字符的计算机处理与显示 外文翻译

本科毕业设计（论文）外文翻译英文翻译1英文ONCOMPUTERISATIONANDREPRESENTATIONOFCHARACTERSTHECOMMERCIALNEEDTOCOMPUTERISECONTOURSOFOBJECTSHASINTENSIFIEDOVERRECENTYEARSASMOREANDMOREAPPLICATIONSENDEAVOURTOSEEKTHEBENEFITSOFVISUALISATIONTHEPRIMARYAIMHASBEENTOGAINACOMPUTERISEDMODELWHICHCLOSELYRESEMBLESTHEORIGINALSHAPEANDFORMTHEDIGITALFORMLENDSITSELFTOBEPROCESSEDBYFASTPROCESSORS,ANDTHEIROUTPUTTOBEDISPLAYEDONGRAPHICDEVICESSUCHASSCREENDISPLAYSANDLASERPRINTERSTHEBENEFITSOFTHEDIGITALFORMAREALSOEXTENDEDTOCATERFORNUMERICALLYCONTROLLEDMACHINESTHESEAREEMPLOYEDTOPRODUCEOUTLINESTHROUGHCUTTINGORENGRAVINGONPAPER,METAL,PLASTICORWOODWHENITCOMESTODIGITLINGTHEOUTLINESOFCHARACTERS,ADDITIONALCONSIDERATIONSHAVETOBEINCLUDEDINTHEMODELLING,DESIGN,PHASETHEAIMOFTHESEISTOCAPTURETHEUNIQUENESSANDTHEDISTINCTFEATURESOFAFONT,WHICHTRADITIONALLYWEREREALISEDBYAPROFICIENTARTISANSHANDANDEYEMODERNAPPROACHESENDEAVOURTOGAINTHESAMEIMPACTBYUSINGASETOFPREDEFINEDSPECIFICATIONSINTHEDESIGNPROCESSTHEGOALOFWHICHISNOTJUSTTOMODELACCURATELYADESIREDFONT,BUTALSOTOENSURETHATTHEDISPLAYEDVERSIONISBOTHLEGIBLEANDAESTHETICALLYACCEPTABLETHISPAPERPROVIDESANINSIGHTABOUTTHEDESIGNMETHODSUSEDTOBOTHMODELANDREPRESENTTHECONTOURSOFLATINCHARACTERSANDFONTSITDESCRIBESTHEROLEOFTHESPLINEASAMEANSOFREALISINGTHEMODELLINGASPECTTOTHISREGARD,THESPLINEDESCRIPTIONSUSEDBYPOSTSCRIPTBCZIERCUBICANDTRUETYPEPARABOLICARELOOKEDAT,ANDACOMPARATIVEANALYSISMADETHEDISCUSSIONTHROUGHOUTISLEVELLEDATPROVIDINGAPRACTICALUNDERSTANDINGOFTHESUBJECTMATTER10INTRODUCTIONTHEQUESTFORANACCURATEANDAESTHETICALLYACCEPTABLEREPRESENTATIONOFOUTLINESOFSHAPEHASTRADITIONALLYBEENUNDERTAKENBYEXPERIENCEDARTISANSTHEYPRODUCEDDESIREDRESULTSBYUSINGASKILLEDHAND,HAVINGANEYEFORFINEDETAILANDANAPPRECIATIONOFTHETYPEANDFORMOFTHESHAPEITSELFTHISPROCESSOFGENERATINGOUTLINESFOUNDPOPULARITYINTHEFIELDOFTYPOGRAPHY,WHEREANEXACTPRODUCTIONANDREPRODUCTIONOFCONTOURSOFCHARACTERSISREQUIREDTHETASKFORTHETYPOGRAPHERWASNOTJUSTTODRAWAGIVENOUTLINE,BUTALSOTOCAPTURETHEDISTINCTFEATURESOFAPARTICULARFONTTYPETHISMANUALPROCESSOFMODELLINGCHARACTEROUTLINESBECOMESRATHERTEDIOUSANDTIMECONSUMINGWHENONEREALISESTHATTHEREARETHOUSANDSOFLATINFONTTYPESAVAILABLE,EACHCOMPRISINGOFATLEAST100CHARACTERSWITHTHEARRIVALOFCOMPUTERS,ATTEMPTSHAVEBEENMADETOAUTOMATETHEDESIGNPROCESSTHISHASRESULTEDINSOFTWAREPROGRAMSUNDERTHEHEADINGSOFCOMPUTERAIDEDDESIGNCAD,MANUFACTURECAMANDGEOMETRICDESIGNCAGDBEINGDEVELOPEDTHEMODEMTYPOGRAPHERUSESAPARTICULARDESIGNPACKAGETOCAPTUREANDMODELADESIREDFONTTHEPROCESSWORKSWITHSOMEPREDEFINEDSPECIFICATIONS,ENSURINGTHATTHEMODELLEDIMAGEEMBODIESTHEDESIREDFONTFEATURESINVIEWOFMODEMCOMMERCIALREQUIREMENTSFORAFASTANDACCURATEMEANSOFCOMPUTERISINGAGIVENOUTLINE,MOSTDESIGNSYSTEMSMAKEUSEOFAMATHEMATICALDESCRIPTIONTHISHASTHEATTRACTION,WHENCOMPAREDTOTHEMANUALAPPROACH,OFPROVIDINGAMODELLEDIMAGEATAFASTERRATEANDYIELDINGWITHIN,ANDBETWEEN,DESIGNSYSTEMSINADDITION,THERESULTINGIMAGEISINAFORMWHICHCANBETRANSFORMEDTRANSLATED,ROTATED,SCALEDFTCWITHOUTDISTORTIONBYUSINGASIMPLEANDANAPPROPRIATEDMATRIXTHESIMPLESTMATHEMATICALDESCRIPTIONMAKESUSEOFSTRAIGHTLINESEGMENTSFROMPOINTTOPOINTAROUNDTHEOUTLINEANEXAMPLEOFTHEAPPROACHISDEPICTEDINFIG1CLEARLY,ITCANBESEENTHATTHERESULTINGMODELGIVESACOARSEREPRESENTATIONOFTHEORIGINALMOREDATAPOINTSANDTHUSLINESEGMENTSWILLBEREQUIREDTOYIELDTHEDESIREDOUTCOMEEVENTHEN,ITISNOTCERTAINWHETHERTHERESULTINGREPRESENTATIONWOULDBEACCEPTABLEFORAESTHETICREASONSANOTHERSHORTCOMINGWITHTHELINEMODELLINGAPPROACHISTHEAMOUNTOFCONTINUITYITGIVESBETWEENJOININGSEGMENTSASITSTANDS,THESYSTEMCANATMOSTPROVIDEZEROCONTINUITY,ENSURINGONLYTHATTWOSEGMENTSWILLTOUCHEACHOTHERFORAPRACTICALSOIUTION,MOSTDESIGNSYSTEMSEMPLOYACURVEDESCRIPTIONTHETYPEOFDESCRIPTIONEMPLOYEDPRIMARILYDEPENDSONTHEAMOUNTOFCONTINUITYREQUIREDCURVESLABELLEDAS“QUADRATICS”SUCHASTHECIRCULAR,ELLIPTIC,PARABOLICANDHYPERBOLICARCSCANGIVETANGENTCONTINUITYWHILST“CUBIC”CURVESCANPROVIDECURVATURECONTINUITYFIG2GIVESASUMMATIVEILLUSTRATIONOFTHESEPROPERTIESHIGHERORDEREDDESCRIPTIONSCANPROVIDEBETTERCONTINUITY,BUTTHISISACHIEVEDATTHEEXPENSEOFCOMPUTATIONALEFFICIENCYANDMODELLINGCONVERSIONRATESFORREASONSOFSIMPLICITY,THEREFORE,CURVEDESCRIPTIONSABOVECUBICORDERARENORMALLYNOTUSEDTOMODELOUTLINESOFSHAPE,INCLUDINGTHATOFCHARACTEROUTLINESWHENCURVEDESCRIPTIONSAREUSED,THEYAREUSUALLYREFERREDTOASSPLINESTHETERMSPLINEORIGINATEDWELLBEFORETHEDAYSOFCOMPUTERGRAPHICS,WHENANOUTLINEWASCONSTRUCTEDBYMEANSOFSOMEWEIGHTSANDAFLEXIBLEMATERIALTHEWEIGHTSALSOCALLEDDUCKSWERELOCATEDTOSHAPETHEFLEXIBLEMATERIALSUCHASWOODTOYIELDADESIREDOUTLINETHEPROCESSISIILUSTRATEDINFIG3,WHEREATHINELASTICMATERIALCALLEDTHE,PHYSICAL,SPLINEISBENTAROUNDSOMEWEIGHTSSUCHMETHODSHADAPPLICATIONSINTHECONSTRUCTIONOFSHIPHULLSANDAIRCRAFTFUSELAGESSPLINESUSEDFORTHEMODELLINGANDGENERATIONOFSHAPEOUTLINES,SUCHASCHARACTERCONTOURS,MAKEUSEOFSIMILARPROPERTIESINTHISPAPER,THEFEATURESRELATINGTOTHETWOMOSTACCEPTABLEDESCRIPTIONS,NAMELYTHEBTZIERCUBICANDTHEPARABOLIC,AREANALYSEDSOMEINSIGHTTOHOWINEACHCASEAMODELISGAINEDANDTHEWAYITMAYBEDISPLAYEDONAFINITERESOLUTIONDEVICEISGIVENTHEPAPERALSOPROVIDESACOMPARATIVEANALYSIS,INSUMMATIVEFORM,OFBOTHDESCRIPTIONS,ANDAIMSTOGIVEAMOREPRACTICALTREATMENTOFTHESUBJECTMATTERTHANOTHERWISE20MODELLINGBYBEZIERCUBICSPLINESTHECLOSESTMATHEMATICALDESCRIPTIONTOTHENATURALPHYSICAISPLINEISREALISEDBYMEANSOFTHECUBICFORMTHISEMBODIESTHENECESSARYFLEXIBIFITYTOPERMITATWISTWITHINITSCONSTRUCTIONVARIOUSCUBICFORMSEXIST,THOUGHTHROUGHTHEPOPULARITYOFTHEPOSTSCRIPTLANGUAGE,THEBEZIERSPLINEHASGAINEDEMPHASISANDISREGARDEDASONEOFTHEPRIMARYDESCRIPTIVETYPESFORMODELLINGFONTOUTLINESABEZIERCUBICCURVESEGMENTCONSISTSOFFOURPOINTSTWOENDPOINTSOFTENCALLEDANCHORORKNOTPOINTSANDTWOCONTROLPOINTSTHEKNOTPOINTSLIEONTHEORIGINALOUTLINEANDAREINTERPOLATEDWHILSTTHEPOSITIONINGOFTHETWOCONTROLPOINTSDETERMINESTHEOVERALLSHAPEOFTHESEGMENTINTHERATIONALPARAMETRICFORM,EACHPOINTALSOHASATENSIONPARAMETERSOMETIMESREFERREDTOASTHEWEIGHTASSOCIATEDWITHITWEIGHTSATTHEKNOTPOINTSARECALLED“POINTTENSIONS”ANDAREUSEDTOSMOOTHOUTACURVESHAPETHEWEIGHTSATTHECONTROLPOINTSAREUSUALLYLABELLEDAS“INTERVALTENSIONS”ANDAREAVAILABLETOTHEUSERTOEITHERPULLOUTWARDSORPUSHINWARDSTHERESPECTIVECURVESHAPETAKINGTHENONRATIONALPARAMETRICFORMFORTHEBEZIERCUBICASANEXAMPLE,THEMODELLINGOFOUTLINESISREALISEDTHROUGHTHREEPHASESTHEFIRSTPHASEATTEMPTSTOFINDASUITABLERELATIONSHIPBETWEENTHEPARAMETRICVARIABLEUSEDINTHEDESCRIPTIONANDTHEGIVENOUTLINETHESECONDPHASECALCULATESRESPECTIVEVALUESFORTHECONTROLPOINTS,WHILSTTHETHIRDSTAGEEVALUATESBOTHTHEGOODNESSOFFITANDALSOUPDATESTHERELATIONSHIPAPPROXIMATEDINPHASEONETHEWAYTHESEPHASESARECONNECTEDTOFORMAMODELLINGALGORITHMISSHOWNINFIG4ALTHOUGHTHEABOVEDESCRIBEDAPPROACHYIELDSTHEDESIREDMODEL,ITDOESSOATAPRICEHOKINGATFIG4,ITCANBESEENTHATTHEALGORITHMUSESBOTHRECURSIVEANDITERATIVEMEANSTOPROVIDEANOUTPUTTHIS,INPRACTICE,MEANSTHATASIGNIFICANTAMOUNTOFTIMEWILLBEREQUIREDTOCOMPUTEANOUTPUTTHESITUATIONDETERIORATESIFMORETHANONESEGMENTWILLBENEEDEDTOMODELTHEGIVENOUTLINEOPTIMISATIONOFTHEALGORITHMISOFTENADDRESSEDTHROUGHIMPROVINGEACHOFTHETHREESTAGESMENTIONEDFARINDISCUSSESSOMEOFTHETECHNIQUESEMPLOYEDFORGAININGINITIALVALUESFORTHEPARAMETRICVARIABLETHEVALUESFORTHETWOUNKNOWNS,THECONTROLPOINTS,CANBEEVALUATEDBYMEANSOFALEASTSQUARESAPPROACHTHEFINALSECTIONCANBEATTAINEDBYAVARIETYOFWAYS,ANOTABLECONTRIBUTIONTOTHISAREAISBYPLASSANDSTONE30MODELLINGBYPARABOLICSPLINESTHEPARABOLICARCBELONGSTOTHEFAMILYOFCONICS,WHICHALSOINCLUDESTHEELLIPTIC,HYPERBOLICANDCIRCULARSPLINEBEINGQUADRATIC,THEYMODELUSINGONELESSPARAMETERTHANTHECUBICCASETHEGENERALCONICDESCRIPTIONITSELFCOMPRISESOFTWOKNOTPOINTS,ONECONTROLPOINTANDATENSIONHENCEFORTHREFERREDTOASTHESHARPNESSPARAMETERVARIATIONINTHESHARPNESSVALUEYIELDSANAPPROPRIATECONICZEROTOONEFORANELLIPTICSECTION,ONEFORPARABOLICARC,ANDBETWEENONEANDINFINITYFORAHYPERBOLICCURVETHEFACTTHATTHESHARPNESSEQUALSONEFORTHEPARABOLICCASEMAKESITATTRACTIVETOUSETHETRUETYPEFONT,DEVELOPEDBYAPPLE,EMPLOYSTHISDESCRIPTIONFORTHEREASONGIVENABOVEANDFORTHEFACTTHATTHEREISAONETOONEMAPPINGBETWEENACUBICANDAQUADRATICMODELINTHISCASETHEFORMULATIONOFAPARABOLICANDTHEGENERALCONICDESCRIPTIONISVIAAGUIDINGTRIANGLEASSHOWNINFIG5,THISISREALISEDTHROUGHTHETWOKNOTTANGENTSWHICHINTUMINTERSECTWITHEACHOTHER,PROVIDINGTHELOCATIONFORTHEDESIREDCONTROLPOINTONCETHECONTROLPOINTISKNOWN,THECURVESEGMENTCANBEGENERATEDUSINGTHEAPPROPRIATEPARAMETRICEQUATIONALTHOUGHSIMPLERINDESCRIPTIONTHANTHEGENERALCONICSHARPNESSEQUALSONE,THEMOSTECONOMICALWAYOFREALISINGAPARABOLICMODELISVIAITSASSOCIATIONWITHITSCONICFAMILYINFACT,ASMANIFESTEDINFIG6,THEAPPROACHREQUIRESTHATACONICMODELBEGAINEDFIRSTTHISISTHENASSESSEDTOSEEHOWCLOSEITISTOTHEPARABOLICCASEIFTBECOMPARISONISACCEPTABLETHENASOLUTIONHASBEENFOUNDANDTHECONICCONTROLPOINTISRECORDEDIFTHEQUALITYOFFITNEEDSIMPROVINGTHENTHECONICISSPLITANDMODELLEDBYTWOORMOREPARABOLICARCSTHISMAYSOUNDALENGTHYPROCESS,BUTINREALITYITISMUCHFASTERTHANTHECUBICCASETHECONICANDTHEPARABOLICMODELSAREGAINEDBYMEANSOFADIRECTAPPROACH,WITHOUTTHENEEDFORITERATIONORRECURSIONTHISAMOUNTSTOONAVERAGEABOUTFIVETIMESFASTERCONVERSATIONRATESTHANFORTHECUBIC40COMPARISONOFSPLINESWHENATTEMPTINGTOCOMPUTERMODELAGIVENFONTOUTLINE,THECRITICALQUESTIONOFWHICHMATHEMATICALDESCRIPTIONTOEMPLOYOFTENARISESVARIOUSFACTORSSUCHASTHEFORMOFTHESUPPLIEDDATA,THELEVELOFCONTINUITYDESIREDBETWEENJOININGARCS,THETECHNIQUESOFEVALUATINGGOODNESSOFFITANDSOFORTH,ARECOMMONCONSIDERATIONSTHEDECISIONTOUSEBKIERCUBICORPARABOLICSPLINESISMADEWITHSIMILARTHOUGHTSANDOBSERVATIONSBOTHDESCRIPTIONSHAVECERTAINATTRACTIONSANDANUMBEROFSHORTCOMINGSTHEMAINATTRACTIONFORTHEBKZIERCUBICSPLINEISTHATITHASANINHERENTCAPABILITYTOTWISTWITHINASINGLESEGMENT,FACILITATINGATMOSTTWOPOINTSOFINFLECTION,ACUSPANDALOOPITSHOULDBENOTEDTHAT,INPRACTICE,OUTLINESEXHIBITINGSUCHFEATURESARESELDOMCAPTUREDUSINGASINGLESEGMENTTHEYARENORMALLYSPLITANDMODELLEDBYTWOORMORESPLINESTHEOTHERAPPEALFORUSERSTOEMPLOYTHEBBIERCUBICSPLINEISTHEPOSSIBILITYOFCURVATURECONTINUITYATTHEJOININGKNOTSALTHOUGHTHISMAYIMPROVETHEAESTHETICOUTLOOKOFAMODELLEDCHARACTER,ITALSOINCREASESFURTHERTHECOMPUTATIONNECESSARYTOGAINANACCEPTABLEREPRESENTATIONINCOMPARISON,THEPARABOLICSPLINEDOESNOTINHERENTLYEXHIBITTHEPROPERTIESOFCURVATURECONTINUITYORTHATOFBEINGABLETOTWISTTHROUGHSPACETHELATTERRESTRICTSASINGLEARCTOMODELLINGOUTLINESWHICHDONOTPOSSESSINFLECTIONPOINTS,CUSPSORLOOPSASMENTIONEDABOVE,THISISNOTASIGNIFICANTLOSSINPRACTICETHERATEATWHICHANOUTLINESCONTOURCANBEMATHEMATICALLYDESCRIBEDFORMSANINTEGRALPARTOFDESIGNTHEFACTTHATITERATIVETECHNIQUESAREREQUIREDFORTHECUBICCASERESULTSINARATHERTIMECONSUMINGENVIRONMENTTHEPARABOLICHASTHEATTRACTIONOFPROVIDINGADIRECTSOLUTION,WITHOUTITERATIONAPARABOLICMODELISINPRACTICEGAINEDATONLYONEFIFTHOFTHETIMEREQUIREDTOGAINACORRESPONDINGBEZIERCUBICREPRESENTATION2中文字符的计算机处理与显示近几年计算机处理物体的轮廓的趋势越来越明显，很多应用者也在寻求更多利益。轮廓处理的最初目的是产生和实体形状相似度很高的计算机模型。数传形式本身可以被处理器快速处理,而且可以在荧屏或激光打印机等装置上显示输出。数传形式还可以应用于数控机器，用以切割或雕刻金属、塑料、木材的轮廓。涉及到字体轮廓的建模、设计和逐步运行时需考虑到数字化的问题。在获取字体的特征方面，传统上是藉由工匠的手和眼睛，而现代则是在设计过程中使用预定义的规范来实现，这样既可以准确地对字体建模又可以使字体的显示清晰美观。1绪论工匠们一直都在探索怎样准确美观地表现物体的轮廓。他们藉由手和眼睛获得形体本身的细节、类型、形状。印刷业需要精确地生成和复制字体，所以字体轮廓的产生过程得到了广泛应用。印刷工人不仅要画出要求的轮廓而且要获得特定字体的特征。数以千计的拉丁字体被应用，每一种又包括至少100个字符，这也使得字符轮廓的建模沉闷费时。计算机的产生实现了程序设计的自动化，归因于CAD、CAM、CAGD等软件的发展。现代印刷业使用特定的设计包对所需字符进行建模，在此过程使用预定义的规范以确保模型能够切实地反应所需字体的特征。现代经济发展要求指定轮廓能够快速精确地计算机化，所以大多设计系统使用数字化描述，这相对手工操作有很大的优势。在模拟图像和设计系统之间可以快速高效地操作，另外图象可以通过简单可行的矩阵不失真地进行转换。简单的数学描述是应用点和点之间的直线段来生成轮廓。如图一所示，可以看出产生的模型大致体现了原始字符，结果的生成需要很多的点和线段，但是不确定结果在美学方面能否被接受图一用直线段描述字符“S”的轮廓直线逼近的另外一个缺点是连接线段的连续性，系统只是零点连续确保两段连在一起，所有实际应用时大多数的设计系统应用曲线逼近，描述类型的选择主要取决于连续性要求。“二次曲线”例如圆、椭圆、抛物线、双曲线可以实现切线方向的连续性，“三次曲线”可以实现曲率的连续性，如图二所示图二两个连接段连续性提高描述的连续性就相对降低了计算的效率和模型转换的效率，所以字符外形的轮廓通常不用三次曲线来模拟。描述应用的曲线通常被称为多项式曲线。多项式曲线产生于计算机绘图之前，可以由重力和柔软性材料创造的轮廓来描述，重力压制柔软材料成型以获得所需轮廓，这种方法已经应用于轮船壳体和航空器机身的制造中，图三显示了弹性材料被重力挤压弯曲的过程。多项式曲线可以应用于形体轮廓的建模和生成，字体轮廓也是相似的原理。图三用重力和柔软性材料说明曲线的构造在形体轮廓例如字符轮廓的建模和生成时应用的多项式曲线具有相同的原理。在这篇论文中主要涉及到两种合适的描述，即BEZIER三次曲线和PARABOLIC曲线。主要研究每种曲线怎样建模以及在指定装置上显示。论文同时也给出了比较性分析，有很大的实际应用作用。材料2BEZIER三次曲线建模最接近多项式曲线的数学描述是三次曲线。虽然有很多的曲线形式，但是重要的是BEZIER曲线，而且被认为是字体轮廓模型主要的描述类型。一条BEZIER三次曲线由四个点组成两个端点（通常被称作锚点或节点）和两个控制点。节点取决于原始轮廓并且是以内插值替换的，两个控制点决定了曲线形状。在有理数参数形式下，每个点都