; TeX output 1997.01.06:1839*tj??{DtGGcmr17X>YO-pic7tReferenceManqualaXQ cmr12Kristo erH.Rose_d!", cmsy10hkrisrose@brics.dki2 K cmsy8 eRossMoSore=hross@mpSce.mq.edu.aui2y&OtVVersion3.3 h1996/12/19i-! /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 [0 @] 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 6 index add exch 3 copy 10 3 roll moveto 1 index dup 5 1 roll 0 7 index arc4pop dup dup 4 1 roll 0 exch 6 index arc4pop 1 index dup 8 1 roll 0 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 M! /dotit{dup currentlinewidth 6 mul div round div /@ exch def [0 @] 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 /xysdfont{4096 add 32 div round 32 mul 4096 sub}def /xydots{xywidth 1 setlinecap [0 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 [0 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 [0 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 [0 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 [0 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 xystroke}bind def /o /circ load def! /circhar{gsave dup 3 gt{7 sub neg}if dup 3 eq{pop dup 2 sqrt -2 div mul}{dup 1 eq{pop dup 2 sqrt 2 div mul} {0 eq{dup}{0}ifelse}ifelse}ifelse 0 translate 3 1 roll circ grestore}bind def /c /circhar load def ! 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0.0 -25.19989 0.0 1.0 q}xy$?" {mark 12.0 -25.19989 6.0 -29.39987 0.0 -25.19989 1.0 1.0 q}xy$A" {mark 36.0 -25.19989 30.0 -29.39987 24.0 -25.19989 0.0 0.0 q}xy$A" {mark 36.0 -25.19989 30.0 -29.39987 24.0 -25.19989 0.0 1.0 q}xy$A" {mark 36.0 -25.19989 30.0 -29.39987 24.0 -25.19989 1.0 1.0 q}xy8|S:Thecurrentimplementationisprogrammedentirely:withiniN\standardTU>'ExXando> logo10METAF9ONT",i.e.,Kusing:TU>'ExX0Pmacros(no\special.08s)andwithfontsdesigned:usingJMETAF9ONT.OptionallyspGecial`drivers'makeit:pGossibleDtoproduceDVI leswith`specials'forextra:graphicsUUcapabilities,e.g.,using&- cmcsc10PostScript.^ٓRcmr71:ff^ J= "5-:Aacmr61L'- cmcsc10PostScriptXisaregisteredTJrademarkofAdob24 9.1 F*rames_...................24 9.2 BracketsU..................26 9.3 FilledUUregionsF...............26 9.4 F*ramingUUasob8jectmoGdi erM.......26 9.5 UsingUUcurvesforframes.........2610 MoreTTipsextensionj12611 LineTst9ylesextensionif2712 RotateTandScaleextensionIgF2813 ColourTextension} 3014 P9atternTandTileextensionK30gw:15;ImpQortTgraphicsextensionN32aU:16;P9ostScriptTbackendqZ34 :f;16.1 ?ChoGosingUUtheDVI-driverxE.........34;16.2 ?WhyUUusePostScript..........34:17;TPICTbac9kendk35:18;em-T eXTbac9kend~@o36"V:I`II Features.36:19;AllTfeatures(36:20;Dumm9yToptionr336:21;Arro9wTandPathfeatureYW36;21.1 ?Paths ...................37;21.2 ?Arrowsҍ...................39:22;Tw9o-cellTfeature41;22.1 ?TypGesettingUU2-cellsinDiagrams8$.....42;22.2 ?StandardUUOptionsͷ.............42;22.3 ?Nudging..................43;22.4 ?ExtraUUOptionsc...............43;22.5 ?2-cellsUUingeneralUQXY U-picturesr.......46:23;MatrixTfeatureK47;23.1 ;XYj?-matrices................47;23.2 ?NewUUcoGordinateformats'.........47;23.3 ?SpacingUUandrotation...........48;23.4 ?Entries|...................49:24;GraphTfeature k50:25;P9olygonTfeature52:26;LatticeTandw9ebfeatureZ}55:27;Circle,TEllipseandArcfeature856;27.1 ?F*ullUUCirclesH................56;27.2 ?Ellipses..................57;27.3 ?CircularUUandEllipticalArcs84.......57:28;KnotsTandLinksfeatureW60"V:IV DriversD564:29;SuppQortTforSpeci cDriv9ersD̖64;29.1 ?dvidrvUUdriverʍ...............64;29.2 ?DVIPSUUdriverT鍍...............65;29.3 ?DVITOPSUUdriver.............65;29.4 ?OzT*eXUUdriver...............65;29.5 ?OzT*eXUUv1.7driver............65;29.6 ?T*exturesUUdriver⍍..............66;29.7 ?T*exturesUUv1.6driver...........66LWj:2n<*tj??gw 29.8 XDVIUUdriverjG................66 D 29.9 CMacT*eXUUdriver.............6730 ExtraTfeaturesusingPostScriptdriv9ers D67 30.1 ColourЍ...................68 30.2 F*rames_...................68 30.3 Line-styles1l.................68 30.4 RotationsUUandscalingM..........68 30.5 PatternsUUandtiles.............6931 ExtraTfeaturesusingtpicdriv9ers--69 31.1 frames.Ѝ...................69"App`endicesbq69A Answ9ersTtoallexercisesZ69B V ersionT2Compatibilit9yY>73 B.1 UnsuppGortedUUincompatibilitiesC......73 B.2 ObsoleteUUkernelfeatures񍍑.........73 B.3 ObsoleteUUextensions&features1.....74 B.4 ObsoleteUUloading֍.............75 B.5 CompilingUUv2-diagrams..........75C CommonTErrors75ReferencesZ75Indexޕ76!$ListffofFigureso 1 hpGosiitions. ҍ................8 2 ExampleUUhplaceis1H.............10 3 hob8jectis..................12 4 hdecoriations................15 5 KernelUUlibraryhdiriectionals.......17 6 hciricles.x..................19 7 SyntaxUUforcurves.q@............22 8 PlainUUhframeis.c..............25 9 BracketUUhframeis.׍.............25 10 Rotations,UUscalingsand ipsO.......30 11 TheUU38standardMacintoshpatterns.8 ..32 12 impGortingUUagraphicforlabelling....33 13 hpathisFύ...................38 14 harrowis...................40 15 PastingUUdiagram.F.............43 16 htwoGcellisލ.................44 17 hgraphisǍ..................51 18 hknot-pieceiUUconstructionset......61 19 knotdNcrossingswithorientationsandla-  bGelUUpositions8}................62 20 knot,gjoins,4withorientations,labGelsand shifts ....................64 21 Extensionimplementationreplacedby useUUofhdriverispGecials...........68gw:Preface:Thisreferencemanualgivesconcisedescriptionsofthe :moGdules!of!XY -pic,Twrittenbytheindividualauthors.:PleasedirectanyTU>'ExXnicalquestionorsuggestionfor:improvement/directlytotheauthorofthecompGonent:inIquestion, preferablybyelectronicmailusingthe:indicatedzqaddress.CompletedoGcumentsandprinted:technicalUUdoGcumentationorsoftwareismostuseful.;The# rstpartdoGcumentstheXY 3#-pickernelwhichis:alwaysloaded.ZTheremainingpartsdescribGethethree:kindsIGofoptions:extensionshinpartIGIextendthekernel:graphiccapabilities,Ufe}'aturesinpartIGIIprovidespecial:input81syntaxforparticulardiagramtypGes,>anddrivers:in|partIVmakeitpGossibletoexploittheprintingca-:pabilities'suppGortedbyDVI driverprograms.N F*oreach:optionEitisindicatedhowitshouldbGeloaded.The:appGendices[containanswerstoalltheexercises,asum-:maryofthecompatibilitywithversion2,andlistsome:reasonsi\whyiXXY \-picmightsometimeshaltwithacryptic:TU>'ExXUUerror.ua:License.XY-picisfreesoftwareinthesensethatitis:avqailableUUunderthefollowinglicenseconditions:ups: SDict begin xyc endǍY2" {0.0 89.88193 -18.49307 -89.88191 18.49307 ov}xyUXY -pic:qGraphsUUandDiagramswithTU>'ExX ፍKc. s1991{1996 Kristo erUUH.Rose  hcEK 1994{1996 RossUUMoGoreA =TheXY-picpackqageisfreesoftware;?;youwritetotheF*reeSoftware'ExXnicaldoGcumentation[15 ]. 1]TheǨX#՟YY-picffimplementationThisޱsectionbrie ydiscussesthevqariousaspGectsofthepresent8XY m<-pichaÎvechosentoannotatethesyntaxwithbriefexplanationsof[the`action'asso'ExXUU[9]).;TherestofthissectiondescribGesthingsyoumust:considerKifyouneedtouseGXY *K-pictogetherwithother:macropackqages,styleoptions,orformats.Theless:yourenvironmentdeviatesfromplainTU>'ExXtheeasier:itrshouldbGe.EConsulttheTU>'ExXnicaldocumentation[15 ]:forƱtheexactrequirementsforotherde nitionstoco-:existUUwithUQXY U-pic.~*:Priv\racy:XY-pic willwarnabGoutcontrolsequencesit:rede nes|thus2youcanbGesurethattherearenocon-: ictsbGetweenXY-pic-de nedcontrolsequences,0those:ofyourformat,Oandothermacros,providedyouload6XYj:-picUUlastandgetnowarningmessageslikez Xy-pic?Warning:`dx:::q'?redefined.:InYgeneraltheYXY ٴ-pickernelwillcheckallcontrolse- :quencesitrede nesexc}'eptthat(1)generictempGoraries:likeW\nextarenotchecked,(2)prede nedfontiden-:ti ers(seex1.3)areassumedintentionallypreloaded,:andWU(3)someofthemoreexoticcontrolsequencenames:usedinternally(like@{-})areonlycheckedtobGedif-:ferentUUfrom\relax.:CategoryJFcoQdes: Unfortunately5uthesituationis:complicatedabythe exibilityofTU>'ExX'sinputformat.:The&culpritisthe`categorycoGde'conceptofTU>'ExX:(cf.X [6,Xp.37]):w6whenloadedXXY -picrequiresthecharac-:tersE\ \{}%EP(the rstisaspace)tohaveE\theirstandard:meaningandallotherprintablecharacterstohavethe:sameNmc}'ategoryaswhenHXY -picwillbeused|in particu-:larthismeansthat(1)youshouldsurroundtheload-:ingMofMXY ͹-picwith\makeatother...c\makeatletter:whenqloadingitfromwithinaL5ffA͉TU>'ExXpackqage,kandthat:(2)M XY -picMshouldbGeloadedafter lesthatchangecat-:egory}coGdeslikethegerman.stythatmakes" active.:Some1hstylesrequirethatyouresetthecatcoGdesforev-:erydiagram,e.g.,withfrench.styyoushouldusethe:commandUU\english0bGeforeUUevery\xymatrix2:.:However,֜itispGossibleto`repair'theproblemincase:anyofthecharacters#$&'+-.<=>`CSchangecategory:coGde::~ff2 ѰLl\xyresetcatcodeskNff2zwillUUloadthe lexyrecat.tex(version3.3)todoit.TIn9tegrationRwithstandardformats This”ishan-dledbythexyidioms.texD leandtheintegrationasaL5ffA͉TU>'ExXUU[9]packqagebyxy.sty"C.xyidioms.tex: This`included leprovidessomecom-monvidiomswhosede nitiondepGendsontheusedfor-mat#suchthatXY ;#-piccanuseprede neddimensionreg-isters9Netc.andyetstillbGeindependentoftheformatLWj:4*tj??gwunder`whichitisused.Thecurrentversion(3.3)han- dleswplainTU>'ExX(version2and3[6]),AU>'M S-TU>'EX(version2.0and2.1[16 ]),RYL5ffA͉TU>'ExX(version2.09[8]and2"[9]),AU>'M S-L5ffA͉TU>'ExX̳(version1.0,1.1[2],and1.2),andeplain(versionUU2.6[3])^3|s.)xy .st9y: IfyouuseL5ffA͉TU>'ExXthenthis lemakesitpGossi-bleStoloadSXY -picasa`packqage'usingtheL5ffA͉TU>'ExX2"|β[9]\usepackageUUcommand:ff2 ɍ+e\usepackageUU[Rhoptioni,?...] ?{xy}'ExX2" (Tgraphics9&ʲbundle:8thesewillautomaticallyinvokeanybackendextensionrequiredtobGestem-ulatetheL5ffA͉TU>'ExX2" bGehaviour(thismeansthat,Te.g.,[dvips]Dzand[textures]canbGeusedasoptionstothe\documentclassUUcommandwiththenormale ect). The_ lealsoworksasaL5ffA͉TU>'ExX2.09[8]`styleoption'althoughyouwillthenhavetoloadoptionswiththe\xyoption2:mechanismUUdescribGedinx7."ۍ1.2Logo,version,andmessages*LoadingPXY 3T-picTprintsabannercontainingtheversionandUauthorofthekernel;TsmallprogressmessagesareprintedXwheneachma8jordivisionofthekernelhasbGeenloaded.AnyoptionsloadedwillannouncethemselfinaUUsimilarfashion. IfnyourefertojXYOn-picinyourwrittentext(pleasedoD[ a(^ h)D[thenyoucanusethecommand\Xy-picDOtotypGe-setɌthe\XY -pic"logo.C/TheversionofthekernelistypGe-setby\xyversionandthereleasedateby\xydate(asfoundinthebanner).nBytheway*,MtheXY -picname[^4originates fromthefactthatthe rstversionwaslittlemoreHRthansuppGortfor(x;y[ٲ)coordinatesinacon g-urablexcoGordinatesystemwherethemainideawasthatall7opGerations/ couldbespeci edinamannerindepen-dent8oftheorientationofthecoGordinates.[pThisprop-erty[hasbGeenmaintainedexceptthatnowthepackqageallowsUUexplicitabsoluteorientationaswell. Messages'thatstartwith\Xy-pic%Warning"areindicationsthatsomethingneedsyourattention;an\Xy-pic"sError"+willstopTU>'ExXbGecause'XY s+-picdoesnotknowUUhowtoproGceed. Iff^ J= "5-:3LThey`v2'featureinÎtro "5-:4LNodescriptionofaTAEMXprogramiscompletewithoutanexplanationXofitsname.gw:1.3:FontsuT:The!XY w%-pic%kernelimplementationmakesitsdrawings :usingUU vespGeciallydesignedfonts:8S/̟L͉ffNfd͟ fffdF*ontCYy fff\VCharacters ffN&Default۟ ffffN͟ ff͟fd\xydashfontCYy ffodashes ffN&xydash10۟ ff͟ ff͟fd\xyatipfontCYy ffNQarrowUUtips,uppGerhalf ffN&xyatip10۟ ff͟ ff͟fd\xybtipfontCYy ffOarrowUUtips,lowerhalf ffN&xybtip10۟ ff͟ ff͟fd\xybsqlfontCYy ffMU7quarterUUcirclesfor ffN&xybsql10۟ ff͟ ffCYz ff\hoGoksUUandsquiggles ff۟ ff͟ ff͟fd\xycircfontCYy ffT&1=8UUcirclesegments ffN&xycirc10۟ ffffN:TheH rstfourcontainvqariationsofcharactersinalarge:numbGerofdirections,"thelastcontains1/8circleseg-:ments.Ɂ:Note: ThedefaultfontsarenotpartoftheXY-pic:kernelsp}'eci cationc:theyjustsetastandardforwhat:drawingcapabilitiesshouldatleastbGerequiredby:anFXYkJ-picJimplementation. 3Implementationsexploit-:ingecapabilititesofparticularoutputdevicesarein:use.tHencethefontsareonlyloadedbyXY -picifthe:controlxisequencenamesareunde ned|thisisusedto:preload:?thematdi erentsizesorpreventthemfrom:bGeingUUloadedatall.Ɂ:1.4:Allo`cationsuT:One nalthingthatyoumustbGeawareofisthatXY 5-:picalloGcatesasigni cantnumbGerofdimensionregis-:ters&andsomecounters,/token&registers,andbGoxregis-:ters,inordertorepresentthestateanddocomputa-:tions.rThe^currentkernelalloGcates4counters,+ 28di-:mensions,2XCbGoxregisters,4tokenregisters,1readchan-:nel,andP1writechannel(whenrunningunderL5ffA͉TU>'ExX;:some4YotherformatsuseslightlymorebGecausestan-:dardTgenerictempGorariesareused).Optionsmayal-:loGcategfurtherregisters(currentlyloadingeverything:loads6dimen-,3toks-,1bGox-,and9count-registers:inUUadditiontothekernelones). :27Pictureffbasics:TheBbasicconceptsinvolvedBwhenconstructing>XY^B-:picturesR+arepGositionsandob8jects,Randhowtheycom-:bineUUtoformthestateusedbythegraphicengine.;TheUUgeneralstructureofanUQXY U-pictureisasfollows:: & ff2 ).>\xyUUhpGosihdecori\endxỷff2Mbuilds&nabGoxwithan&jXY n-picture(L5ffA͉TU>'ExXusersmaysub-stituteUU\begin{xy};*...\end{xy}2U xwhereXyisthe TU>'ExX)dimensiondistancerightrandYb~thedistanceupfromQthezer}'o|DpositionJ0QoftheQXY -picture(0 hasco-ordinatesU<0mm,0mm>4A:,lUofUcourse). uThezeropGositionoftheXY 6-picturedeterminesthebGoxproducedbythe\xy...\endxycommandtogetherwiththefourparam-etersXmin ,(޵XmaxA̲,Ymin,andYmax_setsuchthatalltheob8jectsinthepictureare`contained'inthefollowingrectangle:;B ps: SDict begin xyc endǍ1" {0.0 71.16487 -34.1348 -36.95503 42.68724 ov}xyn O!cmsy7ޟ I0۟" {-21.37505 8.55157 dt}xy-)TU>'ExXUUreferencepGointlnnԟ" {23.99998 9.60002 dt}xynԟ" {-36.98839 0.0 l}xynԟ" {-1024 10 /xy AB}xyv2 wXmin׆" {71.13152 0.0 l}xy׆" {3072 10 /xy AB}xy9 wXmaxǍ۟"$" {0.0 -34.14313 l}xy۟k" {1024 10 /xy AB}xyܟ2ݵYminǍ۟R3" {0.0 42.67891 l}xy۟" {-3072 10 /xy AB}xyܟYmax2ʍwhere0"prin-ciple,Fe.g.,theBindicatedTU>'ExXreferencepGointhascoor-dinatesZ < Xmin ,0pt>,YwithinZ theZXY -picture.ThezeropGositiondoesnothavetobGecontainedinthepicture,but/Xmin2Xmax ^SYminYmaxqOalways/holds.QThepGossibleUUpositionsaredescribedindetailinx3. L When`an`XY -pictureisenteredinmathmo}'de!thenthereference. pGointbecomesthe\vcenter". instead,5i.e.,weuseQthepGoint<Xmin ,-\the\fontdimen22>sPasreferencepGoint.U2.2ObjectsThegsimplestformofputtingthingsintothepictureisto`drop'anobje}'ctatapGosition.bAnob8jectislikea TU>'ExXbGoxexceptthatithasageneralEdge#aroundits referencepGoint|inparticularthishastheextents(i.e.,itisalwayscontainedwithin)thedimensionsL,RDz,OU,andvDawayfromthereferencepGointineachoftheҴfourdirectionsleft, right,up,andҴdown.Ob8jectsarejBencoGdedinTU>'ExXboxesusingtheconventionthatthe(nTU>'ExXreferencepGointofanob8jectisatitsleftedge,thus shifted<< 'L,0pt>;fromthecenter|soaTU>'ExXbGoxmaybGesaidtobearectangularob8jectwithL}=0ptt.HereUUisanexample:'TC bps: SDict begin xyc endǍ32" {0.0 42.65114 -14.23187 -28.48038 22.75652 ov}xygnnԟ" {-28.48038 0.0 dt}xyz8 L" {42.65114 0.0 dt}xyu RǍ3Ο;\" {0.0 -14.23187 dt}xyS#DǍ3Ο>U" {0.0 22.75652 dt}xyp7U-)TU>'ExXUUreferencepGointlbBnԟ" {23.99998 9.60002 dt}xy#Theob8jectshownhasarectangleedgebutothersareavqailable,7eventhoughthekernelonlysuppGortsrectan-gle[andcircleedges.ItisalsopGossibletouseentireXY-picturesasob8jectswitharectangleedge,<0 YmaxN.Thecommandsforob8jectsarede-scribGedUUinx4.gw:2.3:Connections8:Besides`havingtheabilitytobGedroppedataposition :inj$apicture,Wallob8jectsmaybGeusedtoc}'onnect\the:two[currentob8jectsofthestate,i.e.,pandc.IF*ormost:ob8jectsthisisdoneby` lling'thestraightlinebGetween:thecenterswithasmanycopiesaswill tbGetweenthe:ob8jects:>la{8ps: SDict begin xyc end&8O \cmmi5p" {6.00002 0 360 o}xyc5." {0.0 9.00002 -4.00002 -9.00002 4.00002 ov}xy43" {155.89507 38.97359 dd}xyˍc3232)3232Vv3232323232323232Vg3232?J׍3232323232323232323232325׍32323232323232323232323232c3232)3232Vv3232323232323232Vg323284mT}E֠" {-8.53021 0.0 dt}xy]UݳL4֠" {5.69609 0.0 dt}xyIߟUR֠3" {0.0 -5.69609 dt}xy(v.D֠xD" {0.0 8.53021 dt}xyc#U53232y3232Vv3232323232323232Vg3232?c׍323232323232323232323232׍323232323232323232323232323232y3232Vv3232323232323232Vg3232z\ڏ" {-8.53021 0.0 dt}xyEGLڏ" {5.69609 0.0 dt}xy/EGRڏ񍍒GQ3" {0.0 -5.69609 dt}xyjƟ`Dڏ񍍒GQxD" {0.0 8.53021 dt}xysiUyL3232{>ɍ3232Vv3232323232323232Vg3232?yγ׍323232323232323232323232;՟׍32323232323232323232323232yL3232{>ɍ3232Vv3232323232323232Vg3232ԟL(z[" {-8.53021 0.0 dt}xy{34L;ԟ[" {5.69609 0.0 dt}xy4R[3" {0.0 -5.69609 dt}xy D[xD" {0.0 8.53021 dt}xyßU j*3232k3232Vv3232323232323232Vg3232?j׍323232323232323232323232x~%׍32323232323232323232323232j*3232k3232Vv3232323232323232Vg3232p$;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'ExXcommandswhichaddtopictures.:Mostsuchcommandsareprovidedbythevqarioususer:optionsJy(cf.xXx7)|onlyafewareprovidedwithinthe:kernelętofacilitateprogrammingofsuchoptions(and:userUUmacros)asdescribGedinx5.#:2.5:The&aX1"Yv-picstate:Finally0wesummarisetheuser-accessiblepartsofthe6XYj:-picture#stateoftwo#pGositionstogetherwiththelast:ob8jectassoGciatedwitheach:thepr}'evious!,KJp,isthe:pGositionx< uXpR,ǵYpR>withxtheob8jectLpR,Rp,Dp,Up,:EdgepR,andthecurr}'entز,c,isthepGosition< Xc, Yc>:withUUtheob8jectLc,Rc,Dc,Uc,Edgec. 7I;F*urthermore, XY-picMhasacon gurablec}'artesian:c}'oordinate#systemTdescribGedbyanoriginpGosition:<*7X+t}\cmti7originm,~Yoriginm>"qandttwob}'asezvectorsG<Xxbase,筵Yxbase>:and<سXybaseN,KYybaseN>accessedbytheusualnotationus-:ingUUparentheses:Zdf(cx,?y[);q= <*BXorigina+8xXxbase+yXybaseC,*BYorigina+8xYxbase+yYybaseC>:Thisisexplainedinfullwhenweshowhowtosetthe:baseUUinnote3dofx3. 7I;Finally typGesettingaconnectionwillsetupa\place-:mentxstate"forreferringtopGositionsontheconnection:thatXyisaccessedthroughaspGecial? positionconstruc-:tion;UUthisisalsodiscussedindetailinx3.;ThexkXY o-picxostate8ʲconsistsofalltheseparametersto-:gether.?TheyareinitialisedtozeroexceptforXxbasenȲ=:Yybasef=1mm.;The`edgesarenotdirectlyavqailablebutpGointsonthe:edges~maybGefoundusingthedi erenthcorneriforms:describGedUUinx3.LWj:6*tj??gw ItKispGossibletoinsertan`initial'pieceofhposi hdecori4atthestartofevery4XY -picturewiththedecla-ration~ff2 iI\everyxy={hhtextiUU}ff2ThiswillactasifthehtextiwastypGedliterallyrightaftereach\xycommand,*parsingtheactualcontentsasifitfollowsthis{thusitisrecommendedthathtextihasQtheformhpGosi,ʲsuchthatuserscancontinuewithhpGosiUUhdecori. 3LPositionsAԸhpGosiition/isaway/ofspecifyinglocationsaswellasdroppingob8jectsatthemanddecoratingthem|infactanyaspGectoftheXY t-picstatecanbechangedbyahpGosiͲbutmostwilljustchangethecoordinatesand/orshapGeUUofc. AllXpGossiblepositionsareshownin gure1withex-planatoryUUnotesbGelow.{Exercisea#1: WhichofthepGositions0 퀲,<0pt,0pt>4Cs,<0pt>?,(0,0)׹,andhe/0pt/ishedi erentfromtheothers?NotesuT3a.When}doingarithmeticwith+;and-thentheresultingxjcurrentob8jectinheritsthesizeofthehcoGordi,/i.e.,the&rightargument|thiswillbGezeroifUUthehcoGordiisahvectori.gExercise}O2: Howgdoyousetctoanob8jectthesame{sizeasthesaved{ob8ject"ob" butmoved<?X,ߵY8>x?^ 3b.UXSkewing{^using!qjustmeansthatthereferencepGointofcismovedwithaslittlechangetotheshapGeoftheob8jectaspossible,@i.e.,theedgeofcwill/remaininthesameloGcationexceptthatitwillgrowlargertoavoidmovingthereferencepGointoutsideUUc.ExerciseD3: What.doGesthehposi...!R-L>̲do?Bug:Theresultof!Sisalwaysarectanglecur-rently*.^ 3c.8A䖸hpGosic}'oversӲanotherifitisarectanglewithsizesucientlyqlargethattheotheris\underneath".The(. kopGeration(\extends"ahpositocover(anad-ditionalnone|thereferencepGointofcisnotmovedbuttheshapGeischangedtoarectanglesuchthattheUUentirepob8jectiscovered.Bug: non-rectangularob8jectsare rst\trans-lated"intoarectanglebyusingadiagonalthroughtheUUob8jectasthediagonaloftherectangle.gw:3d.?The2opGerations:and::settheb}'asePusedfor :hcoGordiinates5;havingtheform( u8x,?y[)ֲ.xThe: sop-:erationUwillset< ڵXoriginm, [Yoriginm>toUݵp,< Xxbase,:Yxbase>`toӳcroriginU,sIand< XybaseN,YybaseN>to:<*7UYxbase,ʵXxbase>(thisensuresthatitisausual:squareJ coGordinatesystem).nThe::operationmay:thenbGeusedafterwardstomakenonsqarebasesby:just.settingyb}'asetocporigin.RHere.aretwo.ex-:amples: rstly0;<1cm,0cm>:FsetsthecoGordinate:system+5ips: 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\,j cmti9origin=xbase%mybase7R߸@(1,1)p-" {-28.45274 0.0 dt}xyǍ:" {0.0 -28.45274 dt}xy :whileUU<1cm,.5cm>;<2cm,1.5cm>:<1cm,1cm>::de-: nesFp'jps: SDict begin xyc endn" {-28.45276 28.45276 dd}xy͟" {-2048 10 /xy AB}xy- ybase jo cmr9bAefore I-ߤN cmtt9::ȍWR$" {28.45276 28.45276 l}xyW{" {4096 10 /xy AB}xyȍ;%" {0.0 14.22638 l}xy;%-" {-3072 10 /xy AB}xyMj>%origin썍Zxbasem0LybaseS9]ǁ(1,1)ȍ;%" {-28.45276 -28.45276 dt}xyȍWR$" {0.0 -14.22638 dt}xyԇ:where#ineachcasetheisat0 ,thebasevectors:haveUUbGeendrawnandtheisat(1,1)F.F؍:WhenworkingwithcartesiancoGordinatesthese:threeUUspGecialhfactorisareparticularlyuseful: H:ff2 YR\halfroottwoR`r0:70710678 K1K&fes2 )PpHPfeE2 \partroottwoR`r0:2928932218 l1l&fes2PpPfeE2\halfrootthreeR`r0:86602540 K1K&fes2 )PpHPfeE3Fڍ:ff2 7:More(canbGede nedusing\defLD(or\newcommand :inUUL5ffA͉TU>'ExX).:3e.#Ananglef; ZinXY%-picisthesameasthecoGordi-:natewpair( bZcosp z,sin z),where /mustbGeaninte-:ger?interpretedasanumbGerofdegrees.Thusthe:hvectori֑a(0)is֑thesameas(1,0)!anda(90)as:(0,1)*+,UUetc.:3f.:T*odr}'op@anhob8jectiatcwith*~meanstoactu-:allyY\physicallytypGesetitinthepicturewithref-:erenceXpGositionatc|howthisisdonedependson:theθhob8jectiinquestionandisdescribGedindetail:in3޸x4. bTheintuitionwithadropisthatittypGe-:setsXsomethingat<UXc, R޵Yc> 6andsetstheedgeofc:accordingly*.:3g.YThe>7c}'onnect1opGeration**hwill rstcomputeanum-:bGer zofinternalparametersdescribingthedirection:fromIptocandthentypGesetsaconnection lled:withXxcopiesofthehob8jectiasillustratedinx2.3.:The7exactdetailsoftheconnectiondepGendonthe:actuala\hob8jectiandaredescribGedingeneralinx4.:The ffffd TQղSyntax\ActionX-ffd m͍QոhpGosiCI]!d 3hcoGordi\c hcoGordiiJ\jd 3hpGosiUU+hcoordi\c hpGosi5+8hcoGordi"1ɟ^3aJ\jd 3hpGosiUU-hcoordi\c hpGosi58hcoGordi"1ɟ^3azJ\jd 3hpGosiUU!qǸhcoordi\c hpGosithenUUskew^3b ߵcbyhcoGordiJ\jd 3hpGosiUU.qǸhcoordi\c hpGosibutUUalsocovering^3c øhcoGordiJ\jd 3hpGosiUU,hcoordi\c hpGosithenUUc hcoGordiJ\jd 3hpGosiUU;hcoordi\c hpGosiUU,UUswappandc,c hcoGordiJ\jd 3hpGosiUU:qǸhcoordi\c hpGosiUU,UUsetbase^3d C,c hcoGordiJ\jd 3hpGosiUU::qǸhcoordi\c hpGosiUU,UUyb}'aseP c8origin',UUc hcoGordiJ\jd 3hpGosiUU*hob8jecti\c hpGosiUU,UUdrop^3f Hhob8jectiJ\jd 3hpGosiUU**hob8jecti\c hpGosiUU,UUconnect^3g Qusinghob8jectiJ\jd 3hpGosiUU?qǸhplacei\c hpGosiUU,UUc hplacei^3hJ\jd 3hpGosiUU@hstackingi\c hpGosiUU,UUdohstackingi^3oJ\jd 3hpGosiUU=hsavingi\c hpGosiUU,UUdohsavingi^3pQոhcoGordiCI]!d 3hvectori\hpGosiUUishvectoriwithzerosize J\jd 3hemptyijqc\reuseUUlastc(donothing)J\jd 3p\pJ\jd 3xjqy\axisUUintersection^3k Wwith~fe [۟gpciJ\jd 3shdigitijqs{khnumbGeri}\stack^3o QpGositionUUhdigitiorhnumbGeribelowthetopJ\jd 3"i`0hidi"\restoreUUwhatwassaved^3p ߲ashidiearlierJ\jd 3{lhpGosiUUhdecori}\theUUcresultingfrominterpretingthegroup^3lQոhvectoriCI]!d 30\zero J\jd 3\absoluteJ\jd 3\absoluteUUwithequaldimensionsJ\jd 3(lhfactoriUU, ꧸hfactoriUU)\inUUcurrentbase^3diJ\jd 3aUU( ꧸hnumbGeriUU)\angleUUincurrentbase^3eJ\jd 3hcorneri\fromUUreferencepGointtohcorneriofcJ\jd 3hcorneriUU( ꧸hfactoriUU)\TheUUhcornerimultipliedwithhfactoriJ\jd 3/lhdirectioniUUhdimeni/\vectorUUhdimeniinhdirectioni^3miQոhcorneriCI]!d 3LUUj qRUUjDUUjU\o set^3n ߲toUUleft,right,down,upsideJ\jd 3CLUUj qCRUUjCDUUjCUUUjC\o set^3n ߲toUUcenterofside,truecenterJ\jd 3LDUUj qRDUUjLUUUjRU\o set^3n ߲toUUactualleft/down,...cornerJ\jd 3EUUj qP\o set^3n ߲toUUnearest/propGortionaledgepointtopzQոhplaceiCI]!d 3<UUhplaceijq>hplacei\shave^3h (0)/(1)UUtoedgeofp/c,fڧ 0=1J\jd 3(lhfactoriUU) ꧸hplacei\fڧ hfactorizJ\jd 3hslidei\pickUUplace^3h ߲andapplyhslidei@4J\jd 3!q{ ĸhpGosi}Rhslidei\intercept^3j HwithUUlinesetupbyhpGosiandapplyhslidei@4QhslideiCI]!d 3/lhdimeniUU/\slide^3i hdimeniUUfurtheralongconnectionJ\jd 3hemptyi\noUUslideffdRFigureUU1:qǸhpGosiitions.LWj:8 X*tj??gw3h.f`Using? cwill\pickaplace"alongthemostrecent connection2@typGesetwith**:. Whatexactlythismeans@isdeterminedbytheob8jectthatwasusedfortheconnectionandbythemoGdi ersdescribedinUUgeneraltermshere.}썑The\shave"moGdi ersinahplacei,< oand>,changethehdefaulthfactori,턵f,andhhowitisused,by`moving'0IthepGositionsthatcorrespondto(0) and(1)(respGectively):Theseareinitiallysetequalto #pandc,wVbutshavingwillmovethemtothepGoint@oontheedgeofpandcwheretheconnection\leaves/enters"'ExX\jot(usuallyequalto3pt?~)furthertowardstheotherenddoftheconnection(andpastit).FinallythepickiactionVcwillpickthepGositionlocatedthefrac-tion}f/oftheway}from(0)7to(1)wherefϲ= @0.5ifUUitwasnotset(by<R,>,orexplicitly).AlllthisisprobablybGestillustratedwithsomeex-amples:.:Q(0,0)*=0{+}="+"?;Q(2,1)*=0{\times}="*"?**@{.},Q(1,0)*+{A}?;(2,2)*+{B}**@{-}Q?!{"+";"*"}?*{\bullet}\endxy$willUUtypGesetD|O,ps: SDict begin xyc endq!+5@ݸ8ϟ-" {56.9055 28.45279 dt}xy pA4ܲ$BǍ5y͂" {22.03607 44.0722 l}xy#tZ3k.DThepGositionsdenotedbytheaxisinterse}'ctionhcoGordiinatesٴxandyarethepointswheretheline>ff^ J= "5-:5LThe'bracescanboğ_y?BłǍAŸV" {-7.11319 -14.22638 dt}xy+֟" {-21.33954 21.33957 dt}xy>#:ExerciseM4: Givenprede nedpGointsA,sBq,C,:andID-(storedasob8jects"A" ,K"B" {,K"C",KandI"D"),:writej0ahcoGordispeci cationthatwillreturnthe:pGointwherethelines}fe:AB2and}fek`CDuXcross(thepoint:markedUUwithalargecirclehere):?Bps: SDict begin xyc end " {1.00002 0 360 o}xyƵA!j-" {1.00002 0 360 o}xyT~-B2} ޯ" {1.00002 0 360 o}xy5} ޮC8-ϟ@;" {1.00002 0 360 o}xy;-ϟ@:D)R" {3.00002 0 360 o}xyǍ0" {41.8074 60.08694 dt}xyǍ$X" {-25.19963 50.3934 dt}xyKR:3l.:AhpGosihdecorigr}'ouped*in{},-braces^6 )isinter-:pretedjinaloGcalscopeinthesensethatanypand:b}'ase ȲbuiltLmwithinitareforgottenafterwards,N5leav-:ingonlythecastheresultofthehcoGordi.Note::Onlypandb}'ase'ExX:group.\:Exercise S5: Whate ectisachievedbyusingthe:hcoGordiinateUU\{;}"?:3m.TheV{vector/xZ/,VwhereZ isahdimenision,isthe:same]asthevector<ZaIJcoso z,IwZaIJsinS z>ewhere ghisthe:angleofthelastdirectionsetbyaconnection(i.e.,:withUU** O)UUorsubsequentplacement(??)pGosition.[:ItispGossibletogiveahdirectioniasdescribedin:the(nextsection( gure3,note4linparticular):thatawillthenbGeusedtosetthevqalueof z.Itis:alsopGossibletoomitthehdimeniinwhichcaseit:isUUsettoadefaultvqalueof.5pcUI.:3n.?Ahcorneri8isano setfromthecurrent< 5Xc, R޵Yc>:pGositionisa CKsquareG9text!ƍQ]Z2" {0.0 20.00005 -20.00005 -20.00005 20.00005 ov}xy>]X33(e*+(33=]W" {239.99994 -97.81248 dd}xy?y˟!Ƹ]b?(0)@z" {21.6529 13.01283 l}xy@z" {3686 10 /xy AB}xyMy˞!Ƹ#]b?(1)Nz" {21.6529 13.01283 l}xyNz" {3686 10 /xy AB}xyy˟!ƸY۾:?zȞ" {21.6529 13.01283 l}xyzȞ" {3686 10 /xy AB}xyy!/y?(.7)Dޞi" {21.6529 13.01283 l}xyDޞi" {3686 10 /xy AB}xyyʟŸdo?<>(.5)Ǎ]Yw" {0.0 -11.10736 l}xy]Y>" {1024 10 /xy AB}xyyʟŸ]\o?<>(.2)(.5)ȶ+" {-21.65335 -13.01332 l}xyȶ+" {-410 10 /xy AB}xyIy̟1Ƹf]^?@+" {-21.65335 -13.01332 l}xy@+" {-410 10 /xy AB}xy1#'毟?>>>>Ǎ5" {0.0 -11.10736 l}xy5:n" {1024 10 /xy AB}xyyک]+T[?<>(.7)-" {-21.65335 -13.01332 l}xy-" {-410 10 /xy AB}xyyq.Z?>(.7)Ǎ]%kb" {0.0 -11.10736 l}xy]% )" {1024 10 /xy AB}xy,⍍J2FigureUU2:qExamplehplaceisP/)Thex`edgepGoint'E liesontheedgealongtheline from\ptothecentreoftheob8ject,pincontrasttothe`propGortional'XpointP ;whichisalsoapGointontheedgebutcomputedinsuchawaythattheob8jectloGoksUUasmuchUU`awayfromp'aspGossible.0Finally*,a=following( :f) ɲsuxwillmultiplytheo -setUUvectorbythehfactorif.)6Exercise(6: Whatisthedi erencebGetweenthehpGosiitionsUUc?<jandUUc+EL?ExerciseT7: WhatUUdoGesthistypeset?N8\xy?*=<3cm,1cm>\txt{Box}*\frm{-}Q!U!R(.5)?*\frm{..}*{\bullet}\endxyhHintز:*\frmisde nedbytheframeextensionandjusttypGesetsaframeofthekindindicatedbytheargument.0Bug:糲CurrentlyKonlythesingle-lettercorners(L,R,2D,U,C,E,andP)willworkforanyshapGe|theotherssilentlyassumethattheshapGeisrectangu-lar.`3o.'The7stackK\isaspGecialconstructionusefulforstor-ing,asequenceofhpGosiitionsthatareaccessibleusingthespGecialhcoordiinatess Hn,4wherenisei-therasingledigitorapGositiveintegerin{}+s:os0is"alwaysthe`top'elementofthestackandifthestackԪhasdepthdthenthe`bGottom'elementofthestackhasnumbGers{dR1}?.ThestackissaidtobGe|`empty'whenthedepthis0andthenitisanerror toaccessanyofthesInor`pGop'whichmeansremoveԗthetopelement,gshiftingwhatisins1)(tos0 ,s2Q[toܞs1 \,etc.ISimilarly*,`pushܞc'meanstoshifts0Ѳtos1 ɲ,etc.,andtheninsertthecasthenews0./):TheUUstackismanipulatedasfollows: y:ff2 9ōN@hstackingiEPActionc:ff2 A.N@+hcoGordiEPpushUUhcoGordiiN@-hcoGordiEPc hcoGordi&VthenUUpGop N@=hcoGordiEPloadUUstackwithhcoGordiN@@hcoGordiEPdoUUhcoGordi&forUUc stackN@iEPinitialiseN@(EPenterUUnewframeN@)EPleaveUUcurrentframec:ff2:T*o`loadstack',meanstoloadtheentirestackwith:the;#pGositionssetbyhcoordiwithinwhich, Cmeans:`pushUUc'.a:T*o,`dohcoGordiforallstackelements'meanstoset:citoeachelementofthestackinturn,fromthe:bGottomandup,andforeachinterpretthehcoGordi.:Thusthe rstinterpretationhascsettothebGot-:tom&elementofthestackandthelasthascset:tos0-۲.{kIfthestackisempty*,thehcoGordiisnot:interpretedUUatall.:ThesetwoopGerationscanbecombinedtorepeata:particularUUhcoGordiforseveralpoints,likethis:N8:\xy*7@={(0,-10),(10,3),(20,-5)}?@@{*{P}}:\endxy!:willUUtypGesetCӍEgps: SDict begin xyc endOPsޟHP8缟F`P.:Finally*,0the'RstackcanbGeforciblyclearedusing@i L,:however,4thiskisrarelyneededbGecauseof@( Je,which:savesthestackasitis,andthenclearsit,such:whenXithasbGeenused(andisempty),JYand@)is:issued,then itisrestoredasitwasatthetimeof:theUU@( O.LW910 *tj??gwExerciseW8: HowXwouldyouchangetheexample abGoveUUtoconnectthepointsasshownbGelow?#S ps: SDict begin xyc end" {-56.90521 -14.2263 l}xyǍsޟv" {28.4526 36.98839 l}xy8缟 ۶" {28.4526 -22.76208 l}xy%`3p.f`Itj?ispGossibletode nenewhcoordiinatesontheform" hidi"bysavingthecurrentcusingthe...=" *hidi" OhpGosiitionrRform. ȾSubsequentusesof"Qhidi" willthenreestablishthecatthetimeoftheUUsaving.J[Usinga"۸hidi"thatwasneverde nedisanerror,however,osaving7rintoanamethatwaspreviouslyde nedڳjustreplacesthede nitionwithoutwarn-ing,Xi.e.,"Uhidi"alwaysreferstothelastthingsavedwithUUthathidi.However,many}otherthingscanbGe`saved':in}gen-eralUU@RhsavingiUUhaseitheroftheforms 0ff2 ܪ@:"!hidi"V"[hidi"'restores*currentb}'aseܪ@hcoGordi"?hidi"V"[hidi"RreinterpretsUUhcoGordiܪ@@"!hidi"V@="fqhidi"greloads jcurrentVstackff2[TheM rstformde nes" hidi"toMbGeamacrothatrestoresUUthecurrentb}'ase[.The\seconddoGesnotdependonthestateatthetimeIofde nitionatall;itisamacrode nition.Y*ouVcanpassparameterstosuchamacrobylettingitusecoGordinatesnamed"1"Mв,"2"[,etc.,andthenuse=="1"1,$="2"$,$etc.,just=bGeforeeveryuseofitto7settheactualvqaluesofthese.nNote:qitisnotpGossible:touseahcoordioftheform"zhidi"directly:writeUUitas{" Ohidi"} .褍ExerciseW9: W*rite^ amacro"dbl" todoublethesizeofthecurrentcob8ject,e.g.,changingitfromtheUUdottedtothedashedoutlineinthis gure:.ECps: SDict begin xyc end'㑞!+Lq3232$3232K(32323232323232323232323232323232323232323232323232323232323232323232K3232̍^㋶3232O3232323232323232323232323232323232323232323232323232A㋶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=Zxغ" {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}xyغWs" {1024 F d}xyWA ;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'ΦThe nalformde nesaspGecialkindofmacrothatshouldonlybGeusedafterthe@=9вstackoperation:the|xentirecurrentstackissavedsuchthatthestackopGerationUU@="Lhidi"RwillUUreloadit.Note: TherezisnodistinctionbGetweenzthe`namespaces'$ofhidisusedforsaved$coGordinatesandotherUUthings.gw:47Obfjectsэ:Ob8jects xaretheentitiesthataremanipulatedwiththe :*]and&**FhpGosi&operationsabovetoactuallygetsome:outputzinvXYKz-pictures.7AsforhpGosiitionstheopera-:tionsf*areinterpretedstrictlyfromlefttoright,_how-:ever,theHactualob8jectisbuiltb}'eforeYallHthehmoGdi eris:takeme ect.Thesyntaxofob8jectsisgivenin gure3:withreferencestothenotesbGelow.Remark:6\Itis:never㘲allowed toincludebraces{} insidehmoGdi eris!:InҘcaseyouwishtodosomethingthatrequires{ ...}:thencheckinthismanualwhetheryoucanuse(* ...*):instead.+If notthenyouwillhavetouseadi erentcon-:struction!h:Notes :4a.YAnںhob8jectiisbuiltusing\object)box>5V{CuShtexti}?.:\object%box0qisUUinitiallyde nedasN8:\def\objectbox#1{%*7\hbox{$\objectstyle{#1}$}}:\let\objectstyle=\displaystyleg:butA\maybGerede nedbyoptionsortheuser.:The\htextishouldthusbGeinthemoderequired:by6the\objectboxcommand|withthedefault:\objectbox2Qshownj5abGoveitshouldbGeinmath:moGde.J^:4b.?Anhob8jectibuiltfromaTU>'ExXbGoxwithdimen-:sionswв(h+d)willhaveLc yR=fqRc=wD=2,:Uc1 =)Dc=(h+d)=2,Vthus#-initiallybGeequipped:withgMtheadjustment!CN(seenote4f)."pInparticular::in?ordertogetthereferencepGointonthe(center:of)WthebaselineoftheoriginalhTU>'ExXbGoxithen:youshouldusethehmoGdi eri! ;;O1togettherefer-:encepGointidenticaltotheTU>'ExXreferencepGointuse:theUUmoGdi er!!LL./:TU>'ExXnicalremark: xAnymacrothatexpandsto:somethinghxthatstartswithahbGoximaybGeused:asUUahTU>'ExXbGoxihere.:4c.#T*akes`anob8jectandconstructsit,cbuildingabGox;:itisthenproGcessedaccordingtothepreceeding:moGdi ers.;pThisformmakesitpossibletouseany:hob8jectiѲasaTU>'ExXbGox(evenoutsideofXY =-pictures):bGecauseUUa nishedob8jectisalwaysUUalsoabox.:4d.?Severalhob8jectiscanbGecombinedintoasingleob-:jectusingthespGecialcommand\compositewitha:list23ofthedesiredob8jectsseparatedwith*r0sasthe:argument.zThe4resultingbGox(andob8ject)isthe:leastUUrectangleenclosingalltheincludedob8jects.:4e.#T*ake^anentire^XY -pictureandwrapitupasabGox:as8describGedinx2.1."qMakesnestingof4XY 8-pictures:pGossible:̱theinnerpicturewillhaveitsownzeroLW911 ֠*tj??X ffffd T SyntaxĆActionX-ffd fd hob8jectiE%K!^GhmoGdi eriUUhob8jectiĆapplyUUhmoGdi eritohob8jecti LEj^Ghob8jectbGoxiĆbuildUUhob8jectbGoxithenapplyitshmodi erisi hob8jectbGoxiE%K!^G{gahtextiUU}ĆbuildUUdefault^4a Qob8jectLEҸj^GhlibraryUUob8jectijq@\nhdiriĆuseUUhlibraryob8jectiorhdiriectional(seex6)zLEҸj^GhTU>'ExXUUbGoxi{ ꧸htexti}Ćbuild'ExXbGoxiĆcommand,UUe.g.,\hbox_LEҸj^G\objectUUhob8jectiĆwrapUUupthehob8jectiasa nishedobjectbGox^4cLEҸj^G\compositeUU{ ꧸hcompGositeiUU}ĆbuildUUcompGositeob8jectbox^4diLEҸj^G\xyboxUU{ ꧸hpGosiUUhdecori}ĆpackqageUUentireUQXY U-pictureasob8ject^4ez hmoGdi eriE%K!^G!gahvectoriĆhob8jectiUUhasitsreferencepGointshifted^4f HbyhvectoriLEj^G!Ćhob8jectiUUhastheoriginalreferencepGointreinstatedLEҸj^GhaddUUopihsizeiĆchangeUUhob8jectisize^4gzLEҸj^GhjqiĆhob8jectiUUishidden^4h C,invisible^4i@4LEҸj^G[gahshapGeiUU]Ćhob8jectiUUisgiventhespGeci edhshapei^4jLEҸj^G[=UUhshapGei]Ćde neUUhshapGei^4k Wtoreestablishcurrentob8jectstyle LEҸj^GhdirectioniĆsetUUcurrentdirectionforthishob8jecti haddUUopiE%K!^G+jjt(-\j#=oʸj+= 5j}-=Ćgrow,UUshrink,set,growto,shrinktoi hsizeiE%K!^GhemptyiĆdefaultUUsize^4gLEҸj^GhvectoriĆsizeUUassidesofrectanglecoveringUUthehvectoriz hdirectioniE%K!^GhdiagiĆhdiagionalUUdirection^4lzLEҸj^GvUUhvectoriĆdirection^4l ofUUhvectoriLEj^Gq{RhpGosiUUhdecori}Ćdirection^4l fromUUptocafterhpGosihdecoriLEj^GhdirectioniUU:qǸhvectoriĆvectorUUrelativetohdirectioni^4mLEҸj^GhdirectioniUU_?jhdirectioniUU^Ć90^9cloGckwise/anticlockwiseUUtohdirectioni^4m hdiagiE%K!^GhemptyiĆdefaultUUdiagonal^4lLEҸj^Glgajm~ rv]j|/d!juĆleft,UUright,down,updiagonal^4lLEҸj^GldljrrdWjlujruĆleft/down,UU...diagonal^4l hcompGositeiE%K!^Ghob8jectiĆ rstUUob8jectisrequiredLEҸj^GhcompGositeiUU* ꧸hob8jectiĆaddUUhob8jectitocompGositeobjectbGox^4dffd  PofthewidthandheightofNarectangle.o^WhengivenasahvectorithesearejustcthevectorcoGordinates,i.e.,thechvectoristartsinlthelowerlleftcornerandendsintheuppGerrightcorner.]The\pGossiblehaddopierationsthatcanbepGerformedUUaredescribedinthefollowingtable.1B@,L͉fffd͟ ff͟fdhaddUUopi/` ff4#descriptionޟ ffff͟ ff`fd+/` ff4#growޟ ff ͟ ff`fd-/` ff4#shrinkޟ ff͟ ff`fd=/` ff4#setUUtoޟ ff͟ ffpbfd+=/` ff4#growUUtoatleastޟ ff͟ ffpbfd-=/` ff4#shrinkUUtoatmostޟ ffff1yIn\eachcasethehvectorimaybGeomittedwhichinvokes"the\defaultsize"fortheparticularhaddopi:ğL͉fffd͟ ff͟fdhaddUUopi/` ff4#defaultR ffff͟ ff`fd+/` ff4#+g k ff ͟ ff`fd-/` ff4#-g k ff͟ ff`fd=/` ff4#=R ff͟ ffpbfd+=/` ff4#+= ʟ ff͟ ffpbfd-=/` ff4#-=  ffff1B@TheLjdefaultsforthe rstthreearesetwiththecommandsFff2 č \objectmarginUUhaddopi{Rhdimeni} \objectwidthUUhaddopi{Rhdimeni} \objectheightUUhaddopi{Rhdimeni}qbff2where{haddopiisinterpretedinthesamewayasabGove.q`The{defaultsfor+=u/-=are{suchthattheresult-ingob8jectwillbGethesmallestcontaining/largestcontainedUUsquare.ƍExercise 11: How aretheob8jectstypGesetbythehpGosiitionsy\*+UR{\sum}4"and\*+DL{\sum}"en-larged?Bug:E;Currently>changingthesizeofacircularob-jectisbuggy|itischangedasifitisarectangleandqthenthechangetotheR8parametera ectsthecircle.XjThis =shouldbGe xedprobablybyageneral-isationfoftheo ɲshapGetobeovqalsorellipseswithhorizontal/verticalUUaxes.gw:4h.?AhiddenPob8jectwillbGetypesetbuthiddenfrom 6XYj:-picinthatitwon'ta ectthesizeoftheentire:pictureUUasdiscussedinx2.1.%:4i.:AninvisibleOob8jectwillbGetreatedcompletelynor-:mal5exceptthatitwon'tbGetypGeset,i.e.,XY B-picwill:bGehaveUUasifitwas.:4j.:Settingtheshap}'e\޲ofanob8jectforcestheshapGeof:itscedgetobGeasindicated.Thekernelprovides:threeƨshapGesthatchangetheedge,"namely[.],:[],UUand[o],correspGondingtotheoutlines%⊍ %ps: SDict begin xyc endaǷe,(-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}xyaFUyNIJ,UUandps: SDict begin xyc endaǷ" {20.00002 0 360 o}xy" {-20.00002 0.0 dt}xyAǞ L(" {20.00002 0.0 dt}xyP RǍ" {0.0 -20.00002 dt}xy  DǍ" {0.0 20.00002 dt}xy棟 U&&:whereIthedenotesthepGointofthereferenceposi-:tionintheob8ject(the rstisapGoint).\PExtensions:can5providemoreshapGes,Hhowever,all5shapGesset:theUUextentdimensionsL,RDz,DG,andU.:ThedefaultshapGeforob8jectsis[]andforplain:coGordinatesUUitis[.].:F*urthermore].thehshapGeis[r],_$[l],[u],and].[d],:are,de nedforconvenience,toadjusttheob8jectto:theMindicatedsidebysettingthereferencepGoint:suchythatthereferencepGointisthesamedis-:tance6afromtheoppGositeoftheindicatededge:andpGointattheinps: SDict begin xyc endjWideUUtextǍ." {0.0 40.4173 -3.47221 -3.47168 3.47221 ov}xy!Ǹ4߲buttheob8ject:[d]\hbox{Wide?text}`MhasLreferencepGointatthe:*inps: SDict begin xyc endWideUUtextǍ0" {0.0 21.94449 -3.47221 -21.94449 3.47221 ov}xy;!Ǹ0}.@GFinally*,_[c]putsthereference:pGointUUatthecenter.:Note:ExtensionszcanaddnewhshapGeiob8ject:hmoGdi eris2@whicharethencalledhstyleis.These:will7alwaysbGeeitheroftheform[ whkeywordi]or:[*7hcharacteri hargumenti]?.Someofthesehstyleis:doUUotherthingsthansettheedgeoftheob8ject.%:4k.vWhile"typGesettinganob8ject,someoftheprop-:ertiesareconsideredpartofthe`currentob8ject:style'.>;Initiallythismeansnothingbutsomeofthe:hstyleis de nedbyextensionshavethisstatus,+e.g.,:coloursK[red]<,[blue]&say*,usingKthexycolor+ex-:tension,or~vqaryingthewidthoflinesusingxyline"l.:SuchstylesareproGcessedleft-to-rightز;forexample,*[red][green][=NEW][blue]{A}:willtypGesetablueA Nandde ne[NEW]"Ntosetthe :colour9_togreen(allprovidedthatxycolor)2hasbGeen:loaded,UUofcourse).LW913A*tj??gwSa9vingcstyles: OncespGeci edforanhob8jecti, thecollectionofhstyleiscanbGeassignedaname,using[=hwordi]?.Then[ Vhwordi]bGecomesanewhstylei,}suitable$forusewiththesameorotherhob8jectsis.CUseʲasinglehwordibuiltfromordinaryletters.$If[hwordi]alreadyhadmeaningthenewde nition'willstillbGeimposed,\ZbutthefollowingtypGeUUofwarningwillbGeissued:`~Xy-pic?Warning:Redefiningstyle[hwordiԶU]ThexlatterwarningwillappGearifthede nitionoc- curswithinan\xymatrix.wThisispGerfectlynor-mal,e7bGeingb aconsequenceofthewayb thatthema-trixBcoGdeishandled.:$SimilarlythemessagemayappGear'severaltimesifthestylede nitionismadewithinUUan\ar.Thefollowingillustrateshowtoavoidthesemes-sagesMbyde ningthestylewithouttypGesettingany-thing.N8Q\setbox0=\hbox{% \xy\drop[OrangeRed][=A]{}\endxy}.QNote1:[The)currentcolourisregardedaspartoftheUUstyleforthispurpGose.NoteP2:Such~namingsareglobalinscopGe.CTheyareƽintendedtoallowaconsistentstyletobGeeasilymaintainedpbGetweenvqariouspicturesanddiagramswithinUUthesamedoGcument.If #thesamehstyleiisintendedforseveralhob8jectisoGccurringinsuccession,/the[ |P*]hmodi ericanbGe-usedonthelaterhob8jectis.PThisonlyworkswhenC[| *]precedesCanyotherhstyleimoGdi ers;IitisloGcalinscope,&recoveringthelasthstyleisusedatUUthesamelevelofTU>'ExXgrouping.24l.SettingthecurrentdirectionissimplypretendingforthetypGesettingoftheob8ject(andthefollowinghmoGdi eris)UUthatsomeconnectionsetit.ItUUisparticularlyeasytosethdiagionaldirections:DeӍ9bps: SDict begin xyc end6" {12.00002 0 360 o}xy"dlG"=ldǍ8ڟ" {-19.40031 -19.40031 l}xy8ڟ~" {0 10 /xy AB}xy3{0dǍ6)" {0.0 -29.94443 l}xy6'" {1024 10 /xy AB}xyF"drT("=rdQ̟~" {19.40623 -19.40031 l}xyQ̟~" {2048 10 /xy AB}xyc{r`{" {30.375 0.0 l}xy`{" {3072 10 /xy AB}xyFurT(=ruǍRd6-" {20.30309 20.30309 l}xyRd" {-4096 10 /xy AB}xy3{uǍ6'" {0.0 30.8472 l}xy6" {-3072 10 /xy AB}xy޿ulG޿=lu7W" {-19.40622 19.4003 l}xy7W" {-2048 10 /xy AB}xy{l " {-30.375 0.0 l}xy " {-1024 10 /xy AB}xyIpAlternativelyvȨhvectorisetsthedirectionasiftheconnection\from0 tothehvectorihadbGeentypGesetexceptf.thattheorigin*isassumedzerosuchthatdi-rectionsv( 1x,?y[)MƲmeanthenaturalthing,Ҟi.e.,isthedirectionUUoftheconnectionfrom(0,0) ꛲to(Rx,?y[)ֲ.gw:Incasethedirectionisnotassimple,gyoucancon- :struct{ GAhpGosihdecori}thatsetsuppandcsuch:thata~fe [۟gpchasathedesireddirection._Note:-thatyou:mustyusethe(*ls...*)formyifthisistoappGearin:anUUob8jecthmoGdi eri!!^8:Exercise(12: What{e ectisachieved{byusing:hmoGdi erisUUv/1pc/&*andUUv/-1pc/(@?$:4m.Onceutheinitialdirectionisestablishedaseither:thelastoneoranabsoluteonethentheremainder:ofUUthehdirectioniisinterpreted. :Adding]asingle^ or_denotestheresultofrotat-:ingLJthedefaultdirectionarightangleinthepGos-:itiveWPandnegativedirection,i.e.,anti-/cloGckwise,:respGectively*.aNote:-DodnotW`use^^I butonly__to:reverseUUthedirection!:Atrailing: òhvectoriislikev òhvectoributuses:the\hdirectionitosetupastandardsquarebase:suchbthat:(0,1)&²and:(0,-1),meanthesameas::a(90)}andUU:a(-90)+jandUUas^ ꧲and_R,respGectively*.!^8:Exercise(13: What{e ectisachieved{byusing:hmoGdi erisUUv/1pc/:(1,0)EandUUv/-1pc/__2:?#:57Decorations:hDecoriationsareactualTU>'ExXmacrosthatdecoratethe:currentpictureinmannersthatdepGendonthestate.:TheyYareallowedYafterm#thehpGosiitioneitheroftheouter:\xy...\endxyorinside{ F...}꧲. ThepGossibilitiesare:givenUUin gure4withnotesbGelow. ;Mostqoptionsaddtotheavqailablehdecori,ainparticu-:larthev2optionloadsmanymoresinceXY #-picversions:priorUUto2.7providedmostfeaturesashdecori.2:NotestW:5a.YSavingandrestoringallows`excursions'wherelots:ofthingsareaddedtothepicturewithouta ect-:ingtheresultingXY h-picstate, i.e.,c,p,andb}'ase[,:and`withoutrequiringmatching{} #Zs.6vTheindepGen-:denceof{}#isparticularlyusefulinconjunction:withthe\afterPOSXcommand,Hforexample,the:de nitionN8:\def\ToPOS{\save\afterPOS{%j4\POS**{}?>*@2{>}**@{-}\restore};p,}`D:willccausethecoGde\ToPOS$hpositoconstructa:double-shaftedharrowfromthecurrentob8jectto:thehpGosi(computedrelativetoit)suchthat:\xy?*{A}\ToPOS+<10mm,2mm>\endxyŬwilltypGe-:setUUthepictureps: SDict begin xyc endjA 3O8" {3277 /XT tt}xy؟0" {22.24547 4.479 l}xy".LW914J*tj??m6A ffffd TSyntax?ActionX-ffd fdhdecori< B!QhcommandiUUhdecori?eitherUUthereisacommand... BjQhemptyi?...orUUthereisn't.ihcommandi< B!Q\saveUUhpGosi?saveUUstate^5a ,thendohpGosiBjQ\restore?restoreUUstate^5a Qsavedbymatcing\saveBjQ\POSUUhpGosi?interpretUUhpGosiBjQ\afterPOSUU{ ꧸hdecoriUU}hpGosi?interpretUUhpGosiandthenperformhdecoriBjQ\dropUUhob8jecti?dropUUhob8jectiasthehpGosi* ꧲operationBjQ\connectUUhob8jecti?connectUUwithhob8jectiasthehpGosi***operationBjQ\relax?doUUnothingzBjQhTU>'ExXUUcommandsi?anyUUTU>'ExXcommands^5b ߲anduserde nedmacrosthat?neitherUUgeneratesoutput(watchUUoutforspaces!)?norUUchangesthegroupingmaybGeused$_BjQ\xyverbosejq\xytracingj\xyquiet ?tracing^5c òcommandsBjQ\xyignoreUU{RhpGosiUUhdecori}?ignore^5d ۲XY-coGdeiBjQ\xycompileUU{RhpGosiUUhdecori}?compile^5e toUU lehpre xihnoi.xycBjQ\xycompiletoUU{Rhnamei}{ OhpGosiUUhdecori} ?compile^5e toUU lehnamei.xycffd FigureUU4:qǸhdecoriations.gʍ6Note: Savingxthiswayinfactusesthesamestate as*the{}N`grouping',sothecoGdep1|s, x{p2|s\save},...%{\restore}>swill${havec V=p1bGothatthe...andUUattheend!5b.f`OneverytemptingkindofTU>'ExXcommandstopGer-form?ashdecoriisarithmeticopGerationsonthe;XY ?-picstate.&ThiswillworkinsimpleXY f-picturesasdescribGeduherebutbewarned:itKisnotp}'ortablebGecause7all7XY -picexecutionisindirect,=andthisisusedabyseveraloptionsinnontrivialways.+ChecktheTU>'ExX-nicaldoGcumentation[15 ]fordetailsaboutthis! Macrosthatexpandtohdecoriwillalwaysdothesame,UUthough.5c.I\xyecho_willturnonechoingofallinterpreted[XY _-picZhpGosicharacters.Bug:{QNotcompletelyimple-mentedhJyet."\xyverbosewillswitchonatracingofally1XY 5-picy5commandsexecuted,-withlinenumbGers.\xytracingktracesevenmore:theentiregXYwk-picstateUisprintedaftereachmoGdi cation.s;\xyquietrestoresUUdefaultquietopGeration.5d.f`Ignoringn@meansthatthehpGosihdecoriisstillparsedDtheusualwayDbutnothingistypGesetandtheUQXY U-picUUstateisnotchanged.5e.IIt&XispGossibletosave&Xanintermediateformofcom-mandsthatgeneratepartsofanXY-picturetoa'$ lesuchthatsubsequenttypGesettingofthoseparts%issigni cantlyfaster:Qthisiscalledc}'ompil-ing}.S*The}proGduced lecontainscodetocheck}that6:thecompiledcoGdestillcorrespondstothesame :hpGosihdecori\aswellasecient\XY -coGdetoredoit;:ifthehpGosihdecorihaschangedthenthecompila-:tionUUisredone.#:ThereZaretwoZwaystousethis.Thedirectisto:invent=ahnameiforeachdiagramandthenembrace:it9in\xycompileto{HBhnamei}?| {...} {9thisdumps:theUUcompiledcoGdeintothe lehnamei.xyc.:Whenmanydiagramsarecompiledthenitiseasier:toާadd\xycompile{?...} NaroundާthehpGosihdecori:toDbGecompiled.]Thiswillassign lenamesnum-:bGeredconsecutivelywithahpre xiwhichisini-:tiallytheexpansionof\jobname-6IbutmaybGeset:with:ff2 ,Z\CompilePrefix{?hpre xi}%:ff2+t:This|hasthedisadvqantage,however,that|ifaddi-:tionalcompiledXYs-picturesareinsertedthenall:subsequentSpictureswillhavetobGerecompiled.:OnesJparticularsituationisprovided,though:when:used(withinconstructionsthattypGesettheircon-:tentsjmorethanonce(suchasmostAU>'M S-L5ffA͉TU>'ExX:equationUUconstructs)thenthedeclaration :ff2/\CompileFixPoint{?hidi}%:ff2+t:can@bGeusedinsidetheenvironment@to xthe:counterUUtohavethesamevqalueateverypassage.#:Finally*,՘when"Xmany`administrativetypGesetting:runs'K areneeded,Me.g.,readjustingK L5ffA͉TU>'ExXcrossref-:erences~|andsuch,thenitmaybGeanadvqantagetoLW915*tj??gwnottypGesetanyXY -picturesatallduringtheinter- mediatedruns.ThisissuppGortedbythefollowingdeclarationswhichforeachcompilationcreatesaspGecial lewiththeextension.xydcontainingjusttheUUsizeofthepicture: 7ff2 y鍍M]\MakeOutlinesM]\OnlyOutlinesM]\ShowOutlinesM]\NoOutlinesff2эThe rstdoGesnomore.MXThesecondusesthe letotypGesets1\adottedframeoftheappropriatesizein-steaddofthepicture(unlessthepicturehaschangedandisrecompiled,&|thenitistypGesetasalwaysandthe.xyd leisrecreatedforsubsequentruns).*Thethird$showstheoutlinesasdottedrectangles.aThelastUUswitchesoutlineproGcessingcompletelyo .!yT6]Kernelffobfjectlibrary oInthissectionwepresentthelibr}'aryobjectsn providedwithqthekernellanguage|severaloptionsaddmorelibrary'ob8jects.LTheyfallintothreetypGes::0Mostofthekernel8ob8jects(includingallthoseusuallyusedwith**#tobuildconnections)aredir}'ectionals!,TdescribGedinx6.1.TheYremainingkernellibraryob8jectsarecir}'clesofUUx6.2andtextH-ofx6.3.eƍ6.1DirectionalsTheQkernelprovidesaselectionofdir}'ectionals!:Uob8jectsthatm-depGendonthecurrentdirection.NTheyalltaketheUUform pff2a\dirhdiriff2 to3typGesetaparticularhdiriectionalob8ject. AllhavetheUUstructure pff29YhdiriUU q!!hvqarianti{?hmaini}ff2 with[hvqariantibGeinghemptyioroneofthecharacters^_23UIandUUhmainisomemnemoniccoGde.  W*ewillclassifythedirectionalsprimarilyintendedforbuildingconnectionsasc}'onnectorsandthosepri-marilyƱintendedforplacementatconnectionendsorasmarkersUUastips!. Figure5showsallthehdiriectionalsde nedbythekernel(withnotesbGelow;oeachhmainitypGehasalineshowingitheavqailablehvariantis.#Noticethatonlysomevqariants[existforeachhdiri|whenanonexistingvqari-antofahdiriisrequestedthenthehemptyivqariantis!usedsilently*.+Each!isshownineitherofthetwoformsavqailableineachdirectionasapplicable:Fcon-nectingRa toaffffff33ff33ff B(typGesetby**\dir#!@hdiri)andasagw:tip*\attheendofadottedconnectionofthesamevqari- :ant(i.e.,-typGesetbythehpGosi**\dir#nhvqarianti{.}w?>:*\dir*+hdiri). ݍ;As aspGecialcaseanentirehob8jectiisallowedasa:hdiri|xbystartingitwitha* u: \dir*%|visequivqalentto:\object.:Notes:6a.YY*out[mayuse\dir{}(hfora\dummy"directional:ob8ject޳(infactthisisusedautomaticallyby**{}ާ).:Thisisusefulforauniformtreatmentofconnec-:tions,Fe.g.,makingBRthe? ġhpGosiableto ndapoint:on8thestraightlinefromptocwithoutactually:typGesettingUUanything.r:6b.?The#plainQc}'onnectorsgroupcontainsbasicdirec-:tionalsUUthatlendthemselftosimpleconnections.ù:By'ExXrules.)Unfortu-:natelyIrulesisthefeatureoftheDVIIformatmost:commonlyzhandledwrongbyDVImdrivers. 5There-:foreUQXY U-picUUprovidesthehdecoriations:ff2 HAN\NoRulesN\UseRulesߍ:ff2:thatUUwillswitchtheuseofsucho andon.:AscanbGeseenbythelasttwocolumns,ړthese(and:most?oftheotherconnectors)alsoexistindouble:and,xtripleversionswitha2 ora3prepGendedto:thebname.=F*orconvenienceb\dir{=}+andb\dir{:}:aresynonymsfor\dir2{-}5㚲and\dir2{.}/,re-:spGectively;{similarly\dir{==}4$isasynonymfor:\dir2{--}(*.r:6c.#Thegroupofplain1tipsɲcontainsbasicob8jectsthat:areusefulasmarkersandarrowheadsmakingcon-:nections,}&*typGesets㍍Rps: SDict begin xyc endsޟ" {3379 10 /xy AB}xyb" {3379 10 /xy AB}xy{3" {3379 10 /xy AB}xy ޢ" {3379 10 /xy AB}xy/R:Exercise14: TypGeset}thefollowingtwo+sand:aUUtiltedsquare:4Ytps: SDict begin xyc end!+R+" {3584 F d}xy2HcF" {-2560 F d}xyp" {-2560 F d}xya" {3584 F d}xy:Hintز:fthe>dashcreatedby\dir{-}+=ղhasthelength:5pt1.LW916**tj??4dJ}˜Dummy^6a*C\dir{}PlainUUconnectors^6b_\dir{-}^NXHps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy-ycZ" {35.70181 11.15648 dt}xy-ycZ" {35.70181 11.15648 l}xy\dir2{-}^rps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy--e" {35.70181 11.15648 dt}xy-ŸNh" {35.70181 11.15648 dt}xy--e" {35.70181 11.15648 l}xy-ŸNh" {35.70181 11.15648 l}xyB,\dir3{-}^ps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy,टqb" {35.70181 11.15648 dt}xy."B" {35.70181 11.15648 dt}xy-ycZ" {35.70181 11.15648 dt}xy,टqb" {35.70181 11.15648 l}xy."B" {35.70181 11.15648 l}xy-ycZ" {35.70181 11.15648 l}xyF\dir{.}^NXHps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy-ycZ" {35.70181 11.15648 dt}xy-ycZ" {35.70181 11.15648 dt}xy\dir2{.}^rps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy--e" {35.70181 11.15648 dt}xy-ŸNh" {35.70181 11.15648 dt}xy--e" {35.70181 11.15648 dt}xy-ŸNh" {35.70181 11.15648 dt}xyB,\dir3{.}^ps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy,टqb" {35.70181 11.15648 dt}xy."B" {35.70181 11.15648 dt}xy-ycZ" {35.70181 11.15648 dt}xy,टqb" {35.70181 11.15648 dt}xy."B" {35.70181 11.15648 dt}xy-ycZ" {35.70181 11.15648 dt}xy\dir{~}^NXHps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy-ycZ" {35.70181 11.15648 dt}xy)_X " {3392 g}xy"T8 " {3392 g}xy " {3392 g}xy̟ " {3392 g}xy  " {3392 g}xy\dir2{~}^rps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy--e" {35.70181 11.15648 dt}xy-ŸNh" {35.70181 11.15648 dt}xy)',1n " {3392 g}xy"Gh6N " {3392 g}xyg;. " {3392 g}xy@ " {3392 g}xy D " {3392 g}xy)B " {3392 g}xy"@" " {3392 g}xy| " {3392 g}xy " {3392 g}xy " {3392 g}xyB,\dir3{~}^ps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy,टqb" {35.70181 11.15648 dt}xy."B" {35.70181 11.15648 dt}xy-ycZ" {35.70181 11.15648 dt}xy(?~ " {3392 g}xy"{c " {3392 g}xy/C " {3392 g}xyO# " {3392 g}xy p/ " {3392 g}xy)J- " {3392 g}xy"-O " {3392 g}xyiS " {3392 g}xy/X " {3392 g}xyO] " {3392 g}xy)_X " {3392 g}xy"T8 " {3392 g}xy " {3392 g}xy̟ " {3392 g}xy  " {3392 g}xy \dir{--}^NXHps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy-ycZ" {35.70181 11.15648 dt}xy-ycZ" {35.70181 11.15648 dd}xy\dir2{--}^rps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy--e" {35.70181 11.15648 dt}xy-ŸNh" {35.70181 11.15648 dt}xy--e" {35.70181 11.15648 dd}xy-ŸNh" {35.70181 11.15648 dd}xy=/\dir3{--}^ps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy,टqb" {35.70181 11.15648 dt}xy."B" {35.70181 11.15648 dt}xy-ycZ" {35.70181 11.15648 dt}xy,टqb" {35.70181 11.15648 dd}xy."B" {35.70181 11.15648 dd}xy-ycZ" {35.70181 11.15648 dd}xy \dir{~~}^NXHps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy-ycZ" {35.70181 11.15648 dt}xy)w " {3392 g}xy " {3392 g}xy ?5d9 " {3392 g}xy\dir2{~~}^rps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy--e" {35.70181 11.15648 dt}xy-ŸNh" {35.70181 11.15648 dt}xy) " {3392 g}xyg;/ " {3392 g}xy IO " {3392 g}xy*7ӟ* " {3392 g}xyz " {3392 g}xy w!# " {3392 g}xy=/\dir3{~~}^ps: SDict begin xyc end" {5.00002 0 360 o}xy21." {0.0 5.05002 -5.05002 -5.05002 5.05002 ov}xy,टqb" {35.70181 11.15648 dt}xy."B" {35.70181 11.15648 dt}xy-ycZ" {35.70181 11.15648 dt}xy)$ " {3392 g}xy/D " {3392 g}xy \d " {3392 g}xy*o " {3392 g}xygS " {3392 g}xy  " {3392 g}xy)w " {3392 g}xy " {3392 g}xy ?5d9 " {3392 g}xy,,PlainUUtips^6cI\dir{>}񄍑2Bops: SDict begin xyc end" {3392 10 /xy AB}xy" {22.76208 7.11314 dt}xyZ>E\dir^{>}񄍒vps: SDict begin xyc end" {3392 10 /xy A}xy" {22.76208 7.11314 dt}xyr\dir_{>}񄍒gps: SDict begin xyc end" {3392 10 /xy B}xy" {22.76208 7.11314 dt}xy=\dir2{>}1Lps: SDict begin xyc end" {3392 /XT tt}xyݞʙ" {20.37592 6.3673 dt}xyG" {20.37592 6.3673 dt}xyw[\dir3{>}_ps: 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 I\dir{<}񄍑2Bops: SDict begin xyc end" {-704 10 /xy AB}xy" {22.76208 7.11314 dt}xyZ>E\dir^{<}񄍒vps: SDict begin xyc end" {-704 10 /xy B}xy" {22.76208 7.11314 dt}xyr\dir_{<}񄍒gps: SDict begin xyc end" {-704 10 /xy A}xy" {22.76208 7.11314 dt}xy=\dir2{<}1Lps: SDict begin xyc end" {-704 /XT tt}xyݞʙ" {20.37592 6.3673 dt}xyG" {20.37592 6.3673 dt}xyw[\dir3{<}_ps: 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}xyI\dir{|}񄍑2Bops: SDict begin xyc end " {3392 st}xy" {22.76208 7.11314 dt}xyZ>E\dir^{|}񄍒vps: SDict begin xyc endEL:H" {-2752 F d}xy" {22.76208 7.11314 dt}xyr\dir_{|}񄍒gps: SDict begin xyc end" {1344 F d}xy" {22.76208 7.11314 dt}xy=\dir2{|}񄍒Lps: SDict begin xyc endv " {3392 st}xywW " {3392 st}xyv " {22.76208 7.11314 dt}xywW" {22.76208 7.11314 dt}xyw[\dir3{|}񄍒_ps: 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}xyI\dir{(}񄍑2Bops: SDict begin xyc end " {3392 h}xy" {22.76208 7.11314 dt}xyZ>E\dir^{(}񄍒vps: SDict begin xyc end " {3392 ha}xy" {22.76208 7.11314 dt}xyr\dir_{(}񄍒gps: SDict begin xyc end " {3392 hb}xy" {22.76208 7.11314 dt}xyI\dir{)}񄍑2Bops: SDict begin xyc end " {-704 h}xy" {22.76208 7.11314 dt}xyZ>E\dir^{)}񄍒vps: SDict begin xyc end " {-704 hb}xy" {22.76208 7.11314 dt}xyr\dir_{)}񄍒gps: SDict begin xyc end " {-704 ha}xy" {22.76208 7.11314 dt}xyZ>E\dir^{`}񄍒vps: SDict begin xyc end " {3392 ta}xy" {22.76208 7.11314 dt}xyr\dir_{`}񄍒gps: SDict begin xyc end " {3392 tb}xy" {22.76208 7.11314 dt}xyZ>E\dir^{'}񄍒vps: SDict begin xyc end " {-704 tb}xy" {22.76208 7.11314 dt}xyr\dir_{'}񄍒gps: SDict begin xyc end " {-704 ta}xy" {22.76208 7.11314 dt}xy$SConstructedUUtips^6d\dir{>>}񄍑2ps: SDict begin xyc end " {3392 10 /xy AB}xy" {3392 10 /xy AB}xy" {22.76208 7.11314 dt}xyXU\dir^{>>}񄍒kJps: SDict begin xyc end " {3392 10 /xy A}xy" {3392 10 /xy A}xy" {22.76208 7.11314 dt}xy:\dir_{>>}񄍒ps: SDict begin xyc end " {3392 10 /xy B}xy" {3392 10 /xy B}xy" {22.76208 7.11314 dt}xy\dir2{>>}1Nȡps: SDict begin xyc end " {3392 /XT tt}xy" {3392 /XT tt}xyө" {20.26208 6.3319 dt}xywW" {20.26208 6.3319 dt}xyv\dir3{>>}Lps: 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}xy\dir{<<}񄍑2ps: SDict begin xyc end " {-704 10 /xy AB}xy" {-704 10 /xy AB}xy" {22.76208 7.11314 dt}xyXU\dir^{<<}񄍒kJps: SDict begin xyc end " {-704 10 /xy B}xy" {-704 10 /xy B}xy" {22.76208 7.11314 dt}xy:\dir_{<<}񄍒ps: SDict begin xyc end " {-704 10 /xy A}xy" {-704 10 /xy A}xy" {22.76208 7.11314 dt}xy\dir2{<<}1Nȡps: SDict begin xyc end " {-704 /XT tt}xy" {-704 /XT tt}xyө" {20.26208 6.3319 dt}xywW" {20.26208 6.3319 dt}xyv\dir3{<<}Lps: 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}xy\dir{||}񄍑2ps: SDict begin xyc endi " {3392 st}xy " {3392 st}xy" {22.76208 7.11314 dt}xyXU\dir^{||}񄍒kJps: SDict begin xyc end\" {-2752 F d}xyEL:H" {-2752 F d}xy" {22.76208 7.11314 dt}xy:\dir_{||}񄍒ps: SDict begin xyc endi" {1344 F d}xy" {1344 F d}xy" {22.76208 7.11314 dt}xy\dir2{||}񄍒Nȡps: 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}xyv\dir3{||}񄍒Lps: 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}xy\dir{|-}񄍑2ps: SDict begin xyc end " {3392 st}xy" {3392 F d}xy" {22.76208 7.11314 dt}xyXU\dir^{|-}񄍒kJps: SDict begin xyc endEL:H" {-2752 F d}xy" {3392 F d}xy" {22.76208 7.11314 dt}xy:\dir_{|-}񄍒ps: SDict begin xyc end" {1344 F d}xy" {3392 F d}xy" {22.76208 7.11314 dt}xy\dir2{|-}񄍒Nȡps: 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}xyv\dir3{|-}񄍒Lps: 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}xy\dir{>|}񄍑2ps: SDict begin xyc end " {3392 st}xy" {3392 10 /xy AB}xy" {22.76208 7.11314 dt}xyXU\dir{>>|}񄍒kJps: SDict begin xyc end " {3392 st}xy " {3392 10 /xy AB}xy" {3392 10 /xy AB}xy" {22.76208 7.11314 dt}xyD7\dir{|<}񄍒ps: SDict begin xyc end " {-704 st}xy" {-704 10 /xy AB}xy" {22.76208 7.11314 dt}xy\dir{|<<}񄍒Nȡps: SDict begin xyc end " {-704 st}xy " {-704 10 /xy AB}xy" {-704 10 /xy AB}xy" {22.76208 7.11314 dt}xya\dir{*}񄍒Lps: SDict begin xyc endKͷ" {22.76208 7.11314 dt}xy&\dir{+}񄍑2ps: SDict begin xyc end " {3392 st}xy`:" {3392 F d}xy" {22.76208 7.11314 dt}xybՈ\dir{x}񄍒kJps: SDict begin xyc end" {-3608 st}xy՟5<" {-3608 F d}xy" {22.76208 7.11314 dt}xy4\dir{/}񄍒ps: SDict begin xyc end " {3084 st}xy" {22.76208 7.11314 dt}xy\dir{//}񄍒Nȡps: SDict begin xyc end " {3084 st}xy " {3084 st}xy" {22.76208 7.11314 dt}xya\dir{o}񄍒Lps: SDict begin xyc endKͷ" {22.76208 7.11314 dt}xy"LFigureUU5:qKernellibraryhdiriectionalsLW917Bݠ*tj??gw6d.f`TheseoDtipsarecombinationsoftheplaintips providednforconvenience(andoptimisedforef- ciency). New onescanbGeconstructedusing\compositeUUandbydeclarationsoftheform pff2 w0\newdirUUhdiri{RhcompGositei}ff2&whichW(de nes\dirhdiriasthehcompGositei(seenoteUU4dforthedetails).76.2Circlesegments/Circlehob8jectisareroundandtypGesetasegmentofthecircle9DcenteredatthereferencepGoint.ThesyntaxofcirclesisdescribGedin gure6withexplanationsbelow.  Thecdefaultistogenerateafull!cir}'clewiththespGec-i edUUradius,e.g.,퍍d F\xy*\cir<4pt>{}\endxyctypGesetsOI\ps: SDict begin xyc end" {4.00002 0 360 o}xy" \xy*{M}*\cir{}\endxy8,|\ps: SDict begin xyc endjMeU" {5.39583 0 360 o}xy ʪ"AllrtheothercirclesegmentsaresubsetsofthisandhaveUUtheshapGethatthefullcircleoutlines.  Partialicir}'clesegments&hwithTGhorientiationarethepart1qofthefullcirclethatstartswithatangentvec-tor?inthedirectionofthe rsthdiagional(seenote4l)andsendswithatangentvectorinthedirectionoftheotherz?hdiagionalafteracloGckwise(for_<)oranticloGck-wiseUU(for^R)turn,e.g.,/l&df\xy*\cir<4pt>{l^r}\endxyZtypGesetsoA\ps: SDict begin xyc end" {4.00002 90 270 o}xy"f\xy*\cir<4pt>{l_r}\endxyX#|oA\ps: SDict begin xyc end" {4.00002 90 270 o}xy"Ƨ\xy*\cir<4pt>{dl^u}\endxyX#|oA\ps: SDict begin xyc end" {4.00002 135 360 o}xy"Ƨ\xy*\cir<4pt>{dl_u}\endxyX#|oA\ps: SDict begin xyc end" {4.00002 -180 -45 o}xy"&\xy*+{M}*\cir{dr_ur}\endxyX#| \ps: SDict begin xyc endjMeV" {8.39584 135 405 o}xyʬ"IfFthesamehdiagiisgiventwicethennothingistypGeset,e.g.,l&d\xy*\cir<4pt>{u^u}\endxy˲typGesets/D\ps: SDict begin xyc end"SpGecialUUcareistakentosetupthehdiagionaldefaults:"9  After^ Ѳthedefaultisthediagonal90^iβanticloGck-  wiseUUfromtheonebGeforethe^R.L  After \_ Zthe \defaultisthediagonal90^@cloGckwise fromUUtheonebGeforethe_R.The hdiagibGefore^ S?or_isrequiredfor\cirhob8jectsi.7Exercise15: TypGesetthefollowingshadedcirclewithUUradius5ptL:"9a0ps: SDict begin xyc end" {5.00002 0 360 o}xy33" {5.00002 -135 45 o}xyff." {5.00002 -135 45 o}xy;b" {5.00002 -135 45 o}xy"9gw:6.3:TextuT:T*extinpicturesissuppGortedthroughthehob8jecticon- :struction: ff2 ?"6\txtUUhwidthihstylei{Rhtexti}ff2thatGbuildsanob8jectcontaininghtextitypGesettohwidthi.jusinghstylei;inhtexti\\βcanbGeusedasanexplicitr#linebreak;alllineswillbGecentered.0hstyleishould5eitherbGeafontcommandorsomeotherstu toD8doforeachlineofthehtextiandhwidthishouldbGeeitherUU<Rhdimeni>orUUhemptyi. 7 X#՟YY'M-picffoptionsNote:L5ffA͉TU>'ExX2" usersshouldalsoconsultthepara-graphUUon\xy*.sty"inx1.1.h7.1LoadingXY -picfisprovidedwithagrowingnumbGerofoptionssuppGortingŞspecialiseddrawingtasksaswellasexoticoutputxdeviceswithspGecialgraphicfeatures.1Theseshould#allbGeloadedusingthisuniforminterfaceinor-derֱtoensurethatthe֭XY V-picenvironmentֱispropGerlysetUUupwhilereadingtheoption. ff2 ?"@%\xyoptionUU{ ꧸hoptioniUU}@%\xyrequireUU{ ꧸hoptioniUU}ff2-|\xyoptionߙwillcausetheloadingofanߕXY_-picop-tionK# lewhichcanhaveseveralnamesthataretriedinsequence: ^xyhoptioni.tex,ixy鋸hoptioni.doc,xy hshorti.tex,G[andxy0hshorti.doc,wherehshortiishoptioniEtruncatedto6(six)characterstoconformwithUUtheTWG-TDS[17 ]. \xyrequireisthesameexceptitisignoredifanoptionwiththesamenameisalreadypresent(thusdoGesUUnotcheckUUtheversionetc.). Sometimes somedeclarationsofanoptionorheader leorwhateveronlymakessenseaftersomeparticularotheroptionisloaded.PInthatcasethecoGdeshouldbewrappGedUUinthespecialcommandff2 ?" E\xywithoptionUU{ ꧸hoptioniUU}{hcoGdeiUU}ff2which[indicatesthatifthehoptioniisalreadyloadedthenShcoGdeishouldbeexecutednow,otherwiseitshouldzbGesavedzandifhoptionievergetsloadedthenhcoGdei:Mshouldbeexecutedafterwards. Note:;ThehcoGdei=shouldallowmorethanoneexecution;itissavedwithC)thecatcoGdesatthetimeofthe\xywithoptioncommand. Finally*, HitispGossibletodeclaresomehcodeithatxishouldbGeexecutedbeforeeveryactualex-ecution 5of\xywithoption{?hoptioni}{ ...}꧲,andLW918ڠ*tj?? rS8 ffffd T.DSyntaxުActionX-ffd .D\cir+hradiusiUU{ ꧸hciriUU}ުhciricleUUsegmentwithhradiusifffd fd.DhradiusiHO !l.ehemptyiުuseUURch6astheradius OWjl.ehvectoriުuseUUX7ofthehvectoriasradius.DhciriHO !l.ehemptyiުfullUUcircleofhradiusiOWjl.ehdiagiUUhorientihdiagiުpartialcirclefrom rsthdiagionalthroughtothesecondުhdiagionalUUinthehorientiationd.DhorientiHO !l.e^ުanticloGckwiseOWjl.e_ުcloGckwiseffd NFigureUU6:qǸhciricles.r(rsimilarly bGeforeevery\xyoption{>jhoptioni}Dand \xyrequire{)hoptioni}R(collectivelyUUcalled`requests'):: ff2 9%\xyeverywithoptionUU{ ꧸hoptioniUU}{hcoGdeiUU}%\xyeveryrequestUU{ ꧸hoptioniUU}{hcoGdeiUU}Aff2ThisoOismostoftenusedbyanoptiontoactivqatesomehoGokUUeverytimeitisrequesteditself.׭7.2Option leformatuTOptionUU lesmusthavethefollowingstructure: <%%!Qhidenti cationi%%!Qhcopyright,UUetc.i?\ifx\xyloaded\undefined?\inputxy\fi\xyprovide{Mhoptioni}{ hnamei}{hversioni}% <{A@hauthori}{ hemaili}{haddressi}hbGodyUUoftheoptioni\xyendinputThe6argumentsto\xyprovideshouldcontainthe following:Lhoptioni(@Option}loadnameasusedinthe\xyoptioncommand./ThisxshouldbGesafeanddistinguish-ableforanyopGeratingsystemandisthuslimitedto {characterschosenamongthelowercaseletters(a?{z),digits{(0{9),and{dash(-?),andalloptionsshouldLbGeuniquelyidenti ablebythe rst6(six)charactersUUonly*.~hnamei$wDescriptiveUUnamefortheoption.hversioni+jIdenti cationUUoftheversionoftheoption.hauthori)βTheUUname(s)oftheauthor(s).hemaili$wThemelectronicmailaddress(es)oftheau- thor(s)UUorhthealiationifnoemailisavqailable.haddressi-#TheUUpGostaladdress(es)oftheauthor(s).(r:Thisinformationisusednotonlytoprintaniceban- :nerZbutalsoto(1)silentlyskiploadingifthesame:versionwaspreloadedand(2)printanerrormessage:ifUUadi erentversionwaspreloaded. -;The[`dummy'optiondescribGedinx20isaminimal:optionusingtheabGovefeatures.>Itusesthespecial:DOCMODEZpformatKtoincludeitsowndoGcumentationfor:thiswdoGcument(likeallocialwXY -picoptions)butthis:isUUnotarequirement.:7.3:Driveroptionse:The|hdriverioptionsdescribGedinpartIVrequirespe-:cialm'ExX2" #classor:packqageCkoptionsasdescribGedinx1.1).zThespecialthing:abGoutdahdriveriisthatloadingitsimplydeclaresthe:nameofit,establisheswhatextensionsitwillsuppGort,:andQselectsittempGorarily*.Thusthespecialcapabili-:tiesofthedriverwillonlybGeexploitedintheproduced:DVI՘ leչifsomeoftheseextensionsarealsoloadedand:ifthedriverisstillselectedwhenoutputisproGduced.:Generally*,7the^orderinwhichtheoptionsareloaded:isimmaterial. X(Knownexceptionsa ectonlyinter-:nal^>proGcessingandarenotvisibletotheuserinterms:ofElanguageandexpGectedoutput.)CInparticularone:drivercanbGepreloadedinaformatandadi erentone:usedUUforaparticulardoGcument.;TheUUfollowingdeclarationscontrolthis:: Zff2 瑍e\UseSingleDriverg5forcesUUonedriveronlye\MultipleDriversg5allowsUUmultipledriverse\xyReloadDriversg5resetsUUdriverinformation/ff2kff^ J= "5-:7LThekÎernelsupp'ExXthatdonothaveaclearlydistinguishedpreamble. As@theabGove@suggestsitsometimesmakessensetoloadhdriverisintheactualtextualpartofadoGcu-ment,-however,it3isrecommendedthatonlydriversalsoloadedeinthepreamblearereloadedlater,andthat\xyReloadDriversoLisusedwhenthereisdoubtabGoutthestateofa airs.YIncaseofconfusionthespGecialcommand\xyShowDriverswilllistallthepresentlysuppGortedandselecteddriver-extensionpairstotheTU>'ExXUUlog. ItI[isnotdiculttoaddsuppGortforadditionalhdriveris;5dhowisdescribGedintheTU>'ExXnicaldocumen-tation. Mostextensionswillprintawarningwhenacapa-bilityisusedwhichisnotsuppGortedbythepresentlyloadedhdriveri.>Suchmessagesareonlyprintedonce,however,s(forgsomeformatstheyarerepGeatedattheend).T Similarly*, when#thesuppGortofanextensionthatexploitsaparticularhdriveriisusedawarningmessagewillUUbGeissuedthattheDVI leisnotportable.*ٍPartffIs3ISExtensionsmThis@partdoGcumentsthegraphiccapabilitiesaddedbyeach"standardextensionoption.g-F*oreachisindicatedthe!describGedversionnumbGer,theauthor,andhowitisUUloaded. ManyD^oftheseareonlyfullysuppGortedwhenasuit-able+driveroption(describGedinpartIV)isalsoloaded,however,allpYaddedconstructionsarealwayspYac}'ceptedevenUUwhennotsuppGorted.#ʃ8]CurveffandSplineextensionۃ/t : cmbx9Vers.3.3bCyRossMoKore1 cmsy9hross@mpAce.mq.edu.aui Loadas:\xyoption{curve}iThisJ?optionprovidesJ;XY ?-picwiththeabilitytotypGesetsplinecurvesbyconstructingcurvedconnectionsusinggw:arbitrarydirectionalob8jectsandbyencirclingobjects :similarly*.N8Warning}:'ExX'smemory;youshouldthereforelimitthelength:andanumbGerofcurvesusedonasinglepage..Memory:use islesswhencombinedwithabackendcapableof:proGducingXitsowncurves;Ze.g.,YthePostScriptback-:end).ꍍ:8.1:CurvedconnectionsuT:SimpleUUwaystospGecifycurvesinUQXY U-picareasfollows:: ff2 D^r**\crv{6}]hpGoslisti}d'curvedUUconnectionr**\crvs{;Zhdiri}d'get+"hpGoslistifromthestackr\curve{6}]hpGoslisti}d'asUUahdecoriationff2inHwhichhpGoslistiisalistofvqalidhposiitions.Thedecorationform\curve*isjustanabbreviationfor\connect\crv>ܲ.iAs=iusual,B2thecurrentpandcareusedasthestartand nishoftheconnection,VrespGectively*.Withing|hpGoslistithehposiitionsareseparatedby&y.=Afulldescriptionofthesyntaxfor\crvisgivenin g-ureUU7.~+pps: SDict begin xyc end$Al qBlK" {157.31972 -52.38376 l}xyC Բ0I" {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)62X" {mark 0.0 56.90521 28.4526 56.90521 56.90521 56.90521 80.6157 37.9368 0.0791 1.0 bz}xy^" {mark 80.6157 37.9368 104.32622 18.9684 123.29462 -18.9684 139.89197 -30.82364 0.0 1.0 bz}xyb" {mark 139.89197 -30.82364 156.48933 -42.67891 170.71564 -28.4526 170.71564 0.0 0.0 0.92177 bz}xyo؟/447 If#hpGoslistiisemptyastraightconnectioniscom-puted._WhenthelengthofhpGoslistiisoneortwothenthe;ucurveisuniquelydeterminedasasingle-segmentBGezierquadraticorcubicspline.NaThetangentsatpandKcarealongthelinesconnectingwiththeadjacentcontrolpGoint.WiththreeormorehpGosiitionsacubicB-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.́(ExtendingthiscodetoincludetheUUlabGelsissetbelowasanexercise).LW920*tj??gw The'?$-opGerator'ofx3(note3h)isusedto ndarbi- traryUUhplaceisalongacurveintheusualway*.DˍExercise16: ExtendthecoGdegivenforthecurvesinkthepreviouspicturesoastoaddthelabGelsgivingtheUUnumbGerofcontrolpGoints. N Using? willsetthecurrentdirectiontobGetangen-tialatthathplacei,2andonecanhslideispGeci eddis-tancesalongthecurvefromafoundhplaceiusingthe?Q.../꧸hdimeni/Rnotation:UG " {-3155 10 /xy AB}xy>-1lx"Z*x^0Gy $]֟[Q|~P/Ek" {-74.46056 39.55125 l}xyC$Exercise17: SuggestMgcoGdetoproducesomethingliketheZabGovepicture;Ythesplinecurveisthesameasinthepreviouszpicture.Hints!:~Thelineis140ptlongandtouchesGx0:28ofthewayfromAtoBandthexis0.65ofUUthewayUUfromAtoBq. ThedpGositionsinhposlistispecifyc}'ontrol[pointswhichxdeterminetheinitialand naldirectionsofthecurve|leaving淋pandarrivingatc|andhowthecurvebGehavesinbetween,[usingstandardsplineconstruc-tions.јInuEgeneral,}AcontrolpGointsneednotlieupGontheactualUUcurve. AH)`U" {84.69391 -28.44547 dt}xy ˟ ҳ:1fOG:9d" {80.58003 -14.57037 l}xyy̅:2cӅH :8aԫ" {67.61137 -6.14876 l}xy#5{:3\k/:7Z`pœL" {48.4727 -1.81961 l}xy/ڳ:4O :6O " {25.25989 -0.22745 l}xy?:5<ˍExercisews18: W*riteNcoGdetoproduceapicturesuchasɵtheoneabGove.(Hintز:ZSaveɵthelocationsofplacesalongthecurveforlaterusewithstraightconnec-tions.)gw;T*oGhavethesamehpGosioccuringasamultiplecontrol :pGointsimplyuseadelimiter,whichleavesthehpGosi:unchanged.=Thus}\curve{(=hpGosi&} ̲uses}acubicspline,:whereasUU\curve{(@hpGosi}RisUUquadratic. 8;RepGeating#thesamecontrolpointthreetimesinsuc-:cessionresultsinstraightsegmentstothatcontrol:pGoint. UsingߪthedefaultstylesthisisanexpGensive:way5togetstraightlines,;butitallowsforextrae ects:withUUotherstyles.:NotesC:8a.YTheD2\drop"ob8jectissetonce,then\droppGed":manyBtimesatappropriatelyspacedplacesalong:the5curve.Ifdirectional,mthedirectionfrompto:cisused.DefaultbGehaviouristohavetinydots:spacedsucientlycloselyastogivetheappGear-:anceVlofasmoGothcurve.u Specifyingalargersize:forUthe\drop"ob8jectisawayUofgettingadotted:curveUU(seetheexampleinthenextnote).d:8b.?The\connect"ob8jectisalsodroppGedateachplace:alongGthecurve.However,}'ifGnon-empty*,thisGob8ject:usesthetangentdirectionateachplace. Thisal-:lowsadirectionalob8jecttobGespeci ed,ٻwhoseori-:entation8willalwaysmatchthetangent.h?T*oadjust:the]spacingofsuchob8jects,useanempty\drop":ob8jectUUofnon-zerosizeasshownhere:/ɍOps: SDict begin xyc end qA;OB ;:gٟ_\:B:]ן:П$: ~p:$RBx:( :+B:/?t:2rX:6` 짛:9N:=?:Atٟ۟:Ea&`y:Ea&`y:IvUN:Ml:R:?:VL :[@2:`:dX:i՚|:n1=:qlP:suR:v@Q:y*):{Ɔ :~eU:͟ :{:Pi!::3:} :JT:5&:[ ~" {1769 10 /xy AB}xytȟA"" {2065 10 /xy AB}xy {" {2340 10 /xy AB}xy)en" {2542 10 /xy AB}xy3Mϟ"" {2697 10 /xy AB}xy=d$" {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}xyE:\xy?(0,0)*+{A};(50,-10)*+{B}:**\crv{~*=<4pt>{.}?(10,10)&(20,0)&(40,15)}:**\crv{~*=<8pt>{}~**!/-5pt/\dir{>}(10,-20)*7&(40,-15)}?\endxy:When#thereisno\connect"ob8jectthenthetan-:gentcalculationsarenotcarriedout,&resultingin:a(savingoftimeandmemory;othisisthedefault:bGehaviour.:8c.#The@\drop"and\connect"ob8jectscanbGespeci ed:asumanytimesasdesired.OnlythelastspGeci -:cationLofeachtypGewillactuallyhaveanye ect.:(ThisSmakesiteasytoexpGerimentwithdi erent:styles.):8d.?Complicatedqdiagramshavingseveralsplinecurves:can2takequitealongtimetoproGcessandmayuse:alotofTU>'ExX'smemory*._Aconvenientdevice,(PespGe-:ciallywhiledevelopingapicture,F,istoshowonly:theEloGcationofthecontrolpointsortojointheLW921ț*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."eݛcontrolgpGointswithlines,l asastylizedapproxima- tion]tothesplinecurve.Thehcurve-optionis~pand ~l\are providedforthispurpGose.Uppercaseversions^~P=and^~Ldo^thesamethingbutuseanyhcurve-ob8jectis kthatmaybGespeci ed,whereasthelowercase*1versionsuseplaindefaults:~smallcrossfor2~p g,,9straight2linefor~l.MSimilarly~CN^and~csetthe~AsplinecurveusinganyspGeci edhcurve-optionisorUUasa(default)plaincurve.s8e.IUserof~p ,yE~l ?,yEetc.isextendedtoenablebGoththecurveMandthecontrolpGointstobGeeasilyshowninthesamepicture.MixinguppGer-andlower-casespGeci es"whetherthehcurve-optionisaretobeap-plied'tothesplinecurveorthe(linesjoining)con-troltpGoints.ЅSeetheexamplesaccompanyingthenextUUtwonotes.8f.BygdefaultthecontrolpGointsaremarkedwithasmallcross, spGeci edby*\dir{x},߲.PRThe\connect"ob8jectUUisignoredcompletely*.9ޟ. !vgps: SDict begin xyc end qA;OB#3ߟ " {3773 st}xy!$}9" {3773 F d}xy? " {3773 st}xy=[^" {3773 F d}xyxy " {3773 st}xyv^" {3773 F d}xy :gٟ:ٟ::6؟r:]ן:П3: ~py:"l:$R:&1Ze:(  :)ܠT:+B:-vA:/?u6:1&b:2r :4i :6` 2:8,V[:9NX:;:=?):?7ꪩ:At۟T:Cf*:Ea&C:Ea&C:Gfz:IvU&:Ko:M߈l:OMo:R|:TTܴw:VL+:X۪:[@n:]Ne_:`ے:bn:dXܚ5:gX#y0:i՚ޘY:lXe4:n1>:ql:su:v@N|:y*#F:{ƆI:}j:~eUm::͟:Xn:X:G:PiF::+:L$Z:p*:} 7:J::&:,wasUUtypGesetby...N8\xy?(0,0)*+{A};(50,-10)*+{B}**\crv~pC{~*=<\jot>{.}(10,-10)&(20,15)Q&(40,15)}?\endxyݛ:8g.YWithlinesconnectingcontrolpGointsthedefault :\drop"ob8jectisempty*,whilethe\connect"object:isPT\dir{-}+`forPTsimplestraightlines.pIfnon-empty*,:the?\drop"ob8jectisplacedateachcontrolpGoint.:The@\connect"ob8jectmaybGeusedtospecifya:fancyUUlinestyle.E<Ops: SDict begin xyc end qA;OB;.: Ǎ^Bќ pC2x pDN" {mark 12.00002 36.00002 39.6006 19.19826 48.00002 -11.99998 1.0 0.10547 q}xywM" {-1789 10 /xy AB}xyR" {mark 12.00002 36.00002 39.6006 19.19826 48.00002 -11.99998 0.10547 0.86841 q}xyN" {mark 12.00002 36.00002 39.6006 19.19826 48.00002 -11.99998 1.0 0.86847 q}xy;" {46.20657 32.87267 l}xy!>rk}ps: SDict begin xyc end qA>^Bќ pC2x pD;" {46.20657 32.87267 l}xyN" {mark 12.00002 36.00002 39.6006 19.19826 48.00002 -11.99998 1.0 0.10547 q}xywM" {-1789 10 /xy AB}xyR" {mark 12.00002 36.00002 39.6006 19.19826 48.00002 -11.99998 0.10547 0.86841 q}xyN" {mark 12.00002 36.00002 39.6006 19.19826 48.00002 -11.99998 1.0 0.86847 q}xy!>r!ד\xy*+{A}="A";p+/r5pc/+(0,15)*+{B}="B" Q,p+<1pc,3pc>*+{C}="C"Q,"A"+<4pc,-1pc>*+{D}="D",{\ar@/_/"C"}Q,?!{"A";"B"**@{-}}*++{\oplus}\endxy?\quad\xyQ*+{A}="A";p+/r5pc/+(0,15)*+{B}="B",Q,p+<1pc,3pc>*+{C}="C"Q,"A"+<4pc,-1pc>*+{D}="D","A";"B"**@{-}Q,?!{"D",{\ar@/_/"C"}}*++{\oplus}\endxyN8 Whenthelineseparatestheend-pGointsofacurveanintersectioncanalwaysbGefound.NIfthereismorethanonekthenthatoGccurringearliestalongthecurveistheoneUUfound. If=thelinedoGesnotseparatetheend-pointsthentheremaybGenointersectionwiththecurve.IfthereisonetheneitherthelineistangentialornecessarilytherewillalsobGeatleastoneotherintersection.#KAmessage=;perhaps?nocurveintersection,ormany.isc\writtentothelog- le,butasearchforanintersection will$stillbGeperformedanda\sensible"placefoundonthe:curve."Intheusualcaseofasinglequadraticorcubicsegment,theplacenearestthelineisfoundandtheUUtangentdirectionisestablished. TheSfollowingexamplesshowthis,TBandshowhowtogetUUtheplaceonthelinenearesttothecurve.=덍Gps: SDict begin xyc end .g qADK^B rCP pD gA" {mark 60.0 42.67891 59.18091 -19.26114 0.0 0.0 1.0 0.05884 q}xyHş_^" {-3142 10 /xy AB}xy gE" {mark 60.0 42.67891 59.18091 -19.26114 0.0 0.0 0.05884 0.94629 q}xy gA" {mark 60.0 42.67891 59.18091 -19.26114 0.0 0.0 1.0 0.94635 q}xyMO4" {63.7903 14.72514 l}xy/͟5" {-3728 st}xy-T" {-3728 F d}xyǍ/͟" {-5.12988 23.44629 l}xy-xYWF j}ps: SDict begin xyc end .g qADK^B rC\ pD gA" {mark 60.0 42.67891 76.68945 -43.62149 0.0 0.0 1.0 0.04517 q}xyJ͟`" {-2906 10 /xy AB}xy gE" {mark 60.0 42.67891 76.68945 -43.62149 0.0 0.0 0.04517 0.96167 q}xy gA" {mark 60.0 42.67891 76.68945 -43.62149 0.0 0.0 1.0 0.96173 q}xyYC" {75.7903 25.2681 l}xy% 1\xy?*+{A}="A";p+/r5pc/+(0,15)*+{B}="B",Q,p-<.5pc,2pc>*+{C}="C","A"+<6pc,-.5pc>Q,*+{D}="D","A",{\ar@/_25pt/"B"}Q,?!{"C";"D"**@{-}}*\dir{x}="E"Q,+/_2pc/="F";"E"**@{-},?!{"C";"D"}Q,*{\otimes}\endxy\qquad\xyQ*+{A}="A";p+/r5pc/+(0,15)*+{B}="B",Q,p-<.5pc,2pc>*+{C}="C"Q,"A"+<7pc,.5pc>*+{D}="D","A"Q,{\ar@/_40pt/"B"},?!{"C";"D"**@{-}}Q,*{\otimes}\endxygw:Sometimes%TU>'ExXwillrunshortofmemorywhenmany :curvesareusedwithoutabackendwithspGecialsupport:for}curves.Inthatcasethefollowingcommands,that:obGeyUUnormalTU>'ExXgroupings,maybehelpful::sff2 mݍ5\SloppyCurves5\splinetolerance{3hdimeni}{ff2allowNadjustmentofthetoleranceusedtotypGesetcurves.TheL rstsetstoleranceto.8pt,afterwhich\splinetolerance{0pt}qzresets;totheoriginaldefaultofUU necurves.!t8.2CirclesandEllipses_HereUwedescribGethemeanstoaspecifycirclesofar-bitrarysradius,*:drawnwitharbitrarylinestyles._Whenlarge-sized$ob8jectsareusedtheyareregularlyspacedaroundthecircle.ySimilarlyellipsesmaybGespeci ed,but>onlythosehavingma8jor/minoraxesalignedinthestandardrdirections;ispacingofob8jectsisnolongerreg-ular,UUbutisbunchedtowardthenarrowerends. y SuchUUacircleorellipseisspGeci edusing...gff2:e\xycircleinhvectori{?hstylei}{ff2wherethecompGonentsofthehvectorideterminethelengthsoftheaxisfortheellipse;Cthusgivingacir-clegwhenequal. ThehstyleicanbGeanyhconni,kasinF14thatworkswithcurvedarrows|manydo.CAl-ternatively bhstyleicanbGeanyhob8jecti,;ewhichwillbGeplacedequally-spacedabGoutthecircleataseparationtoxsnugly tthehob8jectis.(IfhemptyithenasolidcircleorUUellipseisdrawn. y$t:lps: SDict begin xyc end33n:33n<" {30.0 -30.0 l}xy?"cǍ<" {3072 10 /xy AB}xy/" {3162 10 /xy AB}xy#^" {3251 10 /xy AB}xy[$" {3360 10 /xy AB}xy5u" {3500 10 /xy AB}xy :&cn:%vu:#6:!ٹ:aW:z:l0\xy?0;/r5pc/:*\dir{*}?;p+(.5,-.5)*\dir{*}="c",**\dir{-},*+!UL{c},"c",*\xycircle(1,.4){++\dir{<}},*\xycircle(1,1){++\dir{>}},*\xycircle<15pt,10pt>{};*\xycircle<10pt>{{.}}\endxyLW923@*tj??gw8.3QuadraticSplinesuTQuadratic%BGeziersplines,/KasdistinctfromcubicBGezier splines,*areIconstructedfromparabGolicarcs,using`con-trolpGoints'todeterminethetangentswheresuccessivearcsUUarejoined. V*ariousimplementationsofsuchcurvesexist.Theone{adoptedhereisconsistentwiththexfigdraw-ingutilityandtpicimplementations.bThesehavethepropGertyofbeginningandendingwithstraightseg-ments,~halfKthelengthtothecorrespGondingadjacentcontrol-pGoint.ddF*urthermore-,themidpointbetween-,suc-cessive~control-pGointsliesonthespline,2withthelinejoiningUUthecontrol-pGointsUUbeingtangentthere. Such'curvesarespGeci ed,\/eitherasahdecoriorasanUUhob8jecti,using... F ff2 NA\qspline{}hstylei}yff2QwherethestartandendofthecurveareatpandclrespGectively*.j Thecontrol-pGointsaretakenfromthecurrentCstack, see3o.IfthisstackisemptythenastraightUUlineisconstructed. TheQ7followingexamplecomparesthequadraticsplinewiththegentlercurvingB-splinehavingthesamecon-trolUUpGoints,using\crvsF.='ps: SDict begin xyc endƵP'շ+K+oշ+)֡ƵC7珟" {11.58334 11.58334 l}xy玟7L" {mark 132.00002 54.00002 114.00002 72.00002 96.00002 54.00002 0.0 1.0 q}xy玟7M" {mark 168.00002 54.00002 150.00002 36.00002 132.00002 54.00002 0.0 1.0 q}xy玟7M" {mark 204.00002 72.00002 186.00002 72.00002 168.00002 54.00002 0.0 1.0 q}xy)7" {11.06876 0.0 l}xy玟7c" {mark 78.00002 36.00002 114.00002 72.00002 132.00002 54.00002 150.00002 54.00002 0.0657 1.0 bt}xye" {mark 150.00002 54.00002 168.00002 54.00002 186.00002 72.00002 222.00002 72.00002 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)L9LFframeffandBracketffextensionVers.3.3bCyKristo erH.Rosehkrisrose@brics.dki Loadas:\xyoption{frame}Themframe˲extensionmprovidesavqarietyofwaystoputsframesUUinUQXY U-pictures. TheUUframesareUQXY U-pichob8jectisontheform F ff2 S\frm{RhframeiUU}yff2ߺtobGeusedinhposiitions: wZDroppingaframewith*?...\frm{꛸hframei} willħframethecob8ject;|Pconnect-ingwith**...\frm{꛲...hframei} FwillframetheresultofUUc.?p. BelowwedistinguishbGetween`ordinary'frames,`brackets'Fand` lls';ԾlastwepresenthowsomeframescanbGeaddedtootherob8jectsusingobjectmoGdi erhshapGeis.gw:9.1:Frames:Figureo8showsthepGossibleframesandtheapplicable :hmoGdi erisUUwithreferencetothenotesbelow.V:Notes󍍍:9a.YThe %\frm{}+8frame %isadummyusefulfornot:putting^aframeonsomething,e.g.,in^macrosthat:takeUUahframeiargument.:9b.?R}'ectangularoframes\ginclude\frm{.}+R,*\frm{-}+,:\frm{=}%,l\frm{--}1lm,l\frm{==},land\frm{o-}0.:Theyallmakerectangularframesthatessentially:traceUUthebGorderofarectangle-shapedob8ject. }:Thehframeis\frm{-},뷲and\frm{=}allowanop-:tional_c}'ornert\radius1thatroundsthecornersof:the@framewithquartercirclesofthespGeci edra-:dius.ThisZisnotallowedZfortheotherframes|:the4\frm{o-}6Pframe4alwaysgivesroundedcor-:nersofthesamesizeastheuseddashes(when:\xydashfont5&is thedefaultonethentheseare5pt:inUUradius).%:Exercisep19: HowdoyouthinktheauthortypGe-:setUUthefollowing?*ROQ7Ups: SDict begin xyc end qAn " {6.75 ox}xy(ß!Bߍ#3" {7.0434 ox}xyg3232􍍑32326323232323232323232323232323232323232323232323232323232323232323232326x3232!􍍐Ο3232}32323232323232323232323232323232323232323232323232323232*>3232}3232323232323232323232323232323232323232323232323232323232g3232􍍑32326323232323232323232323232323232323232323232323232323232323232323232326x3232 }:9c.#The frame\frm{,}*putsashade,builtfromrules,:intothepicturebGeneaththe(assumedrectangu-:lar)ob8ject,therebygivingtheillusionof`lifting'it;:\frm<*+hdimeni>{,}'makes3thisshadehdimenideep. }:\frm{-,}&?wcombinesUUa\frm{-}+jwitha\frm{,}(@.:9d.?Circles>Tdonewith\frm{o})Tradiusas(R+ L)=2:andawith\frm<Ƹhdimeni>{o}aɲhavearadiusasthe:hdimeni;I\frm{oo}0RmakesCadoublecirclewiththe:outermost?circlebGeingthesameasthatof\frm{o}&.%:Exercise20: What>isthedi erencebGetween:*\cir{} zandUU*\frm{o}-U=?:9e.#EllipsesbspGeci edusing\frm{e}+ʯhavebaxislengths:(R+L)=2dzand(U7+DG)=2,Iwhilethosewith:\frm<*+hdimen,dimeni>{e}{use{thegivenlengths:forNtheaxes. ]\frm{ee}9Mmakesadoubleellipse:withDoutermostellipsebGeingthesameasthatof:\frm{e}%. }:Withoutz%spGecialsupporttorendertheellipses,Yei-:therTviaahdriveriorusingthearc؟feature,the:ellipsewillbGedrawnasacircleofradiusapproxi-:matelyUUtheaverageUUofthema8jorandminoraxes.LW924*Z*tj??0zd>ps: SDict begin xyc endyMвF*ramedUUwith ZO\frm{} CXFframe^9a?~JF*ramedUUwith p\frm{.} RNframe^9bMڰ3232" 3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232$>݌3232ȍ32323232323232323232323232323232323232323232323232323232323232326݌3232ȍ323232323232323232323232323232323232323232323232323232323232323232ڰ3232" 3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232􍴍IJF*ramedUUwith M\frm<44pt>{.}㍍[sframe^9bč97" {19.02281 37.12471 -19.02283 -37.12471 19.02281 vt}xy%MѲF*ramedUUwith WdQ\frm{-} RXBframe^9b.biF2" {0.0 30.86118 -18.32835 -30.86118 18.32835 ov}xySJ73232L3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232$>J݌3232ȍ3232323232323232323232323232323232323232323232323232323232323232݌3232ȍ323232323232323232323232323232323232323232323232323232323232323232J73232L3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232$QKF*ramedUUwith P\frm<8pt>{-}㍍Nframe^9b.a2" {8.0 34.49974 -19.02283 -34.49973 19.02281 ov}xy793232oc32328'3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323283232&ύ<32323232323232323232323232323232323232323232323232323232323232323232P<3232323232323232323232323232323232323232323232323232323232323232323232793232oc32328'3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323283232$PŲF*ramedUUwith N\frm<44pt>{-}㍍[tframe^9b.`:7" {19.02281 37.12471 -19.02283 -37.12471 19.02281 ov}xy3232+3232>r3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232>b3232&ύ<32323232323232323232323232323232323232323232323232323232323232323232D(<32323232323232323232323232323232323232323232323232323232323232323232323232+3232>r3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232>b3232UMҲF*ramedUUwith WdR\frm{=} RXBframe^9b^^iG2" {0.0 30.86118 -18.32835 -30.86118 18.32835 ov}xy^^iG2" {0.0 28.86118 -16.32835 -28.86118 16.32835 ov}xyL J83232L3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232$>J݌3232ȍ3232323232323232323232323232323232323232323232323232323232323232݌3232ȍ323232323232323232323232323232323232323232323232323232323232323232J83232L3232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232UJ퍍LF*ramedUUwith 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=3232b3232323232323232323232323232323232323232323232323232323232323232N\3232b323232323232323232323232323232323232323232323232323232323232323232 ֞3232S03232GS3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232GD3232FigureUU9:qBrackethframeis.LW925Ib*tj??gw T ojDo:Allow~hframevqariantislikethoseusedfor directionals,mi.e.,\frm2{-}6~shouldbGethesameas\frm{=}.qAddUU\frm{o,}0andUUmorebrackets.#c9.2Brackets The8pGossiblebrackets8areshownin gure9withnotesbGelow.!cNotes 9f.Br}'aces$areQjustthestandardplainTU>'ExXlargebracesinsertedcorrectlyinXY -picpictureswiththe`nib'alignedwiththereferencepGointoftheob8jecttheybrace.&|Exercisep21: HowdoyouthinktheauthortypGe-setUUthefollowing?2oT^"ps: SDict begin xyc end  qA%(ğ!BLgg3232&퍍3232@~3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232@q3232,,Οt3232323232323232323232323232323232323232323232323232323232323232323232323232323232326>t32323232323232323232323232323232323232323232323232323232323232323232323232323232323232g3232&퍍3232@~3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232@q3232Lgz31} Lg|31 ~{ |31 3{)s z31 }ɿ~9g.'Par}'enthesisarelikebracesexcepttheyhavenonibandthusdonotdepGendonwherethereferencepGointUUofcis.} Bug:7вThehbracketsabGoverequirethatthecomputermoGdernUUcmexfontUUisloadedinTU>'ExXfontpGosition3.9.3Filledregions In`additiontotheabGove`thereisaspecialframethat\ lls"Vtheinsideofthecurrentob8jectwithink:[\frm{*}[and\frm?{**};thelatteralso\strokes"theout-line,4usingthethinnestblacklineavqailableontheprinteroroutputdevice.[RSomealterationtotheshapGeis͋pGossible,using*\frm{*}R^.jHencerectangu-lar,.ovqal,circular${*}ffx \rps: SDict begin xyc endg32321B3232J֍32323232323232323232323232323232323232323232JŞ3232Ο{3232M3232323232323232{3232M323232323232323232g32321B3232J֍32323232323232323232323232323232323232323232JŞ32328ps: SDict begin xyc endg32321B3232J֍32323232323232323232323232323232323232323232JŞ3232Ο{3232M3232323232323232{3232M323232323232323232g32321B3232J֍32323232323232323232323232323232323232323232JŞ3232 ups: SDict begin xyc endg32321B3232J֍32323232323232323232323232323232323232323232JŞ3232Ο{3232M3232323232323232{3232M323232323232323232g32321B3232J֍32323232323232323232323232323232323232323232JŞ3232 \rps: SDict begin xyc end͍*" {6.99998 6.99998 15.00003 15.00003 ot}xy8ps: SDict begin xyc end͍*" {6.99998 6.99998 15.00003 15.00003 ot}xy ups: SDict begin xyc end͍*" {6.99998 6.99998 15.00003 15.00003 ot}xy  fhffx,:However, ; llingnon-rectangularshapGeswillresultinarectanglec"unlessadriverisusedthatsuppGortsarbitrary lling.ҹInusomecasestheabGoveu llswillthusallberectangular.gw:9.4:Framingasobjectmo`di erk:Inaddition,BframesmaybGeaccessedusingthespecial :[Fj4hframei]ob8jectmoGdi erhshapeisthatwilladdthe:desiredhframeitothecurrentob8jectexceptthatthe:frame]that tstheedgeoftheob8jectwillbGechosen:(presentlyUUeitherrectangularorelliptical). ݍ;IfshapGemodi ersshouldbeappliedtothehframei:alonethentheycanbGeincludedusing: asseparator::[F-:red]n,will makearedframe(providedthecolor:extension2isactive,9ofcourse);>Badditionallythevqariant:ofyframesusing<vhdimeni>canybGeaccessedbyincluding:[*7...:< *hdimeni>] .;Thefollowingareusedtoensurethatthecurrent:styles,aftertypGesetting,arethoseofthehob8jecti,:ratherUUthanthehframei.;HereUUaresomesimpleexamplesusingthisfeature.%rps: SDict begin xyc end7a-ps: SDict begin {pu {1. 0. 0. rgb}cc}xyg endcolor push rgb 1. 0. 0.' 1Ʉckَps: SDict begin { pp}xyf end color pop-ps: SDict begin {pu {1. 1. 1. rgb}cc}xyg endcolor push rgb 1. 1. 1.'1Ȅ c_׎ps: 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. 0.1ɍS xoXŽps: SDict begin { pp}xyf end color pop-ps: SDict begin {pu {1. 1. 1. rgb}cc}xyg endSbQoldTwhiteonblac9kps: SDict begin { pp}xyf end color pop6.:\xy?*+<1.5pt>[F*:white]++[F**:red]:\txt{text?withbackground}:,+!D+/d1pc/,*++[F*:black][white]:\txt\bf{bold?whiteonblack}\endxy\;Notice thatwhenmultipleframe-moGdi ersareused,:theframesareactuallyplacedinreverseorder,&sothat:earlierUUonesareprintedontopoflaterones.;T oiDo:BThe'ExXgrouping.T$F*urthermore,dottedanddashed:frames7nowhavearegularspacingoftheirconstituent:ob8jects.؆ThewusualwarningsabGoutmemoryrequire-:mentsUUforlargenumbGersofcurvesapplyherealso..D:10PMoreffTipsextensionX:Vers.3.3bCyKristo erH.Rosehkris@diku.dki :Loadas:\xyoption{tips}:Thiszextensionprovidesseveraladditionalstylesof:`tips'eforuse(primarily)asarrowheads,jandmakesit:pGossibletode necustomisedtips.TThisisusedtosup-:pGortTtipsthatmimicthestyleoftheComputerModernLW926k*tj??gwfonts^8'ExXgroupingmecha-nism,UUe.g.,N8\SelectTips{cm}{10}\xy*{}?\ar?@{*{\UseTips\dir_{<<}}-*{\NoTips\dir{>}}}?(20,5)*{}\endxywillUUtypGesetYps: 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}xyregardlessGofwhichtipsareusedotherwiseinthedoGc-ument.%11 fdLineffstylesextensionVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{line}uTThis#extensionprovidestheabilitytorequestvqariouse ectsHrelatedtotheappGearanceofstraightlines;Le.g..thickness,UUnon-standarddashing,andcolour. These{uaree ectswhicharenotnormallyavqailablewithinTU>'ExX.[Insteadtheyrequireasuitable`back-end'option toprovidethenecessary\special1`commands,or߶extrafonts,=togetherwithappropriatecommandstoimplementUUthee ects.qThusw+:ps: SDict begin xyc end !ˍUsingU>thisextensionwillhaveU>no ce ectU>ontheoutputunlessusedwithUaU>backendthatexplicitlysuppGortsit.Ǎa_1" {0.0 97.73973 -18.44452 -97.73973 18.4445 ov}xy The8extensionprovidesspGeciale ectsthatcanbeusedjtwithanyjpXY t-pichob8jecti,byde ning[ qhshapGei]moGdi ers. Themodi cationislocaltothehob8jecticurrentlyWbGeingbuilt,wsowillhavenoe ectifthisob8jectisUUneveractuallyused.mff^ J= "5-:8LThisLfunctionwÎasearliersupp]\,setUUthicknesstohdimeni]n[k|$hhdimeni]\,alsoUUsetstohdimeni]n[k|$h=*ehwordi]\,make[ Shwordi]setcurrent\,styleUUsettingsX+]n[k|$h*]\,reuseUUpreviousstyle]n[butt]\,buttUUcapatends]n[roundcap]\,roundUUcapatends]n[projcap]\,pro8jectingUUsquarecap. qff2dLatersettingsofthelinewidthoverridedearliersettings;multiplekUcallsto[thicker]4and[thinner]compGound,but8theothervqariantssetanabsolutethickness.qTheline-thicknessspGeci cationa ectsarrow-tipsaswellastheClthicknessofstraightlinesandcurves.kThreekindsofIline-capsareavqailable;theyarediscussedbGelowintheUUsectionon`pGoly-lines'.#bߍ9ps: SDict begin xyc endvet},"p",{\ar@*{[|(4)]}"p";"c"<14pt>},"p",{\ar@*{[|(10)]}"p";"c"<4pt>},"p",{\ar@*{[|(20)]}"p";"c"<-16pt>}\endxyW Usingd1thePostScriptback-end,thesizeofthearrow-headgrowsaestheticallywiththethicknessofthePlineusedtodrawit.Thisgrowthvqariesasthesquare-roGot"ofthethickness;` thus"forverythicklines(20+timesnormal)thearrowheadbGeginstomergewithUUthestem. o The}diagramin gure10,page30,usesdi erentline-thicknessesUUandcolours.0EP9oly-lines ByEa`pGoly-line'wemeanapathbuiltfrom ?straightlinesegmentshavingnogapswhereeachsegmentzabutsthenext.ThepGoly-linecouldbetheedgesVeofapGolygon,eitherclosedoropeniftheend-pGointsUUaredi erent. The|reasonforconsideringapGoly-lineasaseparatehob8jecti,ratherthansimplyasahpathibuiltfromstraightdlines,_bGecomesapparentonlywhenthelineshave^appreciablethickness. ThenthereareseveralLW927ߠ*tj??gwstandard-ofhpGosiitionsinthecurrent`stack',[ignoringsizeextents.jThe?macro\xypolyline@?isusedasahdecori;itreadsthehpGosiitionsfromthestack,butleavesthestackUUintactforlateruse. TheYfollowingdiagramillustratestheuseofline-thickness,_line-joinsf*andline-capswithpGoly-lines.GItcontainsUUanexampleofeachofthestyles.3^9.lps: SDict begin xyc end%ps: SDict begin {pu 10.0 lw}xyg end0"ps: SDict begin {pu 0 lj}xyg endW" {0.0 48.0 72.00002 48.0 72.00002 -48.00002 -72.0 -48.00002 -72.0 48.0 0.0 48.0 pl}xyps: SDict begin { pp}xyf endW" {0.0 48.0 72.00002 48.0 72.00002 -48.00002 -72.0 -48.00002 -72.0 48.0 0.0 48.0 pf}xycolor push gray .5-ps: SDict begin {pu 1 lj{.5 gray}cc}xyg end[" {0.00002 36.0 60.00002 36.0 60.00002 -36.00002 -60.0 -36.00002 -60.0 36.0 0.0 36.0 pl}xyps: SDict begin { pp}xyf end color popcolor push gray .5(ps: SDict begin {pu {.5 gray}cc}xyg end[" {0.00002 36.0 60.00002 36.0 60.00002 -36.00002 -60.0 -36.00002 -60.0 36.0 0.0 36.0 pf}xyps: SDict begin { pp}xyf end color popcolor push rgb 1. 1. 1.-ps: SDict begin {pu {1. 1. 1. rgb}cc}xyg end[" {0.00002 24.0 48.00002 24.0 48.00002 -24.00002 -48.0 -24.00002 -48.0 24.0 0.0 24.0 pf}xyps: SDict begin { pp}xyf end color pop"ps: SDict begin {pu 2 lj}xyg end[" {0.00002 24.0 48.00002 24.0 48.00002 -24.00002 -48.0 -24.00002 -48.0 24.0 0.0 24.0 pl}xyps: SDict begin { pp}xyf endhAIB)ps: SDict begin {pu 5.0 lw 0 lc}xyg endc" {0.0 0.0 l}xyps: SDict begin { pp}xyf end)ps: SDict begin {pu 5.0 lw 0 lc}xyg endH" {43.55602 0.0 l}xyps: SDict begin { pp}xyf end)ps: SDict begin {pu 5.0 lw 0 lc}xyg endH" {0.0 0.0 l}xyps: SDict begin { pp}xyf end)ps: SDict begin {pu 5.0 lw 1 lc}xyg endc" {0.0 0.0 l}xyps: SDict begin { pp}xyf end)ps: SDict begin {pu 5.0 lw 1 lc}xyg endH" {43.55602 0.0 l}xyps: SDict begin { pp}xyf end)ps: SDict begin {pu 5.0 lw 1 lc}xyg endH" {0.0 0.0 l}xyps: SDict begin { pp}xyf end)ps: SDict begin {pu 5.0 lw 2 lc}xyg endc" {0.0 0.0 l}xyps: SDict begin { pp}xyf end)ps: SDict begin {pu 5.0 lw 2 lc}xyg endH" {43.55602 0.0 l}xyps: SDict begin { pp}xyf end)ps: SDict begin {pu 5.0 lw 2 lc}xyg endH" {0.0 0.0 l}xyps: SDict begin { pp}xyf endps: SDict begin { pp}xyf end?\xycompileto{poly}%{/r4pc/:,*[|<5pt>][thicker]\xybox{%?*+(3,2){}="X";@={p+CU,p+LU,p+LD,p+RD,p+RU,p+CU}?,{0*[miter]\xypolyline{}}?,{\xypolyline{*}},@i@),"X",*+(2.5,1.5){}="X",@={!CU,!LU,!LD,!RD,!RU,!CU}gw*7,{0*[gray][roundjoin]\xypolyline{}} *7,{0*[gray]\xypolyline{*}},@i@):,"X",*+(2,1){}="X":,@={!CU,!LU,!LD,!RD,!RU,!CU}*7,{0*[white]\xypolyline{*}}*7,{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>}:}}:Note theuseof{0*[...]\xypolyline{..}}Ҳtoapply:style-moGdi ers"Btoapolyline. ؎The@={!..}/omethod:for0xloadingthestackgivesequivqalentresultstous-:ingz;@={p+..}4G_,tsincez\xypolylineCӲignoresztheedge:extentsUUofeachhpGosiinthestack. s;Noted alsothattheargument#1Hto\xypolyline@af-:fectsUUwhatistypGeset.qAllowableUUargumentsare:: ?ff2 e\xypolyline{}g5solidUUlinee\xypolyline{.}g5dottedUUlinee\xypolyline{-}g5dashedUUlinee\xypolyline{*}g5 llUUenclosedpGolygone\xypolyline{?}g5 llpenclosedpGolygonusingg5even-oGddUUrulefde\xypolyline{{*}}g5useUU\dir{*}+jforUUlinese\xypolyline{}{5usingUU\dir{}sff29ڃThelattercasesonehas**\dir{...}AtbGeingusedtoconnecttheverticesofthepGolyline,gwith{{*}}!Obeingneededtoget**\dir{*}4 IJ.fSimilarly**\dir)isusedwhen\ahdriveriisnotavqailabletospGeci callysupportpGolylines;inkparticularthetwok` ll'options* and?willresultinadottedpGolygonoutlinetheregionintendedtoUUbGe lled. In+allcasesitisuptotheusertoloadthestackbGefore[calling\xypolyline{B[ڲ...}꧲.A[particularly[com-monʰcaseistheoutlineofanexistingʬXY J-pichob8jecti,asbintheexampleabGove.SF*uturebextensionsto\frmwill‘provideasimpli edmechanismwherebytheuserneedUUnotcall\xypolyline@jexplicitlyforsuche ects.*_.12 fdRotateffandScaleextensionzVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{rotate}LThis "extensionprovidestheabilitytorequestthatanyob8jectnbGedisplayednrotatedatanyangleaswellasscaledUUinvqariousways. These{uaree ectswhicharenotnormallyavqailablewithinTU>'ExX.[Insteadtheyrequireasuitable`back-end'option toprovidethenecessary\special1`commands,or߶extrafonts,=togetherwithappropriatecommandstoLW928Ĝ*tj??gwimplementUUthee ects.qThus$6덍Bps: SDict begin xyc end !ˍUsingU>thisextensionwillhaveU>no ce ectU>ontheoutputunlessusedwithUaU>backendthatexplicitlysuppGortsit.Ǎa_1" {0.0 97.73973 -18.44452 -97.73973 18.4445 ov}xy%  The8extensionprovidesspGeciale ectsthatcanbe usedwithanyXYY-pichob8jectibyde ning[ hshapGei]moGdi ers. Themodi cationislocaltothehob8jecticurrentlyWbGeingbuilt,wsowillhavenoe ectifthisob8jectisUUneveractuallyused. : The\followingtableliststhemoGdi ersthathavesofar PbGeende ned.ҹTheycomeintwo Ptypes P{eitherasinglekeyword,K1orakey-characterwiththefollowingtextUUtreatedasasingleargument.Mff2 􍍍A[@]fXalignwithcurrentdirectionA[@;hdirectioni]fXalignUUtohdirectioniA[@!U8hnumbGeri]fXrotateUUhnumbGeridegrees:A[*;hnumbGeri]fXscaleUUbyhnumbGeriA[*;hnumix,hnumiy·]fXscaleUUxandy.separatelyA[left]fXrotateHanticloGckwiseby90^A[right]fXrotateUU(cloGckwise)by90^A[flip]fXrotateby180^;ssameasfX[*-1,-1]񍍍A[dblsize]fXscaleUUtodoublesizeA[halfsize]fXscaleUUtohalfsize:ff2 These[hshapGei]modi ersspecifytransformationsofthehob8jecticurrentlybGeingbuilt.rIftheobjecthasarectangleedgethenthesizeoftherectangleistrans-formedtoenclosethetransformedob8ject;gwithacircleedgeUUtheradiusisalteredappropriately*. EachQ8successivetransformationactsupGontheresultofallprevious.6OneconsequenceofthisisthattheorderoftheshapGemodi erscanmakeasigni cantdif-ferencezinappGearance|ingeneral,transformationsdonotݧcommute. Evensuccessiverotationscangivedif-ferentUUsizedrectanglesiftakeninthereverseorder. : Sometimes}thischangeofsizeisnotdesirable.h>ThefollowingcommandsareprovidedtomoGdifythisbe-haviour. ۆff2 􍍍6_\NoResizing]6;preventsUUsizeadjustment6_\UseResizing]6;restoresUUsizeadjustmentsff2 u :The, \NoResizingBcommand, isalsousefultohave, atthe7bGeginningofadocumentbeingtypesetusingadriverthatcannotsuppGortscalinge ects, tinpartic-ularÓwhenappliedtowholediagrams.Inanycaseanunscaledversionwillresult,butnowthespacingandpGositioningwillbeappropriatetotheunscaledratherthanUUthescaledsize.gw:ScalingXandScaledT ext ThehshapGeimodi ercan :containVeitherasinglescalefactor,orapairindicating:di erent6factorsinthex-andy[ٲ-directions.Negative:vqaluesareallowed,toobtainre ectionsinthecoGordi-:nateUUaxes,butnotzero.%ߍ:Rotation0pandRotatedT ext Within*[@...](Bthe:...sareABparsedasahdirectioniloGcally*,xybasedonthecur-:rentqdirection.HThevqalueofcountregister\Direction:contains.theinformationtodeterminetherequested:direction.uWhennohdirectioniisparsedthen[@]{re-:questsUUarotationtoalignwiththecurrentdirection.9;ThespGecialsequence[@!...]._isprovidedtopass:anOPangledirectlytotheback-end. _TheOLXYP-picsize:and%shapGeofthehob8jectiwith\rectangleEdgeO~isun-:changed,eventhoughtheprintedformmayappGearro-:tated.@This(isafeaturethatmustbGeimplementedspGe-:ciallyLbytheback-end.F*orexample,JusingthePost-:Scriptback-end,![@!45]% willshowtheob8jectrotated:by45^insideabGoxofthesizeoftheunrotatedob8ject.;T opDo:`oProvide2exampleofrepGeated,9namedtrans-:formation.%ߍ:Re ections Re ections?canbGespeci edbyacom-:binationofrotationanda ip|either[hflip].or:[vflip] %.:Shear۰transformations T oDo:=Provide|@thestruc-:tureCtosuppGortthese;;'thenimplementitinPost-:Script.:Example Thevdiagramin gure10illustratesmany:ofdthee ectsdescribGedabovedaswellassomeadditional:onesUUde nedbythecolor ꛲androtate&*extensions.:Exercise22: SuggestEthecoGdeusedbytheauthor:toUUtypGeset10.9;TheH3actualcoGdeisgiveninthesolutiontotheexer-:cise.>#UseitasatestofthecapabilitiesofyourDVI-:driver.TheOlabGelsshould tsnuglyinsidetheaccom-:panyingUUrectangles,rotatedand ippGedappropriately*.;Bug: EThis> gurealsousescolours,\altersline-:thicknessandincludessomePostScriptdrawing.:Theg coloursmayprintasshadesofgray*,kywiththeline:fromAtoBbGeingthickerthannormal.Thewider:bandslopingdownwardsmayhavedi erentwidthand:lengthjaccordingtotheDVI-driverjused;u`thisdepGends:on$thecoGordinatesystemusedbythedriver,}when:`raw'UUPostScriptcoGdeisincluded.LW929#*tj??_>Lw+7ps: 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 end;FigureUU10:qRotations,scalingsand ips=_13wlColourffextensionVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{color}uTThis "extensionprovidestheabilitytorequestthatany ob8jectUUbGedisplayedUUinaparticularcolour. Itrequiresasuitable`driver'optiontoprovidethenecessary\special3k޲commandstoimplementtheef-fects.qThusaBps: SDict begin xyc end !ˍUsingU>thisextensionwillhaveU>no  e ectU>ontheoutputunlessusedwithafdvi-driverU>thatexplicitlysuppGortsit.Ǎa_1" {0.0 97.73973 -18.44452 -97.73973 18.4445 ov}xy! ColoursarespGeci edasahshapeimodi erwhichgivesthenameofthecolourrequested.$Itisappliedtoc/thewholeofthecurrenthob8jectiwhetherthisbGetext,?Xan9XY -pic9line,curveorarrow-tip,?XoracompGositeob8ject*Dsuchasamatrixorthecompletepicture.clHow-ever2someDVI2driversmaynotbGeabletosupportthecolourUUinallofthesecases. aÉff2 2C[ ?hcolourUUnamei]\NuseUUnamedcolourߍ\newxycolor{?hnamei}{ hcoGdei}\Nde neUUcolour\UseCrayolaColors\NloadUUcolournamesff2$IftheDVI-drivercannotsuppGortcolourthenarequestforr2colouronlyproGducesawarningmessageinthelog le.AftertwosuchmessagessubsequentrequestsareignoredUUcompletely*.SNamed4coloursandcolourmoQdels Newcolournames%arecreatedwith\newxycolor=寲,Ytakingtwo%ar-guments.!=Firstly:|anameforthecolourisgiven,sfol-lowedbythecoGdewhichwillultimatelybGepassedtotheWoutputdeviceinordertospGecifythecolour.IfthecurrentdrivercannotsuppGortcolour,0orgrayscaleshading,thenthenewnamewillbGerecognised,butignoredUUduringtypGesetting.=_;F*orPostScriptdevices,3theXY -psPostScript :dictionaryde nesopGeratorsrgb,Icmykcandgray2cor-:respGonding)tothestandardRGBandCMYKcolour:moGdels#andgrayscaleshadings.0Coloursandshades:aredescribGedas:rgbrgborc]myk3cmykors:gray.,Uwhere"theparametersarenumbGers"intherange:0ޅr;g[;b;c;m;y;kP;sޅ1.hTheopGeratorslinktothe:built-incolourmoGdelsor,inthecaseofcmykforear-:lierversionsofPostScript,giveasimpleemulation:inUUtermsoftheRGBmoGdel.$:Sa9vingS:colourandstyles Whenkstylesaresaved:using[=0hwordi]?,see,thenthecurrentcoloursetting:(ifany)issavedalso.zSubsequentuseof[햸hwordi]re-:coversthecolourandaccompanyingline-stylesettings. 卒;F*urthercolournamesarede nedbythecommand:\UseCrayolaColoursJthat(loadsthecrayon)6option,:inwhichmorecoloursarede ned. Consultthe le:xyps-col.doc)Bfor,thecoloursandtheirspGeci cations:inUUtheRGBorCMYKmoGdels.;xycra9yon.tex: Thiszoptionprovidesthecommand:toA[installde nitionsforthe68coloursrecognisedby:namebyT*omasRokicki'sdvips맲driver[11 ].GIThiscom-:mandUmustbGecalledfromahdriveri- lewhichcanac-:tuallyUUsuppGortthecolours.29:14PPatternffandTileextensionˍ:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{tile}:This\extensionprovidestheabilitytorequestthata: lledUUregionbGetiledusingaparticularpattern. 卒;This_isane ectnotnormallyavqailablewithinTU>'ExX.:InsteaditrequiresasuitablehdriverioptiontoprovideLW9303*tj??gwtheQnecessary\special0commands,Qtogetherwithany extraGTcommandsneededtoimplementthee ects.Thus"rBps: SDict begin xyc end !ˍUsingU>thisextensionwillhaveU>no  e ectU>ontheoutputunlessusedwithafdvi-driverU>thatexplicitlysuppGortsit.Ǎa_1" {0.0 97.73973 -18.44452 -97.73973 18.4445 ov}xy"IAll:e ectsde nedinthetileuextensioncanbGeimple-mentedgusingmostPostScripthdriveris,Lloadedas\xyoption{$hdriveri}?.P9atterns PatternsarespGeci edasahshapeimodi- er,PsimilartothewaycoloursarespGeci edbyname.TheP8patternisappliedtothewholeofthecurrenthob8jectiJwhetherthisbGetext,ΈanFXY 6J-picline,curveorarrow-tip,gor0acompGositeob8jectsuchasamatrixorthe|completepicture.However|someDVI-drivers|maynotUUsuppGortuseofpatternsinallcases. !ԍ IfthecurrentDVI-drivercannotsuppGortpatternsthenarequestforonesimplyproGducesawarningmes-sageginthelog le."AftertwogsuchmessagessubsequentrequestsUUareignoredcompletely*. ԉff2 83[shnamei]=useUUnamedpattern!ԍ3\newxypattern{?hnamei}{ hdatai}=spGecifyUUnewpatternusinghdatai3\UsePatternFile{c3|h lei}=setsUUdefault leforpatterns3\LoadAllPatterns{hsyh lei}=loadUUallpatternsinh lei3\LoadPattern{Sshnamei}{ h lei}=loadUUnamedpatternfromh lei3\AliasPattern{Xhaliasi}{ hnamei}{h lei}=letUUhaliasidenotepatternfromh lei.!։ff25n[AlthoughpatterndatamaybGespeci eddirectlyus-ingt\newxypatternH[,Mittismoreusualtoloaditfroma h leiinwhichmanypatternsarede nedbyname,eachGtonaseparateline.H$Byconventionsuch lesal-waysendin.xyp[(XY -pattern)sonoextensionshouldbGe/Ospeci ed.Thepatternisthenrequestedusingei-ther,hthenamesuppliedinthe leorbyanalias.d#Once\UsePatternFileR, hasl:bGeenused,qthenanullh leiar-gumentxtotheothercommandswillstill ndpatternsinZthedefault le.IThedefaultremainsine ectforthecurrentUUlevelofTU>'ExXgrouping. !ԍ F*orUUexample,thefollowingpicture"-DXlps: SDict begin xyc endjps: SDict begin {pu {42 }sp}xyg end%3:<ps: SDict begin { pp}xyf endjps: SDict begin {pu {48 <8888888888888888> <888888888888888888888888888888888888888888888888> }sp}xyg endps: SDict begin { pp}xyf end͍ " {15.0 ox}xy"pҍusesUU` lled'framesfromtheframe ꛲feature:N8\AliasPattern{bricks}{mac12}{xymacpat}\AliasPattern{bars}{mac08}{xymacpat}gw:\xy?*+<5pc,3.1pc>{},{*[bricks]\frm{*}} *7,*+<2.5pc>[o]{},*[bars]\frm{*},*\frm{o}:\endxy騍:P9atterndata Aregionistiledusingcopiesofasin-:gleM`cell'regularlyplacedsoastoseamlesslytilethe:entireregion.TThehdataiappGearingasanargumentto:\newxypattern.hisUUultimatelypassedtothedvi-driver. ;TheKsimplestformofpatterndatais:hnumihHex-:datai,wherethedataisa16-characterstringofHex-:adecimaldigits;i.e.O0{9,[A{Fc.EachHex-digitequates:to4binarybits,Jsothisdatacontains64bitsrepresent-:ingpixelsinan8'8array*.Thehnumiisaninteger:countingc@thenumbGerof`0'samongthe64bits.T*aken:asafractionof64,thisnumbGeroritscomplement,rep-:resentsatheaveragedensityof`on'pixelswithinasingle:cellofthepattern.QDriversunabletoprovidethe ne:detailtofapatternmaysimplyusethisnumbGer,|orits:complement,4as+agray-levelorpartofacolourspGeci -:cationUUforthewholeregiontobGetiled.X獒:The lexymacpat.xypG4containsde ningdataforthe:38ŝstandardpatternsavqailablewiththeMacintoshOp-:eratingUUsystem.qFigure11displaysallthesepatterns.p:RotatingnandResizingP9atterns SomeNimplemen-:tationsuofpatternsaresucientlyversatiletoallow:extra\parameterstoa ecttheway\thepatterndatais:interpreted.uFPostScriptղisonesuchimplementation:inTIwhichitispGossibletorotatethewholepatternand:evenUUtoexpandorcontractthesizesofthebasiccell.;Duetotherasternatureofoutputdevices,wnot:allsuchrequestscanbGeguaranteedtoproGduceaes-:theticGMresultsonalldevices.mInpracticeonlyrotations:throughspGeci cangles(e.g30^,̔45^,60^)andpartic-:ularscalingratioscanbGereliablyused.{qThusthere:isnosophisticatedinterfaceprovidedbyXY <-pictoac-:cess3thesefeatures.VHowever3the`PostScriptescapGe':mechanism3doGesallowaformofaccess,:EwhenaPost-:ScriptUUhdriveriishandlingpatternrequests.;SpGecial$PostScriptoperatorspa~Bandpfsetthe:patternBangle(normally0)and`frequency'measured:inc}'ellsperinch.{Hence,whenusedasanhob8jecti-:moGdi er,e[!?30pa18.75pq]eGrotatesbIthepatternby:30^ cloGckwiseandusesasmallerpatterncell(larger:frequency).TheY2defaultfrequencyof12:5=300=(8@3):meansIthateachpixelinapatterncellcorrespGonds,on:aEdeviceofresolution300dpi,|toa3ø3Esquareofdevice:pixels;UUonsuchadevice18:75uses282UUsquares.;At*300dpiafrequencyof9:375)=300=(8ƫ4)*uses:4OE4vsquares.֌Thesematchthenaturalsizeforpixels:ona75dpiscreenandareprettyclosefor72dpiscreens.:Thoughbappropriateforscreendisplays,etheseare`toGo:chunky'A4forhighqualityprintedwork.5eDoublingthe:frequencyistoGo neforsomepatterns,hencetheinter-:mediate|vchoiceof12:5asdefault.*InorderforprintedLW931 =Y*tj??F˟Qv:ps: SDict begin xyc end&7 lled jpatternƍ22" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xy }sp}xyg endê 6k#eps: SDict begin { pp}xyf endmac01LɍK lled jFqpatternU[2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {08 }sp}xyg endCq 6k#eps: SDict begin { pp}xyf endHmac02LȍvE lled jqbpattern 2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {16 }sp}xyg endnb 6k#eps: SDict begin { pp}xyf ends0mac03LǍu lled j>patternp2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {32 }sp}xyg end> 6k#eps: SDict begin { pp}xyf endޒmac04LƍˡQ lled j{patterneL2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {16 <55FF55FF55FF55FF> }sp}xyg end{ 6k#eps: SDict begin { pp}xyf endȌnmac05LōO- lled j(pattern(2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {32 }sp}xyg end( 6k#eps: SDict begin { pp}xyf end:Jmac06Lč lled jpattern*2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {16 }sp}xyg endҟ 6k#eps: SDict begin { pp}xyf end&mac07LÍK lled jFpatternUn2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {48 <8888888888888888> <888888888888888888888888888888888888888888888888> }sp}xyg endC 6k#eps: SDict begin { pp}xyf endHmac08' lled jëpattern*ٍ*2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {40 }sp}xyg end*ٍë 6k#eps: SDict begin { pp}xyf end?mۍmac09'K lled jFqpattern*؍U[2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {56 <8010022001084004> <808080101010020202202020010101080808404040040404> }sp}xyg end*؍Cq 6k#eps: SDict begin { pp}xyf end?mڍHmac10'vE lled jqcpattern*׍ 2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {36 }sp}xyg end*׍nc 6k#eps: SDict begin { pp}xyf end?mٍs0mac11'v lled j?pattern*֍q2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {42 }sp}xyg end*֍? 6k#eps: SDict begin { pp}xyf end?m؍ޓmac12'ˡR lled j{pattern*ՍeM2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {63 <8000000000000000> <808080000000000000000000000000000000000000000000> }sp}xyg end*Ս{ 6k#eps: SDict begin { pp}xyf end?m׍Ȍomac13'O. lled j(pattern*ԍ)2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {58 <8040200002040800> <808080404040202020000000020202040404080808000000> }sp}xyg end*ԍ( 6k#eps: SDict begin { pp}xyf end?m֍:Kmac14' lled jpattern*Ӎ*2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {49 <8244394482010101> <828282444444393939444444828282010101010101010101> }sp}xyg end*Ӎӟ 6k#eps: SDict begin { pp}xyf end?mՍ'mac15'K lled jFpattern*ҍUn2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {34 }sp}xyg end*ҍC 6k#eps: SDict begin { pp}xyf end?mԍHmac16R~ lled jìpatternU[*2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {48 <55A04040550A0404> <555555A0A0A04040404040405555550A0A0A040404040404> }sp}xyg endU[ì 6k#eps: SDict begin { pp}xyf endjmac17R}K lled jFqpatternU[U[2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {50 <2050888888880502> <202020505050888888888888888888888888050505020202> }sp}xyg endU[Cq 6k#eps: SDict begin { pp}xyf endjHmac18R|vE lled jqdpatternU[ 2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {31 }sp}xyg endU[nd 6k#eps: SDict begin { pp}xyf endjs0mac19R{w lled j@patternU[r2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {64 <0000000000000000> }sp}xyg endU[@ 6k#eps: SDict begin { pp}xyf endjޔmac20RzˡS lled j{patternU[eN2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {60 <8000080080000800> }sp}xyg endU[{ 6k#eps: SDict begin { pp}xyf endjȌpmac21RyO/ lled j(patternU[*2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {56 <8800220088002200> }sp}xyg endU[( 6k#eps: SDict begin { pp}xyf endj:Lmac22Rx lled jpatternU[*2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {48 <8822882288228822> }sp}xyg endU[ԟ 6k#eps: SDict begin { pp}xyf endj(mac23RwK lled jFpatternU[Un2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xy7ps: SDict begin {pu {48 }sp}xyg endU[C 6k#eps: SDict begin { pp}xyf endjHmac24}VX lled jípattern *2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {32 }sp}xyg end í 6k#eps: SDict begin { pp}xyf endɏmac25}VWK lled jFqpattern U[2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {48 <1122448811224488> <111111222222444444888888111111222222444444888888> }sp}xyg end Cq 6k#eps: SDict begin { pp}xyf endɎHmac26}VVvE lled jqepattern 2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {48 }sp}xyg end ne 6k#eps: SDict begin { pp}xyf endɍs0mac27}VUx lled jApattern s2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {56 <0102040810204080> <010101020202040404080808101010202020404040808080> }sp}xyg end A 6k#eps: SDict begin { pp}xyf endɌޕmac28}VTˡT lled j{pattern eO2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {56 }sp}xyg end { 6k#eps: SDict begin { pp}xyf endɋȌqmac29}VSO0 lled j(pattern +2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {49 }sp}xyg end ( 6k#eps: SDict begin { pp}xyf endɊ:Mmac30}VR lled jpattern *2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {51 <081C22C180010204> <0808081C1C1C222222C1C1C1808080010101020202040404> }sp}xyg end ՟ 6k#eps: SDict begin { pp}xyf endɉ)mac31}VQK lled jFpattern Un2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {50 <881422418800AA00> <888888141414222222414141888888000000AAAAAA000000> }sp}xyg end C 6k#eps: SDict begin { pp}xyf endɈHmac322 lled jîpatterng*2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {58 <40A00000040A0000> <404040A0A0A00000000000000404040A0A0A000000000000> }sp}xyg endgî 6k#eps: SDict begin { pp}xyf endwimac331K lled jFqpatternfU[2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {51 <038448300C020101> <0303038484844848483030300C0C0C020202010101010101> }sp}xyg endfCq 6k#eps: SDict begin { pp}xyf endwhHmac340vE lled jqfpatterne 2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {46 <8080413E080814E3> <8080808080804141413E3E3E080808080808141414E3E3E3> }sp}xyg endenf 6k#eps: SDict begin { pp}xyf endwgs0mac35/y lled jBpatterndt2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {44 <102054AAFF020408> <101010202020545454AAAAAAFFFFFF020202040404080808> }sp}xyg enddB 6k#eps: SDict begin { pp}xyf endwfޖmac36.ˡU lled j{patternceP2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {26 <77898F8F7798F8F8> <7777778989898F8F8F8F8F8F777777989898F8F8F8F8F8F8> }sp}xyg endc{ 6k#eps: SDict begin { pp}xyf endweȌrmac37-O1 lled j(patternb,2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyjps: SDict begin {pu {48 <0008142A552A1408> <0000000808081414142A2A2A5555552A2A2A141414080808> }sp}xyg endb( 6k#eps: SDict begin { pp}xyf endwd:Nmac38 xFigureUU11:qThe38standardMacintoshpatterns.Tdoutput^tomatchthescreenview,@_aPostScriptop- erator8macfreq,[has8bGeende nedtofacilitaterequestsforUU9:375,via[!macfreq]77. ⍑ Thenextdiagramdisplayschangestothefrequency*.V7ps: SDict begin xyc end&7 lled jpatternƍ22" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xybsps: SDict begin {pu 9.375 pq{48 <0008142A552A1408> <0000000808081414142A2A2A5555552A2A2A141414080808> }sp}xyg end& 6k#eps: SDict begin { pp}xyf end.^9.375Lɍh lled jbnpatternqϠ2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyrps: SDict begin {pu 12.5 pq{48 <0008142A552A1408> <0000000808081414142A2A2A5555552A2A2A141414080808> }sp}xyg end_n 6k#eps: SDict begin { pp}xyf endi12.5Lȍu lled j>patternp2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xysps: SDict begin {pu 18.75 pq{48 <0008142A552A1408> <0000000808081414142A2A2A5555552A2A2A141414080808> }sp}xyg end> 6k#eps: SDict begin { pp}xyf end.18.75LǍE lled jԵpattern@2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyrps: SDict begin {pu 37.5 pq{48 <0008142A552A1408> <0000000808081414142A2A2A5555552A2A2A141414080808> }sp}xyg endѵ 6k#eps: SDict begin { pp}xyf endf`37.5'/# lled j)pattern*ٍ82" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xysps: SDict begin {pu 9.375 pq{34 }sp}xyg end*ٍ& 6k#eps: SDict begin { pp}xyf end?mۍ.^9.375'h lled jbopattern*؍qϡ2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyrps: SDict begin {pu 12.5 pq{34 }sp}xyg end*؍_o 6k#eps: SDict begin { pp}xyf end?mڍi12.5'v lled j?pattern*׍q2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xysps: SDict begin {pu 18.75 pq{34 }sp}xyg end*׍? 6k#eps: SDict begin { pp}xyf end?mٍ.18.75'F lled jԵpattern*֍A2" {0.0 17.91484 -11.95004 -17.91483 11.95003 ov}xyrps: SDict begin {pu 37.5 pq{34 }sp}xyg end*֍ѵ 6k#eps: SDict begin { pp}xyf end?m؍fa37.5V4 Sa9vingkpatterns:I\Whenbstylesaresavedusinghwordi]?,tseenx??,thenthecurrentpattern(ifany)isalso^rsaved.Subsequentuseof[ ohwordi]recovers^rthepatternaswellascolourandline-stylesettings.̂Thisincludesa anyexplicitvqariationsappliedusingthe\StyleEscapGe"UUmechanism. HereLisavqariationofanearlierexample,Nwithextrae ects.%q}ps: SDict begin xyc endHjps: SDict begin {pu {42 }sp}xyg end0ps: SDict begin { pp}xyf endyps: SDict begin {pu macfreq -45 pa{56 <0102040810204080> <010101020202040404080808101010202020404040808080> }sp}xyg endeʎps: SDict begin { pp}xyf end΍" {15.89996 ox}xy7ps: SDict begin {pu {16 <55FF55FF55FF55FF> }sp}xyg end33 ff<ps: SDict begin { pp}xyf end*" {0.0 30.00002 -16.2 -30.00002 16.2 ov}xyff33<;ϟff ff33color push rgb 1. 1. 1.-ps: SDict begin {pu {1. 1. 1. rgb}cc}xyg endy !=R6ff cmss12Kilroywas/hereps: SDict begin { pp}xyf end color pop+\UsePatternFile{xymacpat}\AliasPattern{bricks}{mac12}{}\LoadPattern{mac28}{}\LoadPattern{mac05}{}\xy?*=0[!macfreq-45pa][mac28][|=Bars]{},*+<12pc,4pc>{}*[bricks]\frm{*},-<3.5pc,0pt>,*+<2.65pc>[o]{},*[Bars]\frm{*},*[thicker]\frm{o},+<6pc,0pt>,*+<5pc,?2.7pc>{},*[mac05]\frm{*},*\frm{-,},*[white]\txt\Large\bf\sf{Kilroy\\was?here}d:\endxy-7:15PImps3ortffgraphicsextension_:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{import}S:ThisfeatureprovidestheabilitytoeasyaddlabGels :and3annotationstographicspreparedoutsideTU>'ExXor:L5ffA͉TU>'ExX.&AnqXY Iu-picugraphicsenvironmentuisestablished:whose>coGordinatesmatchthatwithinthecontentsof:the٪impGortedgraphic,:makingiteasytospecifyex-:actlyIwherealabGelshouldbeplaced,orarrowdrawn:toUUhighlightaparticularfeature. @z;Acommand&\xyimport61is&de nedwhichisused,in:conjunctionSwithimpGortedgraphics,Ttoestablishaco-:ordinatesystemappropriatetotheparticulargraphics.:This?enableshpGosiitionswithinthegraphictobeeasily:loGcated,neitheriwforlabellingoraddingextraembellish-:ingUUfeatures.qItisusedineitherofthefollowways:: !ff2 ލ E\xyimport(=width,?height){ hgraphici} E\xyimport(=width,?height)( x-o ,y[ٲ-o ){hgraphici}@|ff2 Acommand}\xyimport9߲is}de nedwhichisused,DinconjunctionSwithimpGortedgraphics,Ttoestablishaco-ordinatesystemappropriatetotheparticulargraphics.This?enableshpGosiitionswithinthegraphictobeeasilyloGcated,neitheriwforlabellingoraddingextraembellish-ingUUfeatures.qItisusedineitherofthefollowways: !ff2 ލ E\xyimport(=width,?height){ hgraphici} E\xyimport(=width,?height)( x-o ,y[ٲ-o ){hgraphici}@|ff2LW932!Z/*tj??Uc Zps: SDict begin xyc end>;Yps: 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@ 4" {0.0 106.20894 -64.52568 -64.52567 106.20892 ov}xyT /oframedUUcontentsofgraphics letps: SDict begin xyc endB>;Yps: 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"T1N ҵ1G.1W5P!ӟ-P|[2P2PEʏ&3PPƟ3P#ָ1(}" {-0.00902 0.00902 l}xy}~EH" {-2048 10 /xy AB}xy}~EH" {-9.22876 9.22876 l}xy}~EH" {-0.00902 0.00902 l}xyh1m?}" {-0.00902 0.00902 l}xydEH" {-2048 10 /xy AB}xydEH" {-9.22876 9.22876 l}xydEH" {-0.00902 0.00902 l}xy-1L+" {0.00902 -0.00902 l}xy95W" {2048 10 /xy AB}xy95W" {9.22876 -9.22876 l}xy95W" {0.00902 -0.00902 l}xyrCN;FigureUU12:qimpGortingagraphicforlabellingQsONormallyGthehgraphicsiwillbGeaboxcontaininga graphicSimpGortedusingthecommandsfrompackqagessuch&asgraphics/, Yepsf sorepsfig%, YorusingothercommandsDprovidedbytheloGcalTU>'ExXimplementation.HoweverthehgraphicicouldbGeanybalancedTU>'ExXma-terialB8whatsoGever;provideditoGccupiesnon-zerosize,bGothUUverticallyandhorizontally*.D The)widthandheightarehnumbGeris)giveninthecoGordinatepsystemforthec}'ontentsofthehgraphicsi.Thesearenotdimensions,butcoGordinate-lengths,us-ing![theunitsappropriatetothepicturedisplayed![byhgraphici. Whenprovided,C( x-o ,?y[ٲ-o ) !givethedistanceincoGordinatei+unitsfrombottom-leftcornertowheretheorigin4kofcoGordinatesshouldbelocated,;usuallywithinarea*Kcoveredbythehgraphici.UsuallythenegativesofEthesenumbGersEwillgivethecoordinatelocationoftheFbGottom-leftcornerofthehgraphici.FIfnoo setsaresuppliedthentheoriginispresumedtolieatthebGottom-leftUUcorner. Normallythe\xyimport8ﻲcommandisusedatthebGeginning6)ofan\xy..\endxyB,1environment.CIt6)isnotnecessarytogiveanybasissetup,2forthisisdeducedbyb>measuringthedimensionsofthehgraphiciandusingthesuppliedwidth,R4heightando sets.ЫThehgraphiciitselfde nesnamedhpGosicalled"import"-,locatedattheoriginandhavingappropriateextentstodescribGethe~areacovered~bythehgraphici.DCThismakesitpar-ticularlyeasytosurroundthehgraphiciwithaframe,as!9ontheleftsideof gure12,+ortodrawaxespassingthroughUUtheorigin. HereOisthecoGdeusedtoapplythelabellingin g-ureUU12:s:\def\ellipA{\resizebox{6cm}{!}{% j4\includegraphics{import1.eps}}}:\xy:\xyimport(3.7,3.7)(1.4,1.4){\ellipA}*\frm{-}:,!D+<2pc,-1pc>*+!U\txt{%*7framed?contentsofgraphicsfile}\endxy:\qquad\qquad:\xy\xyimport(3.7,3.7)(1.4,1.4){\ellipA}:,!D+<2pc,-1pc>*+!U\txt{Rational?points*7on?theellipticcurve:$x^3+y^3=7$}:,(1,0)*+!U{1},(-1,0)*+!U{-1}:,(0,1)*+!R{1},(0,-1)*+!R{-1}:,(2,-1)*+!RU{P},(-1,2)*+!RU{-P}:,(1.3333,1.6667)*+!UR{-2P}:,(1.6667,1.3333)*!DL{\;2P}:,(-.5,1.9)*++!DL{3P},(1.9,-.5)*!DL{\;-3P}:,(-1,2.3)*+++!D{\infty}*=0{},{\ar+(-.2,.2)}:,(.5,2.3)*+++!D{\infty}*=0{},{\ar+(-.2,.2)}:,(2.3,-1)*+++!L{\infty}*=0{},{\ar+(.2,-.2)}:\endxyR};ThishexampleusestheL5ffA͉TU>'ExX2".standardgraphics:packqagebtoimpGortthegraphics leimport1.epsor\illustrationL~commands:inUUTexturesontheMacintosh.E;The#onlypGossibleproblemsthatcanoccurarewhen:thegraphicspackqageisloadedafterXY$-pichasbGeen:loaded.FGenerallyditisadvisabletohave`XY Td-picdloading:afterUUallothermacropackqages.LW933"*tj??gw16wlPostScriptffbackendnVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{ps}OXY-psisa`back-end'whichprovidesXY=-picwiththe abilitytoproGduceDVI lesthatusePostScript\specials"BforUUdrawingratherthantheUQXY U-picfonts. [ Inc#particularthismakesitpGossibletoprintcXY #-picDVI les/onsystemswhichdonothavetheabilitytoloadthespGecialfonts.Thepenaltyisthatthegen-erateddDVId leswillonlyfunctionwithoneparticularDVIW*arning:TheproGducedDVI le  BpisU>notp}'ortable[:ItcontainsPostScript qō!\specialsU>forhoneparticularidriverǍa_2" {0.0 97.73973 -18.94447 -97.73973 18.94446 ov}xy%<AvmorecompletediscussionoftheprosandconsofusingUUthisbackendUUisincludedbGelow.#216.1Cho`osingtheDVI-driverIncluding*\xyoption{ps}IX-within*thedoGcumentpream-ble,tellsdXY -picdthatthePostScriptalternativetothefontsWshouldbGeused,Xdprovidedthemeanstodothisisalso@spGeci ed.4Thisisdonebyalsospecifyingadvi-driverwhichiscapableofrecognisingandinterpret-ing \special1(commands.-Although the lexyps.texisߴreadwhentheoptionrequestisencountered,BKthemacros>containedthereinwillhavenoe ectuntilanappropriateUUdriverhasalsobGeenloaded. [ With\4L5ffA͉TU>'ExX2" bGoththebackend\4anddrivermaybGecspeci ed,alongwithotheroptions,viaasingle\usepackage-&'ExXv1.8+17oztexAAndrewUUT*revorrow'sO4zTU>'ExXv1.7ff<~;Other1\DVI-driversmayalsoworkusingoneofthese : les,VifVtheyuseconventionsVsimilartodvips!G,O4zTU>'ExX:or(Textures.?AlternativelyitshouldnotbGetoodif-: cultdEtowritethe lesrequired,husingtheseasabasis:indicating#thetypGeofinformationneededtosupport:thespGeci c\special1%commands.*JAnyoneattempting:to[edothisshouldinformtheauthorandconvey[easuc-:cessfulJimplementationtohimforinclusionwithinthe6XYj:-picUUdistribution. ;Note:In8somepreviousversionsof4XY 8-picthePost-:Scriptq;backendanddriverwereloadedsimultaneously:byƖacommandoftheform\UsePSspecials{Qihdriveri}?.:F*or backward-compatibilitythesecommandsshould:stillvwork,butnowloadingthelatestversionofthe:givenhdriveri. 5hHowevertheirfutureuseisdiscour-:agedxinfavourxoftheoption-loadingmechanism,@via:\xyoption{jhdriveri}?.\Thislattermechanismismore: exible,7bGothpinhandlingupgradesoftheactualdriver:suppGortandinbeingextensibletosupportmoregen-:eralUUformsof\special0commands.[;OnceoactivqatedthePostScriptbackendocanbGe:turnedOo andonagainatwill,ăusingtheuserfollowing:commands:: ff2  f\NoPSspecialsjV3cancelsUUPostScript f\UsePSspecials?{}jV3restoresUUPostScript ff2LThese=obGeynormalTU>'ExXscopingrulesforenvironments;hence7itissucienttospGecify\NoPSspecialsKGwithinanyenvironmentorgrouping.)UseofPostScriptwillbGeUUrestoreduponexitingfromtheenvironment.16.2%Whyuse>- cmcsc10PostScriptAtsomesitesusershavedicultyinstallingtheex-tralfontsusedbylXY -pic.The.tfmz lescanalwaysbGeinstalledSbloGcallybutitmaybenecessaryforthe.pkbitmapfonts(orthe.mfMETAF9ONTfonts)tobGein-stalledglobally*,Rbythesystemadministrator,forprint-ingjtoworkcorrectly*.]#IfPostScriptisavqailablethenXY -psUUallowsthislattersteptobGebypassed. Note:with^XY(b-psbitisstillnecessarytohavebthe.tfm]font]metric lescorrectlyinstalled,_asthesecon-tainUUinformationvitalforcorrecttypGesetting.[OtherXadvqantagesobtainedfromusingTXY4X-psarethefollowing:LW934#*tj??gw  Circles#andcirclesegmentscanbGesetforarbitrary  radii.6  solidUUlinesarestraighterandcleaner.  TheirangeofpGossibleanglesofdirectionalsis greatlyUUincreased.  SplinecurvesaresmoGother. #1T*ruedottedand dashed0versionsarenowpGossible,g&usingequally spacedUUsegmentswhicharethemselvescurved.  The JPostScript leproGducedbyadriverfrom an\XY a`-ps`DVIB leisingeneralsigni cantlysmaller thanoneproGducedbyprocessingan`ordinary' DVI le8usingthesamedriver.3Onereasonforthis is5thatnofontinformationforthe1XY A5-picfontsis requiredinthePostScript le;=thisfurthermore meansthattheuseofXY !-picdoGesnotinitselflimit theUUPostScript letoaparticularresolution.^9  TheYlatestversionofUXY4Y-picnowenablesspGecial e ectssuchasvqariablelinethickness,gray-level and;colour.$Also,u*rotationoftextand(pGortions of)OdiagramsisnowsuppGortedwithsomedrivers. SimilarlyS"wholediagramscanbGescaledupordown to& tagivenareaontheprintedpage.%:F*uture versionswillallowtheuseofregions lledwith colourtand/orpatterns,aswellasotherattractive e ects.k SomeoftheabGoveadvqantagesaresigni cant,butthey#8comeataprice.pKnowndisadvqantagesofusingXY-psUUincludethefollowing:3  AMDVI lewithspGecialsforaparticularPost- Scriptk&drivercanonlybGepreviewedifapre- viewerisavqailablethatsuppGortsexactlythesame \special2rformat.AauseparateaPostScriptpre- viewerUUwillusuallybGerequired.6 HoweverWrecentversionsofxdvisuppGortviewing ofWIPostScriptusingeithertheGhostScriptpro- gram>Xorvia\DisplayPostScript". ,ThePost- Script{proGducedbywXY h{-pscanbeviewedthisway  DVIi lesjQcreatedusingjMXYQ-psinfactlosetheir \device-indepGendence". So3Upleasedonotdis- tribute4DVI leswithPostScriptspGecials|send eitherQtheTU>'ExXsourcecoGde,yexpectingQtherecipient to]haveYXY s]-pic >c@*^ 9,orsenda(compressed)Post- ScriptUU le.3Thelattercommentappliesto lesinwhichanyspGe-cialf`back-end'suppGortisrequired,+notjusttoPost-Script.WOfLcourseitcanbGeignoredwhenyouknowtheUUcon gurationavqailabletotheintendedrecipient.9bff^ J= "5-:9LMost%TAEMXPostScriptdrivÎersstoretheimagesofcharacters used1inthetextasbitmapsataparticularresolution.ThismeansbXthatthePostScript lecanonlybismoreecienttohavethePostScriptcom-:mandsJ?thatJ;XY ?-psneedsloadedinitiallyfromasepa-:rate \header" le.rT*ousethisfacilitythefollowing:commandsUUareavqailable...:^<ff2 4̿\UsePSheader?{}4̿\UsePSheader?{}4̿\dumpPSdict?{}4̿\xyPSdefaultdict1ff2 靍Normallyitissucienttoinvoke\UsePSheader{}Nj,whichJinvokesthedefaultnameofxy33dict.pro,re-ferring"tothecurrentversionofXY w"-pic.W-Theoptionalh lenameioOallowsadi erent letobGeused. Plac-ing<\dumpPSdict{..}VKwithin'ExXsystem.&"Usuallyitissucienttohavekacopyinthecurrentworkingdirectory*. Invok-ingEthecommand\dumpPSdict{}KTcwillplaceacopyofthe#requisite le,havingthedefaultname,inthecur-rentEdirectory*.This lewillbGeusedasthedictionaryfor^2thecurrentproGcessing,iprovideditisonthecor-rect[directorypath,5\sothatthedrivercanloGcateitwhen needed.CYConsultyourloGcalsystemadministratorifUUyouexpGeriencediculties.$%17 fdTPICffbackendVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{tpic}uTThisoptionallowstheXY -picfontstobGereplacedbytpic\special.{s,\bwhenusedwithadvi-drivercapa-ble"ofsuppGortingthem. +.ExtracapabilitiesincludesmoGother.lines,&$evenlyspaceddotted/dashedcurves,vqariable'ExXimplementationprovidesasuite8of\special3Xcommandstofacilitatethedraw-ingoflines,bGothon-screenandwithvqariousprintingdevices.[UThis`back-end'extensionallowsthelinesinXY -picUUdiagramstobGedrawnusingthesemethods. NoteIthatthisextensiondoGesnothaveItobeusedwithtem-TU>'ExX.ρBetterresultsmaybGeobtainedusingthePostScriptback-endanddvipshdriveri,Tsincea%versionofdvipsisavqailableforem-TU>'ExX.W7However,in-particularforscreenpreviewingpurpGoses,hitmaybeconvenientX,tousethisback-end.dF*urthermorenotethatdvipsUUiscapableofsuppGortingem-TU>'ExX\special)s. Onceǿloadedusing\xyoption{emtex}WǏ,Zwithanap-propriatem'ExXbackendUUo /on. [ff2 Jb\NoEMspecialsbv8turnsUUo em-TU>'ExXspGecials.b\UseEMspecialsbv8reinstatesUUem-TU>'ExXspGecials.ff2u~Of thecurvesde nedinthexycurve,extension,6onlysolidUsplinecurvesaresuppGorted.Thisisdonebytreat-ingethesplineasapGolygon(poly-line)withmanyseg-ments.gw:PartffIs3IIP:F=eatures;:ThispartdoGcumentsthenotationaddedbyeachstan- :dard\featureoption.F*oreachisindicatedthedescribGed:versionUUnumbGer,theauthor,andhowitisloaded. P;Thev rsttwo,1}`all'vand`dummy',describGedinxx19:andƮ20,6aretrivialfeaturesthatneverthelessproveuse-:ful sometimes.mThenexttwo,:Z`arrow' and`2cell',de-:scribGedM+inx21and22, providespecialcommandsfor:ob8jectsthat`pGoint'.Thefollowing,`matrix'inx23,:`graph'u]inx24,}_`pGoly'inx25,and`knot'inx28,arein-:putimo}'desӲthat'suppGortdi erentoverallstructuringof:(partsUUof)UQXY U-pictures."%:19PAllfffeatures}:Vers.3.3bCyKristo erH.Rosehkrisrose@brics.dki :Loadas:\xyoption{all} :AsaspGecialconvenience,#thisfeatureloadsasubsetof6XYj:-pic,^11 |namelyI&theextensions:kcurve!Dz(cf.x8),Kframe:(x9),qcmtip$(x10),qlinew(x11),qrotate)(x12),qcolor:(x13),*and Xthefollowingfeatures:WImatrix&(x23),arrow:(x21),UUandgraph ꛲(x24).)a:20PDummyffoption:Vers.3.3bCyKristo erH.Rosehkrisrose@brics.dki :Loadas:\xyoption{dummy} :This:optionisprovidedasatemplatefornewoptions,:itprovidesneitherfeaturesnorextensionsbutitdoGes:countUUhowmanytimesitisrequested.)a:21PArrowffandPathfeature:Vers.3.3bCyKristo erH.Rosehkrisrose@brics.dki :Loadas:\xyoption{arrow} :Thisafeatureprovides]XY 6a-picwiththearrowparadigm:presentedUUin[12 ]. P;Note:Y\PATH&b²command ff3=lastUUsegmentonly [ ffͤ fffd= ff3=everyUUsegment ffffd(whenDseveralapplytothesamesegmenttheyare insertedUUinthesequence<>+L).Thisisusefultodrawconnectionswitha`centermarker'inparticularwitharrows,e.g.,the`map-sto'[exampleexplainedbGelowcanbechangedintoaUU`breakto'example:qtypingN8\xy*+{0}\PATHQ~={**\dir{-}}Q~>{|>*\dir{>}}Q~+{|*\dir{/}}Q'(10,1)*+{1}?'(20,-2)*+{2}(30,0)*+{3}\endxyewillUUtypGesett?Ops: SDict begin xyc endګ0sߟH1sޟU" {17.45258 1.74956 l}xy5 " {2867 st}xy;罟q28缟" {17.45258 -5.24867 l}xy0-Ο " {2380 st}xyX[ګ3U[" {17.45258 3.48837 l}xyLz* " {2963 st}xyU[" {3277 10 /xy AB}xyeNote,=however,thatVwhatgoGesinto~+{hM...} ishlabGelsiRandthusnotahposi{itisnotanactioninUUthesenseexplainedabGove.gw:21c.# SpGecifying~{hstu i}ڱwillsetthe\failurecontin- :uation"tohstu i._ThiswillbGeinsertedwhenthe:last˸hsegmentiisexpGected|itcanevenreplaceit:orUUaddmorehsegmentis,i.e.,N8:\xy?*+{0}\PATH~={**\dir{-}}j4~{'(20,-2)*+{2}?(30,0)*+{3}}'(10,1)*+{1}:\endxy:isUUequivqalentto:\xy?*+{0}\PATH~={**\dir{-}}j4'(10,1)*+{1}?'(20,-2)*+{2}(30,0)*+{3}:\endxy:typGesettingፍ6)ps: SDict begin xyc endګ0sߟH1sޟU" {17.45258 1.74956 l}xy;罟q28缟" {17.45258 -5.24867 l}xyX[ګ3U[" {17.45258 3.48837 l}xyҍ:bGecause^when\endxy$=Visseenthentheparserknows:that!\thenextsymbGolisneitherofthecharacters:~'` !andChencethatthelasthsegmentiistobGeex-:pGected.pInstead,however,thefailurecontinuation:isZinsertedandparsed,3andthehpathiis nished:byUUtheinsertedmaterial.:F*ailureUUcontinuationscanbGenested::\xy?*+{0}\PATH~={**\dir{-}}*7~{~{(30,0)*+{3}}*7'(20,-2)*+{2}}?'(10,1)*+{1}:\endxy:willUUalsotypGesettheconnecteddigits.Gp:21d.?AUU\straightsegment"isinterpretedasfollows:#1.:First΃pissettotheendob8jectoftheprevious :segmentn(forthe rstsegmentthisiscjust:bGeforethepathcommand)andcissettothe:hpGosi-startingthehsegmenti,5|andthecurrent:hslideiUUisapplied.Gp#2.:Thenthe=sand(.5)ȍhitiAYGv.!Wj#hdigitiUUj qhletteriUUj{ĸhtexti}Rjhcsi:(0,0)*7*+\txt{base}="base"*7\PATH?~={**\dir{-}?>*\dir{>}}%`l(-1,-1)*{A}?^a%`?(1,-1)*{B}?^b%`_ul (1,?0)*{C}^c%`ul^l?"base"?^dLW938' *tj??gwFP"base"?^e \endxyJBug:fT*urns$areonlyreallyresonableforpathsthatUUusestraightlinesliketheoneabGove.܍Note:AlwayswriteavqalidhpGosiafterahturni,otherwiseyanyfollowing^or_labGelscanconfusethe}parser.Soifyouintendthe^r{rin`^rotobGealabGel/thenwrite`,^r#,usingadummy,hpGosiition.Thendefaultusedforturnr}'adiusbcanbGesetbytheopGeration Cwff2 b@%\turnradiusUUhaddopi{Rhdimeni}ލff2thatworkslikethekernel\objectmarginetc.commands;UUitdefaultsto10pt.ExerciseT23: TypGeset;K^kops: SDict begin xyc enddd qA$d" {10.00002 0 360 o}xy " {10.0 45 315 o}xy2" {3829 10 /xy AB}xy usingUUhturnis.21g.(The|xlastsegmentisexactlyasastraightoneex-ceptthatthe>action(ifany)isexecuted(andcleared)UUjustafterthe}(20,7)\endxy :typGesets:Ips: 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":ExerciseT25: TypGesetUUthesearrows:QSslideUUarrow^21s[thehdimeniBSjR|UUhanchorihitiQSbreakUUeachsegmentathanchoriwithhitiBSjR^UUhanchorihitijq_hanchorihitiQSlabGelUUeachsegmentathanchoriwithhitiBSjR@?QSreverseUUmeaningofabGoveandbGelow^21t޸hvqarianti<B%!Rhemptyijq^j_VPj_t0jq1j2j3QShvqarianti:qplain,UUabGove,bGelow,double,ortriple޸htipi<B%!RhtipGchari*QSdirectionalUUnamedasthesequenceofhtipGcharisiBSjRhdiriQSanyUUhdiriectional^21n޸htipGchari<B%!R<[BMja^>ijp(xոj~G)Wjt | ]j%'!jד`ljW+j;/QSrecognisedUUtipcharactersBSjRhletterijqhspaceiQSmoreUUtipcharacters޸hconni<B%!Rhconnchari*QSdirectionalUUnamedasthesequenceofhconncharisiBSjRhdiriQSanyUUhdiriectional^21n޸hconnchari<B%!R-[BMja^.ijp~xոj~G=Wjt :QSrecognisedUUconnectorcharactersffd FigureUU14:qǸharrowis.U-u\newdir{|>}{!/4.5pt/\dir{|} A*:(1,-.2)\dir^{>}A*:(1,+.2)\dir_{>}}rde nesUUanewarrowtipthatmakesN8\xy?(0,0)*+{A}Q\ar?@{=|>}(20,3)*+{B}\endxytypGesetzqL$4ps: SDict begin xyc end qA;HB \Z" {0.01512 0.0 l}xy h" {0.01512 0.0 l}xy6c " {3226 st}xy:ռ" {3029 10 /xy A}xy:ռ" {3449 10 /xy B}xy6;q" {40.8887 6.12706 l}xy6 zO" {40.8887 6.12706 l}xy6Noticej?thatthefactthatthedirectionalusesonlyhtipGchariϲcharactersmeansthatitblendsnaturallywithUUtheexistingtips.qExercise*26: Oftentipsusedas`tails'havetheirinktIonthewrongsideofthepGointwheretheyare-u:placed._F*ortunatelyspaceisalsoahtipGcharisowe :canYde ne\dir{?>}0 togeneratea`tail'arrow.WsDo:thisUUsuchthatN8:\xy?(0,0)*+{A}="a",(20,3)*+{B}="b"*7\ar?@{>->} "a";"b"<2pt>*7\ar?@{>->}"a";"b"<-2pt>:\endxyԻ:typGesets Bfps: SDict begin xyc end qA;HB 0" {3226 10 /xy AB}xy 4џ" {0.01512 0.0 l}xy8M-" {3226 10 /xy AB}xy8M-" {43.11179 6.4614 l}xy8M-" {0.01582 0.0 l}xyGj4" {3226 10 /xy AB}xy8밟!" {3226 10 /xy AB}xy8밟!" {40.6417 6.08992 l}xy8밟!" {0.01582 0.0 l}xyğ :21n.?SpGecifyingdahdiriasahtipiorhconnimeansthat:\dirhdiri7isusedforthathtipiorhconni.mF*orex-:ample,:\xy\ar?@{<^{|}>}(20,7)\endxyLW940)Ve*tj??gwtypGesetsܺS ps: 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}xyWhen޲usingthisyoumustspGecifya{}=^dummy hdiriectionalDinordertoignoreoneofthetail,{+stem,orUUtipcompGonents,e.g.,N8\xy\ar?@{{}{+}>}(20,7)\endxy<typGesetsS ps: SDict begin xyc end8缟" {3430 10 /xy AB}xy8统T " {3430 st}xy6}`" {3430 F d}xy3e " {3430 st}xy1^'Z" {3430 F d}xy.X " {3430 st}xy,1џ(" {3430 F d}xy)b' " {3430 st}xy'{" {3430 F d}xy$6cL " {3430 st}xy!%X" {3430 F d}xy " {3430 st}xyϟ" {3430 F d}xyݷ " {3430 st}xyyc" {3430 F d}xyab " {3430 st}xyT#2" {3430 F d}xy 1D " {3430 st}xy '͟P" {3430 F d}xy X " {3430 st}xyw" {3430 F d}xy,_ " {3430 st}xy!" {3430 F d}xy ~ " {3430 st}xy˟m" {3430 F d}xyIn|particular*hob8jectiisahdirisoanyhobjecticanrbGeusedforeitherofthetail,/stem,orrheadcompGonent:N8\xy\ar?@{*{x}*{y}*{z}}(20,7)\endxy<typGesetsӍPV5ps: SDict begin xyc endx97.z3ß촊y.-y(e[y"Ƣy̪y?ҲyFغy ~ןy#yNote:|AZ* aintroGducesZanhob8jectiwhereasthedi-rectionalUU`ps: SDict begin xyc end33n'istypGesetbythehdiri{*}L.RExerciseT27: TypGeset#S 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统T" {-3572 st}xy7Ƀ" {-3572 F d}xy8统T " {3430 st}xy6}`" {3430 F d}xy3e" {-3572 st}xy2-~" {-3572 F d}xy3e " {3430 st}xy1^'Z" {3430 F d}xy.X" {-3572 st}xy-pן<" {-3572 F d}xy.X " {3430 st}xy,1џ(" {3430 F d}xy)b'" {-3572 st}xy(Dc" {-3572 F d}xy)b' " {3430 st}xy'{" {3430 F d}xy$6cL" {-3572 st}xy#+2" {-3572 F d}xy$6cL " {3430 st}xy!%X" {3430 F d}xy " {-3572 st}xy՟v" {-3572 F d}xy " {3430 st}xyϟ" {3430 F d}xyݷ" {-3572 st}xy4" {-3572 F d}xyݷ " {3430 st}xyyc" {3430 F d}xyab" {-3572 st}xy)" {-3572 F d}xyab " {3430 st}xyT#2" {3430 F d}xy 1D" {-3572 st}xyfӟm" {-3572 F d}xy 1D " {3430 st}xy '͟P" {3430 F d}xy X" {-3572 st}xy :}d`/?,;wheredisahdirectioni}and`ahdimenision,makesthestemacurvewhichissimilartoastraightlinebuthashadUUit'scenterpGoint`dragged'thedistance`ind:./㍍4ps: SDict begin xyc end-" {2.00002 0 360 o}xy:罟" {2.00002 0 360 o}xyF" {mark 56.90521 -28.4526 34.5413 6.08922 0.0 28.4526 1.0 0.02441 q}xyrǟV\"J" {mark 56.90521 -28.4526 34.5413 6.08922 0.0 28.4526 0.02441 0.46426 q}xy9ou" {1707 10 /xy AB}xyJ" {mark 56.90521 -28.4526 34.5413 6.08922 0.0 28.4526 0.53629 0.97095 q}xyF" {mark 56.90521 -28.4526 34.5413 6.08922 0.0 28.4526 1.0 0.97095 q}xyG" {mark 56.90521 -28.4526 22.36339 -6.0887 0.0 28.4526 1.0 0.02441 q}xy\m!#K" {mark 56.90521 -28.4526 22.36339 -6.0887 0.0 28.4526 0.02441 0.46371 q}xy8荟W" {2389 10 /xy AB}xyK" {mark 56.90521 -28.4526 22.36339 -6.0887 0.0 28.4526 0.53574 0.97095 q}xyG" {mark 56.90521 -28.4526 22.36339 -6.0887 0.0 28.4526 1.0 0.97095 q}xy:罟-" {2.00002 0 360 o}xysy" {2.00002 0 360 o}xyM" {mark 113.81042 -28.4526 85.35756 8.61134 56.90521 28.4526 1.0 0.02881 q}xyTaNuP" {mark 113.81042 -28.4526 85.35756 8.61134 56.90521 28.4526 0.02881 0.4733 q}xyrD" {1811 10 /xy AB}xyP" {mark 113.81042 -28.4526 85.35756 8.61134 56.90521 28.4526 0.52628 0.9729 q}xyL" {mark 113.81042 -28.4526 85.35756 8.61134 56.90521 28.4526 1.0 0.9729 q}xyN" {mark 113.81042 -28.4526 85.35756 -8.61082 56.90521 28.4526 1.0 0.02148 q}xyUF^/dR" {mark 113.81042 -28.4526 85.35756 -8.61082 56.90521 28.4526 0.02148 0.46341 q}xyqQ " {2337 10 /xy AB}xyR" {mark 113.81042 -28.4526 85.35756 -8.61082 56.90521 28.4526 0.53659 0.96484 q}xyM" {mark 113.81042 -28.4526 85.35756 -8.61082 56.90521 28.4526 1.0 0.9649 q}xy.sqwasUUtypGesetbyN8\xyQ\POS?(0,10) *\cir<2pt>{}="a",?(20,-10)*\cir<2pt>{}="b"Q\POS"a"?\ar@/^1ex/"b"|\uparrowQ\POS"a"?\ar@/_1ex/"b"|\downarrow%Q\POS?(20,10)*\cir<2pt>{}="a",?(40,-10)*\cir<2pt>{}="b"Q\POS"a"?\ar@/u1ex/"b"|uQ\POS"a"?\ar@/d1ex/"b"|d\endxy<`UUdefaultsto.5pcifomitted.gw:Thisuisreallyjustashorthandforcurvingusing :themoregeneralformdescribGednext:$@/d`/isthe:same*as@`{{**{}??+/C*d2`/}}whichmakesthe:(quadratic)D.curvepassthroughthepGointde ned:byUUthehpGosi**{}??+/-U=d`/?.:21p.?Using Y@(d2|s, pd2|s)whered1|s;d2aresimple:hdirectionisxi(asdescribGedinnote4lexceptit:is:notpGossibletouse()4s)willtypesetthearrow:curvedsuchthatitleavesthesourceindirection:d1ȲandUUentersthetargetfromdirectiond2|s.:ExerciseT28: TypGeset)BEps: 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 hX" {1920 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=iM" {2187 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}xyXX:T oxDo:JݲimplementthisecientlyandpropGerly:getUUridoftheno-() Orestriction!:21q.vTheJ? nalcurveformisthemostgeneralone::@`{1hcontrolkNpGointlistsi} KsetsthecontrolpGoints:explicitlytotheonesinthehcontrolpGointlistsi:(wheretJtheyshouldbGeseparatedby, G).ΦSeethe:curveextensiondescribGedinx8forthewaythe:controlpGointsareused;)whenthecontrolpGoints:listisparsedpisthesourceandcthetargetofthe:arrow.:21r.@[...] ?qandT@*{...}formationsTde newhatob8ject:hmoGdi erisshouldbeusedwhenbuildingob8jects:thatgarepartofthearrow.JThisismostlyusefulin:conjunction1withextensionsthatde neadditional:[*7hshapGei] Hmodi ers,5e.g.,ifKa[red]%hmoGdi eri:changesqthecolourofanob8jecttoredthen@[red]:willmaketheentirearrowred;(similarlyifitisde-:sireds%tomakeandentirearrowinvisiblethen@*{i}:canUUbGeused.:21s. @ j3willslide(eachsegmentof)thearrowthe:dimensionUUDrasexplainedinnote21h.:21t.@?Z[reversethemeaningof`abGove'and`bGelow'for:thisUUparticulararrow.;AllxthefeaturesofhpathisdescribGedabovexareavqail-:ableUUforarrows.(SS:22PTwo-cellfffeature9:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{2cell}?:This/featureisdesignedtofacilitatethetypGesettingof:curvedarrows,$eithersinglyorinpairs,togetherwithLW941*kʠ*tj??gwlabGelstIoneachpartandbetween.ΤThetIintendedmath- ematicalusageisfortypGesettingcategorical\2-cell"morphismsand\pastingdiagrams",forwhichspGecialfeaturesareprovided.78Thesefeaturesalsoallowattrac-tiveUUnon-mathematicale ects.@]22.1Typ`esetting2-cellsinDiagramsUCategorical}\2-cell"morphismsareusedinthestudyof@tensorcategoriesandelsewhere. xThemorphismsareddisplayedasapairofcurvedarrows," {mark 73.79341 0.0 36.8967 -17.5 0.0 0.0 0.09146 0.9046 q}xy) gIǟ" {3465 10 /xy AB}xy," {1024 F d}xy*" {1024 F d}xy,~" {1024 F d}xy*~" {1024 F d}xy+" {1024 /XT tt}xyLjB#a\diagramA\rtwocell^f_g?&B\\\enddiagram'6):ps: SDict begin xyc endjA=" {mark 73.79341 0.0 36.8967 35.0 0.0 0.0 0.09146 0.9046 q}xy)M?fIǟ" {2288 10 /xy AB}xy,>" {1024 F d}xy*>" {1024 F d}xy," {1024 F d}xy*" {1024 F d}xy+>" {1024 /XT tt}xy/  >" {mark 73.79341 0.0 36.8967 -35.0 0.0 0.0 0.09146 0.9046 q}xyIǟ S" {3856 10 /xy AB}xy)NK9h," {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" {60.0 0.0 l}xyI" {0.0 0.0 l}xyLjB3v(\diagramA\ruppertwocell^f{\alpha}\rlowertwocell_h{\beta}\rto_(.35)g?&B\\\enddiagram TheseNcategoricaldiagramsfrequentlyhaveamatrix-likeBlayout,aswithcommutativediagrams. 9WT*ofa-cilitatethistherearecontrolsequencesoftheform:\rtwocell"ܲ,\ultwocell;g,\xtwocell6j,...Banalogoustoythenamesde nedinxyv2foruseindiagramspro-duced$usingxymatrix/$. Asthisinvolves$thede ni-tionsof21newcontrolsequences,ӺmanyofwhichmayneverbGeused,thesearenotde nedimmediatelyuponloadingSdxy2cell)O.kInsteadSdtheusermust rstspGecify\UseTwocells/. < AsUinthesecondexampleabGove,'TjustUtheupperorlowerycurvedarrowmaybGesetusingcontrolsequencesofdtheform\..uppertwocellVand\..lowertwocellRd7.These7?togetherwiththe\..compositemapW.Qfamily*,oinwhich@ktwoabuttingarrowsaresetwithanemptyob8jectatthejoin,/allowfortheconstructionofcomplicated\pastingUUdiagrams"(see gure15foranexample). TheFfollowinginitialisethefamiliesofcontrolse-quencesUUforuseinmatrixdiagrams.gw: +ff2 Ǎ f\UseTwocellstV4twoUUcurves f\UseHalfTwocellstV4oneUUcurve f\UseCompositeMapstV42UUarrows,end-to-end f\UseAllTwocellstV4(allUUtheabGove)eff2 2ş Alternatively\2-cellscanbGesetdirectlyin\XY -pictureswithout:zusingthematrixfeature.InthiscasetheabGovecommandsUUarenotneeded.qThisisdescribGedinx22.5. c F*urthermoreoHanewdirectional\dir{=>}.xcanbGeusedtoplacean\Arrow"anywhereinapicture, afterthedirectionhasbGeenestablishedappropriately*.IItisusedwithUUallofthe2-celltypGes. LabGelsareplacedlabelsontheupperandlowerar-rows,moreBcorrectly`anti-cloGckwise'and`cloGckwise',usingX^@andX_ U.TheseXareentirelyoptionalwiththefollowingԳtoken,morgrouping,givingthecontentsofthelabGel.Whenzusedwith\..compositemapUӲthe^ 3and_spGecifyRlabelsforthe rstandsecondarrows,,Prespec-tively*. NormallyKthelabGelisbalancedtext,dsetinTU>'ExX'smath*moGde,with\twocellstyleOR-settingthestyle.TheUUdefaultde nitionisgivenby... \def\twocellstyle{\scriptstyle}ThiscanbGealteredusing\definversionsofTU>'ExXor\redefine24HincL5ffA͉TU>'ExX.QwHoweverlabGelsarenotrestrictedtobGeingsimplytextboxes.*Anye ectobtainableusingtheXY T-pickernellanguagecanbGesetwithinan\xyboxandZusedasalabGel.QAlternativelyifthe rstcharac-terinthelabGelis* $!thenthelabelissetasanXY r-pichob8jecti,asifwith\dropMi/or*8i;inthekernellanguage.Thecurrentdirectionistangen-tial]tothecurvedarrows.pExtrabracesareneededtogetUUa* ꧲asthelabGel,asin^{{{*}}}0or_{{}*}"C. TheTpGositionofalabelnormaltothetangentialdi-rectionccanalsobGealteredbynudging(seebelow).TwAl-thoughitispGossibletospecifymultiplelabels,Tonlythelast؄usageofeachof^ and_isactuallyset,OpreviousspGeci cationsUUbeingignored. SimilarlygalabGelforthecentralArrowmustbGegiven,after.theotherlabGels,mdbyenclosingitwithinbraces{...}?.zAnemptygroup{}ƲgivesanemptylabGel;/thisisP necessarytoavoidP misinterpretationofsubsequenttokens.eAscabGoveifthe rstcharacteris*thenthelabGelhissetasanhXY -pichob8jecti,mthecurrentdirectionbGeingUUalongtheArrow.,22.2%StandardOptionsˍTheB?orientationofthecentralArrowmaybGereversed,turnedintoanequality*, Roromittedaltogether.[Ineachcases.alabGelmaystillbespeci ed,isoine ecttheArrowmayUUbGereplacedbyanythingatall.LW942+*tj??|[8lDps: SDict begin xyc end" {36.00002 0.0 l}xymRn9f3" {3072 10 /xy AB}xy" {3072 10 /xy AB}xy0j" {0.0 -45.41669 l}xy0j" {1024 10 /xy AB}xy0j" {1024 10 /xy AB}xyJ" {36.00002 -20.57814 l}xySc f4J" {2487 10 /xy AB}xyJ" {2487 10 /xy AB}xyǟ} " {448 F d}xyF " {448 F d}xy9 " {448 F d}xy K " {448 F d}xym~" {448 /XT tt}xy&<( " {384 F d}xytԟ;R " {384 F d}xyΟ>GH " {384 F d}xy!=7 " {384 F d}xy?I" {384 /XT tt}xyـ1vl" {36.00002 -23.50847 l}xyȞ<"gf5ـ1vl" {2404 10 /xy AB}xyـ1vl" {2404 10 /xy AB}xy6VA*!Ö" {29.02002 25.68051 l}xyRf1*!Ö" {3978 10 /xy AB}xy[ " {42.97998 15.01205 l}xy@{˟A̴f2[ " {3430 10 /xy AB}xy24ɟ x" {1632 F d}xy0|" {1632 F d}xy3{1" {1632 F d}xy1S7" {1632 F d}xy6s '" {1632 /XT tt}xyJ" {mark 87.75003 0.0 59.18996 -51.50424 0.0 -51.41669 0.05789 0.97046 q}xy\.v" {-3675 10 /xy AB}xy1M " {36.0 -21.58 l}xy1M " {2458 10 /xy AB}xynEg11M " {2458 10 /xy AB}xy" {36.00002 23.50261 l}xy" {3740 10 /xy AB}xy" {3740 10 /xy AB}xy3j" {36.00002 0.0 l}xyu/f63j" {3072 10 /xy AB}xy3j" {3072 10 /xy AB}xyW" {mark 301.7935 -51.41669 278.77179 -66.41669 255.75009 -51.41669 0.06516 0.84705 q}xy-;7M" {3515 10 /xy AB}xy@lg4)il" {1024 F d}xy)il" {1024 F d}xy+l" {1024 F d}xy+l" {1024 F d}xy3il" {1024 /XT tt}xy8j" {18.41623 23.99998 l}xy +_"f78j" {-3858 10 /xy AB}xy/ߟ-" {15.8029 -20.58333 l}xy)E"f8/ߟ-" {1810 10 /xy AB}xy06VB4e," {78.00003 25.45964 l}xy4e," {3406 10 /xy AB}xy4e," {3406 10 /xy AB}xywW" {81.47446 -7.94243 l}xy[oXg2wW" {2972 10 /xy AB}xyـ4l" {74.52559 33.26144 l}xyVJyӴg3ـ4l" {3529 10 /xy AB}xyIRTܲFigureUU15:qPastingdiagram.m䍍 Theseke ectsarespGeci edbythe rsttokeninthe centrallabGel,whichthushastheform:K{ QHhtokihlabGeli}whereUUhtokimaybGeoneof... k  <|ff2 d1)_LArrowUUpGointscloGckwise1)^LArrowUUpGointsanti-cloGckwise1)=LnoUUtip,denotesequality& \omitLnoUUArrowatall.Qqff2 WhennoneoftheseoGccursthenthedefaultof_۲isassumed.iIfthelabGelitselfstartswithoneofthesecharactersthenspGecify_ explicitly*,ForenclosethelabelwithinŦagroup{...}.¹SeeExtr}'a...Sв,dthe.resultisasinglestraightar-row,itsmid-pGointbGeingtheoriginfornudginglabGels.AXnegativeXAvqalueforhnumiisalsoacceptable;butchecktheЁorientationontheArrowandwhichof^ and_cor-respGondUUtowhichcomponent. TheDoriginfornudginglabGelsiswherethearrowcrossesthebisector._PositivenudgesmovethelabGeloutwardswhilenegativenudgesmovetowards~fe [۟gpcand:pGossibly}beyond.D@Thedefaultpositionofalabelison :theUUoutside,withedgeattheorigin.;TheoriginfornudgingtheArrowisatthemidpGoint:ofe~fe [۟gpc '@.AGpGositiveenudgemovesinthecloGckwisedirec-:tion.ThisUwillbGethedirectionofthearrowhead,unless:itUUhasbGeenreversedusing^R.;LabGels%#ona\..compositemapU areplacedrelativeto:thejTmidpGointofthecomponentarrows.Nudgesarein:units|of1pt.2Movement|isintheusualxXY |-picab}'oveand:b}'elow徲directions, suchthatapGositivenudgeisalways:outsideUUthetriangleformedbythearrowsandline~fe [۟gpc 0.>;The:uspGecialnudgevqalue<\omit>-4ղtypGesetsjustthe:Arrow,|omittingFthecurvedarrowsentirely*.Whenused:withlabGels,athenudgevqalue<\omit>)3causesthefollow-:ingUUlabGeltobeignored.ߍ:ExerciseT29: GiveUUcoGdetotypGeset gure15.:SuchKcoGdeisrelativelystraight-forward, Husing\nudg-:ing"and\omittohelppGositionthearrows,curvesand:Arrows.tItalsousesanexcursion,*asdescribGedbelow:inUUthesubsectionExtr}'aOptions3.ߍ:22.4 j:ExtraOptionsuT:Themfollowingfeaturesareusefulinnon-mathematical:applications.:1.pnoTArro9wuT:ThisMisdeterminedbyspGecialvqaluesforhtokiasthe: rst(oronly)characterinthecentrallabGel,̙asinthe:abGoveUUdescriptionofthestandardswitches.: Sff2|d '1SarrowheadsUUpGointingcloGckwise; `1SarrowheadsUUpGointinganti-cloGckwise; "1SarrowUUtipsonbGothends; !1SnoUUtipsatall.ⅉff2 육ThecentralArrowisomitted,=leavingsymmetricallyplacedJcurvedconnectionswitharrowheadsatthespGec-i edends. ANlabGelcanbeplacedwheretheArrowwouldUUhavebGeen.LW943,*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:qǸhtwoGcellisLW944-բ*tj??gw If;&aspGecialarrowheadisspeci edusing~'{..}%:(see Extra.Options2,6bGelow)thenthiswillbeusedinsteadofUUthestandard\dir{>}(@. ?7#,ps: SDict begin xyc endx㍍Clouds?" {mark 96.61118 0.0 48.30559 50.0 0.0 0.0 0.06955 0.93109 q}xy-c6precipitationk̟" {2152 10 /xy AB}xy@" {mark 96.61118 0.0 48.30559 -50.0 0.0 0.0 0.06955 0.93109 q}xy/6evap,rorationyN" {-1942 10 /xy AB}xy9J?f$cmbx7H@-hcmbx5@2JOjc=OceansCC\xymatrixcolsep{5pc}\diagramQ\relax\txt{Clouds?}\rtwocell<10>Q_{\hbox{\tiny?evaporation}}Q^{\hbox{\tiny?precipitation}}{'{\mathbf{H_2?O}}}&\relax\txt{Oceans}\\\enddiagramw!ցps: SDict begin xyc endx㍍cMathematicsj?" {mark 98.65283 0.0 49.32642 17.5 0.0 0.0 0.19681 0.80505 q}xy92theorybd" {2852 10 /xy AB}xy&Lw" {-802 10 /xy AB}xyj@" {mark 98.65283 0.0 49.32642 -17.5 0.0 0.0 0.19681 0.80505 q}xy2exp,rerimenӍtbd~2" {3292 10 /xy AB}xy&L." {-1246 10 /xy AB}xyeYPhysics$7\xymatrixcolsep{5pc}\diagram\relax\txt{\llap{Math}ematics?}\rtwocell_{\hbox{\tiny?experiment}}^{\hbox{\tiny?theory}}{"}&?\relax\txt{Physics}\\\enddiagram (2.pChangingTTipsandMoQduleMapseލTheTfollowingcommandsareprovidedforspGecifyingthehob8jectitobGeusedwhentypesettingvqariouspartsofUUthetwoGcells.CW͉ffx fdc}'ommanddefaultffx\modmapobject{Oָhob8jecti}U\dir{j} \twocellhead{J?ٸhob8jecti}\dir{>}\twocelltail{J?ٸhob8jecti}\dir{}\arrowobject{J?ٸhob8jecti}x\dir{=>}\curveobject{J?ٸhob8jecti}\uppercurveobject{dʸhob8jecti}8{}\lowercurveobject{dʸhob8jecti}8{}ffxE Thesecommandssettheob8jecttobGeusedforallsubsequentϘ2-cellsatthesamelevelofTU>'ExXgrouping.\curveobject2spGeci es bothoftheupper-andlower-curveAob8jects.6HF*orsomeofthesethereisalsoawaytochangetheob8jectforthecurrent2-cellonly*.jThisrequiresa~Ʋ-hswitchiwhichisdescribGedbelow,exceptgw:for}the\..curveobjectPztypGes,which}arediscussedin :Extr}'aOptions4..э;Theseve ectsarespGeci edbyplacingswitchesaf-:ter"the\..twocelllab}'els!...m.A Eachswitchiseitherasingletoken:htoki,+or`a~]htokiwithasingleargument:~ _ɸhtoki{?ar}'g}}"z.:PossibilitiesTarelistedinthefollowingtable,Γinwhich:{..}?denotesUUtheneedforanargument. d: 0Gff20d \omit>쑲noUUarrows,ArrowandlabGelonly; !>쑲placeUUmoGdule-mapindicator;l~'{..}>쑲changeUUarrow-headto{..}UI;l~`{..}>쑲place/changeUUtailonarrow(s); ~{..}>쑲changeUUob8jectusedtosetcurves;l~^{..}>쑲useUUob8ject{..}tosetuppGercurve;l~_{..}>쑲useUUob8ject{..}tosetlowerUUcurve;,KVff2 ᦍHerewediscusstheuseof! ,~'~,~`[and\omit.Thedescriptionof~^,,`~_and~{..}!isgiveninExtr}'a)Op-tions4..э ThedefaultmoGdulemapindicatorplacesasingledashScrossingthearrowatright-angles,"loGcatedroughlymidwayNalongtheactualprintedpGortionofthearrow,whetherrcurvedorstraight.&PThistakesintoaccountthesizes4oftheob8jectsbGeingconnected,):therebygivinganaestheticfXresultwhenthesesizesdi ermarkedly*.Thisalsoworkswith\..compositemapVwhereanindicatorisplacedoneacharrow. OTheactualob8jectcanbGechangedUUusing\modmapobjectG.. Any,ofthestandard,XY-pictipsmaybGeusedforarrow-heads.+Thisisdoneusing~'{..}#h, eforexample~'{\dir{>>}}C gives double-headedarrows.ӽSimilarly~`{..}#ZcanڲbGeusedtoplaceanarrow-tail.Normallythelarrow-tailis,r{soisnotplaced;xObutifanon-emptytailhasbGeenspeci edthenitwillbeplaced,f^using\drop?.ݙNo#guaranteeiso eredforthedesiredresultbGeing$obtainedwhenanarrow-tailismixedwiththefeaturesUUofExtr}'aOptions1. d#ߍ?7K*aps: SDict begin xyc endjP?" {mark 73.25868 0.0 36.62933 20.0 0.0 0.0 0.09427 0.91327 q}xy'ɻ 'X|EMG" {2614 10 /xy AB}xyIWm" {2614 10 /xy AB}xy " {3527 st}xy@" {mark 73.25868 0.0 36.62933 -20.0 0.0 0.0 0.09427 0.91327 q}xy'ɻ  %CeִM,r 0ncmsy50G^s" {3530 10 /xy AB}xyIW*" {3530 10 /xy AB}xy j " {2617 st}xy*" {0.0 10.0 l}xy," {0.0 10.0 l}xy$1fLjS0ݍ\modmapobject{\objectbox{\otimes}}\xymatrixcolsep{5pc}\diagramP\rtwocell~!~'{\dir{>>}}~`{\dir{|}}?^{<1.5>M}_{<1.5>M'}{=f}&S\\\enddiagramLW945.:*tj??gw3.pExcursionsASyntaxfor\xcompositemapOMand\x..twocell?typGesis a8littledi erenttowhatmightbGeexpectedfromthatforUU\xtoUI,UU\xline"C,UUetc.qF*orexample,a2ff2獍+WW\xtwocell[_9hhopi]{ hdisplacei}... ff2^connectstothehpGosidisplacedbyhdisplaceifromtherelativecellloGcationspeci edbyhhopi.Thedisplace-mentdXcanbGeanystringofvqaliddTXY X-piccommands,hbuttheyDmustbGeenclosedwithinagroup{...}.?WhentheN-cellloGcationisthetarget,Oanullgrouping{}TmustbGeUUgiven. WhenNusedwiththe<\omit>*nudge,suchNexcursionsallowralabGelledArrowtobGeplacedanywherewithinanXY -picdiagram;furthermoretheArrowcanbGeorientedtoUUpGointinanydirection.,4.pF ancyTcurv9esByspGecifying\curveobjectFÈanarbitraryob8jectmaybGe'usedtoconstructthecurvedarrows.bIndeedwitha\..twocell7_di erent}ob8jectscanbGeusedwiththeup-pGer@andlower@curvesbyspGecifying\uppercurveobjectandUU\lowercurveobject\". These.spGeci cationsapplytoall2-cellssubsequentlyconstructedjWatthesamelevelofTU>'ExXgrouping.Alter-nativelyӵusinga~-switch,asinExtr}'aOptions2,allowssuchUUaspGeci cationforasingle2-cellorcurvedpart. Ob8jectssusedtoconstructcurvescanbGeoftwotypGes.Eitherfasinglehob8jectiissetonce,jwithcopiesplacedalong!'thecurve.`bAlternatively!'adirectionalob8jectcanbGe,alignedwiththetangentalongthecurve.InthiscaseUUuseaspGeci cationtakestheform: \curveobject{N?ڸhspaceri~**hob8jecti}?.HerehspacerimaybGeanyhob8jectiofnon-zerosize.TypicallyUUitisemptyspace,e.g.+Rhdimeni{} .,Exercise'30: Give/coGdetotypGesetthefollowingdi-agrams.6 5ps: SDict begin xyc endjUUFUnW?㏟H?#ɟx?)H?/;?5t?;x?Ax?Gg ?MUXH?SCx?Y1ʟH?_ ?ګ ɟ h#;8)sh/5x;g 8AUXGCM1ʟhS 8Y<h^v :Xn9&qƍ_@gaMESgwIҍps: SDict begin xyc end卍Ground  >State-5H" {3687 10 /xy AB}xy1+@" {3636 10 /xy AB}xy6ݟ" {3585 10 /xy AB}xy;c۟}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}xyWc," {3226 10 /xy AB}xy\YQ<<" {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}xyܢ̍@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}xyK՟48" {-1229 10 /xy AB}xyWaX@" {-1127 10 /xy AB}xyT" {-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 td͍c8O" {20.54083 ox}xy͍c8O" {18.44083 ox}xy卍Excited StateQ]:22.5 j:2-cellsingeneral&aX1"Yv-pictures:Two-cellsb@canalsobGesetdirectlywithinanyb*+{B}="B",*7+<2.0cm,0pt>*+{C}="C",*7+<1cm,-1.5cm>*+{D}="D",:"A";\goVia{\uppertwocell^\alpha{}}"B"{}:;\goVia{\twocell^\zeta_\xi{\gamma}}"C"{}:;\goVia{\compositemap{}}"D"{},:"A";\goVia{\lowertwocell{}}"D"{}:\endxyh!B6BFps: SDict begin xyc end I$ qA'q^B`vv^C|z nD $H" {mark 28.45276 42.67914 -15.0357 40.54428 0.0 0.0 0.08237 0.91406 q}xyt $r2Ӛ{" {3217 10 /xy AB}xyP=" {2400 F d}xy8K" {2400 F d}xyhHU" {2400 F d}xyO3c" {2400 F d}xy ޟ;" {2400 /XT tt}xy $R" {mark 85.35828 42.67915 56.90552 60.17914 28.45276 42.67914 0.12375 0.87823 q}xyE]v5X" {2587 10 /xy AB}xy $R" {mark 85.35828 42.67915 56.90552 25.17914 28.45276 42.67914 0.12375 0.87823 q}xyFs]vֲ" {3555 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 ~?Пx" {18.92403 -7.70264 l}xy~?Пx" {2655 10 /xy AB}xyǍ힟S" {-0.28299 -21.52524 l}xy힟7" {1011 10 /xy AB}xys*Ÿ E" {-352 F d}xyrtG" {-352 F d}xyqŸ]" {-352 F d}xyo_" {-352 F d}xynpvv" {-352 /XT tt}xy $C" {mark 113.81104 0.00005 56.90552 -35.0 0.0 0.0 0.0593 0.9361 q}xyyұ" {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.2;The"coGdeshownisacompactwaytoplaceachain:of2-cellswithinapicture.Itillustratesastandard:techniqueforusing\afterPOS8Sto ndahpGositobe:usedforpartofapicture,thensubsequentlyreuseit.:Also)itispGossibletouse\drop!Corhdecoristospecify:theUU2-cells,givingthesamepicture.:\xy?*+{A}="A",+<1cm,1.5cm>*+{B}="B",*7+<2cm,0pt>*+{C}="C",*7+<1cm,-1.5cm>*+{D}="D",:"A";"B",{\uppertwocell^\alpha{}},:"B";"C",{\twocell^\zeta_\xi{\gamma}},:"C";?\afterPOS{\drop\compositemap{}}"D":\POS?"A";*7\afterPOS{\drop\lowertwocell{}}"D":\endxyh!;Theua\connect2ꪲvqariantuaisusuallypreferableasthis:maintainsthesizeoftheob8jectatc,ǖwhilethe\dropLW946/~*tj??gwvqarianteleavesarectangularob8jecthavingpandcon oppGositeUUsides.'-023wlMatrixfffeatureVers.3.3bCyKristo erH.Rosehkrisrose@brics.dki Loadas:\xyoption{matrix}|PThisboptionimplements\XY -matrices",'i.e.,matriceswhereUitispGossibletorefertotheentryob8jectsbytheir?row/columnaddress.'ExXrow&columnXformat,i.e.,whererowsareseparatedwith\\andcontaincolumnsseparatedwith&(wedis-cuss?inthefollowingsectionswhathsetupicanbGe).Thusamatrixwithmaxr}'ow#rowsandmaxc}'olcolumnswhereUUeachentrycontainsr}'ow,Scol]޲isUUenteredas03z Ӵ\xymatrix{) 1,1?&O 1,2?&u 1,maxc}'olp\\) 2,1?&O 2,2?& 2,maxc}'olp\\ԍ~^.~^.~^.d.E.hҟ.k_.) maxr}'ow0,1?&O maxr}'owr,2?& maxr}'ow,maxc}'olŁ}1[l(TU>'ExXnically3the& Hccharacterrepresentsany`alignmenttab',UUi.e.,characterwithcategorycoGde4).  AchmatrixicanappGeareitherinanXY.-picture(ashdecori)UUor\stand-alone". ThevfaspGectsinwhich\xymatrix:,di ersfromor-dinaryFmatrixconstructions,AsuchasPlainTU>'ExX's\matrix{)...} ?andUUL5ffA͉TU>'ExX'sarray ꛲environment,UUare C arbitrarytXY -pictƸhdecoriationsmaybGespeci edineachentryandwillbGeinterpretedinastatewherecUUisthecurrententry*, the9\entirematrixisanob8jectitselfwithreferencepGointUUasthetopleftentry*,and aAprogressmessage\X"isprintedforeachmatrixwithr}'owsHLc}'olsentriesandXY !-piccomplexitysizea(thenumbGerofprimi-tive#opGerationsperformed),-unlessthedeclaration\SilentMatricesUUisissued.gw;{}:\endxyB:willUUtypGeset,Bps: SDict begin xyc end@ qA** qB%C)g%DǍ/" {0.0 45.50868 -43.2643 -6.91075 6.40233 ov}xy" {8.00002 0 360 o}xy9:Bug:qDzMatrixUUnestingisnotsafe. J;Matrices-areoftenquiteslowtotypGesetsoasacon-:venienceallmatricescanbGesettocompile(andnot):automaticallyUUwiththedeclarations:@‰ff2 ZG,\CompileMatricesG,\NoCompileMatricesLff2\MatricesOcanbGecompiledornotindividually*,[byus-ingGtheexplicitcommands\xymatrixcompileand\xymatrixnocompileھaswellasbyencapsulatingintheUUusual\xycompileto{G.name[}{ @U...} ?(seeUUnote5e). Note::IMatrices9willonlycompilecorrectlyifallentriesstartwithanonexpandabletoken,ohi.e.,{0or\relax"CorUUsomenon-activecharacter.!N23.2%Newco`ordinateformats;ItispGossiblewithinentriestorefertoalltheentriesofthe=XY >A-matrixAusingthefollowingspGecialhcoordiinateforms: Nff2 Z "rG,c"^ݲPosition?andextentsofen-^try4LinrowrG,:columnc(top^leftUUis"1,1"F)#d[ rG,c]^ݲrrowsOsbGelow,ccolumns^rightUUofcurrententryX+[Hhhopi*UV]^ݲentryqreachedbyhhopis;^eachhhopiisoneofdulr^ݲdescribing`xone`move'`xtoa^neighbGorUUentry/X+[Hhhopi^+ hplaceiUU]^ݸhplaceionstraightlineto^non-empty7[ wϸhhopi*]ڰff2\SoKthecurrententryhasthesynonyms[0,0]z,[] ,[rl],[ud],[dudu]",etc.,ask!wellasits`absolute'name"rG,c"?. )Wff^ J=w-:12LInpgeneralitisrecommendedthatenÎtriesstartwithanon- expandingAVtokÎen,\Ui.e.,anordinary(non-activÎe)character,\U{,or\relax,XforcompilationtowÎork.LW9470 *tj??gw Theseformsareusefulforde ningdiagramswhere theUUentriesarerelated,e.g.,7Lps: SDict begin xyc endK qA  " {1024 g}xy5 " {1024 g}xy " {1024 g}xy&h: q" {24.75284 -24.0 l}xy%B)8%C9"w" {-23.99998 0.0 dt}xy7 CwasUUtypGesetbyN8$$\xy\xymatrix{QA?\POS[];[d]**\dir{~},[];[dr]**\dir{-}\\QB?&C\POS[];[l]**\dir{.}}\endxy$$ If#anentryoutsidetheXY +#-matrixisreferencedthenanUUerrorisrepGorted. Intcaseseveralmatricesareusedinthesamedia-gram,andptheyrefertoeachother,thenitisusefulto\givethematricesdi erent" hpre xi"hsetupi\suchthat;theycanrefertoeachotherusingthefollowingspGecialTcoordinateformsthatallhavethesamemean-ing\exceptthetargetentryispickedfromaparticularmatrix:ff2 8e{"=xhpre xirG,c"8e{["Buhpre xi"?rG,c]8e{["Buhpre xi"Rhhopi*UV]8e{["Buhpre xi"Rhhopi^+ hplaceiUU]>Zff2 )~InAfactabsolutereferencesmust4alwaysAbGegivenusing"?hpre xihrowi,hcoli",UUeveninsidethematrixitself. HereUUisanexampleusingthis:7MFps: SDict begin xyc end! ` qAF qB %CFƟ%D:ȍƠ3232" {3072 F d}xy)" {3072 F d}xy A" {3072 F d}xy" {3072 F d}xy 8" {3072 F d}xy832321ȍ΃j9" {1024 F d}xy (32" {1024 F d}xy32" {1024 F d}xy32" {1024 F d}xy 32" {1024 F d}xy΃jR~" {1024 F d}xyRK (32" {1024 F d}xy32" {1024 F d}xy32" {1024 F d}xy 32" {1024 F d}xy32Ơ3232" {3072 F d}xy)" {3072 F d}xy A" {3072 F d}xy" {3072 F d}xy 8" {3072 F d}xy83232.e 8A^0|" {0.0 0.00558 dt}xy `" {13.54982 4.06787 dt}xy `" {0.0 0.00557 dt}xy+1 8Bq^0C:" {10.15749 3.37764 dt}xy/qȵC^0(" {0.00368 0.0 dt}xy$f" {13.18733 4.27101 dt}xy$f" {0.00296 0.0 dt}xy+/qȵDG^0:џ(" {0.0 0.00339 dt}xyCƟ%" {9.68733 3.48477 dt}xyCƟ%" {0.0 0.00339 dt}xycJ3232|" {3072 F d}xy -" {3072 F d}xy " {3072 F d}xy" {3072 F d}xy" {3072 F d}xy " {3072 F d}xy32323@$" {1024 F d}xyͱ vƍ32" {1024 F d}xy32" {1024 F d}xy32" {1024 F d}xy v32" {1024 F d}xy$:;" {1024 F d}xy: vƍ32" {1024 F d}xy32" {1024 F d}xy32" {1024 F d}xy v32" {1024 F d}xy32J3232|" {3072 F d}xy -" {3072 F d}xy " {3072 F d}xy" {3072 F d}xy" {3072 F d}xy " {3072 F d}xy3232A)waswetypGeset(usingthe`frame'extensionand`arrow'feature)UUby\xy \xymatrix"*"{%A?&B\\C?&D}% \POS*\frm{--} \POS-(10,3) \xymatrix{%A'?\ar@{.}["*"]&B'\ar@{.}["*"]\\C'?\ar@{.}["*"]&D'\ar@{.}["*"]}% \POS*\frm{--}\endxy23.3%SpacingandrotationuTAny'matrixcanhaveitsspacingandorientationchanged[byaddingsetup`switches'bGetween\xymatrixgw:andUUtheopGening{R. z;ThedefaultspacingbGetweenentriesofmatrixis :changedUUwiththeswitches: Mff2 Kez@RhaddUUopihdimeniKez@ChaddUUopihdimeniKez@UUhaddopihdimenizff2+that|changerowspacing,ƌcolumnspacing,andbGoth,respGectively*, asindicatedbythehaddopiandhdimeni,wherethehdimenimaybGeomittedandcanbegivenas¯oneofR [andCtoindicatethecurrentvqalueoftheparameterUUinquestion.qNote:thereUUisnodefaultز. In)addition,ZXY +^-piccanbGeinstructedtousea` xedgrid'UUforthematrixwiththeswitches Mff2 n@!Rn@!Cn@!zff2+thatuensurethattherowspacing,columnspacing,andbGoth,respectively*,pretendingMthatallֲentrieshavethesizeFofthelargestentry(withoutmoGdifyingtherealsizeofBtheentries,}ofcourse,onlythespacing{togettheentriestor}'eallyBhavethesamesizeusea@* ...ohsetupidescribGedUUinx23.4below).qThespecialvqariants ʉff2]S@!0]S@!=hdimenizff2udpretendxthatentrieshavezeroorhdimeniheightandwidthPforcomputingrowandcolumnspacing;asabGoveinsertingR CCorCjustafterthe! CCmakesthisa ectonlytherowor columnspacing,e.g.,@!R0 *meansthattherowUUspacingonlyisbGetweenthecentersoftherows. z Finally*,nthetspacingofthingsthataretypGesetcanbeadjustedUUseparately: Mff2Kez@MhaddUUopihdimeniKez@WhaddUUopihdimeniKez@HhaddUUopihdimeniKez@LhaddUUopihdimenizff2+willadjusttheentrymargin,entrywidth,entryheight,andlabGelseparationused(thelatterisactuallypassedtoUUthearrowfeature). z ThespacingcanalsobGechangedforenentireTU>'ExXgroupUUbythedeclarations Mff2"Z\xymatrixrowseptphaddUUopi{Rhdimeni}"Z\xymatrixcolseptphaddUUopi{Rhdimeni}zff2+TheUUdefaultspacingforbGothis2pcL. z T oưDo:optimize'5proGcessingofmatriceswithcon-stantUUgrid.LW94817*tj??gw AnentirematrixcanbGerotatedbyaddingarotation hsetupiUUoftheform [։ff2 G\@a͸hdirectioni}ff2pThiszwillsettheorientationoftherowstohdirectioni(theidefaultcorrespGondstor ٲ,i.e.,rowsiareorientedleftUUtoright).,23.4%EntriesuTTheappGearanceofasingleentrycanbemodi edbyenteringUUitas ͝ff2B@*UUhob8jectihpGosihdecori}ff2g7This&makestheparticularentryignoretheentrymoGd-i ers.andtypGesetasakernelob8jectwiththesameref-erencepGointasthe(centerof)thedefaultob8jectwouldhaveUUhad. Additionalob8jecthmoGdi erismaybeaddedtoanotherwiseUUordinaryentrybyusingtheforms ͝ff2B|**[?hshapGei]RhentryiB|**{ReshmoGdi eri*}Rhentryi}ff2pThe rstsetsthedefaulthshapGeiforob8jects(cf.:6note4j),3mthesecondadefaultsize(change,cf.]Anote4g),_;andthelastmakesitpGossibletoaddanyhob8jecti"moGdi erofx4,Ue.g.,for"recenteringentriesaf-terTthedefaultentryformwhichisequivqalentto`!C+< 2oMobje}'ct, mar}'gin;8>@x'(withthee ectofcenteringtheob8jectUUandaddtheobje}'ctmarginc)UUtoallsides.,ExerciseT31: TypGesetUUthefollowingdiagram:pIrps: 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$ǵBQ8A5 ItisalsopGossibletousethese@ hsetupis(asusualbGetweenUU\xymatrix5ꏲandUUtheleading{R): [։ff2OA@*[?hshapGei]OA@*]=haddUUopihsizei}ff2g7whichareequivqalenttochangingallentriestobGehaveaswiftheyhadstartedwiththesimilar**-form.أT oDo:qDzAllowUU** OhaddUUopihsizeihentryiforentries. IfthedefaultsetofentrymoGdi ersshouldbechangedJthenthefollowingdeclarationmustbGeissuedbGeforerthe\xymatrix4@ɲcommand;ithisistheonlywayrtoactuallycswitchtheinitialdefaultcenteringandspacingo :։ff2+\entrymodifiers={ OhmoGdi eri*UV}}ff2upgw:Exercise9|32: HowdidtheauthortypGesetthefollow- :ingUUmatrix?(H{:^Xps: SDict begin xyc endn" {6.0 6.0 6.0 6.0 ox}xy@ qAǍ]E" {20.48532 20.48532 l}xy9" {45.9412 0.0 l}xy]\#" {20.48532 -20.48532 l}xyv"{" {6.0 6.0 6.0 6.0 ox}xy_Bg"{" {6.0 6.0 6.0 6.0 ox}xy Cn?" {6.0 6.0 6.0 6.0 ox}xy; qD&[;Bug:زThe]fourconstructions@*[T...]꧲,#**[㖲...],#@*:haddlopihsizei,rand,**{i...}꧲,rac}'cumulateinreverse:or}'der.ROnlyJentriesstartingwithasingle* ,completely:overrideUUthemoGdi ershsetupiwitha@* O-construction.;Finally*,\thefollowingisspGeciallysuitedfor`one-line':matricesUUincludedintext::S'ff2 $q,@1‰ff2lwill`inserta`mathstrut'(\vphantom(4)intoeachentrytoUUmakeitscenteringappropriatefortext. This/isjustanabbreviationusingthefollowingdec-larationwhichwillsetuphdecorithatshouldbGein-sertedwbGeforeeverythingelseineachentry*.OInitiallyitisUUemptybut Dff2>Ő\everyentry={ OhdecoriUU}‰ff2lwill'inserthdecori rstineachentry;ڌinsidethecounterregisters\Rowand\Colaresettothecurrententry'srowUUandcolumn,respGectively*.qForUUexample,N8\everyentry={{\the\Row,\the\Col}}\xymatrix?@*[F]@*[o]{?{}\POS[];[r]**\dir{..}&\\?{}\POS[];[ur]**\dir{--}}willUUtypGesetUps: SDict begin xyc endn 8*" {7.19443 7.19443 10.22221 10.22221 ox}xy1;1,n" {23.97119 0.0 dt}xyn6*" {7.19443 7.19443 10.22221 10.22221 ox}xy/qƞ1;2#" 8*" {7.19443 7.19443 10.22221 10.22221 ox}xy&EU2;10C~<7" {31.63843 27.18234 dd}xy7$Note:@_When usingcompilation, rchangesto\everyentryB%xande\entrymodifiers_willenot Xqre-sult inrecompilationevenwhentheconstructedmatrixchanges{youmayhavetoremovethe.xyc leUUmanually*.Exercise9|33: HowdidtheauthortypGesetthefollow-ingUUdiagram?PB=Rps: SDict begin xyc endǍ8^$" {0.0 21.00002 -9.0 -21.0 9.0 ov}xy6:r}'ootT" {0.0 -0.0469 l}xy#^g" {2816 10 /xy AB}xy#^g" {18.63062 -4.68636 l}xy#^g" {0.0 -0.0469 l}xyȍ8^$" {0.0 21.00002 -9.0 -21.0 9.0 ov}xy5ގګ^^" {10.0 0 90 o}xy8^" {0.0 0.00095 l}xy^^" {38.0 0.00095 l}xy^^)" {10.0 -90 0 o}xyǍh^," {-0.00195 -16.00098 l}xyM^3" {-1024 10 /xy AB}xyM^3" {-16.99803 0.0 l}xyM^3" {0.0 0.0 l}xy!ɍ8^$" {0.0 21.00002 -9.0 -21.0 9.0 ov}xy5ގ#ڬR^+J" {10.0 0 90 o}xy8^!J" {0.0 -0.00197 l}xyR^!J" {26.0 -0.00197 l}xyR^ΟA" {10.0 -90 0 o}xyǍ\^ΟD" {0.00098 -21.99805 l}xy^AG" {10.0 -180 -90 o}xy^KG" {-52.00098 0.002 l}xy^N" {10.0 90 180 o}xyǍ^N " {-0.00098 57.99805 l}xy#^" {3072 10 /xy AB}xy#^" {5.00098 0.0 l}xy#^" {0.0 0.0 l}xy3ʍ8^$" {0.0 21.00002 -9.0 -21.0 9.0 ov}xy5ގ6ڭ1LW9492R%*tj??gwHints!:The;8arrowfeaturewasusedtomakethebGending arrowsk"andtheframeextensionfortheframesaroundeachUUcell.'ѻ24wlGraphfffeatureVers.3.3bCyKristo erH.Rosehkrisrose@brics.dki Loadas:\xyoption{graph};ThisV-optionimplements`XY -graph',VcaspGecialc}'ombina-toricdr}'awinglanguagev}suitable"fordiagramslike owcharts,directedUwgraphs,andvqariousformsoftrees.}ThebasemofthelanguageisreminiscentofthePIC[5]lan-guage(bGecauseitusesanotionofthe`currentlocation'andOisbasedon`moves'.ButOthecentralconstructionisa`map'combinatorthatisbGorrowedfromfunctionalprogramming. GXY -graph\makesuseoffacilitiesofthe`arrow'featureoptionUUwhichisthereforerequired. Figure?17summarisesthesyntaxofahgraphiwithnotes\bGelow.A hgraphicanappeareitherinanXXY \-picture(ashdecori)or\stand-alone".^13 HNote:ٲIfyouuse\xygraph{?...} |insideconstructionswhere& cissig-ni cant1(likeplainTU>'ExX's\halignorL5ffA͉TU>'EX'sarrayenvironment)tthenmakesuretoaddanextralevelofbracesUUaroundit.Notes;24a.(AUUmoveistoestablishanewcurr}'entnode[.i24b.faT*odr}'aw&somethingissimplytodrawalineorthespGeci edA\harrowifromthecurrentnoGdetothespec-i edRtargetnoGde.Thetargetthenbecomesthecur-rent noGde.AllthefeaturesofarrowsasdescribGedinx21canbGeused,#inparticulararrowscanbelabGelledandsegmented,abutwiththechangethathpath-pGosimeanshnodeiasexplainedinnotex21e.24c.IT*oymapoveralistQissimplytosavethecurrentnoGdeb?andtheninterpretthehlistiwiththefollow-ingUUconvention:i Start|eachelementofthelistwiththecur-rentUnoGdeassavedandpasthepreviouslistelement,UUand4 let Athe?ThnoGdeirefertothesaved AcurrentnoGdeUUexplicitly*.24d.faThe& and\\KspGecialmovesareincludedtomakeitxsimpletoenter`matrix-like'thingsasgraphs{notethattheywillnotbGeautomaticallyaligned,however,UUforthatyoushouldusethe!M*escapGe.4& ois>jthesameas[r]<˲and\\βisthesameas[r]!{y+(0,-1)-(0,0)}mZ$whichIXusesakernelescapGe eff^ J=w-:13LInXfactL#A TAEMXuserscanuseagraphenÎvironment.gw:tomovestothe rstcolumninthenextrow(where :theNM rstcolumnisonthey[ٲ-axisofthecurrentco-:ordinateUUsystem).ፒ:Note:SIfAyouusetheform*{F;...} forAnoGdesthen:youdon'thavetochangethemifyoudecidetouse:anUQXY U-matrix.:24e.# TypGesethitiandmakeitthecurrentnoGde.PAlso:saveswٸhitiforlaterreferenceusing"ָhidi"?:ifhitiis:a9simpleletter,ordigit,thenjustas"6hiti"?;ifhiti:is>oftheform{~text} qвor*...{text} qвthen>as"text"2ղ.:Withthe= additionitispGossibletosaveexplicitly:inJcaseseveralnoGdeshavethesametextoranoGde:has~atextthatitisimpracticaltouseforreference.:Inofactusingtheformhiti=" hidi" lwillonlysave:thecnoGdeas"Ƹhidi"andcnotVas"Ƹhiti"?!$Asaspecial:convenience{""x(thus{theemptyhidi)alwaysrefers:toispGossibletoinsertahmatrixiinagraphpro-:vided"the`matrix'optiondescribGedinx23hasbeen:loaded:NEitCoverwritesthenoGdewiththeresultof:\xymatrix(*hmatrixi.AfterwardsÚthegraphgridis:set3asthetopleft`square'ofthematrix,:ci.e.,with:[d] andjW[r]adjustedjWastheyworkinthetopleft:entry*.:Bug:&[dr]Oimmediatelyafterthematrixwillwork:as[expGected,Je.g.,makethecenterof"2,2"$ theLW9503n*tj??gC ffffd TWSyntaxのActionX-ffd W\xygraph{hgraphi}のtypGesetUUhgraphifffd fdWhgraphi@F!_hstepi*のinterpretUUhstepisinsequenceiWhstepi@F!_hnoGdeiのmove^24aOtoUUthehnoGdeizG=Ej_-dFharrowiUUhnoGdeihlabelsiのdraw^24b8ݲlineUUtohnoGdei,withhlabelsiG=Ej_:dFharrowiUUhnoGdeihlabelsiのdraw^24b8ݸharrowiUUtohnoGdei,withhlabelsiiG=Ej_(ghlistiUU)のmap^24c1currentUUnoGdeoverhlistiWhnoGdei@F!_[ghmoveiUU]のnewUUnoGdehmoveidUUrelativetocurrentG=Ej_&j9jtc\\のnewUUnoGdeinnextcolumn/row^24dG=Ej_"dFhidi"のpreviouslyUUsaved^24e2noGdeG=Ej_?のcurrentlyUUmappGed^24c1nodeG=Ej_hnoGdeiUUhitiのhnoGdeiUUwithhititypesetandsaved^24e2thereG=Ej_hnoGdeiUU= "*hidi"のhnoGdeiUUsaved^24e2as"Rhidi" G=Ej_hnoGdeiUU! ꧸hescapeiのaugmentUUnoGdewithmaterialinanothermodezWhmovei@F!_hhopi*のhhopis^24f޲(dulr)UUfromcurrentnoGdeG=Ej_hhopi*UVhplaceiUUhmoveiのdoUUhhopis^24f޲butuseitshplaceiandhmoveiUUagainiWhlisti@F!_hgraphiUU, ꧸hlistijqhgraphiのlistUUofsubgraphs^24cWhescapGei@F!_{ghpGosiUUhdecori}のpGerformUUhposihdecori^24gzG=Ej_MghmatrixiのinsertUUhmatrixi^24h@4G=Ej_PghpGolygoniのinsertUUhpGolygoni^24iG=Ej_EghellipseiのinsertUUhellipsei^24iG=Ej_~ghsetupiのsetupUUparameters^24jffd FigureUU17:qǸhgraphis*Dgcurrent+`noGde,3butothersmightnot,3e.g.,[rr]_will notnecessarilyplacethecurrentnoGdeontopof"1,3"P.mV24i.DItbispGossibletoinsertahpolygonioranhellipseiinagraphprovidedthepoly)ʲoptiondescribGedinx25orFthearc؃optiondescribGedinx27hasbeenloaded,respGectively:V0itljwillhavecasthecurrentnoGde,pasthepreviousone,andthethecurrentbasehastheUUhhopis[r]jand[u]asbasevectors.Note:+lattices,iknots,etc.,can2QalsobGeusedbutno1]spGecialsyntaxisusefulsincethe!{ W...} syntaxisUUadequate.24j.aThis allowssettingofsomeparametersofthegraph:q!~hsetupiUUshouldbGeoneofthefollowing: ff2 !~:{fQharrowiUU}gwincludeUUwithevery: ꧲arrow!~-{fQharrowiUU}gwincludeUUwithevery- ꧲line!~*{fQhmoGdi ersiUU}gwincludeiwitheverynon-*gwnoGdefd!~hletteri{RhgraphiUU}gwde nenewgraphescapGegw!lthletteriAff2g:These/aredestructive:&Gthepreviousvqalueislost. :Noticep|thatthedefaultforthesecondis!~-{@{-}}:whichishowordinarylinesareobtained,andfor:thethirditis!~*{+}&$whichiswhydefaultnoGdes:areUUinmathmoGdeandhaveUUthedefaultmargin.):The "lastpGossibilityisalsoavqailableasacommand):ff2 Z~\newgraphescape{h}׸hletteri}{ hgraphi}):ff2 ×:that^CmakesthespGeci edescapegeneratethe:hgraphiͲasamacro;withititispGossibletopass:argumentssWtothehgraphiusingthestandardTU>'ExX:\def?methoGd:qTheUUdeclarationcodeN8:\newgraphescape{i}#1#2{*7[]!{+0="o#2"*=<10pt>{};p!#1**{},"o#2"j4-/4pt/*!E\cir<2pt>{}j4+0;p-/:a(-30)24pt/**\dir{-}="X2"j4;p-/:a(-60)24pt/="X1"**\dir{-}j4;?(.5),="i#2",j4p-/:a(-60)24pt/**\dir{-},j4"o#2"."i#2"."X1"."X2"}}x.:isL(rathercomplicatedkernelcoGde)thatmakesthe:noGdeG3escape!i-dntypesetan`inverter'orientedLW9514*tj??gwwith;athedcornerastheoutputwithinputnamed "i n"Mand outputnamed"o n"suchthatthegraphN8\xygraph{?[]!iR1("i1"[l]x-"i1")-[r]z}ԧwillUUtypGeset9Tps: SDict begin xyc end@Ə" {2.00002 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" {30.14235 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}xy - TheUU nalexerciseillustratesmuchUUoftheabGove.b֍ExerciseT35: TypGeseto> ps: SDict begin xyc end1v?w@x18Wz" {0.01625 -0.01009 l}xy=}" {2048 10 /cm AB}xy= " {5.17445 -5.17137 l}xyA辟 \{" {4.42522 -4.4214 l}xyA辟 \{" {0.01625 -0.00862 l}xy%?zǍ2'" {0.0 0.0 l}xy'P }" {0 10 /cm AB}xyǍ'P %" {-10.70714 -10.70714 l}xyǍџ?" {-10.70743 -10.70743 l}xyǍџ?" {0.0 0.0 l}xy26@y" {0.02708 -0.02092 l}xy'Pٟ'6H" {2048 10 /cm AB}xy'TQ'9" {10.72377 -10.72069 l}xy11q" {10.24295 -10.2465 l}xy11q" {0.01997 -0.02708 l}xy@%x2Ǎ8Ύ3:" {0.0 0.0 l}xy=}," {4096 10 /cm AB}xyǍ=}/" {4.68521 4.68521 l}xyǍAğ*" {4.41327 4.41327 l}xyǍAğ*" {0.0 0.0 l}xyǍE"" {0.0 0.0 l}xyEZ#" {-3072 10 /cm AB}xyǍE\" {0.0 7.18527 l}xyǍE" {0.0 7.18527 l}xyǍE" {0.0 0.0 l}xy? " {0.0 0.0 l}xy/˟" {-768 10 /cm AB}xy/˟" {-16.0754 -4.01886 l}xyEw?" {-18.63098 -4.65775 l}xyEw?" {0.0 0.0 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}xyEG;" {0.0 -0.04332 l}xy/ʟh" {2816 10 /cm AB}xy/," {18.63634 -4.68286 l}xy?"" {16.08086 -4.04648 l}xy?"" {0.0 -0.04333 l}xyD(Ӎ25wlPolygonfffeatured4Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{poly}mThisxfeatureprovidesameansforspGecifyingtheloca-tionsڼofverticesforregularpGolygons,AwithanynumbGer(3)8ofsides.oPolygonscanbGeeasilydrawnand/orthevertexpGositionsusedtoconstuctcomplexgraphicswithinanXY 6-picture.Manynon-regularpGolygonscanbGeUUspeci edbysettinganon-squarebasis.ɧ AUUpGolygonismosteasilyspeci edusing... ޜff2 \xypolygon9hnumbGeri{}{UwithUUhnumbGerisides;\xypolygon9hnumbGeri{?htoki}VhtokiUUatvertices;\xypolygon9hnumbGeri{?hob8jecti}UWwithUUageneralhob8jectiateachvertex;)ff2oHere#hnumbGeriisasequenceofdigits,-givingthenum-bGerofsides.AIfusedwithinan\xyZ...\endxy$Kenviron-mentIthenthepGolygonwillbecentredonc,thecurrenthpGosi.$Howeveran\xypolygon=canbeusedoutsidesuchanenvironment,.as\stand-alone"pGolygon;ythewhole picturemustbGespeci edwithinthe\xypolygoncommand. C8 IneithercasetheshapGeisobtainedbyspacingver-ticesequallyaroundthe\unitcircle"withrespGecttothecurrentbasis.Ifthisbasisisnon-squarethenthevertices+ willlieonanellipse.NormallythepGolygon,with[[atmost12vertices,isorientedsoastohavea at)\basewhenspGeci edusingastandardsquarebasis.Withtmorethan12verticestheorientationissuchthatthe>linefromthecentretothe rstvertexishorizon-tal,`pGointing\totheright.Anyotherdesiredorientationgw:canٽbGeobtained,uwithanynumbGerofvertices,ubyusing :theUU~={L...} ?asUUdescribGedbelow.);TheUUgeneralformfor\xypolygon;*is...: ^ff2 Ǎs\xypolygonDhnumbGeri"?hpre xi"{ hswitchesi...}_eff2>ƍwhereu^the"[hpre xi"andu^hswitchesiareoptional.' TheirusesUUwillbGedescribedshortly*. Aڝ\xypolygon<5>establishesڿpGositionsfortheverticesofTapGolygon.AtthesametimevqariousthingsmaybGetypeset,C3accordingtothespeci edhswitchesi.Anhob8jecti5maybGedroppedateachvertex,,\spGokes"drawnltothecentreandsuccessiveverticesmaybGecon-nectedsasthepGolygon's\sides".@LabelsandbreakscanbGeUUspeci edalongthespokesandsides. _c Eachmvertexisautomaticallynamed:"1",2"2"x),2...,"?hnumbGeri" <with"0"3ascentre.f!Whenahpre xihasbGeenmygiven,names"vhpre xi0" ,...,"ոhpre xihnumbGeri"areFusedinstead. FWhilethepGolygonisbeingcon-structedk9themacro\xypolynum9VTexpandstothenumbGerof1^sides,8while\xypolynode@"expandstothenumbGer1^ofeachPvertex,#spGokeandsideatthetimeitisproGcessed.ThisYoGccursinthefollowingorder: vertex1,sp}'oke1,vertex2,esp}'oke2,side1,vertex3,sp}'oke3,side2,...,vertexn,sp}'oken,sidenD1,siden_wherethe nalsidejoinsUUthelastvertextothe rst. Themacro\xypolyname>KholdsthenameofthepGoly-gon,which ishpre xiifsupplied.EInthiscasethevqalueofi\xypolynum:isialsostoredas\\fhpre xiNUMSIDES),'ac-cessibleUUoutsidethepGolygon. AsRstatedabGove,aRpolygonwithupto12verticesis /orientedsoastohavea atbase,6&whendrawnus-ingA|astandardsquarebasis.k)ItsverticesarenumbGeredinjsanti-cloGckwiseorder,commencingwiththeoneathorizontal-rightofcentre,"orthesmallestangleabGovethis~(seeexamplebGelow).Withmorethan12verticesthenvertex"1"isloGcatedonthehorizontal,extendingtotherightfromcentre(assumingastandardsquarebasis)./Byw"providingaswitchoftheform~={7hanglei}thenڱthevertex"1"uYwillbGelocatedontheunitcircleatmhanglei^ anti-cloGckwisefrom\horizontal"|morecorrectly*,NfromMGtheX-directioninthebasistobGeusedwhen|settingthepGolygon,whichmaybGeestablishedusingUUa~:{L...} ?switch.5U䍍)ps: SDict begin xyc endXV VǍ g!" {-20.78467 -36.0 l}xy1!ğ V2 " {41.56934 0.0 l}xyǍ0" {-20.78467 36.0 l}xy|qߡư1ڬ25ڬ3d|q>80f0" {5.00002 0 360 o}xy~0" {5.00002 0 360 o}xyy0" {13.99997 0.0 l}xyr0" {5.00002 0 360 o}xyǍo" {7.09766 12.06885 l}xyǍtY" {-7.09888 12.06885 l}xyZ0" {5.00002 0 360 o}xyǍ\Y" {-7.09888 12.06885 l}xy_0" {-13.99997 0.0 l}xyN0" {5.00002 0 360 o}xyS0" {-13.99997 0.0 l}xyǍPY" {-7.09888 -12.07007 l}xyZ0j" {5.00002 0 360 o}xyǍ\Ymh" {-7.09888 -12.07007 l}xyǍWmh" {7.09766 -12.07007 l}xyr0j" {5.00002 0 360 o}xyǍomh" {7.09766 -12.07007 l}xym0j" {13.99997 0.0 l}xyǍ{[" {7.09766 12.06885 l}xy||q>91p|quY2X|quY3L|q>94X|q5p|q6|q>90Y1۱2ǍⰟX" {-3.66629 6.14026 l}xy|q>93G|" {-6.64182 2.32053 l}xy!۱4(GH" {-6.63336 -2.31851 l}xyџY5Ǎe" {-3.66629 -6.14139 l}xy >96ǍUv" {1.14905 -7.09515 l}xyG ˹7i֟-=" {5.4451 -4.5368 l}xyٟ˹8Ÿ/G" {7.00589 0.0 l}xyEQ >99h " {5.4451 4.53568 l}xyǍ՞^" {1.14905 7.09402 l}xy$IExerciseT36: GiveUUcoGdetotypGesetthese.LW9525r*tj??gw OneimpGortantuseofhpre xiistoallowthevertices ofJ?morethanonepGolygontobeaccessedsubsequentlywithin>>thesamepicture.,Herearesomeexamplesofthis,#incorpGorating&the~:{...} Ͳswitch&toperformsim-plerescalings.YNFirstlytheedgesofadoGdecahedronasaUUplanargraph: ߟK׍&K}ps: 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}xyK`F\xy?/l1.5pc/:,{\xypolygon5"A"{}},{\xypolygon5"B"{~:{(1.875,0):}~>{}}},{\xypolygon5"C"{~:{(-2.95,0):}~>{}}},{\xypolygon5"D"{~:{(-3.75,0):}}},{"A1"\PATH~={**@{-}}'"B1"'"C4"'"B2"},{"A2"\PATH~={**@{-}}'"B2"'"C5"'"B3"},{"A3"\PATH~={**@{-}}'"B3"'"C1"'"B4"},{"A4"\PATH~={**@{-}}'"B4"'"C2"'"B5"},{"A5"\PATH~={**@{-}}'"B5"'"C3"'"B1"},"C1";"D1"**@{-},"C2";"D2"**@{-},"C3";"D3"**@{-},"C4";"D4"**@{-},"C5";"D5"**@{-}?\endxyNextHahexagonalpyramid,arectangularbGoxandanoGctahedralMcrystalspeci edasatriangularanti-prism.Noticethowthe~:{k...} switchtisusedtocreatenon-squarebases, allowingtheillusionof3D-pGerspectiveintheUUresultingdiagrams:,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}xyKps: 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}xyMps: 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}xy \xy/r2pc/:?="A",+(.2,1.5)="B","A",{\xypolygon6{~:{(1,-.1):(0,.33)::}Q~<>{;"B"**@{-}}}}\endxy\quad?\xy/r2pc/:{\xypolygon4"A"{~:{(0,.7)::}}},+(.7,1.1),{\xypolygon4"B"{~:{(.8,0):(0,.75)::}}},"A1";"B1"**@{.},"A2";"B2"**@{.},"A3";"B3"**@{.},"A4";"B4"**@{.}\endxy\quad?\xy/r2pc/:{\xypolygon3"A"{~:{(0,.7)::}}},+(.7,1.1),{\xypolygon3"B"{~:{(-.85,0):(-.15,.8)::}}},"A1"\PATH~={**@{.}}'"B2"'"A3"'"B1"'"A2"'"B3"'"A1"?\endxygw:V ertexb_object: Unless^the rstcharacteris~1[,\signi- :fyinga\switch",լthenthewholeofthebracedmaterial:istakenasspGecifyingthehob8jectiforeachvertex.It:willobGetypesetwithacircularedgeusing\drop[o]...{}{\circ}}},:+/r5pc/,{\xypolygon8{~*{\circ}~<=}}\endxyR:Switc9hes:Theallowableswitchesaregiveninthefollowingtable:: ff2 !O6~:{+-...}[dusefulUUforrescaling.O6~*{+-hob8jecti}[dhob8jectiUUateachvertex.O6~={+-hanglei}[dalignUU rstvertex.O6~<{+-...}[ddirectionalUUfor\spGokes";O6~<<{0O*harrowi}[duseUUharrowiforspGokes;O6~<>{0O*...}[dlabGelsUU&breaksonspokes.O6~>{+-...}[ddirectionalUUfor\sides";O6~><{0O*harrowi}[duseUUharrowiforsides;O6~>>{0O*...}[dlabGelsUU&breaksonsides.\ff2(č/IUsing~<<{/=harrowi} oFor~><{harrowi} oFismostappro-priate}whenarrowheadsarerequiredonthesidesorspGokes,ˏorQwhenlabels/breaksarerequired. Hereharrowi߲isasin gure14,ځsoitcanbGeusedsimplytospGecifythestyleofdirectionaltobeused.^Thus~<<{}sets0eachspGokeasadefaultarrow,ϧpGointingoutwardsfrom&Vthecentre;6~<<{@{-}}5;suppressesthearrowhead,while޵~><{@{}}1Ruses޵anemptyarrowalongthesides.LabGelsandbreaksarespeci edwith~<>{...} wdand~>>{...}꧲,where ]the{ `Z...} use ]thenotationforahlabGeli,UUasin gure13. Whennotipsorbreaksarerequiredthentheswitchesd5~<{$,...} Nܲandd5~>{...} Nܲared5somewhatfaster,sincelessproGcessingisneeded..{\...} andh~>>{...}꧲,,buthnowusingthekernel's˸hplaceinotationof gure1.*Infactanyker-nel)coGdecanbeincludedusingtheseswitches.With~<>thecurrentpandcarethecentreandvertexre-spGectively*,whilefor~>>ۛtheyarethecurrentvertexandu[thepreviousvertex.(Theconnectionfromvertex"?hnumbGeri"Ųtovertex"1" isdonelast.)f ThepyramidabGoveuisanexampleofhowthiscanbeused.BothLW9536Ȋ*tj??gw~<{...} Q:andf~<<{fharrowi} canfbGespeci edtogether, but!onlythelastwillactuallybGeused; similarlyfor~>{...} ?andUU~><{UIharrowi}?.7u *ps: 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$" {-4.43628 -50.71838 dd}xy;؟5" {50.71838 -4.43628 dd}xyǍ?" {4.43628 50.71838 dd}xyp@" {-41.06415 10.23706 l}xyǍ H" {-22.40167 -36.21039 l}xyǍ7 "W" {27.17908 -32.09875 l}xyBt@" {39.23877 15.85327 l}xyǍ?" {-2.95203 42.21881 l}xyl-" {-33.82855 12.31183 dd}xy|Q" {-27.57788 -23.13995 dd}xyǍX$" {6.25177 -35.45398 dd}xy*- !" {33.82855 -12.31183 dd}xyE " {27.57788 23.13995 dd}xyǍ?" {-6.25177 35.45398 dd}xy.LAv" {-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}xyǍo3" {2.5686 -20.12201 l}xyǍ3" {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 g" {-1.09424 -4.38794 dt}xyǍ/" {-0.51581 -4.16711 dt}xyǍ H" {0.03625 -5.16357 dt}xyǍ<" {0.57404 -4.15997 dt}xyǍԟ \" {1.15466 -4.37091 dt}xyǍu7" {1.69409 -4.19238 dt}xyǍ/" {2.20496 -3.94519 dt}xyǍX̟$" {2.68286 -3.64032 dt}xyǍ vj" {3.11792 -3.27338 dt}xyB" {3.50244 -2.857 dt}xy,L" {3.83423 -2.39612 dt}xy2>" {4.10449 -1.89679 dt}xy6 " {4.30884 -1.36615 dt}xy!a" {4.44781 -0.81683 dt}xy$-!" {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" {-0.16472 0.10197 l}xy&h 10.ܑt" {-1517 10 /xy AB}xyܑt" {-16.15808 7.77766 l}xy0.ܑt" {0.0 0.10434 l}xyc]Cџu" {-0.0231 0.01688 l}xyuh " {-918 st}xys\ڟm" {-918 F d}xyuf" {-14.08447 11.23125 l}xyl؟W" {-8.87177 7.07736 l}xyl؟l$" {-0.11792 0.0 l}xy}Hܦ" {-0.16907 -0.0838 l}xymh 2mI" {-531 10 /xy AB}xymŸI" {-16.0344 -7.72081 l}xymI" {0.0 -0.08281 l}xy\} -D컟" {0.0 0.0 l}xyr`A% " {368 st}xyq  " {368 F d}xyr`B%" {-17.54872 -4.00534 l}xyg" {-10.77989 -2.46057 l}xyg " {0.0 -0.05974 l}xyǍfY_" {-0.05368 -0.2626 l}xyX3 3b4V" {790 10 /xy AB}xyǍb4" {-4.19675 -18.385 l}xyǍb4" {-0.05379 0.0 l}xypSe!{ɵEǍ몞j" {-0.00417 -0.00552 l}xy|e s " {1394 st}xy{< O" {1394 F d}xyǍ|ܟ8_" {-7.812 -16.2202 l}xyǍwF " {-5.04942 -10.4847 l}xyǍwFM" {-0.07959 0.0 l}xyǍe; W" {0.08228 -0.115 l}xy^v 4pǟ" {1841 10 /xy AB}xyǍp4JP" {11.22025 -14.062 l}xyǍpǟJP" {0.0 -0.1137 l}xy!{ɵFǍR" {0.03584 -0.02078 l}xy s " {2702 st}xydҟ " {2702 F d}xyǍ:U" {7.82784 -16.22786 l}xyǍX#" {5.06978 -10.50436 l}xyǍX5" {0.10457 0.0 l}xy_$ 5" {3072 10 /xy AB}xy" {17.34105 0.0 l}xy" {0.0 0.0 l}xyI -G" {0.00381 -0.02464 l}xyy5% " {3729 st}xyb$Q" {3729 F d}xyyM" {17.55064 -4.01767 l}xyP*" {11.0882 -2.54253 l}xyF*" {0.0 -0.0845 l}xyǍ6" {0.07521 0.09761 l}xyH 6p " {-3889 10 /xy AB}xyǍ $<" {11.29424 14.1674 l}xyǍp $<" {0.0 0.09769 l}xyǍ" {-0.07747 0.26474 l}xy 7ry)" {-2838 10 /xy AB}xyǍr" {-4.20076 18.40527 l}xyǍrb" {-0.07738 0.0 l}xy?=\def\alphanum{\ifcase\xypolynode\or?A\or?B\orC\orD\orE\orF\orG\orH\fi}\xy/r3pc/:?{\xypolygon3{~={40}}},{\xypolygon4{~={40}~>{{--}}}},{\xypolygon5{~={40}}},{\xypolygon6{~={40}~>{{--}}}},{\xypolygon11{~={40}}},{\xypolygon50{~={40}~>.}},?+/r8pc/,{\xypolygon7{~<<{@{-}}~><{}Q~<>{|*@{x}}~*{\alphanum}Q~>>{_{\alpha_\xypolynode^{}}}}}\endxyN8 Useofthe~={...} 4switchwasdescribGedearlier.Whenusingthe~:{...} ImorecanbGedonethanjustsettingGthebase.InfactanykernelcoGdecanbesup-plied!here.GItisproGcessedpriortoanyotherpartofthebpGolygon.3ThegraphicsstatehascatthecentreofthepGolygon,pattheoriginofcoordinateswithinthepictureJ?andhasbasisunchangedfromwhathaspre-viouslybGeenestablished.7ThecurrentpointcwillberesettothecentrefollowinganycoGdeinterpretedusingthisUUswitch. A4'further4asimpli cationexistsforsidesandspGokeswithoutvkharrowis. Ifhtokiisasinglecharacterthen~>htoki,~>{Ϊhtoki}?,~>{{htoki}}iallspGecifythedirec-tional\dir{9htoki}?;Ksimilarlywiththe~<sPswitch.^OntheQotherhand,compGounddirectionalsrequireallthebraces,UUe.g.q~>{{--}}1and~>{2{.}}-U=. AfterallswitcheshavebGeenprocessed,NremainingtokensareusedtospGecifythehob8jectiforeachvertex.Such%tokenswillbGeuseddirectlyaftera\drope ,.socaninclude+ob8jecthmoGdi erisasin gure3.cIfanhobjectihasalreadybGeenspeci ed,Ousingthe~*nswitch,thentheUUfollowingmessagewillbGewrittentotheTU>'ExXlog:=Xy-pic?Warning: vertexalreadyspecified,$discarding?unusedtokens:with"tokensattheendindicatingwhatremainsunpro-cessed.+SimilarlybextratokensbGeforethe{_...} ~ gener-ateUUamessage:=Xy-pic?Warning:discardingunusedtokens:gw:NestedTP9olygons :When|\xypolygon9xis|spGeci edwithineithera~<>{|u...} :orN~>>{N...} 9switchNforanotherpGolygon, ithenthe:innerpGolygoninheritsanamewhichincorporates:alsothenumbGerofthepartonwhichitoccurs,~4as:givenoby\xypolynode>/.OThisnameisaccessedusing:\xypolyname .8YIn thefollowingexampletheinnerpGoly-:gonisplacedusing~<>inordertoeasilyadjustits:orientationUUtotheoutwarddirectionofthespGokes.Nqps: SDict begin xyc endt>m1hw> " {8.0 ox}xyo[t1;1]t1;2Ǎ1nt" {12.23581 12.23581 l}xyo[t1;3|k" {-12.23581 12.23581 l}xyWYt1;4Ǎdϱ" {-12.23581 -12.23581 l}xyq1lR" {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" {-24.85287 0.0 l}xy+G3'"8 " {8.0 ox}xyN3;1*N3;2Ǎ$Z" {-12.23581 -12.23581 l}xyBN3;3W:-#" {12.23581 -12.23581 l}xy3*N3;4Ǎ4W0N" {12.23581 12.23581 l}xy(" {-12.23581 12.23581 l}xyǍ"8 m+" {0.0 -24.85287 l}xyt>+G4'w> " {8.0 ox}xyWY*N4;1o[BN4;2q1l:-#" {12.23581 -12.23581 l}xy]*N4;3Ǎ1n0N" {12.23581 12.23581 l}xyo[N4;4|" {-12.23581 12.23581 l}xyǍd$Z" {-12.23581 -12.23581 l}xyY=(" {24.85287 0.0 l}xyǍw>" {0.0 24.85287 l}xy[:\xypolygon4{~:{/r5pc/:}*7~<>{*\frm<8pt>{o}\xypolygon4{~:{/-2pc/:}1~*{\xypolyname\xypolynode}}}*7[o]=<5pc>{\xypolynode}};NoticehownestedpGolygonsinheritnames"1,1"9x,:"1,2"*+,W...,"4,1",...,"4,4"$fortheirvertices. DTIf:ahpre xiissuppliedattheoutermostlevelthenthe:names8bGecome:c" hpre xii;j"҈.hJSpecifyingahpre xifor:theinnerpGolygonoverridesthisnamingscheme.The:sameqnamesmaythenbGerepeatedforeachoftheinner:pGolygons, allowingaccessafterwardsonlytothelast|:pGossiblyusefulasamemorysavingfeaturewhenthe:verticesUUarenotrequiredsubsequently*.;F*our,levelsofnestinggivesaquiteacceptable\Sier-:pinskigasket".'M SsymbGolfontmsam5,at:5-pGoint‚size.OF*urtherlevelscanbGeachievedusingthe:PostScriptbackend,otherwiselinesegmentsbGecome:toGoUUsmalltoberenderedusingUQXY U-fonts.CL'Lps: SDict begin xyc end3D ^C"xmsam5CN2)*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):} Q~>{}~<>{?\xypolygon3"b"{~:{(.5,0):}Q~>{}~<>{?\xypolygon3"c"{~:{(.5,0):}Q~>{}~<>{?\xypolygon3"d"{~:{(.5,0):}~<>{?*!/d.5pt/=0{\blacktriangle}}}}?}}}}}}}N8NoteAtheuseofnaminginthisexample;HwhenproGcess-ingthismanualitsaves13,000+wordsofmainmem-oryand10,000+stringcharactersaswellas122stringsandUU319multi-lettercontrolsequences.&26wlLatticeffandwebfeatureVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{web}uTThis\featureprovidesmacrostofacilitatetypGesettingofarrangementsofpGointswithina2-dimensionallatticeorUU\web-like"structure. CurrentlyAtheonlyroutinesimplementedwiththisfeaturetaresome\quickanddirty"macrosfordroppingob8jectsatthepGointsofanintegerlattice."T oyDo:MoresophisticatedroutineswillbGedevelopedforlaterversionsUUofUQXY U-pic,astheneedarises. MathematicallyxspGeaking,letW~uԲandC~v&bevectorspGointinginindependentdirectionswithintheplane.ThenLthelatticespannedby+~u Sband銵~v Ρisthein nitesetofUUpGointsLgivenby:L0=b ca~u +8bG@~v };forUUa,bintegersK̻b SL:WithinXY v-picthevectorsՄ~u and#~v !ӲcanbGeestablished askthecurrentcoGordinatebasisvectors.ThefollowingmacrosUUtypGeseta nitesubsetofanabstractlattice. Hff2 Oi6w\xylattice#1#2#3#4q6#pGointsUUinlattice6w\croplattice#1#2#3#4#5#6#7#8q6#...inUUspGeci crectangle.ff2~⍖~Theparameters#1...#4"are~tobGeintegersamin ,vamaxA̲,bminandbmaxA̲,CsothatthepGortionofthelatticetobGeɟtypesetisthatcollectionofvectorsinLforwhichaminaamax!andUUbminbbmaxA̲.`ˍ.ps: SDict begin xyc endA<>d/<=ȟ<<, <; a<:9<9X<8>ce,cɟc-cac 9c#Yc$;v&f)u)ʟt,.s/ar29q5Zϋp688g&;˟>/AaD9޳ G[̳ H5ڮJh#ڭM̟ڬP0ګSaڪV9کY\ڨZ3J\i!Ib1GeaFh9Ek]Dl0)nj)qΟ )t2)wa)z9)}^)~-QkQϟ Q3QaQ~9Q}_Q|*ylyПy4yay9y`y_͟Hc0Οaz*C3232E덍3232P32323232323232323232323232323232323232323232Pܞ3232TZCa 323273232323232323232323232323232323232323232323232323232b0Ο 32327323232323232323232323232323232323232323232323232323232C3232E덍3232P32323232323232323232323232323232323232323232Pܞ3232bHs^(1)" {0.0 0.0 l}xya" {3072 10 /xy AB}xya" {166.0718 0.0 l}xya" {0.0 0.0 l}xyKRQs^(2)ǍS 0Cw" {0.0 0.0 l}xyS 0Q" {-3072 10 /xy AB}xyǍS 0e" {0.0 135.20674 l}xyǍS 0e" {0.0 0.0 l}xygw:\def\latticebody{% :\ifnum\latticeA=1?\ifnum\latticeB=-1%:\else\drop{\circ}\fi\else\drop{\circ}\fi}:\xy?*\xybox{0;<1.5pc,1mm>:<1mm,1.5pc>:::,0,{\xylattice{-4}4{-3}3}*7,(1,-1)="a"*{\bullet}*+<2pt>!UL{a}*7,(-1,1)."a"*\frm{.}}="L":,{"L"+L?\ar"L"+R*+!L{s^{(1)}}}:,{"L"+D?\ar"L"+U*+!D{s^{(2)}}}:\endxyN8;IntheabGovecode,noticehowthebasisis rstestab-:lishedHthenthe\xylattice:VrtypGeset.NmDoingthiswithin:an\xybox%allowsaxestobGesizedandplacedappropri-:ately*.u SinceVklatticepGointsaredeterminedbytheir(in-:teger)tcoGordinatedisplacements,||theycanberevisited:toaddextrahob8jectisintotheoverallpicture.More:generally*,ntheȜoriginforlattice-coGordinatesisthecur-:renthpGosic,Iwhenthe\xylattice=Fcommandisen-:countered.Easycaccessibilityismaintained,g#asseenin:theUUnextexample.΍;When thebasisvectors~u Wandk~v ϲarenotpGerpendic-:ular5thecollectionofpGointswitha;bintheseranges:willٟ lloutaskewparallelogram.HGenerallyitisuseful:to7plotonlythosepGointslyingwithina xedrectangle.:Thisy&isthepurpGoseof\croplatticeCy,withitsextra:parameters(#5J...#8A̲determining(the`cropping'rect-:anglewwithinwhichlatticepGointswillbGetypGeset.'Other:pGoints$willnotbetypesetevenwhenaandbarewithin:the-spGeci edranges.dExplicitlythehorizontalrangeof:the,croppingrectangleisXmin0toXmaxA̲,withXminbGe-:ingtheX-coGordinateofthevector#5 2~9u,Ewhere#5isa:hnumbGeri_"(notnecessarilyaninteger)..SimilarlyXmax:istheX-coGordinateof#6=)~ug.ZTheverticalextentsare:YminandYmaxA̲,'givenbytheY8-coGordinatesof#7&E~v:andUU#8/x~8v respGectively*.\l+ps: SDict begin xyc endaY_ 2˒*N uϟU$aZ-3N1%& .uП<7o?-Ha[dQ4 A.5I!Ruџ )[+`la\ґu5e. 1M%m\a]M8.!-;uӟn4ka^."(0c^c% vuҟ {ҟ Bf=q" {0.0 39.59988 dt}xyBTџ" {0.0 -39.59988 dt}xyxҟz" {54.71997 0.0 dt}xyB=jI" {-54.71997 0.0 dt}xy%B3232Ce/3232E3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232E3232'Bڧ3232"32323232323232323232323232323232323232323232323232323232323232323232xڧ3232"3232323232323232323232323232323232323232323232323232323232323232323232B3232Ce/3232E3232323232323232323232323232323232323232323232323232323232323232323232323232323232323232E32323Uas^(1)" {0.0 0.0 l}xy3T" {3072 10 /xy AB}xy3T" {187.2005 0.0 l}xy3T" {0.0 0.0 l}xyUh!s^(2)Ǎ]5" {0.0 0.0 l}xy]!" {-3072 10 /xy AB}xyǍ]Z" {0.0 118.79965 l}xyǍ]Z" {0.0 0.0 l}xyFY:\def\latticebody{%:\ifnum\latticeA=1?\ifnum\latticeB=-1%:\else?\drop{\circ}\fi\else:\ifnum\latticeA=0?\ifnum\latticeB=1\else:\drop{\circ}\fi\else\drop{\circ}\fi\fi}:\xy?+(2,2)="o",0*\xybox{%*70;<3pc,1.5mm>:<0.72pc,1.65pc>::,{"o"*7\croplattice{-4}4{-4}4{-2.6}{2.6}{-3}3}LW9558_ˠ*tj??gwQ,"o"+(0,1)="a"*{\bullet}*+!D{\alpha} Q,"o"+(1,-1)="b"*{\bullet}*+!L{\beta}Q,"o"+(0,-1)="c","o"+(-1,1)="d"Q,"a"."c"="e",!DR*{};"a"**\dir{.}Q,"e",!UL*{};"c"**\dir{.}Q,"b"."d"="f",!DL*{};"b"**\dir{.}Q,"f",!UR*{};"d"**\dir{.}Q,"e"."f"*\frm{.}}="L","o"."L"="L"Q,{"L"+L?\ar"L"+R*+!L{s^{(1)}}}Q,{"L"+D?\ar"L"+U*+!D{s^{(2)}}}\endxy6Then\latticebodyKmacro. AtweachlatticepGointwithinthespGeci edrangefora;b(andwithinthecrop-pingrectanglewhen\croplatticeFisused),(amacrocalled ;\latticebodyERis ;expanded.XThisismeanttobGeuser-de nable,soastobGeabletoadapttoanyspeci crequirement.qItUUhasadefaultexpansiongivenby...<D\def\latticebody{\drop{\bullet}}7:TheRfollowingmacrosmaybGeusefulwhenspecifying whatUUtodoateachpGointofthelattice. iff2 i\latticebodye0expandedUUatlatticepGointsi\defaultlatticebodyy0resetsUUtodefaulti\latticeAe0a-vqalueUUoflatticepGointi\latticeBe0b-vqalueUUoflatticepGointi\latticeXe0X-coGord,UUo setinpt Os...i\latticeYe0Y8-coGord, P...fromlatticee0origin.Ӊff2gAsintheexamplespresentedabGove,_+theob8jectdroppGedZ?atthelatticepointcanbevqariedaccordingtoUUitsloGcation,oromittedaltogether. Inthe nalexamplethe\latticebodyFmacropGer-formsoDacalculationtodecidewhichlatticepGointsshouldUUbGeemphasised:荍ps: SDict begin xyc endJ: @Y:s e: iFe:_ e:TПe:'Je:0#蟛O:}4:#s:-iG:6BƸATџ:KJ:U@[:2kIwѸ=},:FWwϸPL֟w[_ :eTҟ:oJ:y@\:W@v:a}%v:ks v:uiIv :_v :Tӟv :Jv :q6T&:{9&:}&:WݸiJ&:_&:Tԟ&:J&:7L:1:}:WiK:_:8E&:Ç*%:}Ÿ$:ڟH[ٟ^(1)" {0.0 0.0 l}xyٟ" {3072 10 /xy AB}xyٟ" {208.80019 0.0 l}xyٟ" {0.0 0.0 l}xy&~s[ٟ^(2)Ǎ.[" {0.0 0.0 l}xy." {-3072 10 /xy AB}xyǍ. V" {0.0 210.59978 l}xyǍ. V" {0.0 0.0 l}xygw:\def\latticebody{\dimen0=\latticeX?pt *7\ifdim\dimen0>0pt?\divide\dimen0by64*7\dimen0=\latticeY\dimen0?\relax*7\ifdim?0pt>\dimen0\dimen0=-\dimen0\fi*7\ifdim?10pt>\dimen0\drop{\bullet}%*7\else\drop{.}\fi?\else\drop{.}\fi}:\xy*\xybox{0;<3pc,2.57mm>:<.83pc,2.25pc>:::,0,{\croplattice{-3}5{-5}5j4{-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*n:27PCircle,Ellipse8=andArcfea-Pture:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{arc}uT:ThistfeatureprovidesameanstoaspGecifycirclesof:arbitraryradius,Pdrawnwithavqarietyoflinestyles.:SimilarlyellipsesmaybGespeci ed,lhavingarbitrary:ma8jor/minorlaxesalignedinanydirection.Alcircular:arcdjoiningtwodpGointscanbGeconstructedwithspeci ed:tangentUUdirectionatoneend.;AlltthecurvesdescribGedhere|circles,}ellipsesand:sectors(ofthese|areconstructedusingthecurvesfrom:thexycurve,extension.AJAssuchanycommentsgiven:thereawconcerningmemoryrequirementsareequally:vqalidhere,P:pGerhapsevenmoreso. 2SUseofthexyps:PostScriptUUback-endishighlyrecommended.:27.1 j:FullCircles:Thepxyarc!ѲfeaturepallowsamuchwiderrangeofpGos-:sibilitiesCfortypGesettingcirclesthanisavqailablewith:\cir..7Firstlytheradiusisnolongerrestrictedtoa: nitercollectionofsizes.ʼSecondlyfancyline(curve):stylesareavqailable,[aswithcurvedarrows. NFinally:thereareavqarietyofwaysofspGecifyingthedesiredra-:dius,g#relativectootherpartsofthepicturebGeingbuilt,:asUUinthefollowingexample..ps: SDict begin xyc endnp,n7c." {30.0 -30.0 l}xyʂ" {p}xyO4" {p}xykx{y" {p}xy *8" {p}xy %q n" {p}xy ß" {p}xy 8" {p}xy I:8" {p}xy Ÿ" {p}xy %8" {p}xy ]" {p}xym" {p}xy֟ /" {p}xy)H V" {p}xy+) " {p}xyP۟ IT" {p}xyu՟ " {p}xy D" {p}xyȟ" {p}xyG@" {p}xyR=" {p}xyaI" {p}xy媟" {p}xy|W" {p}xy" {p}xyCb" {p}xyS9" {p}xyV@x{" {p}xy/O" {p}xy0a" {p}xy#f" {p}xy#x" {p}xy/O" {p}xy0a" {p}xySK" {p}xyV@" {p}xy!" {p}xyC!" {p}xy媟#" {p}xy|# " {p}xyR%~D" {p}xya%r" {p}xyȟ'q" {p}xy'R" {p}xyu՟)X" {p}xy)" {p}xy+)+9" {p}xyP۟+@" {p}xy֟-" {p}xy)H-" {p}xy ." {p}xy/" {p}xy Ÿ0" {p}xy %1Z" {p}xy 82nn" {p}xy I:3\" {p}xy "a4" {p}xy ӟ5R" {p}xykx5 " {p}xy *7 " {p}xyʂ7`" {p}xyO48" {p}xyB8" {p}xyؽ:V" {p}xyص:V" {p}xyBß8" {p}xy{:d" {p}xyv;T" {p}xygn;" {p}xy$=Q_" {p}xy c= " {p}xyᥟ>" {p}xy >:A" {p}xy-?O" {p}xy{?Q" {p}xy{-A " {p}xyIƟ@Pu" {p}xyYB" {p}xyA6" {p}xyBC?" {p}xyBQ" {p}xy5ICޯ" {p}xy ԟB" {p}xy 0vD" {p}xy"ßCV" {p}xy"35EC" {p}xy$2CZ" {p}xy$5E" {p}xy&̟DI" {p}xy&C~FA" {p}xy(Dg" {p}xy(NFE" {p}xy*.Dۋ" {p}xy*dpFI" {p}xy,wE*" {p}xy,tF(" {p}xy.E " {p}xy.G " {p}xy0E*" {p}xy0F(" {p}xy2@Dۋ" {p}xy2FI" {p}xy4}Dg" {p}xy4FE" {p}xy6yDI" {p}xy6FA" {p}xy8j9CZ" {p}xy8gE" {p}xy:]CV" {p}xy:GEC" {p}xy%BQ" {p}xy>5Cޯ" {p}xy?A6" {p}xy@џC?" {p}xyAѧ@Pu" {p}xyB՟B" {p}xyC?Q" {p}xyDOA " {p}xyEZc>:A" {p}xyFsQ?O" {p}xyG ٟ= " {p}xyH>>" {p}xyH;" {p}xyIݟ=Q_" {p}xyJL:d" {p}xyK;T" {p}xyKص8" {p}xyMBß:V" {p}xyMB:V" {p}xyKؽ8" {p}xyMP7`" {p}xyNI8" {p}xyN5 " {p}xyP=T7 " {p}xyO4#" {p}xyQ5M" {p}xyQ&62nn" {p}xyRD3\" {p}xyR=0" {p}xyS1Z" {p}xyS" {p}xyW" {p}xyY" {p}xyW " {p}xyY" {p}xyW" {p}xyY" {p}xyWǀ9" {p}xyY>x{" {p}xyW\" {p}xyY:b" {p}xyW5ş" {p}xyY-W" {p}xyVO=" {p}xyXI" {p}xyVB" {p}xyX/G@" {p}xyU " {p}xyWƟ D" {p}xyTF " {p}xyVʤ IT" {p}xyT" /" {p}xyU4 V" {p}xyS%?5" {p}xy>5d" {p}xyRS" {p}xy*[I" {p}xy)͟ " {p}xy*ݟ J" {p}xy(_" {p}xy*џMc" {p}xy(㳟" {p}xy*$z" {p}xy(V" {p}xy*" {p}xy(V2" {p}xy*`" {p}xy(~" {p}xy*"t" {p}xy(Tv" {p}xy*Ÿ>" {p}xy(+" {p}xy*tH" {p}xy(Tj" {p}xy* " {p}xy(" {p}xy*<" {p}xy(*" {p}xy*Ÿ" {p}xy(4i" {p}xy*"2" {p}xy(T" {p}xy*g$" {p}xy(ł" {p}xy*" {p}xy(V" {p}xy*$" {p}xy(VS" {p}xy*џ" {p}xy(㳟" {p}xy*ݟ#:" {p}xy(" {p}xy*[P9" {p}xy)͟)" {p}xy+p}" {p}xy)>Rm@" {p}xy+1" {p}xy)c" {p}xy+6չ" {p}xy)ß" {p}xy+R" {p}xy)0I" {p}xy+s(K" {p}xy)1k)" {p}xy+OA" {p}xy*" {p}xy+u" {p}xy*O" {p}xy*O" {p}xy+u" {p}xy+8" {p}xy*z " {p}xy,." {p}xy*` IX" {p}xy,2\[" {p}xy*> v" {p}xy,Y" {p}xy+@ " {p}xy,ٟF" {p}xy+ ̄" {p}xy,f-" {p}xy+H 6" {p}xy,>C" {p}xy,!" {p}xy- ?V" {p}xy,K!0" {p}xy-9Xg" {p}xy,!K" {p}xy-fvvT" {p}xy,!c2" {p}xy-" {p}xy-֟!u2" {p}xy-Uh" {p}xy-j!" {p}xy-iV" {p}xy-k!4" {p}xy.*ޟ" {p}xy- !u" {p}xy.`={" {p}xy.@_!y" {p}xy.r" {p}xy.!p" {p}xy.1{" {p}xy.!y" {p}xy." {p}xy/ ^!u" {p}xy/V" {p}xy/m!4" {p}xy/Sh" {p}xy/w!" {p}xy/x" {p}xy/!u2" {p}xy/vT" {p}xy0?!c2" {p}xy/g" {p}xy0!K" {p}xy0/V" {p}xy0ݟ!0" {p}xy0<.C" {p}xy1|!" {p}xy0i-" {p}xy1Y5 6" {p}xy0F" {p}xy1 ̄" {p}xy0" {p}xy1ڜ " {p}xy0[" {p}xy2> v" {p}xy1@" {p}xy2W IX" 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Ifhorientiishemptyithentheori-entationnisdeterminedtogivetheshortestpathalongtheellipse."SpGecifyinganhorientiof^ Ior_willforcetheorientation,evenifthismeanstravelling`thelongway'UUaroundtheellipse.qF*orexample,seenext gure.鍑Alternativ9ecurves Insomecasesthecircularorel-liptictcurvecanbGereplacedbyacurvewithdi erentshapGe,havingwgthesametangentdirectionsattheend-pGoints.WhenZafullcircle/ellipseisspeci edthenonegetsinsteadaclosedcurveconstructedfrom4splinesegments.EFOthervqariantsuseasinglesegment,t2or3segments,Aor\ellipse~e?...{SӸh..i}welliptical,UUasabGove\ellipse~q?...{SӸh..i}wparabGolicUUsegments\ellipse~c?...{SӸh..i}wcubicUUsegments\ellipse~i?...{SӸh..i}winterpGolatingUUcubic\ellipse~p?...{SӸh..i}wcuspidalUUcubic\ellipse~c(>߸hnumi)...{?h..i}cubicUUsegments,wwithUU\loGoseness">ff2ՍIn thelattercasethehnumi,ztypically bGetween0and1,ʱcontrolshowsoGonthecurvebGeginstobendawayfromthetangentdirection.[Smallervqaluesgivetightercurves |0forstraightlines|with~cbGeingthesameasUU~c(1) ꛲andUU~q*isUU~c(.66667)77,UUthatishnumi= K2K&fes3 ). The!curveproGducedbythe\interpGolating"vqariant~i actually*passesthroughthecontrolpGoint"x",3rwithslopGemparalleltotheline~fe [۟gpc ɜ.$SincethetangentsatpandcpGointtoward"x"Ethecurvqatureisquitegentleuntilnear;a"x"6where;athecurvebGendsrapidly*,@yetsmoGothly*.Thisisobtainedalsobyusing~c(1.33333)>Z,thatishnumi= K4K&fes3 ).SinceJ1Q:>1J1the\convexhullpropGerty"doGesynothold;indeedthecurveisentirelyoutsidetheconvex@hullofp,zõcand"x" ,apartfromthosepGointsthemselves. The`cuspidal'vqariant~p |׵>d2thecurveisso\loGose"thatitexhibitsloGops.(Theauthoro ersnoguaran-teesontheusefulnessofsuchcurvesforanyparticularpurpGose;UUhowevertheydoloGoknice. 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Xh" {p}xy, j}" {p}xy.ܟo" {p}xy,ّ" {p}xy.M" {p}xy,C=" {p}xy." {p}xy, " {p}xyU" {mark 120.0 0.0 103.44635 16.55365 76.55365 16.55365 60.0 0.0 0.00198 0.55768 bz}xyP" {mark 150.0 -30.0 150.0 -16.7573 123.1073 -6.00037 90.0 -6.00037 0.0 1.0 bt}xyM" {mark 90.0 -6.00037 56.8927 -6.00037 30.0 -16.7573 30.0 -30.0 0.0 1.0 bt}xyO" {mark 30.0 -30.0 30.0 -43.2427 56.8927 -53.99963 90.0 -53.99963 0.0 1.0 bt}xyR" {mark 90.0 -53.99963 123.1073 -53.99963 150.0 -43.2427 150.0 -30.0 0.0 1.0 bt}xyQ" {mark 90.0 -6.00037 56.8927 -6.00037 30.0 -16.7573 30.0 -30.0 0.75845 1.0 bz}xyS" {mark 30.0 -30.0 30.0 -43.2427 56.8927 -53.99963 90.0 -53.99963 0.0 0.61926 bz}xyS" {mark 60.0 0.0 47.58476 -12.41524 50.94635 -35.94635 67.5 -52.5 0.00003 1.0 bt}xyS" {mark 67.5 -52.5 84.05365 -69.05365 107.58476 -72.41524 120.0 -60.0 0.0 1.0 bt}xyT" {mark 120.0 -60.0 132.41524 -47.58476 129.05365 -24.05365 112.5 -7.5 0.0 1.0 bt}xyL" {mark 112.5 -7.5 95.94635 9.05365 72.41524 12.41524 60.0 0.0 0.0 1.0 bt}xyS" {mark 60.0 0.0 47.58476 -12.41524 50.94635 -35.94635 67.5 -52.5 0.00003 1.0 bz}xyW" {mark 67.5 -52.5 84.05365 -69.05365 107.58476 -72.41524 120.0 -60.0 0.0 0.99738 bz}xyZ\xy?0;/r5pc/:*\dir{*}="p",*+!DR{p}; p+(.5,-.5)*\dir{*}="c",*+!UL{c}**\dir{-},"c",{\ellipse<15pt>_,=:a(45){=}},{\ellipse<>__,=:a(30){-}},{\ellipse(1,.4){.}},{\ellipse(1,.4)_,=:a(120){-}},{\ellipse(,.75){.}},{\ellipse(,.75)_,^,^{-}}\endxy+28wlKnotsffandLinksfeature Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{knot}΍This`featureprovidesalanguageforspGecifyingknots,linksUUandgeneralarrangementsofcrossingstrings. # Thisknotfeatureisreallya`constructionkit',pro-vidingpieceswhichmaybGeplacedappropriatelytoformknotsandlinks.VThetypGesofpiecesprovidedareof߳twokinds:the\crossings",Krepresentingonestringcrossing overorunderanother;hand\joins"whichareused toconnectwhatwouldotherwisebGelooseends.Several typGesofeachareprovided, valongwithasim-ple<wayofspGecifyingwheretoplacearrowheadsandlabGels. All| thepiecesultimatelyusecurvesfromthecurveextension,*Notethat\..cross..@f0and:\..twist../òcrossingsTmaysetthesamecurves,but:withUUdi erentorientationandlabGel-positioning.:Figure"?19displaystheorientationonallthecross-:ings,Øgroupingthemintosubfamiliesconsistingof:right-handed,oleft-handedjjandnon-crossings.Also:indicated?arethedefaultpGositionsforlabelsand:arrow-tips;eachpieceusesthesamecoGdefortips:andUUlabGels,e.g.q\vover<>.q|3>>><{x}Xq|]{y}>{z}q.:The&\x... &=crossings&donotstackeasilysincetheir:tangents4bareat45^FtothecoGordinateaxes.Itis:thei\lastletterinthenamewhichdenoteswhether:theparticularcrossingisverticalorhorizontal.4On:theotherhand\vover$,\vunder+etc.$stackverti-:callyTontopofa\vcross),T\vtwist+iѲetc.;U similarly:\hover:stacksпattheleftof\hcross);X,C\htwist*{etc. ])ps: SDict begin xyc endA" {mark 12.0 0.0 15.0 0.0 17.25 -0.75 18.875 -1.625 0.0 0.0 bz}xyE" {mark 18.875 -1.625 20.5 -2.5 21.5 -3.5 22.375 -5.125 0.0 0.0 bz}xyD" {mark 22.375 -5.125 23.25 -6.75 24.0 -9.0 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243.25 -229.75 0.0 1.0 bz}xyK" {mark 243.25 -229.75 241.5 -226.5 240.0 -222.0 240.0 -216.0 0.0 1.0 bz}xyyK" {mark 264.0 -240.0 258.0 -240.0 253.5 -238.5 250.25 -236.75 1.0 1.0 bz}xyM" {mark 250.25 -236.75 247.0 -235.0 245.0 -233.0 243.25 -229.75 1.0 1.0 bz}xyK" {mark 243.25 -229.75 241.5 -226.5 240.0 -222.0 240.0 -216.0 1.0 1.0 bz}xyyQ" {mark 288.0 -240.0 288.0 -234.0 290.10004 -231.0 290.10004 -228.0 0.0 0.0 bz}xyQ" {mark 290.10004 -228.0 290.10004 -225.0 288.0 -222.0 288.0 -216.0 0.0 0.0 bz}xyڜ" {-2811 10 /cm AB}xy #ݹyyQ" {mark 288.0 -240.0 288.0 -234.0 290.10004 -231.0 290.10004 -228.0 0.0 1.0 bz}xyQ" {mark 290.10004 -228.0 290.10004 -225.0 288.0 -222.0 288.0 -216.0 0.0 1.0 bz}xyyQ" {mark 288.0 -240.0 288.0 -234.0 290.10004 -231.0 290.10004 -228.0 1.0 1.0 bz}xyQ" {mark 290.10004 -228.0 290.10004 -225.0 288.0 -222.0 288.0 -216.0 1.0 1.0 bz}xyyN" {mark 312.0 -240.0 306.0 -240.0 303.0 -238.5 300.70001 -236.25 0.0 0.0 bz}xyZ" {mark 300.70001 -236.25 298.40002 -234.0 296.80005 -231.0 296.80005 -228.0 0.0 0.0 bz}xyZ" {mark 296.80005 -228.0 296.80005 -225.0 298.40002 -222.0 300.70001 -219.75 0.0 0.0 bz}xyN" {mark 300.70001 -219.75 303.0 -217.5 306.0 -216.0 312.0 -216.0 0.0 0.0 bz}xy"Ǡf" {-1312 10 /cm AB}xy}Dx$" {3349 10 /cm AB}xy $)MzyN" {mark 312.0 -240.0 306.0 -240.0 303.0 -238.5 300.70001 -236.25 0.0 1.0 bz}xyZ" {mark 300.70001 -236.25 298.40002 -234.0 296.80005 -231.0 296.80005 -228.0 0.0 1.0 bz}xyZ" {mark 296.80005 -228.0 296.80005 -225.0 298.40002 -222.0 300.70001 -219.75 0.0 1.0 bz}xyN" {mark 300.70001 -219.75 303.0 -217.5 306.0 -216.0 312.0 -216.0 0.0 1.0 bz}xyyN" {mark 312.0 -240.0 306.0 -240.0 303.0 -238.5 300.70001 -236.25 1.0 1.0 bz}xyZ" {mark 300.70001 -236.25 298.40002 -234.0 296.80005 -231.0 296.80005 -228.0 1.0 1.0 bz}xyZ" {mark 296.80005 -228.0 296.80005 -225.0 298.40002 -222.0 300.70001 -219.75 1.0 1.0 bz}xyN" {mark 300.70001 -219.75 303.0 -217.5 306.0 -216.0 312.0 -216.0 1.0 1.0 bz}xyaȍL\voveraȍ4\vunderaȍb-\vunoveraȍL\hoveraȍ\hunderaȍ -\hunoverYFigureUU19:qknotcrossingswithorientationsandlabGelpositionsO4̍28f.aThe`characters<˲,c> wand| areusedtoindicateto which3stringpGortiontheob8jectisassociated;>with| denotingpthestringwhichcrossestheother,while< kand> u]denotetheinitialand nalpGortionsofthe`crossed'UUstring.S̍28g.(A-simple-labGelenclosedinbraces,forexam-ple\vcross>{x}>>,Ɂissetinmath-moGdeusingthe\labelstyle;,/at0japre-determinedplaceonthestringUpGortion,Ushiftedineitherthe`above'Uor`be-low'0directionfromthecurveatthispGoint.(F*oreachcrossingdepictedin gure19onlydefaultvqal-uesUUareusedfortheplaceandshift-direction.)28h.faIfthe rstcharacterwithinthebraces{..}1̲is*e.g.^\htwist>{*9(@hob8jecti}?,lthengageneralhobjectimay)bGeplacedasalabel.BF*urthermoreifthe rstcharacteris^u۲or_or| ,Vthentheinterpretationis,Fe.g.k\vtwist<{^8}hanchorihiti}?,asBin14toplacehitiUUasalabGelalongan\arjofthearrow ꛲feature.28i.DAsecondcharacter< /yor>spGeci esthatanarrow-headshouldappGearatthepre-determinedplaceon9thechosenstring.[tHere>odenotesanarrow-headmpGointingwiththenaturalorientation,iwhile<pGointsagainst.5/Duetothecurvqatureofthestrings,itjisusuallybGestto\UseComputerModernTipsratherUUthannormalarrow-tips.28j.aT*o9mgeneratea`hole'use\knothole4yR,rorsimply\khole!,Has8followingtoken. DThisgeneratesa`break',U inTthesenseof21j.qIndeedsucha`hole'is̍:usedtoseparatethetwopGortionsofthe`crossed' :string.Defaultmsizefortheholeis5pt,whichis:alterableLNvia\knotholesize{M$hdimeni}?;normally:usedUUtosetthesizeforall]޲holesinadiagram.|:28k.wIfCtheresulting\khole&iseithertoGolargeorper-:hapsknon-existent,̚thiscouldbGeduetoatechnical-:ity$inthewaybreaksincurvesarehandled.F3This:problem8shouldnotoGccurwiththestandardcross-:ings,busing,arectangularbasis,butitmayoGccur:with~non-rectangularbases.Aneasy` x'istoin-:cludeganextranull-br}'eakgonthestring,.using< Cd|a,:>*7|# or||8,whichshouldplacethezero-sizedbreak:atOparametervqalue.5onthecurve.oThespGeci ca-:tionI^shouldprecedea\khole$atahigherparameter:vqalue,UUorcomeafteroneatalowerUUvalue.v>:Multiplebreaks,arrow-headsandlabGelsmaybGe:spGeci edalongthetwostringsofacrossing;#sim-:plyplacetheirspGeci cationsoneafteranother;le.g.:<>j4|1>>><{x}-j|2{y}>{z}ZYwasUUusedin gure19.:TheLEonlyprovisoisthatall`breaks'alongasingle:strandmustoGccurwithincreasingorderofparam-:eterNpGosition.o[Onthe`crossed'stringthisincludes:theautomatic`hole'tocreatespacefortheother:string.Hence]pitisadvisabletousejustthe(+..):andIJ(-..)!UvqariantsIJforsmalladjustments,andto:keepUUthesecorrectlyordered.:AdjustmenthofpGositionalongthestringscanbe:achievedusingahfactori,Poasin\vover$j|)(+.1)>I*ܲ.:Allowed syntaxis( hsignihnumi)where hsigniisLW962? **tj??gw+ or-!toincrementordecrementfromthepre- de nedvqalue.?Alsoallowableare= orhemptyitosettheparameterpGositiontohnumi,&iwhichmustlieUUbGetween0and1tohaveanymeaning.֍Arrowheads canalsobGeplacedateither,Sorboth,endsofofthestringsformingacrossing.YThisisgovernedbyapairofbGooleans,initially{FF}.8Itishchangedforallq]subsequentstringsinadiagramby\knottips{..}Iz wheretherecognisedvqaluesare{FF},ta{FT}tU,ta{TF}Nand:{TT}:,tadenoting:tips(T?)ornotZ(F?)atthestartandendofeachstring.IT*oaddʰarrowtipsatthestartofstringsinaparticularcrossing,appGendcthe2-charactercombination=< ;similarly=>8addstipsattheends,Oifnotalreadyrequested.Theϗcombinations==(and=!spGecifybGoth({TT})andnone({FF})respGectively*. These2-characterpairscanbGemixedinwithanyspGeci- cationsjforlabGelsandbreaks,oetc.DMultiplepairscompGoundҴtheire ect;?inparticular=<=>\givesthesamexXresultas== R,while=!=<isneededtochange{FT}fQintoUU{TF}UI.TheseGarebGestusedwithsinglepieces,asinthefollowingUUequation."[r`hcps: SDict begin xyc end?" {mark 12.0 0.0 15.0 0.0 16.5 -2.25 17.25 -3.875 0.0 0.0 bz}xyC" {mark 17.25 -3.875 18.0 -5.5 18.0 -6.5 18.75 -8.125 0.0 0.0 bz}xyC" {mark 18.75 -8.125 19.5 -9.75 21.0 -12.0 24.0 -12.0 0.0 0.0 bz}xy " {3072 10 /cm AB}xy?" {mark 12.0 0.0 15.0 0.0 16.5 -2.25 17.25 -3.875 0.0 1.0 bz}xyC" {mark 17.25 -3.875 18.0 -5.5 18.0 -6.5 18.75 -8.125 0.0 1.0 bz}xyC" {mark 18.75 -8.125 19.5 -9.75 21.0 -12.0 24.0 -12.0 0.0 1.0 bz}xy?" {mark 12.0 0.0 15.0 0.0 16.5 -2.25 17.25 -3.875 1.0 1.0 bz}xyC" {mark 17.25 -3.875 18.0 -5.5 18.0 -6.5 18.75 -8.125 1.0 1.0 bz}xyC" {mark 18.75 -8.125 19.5 -9.75 21.0 -12.0 24.0 -12.0 1.0 1.0 bz}xyC" {mark 12.0 -12.0 15.0 -12.0 16.5 -9.75 17.25 -8.125 0.0 0.0 bz}xyC" {mark 17.25 -8.125 18.0 -6.5 18.0 -5.5 18.75 -3.875 0.0 0.0 bz}xy?" {mark 18.75 -3.875 19.5 -2.25 21.0 0.0 24.0 0.0 0.0 0.0 bz}xyE" {mark 12.0 -12.0 15.0 -12.0 16.5 -9.75 17.25 -8.125 0.0 0.925 bz}xyC" {mark 17.25 -8.125 18.0 -6.5 18.0 -5.5 18.75 -3.875 0.0 0.0 bz}xy?" {mark 18.75 -3.875 19.5 -2.25 21.0 0.0 24.0 0.0 0.0 0.0 bz}xy " {3072 10 /cm AB}xyC" {mark 12.0 -12.0 15.0 -12.0 16.5 -9.75 17.25 -8.125 1.0 1.0 bz}xyC" {mark 17.25 -8.125 18.0 -6.5 18.0 -5.5 18.75 -3.875 1.0 1.0 bz}xyC" {mark 18.75 -3.875 19.5 -2.25 21.0 0.0 24.0 0.0 0.07495 1.0 bz}xyC" {mark 12.0 -12.0 15.0 -12.0 16.5 -9.75 17.25 -8.125 1.0 1.0 bz}xyC" {mark 17.25 -8.125 18.0 -6.5 18.0 -5.5 18.75 -3.875 1.0 1.0 bz}xy?" {mark 18.75 -3.875 19.5 -2.25 21.0 0.0 24.0 0.0 1.0 1.0 bz}xy4`iHժ8r`hcps: SDict begin xyc end?" {mark 12.0 0.0 15.0 0.0 16.5 -2.25 17.25 -3.875 0.0 0.0 bz}xyC" {mark 17.25 -3.875 18.0 -5.5 18.0 -6.5 18.75 -8.125 0.0 0.0 bz}xyC" {mark 18.75 -8.125 19.5 -9.75 21.0 -12.0 24.0 -12.0 0.0 0.0 bz}xyC" {mark 12.0 0.0 15.0 0.0 16.5 -2.25 17.25 -3.875 0.0 0.92505 bz}xyC" {mark 17.25 -3.875 18.0 -5.5 18.0 -6.5 18.75 -8.125 0.0 0.0 bz}xyC" {mark 18.75 -8.125 19.5 -9.75 21.0 -12.0 24.0 -12.0 0.0 0.0 bz}xy " {3072 10 /cm AB}xy?" {mark 12.0 0.0 15.0 0.0 16.5 -2.25 17.25 -3.875 1.0 1.0 bz}xyC" {mark 17.25 -3.875 18.0 -5.5 18.0 -6.5 18.75 -8.125 1.0 1.0 bz}xyG" {mark 18.75 -8.125 19.5 -9.75 21.0 -12.0 24.0 -12.0 0.07504 1.0 bz}xy?" {mark 12.0 0.0 15.0 0.0 16.5 -2.25 17.25 -3.875 1.0 1.0 bz}xyC" {mark 17.25 -3.875 18.0 -5.5 18.0 -6.5 18.75 -8.125 1.0 1.0 bz}xyC" {mark 18.75 -8.125 19.5 -9.75 21.0 -12.0 24.0 -12.0 1.0 1.0 bz}xyC" {mark 12.0 -12.0 15.0 -12.0 16.5 -9.75 17.25 -8.125 0.0 0.0 bz}xyC" {mark 17.25 -8.125 18.0 -6.5 18.0 -5.5 18.75 -3.875 0.0 0.0 bz}xy?" {mark 18.75 -3.875 19.5 -2.25 21.0 0.0 24.0 0.0 0.0 0.0 bz}xy " {3072 10 /cm AB}xyC" {mark 12.0 -12.0 15.0 -12.0 16.5 -9.75 17.25 -8.125 0.0 1.0 bz}xyC" {mark 17.25 -8.125 18.0 -6.5 18.0 -5.5 18.75 -3.875 0.0 1.0 bz}xy?" {mark 18.75 -3.875 19.5 -2.25 21.0 0.0 24.0 0.0 0.0 1.0 bz}xyC" {mark 12.0 -12.0 15.0 -12.0 16.5 -9.75 17.25 -8.125 1.0 1.0 bz}xyC" {mark 17.25 -8.125 18.0 -6.5 18.0 -5.5 18.75 -3.875 1.0 1.0 bz}xy?" {mark 18.75 -3.875 19.5 -2.25 21.0 0.0 24.0 0.0 1.0 1.0 bz}xy4`i+=0z?r`hcps: SDict begin xyc end=" {mark 12.0 0.0 13.5 0.0 15.0 -1.5 16.25 -2.25 0.0 0.0 bz}xyA" {mark 16.25 -2.25 17.5 -3.0 18.5 -3.0 19.75 -2.25 0.0 0.0 bz}xy=" {mark 19.75 -2.25 21.0 -1.5 22.5 0.0 24.0 0.0 0.0 0.0 bz}xy " {3072 10 /cm AB}xy=" {mark 12.0 0.0 13.5 0.0 15.0 -1.5 16.25 -2.25 0.0 1.0 bz}xyA" {mark 16.25 -2.25 17.5 -3.0 18.5 -3.0 19.75 -2.25 0.0 1.0 bz}xy=" {mark 19.75 -2.25 21.0 -1.5 22.5 0.0 24.0 0.0 0.0 1.0 bz}xy=" {mark 12.0 0.0 13.5 0.0 15.0 -1.5 16.25 -2.25 1.0 1.0 bz}xyA" {mark 16.25 -2.25 17.5 -3.0 18.5 -3.0 19.75 -2.25 1.0 1.0 bz}xy=" {mark 19.75 -2.25 21.0 -1.5 22.5 0.0 24.0 0.0 1.0 1.0 bz}xyB" {mark 12.0 -12.0 13.5 -12.0 15.0 -10.5 16.25 -9.75 0.0 0.0 bz}xyA" {mark 16.25 -9.75 17.5 -9.0 18.5 -9.0 19.75 -9.75 0.0 0.0 bz}xyB" {mark 19.75 -9.75 21.0 -10.5 22.5 -12.0 24.0 -12.0 0.0 0.0 bz}xy " {3072 10 /cm AB}xyB" {mark 12.0 -12.0 13.5 -12.0 15.0 -10.5 16.25 -9.75 0.0 1.0 bz}xyA" {mark 16.25 -9.75 17.5 -9.0 18.5 -9.0 19.75 -9.75 0.0 1.0 bz}xyB" {mark 19.75 -9.75 21.0 -10.5 22.5 -12.0 24.0 -12.0 0.0 1.0 bz}xyB" {mark 12.0 -12.0 13.5 -12.0 15.0 -10.5 16.25 -9.75 1.0 1.0 bz}xyA" {mark 16.25 -9.75 17.5 -9.0 18.5 -9.0 19.75 -9.75 1.0 1.0 bz}xyB" {mark 19.75 -9.75 21.0 -10.5 22.5 -12.0 24.0 -12.0 1.0 1.0 bz}xy4`ix򍍑\UseComputerModernTips?\knottips{FT}\def\Conway#1{\mathord{\nabla\Bigl[\,Q\raise5pt\xybox{0;/r1pc/:#1}\,\Bigr]}}$$\Conway\htwist?-\Conway\htwistnegQ\;=\;?-z\,\Conway\huntwist$$# Joins-*28l.DTheN\joins"areusedtoconnecttheloGoseendsofcrossingstrings.Inparticular\loGops"and\caps"areforplacingonendsofhorizontalorvertical`twist'6and`cross'crossings,DleavingthecurrenthpGosi# xed.+0The\bends"joinnon-adjacentcross-ingsjofthesametypGe,2eitherhorizontalorvertical.The\xcap..,_piecesaredesignedtojoinadjacent\xover..0 pieces;OLtheymoveceitherverticallyorhorizontally*, as\appropriate.SFinallythe\xbend..piecesuallowforsmoGothjoinsof45^slopestohor-izontal_orverticalslopGes.F*orthesetheactualpo-sitioningsofthepiece,{Asee gure20,isnotentirelyobvious.FigureL20displaystheorientationonthejoins.Also|yindicatedaredefaultpGositionsforlabelsandarrow-tips;eachzpieceusesthesamecoGde,e.g.\vloop&<>1{|6>>><{x}[z|`{y}>{z}zѲ. F*urthermorejthecurrentθhpGosibeforethepieceisdrawnismarkedusingm^ps: SDict begin xyc end33n ㅲ;UUthatafterwardsisindicatedbym^ps: SDict begin xyc end" {-2048 st}xy;s:" {-2048 F d}xy 8orm^ps: SDict begin xyc end" {-3072 st}xy!" {-3072 T d}xy .gw:The`yabilitytoscaleinsizeandplacearrow-tips, :breaks,:labGels3etc.fapplyalsotohjoinipieces.The:onlyUUdi erenceis...>:28m.Thethreeplacesreferredtoby< t,|ꫲ,>areallon:azsinglestring.5Inparticular|isalwayszatthe:middle ofthehjoini,)whereas< >=and>areate}'ar-:lierandlaterparametervqaluesrespGectively*.iAny:adjustments^28kNinvolving3breaksshouldoGccurin:increasingUUparameterorder.:28n.?A2parameterZcanbGealtered,[using@ 1Whadjusti,to:e ectLsubtleadjustmentstotheshapGeofanyjoin.:Within6aarectangularbasisthehorizontalorverti-:cal tangentsarepreservedandoverallre ectionor:rotation2 symmetryispreserved.fThus2 thisparam-:eter%#a ectsthe` atness'ofacaporloGop,Yorthe:amountBofcurvqatureiss-bGendsandz-bends.iF*or:\xcap..%sand\xbend..-msthe45^6iangleisaltered;:thislisespGeciallyusefultomatchthetangentswhen:a]knot-piecehasbGeenspeci edusingthetechnique:ofUUnote28c.:The4YnormalrangefortheseparametersisbGetween:0band1.OOthervqaluescanbGeusedwithinteresting:results|theZparameterdeterminestheloGcationof:controlUUpGointsforaBGeziercubiccurve.3̍ piece4"vqalueWj&e ectUUon...:ffގ3fd ?\..cap@[.25^ atnessUUofcap;\..loop@[.75^ atnessUUofloGop;\sbend..@[.75^curvqatureUUinthe`s';\zbend..@[.75^curvqatureUUinthe`z';\xcap..C\[.5^heightUUofcap,slopGeatbase;\xbend..C\[.5^curvqature,UUslopGeatbase.ffގ39I;TheơfollowingexamplegivesthreewaysofspGecifying:a?#`trefoil'knot,Cusingthepoly~:featuretoestablishthe:loGcationDoftheverticesforknot-pieces.Ineachthe:hcrossingisZarecalculatedto ttogethersmoGothly;2a:di erentwayofcreatinghjoinisisusedineach.RAlso:the@thirddisplayssubtlechangesofthe^28nuȲjoincontrol.]1}Hps: SDict begin xyc end |RY" {mark 16.68724 9.16116 17.70978 7.39005 18.11198 5.85114 18.31754 4.51245 0.0 0.0 bz}xyX" {mark 18.31754 4.51245 18.52312 3.1738 18.53203 2.03535 18.34877 0.52795 0.0 0.0 bz}xyW" {mark 18.34877 0.52795 18.1655 -0.97946 17.79004 -2.85585 16.79425 -4.5 0.0 0.0 bz}xy |RY" {mark 16.68724 9.16116 17.70978 7.39005 18.11198 5.85114 18.31754 4.51245 0.0 1.0 bz}xyX" {mark 18.31754 4.51245 18.52312 3.1738 18.53203 2.03535 18.34877 0.52795 0.0 1.0 bz}xyW" {mark 18.34877 0.52795 18.1655 -0.97946 17.79004 -2.85585 16.79425 -4.5 0.0 1.0 bz}xy |RY" {mark 16.68724 9.16116 17.70978 7.39005 18.11198 5.85114 18.31754 4.51245 1.0 1.0 bz}xyX" {mark 18.31754 4.51245 18.52312 3.1738 18.53203 2.03535 18.34877 0.52795 1.0 1.0 bz}xyW" {mark 18.34877 0.52795 18.1655 -0.97946 17.79004 -2.85585 16.79425 -4.5 1.0 1.0 bz}xy |RO" {mark 9.0 9.0 10.9218 9.04028 12.73454 8.42723 14.13164 7.83223 0.0 0.0 bz}xyX" {mark 14.13164 7.83223 15.52875 7.23724 16.51021 6.6603 17.56673 5.81293 0.0 0.0 bz}xyX" {mark 17.56673 5.81293 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" {2560 st}xy|" {2560 F d}xy7wn!8" {mark 24.0 -144.0 36.0 -144.0 48.0 -132.0 0.0 0.0 q}xyM_J" {-155 10 /cm AB}xyPU}LxD?" {-512 10 /cm AB}xyF(IUy>Ú" {-768 10 /cm AB}xy>Uz!8" {mark 24.0 -144.0 36.0 -144.0 48.0 -132.0 0.0 1.0 q}xy!8" {mark 24.0 -144.0 36.0 -144.0 48.0 -132.0 1.0 1.0 q}xy9 " {-512 st}xy7|" {-512 F d}xygwn!8" {mark 96.0 -120.0 96.0 -132.0 84.0 -144.0 0.0 0.0 q}xyyE" {-3941 10 /cm AB}xy|\x.j" {-3584 10 /cm AB}xy Vy:zo" {-3328 10 /cm AB}xy~Dz!8" {mark 96.0 -120.0 96.0 -132.0 84.0 -144.0 0.0 1.0 q}xy!8" {mark 96.0 -120.0 96.0 -132.0 84.0 -144.0 1.0 1.0 q}xyu" {-3584 st}xyw3" {-3584 F d}xywn!;" {mark 144.0 -144.0 144.0 -132.0 132.0 -120.0 0.0 0.0 q}xyyg" {1893 10 /cm AB}xyvLx.j" {1536 10 /cm AB}xyVy:" {1280 10 /cm AB}xyz!;" {mark 144.0 -144.0 144.0 -132.0 132.0 -120.0 0.0 1.0 q}xy!;" {mark 144.0 -144.0 144.0 -132.0 132.0 -120.0 1.0 1.0 q}xy " {1536 st}xyeo" {1536 F d}xyaȍ2]\xbendraȍ52]\xbendlaȍe2]\xbenduaȍ2]\xbenddwn!;" {mark 168.0 -120.0 168.0 -132.0 180.0 -144.0 0.0 0.0 q}xyE" {-2201 10 /cm AB}xy ^ѴxIr" {-2560 10 /cm AB}xymc Vy=ڟzo" {-2816 10 /cm AB}xy`Y~Dz!;" {mark 168.0 -120.0 168.0 -132.0 180.0 -144.0 0.0 1.0 q}xy!;" {mark 168.0 -120.0 168.0 -132.0 180.0 -144.0 1.0 1.0 q}xy" {-2560 st}xye[" {-2560 F d}xywn!;" {mark 216.0 -144.0 216.0 -132.0 228.0 -120.0 0.0 0.0 q}xyyg" {153 10 /cm AB}xy v xIr" {512 10 /cm AB}xymcVy=ڠ" {768 10 /cm AB}xy`Yz!;" {mark 216.0 -144.0 216.0 -132.0 228.0 -120.0 0.0 1.0 q}xy!;" {mark 216.0 -144.0 216.0 -132.0 228.0 -120.0 1.0 1.0 q}xyu " {512 st}xyw " {512 F d}xy'wn!;" {mark 288.0 -120.0 276.0 -120.0 264.0 -132.0 0.0 0.0 q}xy.}" {3943 10 /cm AB}xy&/{Mδx6x/G" {3584 10 /cm AB}xy1tEVy{}}!P9"b"{~:{(1.3288,0):}~>{}} Q!P3"c"{~:{(2.5,0):}~>{}}Q!{\vover~{"b2"}{"b1"}{"a1"}{"a3"}}Q!{\vcap~{"c1"}{"c1"}{"b4"}{"b2"}@(+.1)}Q!{\vover~{"b5"}{"b4"}{"a2"}{"a1"}}Q!{\vcap~{"c2"}{"c2"}{"b7"}{"b5"}@(+.2)}Q!{\vover~{"b8"}{"b7"}{"a3"}{"a2"}}Q!{\vcap~{"c3"}{"c3"}{"b1"}{"b8"}}}}%\def\TrefoilC{\xygraph{!{0;/r.75pc/:}Q!P3"a"{~>{}}Q!P12"b"{~:{(1.414,0):}~>{}}Q!{\vover~{"b2"}{"b1"}{"a1"}{"a3"}}Q!{\save?0;"b2"-"b5":"b5",\xcaph?@(+.1)\restore}Q!{\vover~{"b6"}{"b5"}{"a2"}{"a1"}}Q!{\save?0;"b6"-"b9":"b9",\xcaph?@(+.2)\restore}Q!{\vover~{"b10"}{"b9"}{"a3"}{"a2"}}Q!{\save?0;"b10"-"b1":"b1",\xcaph?@(+.3)\restore}}}$$\TrefoilA\quad\TrefoilB\quad\TrefoilC$$浍ChangingTthestring-st9ylerItisnotnecessarytousesolidcurves;anystyleavqail-ableUUtocurvesandarrowscanbGechosenusing... Uff2 x\knotstyle{>߸hchari}/useUU\dir{Fhchari}\knotstyles{Cܸhchari}{ hchari}/twoUUstyles\knotSTYLE{>߸hcoGdei}/useUUhcoGdeiff2+NRIneachcasethenewstyleappliestoallsubse-quent%knotpieces,eexceptthatthetwostylesapplyf:onlytocrossings.Thelattercaseallowsuseofob- :ject {hmoGdi eris. 8Thehcodeiconsistsoftwo {groups:{..}{..}в,/eachecontainingharrowiforms,/asin14and:notes21m,a21r.Onlythe rstharrowiformisused:with$hjoiniswhereasthetwo$formsareusedrespGec-:tivelymwiththetwostringsofahcrossingiintheorder:thatUUtheyaredrawn.+ m:PartffIV/:DrivZers׍:This]partdescribGes`drivers'thatcustomisetheparts:ofdtheDVIc legeneratedfromd XY -picturestoexploit:spGecial*capabilitiesofparticularDVI driver*programs:through~TU>'ExXxs\special3command.CThismakesthe:DVI lesnon-pGortablebutisneededforfullsupportof:someUUoftheUQXY U-picextensions(describGedinpartII). /;Figure21attheendofthispartsummarisesthe:extensionsUUsuppGortedbyalldrivers.$Ng:29PSupps3ortffforSpeci cDrivers Ǎ:29.1 j:dvidrvdriver:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{dvidrv}:ThisdriverprovidessuppGortforthe\emtex"\special:commands,Ewhenusingoneofthestandarddvi-drivers::dvidotj(,$dvihplj*仲,$dvimsp%,$dviscr+9ordvivik%ٲ,$that:comeUUwithEbGerhardMattes'em-TU>'ExXdistribution.;SuppGortedUU\special0e ectsUUare...LW964A ȃ*tj??gw em-TU>'ExXUUline-drawing\special-U=s. vqariableUUline-widths&29.2DVIPSdriverDVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{dvips}DThis_driverprovidessuppGortforall#extensions2when usingthedvipsdriverbyT*omasRokicki[11 ]. IthasbGeen'testedwithdvipsversion5.55aanddvipskver-sionUU5.58f.  SuppGortedUU\special0e ectsUUare... colour,UUusingdirectcolorspGecialsandD- cmcsc10DPostScript. crayonUUcolours. DPostScriptUUback-end. rotated/scaled7diagramsandtext,usingDPost- Script. vqariable line-widthsandpGoly-lines,VusingDPost- Script. extraUUframesand lls,usingDPostScript. patternsUUandtiles,usingDPostScript. tpicUUdrawingcommands. em-TU>'ExXUUdrawingcommands.&29.3DVITOPSdriverDVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{dvitops}DThisa leprovidessuppGortforthedvitopsdriverbyJames;Clark.xxAsofSeptembGer1995,-tithasnotbeenfullyUUtested.  SuppGortedUU\special0e ectsUUare... colour,xiusingqedirectcolorspGecialsforgrayqY,rgbŲand hsbncolournmoGdels;andDPostScriptcolourwithin diagrams; crayonUUcolours. DPostScriptUUback-end. rotated/scaledlFdiagramsandtext,usingdvitops spGecials;UUhoweverthesemaynotbGenested. vqariable line-widthsandpGoly-lines,VusingDPost- Script. extraUUframesand lls,usingDPostScript. patternsUUandtiles,usingDPostScript tpicUUdrawingcommands.gw:29.4 j:OzTeXdriveruT:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{oztex}uT:ThisqdriverprovidesthenecessaryinterfacetosuppGort :theDPostScriptback-endandotherDPostScripte ects:when>"usingtheDVI=driver>"ofversions1.8+ofO4zTU>'ExXby:AndrewaT*revorrow,^15 =xEarliernversionsofOzw}TKß'E-Xshould:inste}'adusethedriveroption\xyoption{17oztex}b.;E ectssuchascolour,line-thicknessandrotatedor:scaleddiagramsareonlypartiallysuppGortedinthat:theQe ectscannotbGeappliedtoanytextorsymbGols:placed)usingfonts.^ThisisduetothenatureofO4zTU>'ExX:hdriveri,whoseoptimizationoftheplacementoffont-:characters/precludestheapplicabilityofsuche ects.:F*urthermoretheDPostScriptdictionarymustbGeavqail-:able:ina lecalledglobal.ps9orappGendedtothe:OzTeXdict.pro+*.Howeverlwithversion1.8andlater:ofkO4zTU>'ExX,2thereisthealternativeofusingthedvips:hdriveri,+which`doGessupportalltheDPostScripte ects:avqailableUUinUQXY U-pic.;Note:D(T*ouseXY z-pice ectivelywithO4zTU>'ExXrequires:changingseveralmemoryparameters.  Inparticular:agn`Big-TU>'ExX'isneeded,alongwithanincreaseinthe:pool_size+parameter.Explicit` instructionsarecon-:tained inthe leINSTALL..OzTeXLgofthe XY -picdistri-:bution.;SuppGortedUU\special0e ectsUUare...s:;colour,uusing|DPostScript,butnotoffont-characters.ݍ:;crayonUUcolours,similarlyrestricted.:;DPostScriptUUback-end.:;vqariable line-widthsandpGoly-lines,VusingDPost- ;Script.:;extraUUframesand lls,usingDPostScript.:;patternsUUandtiles,usingDPostScript.:;rotated/scaled}Tdiagramsandtext,Srecognisedbut;notUUsuppGorted.!捍:29.5 j:OzTeXv1.7driveruT:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{17oztex}uT:This4optionprovidesthenecessaryinterfacetosuppGort:theDPostScriptback-endandotherDPostScripte ects:whenj3usingtheDVIj-driverj3ofversion1.7ofO4zTU>'ExXby:AndrewT*revorrow,^16 L}'ater%{versionsofOzw}TKß'E-Xshould:inste}'adyusethedriveroption\xyoption{oztex}WI.IJUp-:gradingUUtoversion1.9+ofO4zTU>'ExXisrecommended.:o;ff^ J=w-:15LOzTAEMXisasharewÎareimplementationofTAEMXforMacintosh aÎvailablewfrommanybulletinbw-:16LOzTAEMXisasharewÎareimplementationofTAEMXforMacintoshaÎvailablewfrommanybulletinb'ExXrequireschangingseveralmemoryparameters.  Inparticularagn`Big-TU>'ExX'isneeded,alongwithanincreaseinthepool_size#parameter.Explicit` instructionsarecon-tained inthe leINSTALL..OzTeXLgofthe XY -picdistri-bution. SuppGortedUU\special0e ectsUUare...FH colour,uusing|DPostScript,butnotoffont-characters. crayonUUcolours,similarlyrestricted. DPostScriptUUback-end. vqariable line-widthsandpGoly-lines,VusingDPost-  Script. extraUUframesand lls,usingDPostScript. patternsUUandtiles,usingDPostScript. rotated/scaled}Tdiagramsandtext,Srecognisedbut notUUsuppGorted.'+29.6TexturesdriverލVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{textures}ލThis;udriverprovidessuppGortforversion1.7+ofBlue6rSkyResearch'sTexturesapplicationforMac-intosh^17x./ItxincorpGoratessupportforcolourandallcof_XYJc-pic'sDPostScripte ects. EarlierversionsofTexturesshouldinsteadusethedriveroption\xyoption{16textures}^Pɲ.  Notice'thatversion1.7su ersfromaprintingbugwhichC%maycauseaDPostScripterror.kAC! xiskludgedby!makingsurethe rstpagehasbGeenshownintheviewerZ~bGeforeanypageswithdiagramsaresenttotheprinter. SuppGortedUU\special0e ectsUUare...FH colour,UUbGothon-screenandwithDPostScript crayonUUcolours. DPostScriptUUback-end. rotated/scaled7diagramsandtext,usingDPost- Script. vqariable line-widthsandpGoly-lines,VusingDPost- Script. extraUUframesand lls,usingDPostScript. patternsUUandtiles,usingDPostScript.佉ff^ J=w-:17LMacinÎtoshXisatrademarkofAppleComputerInc.gw:29.7 j:Texturesv1.6driveruT:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{16textures}uT:This9NdriverprovidessuppGortforversions1.5band1.6of :BlueSkyResearch'sTexturesapplicationforMacin-:tosh^18x.DItincorpGoratessupportforDPostScriptcolour:andxthexXY -psDPostScriptback-end.(NThiswillnotwork:withversions1.7andlater;#theserequirethehdriveri:optionUU\xyoption{textures}g.;SuppGortedUU\special0e ectsUUare...ȃ:;colour,UUusingDPostScript!:;crayonUUcolours.:;DPostScriptUUback-end.:;rotated/scaled7diagramsandtext,usingDPost- ;Script.:;vqariable line-widthsandpGoly-lines,VusingDPost-;Script.:;extraUUframesand lls,usingDPostScript.:;patternsUUandtiles,usingDPostScript.!օ:29.8 j:XDVIdriveruT:Vers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui :Loadas:\xyoption{xdvi}uT:This4YdriverprovidessuppGortforextensionswhenus-:ingvqariantsofthexdvi&.driver,BbyEricCoGoper,BBob:Schei er,MarksEichinandothers.`IthasbGeenused:successfullywithxdvi1patchlevel20,\byPaulV*o8jta,:andUUxdvik ꛲versionUU18f,byKarlBerry*.;Some7ofthesuppGortedfeaturesassumethattheim-:plementationwofxdvihislinkedtoaDPostScriptren-:derer;ze.g. .GhostscriptnorDisplaUTyofDPostScript.If:such suppGortisnotavqailable,.ytheninvokingxdvi us-:ingthecommandxdvi?-hushspecialsfwillsuppress:warning%^messagesthatmightotherwisebGeproduced.:OnefdrawbackofsuchasetupisthatmuchoftheDPost-:Scriptisnotrendereduntilafterallofthefontcharac-:ters,Šetc.4havebGeenplacedonthepage.Thustextthat:wasVmeanttobGeplacedontopofa lledorpatterned:regionmayappGeartobeobscuredbyit.0Howeverwhen:printed, |usingEaDPostScriptprinter, |thecorrectplace-:mentUUisobtained.;SuppGortedUU\special0e ectsUUare...ȃ:;colour,UUusingDPostScript.;Notallversionsofxdvi,suppGortcolor\special,s, 'so;thereWisnodirectsuppGortforcolour.yOHoweverWparts;of8picturesrenderedusingDPostScriptmayappGear;coloured,jdue3tointerpretationofcolourcommands;withinUUtheDPostScript.:;crayonUUcolours.:*tj??gw DPostScriptUUback-end.A rotated/scaled7diagramsandtext,usingDPost-  Script. vqariable line-widthsandpGoly-lines,VusingDPost- Script. extraUUframesand lls,usingDPostScript. patternsUUandtiles,usingDPostScript. tpicUUdrawingcommands. ThefollowingTU>'ExXimplementationisalsosuppGorted,butUUcurrentlyusesthedvipsdriver.#Q29.9CMacTeXdriverRVers.3.3bCyRossMoKorehross@mpAce.mq.edu.aui Loadas:\xyoption{cmactex}RThomas9Ki e'sCMacTU>'ExXapplicationusesdvipsasitsdvi-driver.A OtherimplementationsnotspGeci callymentionedhereamaywellworkwithoneofthenamedhdriveris,though;"pGerhapsnotallfeatureswillactuallybesup-pGorted.(ߍ30wlExtra efeaturesusingE-ff cmcsc10EPost-wlScriptffdriversThiswesectionacknowledgeswethesuppGortforextrafea-turesUavqailablewhenusingahdriverithatsuppGortsuseof\special0commandswithnativePostScript.Extra>macrosarerequiredtotakeadvqantageofthis;theseareloadedautomaticallyinconjunctionwithex-tensionsFspGeci edusingthe\xyoption56qcommand, Ipro-vided,ahdriveriwhichsuppGortstheextension,4asindi-catedUUin21,hasalsobGeenspeci ed. k: Commands:?arealsoprovidedtoturno /onuseofthesefeatures.8Suchswitchesareparticularlyusefulwhendevelopingcomplicateddiagrams,&orwhentheintendedoutputdevicedoGesnotsupportPostScript;e.g. `&forOuon-screendisplay*.Alternatively*,whenOuat-tempting?tousedriversforwhichnoexplicitsuppGorthasbGeenprovided,ysomefeaturesmayworkothersmaynot.|PleaseXinformtheauthorsofXXY -picofanysuc-cessesUUorfailuresofsuchattempts. This"included le(version3.3)providessuppGortforPostScript\special1ERcommandsusedbythepsbackend6extensionaswellasPostScript-basedop-tions,toproGducespeciale ectsnotavqailabledirectlywithUUTU>'ExX.gw:PostScriptescap`e̛:An|extrahshapGeimodi erkeyallowsarbitraryPost- :ScriptUUcoGdetobeappliedtothecurrenthob8jecti. .: 1ff2 I Ҿ[!RhpGostscriptUUcodei]j۲forUUspGeciale ects Ҿ[psxy]j۲storesUUcurrentloGcation..ff2ˍzNormallythehpGostscriptcodeiwillbeasimplecom-mandtoalterthePostScriptgraphicsstate:|e.g.[!1?00setrgbcolor]nUchangesבthecolourusedtorenderppartsofthehob8jecti. AnynumbGerofsuchhshapGeipmodi ersisallowable,howeveritismoree-cientasthismayupsettheXY 6-pichob8jectiparsing.'ExXandXY u-pic,notfordrawingnewob8jectswithinPostScript.DNoguar-anteetcanbGegivenofthecurrentloGcation,(version3.3)providesPostScriptsuppGortforthee ectsde nedinthecolor NextensionUUinx13. x؍ ThisP8 leisloadedanditse ectsareactivqatedau-tomaticallywhenever\xyoption{color}[sisrequestedandD4thecurrenthdriverisuppGortscoloursusingPost-Script. 8ShouldtherebGeanyneedtoturno thissuppGort,thefollowingcommandsareavqailable;0=theyobGeyUUusualTU>'ExXgroupings. 1ff2 <]\NoPScolorZ(version3.3)providesPostScriptsuppGortforthee ectsde nedintheframeextensionݩdescribGedinx9. Itimplementssomee ectsUUotherwiseunattainable. x؍ ThisP8 leisloadedanditse ectsareactivqatedau-tomaticallywhenever\xyoption{frame}[sisrequestedandm6thecurrenthdriverisuppGortsPostScripte ectsforframes.EShouldtherebGeanyneedtoturno this :suppGort,thefollowingcommandsareavqailable;0=they :obGeyUUusualTU>'ExXgroupings.: @ff2 lC6_\NoPSframes]6;removeUUPostScriptsuppGort6_\UsePSframes]6;reinstateUUPostScript.ff2MZWithoutPostScriptsuppGortellipsesmaybeshownas\circlesandall lledregionsmaybGerepresentedas1\blackrectangles. Thesecommandsareprovidedprimarily#fortestingandtrouble-shoGoting;e.g.withhdrivericon gurationsuntestedbytheauthorsofXY ]-pic,UUwhoshouldbGenoti edofanydiculties.")30.3%Line-stylesAThe included lexyps-l.tex>(version3.3)providesPostScriptdsuppGortforthee ectsde nedinthelineextensionUUdescribGedinx11. ߍ ThisSa leisloadedanditse ectsareactivqatedauto-matically whenever\xyoption{line}SisrequestedandtheecurrenthdriverisuppGortsPostScriptlinestyles.Should[therebGeanyneedtoturno thissupport,]thefollowingVcommandsareavqailable;theyobGeyusualTU>'ExXgroupings. cff2]\NoPSlinesZ(version3.3)providesPostScriptsuppGortforthee ectsde nedintherotate"CextensionUUdescribGedinx12. ߍ ThisSa leisloadedanditse ectsareactivqatedauto-maticallywhenever\xyoption{rotate}b[isrequestedLW968E \b*tj??gwandgIthecurrenthdriverisuppGortsPostScriptrota- tions.=bShouldtherebGeanyneedtoturno thissup-pGort,EtheBfollowingcommandsareavqailable;HtheyobGeyusualUUTU>'ExXgroupings.ff2 }6_\NoPSrotate]6;removeUUPostScriptsuppGort6_\UsePSrotate]6;reinstateUUPostScript.3ff2 FneWithoutPostScriptsuppGortdiagramscanbeexpGectedztobedisplayedzunrotatedandunscaled.TheseYcommandsareprovidedprimarilyfortestingandtrouble-shoGoting;e.g.withhdrivericon gurationsuntested;bytheauthorsof;XY -pic,@WwhoshouldbGenoti- edUUofpGersistentdiculties.30.5%PatternsandtilesuTThe included lexyps-t.tex>(version3.3)providesPostScriptdsuppGortforthee ectsde nedinthetileextensionUUdescribGedinx14. ThisSa leisloadedanditse ectsareactivqatedauto-matically whenever\xyoption{tile}SisrequestedandthecurrenthdriverisuppGortsPostScriptpatterns.Should[therebGeanyneedtoturno thissupport,]thefollowingVcommandsareavqailable;theyobGeyusualTU>'ExXgroupings.Wff2]\NoPStilesZ(version3.3)providestpic2 suppGortforsomeofthee ectsde nedintheframeextension.Thisv leisloadedanditse ectsareactivqatedFautomaticallywhenever\xyoption{frame}is! requestedandthecurrenthdriverisuppGortsbothtpichandframes.ShouldtherebGeanyneedtoturno 7thissuppGort,pthefollowingcommandsareavqailable;theyUUobGeyusualTU>'ExXgroupings.ff2b\NoTPICframesbv8removeUUtpicsuppGortb\UseTPICframesbv8reinstateUUtpic.3ff2l:Appendices.]:AY(Answersfftoallexercisese:Answ9erztoexercise1(p.7): Indthedefaultsetup :theyarealldenotethereferencepGointoftheXY /-picture:butOthecartesiancoGordinatehposi(0,0)denotesthe:pGointorigothatmaybGechangedtosomethingelseus-:ingUUthe: ꧲opGerator.en:Answ9ertoexercise2(p.7): Use&thehpGosiition:<*7X,ߵY8>+"ob"!Ҳ.:Answ9ertoexercise3(p.7): It= rstsetscaccording:to\...".ThenitchangesctothepGointrightofcat:thesamedistancefromtherightedgeofcasitswidth,:wD,UUi.e., 3|ps: SDict begin xyc endTheUU...C|31 {1ȟCz31 }:3wK㑞!Ǹ'C|31 {<XCz31 }83w+:Answ9er toexercise4(p.9): The 4hcoGordi:\{"A";"B":5"C";"D",d x}oz"returnsthecrosspGoint.:HereTishowtheauthortypGesetthediagramintheex-:ercise:N8:\xy*7%*7%?setupandmarkA,B,C,andD:*7(0,0)="A" *\cir<1pt>{}*+!DR{A},*7(7,10)="B"?*\cir<1pt>{}*+!DR{B},*7(13,8)="C"?*\cir<1pt>{}*+!DL{C},*7(15,4)="D"?*\cir<1pt>{}*+!DL{D},*7%*7%?gotointersectionandname+circleit:*7{"A";"B":"C";"D",x}?="I"*\cir<3pt>{},*7%*7%?makedottedlines:*7"I";"A"**{}?+/1pc/;-/1pc/**@{..},*7"I";"D"**{}?+/1pc/;-/1pc/**@{..}*7%:\endxy퍒:AUU?! O...hplaceiUUcouldalsohaveUUbGeenused.:Answ9er{toexercise5(p.9): T*ocopythepvqalue:toUUc,i.e.,equivqalentto\p?".:Answ9er:Xtoexercise6(p.10): Whenΐusingtheker-:nelΤconnectionsthatareallstraightthereisnodif-:ference,e.g.,**{}?<)"Ҳand6**{}+E(Zdenote6exactlythe:same8pGosition.KHowever, forotherconnectionsitisnot:necessarily#thecasethatthepGointwheretheconnec-:tion_ventersthecurrentob8ject,adenotedby?< p,aandthe:pGointcwherethestraightlinefrompenterstheob8ject,:denotedUUby+E O,coincide.LW969F u*tj??gwAnsw9ertoexercise7(p.10): TheGcoGdetypesets theUUpicturet;;ps: SDict begin xyc end q"#0BoxǍ*1" {0.0 42.67915 -14.2264 -42.67914 14.22638 ov}xygӍg3232$3232=323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232=3232y Ο%3232323232323232323232323232323232323232323232323232U[%323232323232323232323232323232323232323232323232323232g3232$3232=323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232=3232=ʟ񠷸#Answ9eretoexercise8(p.10): This'doGesthejob,saving![eachpGointtomakethepreviouspGointavqailableforUUthenextpiece:N8\xyQ@={(0,-10),(10,3),(20,-5)},Qs0="prev"?@@{;"prev";**@{-}="prev"}\endxyYNoticehowweclosethelineby rstsavings0 e,thelastpGointjvisited,suchthatthe rstpGointwillbGeconnectedtoUUit.7퍑Answ9erTtoexercise9(p.11): TheUUauthorused\xy?={.{+DL(2)}.{+UR(2)}}"dbl",Q*+<3pc,2pc>{+}*\frm{.},?"dbl"*\frm{--}\endxyYtoUUtypGesetthe gureintheexercise.7퍑Answ9erWctoexercise10(p.13): Them rsttypGesets\a"ycenteredaround0 andthenmovesctothelowerrightҞcorner,thesecondtypGesets\a"aboveҞthe0 9pointandldoGesnotchangec.\Witha\+"at0 lղtheylooklikethis:qps: SDict begin xyc end+>'a:andqUUps: SDict begin xyc ende+a .Answ9er+Gtoexercise11(p.13): Theyvhavetheout-lines dH*ps: SDict begin xyc endëPǍ+" {0.0 7.9167 -7.5001 -7.9167 7.50009 ov}xy!Dz+bvand|ps: SDict begin xyc endrëPǍ-" {0.0 2.63892 -2.50005 -2.6389 2.50003 ov}xy!Dz+bGecauseEthe rstisenlargedbythepositiveo settotheUuppGerrightcornerandthesecondbythenegativeo setUUtothelowerUUleftcorner.Answ9erUotoexercise12(p.14): TheV rsthasnoe ectsincethedirectionissettobGethatofavectorinthecurrentdirection,%however,thesecondreversesthecurrentUUdirection.Answ9erjtoexercise13(p.14): NoneinbGothcases.Answ9erTtoexercise14(p.16): OneUUwayisN8$$\xyQ*{+};?p+(6,3)*{+}**{}?(1)Q*@{-}?*!/-5pt/^\dir{-}Q*^\dir{-}?*!/^-5pt/\dir{-}\endxy$$Y ThusUwe rstcreatethetwo+saspandcandcon-nectǖthemwiththedummyconnection**{} tosetupthe9directionparameters.+sThenwemove`ontopofc'gw:with .?(1)Pand .pGositionthefoursidesofthesquareus- :ing^ Cand_forloGcaldirectionchangesand/hdimeni/:forskewingtheresultingob8jectbymovingitsreference:pGointUUintheoppositedirection.A:Answ9ertoexercise15(p.18): OneM wayistoadd:extraxhalfcirclesskewedxsuchthattheycreatetheillu-:sionUUofashade:N8:$$\xy*7*\cir<5pt>{}*7*!<-.2pt,.2pt>\cir<5pt>{dr^ul}*7*!<-.4pt,.4pt>\cir<5pt>{dr^ul}*7*!<-.6pt,.6pt>\cir<5pt>{dr^ul}:\endxy$$y:Answ9erKtoexercise16(p.21): ThisisthecoGde:thatUUwasactuallyused::\xy?(0,20)*[o]+{A};(60,0)*[o]+{B}="B":**\crv{}?\POS?(.4)*_+!UR{0},"B":**\crv{(30,30)}?\POS?*^+!D{1},"B":**\crv{(20,40)&(40,40)}?\POS?*^+!D{2},"B":**\crv{(10,20)&(30,20)&(50,-20)&(60,-10)}:\POS?*+^!UR{4}?\endxyy:Answ9erKtoexercise17(p.21): ThisisthecoGde:thatUUwasusedtotypGesetthepicture::\xy?(0,20)*+{A};(60,0)*+{B}:**\crv{(10,20)&(30,20)&(50,-20)&(60,-10)}*7?<*\dir{<}??>*\dir{>}*7?(.65)*{\oplus}?*!LD!/^-5pt/{x}*7?(.65)/12pt/*{\oplus}?*!LD!/^-5pt/{x'}*7?(.28)*=0{\otimes}-/40pt/*+{Q}="q"*7+/100pt/*+{P};"q"?**\dir{-}:\endxyy:Answ9er,toexercise18(p.21): HereisthecoGde:thatUUwasusedtotypGesetthepicture::\def\ssz#1{\hbox{$_{^{#1}}$}}:\xy?(0,0)*+{A};(30,-10)*+{B}="B",**\dir{-},:"B"**\crv{(5,20)&(20,25)&(35,20)}*7?<(0)*\dir{<}="a"??>(1)*\dir{>}="h"*7?(.1)*\dir{<}="b"??(.9)*\dir{>}="i"*7?(.2)*\dir{<}="c"??(.8)*\dir{>}="j"*7?(.3)*\dir{<}="d"??(.7)*\dir{>}="k"*7?(.4)*\dir{<}="e"??(.6)*\dir{>}="l"*7?(.5)*\dir{|}="f",*7"a"*!RC\txt{\ssz{(\lt)}};j4"h"*!LC\txt{\ssz{\;(\gt)}},**\dir{.},*7"b"*!RD{\ssz{.1}};j4"i"*!L{\ssz{\;.9}},**\dir{-},*7"c"*!RD{\ssz{.2}};j4"j"*!L{\ssz{\;.8}},**\dir{-},*7"d"*!RD{\ssz{.3}};LW970G r*tj??gw"k"*!L{\ssz{\;.7}},**\dir{-}, Q"e"*!RD{\ssz{.4}};"l"*!LD{\ssz{.6}},**\dir{-},Q"f"*!D!/^-3pt/{\ssz{.5}}\endxy!)Answ9erTtoexercise19(p.24): HereUUishow:N8\xyQ(0,0) *++={A}?*\frm{o};Q(10,7)?*++={B}*\frm{o}**\frm{.}\endxyAnsw9ertoexercise20(p.24): TheJ*\cir?{}0op-erationЬchangesctobGeroundwhereas*\frm?{o}4=doesnotUUchangecatall.zAnsw9erTtoexercise21(p.26): HereUUishow:N8\xyQ(0,0) *+++{A}?;Q(10,7)?*+++{B}**\frm{.}Q**\frm{^\}}?;**\frm{_\}}\endxym The)trickinthelastlineistoensurethattheref-erencepGointofthemergedob8jecttobebracedistherightUUoneineachcase.Answ9ertoexercise22(p.29): ThisishowtheauthorUUspGeci edthediagram:N8\UseCrayolaColors\xy\drop[*1.25]\xybox{\POS(0,0)*{A};(100,40)*{B}**{}Q?<<*[@_][red][o]=<5pt>{\heartsuit};Q?>>>*[@_][Plum][o]=<3pt>{\clubsuit}Q**[|*][|.5pt][thicker]\dir{-},?(.1)*[left]!RD\txt{label?1}*[red]\frm{.}?(.2)*[!gsave?newpathxyXpos?xyYposmoveto50duprlineto20?setlinewidth001setrgbcolorstrokegrestore][psxy]{.},?(.2)*[@]\txt{label?2}*[red]\frm{.},?(.2)*[BurntOrange]{*},?(.3)*[halfsize]\txt{label?3}*[red]\frm{.}?(.375)*[flip]\txt{label?4}*[red]\frm{.}?(.5)*[dblsize]\txt{label?5}*[red]\frm{.}?(.5)*[WildStrawberry]{*},?(.7)*[hflip]\txt{label?6}*[red]\frm{.}?(.8)*[vflip]\txt{label?7}*[red]\frm{.}?(.9)*[right]!LD\txt{label?8}*[red]\frm{.}?(.5)*[@][*.66667]!/^30pt/Q\txt{special?effect:alignedtext}Q*[red]\frm{.}}\endxygw:Answ9er9toexercise23(p.39): Here>Hiswhatthe :authorUUdid:N8:\xy?*+{A}*\cir<10pt>{}="me"*7\PATH?~={**dir{-}}j4`ul^ur,"me"?"me"|>*:(1,-.15)\dir{>}:\endxy;Thetrickisgettingthearrowheadright:the: moGd-:i erUUtotheexplicit\dirhob8jectidoGesthat.E:Answ9erTtoexercise24(p.39): TheUUauthordid:\xy(0,0)*7\ar?@{-->}(30,7)^A="a"*7\POS(10,12)*+\txt{label}?\ar"a":\endxy:Answ9eritoexercise25(p.39): Heremistheentire6XYj:-pictureUUoftheexercise::\xy?;<1pc,0pc>:*7\POS(0,0)*+{A}*7\ar+(-2,3)*+{A'}*\cir{}*7\ar?@2+(0,3)*+{A''}*\cir{}*7\ar?@3+(2,3)*+{A'''}*\cir{}*7\POS(6,0)*+{B}*7\ar?@1{||.>>}+(-2,3)*+{B'}*\cir{}*7\ar?@2{||.>>}+(0,3)*+{B''}*\cir{}*7\ar?@3{||.>>}+(2,3)*+{B'''}*\cir{}:\endxy;TheUU rstbatchusethedefault{->}spGeci cation.E:Answ9erTtoexercise26(p.40): TheUUauthorused:\newdir{?>}{{}*!/-5pt/\dir{>}}:Answ9erTtoexercise27(p.41): TheUUauthorused:\xy*7\ar?@{>>*\composite{\dir{x}*\dir{+}}<<}*7(20,7):\endxy:Answ9erTtoexercise28(p.41): TheUUauthorused:\xy?*{\circ}="b"\ar@(ur,ul)c*7\ar@{.>}@(dr,ul)?(20,0)*{\bullet}:\endxy:NotethatitisessentialthatthecurvingspGeci cation:comesUUafterthearrowstyle.E:Answ9er,toexercise29(p.43): HereisthecoGde:usedUUtotypGesetthep}'astingdiagramUUin gure15.:\xymatrixrowsep{1.5pc}:\xymatrixcolsep{3pc}:\diagramLW971H O*tj??gwQ&&\relax\rtwocell<0>^{f_3^{}\;\;}{\omit} Q&\relax\ddtwocell<0>{\omit}\drtwocell<0>^{\;\;f_4^{}}{<3>}\ddrrtwocell<\omit>{<8>}\\&&&&\relax\drtwocell<0>^{\;\;f_5^{}}{\omit}\\A?\uurrlowertwocell<-6>{\omit}\relax\uurrcompositemap<2>_{f_1^{}}^{f_2^{}}{<.5>}Q\drtwocell<0>_{g_1^{}\;}{\omit}Q&&&\relax\urtwocell<0>{\omit}Q&&\relax\rtwocell<0>^{f_6^{}\;}{\omit}Q&\relax\rlowertwocell<-3>_{g_4^{}}{<-1>}Q\rcompositemap<6>_{f_7^{}}^{f_8^{}}{\omit}Q&?B\\Q&\relax\urrtwocell<0>{\omit}Q\xcompositemap[-1,4]{}%<-4.5>_{g_2^{}}^{g_3^{}}{\omit}\\\enddiagramhF*orUthestraightarrows,UitwouldhavebGeensimplertouseK\..to ףprovidedKxyarrow+WhasKbGeenloaded.nInstead\..twocell<0>...{\omit?}pκwasusedtoillustratetheversatility3ofnudgingand\omit#;thusxy2cell-']cancompletelyhandleawiderangeofdiagrams,withoutrequiring}xyarrow']h.4Note}alsotheuseof\relax)atthestartofeachnewcell,toavoidprematureexpansionofaNcomplicatedmacro,,whichcanupsetthecompilingmechanism.뵍Answ9er,toexercise30(p.46): HereisthecoGdeusedUUbytheauthortosetthe rstdiagram.N8{\uppercurveobject{{?}}Q\lowercurveobject{{\circ}}\xymatrixcolsep{5pc}\xymatrixrowsep{2pc}\diagramQ\relax\txt{?FUn}\rtwocell<8>{!\&}Q&?\relax\txt{gaMES}Q\enddiagram}| HereUUisthecoGdeusedfortheseconddiagram.\xymatrixcolsep{2.5pc}\xymatrixrowsep{4pc}\diagramQ\relax\txt<1.5cm>{\bf?GroundState}Q\rrtwocell<12>~^{+{}~**!/-2.5pt/\dir{>}}Q~_{++{}~**!/5pt/\dir{<<}}Q^{<1.5>\txt{\small?continuouspower}}Q_{<1.5>\txt{\small?pulsedemission}}{!}&?\relax\;\;N\!i\,C\!d\;\;\Circled&?\relax\txt<1.50cm>{\bfExcitedState}\enddiagram!9퍑Answ9erTtoexercise31(p.49): TheUUauthordid\xymatrix?@!=1pc{Q**[l]?A\timesBgw*+\ar[r]^{/A}?\ar[d]_{/B} *7&?B\ar[d]^{\timesA}:\\*7A\ar[r]_{B\times}*7&?**[r]B\timesA:} ꍒ:Answ9ertoexercise32(p.49): MoGdi ers;pareused:tomakeallentriesroundwithaframe{thegeneral:form{isusedtoensurethatthesequenceiswell-de ned.:FinallyzthematrixisrotatedtomakeitpGossibleto:enterUUitasasimplesquare:N8:\entrymodifiers={=<1pc>[o][F-]}:\xymatrix?@ur{*7A?\save[];[r]**\dir{-},"[];[dr]**\dir{-},"[];[d]?**\dir{-}\restore1&?B\\*7C?&D}:Answ9erTtoexercise33(p.49): HereUUishow:N8:\objectheight{1pc}?\objectwidth{3pc}:\xymatrixrowsep={0pc}:\xymatrix?@*[F-]{%*7:?\save+<-4pc,1pc>*\hbox{\itroot}*+\ar[]1\restore:\\*7{\bullet}1\save*{}.\ar`r[dd]+/r4pc/`[dd][dd]1\restore:\\*7{\bullet}1\save*{}.\ar`r[d]+/r3pc/`[d]+/d2pc/j`[uu]+/l3pc/`[uu][uu]1\restore:\\*71?}:Answ9ertoexercise34(p.50): Thez rstAwas:namedUUtoallowreferencefromthelast:N8:\xygraph{*7[]A="A1"?:@/^/[r]Aj:@/^/?[r]Aj:@/^/?"A1"}:Answ9erTtoexercise35(p.52): TheUUauthordidN8:\SelectTips{cm}{}:\objectmargin={1pt}:\xygraph{?!{0;(.77,-.77):0}LW972I **tj??gwQ!~:{@{-}|@{>}} Qw?(:[r(.6)]{x_1},:[d]z:[r]y:[u(.6)]{x_2}:"x_1":"z":@(?{"w";"z"},{"y";"z"})"z":"x_2")} Italsoshowsthatonec}'anquse{}Psinsidedelimitedargumentslpr}'ovidedu_oneaddsaspacetoavoidthe{} вsbGeingUUshavedo !^Answ9er,toexercise36(p.52): HereisthecoGdeactuallyRusedtotypGesetthe\xypolygon=e1s,Qwithinan\xygraphP.Itillustratesthreedi erentwaystoplacetheUUnumbGers.qOtherwaysarealsopGossible.N8\def\objectstyle{\scriptscriptstyle}\xy?\xygraph{!{/r2pc/:}[]?!P3"A"{\bullet}"A1"!{+U*++!D{1}}?"A2"!{+LD*+!RU{2}}"A3"!{+RD*+!LU{3}}?"A0"[rrr]*{0}*\cir<5pt>{}!P6"B"{~<-\cir<5pt>{}}"B1"1?"B2"2"B3"3"B4"4"B5"5"B6"6"B0"[rrr]0?!P9"C"{~*{\xypolynode}}}\endxy'\$B ~Vfersionff2Compatibility[Vers.3.3bCyKristo erH.Rosehkrisrose@brics.dki Loadas:\xyoption{v2}'ThisUappGendixdescribesthespecialbackwardsUcompat-ibilitydwithdXY -picversion2:)diagramswrittenaccord-ing?tothe\TypGesettingdiagramswith;XY ?-pic:˜User'sManual"L[13 ]shouldtypGesetcorrectlywiththisloaded.The[compatibilityisavqailableeitherasanWXY i[-optionorthrough1thespGecial lesxypic.sty4Gandxypic.texde-scribGedUUbelow. _Ǎ There areafewexceptionstothecompatibility:M thefeatures?describGedinxB.1belowarenotprovidedbGe-causefXtheyarenotasusefulastheauthororiginallythoughtqqandthusvirtuallyneverused.AndoneextracommandisprovidedtospGeeduptypGesettingofdocu-mentsαwithέXY N-picversion2diagramsbyallowingthenewUUcompilationfunctionalitywitholddiagrams. Theweremainingsectionslistalltheobsoletecom-mands?andsuggestways?toachieve?thesamethingsusingl,XY 0-picl03.3,i.e.,withouttheuseofthisoption.Theyg"aregroupGedastowhatpartofgXY "-picreplacesthem;UUthecompilationcommandisdescribGedlast. Note: i\version,2"ismeanttocoverallpublicre-leasesofXY-picin1991and1992,i.e.,version1.40and9Nversions2.1through2.6.Thepublishedmanualcited?abGove(forversion2.6)isthereferenceincaseof;^vqariationsbGetween;^theseversions,tandonlythingsdoGcumentedinthatmanualwillbGesupportedbythisoption!^19 Kff^ J=w-:19LIn#additionafewoftheexpEncloseitinbraces,i.e.,}+W(or\tipK̲)withvqariants'M S-T<8E3sXidioms:Some~idiomsfromAU>'M S-TU>'ExXarenolongerusedbyzXY j~-:pic:the de nitioncommands\defineand\redefine,:andthesizecommands\dsize,ȭ\tsize,\ssize,and:\sssize.}Pleaseusethecommandsrecommendedfor:your&format|forplainTU>'ExXtheseare\def@forthe rst:twoDand\displaystyleG,H\textstyle7,H\scriptstyleBG,: ff^ @v2.7{2.12Xarealsosupp'M S-TU>'ExX\textanda(non-ob8ject)bGoxconstruction\Textwhichareemulated|\text=isDonlyde nedifnotalreadyde ned,޿however,using:thenativeone(ofAU>'M S-TU>'ExXorAU>'MS-L5ffA͉TU>'ExXorwhatever)vmifpGossible.Pleaseusethe\txtβob8jectcon-struction/describGedinx6.3directlysinceitismoregen-eralUUandmuchUUmoreecient!NObsoleteTstateuTUpto]version2.6userscouldaccessthestatevqariables\cL,UU\cR,\cH,and\cD,whicharede ned. F*rom"v2.7to2.12userscouldusethenamesoftheLstate\dimen(Lregisters\Xmin,\Xmax,\Ymin,and\Ymax;_\Xp,s\Yp\Dp,\Up,\Lp,and\Rp;_\Xc,\Yc\Dc,\Uc,\Lc,andO\Rc;\Xorigin,\Yorigin,\Xxbase,\Yxbase,\Xybase,and\Yybase.-sNowthesameef-fectrcanbGeachievedrusinghcornerisbutv2޲de nesthealiases.ObsoleteTpQositionmanipulationuTInUversion2manythingsweredoneusingindividualhdecoriFcontrolsequencesthatarenowdoneusinghpGosiopGerators.^ff2 ፍ V*ersionUU2pGositioningkReplacement4ff2 \gohpGosik\POS;p,hpGosi \aftergo{?hdecori}hpGosiG\afterPOS{|@hdecori};p,hpGosi \mergek\POS.p\relax \swapk\POS;\relax \Drop{?htexti}k\drop+{htexti}ff2rNObsoleteTconnectionsuTThesep connectionsarenowimplementedusingdirec-tionals.l؉ff2 ፍ V*ersionUU2connectionlyReplacementff2 \nonely\connect?h\dir{} \solidly\connect?h\dir{-} \Solidly\connect?h\dir2{-} \Ssolidly\connect?h\dir3{-} \dashedly\connect?h\dir{--} \Dashedly\connect?h\dir2{--} \Ddashedly\connect?h\dir3{--} \dottedly\connect?h\dir{.} \Dottedly\connect?h\dir2{.} \Ddottedly\connect?h\dir3{.} \dottedwith{?htexti}ly\connect?h{9htexti}ff2 9DNotehowthe`hidden'spGeci erh shouldbeusedbe-cause0version2connectionsdidnota ectthesizeofdiagrams.gw:ObsoleteTtips :TheseUUob8jectsallhaveUU\dirUI-namesUUnow:: ff2 !fV*ersionUU2tipY3ReplacementPff2f\notipY3\dir{} f\stopY3\dir{t$|yO!}f\astopY3\dir^{yO!|~}f\bstopY3\dir_{yO!|~}f\tipY3\dir{>}f\atipY3\dir^{>}f\btipY3\dir_{>}f\TipY3\dir2{>}f\aTipA3\object=<5pt>:(32,-1)\dir^{>}f\bTipA3\object=<5pt>:(32,+1)\dir_{>}f\TtipY3\dir3{>}f\ahookY3\dir^{(}f\bhookY3\dir_{(}f\aturnY3\dir^{'}f\bturnY3\dir_{'}ff2 z P The@oldercommands\pit@,{\apit,{and\bpit,arenotUUprovided.ObsoleteTobjectconstructions The(followingob8jectconstructionmacrosaremadeob-soleteUUbytheenrichedhob8jectiformat: ff2 ! oV*ersionUU2ob8jectkO+Replacementff2 o\rotate(?hfactori)htipi GO+\object:(vhfactori,?hfactori){ htipi} o\holekO+\object+{} o\squashhtipikO+\object=0{ htipi} o\growhtipikO+\object+{htipi} o\grow<*]hdimeni>?htipikO+\object+<hdimeni>{ htipi} o\squarify{?htexti}kO+\object+={ htexti} o\squarify{ htexti}GO+\object+=<{ hdimeni>{ htexti}ff2Awhere[rotationisdoneinaslightlydi erentmannerinversionUU3.3(itwasneveraccurateinversion2).B.3!Obsoleteextensions&features V*ersion?p2hadcommutative?pdiagramfunctionalitycor-respGonding7totheframes'extensionandpartsofthematrix"!and.arrowMfeatures.5These.arethereforeloadedandLsomeextrade nitionsaddedtoemulatecommandsthatUUhavedisappGeared.F ramesTheyversion2framecommandsareemulatedus-ing(theframeextension(aswellasthe\dotframed9 ,LW974K 3*tj??gw\dashframed),\rounddashframed_OͲcommandsecomm- unicatedUUtosomeusersbyelectronicmail):Iff2 lōeV*ersionUU2ob8jectg5Replacementcff2e\framedg5\drop\frm{-}e\framed<8Mhdimeni>g5\drop\frm<6hdimeni>{-}e\Framedg5\drop\frm{=}e\Framed<8Mhdimeni>g5\drop\frm<6hdimeni>{=}e\dotframedg5\drop\frm{.}e\dashframedg5\drop\frm{--}e\rounddashframedg5\drop\frm{o-}e\circledg5\drop\frm{o}e\Circledg5\drop\frm{oo}cff2'DMatricesuTTheA\diagramhrowsi\enddiagramcommandispro-vided~asanaliasfor\xymatrix{>޸hrowsi}`centeredin)mathmoGdeand\LaTeXdiagramschangesittouse\begin"...Y\endsyntax.Zv2뎲setsaspGecialinternal`oldmatrix' agsuchthattrailing\\+zareignoredanden-triesUUstartingwith* ꧲aresafe. \NoisyDiagramsزisignoredbGecausethematrixfea-tureUUalwaysoutputsprogressmessages. Finally VVtheversion2\spreaddiagramrows,\spread$diagramcolumnsqspacingYcommandsareemu-latedUUusing\xymatrixrowsepUj}and\xymatrixcolsepR(:Arro9wsuTThe5mainarrowcommandsofversion2werethe\morphismͲand\definemorphismcommandswhichnowUUhavebGeenreplacedbythe\arjcommand. v2providesdthemaswellasusesthemtode nethe&version2commands\xto,M\xline,\xdashed,\xdotted, V\xdouble,andallthederivedcommands\dto,(\urto ,(...;_the\e\arrow*8commands\eofthe -releasesUUofv3isalsoprovided. Instead?ofcommandslike\rrto oand\uldouble5cyoushouldPusethearrowfeaturereplacements\ar[rr])aand\ar@{=}[ul]9߲. TheqBprede nedturningsolidarrows\lltou$0,<...,\tord5areDde nedaswell;,'ExX2.09`style{option'[xypic]*f. 9Thisismadesynonymouswith|loadingthisoptionbythe lesxypic.texandxypic.styUUdistributedwiththev2*option.㍍xypic.tex/?:7qThiss le(version3.3)justloadsthev2feature.xypic.sty/?:7qLoadsUUxy.sty&*andUUthev2*feature.gw:B.5Compilingv2-diagrams:InordertomakeitpGossibletousethenewcompilation :featuresevenondoGcumentswrittenwithXY B-picv2,ߑthe:followingUUcommandwasaddedinv2.12::ff2 > 6\diagramcompileto{lUhnameiUU} ꧲...\enddiagramײff2(whichfisliketheordinarydiagramcommandexcepttheresult5iscompiled(seenote5e).NNotethatcompilationisUUnotquitesafeinallcases! װ Thereisalsothefollowingcommandthatswitcheson5jautomaticvc}'ompilationͲofalldiagramscreatedwiththeUUv2\diagram0...\enddiagramB3command:Nff2* (\CompileAllDiagramsD{hpre xiUU}* (\NoCompileAllDiagrams* (\ReCompileAllDiagramsײff2/awillNapply\xycompileto{Ghpre xin}{ ...} 9toNeachdia-gram withnasequencenumbGer startingfrom1.(Use\CompileMatricesWU%andUU\CompilePrefixP*instead! װ If~forsomereasonadiagramdoGesnotworkwhencompiled thenreplacethe\diagram4 commandwith\diagramnocompile_c(or$!incaseyouareusingtheL5ffA͉TU>'ExXUUform,\begin{diagramnocompile}U ).-9}CdCommonffErrorsxIn`xthisappGendixwedescribesomecommoncaseswheresmall|mistakesinxXY |-picturesresultinTU>'ExXerrormes-sagesUUthatmayseemcryptic.v!pBo9xTexpQected.!AhbGoxi7w9assuppQosedtobehere. Thismes-sage\iscommonwhenan\XY -pichob8jectiismistypGedsuchthatXY b-picexpGectsbutdoesnot ndaTU>'ExXhboxiconstruction.!LaT eX+Error:=Bad+mathen9vironment+delim-iter.!Fileendedwhilescanninguseofձ\xycompiled.!jArgumen9t"of:\codeof@hasanextraFɌ cmbsy10Fg. Theseerrorsh(canhappGenwhilereadinganincompletecom-piledpicture(suchabGeastiscreatedwhenXYd-piccrashesduringcompilationduetoasyntaxerrororotherUUsuchproblem).!]Missing@Fginserted. ThishappGenswhen\endxywasUUleftout.6q T oTDo:qDzAlsoUUincludethemoreobscureones...LW975L x*tj??gwReferences [1]DAdobGeSystemsIncorporated. QPostScriptL}'an- DguageR}'eferenceManual,UUsecondedition,1990.P [2]DAmerican6MathematicalSoGciety*.ֶAU>'M S-L雍QATKß'E-XDV;ersion1.1User'sGuide,UU1.1edition,1991. [3]DKarl6Berry*.fExp}'andedplainTKß'E-X,version2.6edi-Dtion,May1994.yAvqailableforanonymousftpfromDCT*ANUUinmacros/eplain/doc. [4]DMichelQGoGossens,F*rankMittelbach,andAlexan-Dder|Samarin.TheL雍QATKß'E-XComp}'anion.Addison-DW*esley,UU1994. [5]DBrianՖW.Kernighan."PIC|alanguagefortypGe-Dsettingfgraphics.Softwar}'ePracticeandExperi-Denc}'e,UU12(1):1{21,1982. [6]DDonaldE.Knuth.The-TKß'E-Xb}'ook.Addison-W*esley,D1984. [7]DDonald,E.Knuth.ComputerZMo}'dernT;ypefaces,DvolumeAofComputers&T;yp}'esetting.A%Addison-DW*esley,UU1986. [8]DLeslie+LampGort.5L雍QATKß'E-X|A)Do}'cument)PreparationDSystem.nAddison-W*esley,UU1986. [9]DLeslie+LampGort.5L雍QATKß'E-X|A)Do}'cument)PreparationDSystem.nAddison-W*esley,UU2ndedition,1994.[10]DP*.5Nauretal.*RepGortonthealgorithmiclanguageDALGOL460.Communic}'ationsFoftheACM,I3:299{D314,UU1960.[11]DT*omasuRokicki. DVIPS:AjTKß'E-XDriver.Dis-Dtributeda withthedvipsprogramfoundonCT*ANDarchives.[12]DKristo erH.Rose.HowtotypGesetprettydia-DgramarrowswithTU>'ExX|designdecisionsusedin@XYD-pic.RIn/JiuUrqZlatuxskqa,editor,Eur}'oTKß'E-X '92|DPr}'oceedings,ofthe7thEur}'opean,TKß'E-XConfer}'ence,Dpages?183{190,z?Prague,Czechoslovqakia,z?Septem-DbGerUU1992.CzechoslovqakUUTU>'ExXUsersGroup.[13]DKristo erH.Rose.xKTypGesettingdiagramswithXY >-Dpic:yUser's.manual.9gInJiuUrqZlatuxskqa,editor,Eu-Dr}'oTKß'E-X'92|Proceedingsofthe7thEuropeanTKß'E-XDConfer}'ence,3pages273{292,Prague,Czechoslo-Dvqakia,|SeptembGerbA1992.CzechoslovqakTU>'ExXUsersDGroup.[14]DKristo erxH.Rose.XY -picAUser'sGuide.DIKU,DUniversity\ofCopGenhagen,Universitetsparken\1,DDK{2100UUKbGenhavn,3.0edition,June1995.[15]DKristo ermH.RoseandRossR.MoGore.fXY uj-piccom-DpletegsourceswithTU>'ExXnicalcommentary*.notyetDavqailable,UUJune1995.gw:[16]xvMichaelWzD.Spivqak.uTTheJoyofTKß'E-X|AGourmet xvGuideWtoT;yp}'esettingwiththeAU>'M S-TKß'E-XMacroxvPackage.American$MathematicalSoGciety*,-secondxvedition,UU1990.f:[17]xvTUG*W*orking*GroupTWG-TDS. 2AdirectoryxvstructureforTU>'ExX lesversion0.98. URL,Mayxv1995. Avqailable6withURL5ftp://jaspGer.ora.com/xvpub/twg-tds/.D:Index:!,UU8 :&,UU47:',UU38:(),UU8:(0),UU8:(0,0),UU69:(1),UU8:*,UU8,38,39,41,47,49,73:**,UU8,39,49:+,UU8:,,UU8,39:-,UU8,38:.,UU8:.xyd,UU16:/,UU37,38,41://,UU8::,UU8,12:::,UU8:;,UU8:<,UU8,37{39:<>,UU8:<>(.5),UU38:=,UU8,37{39:>,UU8,37{39:?,UU8,39:@,UU8,38,40,48:@!,UU40,48:@!0,UU48:@!=,UU48:@!C,UU48:@!R,UU48:@(,UU10,40,41:@),UU10:@*,UU40,49:@+,UU10:@-,UU10:@/,UU40,41:@1,UU49:@<,UU40,41:@=,UU10:@?,UU40,41LW976M K*tj??gw@@,UU10 /@C,UU48@H,UU48@L,UU48@M,UU48@R,UU48@W,UU48@`,UU40@i,UU10[.],UU13[=,UU12,14,30,32[],UU13[c],UU13[d],UU13[dvips],UU5[l],UU13[o],UU13[r],UU13[textures],UU5[u],UU13\\,UU47^,UU38{40_,UU38{40`,UU38|,UU38,40|<<,UU73~,UU38^g0,UU6,8,401,UU402,UU403,UU4010,UU2711,UU2712,UU27a,UU8activeUUcharacters,4haddUUopi,12\aftergo?,UU74\afterPATH?,UU37\afterPOS?,UU14,15,37\ahook?,UU74alloGcation,UU5AU>'M S-L5ffA͉TU>'ExX,UU5,15AU>'M S-TU>'ExX,UU5\apit?,UU73\ar?,UU14,37array,UU50arrowUUhead,39arrowUUstem,39arrowUUtail,39\astop?,UU74\aTip?,UU74\atip?,UU74\aturn?,UU74banner,UU5gw:\bhook?,UU74 $:BNF,UU4:hbGodyUUoftheoptioni,19:\bpit?,UU73:\bstop?,UU74:\bTip?,UU74:\btip?,UU74:\bturn?,UU74rЍ:C,UU8,10:c,UU6:c,UU8:cartesianUUcoGordinatesystem,6:categoryUUcoGde,4:CD,UU8:\cD?,UU74:\cH?,UU74:hciri,UU19:\cir?,UU18,71:\Circled?,UU75:\circled?,UU75:circles,UU5:CL,UU8:\cL?,UU74:cm,UU27:\Col?,UU49:columnUUspacing,48:hcommandi,UU15:\CompileFixPoint?,UU15:\CompilePrefix?,UU15:compiling,UU15:hcompGositei,UU12:\composite?,UU11,12,18:connect,UU6:\connect?,UU15:hcoGordi,UU8:COPYING,UU4:copyright,UU3:hcorneri,UU8:CR,UU8:\cR?,UU74:CU,UU8:currentUUob8jectstyle,12,13:DG,UU6:D,UU8,10:Dc,UU6:DpR,UU6:\Dashed?,UU74:\dashed?,UU74:dashes,UU5:\dashframed?,UU75:\Dc?,UU74:\Ddashed?,UU74:\Ddotted?,UU74:hdecori,UU15:decoration,UU6LW977N *tj??gwdefaultUUentry*,49 5\define?,UU73\definemorphism?,UU75hdiagi,UU12\diagram?,UU75dimensionUUregisters,5\dir?,UU16,18,39,40hdirectioni,UU12\documentclass?,UU5\dotframed?,UU75\Dotted?,UU74\dotted?,UU74\dottedwith?,UU74\Dp?,UU74hdriveri,UU19\Drop?,UU74\drop?,UU15\dsize?,UU73\dumpPSdict?{},UU35ߍE,UU8,10Edge,UU6Edgec,UU6EdgepR,UU6\enddiagram?,UU75\endxy?,UU5,6,14entryUUheight,48entryUUmargin,48entryUUwidth,48\entrymodifiers?,UU49Error,UU5hescapGei,UU51eu,UU27\everyentry?,UU49extension,UU19extents,UU6 xedUUgrid,48fonts,UU5formats,UU4\Framed?,UU75\framed?,UU75freeUUsoftware,3french.sty,UU4\frm?,UU10,24\frm?{**},UU26\frm?{*},UU26german.sty,UU4GNUUUGeneralPublicLicense,3\go?,UU74hgraphi,UU51\grow?,UU74h,UU12\halfrootthree?,UU7\halfroottwo?,UU7\halign?,UU50gw:\hbox?,UU12 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5\object?,UU12,16hob8jectbGoxi,UU12\objectbox?,UU11,39\objectheight?,UU13\objectmargin?,UU13,39\objectwidth?,UU13\OnlyOutlines?,UU16horienti,UU19orientation,UU48ߍP,UU8,10p,UU6p,UU8packqage,UU5\partroottwo?,UU7\PATH?,UU37\PATHaction?,UU37\PATHafterPOS?,UU37\pit?,UU73hplacei,UU8placementUUstate,6plainTU>'ExX,UU5hpGosi,UU8\POS?,UU15,37pGositions,UU6privqacy*,UU4q,UU12RDz,UU6R,UU8,10Rc,UU6RpR,UU6hradiusi,UU19\Rc?,UU74RD,UU8\redefine?,UU73rede ned,UU4\relax?,UU4,15\restore?,UU15\rotate?,UU74\rounddashframed?,UU75\Row?,UU49rowUUspacing,48\Rp?,UU74RU,UU8s,UU8\save?,UU15\SelectTips?,UU27\ShowOutlines?,UU16\SilentMatrices?,UU47hsizei,UU12hslidei,UU8\Solid?,UU74\solid?,UU74spacing,UU48gw:\spreaddiagramcolumns?,UU75 ۍ:\spreaddiagramrows?,UU75:\squarify?,UU74:\squash?,UU74:squiggles,UU5:\ssize?,UU73:\Ssolid?,UU74:\sssize?,UU73:state,UU6:hstepi,UU51:\stop?,UU74:style,UU13:styleUUoption,5:\swap?,UU74o:TU>'ExXUUreferencepGoint,6:\Text?,UU74:\text?,UU74:\Tip?,UU74:\tip?,UU74:tips,UU5:\tsize?,UU73:\Ttip?,UU74:\turnradius?,UU39:\txt?,UU18:U,UU6:U,UU8,10:Uc,UU6:UpR,UU6:\Uc?,UU74:\Up?,UU74:\UseCrayolaColors?,UU30:\usepackage?,UU5:\UsePSheader?{},UU35:\UsePSheader?{},UU35:\UsePSspecials?{},UU34:\UseRules?,UU16:\UseSingleDriver?,UU19:\UseTips?,UU27:v,UU12:hvectori,UU8:version,UU5:Warning,UU5:warningUUmessages,4:warranty*,UU3:X,UU6:x,UU8,9:Xoriginm,UU6:Xxbase,UU6:XybaseN,UU6:Xc,UU6:XpR,UU6:XmaxA̲,UU6:Xmin ,UU6:\Xc?,UU74LW979P 6*tj??gw\xdashed?,UU75 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,UU6:\Yc?,UU74:\Ymax?,UU74:\Ymin?,UU74:\Yorigin?,UU74:\Yp?,UU74:\Yxbase?,UU74:\Yybase?,UU74N8:zeroUUpGosition,6LW980 C;lPFɌ cmbsy10E-ff cmcsc10D- cmcsc10C"xmsam5@-hcmbx5?f$cmbx7>- cmcsc10=R6ff cmss12 logo10 !", cmsy10 O!cmsy7 0ncmsy5 b> cmmi10 0ercmmi7O \cmmi5K`y cmr10ٓRcmr7Zcmr5u cmex10 K