloadedexceptthatsometimesthespac-eKingv%withversion3isslightlydi erentfromthatofeKversionUU2.6whichhadsomespacingbugs.a-eKB.2/Obsoletekernelfeatures eKThezfollowingthingsareaddedtothekernelbythiseKoptiong6anddescribGedhere:idioms,obsoletepositions,eKobsoleteconnections,andobsoleteob8jects.MF*oreacheKweshowthesuggestedwayofdoingthesamethingeKwithoutUUthisoption:a-eKRemo9vedTAU>'M S-T<8E3sXidiomseKSome%idiomsfromAU>'M S-TU>'ExXarenolongerusedeKby3XY-pic:.Tthe 3de nitioncommands\defineeKand(u\redefine,=andthesizecommands\dsize,eK\tsize, \ssize,and \sssize. PleaseuseeKthenBcommandsrecommendedforyourformat|foreKplaintTU>'ExXtheseare\def!forthe rsttwotandeK\displaystyle%$,7\textstyle;Ҳ,7\scriptstyleF7̲,7andeK\scriptscriptstyleBƲfortherest.LThev2K\optionen-eKsuresUUthattheyareavqailableanyway*. eKV*ersionalso2usedtheAU>'M S-TU>'ExX\textandeKat(non-ob8ject)bGoxconstruction\TextwhichareeKemulated|\texṱisonlyde nedifnotalreadyde-eK ned,however,usingthenativeone(ofAU>'M S-TU>'ExXoreKAU>'M S-L5ffA͉TU>'ExXorwhatever)ifpGossible.ePleaseusetheeK\txtob8jectconstructiondescribGedinx6.3directlyeKsinceUUitismoregeneralandmuchUUmoreecient!ffff[ J=w-:19LInXadditionafewoftheexp}B\atip9t~\dir^{>}B\btip9t~\dir_{>}B\Tip9t~\dir2{>}B\aTip!t~\object=<5pt>:(32,-1)\dir^{>}B\bTip!t~\object=<5pt>:(32,+1)\dir_{>}B\Ttip9t~\dir3{>}B\ahook9t~\dir^{(}B\bhook9t~\dir_{(}B\aturn9t~\dir^{'}B\bturn9t~\dir_{'}eKff2 TTheeoldercommands\pitY,b\apitS,band\bpitV,arenotUUprovided.ׅObsoleteTobjectconstructionsuTThe?qfollowingob8jectconstructionmacrosaremadeobsoleteUUbytheenrichedhob8jectiformat: ff2 9u ]oV*ersionUU2ob8jecti+Replacementff2 ]o\rotate(?hfactori)htipi E+\object:(thfactori,?hfactori){ htipi} ]o\holei+\object+{} ]o\squashhtipii+\object=0{ htipi} ]o\growhtipii+\object+{htipi} ]o\grow<(]hdimeni>?htipii+\object+<hdimeni>{ htipi} ]o\squarify{?htexti}i+\object+={ htexti} ]o\squarify<=Qhdimeni>{ htexti}E+\object+={ htexti}ff2where~rotationisdoneinaslightlydi erentmannerinUUversion3.7(itwasneveraccurateinversion2).ׅB.3!Obsoleteextensions&featuresuTV*ersion2hadcommutativediagramfunctionalitycorrespGondingtotheframes'J*extensionandpartsofthePmatrix&ԎandParrow!features.pTheseParethereforeloadedandsomeextrade nitionsaddedtoemulatecommandsUUthathaveUUdisappGeared.ׅF ramesTheyversion2framecommandsareemulatedus-ing(theframeextension(aswellasthe\dotframed8# ,\dashframed9߲,@*\rounddashframedZzٲcommands:comm-unicatedUUtosomeusersbyelectronicmail): ff2 9u eV*ersionUU2ob8jecte5Replacementff2 e\framede5\drop\frm{-} e\framed<6Mhdimeni>e5\drop\frm<vhdimeni>{-} e\Framede5\drop\frm{=} e\Framed<6Mhdimeni>e5\drop\frm<vhdimeni>{=}LWeJ76M а*tj??gw~\dotframedIN\drop\frm{.} ~\dashframedIN\drop\frm{--}~\rounddashframedIN\drop\frm{o-}~\circledIN\drop\frm{o}~\CircledIN\drop\frm{oo}4Bff2 hnMatrices֒The1\diagramhrowsi\enddiagramcommandispro-vided0~asanaliasfor\xymatrix{<޸hrowsi} centeredin)mathmoGdeand\LaTeXdiagramschangesittouse\begin#ڣ..._\end`syntax.v2\setsZaspGecialinternal`oldmatrix' agsuchthattrailing\\allthederivedcommands\dto,E\urto%6,E...;5BtheH\arrow(~commandsHofthe -releasesUUofv3isalsoprovided.Insteadofcommandslike\rrto"ACand\uldoubleyoushouldusethearrowfeaturereplacements\ar[rr](@andUU\ar@{=}[ul]=4.Theprede nedturningsolidarrows\lltou#,...,\tord$arede nedaswell;,'ExX2.09`style{option'[xypic])f. [9Thisismadesynonymouswith|loadingthisoptionbythe lesxypic.texandxypic.styUUdistributedwiththev2*option.xypic.tex/?:7qThiss le(version3.3)justloadsthev2feature.9xypic.sty/?:7qLoadsUUxy.sty&*andUUthev2*feature.B.5!Compilingv2-diagrams֒Inh3ordertomakeitpGossibletousethenewcompila-tionfeaturesevenondoGcumentswrittenwithXY -picgweKv2,UUthefollowingcommandwasaddedinv2.12:eKff2 =I6\diagramcompileto{iUhnameiUU} ꧲...\enddiagram^ff2~whichpisliketheordinarydiagramcommandexcept thebresultiscompiled(seenote5e)..Notethatcom-pilationUUisnotquitesafeinallcases! \There\isalsothefollowingcommandthatswitchesonNautomaticGc}'ompilationofalldiagramscreatedwithUUthev2\diagram0...\enddiagramB3command:Nff2&(\CompileAllDiagramsD{3hpre xiUU}&(\NoCompileAllDiagrams&(\ReCompileAllDiagrams^ff2.willapply\xycompileto{G(Yhpre xin}{ ...} 'toeachdi-agram\withnasequencenumbGer\startingfrom1.Use\CompileMatricesWU%andUU\CompilePrefixP*instead! \If)forsomereasonadiagramdoGesnotworkwhencompiledcthenreplacethe\diagram1ʮcommandwith\diagramnocompile^c(or$!incaseyouareusingtheL5ffA͉TU>'ExXUUform,\begin{diagramnocompile}U ).4KCdCommonffErrorsTXIn_thisappGendixwedescribesomecommoncaseswhere'smallmistakesin'XY -picturesresultinTU>'ExXer-rorUUmessagesthatmayseemcryptic.#!pBo9xTexpQected.!WAhbGoxiw9assuppQosedtobehere. This4mes-sage|iscommonwhenan|XY -pichob8jectiismistypGedsuch that XY-picexpGectsbutdoesnot ndaTU>'ExXhbGoxiUUconstruction.!}LaT eXEError:Badzmathen9vironmentzdelim-iter.!Fileendedwhilescanninguseof\xycompiled.!Argumen9t(of?\codeof@hasanextraFɌ cmbsy10Fg. Theseerrorsh(canhappGenwhilereadinganincompletecom-piledpicture(suchabGeastiscreatedwhenXY-piccrashesduringcompilationduetoasyntaxerrororotherUUsuchproblem).!ڒMissingFginserted. ThishappGenswhen\endxywasUUleftout.!4ˍT oTDo:qDzAlsoUUincludethemoreobscureones...LWeJ77N *tj??g卑References:ߍ[1]UAdobGeuSystemsIncorporated.uPostScriptL}'an- UguageR}'eferenceManual,UUsecondedition,1990.@[2]UAmericank_MathematicalSoGciety*. cAU>'M S-L雍QATKß'E-XUV;ersion1.1User'sGuide,UU1.1edition,1991.[3]UKarlMBerry*.TExp}'andedplainTKß'E-X,version2.6edi-Ution,2May-1994.AvqailableforanonymousftpUfromUUCT*ANinmacros/eplain/doc.[4]UMichel^GoGossens,~F*rankMittelbach,~andAlexan-UderSamarin.The1L雍QATKß'E-XComp}'anion.Addison-UW*esley,UU1994.[5]UBrianjW.Kernighan.PIC|alanguagefortypGe-Usettinggraphics.Softwar}'efPracticeandExperi-Uenc}'e,UU12(1):1{21,1982.[6]UDonaldKE.Knuth. TheTKß'E-Xb}'ook.Addison-UW*esley,UU1984.[7]UDonaldEE.Knuth.Computer]Mo}'dernT;ypefaces,UvolumeAsofComputers&T;yp}'esetting.6wAddison-UW*esley,UU1986.[8]ULeslieLampGort.8L雍QATKß'E-X|AK0Do}'cumentK_Prepara-UtionSystem.nAddison-W*esley,UU1986.[9]ULeslieLampGort.8L雍QATKß'E-X|AK0Do}'cumentK_Prepara-Ution#System.JAddison-W*esley,2ndxedition,1994.[10]UP*.lNauretal.$RepGortonthealgorithmiclan-UguageX)ALGOLW60.?Communic}'ationsoftheACM,U3:299{314,UU1960.g卍eK[11]T*omasRokicki.YDVIPS:JATKß'E-XDriver.Dis- tributeda withthedvipsprogramfoundonCT*ANarchives.FeK[12]Kristo er 3H.Rose.HowtotypGesetprettydia-gramarrowswithTU>'ExX|designdecisionsusedinXYs-pic. InJiuUrqZlatuxskqa, ;editor,Eur}'oTKß'E-X'92|Pr}'oceedingshtofthe7thEur}'opeanhtTKß'E-XCon-fer}'ence, pages183{190,Prague,Czechoslo-vqakia,SeptembGer"1992.CzechoslovqakTU>'ExXUsersGroup.eK[13]Kristo erH.Rose.TypGesettingdiagramswithXYs-pic:KUser'sB[manual. ,(InJiuUrqZlatuxskqa,edi-tor,QEur}'oTKß'E-X '92|Proceedingsofthe7thEu-r}'opeanpTKß'E-XConfer}'ence,6pages/273{292,Prague,Czechoslovqakia,[SeptembGer1992.CzechoslovakTU>'ExXUUUsersGroup.eK[14]Kristo er[H.Rose.{XY 6-picUser'sGuide.DIKU,UniversityofCopGenhagen,Universitetsparken1,DK{2100AKbGenhavn,E3.0edition,June1995.eK[15]Kristo erTH.RoseandRossR.MoGore. #XY_'-pica{completesourceswithTU>'ExXnicalcommentary*.notUUyetavqailable,June1995.eK[16]MichaelbD.Spivqak.TheJoyofTKß'E-X|AGourmetGuidetoT;yp}'esettingwiththeAU>'M S-TKß'E-XMacroPackage.'AmericanMathematicalSoGciety*,R[sec-ondUUedition,1990.eK[17]TUG)W*orking)GroupTWG-TDS.Adirectorystructure1forTU>'ExX lesversion0.98.`URL,May1995.AvqailablezwithURLaftp://jaspGer.ora.com/pub/twg-tds/. Index㍍7!,UU8 &,UU48',UU39(),UU8(0),UU8(0,0),UU71(1),UU8*,UU8,39,40,42,48,50,75**,UU8,40,50+,UU8,,UU8,40-,UU8,39.,UU8.xyd,UU15/,UU38,39,42//,UU8:,UU8,127r:::,UU8 r:;,UU8r:<,UU8,38{40r:<>,UU8r:<>(.5),UU39r:=,UU8,38{40r:>,UU8,38{40r:?,UU8,40r:@,UU8,39,41,49r:@!,UU41,49r:@!0,UU50r:@!=,UU50r:@!C,UU49r:@!R,UU49r:@(,UU10,41,42r:@),UU10r:@*,UU41,507=X[@+,UU10 =X[@-,UU10=X[@/,UU41,42=X[@1,UU50=X[@<,UU41,43=X[@=,UU10=X[@?,UU41,43=X[@@,UU10=X[@C,UU49=X[@H,UU50=X[@L,UU50=X[@M,UU50=X[@R,UU49=X[@W,UU50=X[@`,UU41=X[@i,UU10=X[[.],UU13LWeJ78O *tj??gw[=,UU12,14,30,33 /[P:,UU37[],UU13[c],UU14[d],UU14[dvips],UU5[l],UU14[o],UU13[r],UU14[textures],UU5[u],UU14\\,UU48^,UU39{41_,UU39{41`,UU39`s,UU66|,UU39,41|<<,UU75~,UU39^g0,UU6,8,411,UU412,UU413,UU4110,UU2711,UU2712,UU27a,UU8activeUUcharacters,4haddUUopi,12\aftergo?,UU76\afterPATH?,UU38\afterPOS?,UU15,16,39\ahook?,UU76alloGcation,UU5AU>'M S-L5ffA͉TU>'ExX,UU5,15AU>'M S-TU>'ExX,UU5\apit?,UU75\ar?,UU14,38,66array,UU51arrowUUhead,41arrowUUstem,41arrowUUtail,41\astop?,UU76\aTip?,UU76\atip?,UU76\aturn?,UU76banner,UU5\bhook?,UU76BNF,UU4hbGodyUUoftheoptioni,19\bpit?,UU75\bstop?,UU76\bTip?,UU76\btip?,UU76\bturn?,UU76gwr:C,UU8,10 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