; TeX output 1996.03.05:1502l'&Ә>DtGGcmr17Curvqes7tinLdKG0XQ cmr12AT[-E;gXPicturesFnA7tManqualforI߆TG cmtt12ICURVES.STYandICURVESLS.STYSQVVersion7t1.41_IanMaclaine-cross2K cmsy8=o cmr9Sc9hoAolTofMechanicalandManufacturingEngineeringTheTUniv9ersityofNewSouthW:alesSydneyTAustralia2052A22ndAugust1995:ō?'ExX^1/macropackqageforTU>'EX^2/allowssimple ?line\ndrawingusingcharacters.Thesecharactersincludequadrantcirculararcs,?solid#diskswithdiametersfrom1to15pt^3andshortlineswithalimitedrangeof?slopGesintwothicknesses.[.Ay$'ExXpicture.NL5ffA͉TU>'ExX&3picturessave&3diskspaceforsourcedescriptionsandcomputertimein?proGducingvdocumentscomparedwithprintercommandsorbitmappGedgraphics.?F*rominitialpGencilsketchonsquaredgraphpaperto nalprintout,theytake?halfdthetimeformanualpGendrawings.!ThelabGorsavingsarehigherforrevisions?and'rewrites.bUnfortunatelystandardL5ffA͉TU>'ExXcannotyetdrawcurveslikeapGen,?compassUUandF*renchcurvescan.NSupGerimposingcharacterscloselycandrawanycurve.LDisksgivedirectional?indepGendencecoflinethicknessandvisualsmoothnessatlargepitch.!DSmoothness?increasesywithoutputresolutionbutisalmostindepGendentofdiskpitchbGelow?aFcriticalmaximum.EJThefollowingtablesuggeststhismaximumvqariesfrom?0.34ptUUforan0.5ptthickcurveto3ptfora15ptcurve.R eLƍdNThickness29Magni edָComments%<LineUUat1/6slopGe^Nffb15ptE !", cmsy101o\1ptUUpitchdisksb< lcircle10~2Dh~՞~f8~Ѡu~pS~@0p~ ~;@~ծ̟Ȩ~~]~Mx~`~>H~ټ~ڌ2~[ßր~+T~P~vn~ޚL ~i)~9)~X~K~ܟ(~wm|~FY~7`~ ~浱0~BϘ~Tӟ~$dh~g~ÆE8~"~b~29p~ʟ~[@~u~p}S~@0x~ ~0H~Ȱ~~R~M~t`~>P~~' ~[ֈ~+I~ڟX~kn~L(~i)~9~`~@~џ0~wb|~FZ~7h~~8~7Ϡ~Tȟ~$Yp~g~{E@~ "~ b~15ptE1o\3ptUUpitchdisksb~ⳞV~b*~ⳟ~bUX~ⳟ~b~ⳟZ~b~ⳟ@~b\~ⳟj~b~ⳟ^~b*~ⳟ ~bU`~ⳟ~b ~ⳟb~b~ⳟ@~bd~ⳟj~ b~ qƸ0.5ptE1fL5ffA͉TU>'ExXUU\line(6,1)bO line10(bUV(b(b(bUX(b( qƸ0.5ptE1ht0.34ptUUpitchdisks`N9Zcmr5.ͷ5?. 1w.cɞ#.κ.]T.f.ϼ.;1.i.пϞo..lc.­L..oAv.ŋh).՟Y.rKg.i=...t D.G.!.w۟!.%.$o_.z..'M<.}.z.*+.؀us.ֿeW.- V.كSH.ٝ:4./+.چ1r.{.2ş.ۉO.Y.5Ս.܋,.7.8j.ݎ˟ ..;_G.ޑp.b.>=T$.ߔE.џ7b.A).e. ?.C.C}..Fןһ.!Z.k.I.7.I.L|u.ݟn.'_.OqQR.奻B.4.RO&/.標. m.U- .w.J.X .U.'.Z.3e.}.]ǟy.kB. 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XsmoGothness.NXCurveUUthicknessadjustablefrom0.5to15pt(0.17to5mm).NXCurvesUUhavecontinuousslopGe.NXCurvesUUforanynumbGerofpointsgreaterthanoneusing\curve.NXControlUUofendslopGesusing\tagcurve.NXClosedUUcurveswithcontinuousslopGeusing\closecurve.NXLargeUUcircles\bigcircleandcirculararcs\arc.NXIndepGendentUUscalingofcurveabscissaandordinatesto tgraphs.NXAneUUscalingformakingarcsorcircleselliptical.NXSymbGolsUUanddashpatternscombinedwithoutinterference.NXAnyUUdashlengthorspacing.NXThreeUUmethoGdsfor ttingdashpatternstocurves.ꍑNParabGolas:approximatethesegmentsbGetweenthespGeci edcoordinatepoints.?At#aninternalpGoint,ʗtheslopGeoftheparabolasjoiningfromeithersideisthe?sameERasthestraightlinejoiningthepGointsoneitherside.lqF*oranendsegment,?theinsidepGointoftheparabolaismadeavertexwhichdeterminestheslopGe?oftheendpGoint..~\tagcurvehashiddenendsegmentswhichallowscomplete?controlUUofslopGeatthevisibleendpointwhendesired.NThe$fourpGointsattheendandadjacenttoasegmentmaymakeaparabGola?inappropriate.qThepGointscouldbeclosetoastraightlineorconsistentwith?anin exionpGoint.-.Astraightlinethenreplacestheparabolaandoptionallya?warningUUisissued.NTherparabGolasaredrawnasaseriesofshortstraightlinesegments."F*or?curvesls.sty,thedvidriverdrawsthestraightlinesasinstructedby\special?commands.PF*orcurves.sty,6thestraightlinesaredrawnasoverlappingdisks?ffv J= "5-:6LSeeXyÎourLo "5-:7LMicÎhelvGoFJrankMittelbachandAlexanderSamarin,>XTheL"YApXTAEMXCompanion, Addison-WJesley,X1994.'|l?2 INST*ALLATION*4'?at )highspGeedusingasimpletailchasingmacro.YThismacro'sarithmeticcalcu- 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haveRnotchecked?compatibilityUUwithcurvesorcurveslsbGecauseIdonotusePIjCTU>'ExX.Ncurvesls.sty%'useslinedrawing\specialstoreducerequiredmemoryand?increase)spGeed.McAsoriginallysupplieditusesthe\specialsofemTU>'ExXbyEber-?hard/MattesforIBM/PCcompatibles.emTU>'ExX/isavqailablefromCT*AN^9#and?therTU>'ExXUsers'Group.ɜTheemTU>'EX\specialsarealsoavqailableforT*omas?Rokicki's)dvips.DIfyouusedvips,askiftheyhavebGeencompiledin.DT*ouse?otherlinedrawing\specialssubstitutethematcurvesls.sty'sstart.Y*our?system'ExXedwitheithercurvesorcurvesls.?ffv J= "5-:8LMicÎhaelIJ.Wichura,XTheP&c`I\nCTAEMXManual,Chicago,1987,availableIfromTAEMXUsers' Group. > "5-:9LDirectoryXS/tex-archive/systems/msdos/emtexatSftp.shsu.eduforexample.3l?3 CURVES*5'59LcgqxqxcBIh7R6 cmss12BOrX4qxcccg FigureUU1:qThisisabGox.NAdrawingfrequentlyusesauxiliarycommandstosize,place,labGelandcap- ?tionUUit.qThefollowingcommandsdrawthebGoxinFigure1onpage5:I\begin{figure}I\begin{center}I\setlength{\unitlength}{1mm}I\begin{picture}(100,50)?\large\sfI\linethickness{1mm}I\put(20,5){\framebox(60,40){BOX}}I\end{picture}I\end{center}I\caption{This?isabox.}I\label{box}I\end{figure}?LampGort^1βexplainsZ[thesecommands.Thisexampleisforthoseunfamiliarwith?theL5ffA͉TU>'ExXpictureenvironment._Thefollowingexamplesavoidthefigureenvi-?ronmentUUbutitisoftenessential.!č?3WLCurves?Thecurvedrawingcommands,f\curve,\closecurveƲand\tagcurve,fdraw?parabGola}segmentsbetween}coordinatepointsintheargument.A@Thesegments'?tangents&atthesepGointsareparalleltoeachotherandtostraightlinesthrough?thezpGointseitherside.SegmentsatcurveendsarefromparabGolasthroughtheBl?3 CURVES*6'?last}threepGoints.I\closecurveaddsaparabolabetween}endpointstoclosethe ?curve.J\tagcurve&ֲomitsthe rstandlastsegmentsdrawingcurveswithend?tangentsUUspGeci 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cmmi10:9781andsinG12^0:2079NAxonometric1pro8jectionisanotherscalingapplication.CirclesbGecomeel-?lipses?andcirculararcsbGecomeellipticalarcs. 3Thecommandsdrawingthe?ellipseUUandarcinthefollowingwasherare:I\put(20,5){S\renewcommand{\xscale}{1}S\renewcommand{\xscaley}{-1}pl?5 SYMBOLSf8'S\renewcommand{\yscale}{0.6} S\renewcommand{\yscalex}{0.6}S\scaleput(10,10){\bigcircle{10}}S\put(0,-2){^\scaleput(10,10){\arc(5,0){121}}^\scaleput(10,10){\arc(5,0){-31}}^}S}?(20,5)arethedrawingcoGordinatesoftheuppervertexofthewasherclosestto?theUUreader.qTheanglesforthe\arcswerefoundbytrialanderror.`Mavׄ̎b׀b̀bÀbbDբ:b$VR3̎gϡmbgɡmbgámbgmbgmb}b""" ""gբ:"Dϡm"Dɡm"ƘDám"ИDm"ژDm"}"v"v"v" v"v"gS"vb׀vb̀vbÀvbvbDSb1ޟR3̎y`.JE?..{.ޟƨ.Пt.FŸ@.ԟ.\D.ə.s š.zC..R.@*.r...'A͔.ﮆķ.5˟ġ|.ċp.DUud.˚_X.NW.fP.R̟IJ.2A.W:.3<.\d+.ʟ$.a0+.㖟3:.e:.bA.jȟIE..P.oW._P.y?u[.ċf.ɟġq.ķ|.S͇..ݟ.,".n4.Y. .k>=.jo<.ۥvǭS.@.܂;.xȃ.O.ٯ.JX.۟ɩ.رQ.d]K.ʛ.ߟ.~ =Y.I˗..>i.֟ϟҞ.g`;..ͤ.+.e~j.矟P.ٟX6.ո.5.ɟУ.ޜ.o.B. 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Ze."\ϟx."D.#P.#T..#.#.$KD.$.$w.%B%.%a98.%֟Lu.&:K_.&r.&5,.'1i.'.'֔.() .({~].(.) h .)rݟ .)R3Q.*ǟF.*j3ؙO4>[>5fG6 -7>[G8CentrelinesUUandSymbGols!č?7WLErrors?SyntaxE*errorslikeincorrectormissingpunctuationwhileusingcurveswillresult?inTU>'ExXorL5ffA͉TU>'EXerrormessages.ETheTU>'EXbGook^2MandL5ffA͉TU>'EXmanual^1Mexplainthe?meaningjandcorrectionoftheseerrors.ThepreviousexamplesandSection9?shouldUUmakethecorrectsyntaxforcurvescommandsclear.Ncurves#/willwriteaLaTeX?error.amessagetothescreenandlog leifyou?supplyUUanincorrectnumbGerUUofcoordinates.NIfvfoursequentialpGointsinadrawingcommandargumenthavetheline?throughUUthe rstandthirdparalleltothelinethroughthesecondandfourth:NXexactlyorclosely*,RcurvesknowsitcannotdrawaparabGolatangenttotwoXparallelUUlines,issuestothescreenandlog le:XLaTeX?Warning: \curvestraightfrom...XandUUdrawsastraightline;NXormapproximately*,&curvesmaydrawanunexpGectedcurvewithnowarning. Nl?8 PLEASUUFORTHEFUTURE?12'?IffoursequentialpGointsinadrawingcommandargumenthavethelinethrough ?theUU rstandsecondparalleltothelinethroughthethirdandfourth:NXcurvesUUdrawsaparabGolawhichmaybGenowherenearthecurve.?IfthefourpGointswereonastraightline,XremovingoneormorepGointsisa?remedy*."IfFtheyarenotonastraightline,addingpGointsmayhelp."SpGecifying?manypGointswillgiveyouasatisfactorycurvewithpGerhapsanannoyingnumbGer?of\curve?straightwarnings.PAftera\curvewarnfalse,curvesstillusesthe?straightUUlinesbutdoGesnottellyou.NCurvqature#changessignoncurveslikey"=sin޵x.a:SpGecifyingin ectionpoints?as)curvecoGordinateswillreduceerrorandspecifyingsucientcoordinateswill?then^5givesatisfactoryresults.hF*ordiscontinuoustangentssplittingacurveinto?piecesisunavoidable.GQSplittingacurveintopieceswithcurvqaturethesamesign?can8givesatisfactoryresultswithfewercoGordinates.q\tagcurvecanprevent?tangentdiscontinuities.Ifanin exionpGoint'sexactloGcationisunknown,>=try?theUUmidpGointofthestraightlinethroughtheendsofitssegment.NCurvesiappGearrougherthanhorizontalandverticallines.Picturedigitiza-?tionicausesthisnotinaccuracyinTU>'ExX,ncurves.styorcurvesls.sty. Setting?\diskpitchstretchPtoavqaluelessthanonewith\renewcommandmaysmoGoth?anUUunusuallyroughcurve.NSymbGols%andsymbGolspacesmisalignedareusuallyduetoroundingerror.?Adjusting2\diskpitchstretchbGelowonecanreduceroundingerrorandin-?creasealignmentaccuracy*.\ThisshouldbGelimitedtothemisalignedcurvewith?f?g^1|s.NTheMreplacement\bezierdoGesnotgiveexactlythesameresultsasthe?originalinbezier.styorinLaTeX2e.7Thedi erenceisextremelysmallbutifit?isVimpGortanttoyoucommentoutthe velinesofcoGdefor\bezierand\@bezier?nearǍthestartofcurves.styorcurvesls.sty.BY*ounowhavea\bezierwhich?is"slowerandneedsmorememorybuthasonlyitsoriginalcapabilitiesandgives?onlyUUitsoriginalresults.NPleaseemailmeexamplesofanyerrorsnotcoveredabGove.Y*oumayhave?foundUUabuginthecoGdeordocumentation.!č?8WLPleasfffortheFfuture?curvesdwillneverworkwithplainTU>'ExXanditwillneverbGeaspowerfuldasMET*A-?FONTRorbimpGortingencapsulatedPostScript les.+Suggestionsorcriticismsby?emailNarewelcome.TV*ersion1.41hasbGene ttedgreatlyfromprevioushelp.The?latestUUversionsare rstavqailableatURL:D?ftp://ilm.mech.unsw.edu.au/pub/latex/macros/curves/ )l?9 CURVESUUSUMMAR*Yꝲ13'?ThexNIPxEnumbGeris149.171.228.99butuseyourloGcalCT*ANxEmirrortoreduce ?InternetUUload.Ncurvesls.stypbusesmuchpblessTU>'ExXmemoryandisfasterthancurves.sty.?MoreZRpGeoplecouldusecurvesls.styifemTU>'ExXorequivqalentlinedrawing?\specialsNwerecompiledintodvidriversforviewingandprinting.6Askyour?systemUUpGeopleforthis!NA1.dvi1ϲ lecontainingcurvesproGducedwithcurvesls.styhasmanyoGc-?currencesofthetextstringsem:lineto,em:movetoandem:linewidth?XXXXpt?placedd'bytheemTU>'ExX\specials.>ThesestringswouldhaveearlieroGccupied?TU>'ExXmemory*.OKExtraspaceisalsotakenbythediskscurveslsusestocoverthe?cracksbGetweensquarelineendsataslightangle.Renamingthese\specials?to{IL,MzandW?XXXXptrespGectivelywouldsaveTU>'ExXmemory*.EvenbGetter,W?XXXXpt5couldalsocalculateandstorethebitmapofadiskwhichL&wouldadd?toitslineendtorounditsocurveslsneednotadddiskstocovercracks.A?fourth\special,ɇD,couldplacethediskatthecurrentpGositionwhichcurvesls?wouldusetoroundthebGeginningofacurve.ppIfyouwritedvidrivers,*please?addUUthesefourpropGosed\specials.!č?9WLCurvesffSummary?ThecommandsfollowingareforthepictureenvironmentintheL5ffA͉TU>'ExXmanual^1|s.6?5N cmbx129.1]ArgumentsofCommandsuT?UUdecimalnumbGerUUofblank.qNotnegative.?UUisanythingwhicha\putor\multiputmaydraw.?FaredecimalnumbGersFgivingalternatexandyزcoordinatesof NtheUUcurveasmultiplesof\unitlength,commaseparated.?<[,dash...]>i߲optionalcontinuationiofalternatingdashandblanknumbGersiofNunitUUlengths,commaseparated.qNotnegative.AllowsUUdecimalpGoints.?UUisadecimalnumbGerUUgivingthediameterin\unitlengths.?UUisthenumbGerUUofsymbolsorpatternstobedrawn,default0.?unitlengthdimensione.g.,2.5mm,10pt,usedinmeasuringblanksNandUUdashes.qNotnegative.Defaultvqalueis\unitlength.6?9.2]LengthsusedbyCommandsuT?\csdiameterFisthesizeofthespaceleftforasymbGolandcanbeincreasedorNsetUUwith\settowidth{\csdiameter}{}.?\curvelengthwisthetotallengthofthecurvecalculatedbGeforedrawingbyusingNSimpson'sUUruleoncebGetweenUUeachpairofcoGordinatepoints.7 l?9 CURVESUUSUMMAR*Yꝲ14'?\overhangUUlengthofasdrawndashpatternoverlappingstartofpatterns.?9.3]ControlCommandsuT?\curvewarntrue۲turnswarningofparabGolareplacementbystraightlineson N(default).$?\curvewarnfalseUUturnswarningofparabGolareplacementbystraightlineso .?9.4]ParameterSettingCommands?\curvesymbol{}UUsetssymbGoland\csdiameter.$?\curvedashes[]{<[,dash...]>}jAMdrawingcom- NmandibGeforea\curvedashesorafteronewithanemptyorzerolengthNpatternUUwilldraw:HNifUUiszeroormissing,acontinuousUUcurve; $NelseifispGositive,-1squaresoflinethick-]nesssizebGetweenandadditionalsquaresatcoordinatesorbezierend]pGoints;NelseUUifnoUUexists,nothing;Nelse,&--1charactersorsymbGolsbetweencoordinatesand]additionalUUonesatcoGordinatesorbezierendpoints.HNAfter^a\curvedashescommandde ningapatternwhoselengthexceedsNzero,UUcommandsdraw:NifͮiszeroormissingthenataspacingequaltothespGeci ed]patternUUlength,H]ifҨnoҨexists,adashpatternreducedinlengthlbyUU\csdiameterto tbGetweensymbGolspacesof\csdiameter, $]else+Fif\overhangisnot0pt,3a+FatallpGositions,]elseUUaUUwiththe rstpGositionblank;Nelse, \csdiameterwidesymbGolspaces,oneatand||-1 ]bGetweenUUcoordinatepointswithdashpatternlengths,]ifUUnoUUexists,exactbutbrokenbythespaces,]else,UUadjustedtogiveawholenumbGerofpatternsbetweenUUspaces.l?\diskpitchstretch&*isinitially1but\renewcommandcanchangeittoahigherNvqalue"like5tosavememoryindraftsofcomplexdoGcumentsoralowerloGcalNvqalueUUlike0.5tosmoGothcurvedigitization.$?\linethickness{}Usetslineordashthicknessestofrom0.5ptupNto15pt(0.17mmto5mm).:\thicklinesand\thinlinesalsosetthickness.?\xscale,\xscaley,\yscale̲and\yscalexarescalefactorsinitiallysetto1,N0,UU1and0respGectivelywhich\renewcommandor\defcanreset.Cl?9 CURVESUUSUMMAR*Yꝲ15'?9.5]CurveDrawingCommandsuT?CurvessdrawnconsistofparabGolicarcsbetweencoGordinatepointswithtangents ?atUUeachpGointparalleltothestraightlinethroughadjacentpGoints.?\arc[](X1,Y1){}Jdrawsacirculararccentredoncur-NrentvpGosition,Dstartingfrom(X1,Y1)andproceedingcounterclockwisevforNUUdegrees.?\bezier{}(X1,Y1)(X2,Y2)(X3,Y3)b:drawsacurvethroughtheNendppGoints(X1,Y1)and(X3,Y3)tangenttothestraightlinesjoiningeachNofUUthemto(X2,Y2).qExtendedfasterreplacementforbezier.styversion.?\bigcircle[]{}ydrawsacircleofdiameterequalNtoUUtimes\unitlength.?\closecurve[]()drawsaclosedcurvewithNcontinuousUUtangentsatallpGoints.qAtleast6coGordinatesrequired.?\curve[]()RdrawsacurvethroughthespGeci-N edUU.qF*or4coGordinatesthisisastraightline.?\scaleput(X1,Y1){}>placesapictureob8jectinapGositionNscaledhby\xscale,l\xscaley,\yscalehand\yscalexforaxonometricpro-NjectionUUorrotations.?\tagcurve[]()>drawsacurvewithoutits rstNandUUlastsegmentsbutifonly6coGordinatesdrawsthelastsegmentonly*.OW;l Y8)cmsl8X8)cmsl8SCscmtt8M- cmcsc10I߆TG cmtt12>DtGGcmr17 cmmi10K`y cmr10ٓRcmr7Zcmr5< lcirclew10< lcircle10O linew10O line10V@