歐洲道路標準13201-3-1

EN13201-3Edition:2007-06-01路燈第三局部：性能計算RoadlightingPart3:CalculationofperformanceNationalForewordThepresent?NORMENhasbeenreissuedwithoutpriorpublicenquiryandrepresentsaconsolidatednationalneweditionofEN13201-3:2003-11,includingCorrigendumEN13201-3:2003/AC:2007-02.TheprecedingEuropeancorrigendumEN13201-3:2003/AC:2005-06hasbeenconsideredandincorporatedinthisversionof?NORMEN13201-3.Followingclauseswerechanged:Ad7.1.5:Figure11wasreplacedTextafterfiguretitlewasaddedAd7.2.2:Equation(35)wasincludedEnglishversionRoadlighting-Part3:CalculationofperformanceThisEuropeanStandardwasapprovedbyCENon1September2003.Thiscorrigendumbecomeseffectiveon22June2005.Thiscorrigendumbecomeseffecticeon28February2007.CENmembersareboundtocomplywiththeCEN/CENELECInternalRegulationswhichstipulatetheconditionsforgivingthisEuropeanStandardthestatusofanationalstandardwithoutanyalteration.Up-to-datelistsandbibliographicalreferencesconcerningsuchnationalstandardsmaybeobtainedonapplicationtotheManagementCentreortoanyCENmember.ThisEuropeanStandardexistsinthreeofficialversions(English,French,German).AversioninanyotherlanguagemadebytranslationundertheresponsibilityofaCENmemberintoitsownlanguageandnotifiedtotheManagementCentrehasthesamestatusastheofficialversions.CENmembersarethenationalstandardsbodiesofAustria,Belgium,Bulgaria,Cyprus,CzechRepublic,Denmark,Estonia,Finland,France,Germany,Greece,Hungary,Iceland,Ireland,Italy,Latvia,Lithuania,Luxembourg,Malta,Netherlands,Norway,Poland,Portugal,Romania,Slovakia,Slovenia,Spain,Sweden,SwitzerlandandUnitedKingdom.ContentspageForeword4Introduction51Scope52Normativereferences53Terms,definitions,symbolsandabbreviations53.1Termsanddefinitions53.2Listofsymbolsandabbreviations84Mathematicalconventions105Photometricdata105.1General105.2The_-table105.3Interpolationinthe_-table125.3.1General125.3.2Linearinterpolation125.3.3Quadraticinterpolation135.3.4QuadraticinterpolationintheregionofC=0_,or_=0_or180_155.4Ther-table155.5Interpolationinther-table186Calculationof_(C,_)196.1General196.2Mathematicalconventionsfordistancesmeasuredontheroad196.3Mathematicalconventionsforrotations206.4CalculationofCand_217Calculationofphotometricquantities227.1Luminance227.1.1Luminanceatapoint227.1.2Totalluminanceatapoint237.1.3Fieldofcalculationforluminance237.1.4Positionofcalculationpoints247.2llluminance297.2.1General297.2.2Horizontalilluminanceatapoint297.2.3Hemisphericalilluminanceatapoint297.2.4Semicylindricalilluminanceatapoint307.2.5Verticaliluminanceatapoint317.2.6Totalilluminanceatapoint327.2.7Fieldofcalculationforilluminance337.2.8Positionofcalculationpoints337.2.9Luminairesincludedincalculation347.2.10llluminanceonareasofirregularshape358Calculationofqualitycharacteristics358.1General358.2Averageluminance358.3Overalluniformity358.4Longitudinaluniformity358.5Thresholdincrement358.6Surroundratio368.7Measuresofilluminance398.7.1General398.7.2Averageilluminance398.7.3Minimumilluminance408.7.4Uniformityofilluminance409Ancillarydata40Bibliography41ForewordThisdocument(EN13201-3:2003)hasbeenpreparedbyTechnicalCommitteeCEN/TC169“Lightandlighting”,thesecretariatofwhichisheldbyDIN.ThisEuropeanStandardshallbegiventhestatusofanationalstandard,eitherbypublicationofanidenticaltextorbyendorsement,atthelatestbyMay2004,andconflictingnationalstandardsshallbewithdrawnatthelatestbyMay2004.ThisEuropeanStandardwasworkedoutbytheJointWorkingGroupofCEN/TC169"Lightandlighting"andCEN/TC226"RoadEquipment",thesecretariatofwhichisheldbyAFNOR.ThisdocumentincludesaBibliography.Thisstandard,EN13201Roadlighting,consistsofthreeparts.Thisdocumentis:Part3:CalculationofperformanceTheotherpartsofEN13201are:Part2:PerformancerequirementsPart4:MethodsofmeasuringlightingperformanceAccordingtotheCEN/CENELECInternalRegulations,thenationalstandardsorganizationsofthefollowingcountriesareboundtoimplementthisEuropeanStandard:Austria,Belgium,CzechRepublic,Denmark,Finland,France,Germany,Greece,Hungary,Iceland,Ireland,Italy,Luxembourg,Malta,Netherlands,Norway,Portugal,Slovakia,Spain,Sweden,SwitzerlandandtheUnitedKingdom.IntroductionThecalculationmethodsdescribedinthisPartofthisEuropeanStandardenableroadlightingqualitycharacteristicstobecalculatedbyagreedproceduressothatresultsobtainedfromdifferentsourceswillhaveauniformbasis.引言本局部歐洲標準中描述的計算方法能使路燈指標通過認可的程序計算出，以使不同光源的結(jié)果具有統(tǒng)一的計算依據(jù)。1ScopeThisEuropeanStandarddefinesanddescribestheconventionsandmathematicalprocedurestobeadoptedincalculatingthephotometricperformanceofroadlightinginstallationsdesignedinaccordancewithEN13201-2.1適用范圍本歐洲標準定義和描述的約定和數(shù)學過程可用于依照EN13201-2設計的路燈裝置的光度性能的計算。2NormativereferencesThisEuropeanStandardincorporatesbydatedorundatedreference,provisionsfromotherpublications.Thesenormativereferencesarecitedattheappropriateplacesinthetext,andthepublicationsarelistedhereafter.Fordatedreferences,subsequentamendmentstoorrevisionsofanyofthesepublicationsapplytothisEuropeanStandardonlywhenincorporatedinitbyamendmentorrevision.Forundatedreferencesthelatesteditionofthepublicationreferredtoapplies(includingamendments).prEN13032-1,Lightandlighting—Measurementandpresentationofphotometricdataoflampsandluminaires—Part1:Measurementandfileformat.EN13201-2,Roadlighting—Part2:Performancerequirements.2引用標準本標準包含了一些其他刊物登出的標注日期或未標注日期的引文。本文在適當之處引用了局部標準的引文，并在其后列出了來源刊物。對標注了日期的引文，僅引用所標注的版次。對未標注日期的引文，以最新版〔包括增修局部〕為準。prEN13032-1,Lightandlighting—Measurementandpresentationofphotometricdataoflampsandluminaires—Part1:Measurementandfileformat.EN13201-2,Roadlighting—Part2:Performancerequirements.3Terms,definitions,symbolsandabbreviations3術(shù)語、定義、符號和縮寫3.1TermsanddefinitionsForthepurposesofthisEuropeanStandard,thefollowingtermsanddefinitionsapply.3.1術(shù)語和定義本歐洲標準中，采用了以下術(shù)語和定義verticalphotometricangle(ofalightpath)(_)anglebetweenthelightpathandthefirstphotometricaxisoftheluminaireNOTE1Unit_(degrees).NOTE2SeeFigure〔光路的〕垂直角γ光路與燈具主光軸的夾角，如圖1。單位：°〔度〕。azimuth(ofalightpath)(C)anglebetweentheverticalhalf-planepassingthroughthelightpathandthezeroreferencehalf-planethroughthefirstphotometricaxisofaluminaire,whentheluminaireisatitstiltduringmeasurementNOTE1Unit_(degrees).NOTE2SeeFigure〔光路的〕方位角C當燈具在測量時處于傾斜狀態(tài)，通過光路的垂直半平面與通過燈具主光軸的零基準半平面的夾角，如圖1。單位：°〔度〕。angIeofincidence(ofalightpathatapointonasurface)(_)anglebetweenthelightpathandthenormaltothesurfaceNOTE1Unit°(degrees).NOTE2SeeFigure4,Figure13andFigure〔光路在外表上某點處的〕入射角ε光路與外表法線的夾角，如圖1、圖13和圖14。單位：°〔度〕。angleofdeviation(withrespecttoluminancecoefficient)(_)supplementaryanglebetweentheverticalplanethroughtheluminaireandpointofobservationandtheverticalplanethroughtheobserverandthepointofobservationNOTE1Unit_(degrees).NOTE2SeeFigure偏向角〔與亮度系數(shù)有關(guān)〕β通過燈具和觀測點的垂直面與通過觀察者和觀測點的垂直面的補角，如圖4。單位：°〔度〕。luminancecoefficient(atasurfaceelement,inagivendirection,underspecifiedconditionsofillumination)(q)quotientoftheluminanceofthesurfaceelementinthegivendirectionbytheilluminanceonthemediumNOTE1Unitsr–1NOTE2E=L/Ewhere:qistheluminancecoefficient,inreciprocalsteradiansListheluminance,incandelaspersquaremetreEistheilluminance,inlux3.1.5亮度系數(shù)〔在單位面積，在給定方向，特定條件的照明〕q給定方向上單位面積的亮度與平均照度之比，單位為sr-1。注：q=L?E〔1〕其中，q為亮度系數(shù)，單位為球面度的倒數(shù)〔sr-1〕；L為亮度，單位為坎德拉每平方米〔cd/m2〕；E為照度，單位為勒克斯〔lux〕。reducedluminancecoefficient(forapointonasurface)(r)luminancecoefficientmultipliedbythecubeofthecosineoftheangleofincidenceofthelightonthepointNOTE1Unitsr–1NOTE2Thiscanbeexpressedbytheequation:r=qcos3(2)where:qistheluminancecoefficient,inreciprocalsteradians_istheangleofincidence,indegreesNOTE3Theangleofobservation,_inFigure4,affectsthevalueofr.Byconventionthisangleisfixedat1_forroadlightingcalculations.risreasonablyconstantforvaluesof_between0,5°and1,5°,theanglesoverwhichluminancecalculationsfortheroadsurfacearegenerallyrequired.3.1.6簡化的亮度系數(shù)〔外表上一點〕r亮度系數(shù)乘以該點處光線入射角的余弦的立方，單位為sr-1。注：r=q〔2〕其中q為亮度系數(shù)，單位為sr-1；ε為入射角，單位為°〔度〕。注：觀察角度，圖4中的α，對r的值有影響。按照慣例，路燈計算中這個角度固定為1°。α的值在0.5°-1.5°間，r的值根本不變，在道路外表亮度計算中這個角度是通常都需要的。tiltduringmeasurement(ofaluminaire)(_m)anglebetweenadefineddatumaxisontheluminaireandthehorizontalwhentheluminaireismountedforphotometricmeasurementNOTE1Unit°(degrees).NOTE2SeeFigure8.NOTE3Thedefineddatumaxiscanbeanyfeatureoftheluminaire,butgenerallyforaside-mountedluminaireitliesinthemouthoftheluminairecanopy,inlinewiththespigotaxis.Anothercommonlyusedfeatureisthespigotentryaxis.3.1.7〔燈具〕測量時的傾斜度θm對光度測量時安裝的燈具，定義的燈具基準軸與水平線的夾角，如圖8。單位為°〔度〕。注：定義的基準軸可以是燈具的任一特征，對于側(cè)邊安裝的燈具基準軸通常位于燈罩面，與套管軸一致。另一個通用特征是套管入口軸。tiltinapplication(ofaluminaire)(_f)anglebetweenadefineddatumaxisontheluminaireandthehorizontalwhentheluminaireismountedforfielduseNOTE1Unit_(degrees).NOTE2SeeFigure1andFigure8.NOTE3Thedefineddatumaxiscanbeanyfeatureoftheluminairebutgenerallyforaside-mountedluminaireitliesinthemouthoftheluminairecanopy,inlinewiththespigotaxis.Anothercommonlyusedfeatureisthespigotentryaxis.3.1.8〔燈具〕應用時的傾斜度θf對現(xiàn)場應用時安裝的燈具，定義的燈具基準軸與水平線的夾角，如圖8。單位為°〔度〕。注：定義的基準軸可以是燈具的任一特征，對于側(cè)邊安裝的燈具基準軸通常位于燈罩面，與套管軸一致。另一個通用特征是套管入口軸。orientation(ofaluminaire)(_)angleachosenreferencedirectionmakeswiththeC=0°，γ=90°measurementdirectionoftheluminairewhenthefirstphotometricaxisoftheluminaireisverticalNOTE1Unit°(degrees).NOTE2Whentheroadisstraightthereferencedirectionislongitudinal.NOTE3SeeFigure7,whichillustratesthesignconventions.3.1.9〔燈具的〕方向ν在燈具的主光軸豎直時，選定的參考方向與燈具C=0°，γ=90°測量方向的夾角。單位為°〔度〕。注：筆直道路的參考方向為縱向方向。注：圖7給出了該符號的定義描述。rotation(ofaluminaire)(_)anglethefirstphotometicaxisoftheluminairemakeswiththenadiroftheluminaire,whenthetiltduringmeasurementiszeroNOTE1Unit°(degrees).NOTE2SeeFigure7,whichillustratesthesignconventions.3.1.10〔燈具的〕旋轉(zhuǎn)度ψ測量時燈具傾斜度為零，那么燈具主光軸與燈具底面的夾角為旋轉(zhuǎn)度。單位為°〔度〕。圖7給出了該符號的定義描述。firstphotometricaxis(ofaluminairewhenmeasuredinthe(C,_)coordinatesystem)verticalaxisthroughthephotometriccentreofaluminairewhenitisatitstiltduringmeasurementNOTE1Thepolesofthe(C,_)coordinatesystemlieinthisaxis.SeeFigure1.NOTE2Thisaxisistiltedwhentheluminaireistiltedfromitstiltduringmeasurement.3.1.11〔〔C，γ〕坐標系統(tǒng)中測量時燈具的〕主光軸通過處于測量傾斜態(tài)的燈具的發(fā)光中心的垂直軸。如圖1，〔C，γ〕系統(tǒng)中的極軸即為主光軸。在測量時，燈具相對原傾斜態(tài)發(fā)生傾斜時，那么主光軸會發(fā)生傾斜。longitudinaldirectiondirectionparalleltotheaxisoftheroad3.1.12縱向方向平行于道路軸線的方向transversedirectiondirectionatrightanglestotheaxisoftheroadNOTEOnacurvedroadthetransversedirectionisthatoftheradiusofcurvatureatthepointofinterestontheroad.3.1.13橫向方向垂直于道路軸線的方向注：彎曲道路的橫向方向是指路段相關(guān)點的曲率半徑的方向。installationazimuth(withrespecttoagivenpointontheroadsurfaceandagivenluminaireatitstiltduringmeasurement)(_)angleachosenreferencedirection(whichislongitudinalforastraightroad)makeswiththeverticalplanethroughthegivenpointandthefirstphotometricaxisoftheluminaire,whentheluminaireisatitstiltduringmeasurementNOTE1Unit_(degrees).NOTE2SeeFigure4安裝方位角〔與道路外表的給定點和給定的測試時處于傾斜態(tài)的燈具有關(guān)〕φ燈具處于測試的傾斜態(tài)，選定的基準方向〔筆直道路中為縱向方向〕與通過給定點和燈具主光軸的垂直面的夾角。如圖4，單位為°〔度〕。3.2ListofsymbolsandabbreviationsThesymbolsandabbreviationsusedinthisstandardarelistedinTable1.3.2符號和縮寫的列表本標準中使用的符號和縮寫列于表1中。表1符號和縮寫量單位Symbol符號Nameordescription定義描述CPhotometricazimuth光度方位角〔圖1〕°〔度〕DSpacingbetweencalculationpointsinthelongitudinaldirection縱向方向計算點的間距mdSpacingbetweencalculationpointsinthetransversedirection橫向方向計算點的間距mEIlluminance照度lxHMountingheightofaluminaire燈具的安裝高度mj,mIntegersindicatingtheroworcolumnofatable表格的行或列的標志數(shù)-LLuminance亮度cd/m2ILuminousintensityperkilolumen每klm的發(fā)光強度cd/klmLpTotalluminanceatapointPP點的總亮度cd/m2MFProductofthelampfluxmaintenancefactorandtheluminairemaintenancefactor燈光通量的維護系數(shù)與燈具維護系數(shù)的乘積-NNumberofpointsinthelongitudinaldirection縱向方向上點的數(shù)量-nNumberofluminairesconsideredinthecalculation計算中需要考慮的燈具數(shù)-qLuminancecoefficient亮度系數(shù)sr-1Q0Averageluminancecoefficient平均亮度系數(shù)sr-1rReducedluminancecoefficient簡化亮度系數(shù)sr-1SSpacingbetweenluminaires燈具間距mTIThresholdincrement閾值增量%LνEquivalentveilingluminance等效耗散亮度cd/m2WLWidthofdrivinglane機動車道寬度mWrWidthofrelevantarea相關(guān)區(qū)域的寬度mWSWidthofstrip街道寬度mxAbscissain(x,y)coordinatesystem(Figure6)〔x，y〕坐標系統(tǒng)中的橫坐標〔圖6〕myOrdinatein(x,y)coordinatesystem(Figure6)〔x，y〕坐標系統(tǒng)中的縱坐標〔圖6〕mΦLuminousfluxoflamporlampsinaluminaire燈具中的燈的總光通量klmαAnglebetweentheincidentlightpathandthenormaltotheflatsurfaceofthesemicylinderusedformeasuringsemicylindricalilluminance(Figure13),orthedesignatedverticalplaneusedforverticalilluminance(Figure14)入射光路與測量半柱面型照度時使用的半柱面的平面的法線的夾角〔圖13〕，或測量垂直照度使用的特定垂直面〔圖14〕°〔度〕βAngleofdeviation(Figure4)偏向角〔圖4〕°〔度〕γVerticalphotometricangle(Figure1)垂直光度角°〔度〕δTiltforcalculation(Figure8)計算用傾斜度°〔度〕εAngleofincidence(Figure4)入射角°〔度〕θ1Tiltinapplication(Figure8)使用時的傾斜度°〔度〕θmTiltduringmeasurement(Figure8)測量時的傾斜度°〔度〕υOrientationofluminaire(Figure7)燈具的方向°〔度〕σAngleofobservation(Figure4)觀測角度°〔度〕φInstallationazimuth(Figure4)安裝方位角°〔度〕ψRotationofaluminaire(Figure1)燈具旋轉(zhuǎn)度°〔度〕4MathematicalconventionsThebasicconventionsmadeinthemathematicalproceduresdescribedinthisstandardare:_theluminaireisregardedasapointsourceoflight;_lightreflectedfromthesurroundsandinterreflectedlightisdisregarded;_obstructiontothelightfromluminairesbytreesandotherobjectsisdisregarded;_theatmosphericabsorptioniszero;_theroadsurfaceisflatandlevelandhasuniformreflectingpropertiesovertheareaconsidered.4數(shù)學慣例本標準在闡述數(shù)學過程中基于以下根本約定：—燈具被認為是一個點光源；—忽略了環(huán)境對光的反射和屢次反射光；—忽略了樹木或其他物體對光的遮斷；—大氣吸收為零；—相關(guān)區(qū)域的道路是平直的且具有相同的發(fā)射特性。5Photometricdata5.1GeneralPhotometricdataforthelightdistributionoftheluminairesusedinthelightinginstallationareneededforcalculatingthelightingqualitycharacteristicsinthisstandard.Thesedataareintheformofanintensitytable(_-table)whichgivesthedistributionofluminousintensityemittedbytheluminaireinallrelevantdirections.Whenluminancecalculationsaretobemade,photometricdataforthelightreflectingpropertiesoftheroadsurfacearerequiredintheformofanr-table.Interpolationwillbeneededinusingboththesetablestoenablevaluestobeestimatedfordirectionsbetweenthetabulatedangles.5相關(guān)光度數(shù)據(jù)5.1概要本標準中計算燈具品質(zhì)特性需要用到照明裝置中燈具的光分布的光度數(shù)據(jù)。這些數(shù)據(jù)列于強度表格(I-table)中，給出了燈具在各個相關(guān)方向上的發(fā)光強度的分布。在亮度計算時，需要r-table格式的、道路外表光反射特性的光度數(shù)據(jù)。對這2個表格使用插值法可以估算出在表列角之間的方向上的值。5.2The_I-tableForcalculationsmadetothisstandard,anintensitytable(_-table)preparedinaccordancewithprEN13032-1isrequired.Thecoordinatesystemusedforroadlightingluminairesisthe(C,_),showninFigure1,althoughthe(B,_)coordinatesystemmaybeusedforfloodlights.Inthefigure,theluminaireisshownatitstiltduringmeasurement.Luminousintensityshallbeexpressedincandelasperkilolumen(cd/klm)fromallthelightsourcesintheluminaire.5.2強度表格為了本標準中的計算，需要一個符合prEN13032-1標準的強度表格(I-table)。路燈燈具使用的坐標系是〔c，γ〕坐標系，如圖1，盡管〔B,β〕坐標系也可用于泛光照明。如圖，燈具在測量時處于傾斜態(tài)。燈具中所有光源的總發(fā)光強度以cd/klm表示。KeyKey注1Luminaireattiltduringmeasurement1測量時傾斜的光源2Longitudinaldirection2縱向方向〔軸向〕3Firstphotometricaxis3主光軸4Directionofluminousintensity4發(fā)光強度的方向Figure1—OrientationofC,_coordinatesysteminrelationtolongitudinaldirectionofCarriageway圖1車道縱向上的〔c，γ〕坐標系方向Maximumangularintervalsstipulatedinthisstandardhavebeenselectedtogiveacceptablelevelsofinterpolationaccuracywhentherecommendedinterpolationproceduresareused.在采用推薦的插值程序時，選取了本標準規(guī)定的最大間隔角以使插值精度處于可接受的等級。Inthe(C,_)systemofcoordinates,luminousintensitiesshallbeprovidedattheangularintervalsstatedbelow.在〔c，γ〕坐標系中，發(fā)光強度由以下規(guī)定的間隔角給出。Forallluminairestheangularintervalsinverticalplanes(_)shallatmostbe2,5°from0°to180°.Inazimuththeintervalsshallbevariedaccordingtothesymmetryofthelightdistributionfromtheluminaireasfollows:對所有的燈具，垂直面〔γ面〕的間隔角在0°-180°間最多為2.5°。方位角的間隔角度根據(jù)燈具光分布的對稱性會有多種情況，如下：luminaireswithnosymmetryabouttheC=0_plane:theintervalsshallatmostbe5°,startingat0_,whentheluminaireisatitstiltduringmeasurement,andendingat355°;a〕燈具不關(guān)于c=0面對稱：間隔角不超過5°，起始角度0°，燈具處于測試傾斜態(tài)時，終止于355°。b)luminaireswithnominalsymmetryabouttheC=270°-90°plane:theintervalsshallatmostbe5°,startingat270°,whentheluminaireisatitstiltduringmeasurement,andendingat90_;b〕燈具關(guān)于c=270°-90°面名義上對稱：間隔角不超過5°，起始角度270°，燈具處于測試傾斜態(tài)時，終止于90°。c)luminaireswithnominalsymmetryabouttheC=270°-90°andC=0°-180°planes:theintervalsshallatmostbe5°,startingat0°,whentheluminaireisatitstiltduringmeasurement,andendingat90_;c〕燈具關(guān)于c=270°-90°面和c=0°-180°面名義上對稱：間隔角不超過5°，起始角度270°，燈具處于測試傾斜態(tài)時，終止于90°。d)IuminaireswithnominallythesamelightdistributioninallC-planes:onlyonerepresentativesetofmeasurementsinavertical(C-plane)isneeded.d〕燈具在所有c平面內(nèi)具有名義上相同的光分布：僅需要在一垂直面〔c面〕內(nèi)測量的具有代表性的設定即可。NOTETheangularspacingsrecommendedinCIEPublication140for_-tablesarewiderthanthoserecommendedabove,andmaynotgiveresultswhichareofasatisfactoryaccuracyforilluminancecalculations.注：CIEPublication140中為強度表格I-table推薦的角間距寬于上面的推薦，它們可能不能為照度計算提供滿意精度的結(jié)果值。5.3Interpolationinthe_-table5.3.1GeneralWheretheintensityisrequiredinadirectionwhichdoesnotlieinoneofthedirectionsinwhichmeasurementsarerecorded,eitherlinearorquadratic,interpolationwillbenecessarytoestimatetheintensityinthedesireddirection.Linearinterpolationisthesimplerprocedureandmaybeusedwheretheangularintervalsareinaccordancewiththosestipulatedin5.2.Iftheangularintervalsaregreaterthenitwillbenecessarytousequadraticinterpolation.5.3強度表格I-table中的插值5.3.1概要當需要某一方向上的強度值，而記錄的測量數(shù)據(jù)中又沒有該方向上的數(shù)據(jù)時，那么需要通過線性或平方插值法來估算該方向上的強度值。線性插值是較簡單的過程，當間隔角符合5.2節(jié)中的規(guī)定時，可選用線性插值。當間隔角更大時，需要使用平方插值法。5.3.2LinearinterpolationToestimatetheluminousintensity__C,_)inthedirection(C,_),itisnecessarytointerpolatebetweenfourvaluesofluminousintensitylyingclosesttothedirection,seeFigure2.為估算〔c，γ〕方向上的發(fā)光強度I〔c，γ〕，需要在最接近該方向的4個發(fā)光強度值之間進行插值，如圖2。Figure2—Anglesrequiredforlinearinterpolationofluminousintensity圖2發(fā)光強度線性插值時需要的角度Forthispurpose,thefollowingequationsormathematicallyequivalentequationsshallbeused:為此，需要用到以下方程或數(shù)學等價方程：K(3)K(4)where:K1andK2areconstantsdeterminedfromtheequationsCistheazimuth,measuredaboutthefirstphotometricaxis_istheverticalanglemeasuredfromthefirstphotometricaxisj,j+1,m,m+1areintegersindicatingthenumberofthecolumnorrowinthe_-table其中K1和K2是由方程確定的常數(shù)C是相對于主光軸的方位角γ是相對主光軸的垂直角j、j+1、m、m+1是強度表格中的列數(shù)和行數(shù)I(5)I(6)I(7)where:_(Cm,_j)indicatestheintensityincolumnnumbermandrownumberjofthe_-table,andsoonfortheothersimilarsymbols.其中ICIntheseequationsinterpolationisfirstcarriedoutinthe_cones,andthenintheC-planes.Ifdesiredthisprocedurecanbereversed(thatis,theinterpolationisfirstcarriedoutintheC-planesfollowedbythe_cones)andthesameresultobtained.在這些方程中，插值首先會在錐角γ執(zhí)行，然后是c平面。如果將步驟顛倒〔即先執(zhí)行c平面的插值，再是錐角γ的插值〕，也能獲得相同的結(jié)果。5.3.3QuadraticinterpolationQuadraticinterpolationrequiresthreevaluesinthe_-tableforeachinterpolatedvalue.Figure3indicatestheprocedure.Ifavalueof_isrequiredat(C,_),interpolationisfirstcarriedoutdownthreeadjacentcolumnsofthe_-tableenclosingthepoint.Thisenablesthreevaluesof_tobefoundat_.Interpolationisthencarriedoutacrossthetabletofindtherequiredvalueat(C,_).Ifpreferred,thisproceduremaybereversed;thatis,interpolationcanbecarriedoutacrossandthendownthe_-tablewithoutaffectingtheresult.5.3.3平方插值以平方插值獲得的值在平方插值時需要用到強度表格中的3個值。圖3描述了該過程。如果需要〔c，γ〕點的強度值I，插值首先會在強度表格中臨近該點的3個表列數(shù)據(jù)中執(zhí)行。這可根據(jù)γ得出I的3個值。然后插值會在表格的行繼續(xù)執(zhí)行并得出〔c，γ〕的待求值。如果你愿意，這些步驟也可以顛倒，即先根據(jù)表格的行執(zhí)行插值，再根據(jù)表格的列執(zhí)行插值，這樣做對結(jié)果不會有影響。Toreduceinterpolationinaccuraciesasfaraspossiblethefollowingtworulesshouldbefollowedinselectingthevaluesforinsertionintheinterpolationequations:為盡可能減少插值誤差，在為插值方程選擇插值數(shù)據(jù)時應當遵從以下2個原那么：1)Thetwotabularanglesadjacenttotheangleforinterpolationareselectedforinsertionintheinterpolationequationsandtheaveragecalculated.1〕插值方程和求平均值時選擇插入的2個列角應該要靠近該待插值求解的角。2)Iftheangleforinterpolationissmallerthanthisaveragethenthethirdtabularangleisthenextlowertabularangle(asshownforCinFigure3);iftheangleforinterpolationisgreaterthanthisaveragethenthethirdtabularangleisthenexthighertabularangle(asshownfor_inFigure3).2〕如果待插值求解角小于平均值，那么第三個列角應該選擇更小的一個列角〔如圖3中的c〕；如果這個角大于平均值，那么第三個列角應該選擇更大的一個列角〔如圖3中的γ〕。Figure3—Valuesrequiredforquadraticinterpolation圖3平方插值需要的值WheninterpolationiscarriedoutintheregionofC=0_,ory=0_or180_,see5.3.4.Theformulaforquadraticinterpolationis當在c=0°，或y=0°或180°區(qū)域內(nèi)執(zhí)行插值時，見5.3.4節(jié)。平方插值的公式是y(8)whereitwillbenoticedthatthereiscyclicpermutationofthesuffices.可以看出，這是條件的循環(huán)置換。ThisinterpolationcanbeappliedtoeitherCor_.WhenitisfirstappliedtoC,thisparameterissubstitutedforxintheaboveequation:這個插值法可以應用于C或γ。如果先應用于C，那么上面公式中的x用以下參數(shù)替換：x=Cx1=Cmx2=Cm+1x3=Cm+2where:Cistheangleatwhich_istobefoundbyinterpolationm,m+1,m+2areintegersindicatingthenumberofthecolumnsinthe_-tableCm,Cm+1andCm+2arevaluesofCforthecorrespondingcolumnnumbers其中C是待通過插值法求強度值I的角度；m、m+1、m+2是強度表格的列數(shù)Cm、Cm+1、Cm+2是相應列的C的值。Fromthissubstitutionthreeconstantscanbedefined,whichcanbeconvenientlyevaluatedbyasubroutineprogram:通過替換可以定義3個參數(shù)，它們可以通過一個子程序便利地估算出。K(9)K(10)K(11)FromthesethreeequationsitfollowsthatK1+K2+K3=1.Asetofthreeequationscanthenbewrittenallowingevaluationinacalculationloopinacomputerprogramwiththevariationofj:這3個方程滿足K1+K2+K3=1。可以寫出一個3方程的方程組，在電腦程序的循環(huán)計算中引入變量j可求解該方程組：I(12)I(13)I(14)Forinterpolationofthe_anglesfurtherapplicationofEquation(3)givesthreenewconstants:為對γ角插值求解，公式〔3〕的進一步的用處是給出了3個新的常數(shù)：K(15)K(16)K(17)Fromthesethreeequationsitfollowsthatk1+k2+k3=1and:(,)1(,j)2(,j_1)3(,j_2)這3個方程滿足k1+k2+k3=1和IC,Theorderoftheinterpolationprocedure,firstfor_andthenforC,maybereversedwithoutalteringtheresult.插值過程的順序，即先γ再C，可以顛倒且不會影響結(jié)果。5.3.4QuadraticinterpolationintheregionofC=0_,or_=0_or180_ForquadraticinterpolationintheseregionsitmaybenecessarytotakethethirdvalueofluminousintensityfromtheC=90_throughtoC=180_to270_hemisphereoftheluminousintensitydistribution,whichmayberegardedasamirrorimageoftheC=270_throughtoC=0_to90_hemisphereoftheluminousintensitydistribution.c=0°，或γ=0°或180°區(qū)域的平方插值這個區(qū)域的平方插值需要從C=90°至C=180°至C=270°發(fā)光強度分布的半球中選取一個發(fā)光強度的第三值，這可看成為C=270°至C=0°至C=90°發(fā)光強度分布半球的鏡像。5.4Ther-tableRoadsurfacereflectiondatashallbeexpressedintermsofthereducedluminancecoefficientmultipliedby10000,attheangularintervalsandinthedirectionsgiveninTabl