Perspective Without Pain (North Light 20th Anniversary Classic Editions)

PerspectiveWithoutPain

PhilMetzger

NORTHLIGHTBOOKSCincinnati,Ohio

www.artistsnetwork.com

http://www.artistsnetwork.com

PerspectiveWithoutPain.Copyright©1992byPhilMetzger.ManufacturedinChina.Allrightsreserved.Nopartofthisbookmaybereproducedinanyformorbyanyelectronicormechanicalmeansincludinginformationstorageandretrievalsystemswithoutpermissioninwritingfromthepublisher,exceptbyareviewer,whomayquotebriefpassagesinareview.PublishedbyNorthLightBooks,animprintofF+WPublications,Inc.,4700EastGalbraithRoad,Cincinnati,Ohio45236.(800)289-0963.Firstedition.

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LibraryofCongressCataloging-in-PublicationDataMetzger,PhilipW.

Perspectivewithoutpain/PhilMetzger.—1sted.

p.cm.

ISBN-13:978-0-89134-446-9

ISBN-10:0-89134-446-2

1.Perspective.2.Drawing—Technique.I.TitleNC750.M481992

742—dc20

91-43309

CIP

Designer:ClareFinney

ToShirleyPorter

Acknowledgments

When North Light asked me to consider writing a book on perspective, mygreedyeyes litupand I said,“SURE!” I figuredperspectivewasasnapand Icould knock it off in a few weeks. Months later and somewhat chastened, Irealized that there wasmore to the subject thanmet the eye. There are thickbooksaboutperspectivethatdigdeepintothemathematicsandmysteryof thesubject. My job was to come up with a book that dispelled the mystery andconcentrated on those aspects of perspective that someone in the “fine arts”wouldneed toknow. Ifyou'reanarchitectoranengineer, thisbook isnot foryou.But ifyoudrawandpaintasahobbyorfora living,I thinkyou'll finditjustaboutright.

Iwant to thank twopeoplewhoparticipated in producing this book:LindaSanders, my excellent editor at North Light, who kept steering me in thedirectionabookofthiskindmusttakeandreallyworkedwithmeratherthansitbackandacceptwhatever I threwherway;andShirleyPorter,whosuppliedacouple of the sketches in the book, but who mainly read my prose before Isubmitted it to Linda and savagely deleted most of the dumber things I hadwritten.Ihonestlythankyouboth.

Perspective:thescienceofpaintinganddrawingsothatobjectsrepresentedhaveapparentdepthanddistance.…TheMerriam-WebsterDictionary

Contents

PartOne:TheBasics

Overlap

SizeandSpaceVariation

Modeling

DetailandEdges

ColorandValueChange

ConvergingLines

VanishingPointandEyeLevel

EstimatingAngles

PartTwo:BoxesandBeyond

ASimpleBoxinPerspective

DrawingThrough

FindingHiddenEdges

PlayingwithVanishingPoints

GettingtheAnglesRight

ThePerspectiveCenter

UsingthePerspectiveCenter

Troubleshooting

PlacingDoorsandWindows

BoxesWithinBoxes

BuildingaGlassHouse

Collections

DifferingElevations

PartThree:CurvesandInclines

CirclesandEllipses

CircularObjects

CombinationsofCylinders

Arches

ExaggerationasanAidtoSeeing

MeasuringRelativeSizes

MoreVanishingPoints

SomeVerticalLinesConverge

LookingUp

Inclines

Roads,Paths,andStreets

FieldsandStreams

Stairs

BeyondEyeballing

CommonGoofs

Conclusion

PartOne:TheBasics

If you're likemost painters, you probably work hard at trying tomake a flatsurfaceappeartohavedepth.Youlookatthethree-dimensionalsceneinfrontofyou and sweat to get it down convincingly on your two-dimensional paper orcanvas,butsometimesyou'refrustrated.Adistantobjectdoesn'tlooksodistanton your paper, or an object seems the wrong size compared to another, or abuildinglooksasthoughit'sslidingoffthepage.

You'renotalone.Weallstrugglethroughoutourcareerstomakeourdrawingmoreconvincing.Someteacherssaythatourdrawingproblemsareallmagicallysolvedoncewelearntoseebetter.Ifyouseebetter,sotheargumentgoes,you'llautomaticallydrawbetter.

Ithinkthat'stoosimplistic.Inordertodrawwell,fourthingsareneeded:

1.Seeing2.Understanding

3.Practice4.Technique

Seeing

Seeingmeanslookingat thesubjectyou'reabouttodrawandanalyzingitasabunchofabstractshapes,colors,valuesandtextures.

Youmust overcomewhat you “know” about theobject.An editor atNorthLight Books who teaches figure drawing says that students drawing a modelstandingonaplatformoftenhavetroubledrawingtheplatformcorrectly.They“know”thesurfaceoftheplatformisarectangle,andtendtodrawitthatway.Theresultissomethinglikethedrawingatupperright.

If they were to draw what they actually see, rather than what they know,they'dcomeupwithsomethinglikethesecondsketch.

TheBasics

Trytoforgetaboutwhatthethingreallyis.Insteadofseeingapersonstandingonaplatform,trytoseefirstacombinationofshapes.Don'tconcentrateonanarmwithelbowoutwardandhandonhip,asatbottomleft.

Instead,firsttryseeingshapesonly,asshownatbottomright.You'll find that as you get adjacent shapes right, the figure will gradually

emerge.When the shapes are right relative to one another, add color, texture,shading,andsoon.Asyoudoso,theseadditionswillforceyoutoreconsidertheshapesyoucameupwiththatyouthoughtweresoperfect.Forexample,whenyougetthe“value”(thelightnessordarkness)ofthespacebetweenthearmandthe body fairly correct, you may find that the shape of that space no longerseemsright.Everythinginadrawingaffectseverythingelse.Soyoufiddlewiththeshape,andplaythisback-and-forthgameuntilyoufeelcomfortablewiththeobjectyou'vedrawn.

Understanding

Understandingmeansknowingwhat'sreallygoingoninanobjectyou'retryingtodraw,even though fromwhereyou're standing theobjectdoesn't lookatall“correct.”Themodel'splatformisagoodexample.Youknowit is rectangularbutallyoucansee is thatcrazyshape!Youmaywonderwhatgood itdoes toknow what shape a thing really has if the idea is to draw it as you see it.Rembrandthaditaboutrightwhenhesaid,“Ifyouwanttopaintanappleyou'vegottobeanapple!”Ifyouwanttopaintsomethingconvincinglyyou'vegottoknowit intimately.(Thatmightbea littleeasierwithanapplethanwitha livemodel!)Seeingaccuratelyandabstractlygivesyoutheabilitytorenderasubjectwithmechanicalexactness;understandingthesubjectenablesyoutogiveitsoul.

Practice

Practice iswhatenablesyou toputyourability to seeandunderstand togooduse.It'sthetrainingyouneedtotranslatewhatyouseeandunderstandinyourbrain into shapes and colors and shades and textures on a piece of paper or acanvas. This book will offer you plenty of exercises for practicing the ideasdiscussed.

Technique

Topracticeanythingyouneed to learnproven techniquesdevelopedbyothersand add your own as you gain experience. One set of drawing and paintingtechniquesusedbyartistsforcenturiesiscalledperspective.

Perspective is simply a set of techniques used to draw a three-dimensionalsceneonatwo-dimensionalsurface.Inotherwords,perspectiveisanapproachtoward getting the illusion of depth in a drawing or painting.We'll playwithseveralperspectivetechniquesinthisbook.Theyareallsimpleonceyougettoknowthem,andtheyshouldallbecomepartofthebackgroundknowledgeeverypaintercomestousequiteautomatically.

Tomakethetechniqueseasiertolearn,I'vearbitrarilydividedthemintothefollowingcategories,whichwe'lltakeoneatatime:

•overlap•sizeandspacevariation•modeling•detailandedges•colorandvaluechange•converginglines

ThisBook

There are three parts to this book. In this part I'll define and illustrate eachperspectivetechniqueandofferexercisestohelpyoupracticeusingthem.Intheremainingtwopartswe'lldigdeeperintohowthesetechniquescanbeappliedtorealdrawingandpaintingproblems.Asyou'llsoonsee, it's rare thatyou'lluseonetechniqueandnoothers.Theycomeintoplayinlotsofcombinations.Mostoftheillustrationsandexerciseswillusemorethanonetechnique.

TheBasics

Thebookfollowsadefiniteprogressionfrombasictomorecomplexmaterials,so it makes sense to study the book in order. Please don't skip any of theexercises.Someofthemmayseemtoosimpletobotherwith,buteachoneofferssomethingtostrengthenyourabilitytohandleperspectiveconvincingly.

MaterialsYou'llNeed

Thethingsyou'llneedareinexpensiveandsimple.First,somepencils(2B-soft,HB-medium,and2H-hardwillsuffice),orcharcoal ifyouprefer;sometracingpaper;occasionallyastraightedge;acoupleofcoloredpencils(orwatercolororpastels);scissors;somecardboardandapaperclasp;aflashlight;twopushpins;a piece of string about a half-foot long; a hand-held mirror; a piece of rigidplastic,suchasPlexiglas;drawingpaper;andafewotheroddsandendsthatyouprobably have around the house. Most of the drawing paper you'll need isalreadysuppliedwiththebook.

ThePictureSurface

Althoughyoumayactuallybedrawingorpaintingonapaperorcanvas lying

flatonatableorataslantonaneasel,alwaysimaginethatpaperorcanvastobeset up vertically between you and the things you're drawing or painting, andimagine that you're actually seeing through the paper or canvas and simplytracingonit.

Thatimaginarysurfaceiscalledthepicturesurfaceorthepictureplane,andI'll refer to it frequently throughout this book.When I speak of something asbeing “parallel to your picture surface,” for example, I don'tmean parallel toyour actual paper or canvas, which may be held at any angle you findcomfortable; I'm referring to the surface of the paper or canvas as it wouldappearifheldupverticallybetweenyouandyoursubject,asshownbelow.

Overlap

The remainder of Part One discusses each of the six perspective techniques:overlap; size and space variation;modeling; detail and edges; color and valuechange;converginglines.Let'sbeginwithoverlap.

Supposeyouhadtobetyourlastdollaronwhichobjectinthesketchattoprightisfarthestforward.Couldyouwin?There'sreallynowaytoknowforsurewithoutreceivingaclue.Theboxandballcouldbesittingsidebyside,or theboxcouldbeabuildingsofaroffinthedistancethatitlooksnearlyassmallastheball.

The clue can be provided by simply overlapping the two objects. In thesecondsketchI'veput theball infrontof theboxsimplybyhidingpartof theboxbehindtheball.There'sanimmediatesuggestionofdepthwheretherewasnonebefore.

In the examplebelow we have a similar situation. Is the tree a small one,closertotheviewerthanthefence?Maybe,butontheotherhand,thiscouldbealargetreeinthedistancebehindthefence.Youcandecidewhichobjectistobemore distant simply by overlapping one with the other. Using a piece oftranslucenttracingpaper,roughlytracetheoutlineofthetreeandthenshiftthepapertotherightsothatthetracedtreepartlyoverlapsthefence.Makethetreeappeartobeinfrontofthefencebytracingonlytheportionsofthefencethatwouldbeseenoneithersideof the tree.Then try theopposite: trace thefencefirst,shiftthepapertotheleft,anddrawthepartsofthetreenotblockedbythefence.

Overlap

Sometimes the overlapping you use might be less obvious. In the tree studybelow, the placing of branches in front of other branches is important. If nobranchescameforwardorreceded,thetreewouldbemerelyasilhouettewithnodepthatall.

By simply rearranging objects so that they overlap, all doubt about theirrelative positions is resolved and some added depth is introduced.While youcan'tactuallymovesomeobjects,suchasthetreeorthefence,youhaveperfectfreedomtoshifttheminyourpainting.Whypaintifyou'reaslavetowhatyousee before you?Use the actual scene as a starting place andhave fun adding,subtracting,andchangingwhat'sthere.Withthepossibleexceptionofaportrait,you'reneverobligedtopaintanythingliterally.

Exercise:Overlap

Here are four boxes lightly drawn in, with no clue as to which boxes areforward,whicharebehind.Useoverlappingtomakesomeboxesrecede,otherscomeforward.Startbytracingoverallthelinesofoneparticularbox.Thentracein the linesof a secondbox,omittinganyof its lines that fall behind the firstbox.Traceinthethirdandfourthboxesinasimilarway.

Makeadifferentboxfarthest forward ineachpicture.Notice that theboxIhavemadesmallestcouldactuallybethelargest ifyousimplymakeit theonefarthestaway.Howyouplaceeachboxrelativetotheotherstellsthevieweralotabouttheboxsizes.


Herearesomefencepostsmarchingacrossthelandscape.Thetoprowofpostsdoesnothingtoadddepthtothepicture.

But supposewe change the posts' relative sizes so thatwe have somethinglikethebottomrow.It'sapparentthattheleftmostpostisclosesttotheviewerandtheonestotherightarefartherandfartheraway.Thisisthepsychologyofhowweseethings:ifyouknowcertainobjectsarenormallythesamesize,butyou see a picture in which those objects are not the same size, you'llautomaticallyandunconsciouslyassume that someof thoseobjects are fartherawaythanothers.

There'sanotherdifferencebetweenthetwosketches.Inthefirstthepostsareroughly thesamedistanceapart.That'showthey'reusuallyplanted.But in thesecond sketch I've shown a constantly diminishing distance between posts astheyrecede.Again, that'showwesee things.Thesizesofall things, includingthe spaces between them, seem todiminish as their distances from theviewerincrease.

Atthebottomisanotherexampleofsizeandspacevariation.Youcantryoutsizevariationandspacingrightonyourdeskor tableoron

the floor. Find a half-dozen or more objects that are about the same size:crayons, flashlightbatteries, rollsofLifeSavers–anythingyoucanmakestand

onend.Standthemallupinastraightrow,allthesamedistanceapart.Nowgetyourchindownonthetableorfloornearoneendof therowandsquintdowntherowofobjects.You'llseethatthefarthestonelookssmallerthanthenearestandyou'llseethattheequalspacesbetweentheobjectsdon'tlookequal.

LouisCaravaglia,photographer;LakeErieBalletCompany


If you lookdowna railroad trackyou'll see that thewooden ties towhich thesteel tracks are fastened seem to get closer together as the track recedes fromyou.Otherthingsdiminishaswell.Thefarendofthetrainstationseemssmallerthan thenearend; the tracksappear to squeeze togetheras theydisappear intothe distance; even the pieces of gravel between the ties are “larger” andmoredistinctintheforegroundthaninthedistance.

Even though we may know that objects appear smaller as they recede,sometimeswhenwedrawsomethinglikearowofpolesorafencegoingbackinto the distance,we're a little chicken about emphasizing the size differencesbetweenthenearestandfarthestobjects.

Take a peek ahead at the exercise. The fence post just to the left of themailboxisnearlyashighasthebarn!Don'tbelieveme?Measureitwitharuler.You'llseethatthebarnisnotmuchhigherthanthepost.Asifthat'snotenough,themailboxisactuallybiggerthanthehouse!Yetboththepostsandthemailboxfeelrightinthepicture,don'tthey?


Measuring

Whenyou'reinthefieldpainting,orinyourstudiodoingastilllifeoraportrait,you'llconstantlybemeasuringthings.Youneedtomeasurehowbigthingsare,howfaraparttheyare,wheretheircenterslie,howbigoneobjectiscomparedtoanother, and so on.Youwon't care about theiractual sizes–what you need toknow are relative sizes. The simplest (and handiest!) tool in the world formakingsuchmeasurementsisyourthumb,alongwithapencilorpenorarulerorastick.

Supposeyou'relookingattwoobjects,abrandyglassandadecanter,inastilllifeyou'redrawing.Youknowthedecanterisabouttwiceastallastheglass,asshownattop,buttheglassisintheforeground,closertoyouthanthedecanter,so in your drawing the glass will not be half the height of the decanter butsomethingmorethanhalfashigh.Howmuchmore?Youdon'tneedtoknowininchesorcentimeters.Allyouneedtoknowistheirrelativeheights.

Standing at your easel, hold up vertically at arm's length any straightedge,suchasapencil.Closeoneeye(onlyone,please!)andsightalongthetipofthepencil to align it with the top of the glass. Then slide your thumb along thepencilshafttowhereitmarksthebottomoftheglass,belowright.

Okay,that'showhightheglassis.Now,withoutmovingyourthumbfromitsposition on the pencil, align the thumb-markwith the bottom of the decanter.Nowlookatwherethepenciltipfallsandmakeajudgment:howmuchhigherdoesthedecanterappearthantheglass?Certainlynottwiceashigh,whichyouknowtobethecase.No,itappearstobelessthantwiceashigh.Makeamentalcalculation. Perhaps the decanter seemsone-and-a-half times the height of theglass.Trythatoutlightlyonyourdrawingandseeifitfeelsright.Iftheglassinyourdrawingisfourincheshigh,makethedecantersixincheshigh.Ifitdoesn'tfeelquiteright,tryagain.

Youmayfeelalittleuneasyabout“measuring”withoutcomingoutwithananswerininchesorfeet.AnoldfellowIworkedwithasaboyusedtomeasurethewidthoffoundationholesweweredigginginsuchtermsas,“It'saboutsixpickaxe handles and a hammer!” If such estimating troubles you at first, tryusingarulerinsteadofapencil.Useitinthesamemannerasthepencilandnotewhereyourthumbrestsaftermarkingtheheightoftheglass.Let'ssayit'satthethree-inchmarkon theruler.Nowdo thesamefor thedecanter. Ifyour thumbrestsat the four-and-a-half-inchmark, thatmeans that indeed thedecanteryoudrawshouldbeabouthalfagainashighas theglass.Ofcourse,yourdrawing

canbe any size (maybe a two-foot highglass and a three-foot highdecanter).Whatmattersisproportion–thatis,therelativeheightsofthings.

What'sthepayoffforgettingproportionsright?Yourrewardisaconvincingillusionofdepth–andthat,afterall,iswhatthisbookisallabout.Spendafewminuteswithjustyourpencilasameasureranddosomerelativemeasurementsonthethingsyouseearoundyou.You'llbesurprisedathow“big”somesmallishitemscanseemjustbecausethey'reclosertoyouthansomeitemsyouknowarelarger.I'msittinghereandmeasuringsomeofthethingsinmyofficeandhere'swhat I discover.My left foot is about half as long as the height of my five-drawerfilecabinet.Comeon,now!Myfeetarebig,but…!Andthewindowattheendoftheroomisexactlyashighasmypencil.Thecoffeemugatmysideisbiggerthanthewastebasketoveragainstthewall.That'salotofcoffee!

Asyougo throughyourday,notice the relative sizesof thingsaroundyou.There's always a pencil or pen handy.Hold one upwhen you're stopped at atraffic light.Compare the relative sizesof cars, people,buildings,poles.Don'tworryaboutthelight.Thecreepbehindyouwillleanonthehorntotellyoutogetmovingtheinstantthelightturnsgreen.

Exercise:SizeandSpaceVariation

Complete each of the three drawings in this exercise in such a way that youshow depth by gradually diminishing the sizes of, and the distances between,similarobjectsastheygointothedistance.Sometimesit'shelpfultodrawlightguidelinesasI'vedoneforyouinthewarehouseexamplesothatyoucan“fit”alltheobjects(suchasalongrowofwindows)betweenthelines.Usethisdevicesparingly, though, so that you don't make your drawing too rigid. In thewarehouseexample,it'squitelikelythewindowswillbeallthesamesize,butinthenextexample, it'snot likely thepoliceofficerswillallbe thesameheight.Don't worry about making perfect cops or windows or pickets; the importantthing is to understand the usefulness of size variation and space variation inachievingtheillusionofdepth.

Exercise:SizeandSpaceVariation

Modeling

Lookat theexampleabove left.What theheck are these things?Apretty flatwalnutandanevenflatterapple.Nowseewhatalittlemodeling,orshaping,cando,aboveright.

Althoughwegivea lotof space in thisbook to the ideaofgetting literallymilesofdepth(treelinesstretchingawaytoforever,mountainrangesgoingbackasfarastheeyecansee),notalldepthismeasuredinmiles.Sometimesyou'reconcernedaboutinches.That'swhenmodelingcomesintoplay.

WhatImeanbymodelinginthiscontextisgivingformtoanobject.Partlythis isaccomplishedbylinework,butwhatI'minterestedinhereis theuseofshadow.Whetheryou'repaintinganapple,asilo,apole,orevenasquarebox,modeling is necessary to indicate form and give the picture life. There are acoupleofbasicstopayattentiontowhenyou'remodelinganobject:

1.Determineexactlywherethelightsourceistobe.Ifyou'repaintingarealscene, the sun,or someartificial light suchasa lamp, isyour sourceandthere's no problem remembering where the light is coming from. But ifyou'reimaginingascene,orifyou'rearbitrarilychangingthepositionofthelightsource,youneed tonotewhere it's tobe locatedand thenmodel theobjectsinyourpictureaccordingly.Don'tstartoffwiththesunshiningfromthe upper right and then halfway through the picture forgetwhere itwassupposed to be and start modeling and painting shadows in the wrong

directions. I often draw a little circle representing the light source at theupperrightorupperleftofmypaintingincaseIgetdistractedandforgetwhatIwasdoing.Ialsoaddalittlethree-dimensionalarrowtoremindmewhetherthelightsourceisbehindmeorinfrontofme.

2.Observecarefullyjusthowtheobjectismodeled.Astheroundedformofthe apple, for example, turns away from the light, youmight expect theedgeawayfromthelighttobeconsistentlythedarkestpartoftheapple.

Butthat'snotalwaysso.Thereareprobablyothersourcesoflightintheroom,orlightfromyoursinglesourcemaybereflectedfromotherthings,suchasatableclothorothernearbyobject.Thatreflectedlightcanreachtheshadowedpartoftheappleandmakeitappearlighterthanyouexpected.Infact,therecanbesomuchreflectedlightorlightfromothersourcesthatyouseecomplexvariationsinashadowyouthoughtwouldlookprettyuniformlydark.

Youcanexperimentwithsuchlightshenanigansbysettingupafewobjectsinadarkened roomwith a single lamp as a light source.Move things around andobserve theeffectsof light reflected into shadowareas. Ifyougetachance toobserve two silos (or any two large, shiny objects) side by side in strongsunlight, look carefully into the shadowed side of one and find there somereflected light fromtheother.One thinghasbecomeclear tomeafteryearsofpainting shadows: themore intently you look at an area of shadow, themorevaried and interesting you'll find it. Shadows are not dead; they're verymuchalive.

Togetmorepractice in theuseofshadows, findanapple, set itonawhitesurface,darkentheroom,andspotlighttheapplewithasinglelamp.Thenmakeanumberofcharcoalsketchestryingtorecordthesubtlegradationsofshadowthatgivetheappleform.Movethelamptodifferentpositionsandsketchagain.Then place awhite cup alongside the apple and sketch again, noting how thereflectionsfromthecupaffecttheshadowsontheapple.

DetailandEdges

Supposeyou'retakingaphotographofyourgrandmothermakingherdebutasawrestler.It'sherbignightandyouwanttogetitright,soyouaimyourcameraather as she'sbeing introduced in themiddleof the ring, carefully focusonher,andreleasetheshutter.Whenthepictureisdeveloped,whatyouseeisGranny,crisp and clear, alongwith the referee. It's easy tomakeout the details of thearea you focused on–Granny's missing front tooth, her gnarled muscles, herbaggy shorts, the pink ribbon in her hair–but the rest of the picture is lessdistinct. You canmake out the crowd in the distance, impatientlywaiting forsomeblood,buttheformsaremoreandmorefuzzythefarthertheyarebehindGranny.Youcanbarelymakeouttheshadowyshapesattherearofthearena.

Your eyes work the same way. They can focus on objects at one distanceaway;theycannotfocusonobjectsnearandfaratthesametime.Lookintentlyat someobject in the room right now, say, your thumb at arm's length.Whilekeeping your eyes focused on your thumb, notice how everything else in theroomisoutoffocusandhowlittledetailortextureyoucanmakeoutonobjectsfartherandfartherfromyourthumb.

You can give your drawing or paintingmore depth by treating a scene thewaythecameraortheeyewouldseeit:pickadistanceyouwanttobemostinfocusandthenmakeallobjectsbeyondthatdistancegraduallylessdistinct.Youcanhelpaccomplishthisby(1)blurringtheedgesofmoredistantobjects,and(2)showinglessdetailinthedistantobjects.

At right are two versions of the same subject. In the first, I've madeeverythingprettymuchinfocus,boththestilllifeandthebusywallpaperbehindit.InthenextsketchthereisgreaterdepthbecauseI'vepicturedthingsmoreastheeyeorthecamerawouldnormallyseethem,focusingonthecloserobjectsand letting the distance become fuzzy and less detailed. Not only does thepicturegainsomedepth,butitbecomeslessbusyaswell.

DetailandEdges

Inthissketchthefocusisagainonnearerobjects.Theedgesofthemoredistantthingsareblurredandtheirdetailminimized.

Sothelessonissimple:Tohelpgetdepthinyourpicture,paintthingsasyouseethem,usingharderedgesandmoredetailforonedistancewhilelettingotherdistancesbecomegraduallylessinfocusandlessdetailed.

There'sarelatedconsideration,nothavingtoomuchtodowithgainingdepth,buthavingplentytodowitheffectivepainting.Paintersoftenfeelcompelledtomaketheforegroundofapaintingverydetailed,eventhoughtheforegroundisnotthecenterofinterest.Thereisnorationalefordoingthis;ifyouwereatthescene focusing on themiddle distance, the grass at your feetwould be only ablur.When you shotGranny in the ring, the people between you andGrannycame out blurred in the photograph, didn't they? If, on the other hand, theforegroundistobeyourcenterofinterest,thenbyallmeansgoaheadanddrawinall those littlegrassesorwhatever,butbesure tomakeeverythingelse lessdistinct.

Exercise:DetailandEdges

Carefully render thedrawingon thenextpage,usingeitherpencilorcharcoal.Maketheboat thecenterof interestandsubordinateeverythingelse to it.Bluredgesandshowlessdetailinareasfartherfromtheboat.

Youcaneitherstartwiththelightestshadinginthefardistanceandworkupto the strong edges and details in the boat, or vice versa. It's a good idea toestablisha rangeof lightsanddarks rightoff thebat, so thatyouknowwhereyou'regoingtoplacethelightest,mostblurredareas,andwhereyou'regoingtoputthedarker,morecrispareas.Onceyou'veestablishedyourrange,youcanfiteverythingelseinbetweenthoseextremes.

The little thumbnail sketch will give you a start. Notice I've indicated thedirectionofthesunlight.Changethedirectionifyouwish,butuseyourlightandshadowconsistently.Inmodelingaclumpoftreesorshrubs,forinstance,maketheundersidesandthesidesawayfromthelightsourcegenerallydarkerthanthesunlitsides.

ColorandValueChange

Takealookthroughyourwindow.Ifyoucanseeveryfar–say,amileormore–you'llnoticethatdistantobjectsappearmuchlesscolorfulthantheyactuallyare.Adistant skyscrapermight lookgrayeven though it'smadeofpinkgraniteorgreen-tintedglass.Far-offhillsormountainslookbluishorpurplish,dependingonhowfarawaytheyareandwhatsortofweatheryou'rehaving,yetyouknowtheywouldnotappearblueorpurpleifyouwereactuallythere,climbingthem.

Thereasonthecolorsofobjectsseemdifferentfromadistanceisthatthereisasortofveilyou'relookingthroughtoseethem,andthefartherawayyouare,thethickertheveil.Theveil,ofcourse,isthelayerofairbetweenyouandtheobject. All air contains tinywater droplets and impurities such as automobileexhaustfumesandsmokeanddustparticles.Theeffectofthisslabofnot-quite-transparent air is to act as a filter, letting certain wavelengths of light passthrough, but blocking others out. The cool colors (such as blues) get throughmosteasily,whilealotofthewarmcolors(suchasreds)getfilteredoutbeforetheyreachyoureyes.

Theactualcontentoftheairvariesfromoneregiontoanother,evenfromonetowntoanother,anditvariestremendouslywiththeweather.Butnomatterhowcleartheday,distantthingswillstilllookbluerthansimilarnearbythings;thereisstillaveilbetweenyouandwhatyou'relookingat.

Something elsehappenswhenweview things fromafar.Distant thingsnotonlylookbluer,butusuallylighterinshadeaswell.Belowisacountrysceneasitmightappearinablack-and-whitephotograph.

Noticethatthehillsgetlighterthefartherawaytheyare.Ifthiswereprintedincolor,thehillswouldbetendingtowardpalerbluesastheyrecede.Eventhebirdsshowupfainterwhentheyarefartherbackinthepainting.Thereissimplylesslightreachingoureyesfromadistantobjectthantherewouldbeifwewereclosetotheobject.Again,partofthereasonisthattheveilofairisfilteringoutsomeofthelight.Asecondreasonisthatthefartherawayanobjectis,themorewidelydiffusedisthelightgivenoffbytheobject.

ColorandValueChange

Painters,likeeveryoneelse,liketoattachfancynamestothings.Herearetwoofthem:thelightnessordarknessofanareaiscalleditsvalue;alightareahashighvalue, a dark area has low value. (When a student asked a teacher I know tocommenton thevalueof an areahehad shaded in, the teachergrumped, “It'spriceless.”)Together, the twophenomenawe've beendiscussing, color changeandvaluechangeoverdistance,areusuallycalledaerialperspective.

It's importanttounderstandthattherearemanyfactorsaffectinghowthingsappear at a distance, and no given scenewill look exactly the same fromonehourtothenext,letaloneonedaytothenext.Moremoistureorpollutionintheairwillalter things;acloudcastingashadowoveradistanthillcanmakethathill appear darker than the nearer ones, thus reversing our “rules”; a faraway,tree-covered hillside in the winter will appear cooler (more bluish) than thatsamehillsideinthefall.What'sreallyimportanttounderstandisthatyouhaveagreatamountofleewayincoolingthecolorsandlighteningthevaluesofobjectstomakethemfeelfartheraway.

Wetendtothinkabouttheobviouspartsofascenewhenweconsideraerialperspective–distantmountains,acityskylinemilesaway–thosethingsthattendtolookbluishorgrayish.Buthowaboutthingsthatarenearerandnotatallblueorgray?Consideraredbarninayellowishmeadow.Ifyou'replacingthebarnandmeadowprominentlyneartheforegroundofyourpainting,thenpaintthemasredandyellowasyouplease.Butifthissamebarnandmeadowareaquarter-mile away and you paint them as red and as yellow as they really are, they'll

jumpforwardandfalloutofthefrontofthepicture.Warmcolorstendtocomeforwardandcoolcolorstendtorecede,sotopushanobjectfartherbackintothepicture,makeitscolormorecool(orlesswarm).Dullthatredforthebarnjustalittle–try a dab, and see how it feels. If it still shouts “Gangway! I'm comingforward!” then dull it a little more until it feels right for the distance you'regivingitinthepainting.Thesamegoesfortheyellowmeadow.Perhapsupcloseitlooksasbrightascadmiumyellow,butmaybetopushitbackyouneedyellowochre.

Ihopeyoudon'ttakeanyofthisasanythingmorethanguidelines.Therearemany factors affecting the look and feel of your painting, so don't be caughtconcentratingtoomuchononefacet.Don't,forexample,slavishlydulldowntheredpaintforthebarnwithoutconsideringalsothecolorsthatadjointhebarn.Ifthebarnissetagainstabackdropof,say,greenwoods,youmayneedtodulltheredmore than if thebackdropwerebrownautumn foliage, becausegreen is acomplementary color to red and its presence tends tomake any red look evenredder. If there is any rule in painting, it's this: Learn all the devices andtechniquesandtricksandgoofballideasyoucan,butthenkeepyoureyeonhowthewholepainting isdeveloping, rather thansomeisolatedpart;and then trustyour instincts. The more you paint, and the more you look at other people'spaintings,themoretrustworthyyourinstinctswillbecome.

LestIleaveyouwiththenotionthatareasinthebackgroundmustalwaysgetlighterthantheforegroundareas,lookatwhathappenstothesketchaboveleftwhenwedarkenthebackground,aboveright.Thevaluecontrastseparatesthetreefromitsbackgroundandseemstothrustthetreeforward(orthebackgroundback).

Further depth can be attained by employing some of the other techniques,such as modeling the trunk and branches to make them feel round. Usingordinarypencilordilutedinkorwatercolor,dosomecarefulmodelingrightonone or both of these sketches.Be sure to decide first the position of the lightsourceinthescene,andthendoyourmodelingaccordingly.Ifyouchoosealightsourcetowardtheleft,forexample,darkenthetrunkmorearoundtherightside.

ColorandValueChange

The tree illustration demonstrates that you can introduce separation betweenareas,andthereforedepth,simplybyhavingafairlystrongchangeinvalues.Inthatexamplewewentfromlightforegroundtodarkbackground.In thesketchabove,thesamesortofthingisaccomplished,butinthiscasewegofromdarkto light.Anabruptvaluechange ineitherdirection isoftenagoodvehicle forintroducingdepth.Suchavaluechangehasnotmuchtodowithgreatdistancesorveilsofatmosphere.Itsimplyworks!

Exercises:ColorandValueChange

ColorChange

Color in thesceneon thefollowingpagewithcoloredpencils (orpaint, ifyouprefer).Youmightmaketheskysimplyblueandwhite, the treesgreenish, thebarn roof gray, the ground areas yellows and greens, the path, roadway, andfencepostsbrown.Don'tcolorinthemailboxflag(1),thebarnfront(2),orthebrickhouse(3).

Makeatleastthreetracingsofthebarnfrontandthebrickhouse.Transferthetracings to paper you canpaint on, and cut themout.Let's assume that in theactualsceneallthreenumberedareasarethesamered.Pickafairlystrongredandpaint all threeareas (1,2, and3)with that same red righton thispracticesheet.Noticethatthebarnandhousedon'tyetfeelasdistantastheyshould.

Nowusethesamered,slightlydulled,topaintoneofthecutoutsforthebarn.Lay thecoloredcutouton thepaintingandsee if it feels right.Toored?Coloranothercutout, this timedullingtheredevenmore.Still toored?Tryagainonanothercutout,butthistimeinadditiontodullingthered,trymakingthecolorlessintenseaswell–thatis,lightenitsvalue.Whenyoufinallygetaredbarnthatfeels right, dull the color evenmore and use it on a cutout of the evenmoredistanthouse.Whenyougetfinished,thereshouldbeanoticeabledullingoftheredsasyougobackintothesceneandagreaterfeelingofdepththantherewaswhenallthreeobjectswerepaintedthesamered.

Youmighttraceofftheentirescene,transferthedrawingtoanothersheetofpaper,anddosomefurtherexperimentingwithotherrecedingcolors.Thistimeimagine the flat ground areas to be either yellows or greens. Make the frontgroundareas thebrightestgreens (oryellows), themiddleareasmoresubduedgreens(oryellows),andthedistantareasstilllessbright.

ValueChange

First, make several copies of the sketch by tracing it onto pieces of ordinarytypingpaper.Then,usingcoloredpencilsorpastels,carefullycoloronecopyofthesceneas awinter scene:Make themostdistanthills very cool (blues) andlightinvalue;middleareasprogressivelylesscoolanddarkerinvalue;andtheforeground essentially white with snow on the ground and on some of thebranches of the large tree. Although the foreground will thus be the lightestvalueofall,itwillnotautomaticallyrecedebecauseyou'llincludeenoughdetailandsharpedgestomakeitseemclosetotheviewer.

Then on another copy of the same page, create a fall scene from the samesketch:Make themostdistanthills light invalueandcool incolor,butnot ascool as in the winter scene–try more purplish than bluish; intermediate hillsgraduallywarmer;foreground,detailedtreesandrocks,withplentyoftouchesofwarmcolors.

ConvergingLines

Standwithyourbacktothewallinanyroominyourhouseorofficeandfacetheoppositewall. Ifyours isa“normal” rectangular room,you'll find the left andrightwallsseemtobeclosertogetheratthefarendoftheroomthanattheendwhereyou'restanding.Thelineswherethesidewallsmeettheceilingseemtobeconvergingandwouldapparentlymeetsomewhereiftheywereextendedfarenough.

Flip back to some of the earlier illustrations in this book, such as the trainstationonSizeandSpaceVariation.Noticethatthetracksseemtobeconvergingastheygooffintothedistance.Youknowthattheydonosuchthing–iftheydid,thefirst train tocomealongwouldbe ina lotof trouble!In thatsamepicture,notice that the buildings seem to squeeze smaller as they recede. If you drawlightlinesextendingthemainrooflinesandthefoundationlinestowardtherightyou'llfindthattheymeetatapointapproximatelyalongthebottomedgeofthedistant row of trees. Now do the same with the straight portions of the traintracks–extend them and you'll find they meet at a point along that samehorizontallineatthebaseofthedistanttrees.

Lookatthebrickwalkwayinthesketchabove.Youcanprettymuchassumethis path is about the samewidth all theway along, but there it is squeezingtogetherasitrecedesfromyou.

It'sthewayweseethings.Linesthatweunderstandarereallyparalleltoeachother seem to converge as they recede fromus.We intuitivelyunderstand thisapparentconvergenceasrepresentingdepth,ordistance.Indrawingandpainting

wemakeuseofthisunderstandingtogiveourpicturestheillusionofdepth.Theuseofconverginglinestosuggestdepthisusuallycalledlinearperspective,andit'soneofthemosteffectiveofalltheperspectivetechniques.

ConvergingLines

Somedefinitionsareinorder.Imagineyourselfonalong,straightroadinTexasthatstretchesawayovermilesofperfectlyflatlandandfinallydisappearsonthehorizon.Weallunderstandthehorizontobeanimaginaryhorizontallinewheretheskymeetsthelandorwater.Thetwosidesofourroadwillappearactuallytomeetatthehorizon,andthepointwheretheyseemtomeetiscalledavanishingpoint(VP).It'swheretheroad“vanishes.”

Nextweneedtounderstandsomethingcalledtheeyelevel.Theeye level issimplyanimaginaryplanepassingthroughtheeyesoftheartistorotherviewerofascenewhenheorsheis lookingstraightahead.InourTexasexample, theeye level issynonymouswith thehorizon.Infact, they'realwayssynonymous,butbecausetherearetimeswhenyoucan'tactuallyseethehorizon(theremaybe mountains, buildings, or other objects in the way) we discard the use of“horizon” indiscussionsaboutperspectiveanduse the safer term,“eye level,”instead.

Establishing the eye level in a realistic picture is crucial because, as you'llsoon see, everything else in the picture is drawn relative to the eye level. Toillustrate,considerthethreesketchesatrightrepresentingourTexashighway.

In the first, imagine you're simply standing and looking straight ahead towhere the road “vanishes”–the vanishing point. Then suppose you lower youreye level by lying with your chin on the ground and looking straight ahead.What you'd see is something like the second sketch (less ground,more sky–aworm's-eye view).Now suppose you're carried aloft by aTexas-sized buzzardand againyou look straight ahead towhere the road “disappears.”Nowyou'llnoticemorelandbeneathyouandrelativelylesssky,asinthethirdsketch.

Remember:Theeyelevel(EL)isthehorizontallevelinlinewithyoureyeswhenyou'relookingstraightahead.Theeyeleveldoesnotchangewhenyoutipyourheadbackorforward,orwhenyourollyoureyesupordown.

ConvergingLines

Letmeputitanotherway:Theeyelevelinyourpicturetellstheviewerofthepicturehowhighupyou

werewhenyoupaintedit.Onceyou'veestablishedhowhighyouareinrelationtoyoursubject,itdoesn'tmatterwhetheryoulookupordown.

For instance, supposeyou'redrawingabird inanestona limbaboveyourhead,belowright.Theeyelevelinthatscenewillbelow.You'llbeseeingthebirdandnestfromunderneath.

Nowsupposeyoudrawanestinthegrassesatyourfeet,belowleft.Theeyelevelisveryhigh,sohighthatit'soutofyourpicture.

The eye level changed between these two scenes because your physicalrelationshiptothesubjectchanged(inthiscase,thenestchangedplaces,buttheeffectisthesamewhetherit'stheartistorthesubjectthatmoves).

Inboththeseexamples,youhadtobendyourheadeitherupordowntoseeand draw the subject. But that didn't affect the eye level. The earth's horizonneverchanged,didit?Nomatterhowsharplyyoulookupordown,thehorizon,oreyelevel,staysput.

ConvergingLines

Nowlet'sgobacktoyourordinaryrectangularroomandassumeyou'restandingsmackin themiddleof it, facinganendwall.You'refarenoughbackthatyoucanseeportionsofwalls,ceiling,andfloor,asshownabove.

Ifyoureyesare,say,fivefeetabovethefloor,thentheeyelevelinthesceneyouarewitnessing isalso five feetabove the floor. Ifyoudecide topaint thissceneasyouseeitfromwhereyou'restanding,you'llneedtodrawlightly(oratleastimagine)ahorizontallineacrossyourcanvasrepresentingtheeyelevelinthe scene you're about to paint, and then you must relate everything in thepicturetothateyelevel.

ConvergingLines

Inascenesuchasthisthereisasinglevanishingpoint(VP).Ifyou'restandingequidistant from the twosidewalls, theVP ishalfwayacross the farwall andfivefeetupfromthefloor(theheightofyoureyes).Ifachildwerepaintingthescenefromthesamespot,theeyelevelwouldbemuchlowerandtheresultantpaintingquitedifferentfromyours.Thechildwouldseemoreceiling,lessfloor.

In thissimple roomtherearesomehorizontal lines receding fromyou.Thelineswheretheceilingmeetsthewallsareaboveyoureyelevel,andtheyseem

to aimdownward toward eye level.The lineswhere the floormeets thewallsseemtoaimupwardtowardeyelevel.Infact,ifyoumentallyextendallfourofthose lines into thedistanceyou'll find that theyallmeetatasinglepoint (thevanishingpoint),andthatpointsitsrightontheeyelevel.

InthesecondsketchI'veaddedafewsimpleitemstotheroom:alowtable,awindow, and a door. Look at the receding “horizontal” lines in each of thoseobjects.TheyallmeetatthesameVP.

ConvergingLines

Ifyoucouldseethroughthewallandfarenoughintothedistance,you'dseetheearth'shorizonpassing through thevanishingpoint. I'veputa largewindowinthefarwallsoyoucanseethiseffect.

What we've sneaked up on here is a technique called one-point linearperspective.Thereisonlyasinglevanishingpointinthescene,andonefaceoftheobjectbeingdrawn(theroom)isparalleltothepicturesurface.Hadwenotarrangedthingssoneatly–forexample,ifthetablehadbeenturnedatanangle,orwehadfacedacornerratherthanthefarwall–wewouldhavefoundthatnotallparallel linesinourpictureconvergednicelytoasinglepoint.TherewouldhavebeentwoormoreVPs.We'llgettothatinPartTwo.

ConvergingLines

One-pointlinearperspectiveisnotusedasextensivelyinpresent-dayartastwo-point.One-pointtendstobestaticandformal,andwe'renottoostaticandformalthese days. A couple of centuries ago, however, this form of perspectivewasused often. A good example of its use is Leonardo'sLast Supper, which I'vesketchedhere.

Where doweuse one-point perspective these days? It's quite often used inportraitpainting,wheretheartistattemptstofocusattentiononthesubjectoftheportrait by arranging the surroundings in one-point perspective. For example,Leonardo's work focuses attention on the central character by making therecedinglines in theroomconvergeverynearJesus'head.Oftenin landscapeswhereIhaveanumberofbuildings in two-pointperspective,I includeat leastonebuildinginone-pointtohelpsettlethingsdown.Toomanyobjectsintwo-pointcanbeconfusingorunsettling,buttheinclusionofanobjectinone-pointcanhelprestorealittleorder,asenseofcalm.Again,we'lldiscussthisfurtherinPartTwoofthisbook.

Somethingyou'llnoticeaboutrecedinghorizontallines,besidesthefactthattheyallmeetatavanishingpoint:thelinesbeloweyelevelwillslantUPtomeetthe eye level and those above the eye levelwill slantDOWN tomeet the eyelevel.

Exercise:ConvergingLines

Let'sconstructasimplebox,liketheoneshownhere.Usingthefrontfaceofarectangular box provided on Exercise: Converging Lines and the eye levelindicated,followtheconstructionstepstoaddtherestofthebox,includingthehiddenedges.

Afteryou'vecompletedaboxusingthefacegiven,constructyourownfrontface on a blank sheet of drawing paper, establish an eye level, and repeat theexercise.

Step1 : Imagine this tobeaglassboxso thatyoucansee the rearedgesandcorners.Thefrontfaceisparalleltothepicturesurfaceandtheboxisbeloweyelevel.


Step2:Dependingonwheretheviewerisstanding–atcenter,orleftorrightof

center–thevanishingpointmayfallanywherealongtheeyelevel.Let'sassumethe viewer is a little left of center (a socialist, maybe) so the VP will besomewhere leftofcenter.Butwhere? Ifyouwereactuallyseeinganddrawingthis box, youmight hold a straightedge at arm's length, angle it tomatch theangle of one of the receding edges of the box, carefully move the angledstraightedge toyourdrawingsurface,andsketch in thatedgeonyourdrawingalongsidethestraightedge.Let'ssaytheresultantedgeoftheboxislinea.

Step 3: The rest is easy. Where line a meets the eye level, you have yourvanishingpointCVP).Toget theother threerecedingedgesof theboxsimplyconnect the remaining corners of the front face to the VP. Notice that, inaccordance with our guideline, since the box is below eye level all recedingedgesslantUPtomeettheeyelevel.


Step 4: The next thing to determine is how deep this box is. In practice youestimatethatbyeyeballingthescenebeforeyouandcomparingthedepthoftheboxtootherdimensions,suchastheheightofthebox.Whateveryouarriveatwillbeyourbestguess.Drawinlinebwhereyouthinkitbelongs.Ifitdoesn'tlookright,moveitforwardorbackuntilitdoes.

Step5:Thisisprobablyagoodplacetotellyousomethingyoualreadyhaveasneakingsuspicionistrue:There'salotofcomplicatedgeometryyoucanusetoarriveatvariouslinesandanglesinaperspectivedrawingtogetitjustright.Butunlessyou'reanarchitectoranitpickerbeyondallredemption,forgetit.Ifyouget too technical,you'llonlysucceed indrainingyourartof itscreativespark.You'll end upwith a drawing that's technically accurate, but nobodywill careandyou'llbeexhausted.

Backtoourglassbox.It'sfinished,ifyousimplyerasetheconstructionlines.But this is a glass box for a reason –I want you to be able to visualize thenormallyunseenrearedges.Tolocatethemexactly,drawverticallinesthroughthepointswherelinebintersectslinesaandc.

Wherethoseverticallinesintersectthebottomrecedingedges,youhavetheremainingcornersofthebox.Connectthosecornerswithlined.Noweraseun-neededconstructionlines,andthereyouhaveit.

Sofarwe'vesaidlittleaboutverticallines.We'vejustleft themvertical.Novanishingpoints,noslanting,nopizazzatall.Thereasonweleaveverticallinesaloneisthis:Inthegreatmajorityofthesubjectswechoosetopaint,theverticallinesarerelativelyshort,andanypointalongavertical lineseemsroughlythesame distance from our eyes as any other point along that line. There is noillusionthatthelineismovingawayfromus.InPartThree,however,we'lldealwithverticallinesthataresotallthatapairofthemrisingskywardordivingintoavalleywillindeedbemoving“away”fromusandwillseemtobeconvergingtowardavanishingpointjustashorizontallines,suchasrailroadtracks,seemtoconvergeastheymoveawayintothedistance.


VanishingPointandEyeLevel

Here's a room drawn in one-point linear perspective, with one side wallestablished.ExtendthetopandbottomoftheexistingwalltofindtheVP.Thendrawintheeyelevelandtherightwall,ceiling,andfloor.(Remember,theeyelevel is simply a horizontal line drawn through the VP.) Exercise: Vanishing

PointandEyeLevel

Hereyou'restandingonaleveldocklookingoutacrossthewateratthehorizon.Choosethemostlogicalhorizonanddrawitin.

You'resixfeettallandstandingonalevelboardfloorlookingstraightaheadatanoppositewall.Thewallhasanormalseven-footdoorwayinit.Choosethemostappropriatedoorwayanddrawitin.

Thecorrectchoicesarethemiddlehorizonandthesmallerdoor.

Exercise:VanishingPointandEyeLevelHereareportionsofthreerectangularboxes.Finishdrawingeachinone-pointperspective,usingVPasthesinglevanishingpointforallthree.

EstimatingAngles

Linear perspective involves the constant observation and drawing of angles.Hereisausefultechniqueforestimatinganglesaccurately.First,makeasimpleangle-measuringdeviceshapedlikescissors.Cut twostripsofcardboardabouteightincheslongandaninchwide.Fastenthestripstogetheratoneendwithapaper clasp, a thumb tack, a screw, orwhatever. The idea is to hinge the twostripssothatthey'resnugbutmovable.Youcouldalsouseafoldingcarpenter'srule,ifthereisonehandy.

Withyourbacknearonewallofarectangularroom,setupapieceofpaperonyoureaselatarm'slengthinfrontofyou,asshownatcenter.

Using charcoal, draw in a rectangle roughly representing the far endof theroom. I've roughed ina faintoutlineofa typical farwall,butyoursmayhavedifferentproportions;ifso,changemysketch.

Nowuseyourcardboardmeasuringdevicetofindtheanglesatwhichthesidewalls,ceiling,andfloorseemtomeetthatfarwall.Here'show.Holdthedeviceatarm'slengthsothatitalwaysstaysparalleltothatfarwall(andparalleltothepaperonyouruprighteasel).Use thecardboard scissors tomeasureanangle–let'ssaytheanglebetweenthehorizontaltopofthefarwallandthelinewheretheceilingandleftwallmeet.Don'tswivelthescissorstomatchanangle–keepthedevice flat (parallel to the farwall)andvaryonly theamountyouopenorclosethehingedjaw.Whentheanglebetweenthecardboardsmatchestheangleyou'remeasuring, carefullymove the cardboards, still at arm's length, to yourpaperand traceoff theangle.Do the same foranyangleyouwant tocapture,includingtheshapesofpictureframes,doors,windows,etc.Withpracticeyou'lllearntokeepthemeasuringdeviceparalleltoyourpaperandnotletitswivelinyourhand.

PartTwo:BoxesandBeyond

Johnwasoneofmy students a fewyears ago.Hewas impatient.He loved todisagree.Heinsistedskieswereblueandwhiteanditwasridiculousformetodemonstrate one that was purple and gray. One evening I was demonstratingsomesimpletwo-pointperspective.

“Phil,whybother?”ItwasgoodoldJohn.“Whybotherwithwhat,John?”“Withallthisconstruction.”“Because sometimes it's tough to get down on paperwhat you see and it's

goodtohavesomebasicstofallbackon,John.”“Butweallknowhowtodrawthingsinperspective.”Iwas a verypatient teacher, I think, but occasionallymypatiencedeserted

me.Isaid,“John,howaboutyourfarmscene,theonewecritiquedlastweek…didn'twefindacoupleofperspectiveproblemsthere?”Actually,hehaddrawnonebarnslidingofftheleftsideofthepaperandanotherseemedtobesinkingintoquicksand.

“Naw,Phil,”helaughed,“itwasjustcoldthedayIwaspainting…littletoomuchbrandyinmycoffee!”

“Well,”Iwenton,smilingandtryingtoaddressthewholeclass,“Iknowthatpeople get scared of perspective because they think it's mysterious andcomplicated…”Johnwassettlingbackandhiseyelidsweregettingheavy.“Butbasically it's pretty simple. It's just a set of ideas that help you tomake soliddrawings of solid things.” I threwan eraser in John's direction and joltedhimawake.“Right,John?”IlaughedandJohnsemi-smiled.

“Now,” I continued, “I don't want to leave the slightest impression that acreative painting or drawing is something bound up in rules. What we callperspective is justanothersetof tools that'llhelpyourcreativity,nothinder it.Themoreyouknowoftechniques,tricks,andtools,themoreyoucanletlooseandfreeupyourcreativetendencies.Right,John?”

“You'retheteacher,Phil,”saidJohnwithplayfulsarcasm.IdecidedtotakeonemorestabatconvincingJohnheoughttopayattention

toperspective.“Lookatitthisway,John.Learningwhathappenstoanobjectinperspective

isreallynodifferentfromlearningthatmixingredandyellowgivesyouorange.

Thesearesimplypartofthestoreofknowledgeyouaccumulateandtuckawayinyourbrain,andthencallonautomaticallywhenyou'recreatingapicture.Youwon'tnormallysay,‘Nowlet'ssee,thislinehastogotothisvanishingpointandthatlinegoestothatvanishingpoint’anymorethanyouwouldsay,‘Now,let'ssee,Ineedblueandyellowtomixagreen.’”

“How's that again, Phil,” John was suddenly awake and scribbling in hisnotebook.“Blueandyellowmakewhat…?”

InPartOnewediscussedavarietyoftechniquesusefulforgettingafeelingofdepthinapaintingordrawing.Thesetechniquesareusuallylumpedtogetherandcalledperspective.The lastperspective techniquewediscussedwas linearperspective, the use of converging lines to suggest depth. When we drawsomethinginlinearperspective,allwe'redoingismakinglinesthatareactuallyparalleltooneanotherappeartoconvergeatsomedistantvanishingpoint.Likealltheotherperspectivetechniques,thisissimplyanimitationofhowoureyesandbrainsactuallyinterpretthings.

In Part Two we'll concentrate on drawing rectangular objects in linearperspective.Mostoftheotherthingswedrawcanbethoughtofasvariationsofrectangular objects, so once these are mastered you can draw practicallyanythinginperspectiveandgetitright.

Intheexamplessofar,we'vedealtwithone-point linearperspective–simplesituations in which all receding lines meet at a single vanishing point on thehorizon,oreyelevel.Herewe'lldealwithamorecommonsituation,two-pointlinear perspective.Thismeanswehave twovanishingpoints,with some linesrecedingtooneofthemandsometotheother.


Layastraightedgealongeachofthesevenlinesinthisboxanduseapenciltoextendeachofthemafewinchesinbothdirections.

What do you see? First, the vertical lines stay parallel to each other andapparentlydon'tplantomeet,nomatterhowfaryouextendthem.Buttheotherlines,the“horizontal”ones,domeet.Theright-handonesmeetatapointtotheright,theleft-handonesmeetatapointtowardtheleft.Nowuseastraightedgetoconnectthosetwomeetingpoints.

The secondsketchestablishes somenameswe'lluse.Thepointwhere linesmeet at the right is vanishing-point-right, or VPR, and the one on the left isvanishing-point-left,orVPL.Thelinetheylieonistheeyelevel,EL.ThesearethesametermsandconceptsweusedinPartOne,exceptnowwe'redealingwithtwovanishingpointsinsteadofone.

ThedifferencebetweenthisboxandsimilarobjectsdiscussedinPartOneisthatnoneofthefacesofthisboxareparalleltothepicturesurface.Bothvisiblefaces of this box are turned away from the viewer into the distance, and theirhorizontaledgesmeetatoneoftwovanishingpoints.


Here I've shown threeboxes,onewith itsbottomateye level,oneabove,andonebeloweyelevel.Eachistwistedatadifferentanglefromtheviewer.

Noticesomethingveryimportantinthis“scene”:Eachboxhasitsownpairofvanishingpoints,butallthevanishingpointsliealongthesameeyelevel.Theseboxes could represent houses in a village with hills and valleys. Each housewouldhaveitsownsetofvanishingpoints,buttheentirescenewouldhaveonlyasingleeyelevel,andthevanishingpointsforallthehouseswouldfallonthateyelevel.

So letmerepeatsomethingfromPartOne:Whenyoudrawanyscene, firstestablish theeye level fromwhichyouwish toviewthescene,and thenrelateeverythingtothateyelevel.Itmakessense,doesn'tit?Ifyoudrawoneobjectasitwouldbeseenatoneeyelevelandanotherobjectasitwouldbeseenfromadifferenteyelevel,howcouldthetwoobjectspossiblyfeelrighttogetherinthesamepainting?Thiswouldworkforanobserverfromanotherplanetwitheyesin both his head and in his knees.Here on ourmundane earthwe have to becontentwithonesetofeyesperhumanoid.Chooseaneyelevelandstickwithit!

DrawingThrough

Todraworpaintathree-dimensionalobjectconvincinglyyouneedtounderstanditsvolume–youneedtobeableto“getyourarmsaroundit”mentally.Ifyoucan“feel” the roundness of a tree trunk, you canbetter get it downonpaper as athingthathasthickness;ifyouonlyseethetrunkasaflatshape,you'llprobablydrawitasaflatshape.Awaytotrainyourselftocapturethevolumeofanobjectis to constantly draw its hidden lines, especially when you do your rough,preliminarysketching.

Herewehavea flashlight,anelectricpencilsharpener,andashed. In thesesketches I've tried to remind myself of the depth these objects have. Theflashlight is not just the flattish surface I see when I glance at it, but rathersomethingthatcurvesawayandaroundandbackagain–itevencontainsroundbatteriesthatIcan'tsee,butIsketchtheminanywaytohelpmefeelthesolidityof thesubject. Including thebatteriesalsoservesasacheckon the flashlight'sproportions; had I found I had left too much or too little space for the twobatteriesIknowareinthere,Iwouldhaveshortenedorlengthenedtheshaftofthe flashlight. The pencil sharpener and the shed are relatively simple-shapedobjects,butevensotheycangiveyouafitifyoudon'tlocate(atleastmentally)theirhiddencornersandedges.Roughinginsomeconstructionlinesandfindingthose edges and corners canmake the difference between a solid, convincingdrawingandadrawingthatisunexplainablyoutofkilter.

Sketchinginthiswayissometimescalleddrawingthrough.Drawthroughanobjectandseewhereitgoeswhenyou'renotlooking.

InPartThreewe'llfurtherexplorethevalueofdrawingthroughwhendealingwith curved or odd-shaped objects.Right nowwe're concernedmorewith therectangularbox,butevenhereit'sextremelyhelpfultobeableto“see”throughtheobject.

FindingHiddenEdges

Let'sreturntothesimpleboxandseehowtolocateitshiddenedges.Followmeastepatatime,drawingrightonthissketch.

First, let's locate thevanishingpoints,VPLandVPR.Do thisbyextendingthehorizontaledgesoftheboxuntiltheymeet.Thendrawintheeyelevel(EL),connectingVPLandVPR.

Where are the rear (hidden) walls in this box?What are their shapes andwhere do they meet? If we can figure out where they meet, we'll have therearmost(hidden)verticaledgeofthebox.

Actually,it'seasy.Thehiddenhorizontaledgesoftheboxobeythesamerulesas the visible horizontal edges: they slant toward the appropriate vanishingpoints. Connect the leftmost vertical edge with VPR. Do you see that line ashows the slant of the rear upper edge of the box as it recedes toward itsvanishingpoint,andlinebshowstheslantof therear loweredgeas it recedestowardthevanishingpoint?

FindingHiddenEdges

Now connect the rightmost edge of the box to the other vanishing pointwithlinesdande.

Theright-slantinglines,aandb,defineoneofthehiddenwalls,andtheleft-slantinglines,dande,definetheotherhiddenwall.Wherethosetwowallsmeetislinec,thehiddenverticaledgeofourbox.

Linesaandd shouldmeetatapointdirectlyabove thepointwhere linesbandemeet,butunlessyou'realotmorecarefulthanI,theywon'texactly.Don'tworryabout it.You'resketchingabox,notdesigningabomb.Only ifyouusethemostextremecare inallyourgeometrywill thingscomeoutperfectly,butit'snotworththebother.

If we erase unnecessary construction lines and imagine our box astransparent,we see something like this.An understanding of this constructionwillenableyoutodrawpracticallyanyrectangularobjectwithauthority.

Exercise:HiddenEdges

Here are the beginnings of three boxes. For each one, an eye level and twovanishing points have been established. In each case I've shown the mostforward vertical edge of the box. Complete each box, placing the remainingvertical lines wherever you wish to establish the lengths for the sides of theboxes.Ifyouhavetrouble,lookbackatFindingHiddenEdges.Useblackpencilto represent lines that would be visible to a viewer and colored pencil for“invisible”lines.


Sofar,I'vebeenprettydictatorial.I'vetoldyouwherethevanishingpointsare,period.Butwhenyou'reout theresketching,you'reonyourown.Howdoyouknowwheretoputthevanishingpoints?

Let'sassumeyou'rebeginningthedrawingofabarn.First,youmightlightlydrawintheverticalbarnedgethat'snearestyou.Thenyoucouldfindapairofhorizontaledgesthatseemtoberecedingfromthatverticaledgetoavanishingpoint.Let's say the twohorizontal edgeswere the roofline and the foundationlineononesideof thebarn.You'dholdastraightedgeout in frontofyouandslantittomatchtheslantoftherecedingroofline,thenmovethestraightedgetoyourpaper(maintainingtheslant)andlightlysketchintheroofline.You'ddothesameforthefoundationline.Wherethetwolinesmetonyourpaperwouldbeone of the vanishing points. Youmight need tomake several attempts at thisbefore getting something that seems right because you're liable to change theslantofthestraightedgeasyoumoveittoyourpaper.Withalittlepracticethiswillnolongerbeaproblem.

Next,you'ddothesamethingwiththeothersideofthebarn—thatis,locateitsvanishingpointusingthestraightedge.

All'swellifbothvanishingpointsendupneatlyonyourpaper,butoftenoneorbothseemtofallsomewherebeyondtheedgesofyourpaper.Frequently,onevanishing pointmay seemvery far to the side.You can do one of two thingsaboutthis:1. If it's feasible for you to temporarily tack on additional paper alongsideyour picture and locate the vanishing points on this temporary paper, goaheadanddoso.Thismaybe reasonable ifyou'reworkingatadeskandhaveroomtolayoutthepapertotherightandleftofyourdrawing;inthefield,it'srarelyreasonableorconvenient.

2.Ifyoucan'tusetemporarypaper,forgetaboutactuallyputtingdownapointthat says “vanishing point.” Instead, just sketch in guidelines that, ifextended far enough off your paper,wouldmeet at a vanishing point. Inotherwords,youkeepamentalpictureofwherethevanishingpointisbutnever actually put it down on paper. The guidelines aiming toward thevanishingpointarereallyallyouneed.Afterall,theonlyreasonyouneedvanishingpointsinthefirstplaceistohelpgetthecorrectslantonvariouslinesinyourdrawing.Whatyouendupdoing,then,iscomparingtheslantsof all the lines you draw with the slants you established with your

straightedge.Obviously,youcoulduse thestraightedge toget theslantofeverylineyoudraw,butthat'stediousandunnecessary.Onceyouestablisha couple of basic guidelines with the proper slant, you can use them toestimatetheslantsforallyourotherlines.

What'sLegal?

Supposeyou'relookingatanddrawingasceneanddecideyouwanttochangethe locations of the vanishing points. Is that legal? ANYTHING IN DRAWING ORPAINTINGISLEGALIFITGETSYOUWHEREYOUWANTTOGO.Let'sfaceit—ourlivesare governed by all kinds of laws mostly intended to keep us from harmingourselvesorourneighbors.Butinyourownart,youarefreetodowhateveryouwish,shortofcopyingsomeoneelse'sideas.Ofcourse,youmaybetheonlyonewholikestheresult,butthat'sanothermatter.

Youmayaskhowsuchalawcanbestatedinabookfullofdirectionsabouthow to draw in “proper” perspective. The answer is this: If you first learn todrawthingsastheyreallyareandasmostnormalhumanswouldseethem,youhave a foundation from which you can extrapolate. Your art can become asstrangeandtwistedandwarpedasyourfrenziedbraincanmakeit,butit'seasierto get anywhere if you start from somewhere.Youonlyneed look at theveryearlyworksofPicasso toseewhat Imean.Hestartedwithperfectly“normal”images—for example, people whose parts were all in the usual places—andendedwithpicturesofpeoplewhosepartswerewhereverhedamnwellpleasedtoputthem.


TakingLiberties

HereisapictureIpaintedfrominsideanoldshedIonceowned.Theshedhadbeenwhackedoffitsfoundationbysomebodyusingitasagarageandtryingtosqueezetoolongacarintoit.Usingsomehydraulicjacksandalotofsweat,Iraisedthetwosidesofthebuildingthatwereoffthefoundation.ThenIwrappedahugeropearoundthewholebuilding, tiedit to thebumperofmy '65Chevy,andtuggedthebuildingoffthejacksandbackontothefoundation.Astheshedgroanedmoreorlessintoplace,Iavoidedmakingeyecontactwithaneighborwatchingwithabemusedlook.Shewassurethatmorethantheshedwasoffitsfoundation!

Igottheshedprettymuchbackinplace,butitwasneveragainreallyplumb.AsahomeownerIwasn'tcrazyaboutthat,butasapainterIlikeditandpaintedprettymuchwhatIsaw.Youmightuseastraightedgetoextendsomelinesinmypaintingandseeforyourselfhowthey“almost”meetatpropervanishingpoints.

There'splentyoflinearperspectiveinvolvedhere,forcingtheeyethroughthevariousopeningsandoff into thedistance.The fact that some linesdon'tmeetneatlyatpropervanishingpointsdoesn'tmatter.Theperspectivelinesaimintheright directions and are accurate enough tomake this a plausible building butinaccurateenoughtosuggestageand,inthiscase,mistreatment.BecauseIhadhad some experience observing how things are built I couldmake reasonablejudgments about what to “straighten up” in my painting and what to leavecockeyed.Iwasabletokeepsomelinesandshapesthatwerenotquite“correct”but not have the painting look as though I simply didn't know any better.Incidentally, notice that there are perspective techniques other than linearperspectiveatworkhere:•Sizevariation: boards in the nearwall arewider than those in the distantattachedshed;andthedistantdoorwayseemsmuchsmallerthanthenearestdoorway,eventhoughthey'rereallythesamesize.

•Value change: the sudden switch from dark interior to sunlit exterior andback again to dark interior forces a feeling of stepping back into somedistance.Thereisalsoastrongcolorchange(warmcolorsupclose,coolsinthe distance), but of course that gets lost in this black-and-whitereproduction.

•Overlap:thefarwallsareoverlappedbythenearestwall;thesupportpostisinfrontofthefence,andthefenceisinfrontofthebushes;eventheshovel

leaningagainstawallhelpstopushthatwallback.•Blurrededges:thefocusisontheareawheretheshovelis.Thenearestareaissomewhatblurred,asarethedistantbushes.

Inside-Out,PhilMetzger,watercolor,36″×28″


AchievingDistortion

Rotatinganobject andusing itsnewvanishingpoints tocheckuponwhetheryoudrewtherotatedobjectcorrectly isfairlystraightforward.Thereisanotherwayyoucan fiddlewith thevanishingpoints:youcansqueeze themtooclosetogetherorseparatethemtoowidelyinordertodistorttheobjectyou'redrawing.Thelawallowsyoutodothat.

You've probably seen book or magazine illustrations in which a hauntedhouseisshowndistortedsomethingliketheoneabove.Inperspectiveterms,theartisthasmovedthevanishingpointsclosetogethertogetthiseffect.Intruth,ofcourse, theartistprobablydoesnotevenconsciouslyconsidervanishingpointswhendoingadrawinglikethis,butheorsheiscertainlymakinguseofthelogicoflinearperspectivetomakethedrawingwork.


Thesketchofthehauntedhouseattopshowshowthedrawingonthepreviouspage used linear perspective. Even though the vanishing points are closertogetherthaninreality,IwascarefultomakesureallhorizontallinespointedtothesametwoVPs.

In the second sketch I've drawn the same haunted house without beingconsistent with the distortions. I've neglected to slant the right-handwindowstowardVPR.Theresultisclearlynotright.Consistencyisanecessaryelementofanydrawing,evenadistortedone.

You can try some distortion easily. Take any picture you have handy of anormalhouse,traceitoffroughly,andonthetraceddrawinglocatetheeyeleveland thevanishingpoints.Thenuse thesameeye levelbutmove thevanishingpoints very close together and redraw the house.Always keep inmind that ifyou'regoing todistortsomething, thereshouldbesomepoint to thedistortion,suchascreatingaparticularmood.

Thereisnoabsolutely“correct”placementforapairofvanishingpoints.Youcoulduseallthefancygeometryintheworldtogetsomethingdrawnjustright,withtheVPsexactlywheretheybelong,andyetfindthattheobjectsimplydoesnot feel right in your picture. When that happens, be sure the problem isn't

elsewhere in the picture—maybe the barn is perfect but the surroundinglandscapeisdrawnpoorly,forinstance.

But then take a look at that perfect barn and use your good sense andjudgmenttomakealittlechangehere,anotherthere,untilyou'rehappywiththeresult.Theresultmaynotbeinperfectlinearperspective,butthat'sokay.Noticethat inmydistortedhouselotsofperspectivelineswobbleontheir journeystotheirvanishingpoints;somemissbyquitealot.Allthatmattersintheendisthatthe picture feels right to you, regardless of how it got there. I've seen someperfectlydrawnbuildingsandstilllifes(morethanafewofthemmyown)thatdidn'tworkbecausetheyweretooaccurate,too“right,”toowithoutpersonality.

Iremembersomepicturesinoneofmyclassesofwhatweresupposedtobetumble-downbarnsthatweredoneinsuchperfectperspectivethattheylookedbrand-new.The point is, use the “rules” of perspective to give the structure aplausible foundation, observe what has happened to this object over years ofwear to hammer it out of its original perfect shape, and then drawwhat youobserve. Just knowing what an original, perfect structure would be like willallow you to take artistic license in amore informed and effective way. Thisnotionappliestowhateveryouwanttodraw—people,plants,animals,anything.

Exercise:PlayingwithVanishingPoints

Hereareseveralboxes,eachwithaneyelevelindicated.Locateroughlywheretheirvanishingpointsarebyextendingappropriate lines tomeet theeye level.Then,ineachcase,movethevanishingpointsinclosertotheobjectsandredrawthem.


Drawingthingsconvincinglyinlinearperspectiveinvolvesconstantattentiontotheanglesatwhichvariouslinesmeeteachother.Unlessyou'retakingahead-onview of something, you won't usually be dealing with nice, neat right angles(thatis,angleswhereonelineisperpendiculartoanother).

Look at this simple file drawer in two-point perspective. In reality, all theangles shown (a, b, c, etc.) would measure the same if this were a well-constructed box. They'd all be 90 degrees. But because the box is shown inperspective, they're all different from 90 degrees. In fact, they're all differentfromeachother.(Angleais79degrees,bis104degrees,cis113degrees,dis66degrees,andsoon.)Ifyoudon'tbelieveme,youcanuseaprotractortocheckup onme and carefullymeasure each angle. But really, it doesn'tmatter howmanydegrees thereare inanyof theseangles.Allwewant is toget the thinglookingrightonpaper.Howdoyoumanagethis,shortofhiringEuclid?

Let'sassumeyou'reentrancedbyalovelyoldVictorianhousesittingonahill.Thehousehasallkindsofanglesandcurvesandevenasix-sidedturretononeend.You'reanxioustogetintoallthefancygingerbreadtrim,butthefirstthingyouneedtodoisdecidefromwhichvantagepointyou'lldothisdrawing.Onceyou'vewalkedaround thehouseandstudied itanddecidedwhichviewisbestfor your purposes, you stop, set up your easel, and staremorosely at a blankpieceofpaper.Maybeyoudoacoupleofsmallthumbnailsketchestodecideontheplacementofthemainshapesonthepageandtodecidewhatsortoflightingyou want—will you accept the light and shadow you see now or will youarbitrarilychangeit?Youmakesomenotestoremindyouofyourdecisionssothatlater,whenthesunhasaggravatedyoubymovingon,you'llrememberwhatyoudecidedtodo.

Onceyou'vedecidedontheplacementofthemainshapesinyourpicture(thehouse, the hill it's on, some trees, a path or roadway, the sky, the foreground,etc.) you probably very lightly and only roughly indicate these shapes on thepage.Veryfewpeoplecanstart right inwithdefinite, finisheddrawingononepartofthepageandgettotheoppositesideofthepaperwithouthavingrunoutofroomorhavingtoomuchpaperleftover.

About eight cups of coffee later you're ready for some real drawing. Youmakesometentativepencillinesdescribingthewallsandtheroof,andquicklyfindthatthingsarenotmeetingattheproperangles.Theroofslantsmorethanyouthoughtpossible.Bettercheckuponit,buthow?

Suppose therewereavertical sheetofglass standingat arm's lengthbeforeyou, between you and the house, somehow secure against falling over. If youwere to stand in one spot and draw on that glass (with a grease pencil, forinstance)youcoulddrawtheentirehouseby“tracing”itontheglass.Youwouldsimply copy each line of the house, as seen through the glass, and the resultwouldbeperfectlyaccurate.


It's not practical to lug around a sheet of glass, and besides, you want yourdrawingonpaper,sowhattodo?

Getoutyourwonderfulscientificangle-measuringscissorsdevice,whichyoumadeinPartOne.Remember?Itlookslikethedrawingatright.

Now imagine that youhave a sheetofglass standingverticallybeforeyou.Hold the anglemeasurer out at arm's length flat against the “glass,” as shownbelow.


Withyourfreehandarrangethetwoarmsofthemeasurersothat,stillpressedflatagainsttheimaginaryglass,theycoincidewithsomeangleinwhichyou'reinterested—perhapstheanglethemainrooflinemakeswithanyverticaledgeofthehouseorwiththeverticaledgeofyourpaper,asshownatright.

Whenyougettheangleright,carefullymovethemeasurertotheappropriatespotonyourdrawingpaper,positiontheverticalpartofthemeasurersothatit'sparalleltoaverticaledgeofyourpaper,andmarktheangle,below.

AnotherWay

There'sanevensimplermethodofgettinganangleright,amethodwetouchedonearlier.Although itmaybeabitmoreerror-prone thanusing thecardboardscissors,it'susedbypracticallyeveryartist.Insteadofactuallygettingtheanglebetween two lines, just get the slope of each line separately. If you do thisaccurately enough, the two lines youget on your paperwillmeet at the sameangle as the two lines on the distant object you're drawing. Simply hold astraightedge (pencil,brush, ruler)atarm's length in thedirectionofoneof thelines whose slope you want to determine. Keep the straightedge FLATAGAINSTANIMAGINARYSHEETOFGLASSPLACEDBETWEENYOUANDTHEOBJECT,justasthoughyouwereusingthecardboardscissors.Tiltthestraightedgeuntilitmatchestheslopeofthelineyou'reafter.Carefullymovethestraightedge toyouractualdrawingpaper,maintaining this tilt.Don't twistyourwristorbendyourelbowalongtheway.Wherethestraightedgecomestorest on your paper, you have the slope you're after.Repeat for the other lineswhose slopesyouneed.The trickhere is to avoid twisting the straightedge asyoulowerittoyourpaper.

Exercise:GettingtheAnglesRight

Findawindowthatlooksoutonsomebuildingsorotherobjectsanddrawonthewindowusinggreasepenciloranyremovablepaint.Onceyougetset,withyourfeetfirmlyplantedandyourheadinaparticularposition,don'tmoveupordownorsideways;ifyoudo,you'llchangewhatyou'reseeingthroughtheglass.Ifyouhaveadoorinsidethehouseorstudiocontainingpanesofglass,useittodoaninteriordrawing.Youcanswingthedoorsothatyoucanfocusonanypartoftheroombeyond, thenblock thedoor tokeep it fromswinging,andgoaheadanddraw. You can even drive your car to an appropriate scene and draw on itswindows!Inanycase,you'llreproduceascenethat'sveryaccurate,anglesandall.You'reusingwindowsasyouwouldapieceoftracingpaper.Infact,ifyouusethinenoughtracingpaperorclearplastictapedtoyourwindow,youwon'tneedtoactuallymarkonthewindowatall.

ThePerspectiveCenter?

It's often necessary to locate the center of an object so that you can placesomethingtherethatyouknowshouldbecentered—adoorway,perhaps.If theobject isshowninperspective,youmaystillneed toknowwhere itscenter is,but now we're talking about its perspective center. Here's how to locate aperspectivecenter.

First,where's theactualcenterof therectangle?Howdoyoufindit?Ifyouremember your high school geometry, all you need to do is draw in therectangle'sdiagonals,andwherevertheymeet,that'sthecenter.

Suppose the rectangle is tilted away from you—that is, thrown intoperspective.Nowwhere's its center?Or, to frame the questionmore precisely,whereistheperspectivecenter?Sameanswerasbefore:Drawinthediagonals,andwheretheymeetistheperspectivecenter.

UsingtheperspectiveCenter

Let'ssayyouwanttodrawastorefrontanditssigninperspectiveandhavethelettersonthesignappearinproperperspective.Youmightfindthe“center”ofthe sign by crossing diagonals, sketch in the middle letter at the perspectivecenter, and distribute the other letters to the left and right of that letter, withlettersthatareclosertoyoufartherapartthanthoseawayfromyou,above.

Orsupposeyouwanttofindthemiddleoftheendofahouseinperspectivesothatyoucanproperlyplacethepeakofthehouse.Forsimplicity,we'lluseaMonopoly game housewith no overlapping roof or other distractions. At toprightishowthehousemightappearlookingatitstraighton.

Now if we turn the house so that we're seeing it in two-point perspective,centerright, theperspectivecenter line isno longerhalfwaybetween the twoedgesof thehouse;youcan't locate itbymeasuringwitha ruler.Toplace theperspectivecenterline,allyouneeddoisdrawinthediagonalsoftheendofthehouse(ignoringthetriangularportion,orgable,foramoment).Drawaverticallinethroughthepointwherethediagonalscross.Thepeakofthegablewillliealongthatline.

Itwouldberaretofindahouseactuallybuiltliketheonewe'vejuststudied.Moreoftenwefindthesortofconstructionshownatbottomright.Inthisviewthepeakofthegableishiddenundertheroof.Soisoneofthecornerstowhichyouwoulddrawyourdiagonals.Whendrawingsuchastructure,withitshiddencorners, rely first on drawing what you see, as always, but when the resultdoesn'tfeelquiteright,gobackanddoalittleconstruction.Lightlysketchintheendofthehouseasitwouldappearwithouttheoverhangingroof.Thenaddtheroof.AnexerciselaterinPartTwowillexplorethisideafurtherasyoubuildahousefromscratch.

Exercise:UsingthePerspectiveCenter

In thesefigures the“centers”of thegabledendshavebeen located incorrectly.Toshapethegablecorrectly,startbydrawingdiagonalstolocatetheperspectivecenter.Thenextendtherooflineanddrawaverticallinethroughtheperspectivecenter to meet that line. From there, you should be able to draw the correctgable.


LocatingaDoororWindow

Thereareanumberofwaysyoucanaddadoorwaytothegabledendofahouse,andI'llshowyouonemethodhere.Butfirstlet'sstartwithafinisheddoorwayand make some observations about it so that in the construction steps you'llknowwhatwe'reaimingfor.

Noticefirstthatinthehead-onview,above,witheverythingneatlycentered,distanceaequalsdistanceb.Second,thereisasmuchdoorwaytotheleftofthecenterlineasthereistotheright.Nosurprisesthere.

In the perspective view, however, distanceb is greater thana, and there ismoreof thedoorwayto therightof theperspectivecenter line thanto the left.Everythingseems to squeeze smalleras itgoesaway from theviewer into thedistance.Notice,too,thatthetopandbottomofthedoorway,whicharesimplehorizontallinesinthehead-onview,slanttowardtheleftvanishingpointintheperspectiveview.Thesearethingstolookforconstantlyinyourdrawing.Again,draw what you see, but when you get in trouble do some basic construction(sometimesonyourpaper,sometimesonlyinyourhead)togetthingsright.

Let'sseehowwemightactuallyconstructadoorwayintheperspectivecenterofawall.We'llstartwithawallwhoseperspectivecenterlinewe'vealreadyfound.Thetoplevelofthedoorwayisalreadyindicated.

Theeasiestwaytoproceed(thereareotherwaysinvolvingmoregeometry)istoestimatewhereyouwantoneoftheverticalsidesofthedoorwayanddrawitin.HereI'veputintheright-handside.


WhatIwouldreallydonextissimplydrawintheleft-handedgealittleclosertotheperspectivecenterlinethanIdrewtheright-handedge.Buttogetitwhereitbelongs through construction, mark the center of the height of the doorway.Measurebetweenthetopandbottomofthedoorwaywitharuler,orjusteyeballit.Forpracticalpurposes,thiswillbetheperspectivecenterofthedoorway.

Nowdrawoneofthediagonalsofthedoorwaybydrawingalinefromoneofthecornersthroughtheperspectivecenter.I'vedrawntheonegoingfromlowerrighttoupperleft.


Drawaverticallinethroughthepointwherethediagonalhitstheupperedgeofthedoorway.Thedoorwayisnowoutlinedinproperperspective.

The important thing toobserve inadrawingsuchas theoneatright is thesqueezingdownofvariousdimensionsas they recede farther from theviewer.You can always get a quick fix on where to place objects such as doors andwindows if you locate the perspective center first by crossing a couple ofdiagonals.Ifyou'replacingobjectsthatarenotcentered,butareequallyspacedinawall(suchasarowofwindows), it'sstillhelpful tolocatetheperspectivecenterandthen,usinggoodoldeyeballing,placetheobjectstoeithersideofthatcenter,asI'vedonehere.

Notice that I've done three things to enhance the feeling of depth: (1) thewindows get progressively smaller; (2) the spaces between them getprogressively smaller; and (3) the space to the left of the nearest window isgreaterthanthespacetotherightofthefarwindow.

Remember, thebuildingyouaredrawingmaynotbeconstructedwith suchneat symmetry. Many aren't, of course, and therein may lie their particularcharm. Still, if you understand the basics of what happens in a symmetricalstructure,youcanextendthatknowledgetofigureoutwhat'shappeninginlessorderlysituations.

Troubleshooting

Supposeyou'redrawingasceneinwhichthereareseveralbuildingsofdifferingsizes situated at various distances and angles from the viewer. You've drawneverything in proper linear perspective, but the scene seems too static.Thingsare lined up too neatly. Your eyelids are becoming heavy and you knowsomething iswrong.Soyoudisruptyourstaticsceneand turnabuildingatanangledifferentfromwhatyouactuallysee.Whatareyoureallydoingwhenyoutwistthatbuildingatanewangle?You'rerelocatingitsvanishingpoints.

Here'sasketchinwhichIdon'tlikethepositionofthetablebecauseIcanseethesameamountof the leftsideasof theright.Thingsdividedexactly inhalfcanbeboring.

So Imentally rotate the tablea little, and try tocreatemorevisual interest.Wheneveryourotateanobjectlikethis,whatyou'rereallydoingischangingitsvanishing points.As you can see, I've left the eye level the same and haven'tchanged the table's height or other characteristics. But clearly, I goofed.Something's not right. Thiswill often happen, but itwon't always be obviouswhatisnotright.

Troubleshooting

Tohelpfigurethingsout,Idrawinacoupleoflightconstructionlinesandfindwhere they intersect the eye level—those pointswill bemy vanishing points,VPLandVPR.

Okay,let'ssayI'msatisfiedwiththeangletheconstructionlinesmakewheretheymeetat thefrontcornerof the table. (If I'mnotsatisfied, I'llhave tostartagain,whichreallymeansmovingthevanishingpointssothatthelinesmeetatthecornerof the tableatanangle that feels right.)NowIwant toseewhetherI'vedrawntherestofthetableconsistentwiththepartIlike.Idrawinacouplemore construction lines and see that the rear edges of my tabletop are prettysloppy.

Troubleshooting

That problem is easily fixed—all I do ismake the table edges conform to theconstructionlines.

NowIwonderabout the legs.Onanordinary four-legged table,youwouldexpectthelegstoactasthoughtheyweretheedgesofabox,wouldn'tyou?SoIdrawintwomoreconstructionlinesandfindthatmylegsaren'tquiteright.

I'vechoppedoffsomeoftheleftandrightlegstomakethemconformtotheconstruction lines.So far, sogood,but the rear leg stilldoesn't seem right.ToplaceitIdrawintwomoreconstructionlinesandwheretheymeet(atY)shouldbewheretherearleggoes.

Troubleshooting

I'vemoved the rear leg to itsnewposition, and finallymy table looksdecent.Trace this tableandoverlay iton theoriginalone (reprintedbelow) to see theeffectofthechangeswroughtbyalittlefiddlingwithperspective.

PlacingDoorsandWindows

Following the steps outlined at right, place a doorway and two windowopenings in the long side of this house. I've indicated the lines of the roofbeneaththeoverhangtomakeiteasier.

Step1:Drawinthediagonalsofthesideofthehouseandlocatetheperspectivecenter.

Step 2: Draw a light construction line representing the tops of the door andwindows.Itshouldslanttowardtheright-handvanishingpoint.Drawasimilarlinetorepresentthebottomedgesofthewindows.

Step3:Drawinthedoorwayusingthemethoddescribedinthetext.

Step4:Locatetheperspectivecenteroftheportionofthewalltotheleftofthedoorway.

Step5:Drawaverticallinewhereyouwantoneside(I'veshowntherightside)ofthewindowtobe.Drawthewindow'sdiagonal.

Step6:Wherethediagonalintersectsthetopofthewindow,drawaverticalline.This is the other side of thewindow.This is the samemethod used earlier toconstructthedoor.Nowlocatetheperspectivecenteroftheportionofthewalltotherightofthedoorwayandconstructtheright-handwindowexactlyasyoudidtheleft.Ifyoufeellikeexperimentingfurther,tryconstructingasmallwindowinthedoor.

BoxesWithinBoxes

Manyof thesubjectsofyourdrawingsandpaintingsmaybecomplex-lookingbuildings,vehicles,machinery,furniture,andsoon.Butmostofthemarenotascomplex as you might think. Often they are combinations of boxes inperspectivetackedontootherboxesinperspective.Ifyouvisualizetheminthatway,thejobofdrawingbecomesaloteasier.Herearesomeexamplesofboxeswithinboxes,explodedtoillustratethateachparttakenbyitselfisquitesimple.The first is my desk, which normally does look as though it had exploded,below.

As an exercise, look around you for some common items, such asbookshelves, cabinets, computers, toys, houses, chairs, and so on, and trydrawing them in “exploded” fashion. Don't worry about a fussy, technicallyaccurate rendering—just see if you canmentally break an object into a set ofmoreorlessrectangularpiecesanddrawtheminroughlinearperspective.Themore you practice this exercise, the better feel you'll get for the volume andhiddenedgesofthings.

IndiscussionsuptonowI'vetalkedaboutsuchthingsas“doorways”ratherthan “doors” and “windowopenings” rather than “windows.”That's because Ididn'twanttoconfusethedrawingsbybecomingconcernedwiththethicknessesofthoseobjects.Adoorwaycanbethoughtofasanopeningwithnothickness,butadoorisachunkofstuffthatdoeshavethickness.IntheexplodedhouseonthenextpageI'veshownthethicknessofsomepartsofthehousetoemphasizethattheyaremostlyboxes—thinones,maybe,butboxesnonetheless—andlikeanyboxtheyaresubjecttothe“rules”oflinearperspective.Notice,forinstance,that thewindowsareboxes,or slabs, eachhaving itsownslantingperspectivelines.

Whatgetsinterestingisthewayobjectsconnect.Whentwoboxesconnectatright angles—the chimney against the side of the house, for example—theirconnectionisdefinedbyastraightline.That'seasy.Butwhereslantedsurfacessuchasroofsjoin,theirintersectionwilloftenbesomecrazilyslantedline.

BoxesWithinBoxes

BuildingaGlassHouse

Thefollowingexercisewillleadyouthroughtheconstructionofahouse.It'sasimple one, but its construction nonetheless can become quite involved, soplease follow the exercise steps carefully.Once you'vemastered this exercise,you'll be able to tackle practically any rectangular shape in two-pointperspective.

IsuggestyoustartbyglancingattheentiresetofstepsI'velaidoutbeginningonStageOneandthengobacktothebeginningandbuildthehousealongwithme,usingthepracticeareasonExercise:BuildingaGlassHouse.Thinkofthehouse as transparent so that you can see all its edges and corners. Use lightpencil lines or colored pencil for construction lines and darker pencil foremphasizingcertainareas tohelpyou tovisualize theemerging structure.Youmighteraseconstructionlineswhenyounolongerneedthem,butdon'tbe toohasty;sometimesyou'llwishyoustillhadanearlierlinetohelpguideyou.

Whenyou'refinished,youmightwanttogiveyourstark-lookinghousemorerealitybygivingtheroofsomethicknessandaddingdetailssuchasdrainpipes,windowpanes,andsoon.

There is roomon theexercise sheet foranumberof triesat thisdrawing. IsuggestyoufirstdooneexactlyasIhave(I'veplacedacoupleofstartinglinesand the vanishing points for you). Then follow all the same steps but do adifferentbuilding–oneofdifferentsize,oroneorientedfartheraboveorbelowthe eye level, for example. Depending on where you place your house, beprepared for somestrange things tohappen.For instance, ifyouviewahousethat is high enough above your eye level, you'll see nothing of the exposedsurfaceoftheroof;allyou'llseeistheedgeofthesideoftheroofnearestyouandabitoftheundersideofthepartoftheroofawayfromyou.Ifyou'relookingsharplydownatahouse,however,youmightseelittleotherthanitsroof.

BuildingaGlassHouse

Whendrawingahouse fromaveryhighviewpoint,you'llget averydifferentdrawing thanyouwould fromground levelor frombelow it.Experimentwithdifferenteyelevelsandanglestoexploreeffectslikethese.

Exercise:BuildingaGlassHouse

Followstep-by-stepinstructionsbeginningonStageOne.

StageOne

Step1:Establishtheeyelevel.

Step2:Drawthenearestverticaledge,a.

Step 3: Select the left and right vanishing points, VPL andVPR. I've placedthemcloseenoughtothebuildingtokeepthemonthedrawingpaper.

Step4:ConnectthetopandbottomofatobothVPs.

Step5 :Decideon the lengthof the right sideof thehouse anddrawverticaledgeb.Dothesameontheleftanddrawedgec.Twowallsofthehousearenowestablished.

StageTwo

Step 1 : Now find the right (hidden) end of the house. Connect the top andbottomofverticaledgectoVPR;connectthetopandbottomofverticaledgebtoVPL.

Step2:Wherethoselinescross,atXandatY,drawvertical(hidden)edged.

Step3:With the flatof thepencil,orwithcoloredpencil, lightlyshade in thehouseendstohelpvisualizethestructure.

StageThree

Step1:Establishthegables(thetriangularends)ofthehouse.Beginbylocatingtheperspective centerof the left endof thehouse.Draw thediagonals;wheretheycrossistheperspectivecenter.

Step2:Drawaverticallinethroughtheperspectivecenter.

Step3:Repeatsteps1and2fortheright-handendofthehouse.

Step 4: Decide how high youwant the peak of the roof to be.Mark off thisheightatH.

Step5:DrawalinethroughHandVPR.Thisgivesyoutheslopeoftheridgeoftheroof.IntersectionJistheheightoftheright-handgable.

Step6:Completetheleftgable(thetriangle)bydrawingeandf.Completetherightgablesimilarly.Shadethemin.


StageFour

Step1: Install the roof cap. First decide how far youwant the roof to extendbeyondtheleftendofthebuildingandmarkoffthatlengthatM.

Step2:DrawalinethroughpointMparalleltof.Thisisthefar-sideoverhang.

Step3:Decidehowfardowntowardthegroundyouwantthatoverhangtogoandmarkit,pointK.ConnectKtoVPR.

Step4:DrawalinethroughpointMdownwardtotheright,paralleltoe.

Step5:Drawa linefromVPLthroughpointKandextendit towardtheright.ThisintersectsthelastlineyoudrewatpointL.

Step6:ConnectLtoVPR.Younowhavethenear-sideoverhang.

Step 7: Look at the distance between points M and H. Mark off that samedistance (or slightly shorter) from point J toward the right at N. Draw a linethroughpointNparalleltog.Wherethislineintersectsthelastlineyoudrew,atP,isthefinalcornerofthevisibleroof.

Step8:Ifyouwish,darkenintheslabofroof(MLPN)facingyou.Blackeninmuchdarkertheundersideoftheleftoverhang.

StageFive

Step1: Installachimney.Thinkof thechimneyasanothersmallerrectangularboxinperspective,perchedatoptheroof.Firstdrawaverticallinerepresentingthenearestverticaledgeofthechimney.

Step2:Decidehowhighthechimneyistobe,pointQ.

Step3:DrawlinesthroughQtobothvanishingpoints.


StageSix

Step 1: Decide how thick each face of the chimney is to be and draw twoverticallines.

Step2:Let's say this chimney is to be totally on thenear sideof the roof, asshownintheinset.

Step3:DrawalinefrompointRdowntheslopeoftheroofparalleltothefrontedgeoftheroof.

Step 4: Draw a line from intersection S toward VPR. You now have yourchimney.Darkeninthefrontandsidesurfaces,onedarkerthantheother,tohelpshowsomeform.

StageSeven

Step1: Installadoorintheleftendofthehouse.First,drawalinefromVPLthroughtheendofthehousetoshowtheheightthedoorwayistohave.

Step2:Drawtwoverticallines,rands,oneithersideofperspectivecentertoshow thewidthof thedoorway.Don't forget thatmoreof thedoorway shouldshowtotherightthantotheleft.

Step3:Toshowthe thicknessof thedoorwayandthedoor itselfsetbackintothewall,drawashortconstructionlinefrompointTtowardVPR.

Step 4: Draw vertical line w (see the inset) to show the doorway thickness(whatever thicknessyouwish).Drawliney toshowthethicknessof theupperedgeofthedoorway(this lineshouldconnect toVPL).Darkenintherecessededges.

Step5:Installapairofwindowsinthelongsideofthehouse.Firstestablishaheightforthetopsofthewindows.It'softenthesameastheheightofthedoor,sodrawalinefrompointVtowardVPR.Younowhavethetopsofthewindowopenings.

Step6:DecidehowlowyouwantthebottomofthewindowopeningstobeanddrawalinefromVPRtorepresentthatheight.

Step 7: Now draw four vertical lines representing the sides of the windowopenings.Putthemwhereyouwantthem.

Step 8: Give the windows depth the way you did the doorway. Shade therecessedsurfaces.Seetheinsetforalittlemoredetail.

Step 9: Erase construction lines and add anything you wish, such as morewindowsorasecondchimney.

Step10:Ifyougotitallright,helpyourselftothepie!

Collections

Supposeyou'redrawingacollectionofobjects,suchasthebuildingsinavillageor thevarious items in a still life, andyouwant todraw them just asyou seethem.Thefirstthingyoumustdoisdecidethepositionfromwhichyouwanttodo your drawing. Remember, a scene drawn or photographed by two peoplestandingevenjustashortdistanceapartwillbedifferentinthetworenderings.Thesameistrueifthereisonlyoneobserverwhosimplycan'tdecidewhethertostand or sitwhilemaking the drawing.You've got to decide on your viewingpositionand stickwith it.This isparticularly trueconcerning theviewer's eyelevel.Anychangeinyoureyelevelaffectswhatyou'reseeing.

Onceyou've established the eye level fromwhichyou'regoing todraw thescene,drawa lighthorizontal lineacrossyourpaper to indicatewhere theeyelevelinthedrawingisgoingtobe.Nowgoaheadanddraw,constantlyrelatingeverything to the eye level line you've established on your paper. If there's ahousedowninthevalleybelowyoureyelevel,it'llbeplacedonthepaperbelowthateyelevelline,andtherewillbelinesinthatbuildingslantingUPtowardtheeye level line. If there is a building on a hilltop in this same scene, itwill besomewhereonyourpaperabovetheeyelevellineanditwillhavelinesslantingDOWNtowardtheeyelevelline.

What about the vanishing points for all the buildings scattered throughoutyour scene?Each buildingwill have its own set of vanishing points, but theywillALLliealongthesameeyelevelline.Dependingonhowthebuildingsaresituated,someoftheirvanishingpointsmaycoincide.Some,suchasthehousein the final exercise,mayhaveonly a single vanishingpoint.That's one-pointlinearperspective,discussedinPartOne.I'veincludedthehouseinone-pointinorder tocalmthesceneabit. Ifall theobjects inasceneare rendered in two-point, there may be a feeling of disarray. The house in one-point provides arestingplacefortheeye.

Exercise:Collections

Gatherseveralboxesandpretendtheyarebuildings.Placesomeonalowcoffeetable,someonthefloor,andsomeonahighertable.Sitsothatyoureyelevelisanywhere between the highest box and the lowest. Sketch the assortment ofboxes after first deciding on an eye level. Carefully determine the vanishingpoints foreach.Allvanishingpoints should fallon thesameeye level line,of

course,butsomemayfallfaroutofthepicture–infact,faroutoftheroom–andwillneedtobeimagined.Notethatyoucanmakeavanishingpointfallclosertotheobjectbyturningtheobjectatadifferentangletoyourlineofsight.Ifyouplaceoneoftheboxesdirectlyinfrontofyouandyou'reseeingitsfaceflat-on,therewillbeonlyasinglevanishingpointandallyou'lldrawisarectangle.

DifferingElevationsHereisasceneinwhichbuildingsaresittingatdifferingelevations.Usingastraightedge,determinewherethevanishing

pointsareforonebuildingandusethatinformationtodrawintheeyelevel.(Youmayneedtoattachextrapaperontherightanddrawacrossthetextontheleft.)Thenlocatethevanishingpointsfortheotherbuildingsandnoticethatalthoughquitescattered,theyallfallonthesameeyelevel.

Notice this, too: The vanishing points for a couple of objects, such as thebroken-downmailbox and the sloping rightmost roof area of the nearest shed,don'tfallontheeyelevelline.The“rules”we'vebeenusingapplytoobjectsthatareorientedthewaynormal,soundhousesare–floorsorbasesflatandparalleltotheground,sidesvertical.IntroduceabuildingslidingdownamuddyCaliforniaslopeandallbetsareoff.Thatbuildingwon'tconformtoanybody'srules.Ifthemailboxin thedrawingbelowwereproppedupright,as itprobablywasbeforesomejoyriderwhackedit,itwouldobeytherules.

Thereare, however, perfectly legitimatevanishingpoints that don't landontheeyelevel.They'llbediscussedinPartThree.

PartThree:CurvesandInclines

Sofarinthisbook,we'vedealtmostlywithneatblocks,straightlines,andtwovanishingpoints.Happily,there'salotmorevarietythanthatamongthethingswedrawandpaint.Thereareallkindsofcurvesandinclines,forexample,andthereare,asastronomerCarlSaganmightsay,billionsandbillionsofvanishingpoints.Suchrichvarietyoffersendlesspossibilitiesforourart,butdoesitalsobringonendlessheadaches?Howdoweapproachdrawingallthoseoddshapesinperspective?Andhowdowedealwithmultiplevanishingpoints?

Thewaytodealwithanapparentlynewproblemistostartwiththethingswealready know.We know how to draw rectangular objects in perspective, so itmakessensetotrytoseeanew,odd-shapedobjectasbeingroughlyrectangularorasbeingmadeupofanumberofrectanglesorpartsofrectangles.Ifanobjectiscurved,wecanusuallyenvisionitasbeingplacedwithinarectangularbox,sowedrawthatboxinperspectiveand“fit”thecurvedobjectinsideit.Asforallthose vanishing points, we normally have only two, or at most three, to beconcernedwithatanyone time.Veryoftenweonlyneed toknow thegenerallocationsofvanishingpointsandneverhavetopinthemdownprecisely.AsPartThreewilldemonstrate,youcansolvemostperspectiveproblemswiththetoolsyoualreadyhave.

GettingStarted

To begin learning how to handle the problems presented by curves inperspective,we'll first address the circle.Drawing circlesmay seem easy, butwhen they're seen in perspective, they are transformed into a lesswell-knownrelativeofthecircle,anellipse.

Justwhatisanellipse?Althoughthereisaprecisemathematicaldefinitionofanellipse,it'seasierjusttothinkofitasasquashed-downcircle.J.D.Salingerdescribesacharacterinoneofhisstoriesashavingaheadthatappearedtohavebeensqueezedinacarpenter'svise.Thatheadwouldbeanellipse.

Ellipses can be fat (almost circular) or thin (almost a straight line) oranywhereinbetween.Thereareplentyofobjectsaroundthatareactuallymadeinanellipticalshape–platters,servingbowls,swimmingpools,andsoon.Mostellipses we see, however, are really circles seen in perspective, and it's thoseellipseswe'remostconcernedwithhere.

CirclesandEllipses

Takeacanofbeansfromthepantryandlookatitstop.Ifyouviewitstraighton,it'scircular.

Butifyouviewitfromtheside,thetopmaylooklikeoneoftheothertwodrawingsatleft.

Thinkofanellipsethisway:it'sacircletiltedawayfromyou.Asyou snoop around the pantry you'll find elliptical shapes galore.Glance

outthewindowatyourcar.Ifit'sparkedatanangletoyou,itswheelsandtireswillappearelliptical.Lookatthetopofalampshade,aphonographrecordlyingatadistance,asaucer–they'reallreallycircular,buttheyappearellipticalwhenviewedfrommostpositions.

Letmerepeat:Anellipseisacircleinperspective.Ifwecanfigureouthowtodrawacircleinperspective,we'llendupwithanellipse.Tofindouthowtodrawacircleinperspective,we'llgobacktoamorefamiliarobject,thesquare.Asyouprobablyknow,asquareisarectanglewithallfoursidesequal.Acirclecanalwaysbedrawninsideasquare,anditwilltouchthesquareatthemiddleof

eachofitssides.Thecenterofthecirclewillbeatthesamepointasthecenterofthesquare–thatis,theplacewherethesquare'sdiagonalscross.Belowleftisacircledrawninsideasquare(or,ifyouprefer,asquaredrawnaroundacircle).

Supposeweturnthissquareslightlyawayfromus,belowright.Thesquareis now in perspective, its top and bottom edges retreating to some distantvanishingpoint.Butthecirclehasalsotakenonadifferentshape:it'sbecomeanellipse.Drawthediagonalsinthefiguretolocatethesquare'sperspectivecenter,asshowninPartTwo.Thatpointisalsotheperspectivecenteroftheellipse.

CirclesandEllipses

DrawingEllipses

Youcandrawellipsesinavarietyofways.Donefreehand,theymayatfirsttendtolookliketheonesatright.Therearetwoproblemshere.Thefirst isthatanellipseneverhassharppointsanymorethanacircledoes.Keepinmindthatatitsnarrowed“ends”anellipseisstillacurve;itneverstopsabruptlytochangedirection, but simply keeps curving around until it has gradually changeddirection.Thehorsesatanovalracetrackdon'tstopandchangedirections;theyjustkeeponleaningandtraversingthecurvedtrack.

The second thing to remember is that anellipse is auniformcurve; it'snotteardrop-shaped,fatteratoneendthanattheother.

Mostofthetimeyou'llsketchanellipsewithoutactuallystickingitinsideaperspective square.But if you'redoing some ticklishdrawingwhereyouwantmore accuracy–maybe you're illustrating a piece ofmachinery, for instance–itmaybeagoodideatostartwiththesquare,withitsperspectivecenterlocated,right.

Thenmarktheperspectivecenterofeachsideofthesquare,farright.

Nowlightlysketchinacurvethat touchestheperspectivesquareateachofthe four points you'vemarked, andnowhere else. (Inmathematics, onewouldsay thosefourpointsarewhere thecurve is tangent to thesquare.)Notice thatthe curve sweeps smoothly through the four points where it touches theperspectivesquare,rather thanchangedirectionabruptlyat thosepoints,right.It's important to remember those smooth curves so that you avoid drawingcurvesliketheoneatfarright.

Exercise:GettingtheFeelofEllipses

In this exercise we'll construct some ellipses that actually conform to themathematicaldefinitionofanellipse;however,wewillnotget intoanyof themathematics.AllIwantisforyoutounderstandtheshapeofatrueellipse.I'mnotproposingyouactuallyconstructellipses in thismanner inyourdrawings–NEVER!

You'llneedtwopushpins,apencil,apieceofstring,andapieceofcardboard.

Step1 : Stick two pushpins into a piece of cardboard; place them about fourinchesapart.Fastentheendsofapieceofstringaboutsixincheslongtothetwopushpins.(Theeasiestwaytofastenthestringistostickthepinsrightthroughit.)Makethestringtautbyinsertingthetipofapencilintothelooseloop.

Step2:Keepingthestringtautwiththepencil,drawaclosedcurve.Don'tworryaboutdoingthisallinonesmoothmovement–thestringwillgetwoundaroundthepencilpointandyou'llhavetountanglethingsonceortwice.Ifyousucceedwithoutpullingthepushpinsloose,you'llendupwithatrueellipse.

Nowtrythesameexercise,varyingboththedistancesbetweenthepushpins

andthelengthofthestring.Justforyourinformationandintellectualenlightenment,thenamesofthetwo

pointswherethepinsarelocatedarethefoci;thelongdimensionthefocifallonisthemajoraxis;thelineperpendiculartothemajoraxisandbisectingitistheminoraxis.Nowdon'tyoufeelsmart?

Exercise:GettingtheCurvesRight

Herearetwosquaresinperspective.InbothIhaveindicatedthepointsatwhichan inscribed ellipse should touch the sides. In the first I've already drawn anellipsefreehand,whichlooksreasonable.Noticethatitonlytouchesthesquareattheleftandrighttangentpoints.Notice,too,thataftertouchingthesquareatthe left and right tangentpoints, thecurvecurves evenwiderbeforegraduallychangingitsdirection.Thewidestdimensionoftheellipseisnotatthetangentpoints.

Trace over the curve to get the feel of how it travels. Then draw a similarcurveintheremainingperspectivesquare.

Hintondrawingcurves:Formostpeople, it's easiest todrawacurve thatcurvesawayfromone'sbody.Todoso,drawpartof thecurveandthenrotatethepapertodrawthenextportion.Acoupleofrotationslaterthecurvewillbeclosed.

Exercise:DrawingEllipsesinBoxes

Here are some squares in perspective. Practice making ellipses (circles inperspective) by inscribing an ellipse in each “square.” Some of the squaresalready have their diagonals drawn, some have tangent points shown.Remember,thecurveoftheellipsetouchesthesidesofthesquareonlyatthosetangentpoints.Besureyourcurvessweepgracefullythroughthetangentpointsratherthanabruptlychangedirectionatthosepoints.

CircularObjects

We'renotoftenconcernedwithdrawingsimple,flatcirclesinperspective.Whatwe're generally concerned with is drawing three-dimensional objects whosecrosssectionsarecircular–objectssuchasbottles,columns,silos,andtrees.Let'sseehowwhatwe'velearnedaboutellipsesappliestotheseobjects.

TheImportanceofEyeLevel

Beforewebegin, though, letmerepeatoneimportantpieceofadvice.InPartsOneandTwo,Istressedtheimportanceofestablishingtheeyelevelinapicturebefore doing any drawing. This admonition applies not only to rectangularobjects,buttocircularandothercurvedobjectsaswell.Failuretonaildowntheeyelevelisoneofthemostcommonerrorsinpaintinganddrawing.

IncountlessstilllifesI'veseenweirdvasesliketheoneatright.Thetopofthevasesuggeststhattheeyelevelinthepictureissomewhereaboveit.Buttheflattenedbottominsiststhattheeyelevelisevenwiththebottomofthevase.Itmaybethatthestilllifepainterwasimitatingafamousartistwhouseddistortiontomakeapoint.Byallmeans,distortthingsifyouwill,butbesureyou'redoingitonpurpose.

Now let's go back to the pantry and get out that can of beans. Instead ofviewing only its ends as circles inside squares, let's see the entire can as acylinderencasedinarectangularbox,right.

I'veincludedonlyenoughconstructionlinestosuggestthebox;asanexerciseyoumaywanttofillinthehiddenedgesofthebox.It'simportanttonoticethatthe bottom of the can, the end farthest from your eye level, shows up as aslightlyfatter(rounder)ellipsethanthetop.

Thecloserthetopofanobjectlikeacangetstoyoureyelevel,thenarrowertheellipse,asshownhere.Whenthetopofthecanispreciselyatyoureyelevel,thereisnomorecurvevisible–whatyouseeisastraight line.Andifyouraisethecanaboveyoureyelevel,thetopellipseisnowthefatterone.Anellipseneareyelevelisnarrowerthanonefartherfromeyelevelbecauseyou'reseeingitinmoresevereperspective.

CircularObjects

Now forget about beans. Let's talk MONEY!Above is a picture of my firstroyalty payment forwriting this book. Let's removewhat the IRSwill claim.Thatleavesuswithaboutseventy-fivecents,aboveright.

Notice that each coin is an ellipse drawn in a square in perspective. Thefartherawayfromyoureyelevel,thefattertheellipse.

Let'slooknextatalandscapeexample.Inthesketchabove,thebarnandoneofthesilosseemtohavewithstoodweatherandage.TheothersilowasdonebyaguyfromPisa.

The problem with the leaning silo is one of exaggerated perspective. Thebands encircling the silo have been given toomuch curvature. This is usuallycausedbystartingthedrawingofthebandsatthewrongplace.Ifyoustartnearthebottom,wheretheeyelevelisinthiscase,you'llnaturallyenoughgiveeachsucceedingbandmorecurvatureasyougoupthesilo–theellipsesgetfatterastheygetfartherfromeyelevel.Bythetimeyougettothetopband,yougiveitmore curvature than all the rest; you've overdone it and your silo falls overbackwards.

Awaytoavoidthisistostartattheendwiththemaximumcurvature–thetopinthisexample–andthenworkyourwaytowardtheotherend.

Exercise:CurvesandEyeLevel

Hereisasimpleexercisetohelpyoupracticegettingcurvesright.You'llnoticethe exercise doesnot askyou to drawperspective squares and inscribe curveswithin them. You could proceed in that manner, but that would take a lot ofwork–ugh!Andevenso,you'dstillneedtoresorttotrialanderrorjusttogettheperspectivesquaresfeelingright.

These parallel vertical lines are the sides of three silos. The silos have flattopsandbottoms.I'veindicatedtheeyelevelineachcase.Completeeachsilobydrawing in perspective its top, bottom, and five or so intermediate bands,keepinginmindhowtheeyelevelwillaffectthecurvatureofthebands.


Manyoftheobjectsyoudrawarenotneat,singlecylinders,likethesilooracanofbeansorastackofcoins.Someareoddcombinationsofintersectingshapes.One of themost common objects we draw is a tree, and its skeletonmay bethoughtofasanetworkofintersectingcylindricalshapes.Imaginethistree,top,tobecomposedofcylindersorabunchofpipesinstalledbyacrazedplumber,bottom.

Sometimes it's easier to visualize pieces of pipe stuck together than to seewhat'shappeningtotreebranches.Ipainttreesoften,yetIstillfindthisconceptextremely helpful when I'm having trouble getting branches to advance orrecede.Youcouldplaywiththesameideabyholdingcansorothercylindricalobjectsatvariousanglestoeachother,althoughyou'dbelimitedbyhowmanyobjectsyoucouldmanage.Ifthere'saTinkertoysetinthehouse,youcanbuildaquiterespectablethree-dimensionaltreefromitsparts.


People

Youcanapplythesameideatothehumanbodytogiveitformandputitspartsinperspective,right.

Peoplearefullofcurves!Youmightnotatfirstthinkofhumananatomyasanappropriate topic in a book on perspective, but please reconsider. One of thequalitieswe usually strive for in a drawing of a person is a sense of form, orsolidity,asopposed to flatcritterswithnodepth.Andphysical (asopposed tointellectual) depth is what perspective is all about. In a landscape we'reconcernedwithmilesofdepth;inpeoplewe'reconcernedwithinchesorfeet.

Thehumantrunkandlimbsarenotsodifferentstructurallyfromthetree.Inbothcases,it'shelpfultothinkofthepartsascylindersorapproximatecylinders

connectedinavarietyofways.Aswithdrawingtrees,suchanalogiesarehelpfulintryingtoshowhumanlimbsadvancingorreceding.

(Thetermforeshorteningisusuallyusedindiscussingdrawingssuchasthese.Thatsimplymeansgettingtheappearanceofdepthbyshorteningcertainlines,suchasthelinesofthearmorthelinesofthebranch.Whenweturnabuildingawayfromussothatoneofitssidesappearstobeshorterthanweknowittobe,we'reforeshorteningthatbuilding.)

Thinking of the body as a combination of cylinderswill help you to get itright.When you do a torso or an arm or a leg or a head, “draw through,” asdiscussed in Part Two, to get a feel for its roundness.When you get down tosmallerdetails, suchasnosesandeyes, “draw through” themand see themassolid objects, not simply outlines. It's common, for example, to see eyesexpressedasflatalmond-likeshapes.

Ifyoustartwiththeunderstandingthataneyeballisnearlysphericalandthatlidswraparoundthissphere,you'llcomeclosertodrawingabelievableeye.

Addsomeshadowcastbytheupper lidandsomeshadowing(modeling)astheeyeballcurvesawayfromus,andyoureyebeginstolive.


BoxThemIn

Astheexamplesofthetreeandthehumanbodyillustrate,notallcurvedobjectsare upright cylinders. But whatever the subject, curved or not, it can be anenormoushelptosketchinsomeconstructionlinesandputobjectsinboxes,asshown here. This is helpful because an ordinary box is something we all arefamiliarwith.It'sanorderly,understandablething.Anythingwecanforceintoabox,therefore,willalsobecomemoreorderlyandunderstandable.

Exercise:ATreeasaCombinationofCylinders

Aneffectivewaytomakea tree limbcomeforwardorgoback is toshowthecurvewherethelimbjoinsthetrunkoranotherlimb.

In these twosketches,useasoftpencil todarken theappropriateportionofeachcircleorellipsetomakelimbsgo:•Forward(F)•Backwards(B)•Sideways(S)

as in theexampleatright.Beginningwith identical silhouettes,you'll see thatyoucanendupwithquitedifferenttrees.

Whenyou'resatisfiedthat thelimbsgowheretheyshould,youmightenjoygiving the treemore life by doing somemodeling.Choose a light source (thesun)andthencarefullydarkeneachroundedsurfacefacingawayfromthelight.Gradually fade the shadows as each limb comes around toward the light.Youmightalsoaddsomesmaller,twiggybranches,whichI'veleftoutinordernottoconfusethepicture.

In the two sketches on the next page, use a soft pencil to darken theappropriateportionofeachcircleorellipsetomakelimbsgoasindicated.

Arches

There aremany curved objects around us whose drawing ismore demandingthan that of silos, cans, trees, andvases.Oneof themost familiar is the arch.Arches come in all sizes and shapes, some elliptical, some circular, someparabolic,andothersratherfree-form.

Arches such as those built intomany bridges and public buildings provideattractive shapes for drawings and paintings. Some are complex and defy anyeasyapproachtotheirdrawing,butmostcanbeconstructedusingsomeofthebasic ideaswe'vealreadyexplored.Supposewehavea simplebridge, suchastheonetopright.

We'llassumethetopofthebridgeisalevelroadwaywithoutanycurvature,althoughmostbridges rise some toward theirmidpoints.Onceyouget abasicstructuredrawnyoucaneasilyaddsuchdetails.

Wheredoyoustart?Iwouldlocatetheeyelevelandthentrythebridgefree-hand,asIwouldmostsubjects.ButwhenIgotintrouble(asIoftendo)I'dfallback on a little construction. First, I'd rough in a couple of light linesrepresentingtheupperedgeofthebridgeandthewaterline,andindicatethetwoendsofthebridgewithacoupleofverticallines.Theendsofthebridgemightnotbeneatvertical lines,butyouneedsomeideawherethebridgebeginsandends.

Next, find the perspective center of the side of the bridge by crossingdiagonals.

Arches

Nowdraw in aperspective line,h, representing theheightof thearches.Eacharchwillcurveupandtouchthisline.

Freehand,drawverticallinesrepresentingthewidthsofthearches.Thisisthesameasplacingwindowsalongthesideofabuilding.Ifthereisanoddnumberofarches,onearchwillbeinthemiddleofthebridgespan,sostartbylocatingan archwith its perspective center at about the same point as the perspectivecenteroftheentiresideofthebridge.Ifthereisanevennumberofarches,draw

twoverticallines,oneoneithersideofperspectivecenter,representingthewidthofthesolidbridgesupportbetweenarches.

Now work to either side of the start you made in the middle, guessing atincreasinglylargerarchesandsupportstotheleftandsmallertotheright.

Arches

Ifyou'resatisfiedwiththespacedivisions,limberupyourwristandsketchinthearches. Itmight be helpful to locate the perspective center of each arch spacefirstbydrawing in thediagonalsas I'vedone inFigure1 for thenearestarch.Thiswill tell you atwhat point the arch is to touch the line you drew earliershowing the height of the arches. In small sketches, such as I'm using here,findingtheperspectivecenterforeacharchisprobablyoverkill.Ishowitonlybecauseinalarger,full-sizepainting,whereallyourdimensionsmightbemuchlargerthanhere,suchconstructionscanmakearealdifference.

Figure1

Nowthebridgeneedswidth,orthickness.Ifyoucanseethroughthearchesfromwhereyou'reviewingthebridge,thendrawthespacesyousee.InFigure2,inadditiontoshowingthosespacesI'veaddedafewconstructionlinesheretoremind you that this entire bridge can be thought of as a three-dimensional,rectangularsolidwithcurvedholesinit.Notethatlinesaandbslanttowardavanishingpointattheleft.Alsonoticethatthewaterlineunderthearchesaimsforthatsameleftvanishingpoint,whilethewaterlineonthefaceofthebridgeheadstowardtherightvanishingpoint.

Figure2If this bridge were built of regular blocks of some kind, the mortar lines

between the blocks would obey the rules of linear perspective. Those visibleunder thearcheswouldslant toward the leftvanishingpoint,as I've indicated,andthoseinthefaceofthebridgewouldslanttowardtherightvanishingpoint,showninFigure3.

Figure3

Allthat'sleftistoembellishyourbridgewithdetailand,ofcourse,itwouldbeniceifthebridgewentfromsomethingtosomething.

Thisisarelativelysimplebridge.Therearemanypossiblevariations.Whenpresentedwithanyofthestrangecurvesyoumayfindinbridges,buildings,andother engineered objects, start with something basic that you're familiar with(such as the essentially rectangular side of the bridge in our example) andproceedfromthere.Youcanalmostalwaysmentallycarveoutsectionsthatcanbeseenasrectangularsolids,likethatshowninFigure4.

Figure4

ExaggerationasanAidtoSeeing

Sometimesit'sdifficulttodecideonthesizeorshapeofsomethingcomparedtosomethingelsebecause theobjectsarequiteclose insizeandshape.Youmaydecidethatthedifferencebetweenthetwoobjectsistoosmalltomatter.Butifitdoesmatterandyoustillcan'tquitedecidewhat'sgoingon,youmighttrywhatIoftendo.Ivisualizetheobjectsinsomeextremeorexaggeratedsettingandthenseehowtheycompare.Forexample,supposeI'mfacingastackoffattiresandtryingtodecide(a)whetherthetopmosttireappearsrounderthanalowerone,and (b) how much of the edge (the tread area) of the topmost one I'd seecomparedtothelowerone,belowleft.

Iknowthetopmosttirewouldlookrounder(morenearlycircular)andIknowI'dsee less treadof the topmostone than the lowerone. Ihad topass that testbefore North Light would let me write this book. But if I were unsure, I'dmentallyexaggeratetheheightof thestackuntil itwasmuchhigher,farabovemyeyelevel,untilthetoptirewassofarovermyheadthatI'dgetacrickinmynecktryingtoseeit,belowcenter.ItwouldbecleartomethenthatwhatI'dseewayuptherewouldbealmostcircular,certainlyrounderthanatiredownclosertomyeyelevel.Notonlywoulditclearlylookrounder(thatis,afatterellipse),but I'd seevery littleof its tread. If itwerehighenough,all Iwouldsee is itscircularbottomandnoneofitstread.Inotherwords,thehigheratiregetsabovemyhead(assumingitkeepslevelasitrises),themoreIseeofitsundersideandthelessIseeofitsedges.

Youcanusethesametrickinsituationsnotreallyinvolvingeyelevel.Earlier,whenIwassketchingthebridgeanditsarches,IwasunsurehowmuchspaceontheothersideofthebridgeIwouldseethrougheachofthearches–thatis,wouldthoselittleopeningsgetprogressivelywiderastheycametowardme,orsmaller,orwouldtheystaythesame?(Iwasnotactuallylookingatarealbridgeatthetime.)SoIimaginedthebridgeextendingintothedistanceinbothdirections.Itwas immediatelyobvious that at somepointas thebridge“passed”meonmyleftIwouldactuallybelookingthroughatotallyopenarchandthatI'dseethewholeworldontheothersideofthebridgethroughthatarch.Itwasclear,then,thatI'dseemorethroughtheneararchesthanthefar.


It's important to keep measuring relative sizes of things as your drawingproceeds.InthisviewoftheCapitolinWashington,D.C.,thatIdugoutofoneof my old sketchbooks, I had made a couple of notes to myself regardingdimensions.

Thedomeshouldbe“moresquat”;thewidthXshouldbeabouthalfagainaswideasheightY.Isimplyusedthepencil-and-thumbmethoddescribedinPartOnetocomparevariousdistances.

I find that I have somewhat more need to check up on myself when I'mdrawing rounded objects than when drawing rectangular things. The curvesthrowmeoff.Bytheway,thelittleinsetattheupperleftremindedmethatIwasviewingtheCapitol throughabreakinsometreefoliage.WhenI laterpaintedthescene,Imovedthebuildingfartheroff-centertoavoidtoomuchsymmetry.


Here's another casewhere I found Ineeded tomakeconstantmeasurements. Imarkedthefloortoknowwheretoreturnwhenevermydrawingorpaintingofthisstilllifewasinterrupted.Iwassoclosetothesubjectthateverylittleshiftingofmybodycausedmetoseequiteadifferentscene. (InafamousdrawingbyDürer,anartistisseendrawinganearbysubjectbyclosingoneeyeandkeepingapointedsightingstickdirectlyinfrontofhisopeneye.Thesightingstickisinafixedpositionandcannotbemovedbytheartist.Aslongastheartistkeepshisopeneyepreciselybehind thepointof thesightingstick,heknowshehasnotmovedthepositionofhishead.)

Inaddition tobeingcarefulaboutmyposition, Imadesure the lightsourcewasnotdisturbedsothattoday'sshadowswouldstillbetheretomorrow.AndIconstantlycomparedtheheightsandwidthsofobjectsagainstoneanother,allbythepencil-and-thumb technique.Thereare lotsof surpriseswhenyoumeasureobjects close to you in a still life. You think you know how big one thing iscompared to another, but because you're so close, size differences becomemagnified.

Thispicturetaughtmethatthere'sanotherwayyoucanbefooledwhenyouare drawing objects such as a decanter or wine bottle. The differences in thecurvaturesofthetwoendsoftheobjectcanthrowyouoff.

Let'ssayyou'relookingslightlydownwardattwoitems,adrinkingglassandawinebottle,asshownatright.Intheglass,thecurveofthebottomwillappearmoreroundedthanthecurveofthetop,becausethebottomoftheglassisfartherawayanditsellipsewillbefatterthanthetopoftheglass.That'sfineaslongasthetopandbottomoftheglassareessentiallythesamesize.Inthewinebottle,however,thetopismuchsmallerthanthebottom,andeventhoughthebottomisfartherawayfromyou,itscurvewillappearlesssevere,less“rounded”thanthecurveofthetop.Ifthisdoesn'tmakesensetoyou,tryimaginingabottlewhosetopisaone-inchcircleandwhosebottomisathree-footcircle.Nomatterhowyou view this bottle, the top will have the “rounder” curve. Observing suchdetails canmake the difference between a convincing picture and one that isunexplainably awkward. The following exercises offer ways of making suchcurvesmoreaccurate.

Reflections,PhilMetzger,watercolor,34″×44″

Exercise:CheckingCurves

Findacurvedobject,suchasawinebottle,andset itupafewfeetawayonatabletop. Imagine this bottle as part of a still life you intend to draw. Thedifferingcurvesof its topandbottomcanbeasourceof trouble.Herearetwowaysofcheckinguponwhetheryou'vedrawntopandbottomcurvescorrectly,relativetoeachother.

Method1:Setupapieceofclearplasticandviewthebottlethroughtheplastic.Withagreasepencil,drawthecurveofthetopofthebottle.Then,standinginthesameposition,movetheplasticdownsothatyousee thecurveyou've justdrawn adjacent to the curve you now see at the bottomof the bottle.By thuscomparingthecurves,you'llknowhowtodrawthemonyourpaper.

Method 2: Sketch the bottle on your paper. Then cut a piece of scrap papercarefullytofitthecurveofeitherthetoporbottomofthebottleinyourdrawing.Holdthecurvedcutoutatarm'slengthbetweenyouandthewinebottleandseewhether the cutout curve matches what you see on the bottle. Change yourdrawinguntilyougetadrawncurve tomatch thereal thing.Thenholdup thecutoutandcompare it to thecurveat theotherendof thebottle.Again,adjustyourdrawingtogetthetwocurvesrightrelativetoeachother.

Exercise:AchievingSymmetry

Drawing symmetrical objects and having them come out looking symmetrical

givesalotofusaheadache.Herearetwowaysyoucanhelpgetshapesright.Becarefulusingsuchtechniques.Ifyougettoorigidandfussy,yourdrawing

willbecorrectandboring.

Method1:Ifyoureallywantgoodsymmetry,trythis.Drawthebottlethebestyou can–just its outline. Then trace its outline on a scrap of tracing paper.Measurethedistancebetweenthetwosidesofthebottleanddrawalinecuttingthebottle inhalf from top tobottom.Fold the tracingpaperalong that line sothatyou'll seeonehalfof thebottle laidover theother.Betyouanickel theywon'tmatch.

Exercise:AchievingSymmetry

Method 2: Get out the old wine bottle again (you've probably emptied it bynow).Drawitssilhouette.Theroundedtopsandbottomsofsuchobjectsgiveustrouble enough, but so do the rounded shoulders where the bottle's neckbroadensintoitsbody.Unlessyou'reeitherluckyorgifted,yourfirstshotatthebottlewillprobablynotbesymmetrical.

Turnyourbackonyourdrawingandlookatitoveryourshoulderinamirrorheld in front of you. You'll see your drawing in reverse and instantly spotdeformities you never saw looking at it straight on.We have a psychologicaltendencytodrawthingswithacertaindirectionalbias,andseeingthedrawinginreverse shows up that bias. You'll be absolutely dumbfounded, if you haven'ttriedthisbefore,attheflawsthatwillshowupinthemirror.

Actually,thisworkswhetherornotthethingyou'redrawingisasymmetricalobject. Use the mirror no matter what you're drawing. It's particularly handywhendoingaportrait.Manypeoplehavethetendencytogetaface,forexample,out of whack–one eye higher than the other, maybe. That sort of goof willinstantlyshowupinthemirror.

MoreVanishingPoints

InPartsOneandTwoof thisbook,wediscussedpictures inwhich therewerebutoneortwovanishingpoints.Thetruthis,friends,therearemorevanishingpointsthanyoucanshakeastickat.Luckily,weusuallydealwithonlyoneortwo,sometimesthree.But it's important tounderstandthat theremaybemore.Otherwise,onemightbetemptedtoforceeverylineinapicturetogotooneortwovanishingpoints,withdisastrousresults.

We'llstartwiththree.I'vealreadyshownyoulotsofdinkylittlebuildingsliketheoneattopright,withtwovanishingpoints,onesomewheretotheleftandoneto theright.We'vesofar let linessuchasaandb seemparallel.Actually,though,they'renot.Considerthis:thoselinesareactuallyrecedingfromyou,aretheynot?Aren'ttheyheadedintofarleftouterspace?Tiltapadofpaperthewaytheroofistilted.Doyouseethattheedgescorrespondingtoaandbintheroofareheadedawayfromyou?

They are parallel lines, and our laws of the perspective jungle tell us thatparallellinesrecedingfromtheviewerseemtomeet,or“vanish,”atavanishingpoint.Thedifferencebetweentheselinesandtheotherparallellineswe'vedealtwith is that these lines vanish at points not on the eye level. OnlyHORIZONTAL lines vanish at eye level. All these other queer lines vanishelsewhere.Let'sfindoutwhere.

Ifyoulayastraightedgealonglinesaandbandextendthemtofindwherethey meet, you'll get a drawing like the one bottom right. Where they meet(we'llcallitVP3)isdirectlyaboveoneofthegoodoldgarden-varietyeye-levelvanishingpoints(inthiscase,VPL).

MoreVanishingPoints

Veryoftenwedrawroofedges(suchasaandb)sothattheydivergeratherthanconverge top right–and, of course, that's just not correct. It's not only notcorrect,butmoreimportant,itdoesn'tlookrightinthedrawing.

Thereasontheselinessooftengetdrawnasthoughdivergingisthat,thankstoanopticalillusion,that'softenwhatappearstobehappening.Ifyouholdupyourpencilandcomparethetiltsofthesetwolinesonarealbuilding,you'llseethattheydoconverge,astheorysaystheyshould;butwhenyousimplylookat

the building with your naked eyes, they might indeed seem to diverge. Theillusioniscausedbytheotherlinesandshapesnearby.What'simportantisthatthedrawingwill feelbetter ifyoumake these linesbehaveandcome togetherout in space. No need to do any measuring or locating of vanishing points;simplyuseyourstraightedgeandaimthelinesslightlytowardeachother.

You'veprobablyalreadyguessedatwhereafourthvanishingpointmightbe.Yes,theedgesoftheothersideoftheroof(candd)arerecedingandtheyvanishatapointdirectlybelowoneoftheeyelevelvanishingpoints,asshownbottomright.Allthesevanishingpointswouldnotlineupinsoorderlyafashionifourbuilding were not such a perfectly symmetrical, humdrum little Monopolyhouse.


There'samoreimportantuseofathirdvanishingpointthanintheserooflines.So far,we've notmolested the vertical lines in our buildings.We've left themvertical. That's appropriate if we're dealing with relatively low, squat objects,because all points along the vertical lines in such objects are nearly the samedistance from our eyes. Those lines, in other words, are not visibly recedingfromtheviewer.

Imagineyou'redrawinga skyscraper fromapointon the sidewalknear thefootof thebuilding.Assumeit'sa rectangularblob,nota taperedbuilding.Asyouglanceupatthebuilding,insteadoflookinglikearectangularsolid,itlookssomethinglikethedrawingabove.

What you're seeing is the side edges of the building converging toward avanishingpointhighinthesky.Asyoulookupatthebuilding,itsparallelsidesare moving away from you, and they seem to converge exactly as a pair ofhorizontallineswouldappeartoconverge–onlytoadifferentvanishingpoint.

Fromadistance,sayfromanotherskyscraper'swindow,thescenemightlooklikethis.

Ifyouwereinanairplanethatsameskyscraperwouldlookmorelikethis.The vanishing point for the vertical edges of this building is somewhere

aroundChina.Noticethatouroldfriends,vanishingpointsleftandright,arestillwithus,faroutofthepicture.You,intheairplane,haveaveryhigheyelevel,orhorizon.Theentirecityisbelowyoureyelevel.


Theuseofathirdvanishingpointmaybeimportantifyouaredrawinganyhighobject,oragroupofhighobjects, as inacityscape.Youmightbedepictingascenelikeeitherofthoseshownhere.

InbothcasesI'vekeptthethirdvanishingpointfairlyclosetothesubjectandhavegottenadistorted,bunchingeffect.Ifthat'snotwhatyou'reafter,youneedtoraisethevanishingpointmuchhigher(orlower,ifyou'redoingaviewfromanairplane).Asintwo-pointperspective, thecloserinyoubringthevanishing

points,themoredistortionyou'llget.Ifyouwantallverticalstostayverticalinyourdrawing, as thingsmight appear fromadistantview,goaheadand leavethemthatway–inthatcasetherewillbenothirdvanishingpoint.

Let'sassumeyou'redrawingacityscapefromstreetlevel.Thereareacoupleof things to watch out for. First, many “rectangular” skyscrapers are notrectangularatall.Someofthemarebuiltwithgraduallytaperingwidthssothatat the top floors thewidthof thebuildings is smaller thanat street level.Thatmeans that some of the apparent tapering you see as you look up from streetlevelisreal.Inotherwords,thosetall“vertical”edgesaren'treallyvertical.Thistaperingcouldthrowyouoffifyou'reunawareofitbecausethethirdvanishingpoint fora taperedbuildingwillbe lower than the thirdvanishingpoint foranuntapered building standing right next door. If all the buildings in your scenewere truly vertical (no tapered sides), they would all share the same thirdvanishingpoint.

Second,eachskyscraperhasitsownsetofleftandrightvanishingpoints,justasanyotherbuildingwouldhave.Theybothlieontheeyelevel.

I said earlier that there are billions and billions of vanishing points. Thenumberactuallyisinfinite.Althoughyou'llrarelybeconcernedwithmorethanthree, it's enlightening to know that for every pair of parallel lines in a scenetherecanbeadifferentvanishingpoint.

Theimportantthingstoknowaboutvanishingpoints,especiallythosenotontheeye level,are(1) that theyexist,and(2)roughlywhere theyare.Knowingjust thatmuchwill remind you to draw lines heading toward those vanishingpointswithanappropriateamountofconvergence.

Knowing, for example, that the slanting roof edges of ourMonopoly-gamehousereallydoconverge towardavanishingpointwillstick inyourmindandprevent you frommaking the common error of drawingdiverging, rather thanconverging, lines. You need never actually find the exact location of thatvanishing point. It's usually enough to know that it's “right about here at theupperleft.”

Exercise:MoreVanishingPoints

Locateatleasttenvanishingpointsinthisscene.Ananswerdiagramissuppliedonthenextpage.

Exercise:MoreVanishingPoints

Thisanswerdiagramshowsthirteenvanishingpointsforthisscene.Notethatitassumesthatshortverticallinesareleftverticalandnotgivenvanishingpoints.

Exercise:RoofEdges

Correct sloping linesa, b, c, andd on these structures freehand.When you'refinished,useastraightedgetomakesurethatthenewlinesyou'vedrawnslightlyconvergetowardtheirpartners,a',b',c',andd'.

Exercise:LookingUp

Here isasimplifiedwater towerseenfromadistancebyaviewerstandingontheground.Looselysketchthetowerfromthesameeyelevel,butclosertothetower,sothatyouwouldhavetotiltyourheadfarbacktoseethetop.

Hints:

1.Youmightstartwiththeplatformonwhichthetankrests,sinceit'stheonlythinginthisscenethat'sagoodoldrectangularsolid.Drawtheplatformonwhichthetankwillrest,drawinginone-pointperspective.

2.Youcanplacethetankontheplatformproperlybylocatingtheperspectivecenter of thehidden topof theplatform.The tank is cylindrical, its sidesvertical.Aboveyourheaditwouldlooksomethinglikethisifyoucouldseeitwithoutanythingelseintheway.

3.Doplentyof“drawingthrough.”Showtheconicaltopthroughthetank,thetankthroughtheplatform,etc.

4.How about the cone on the top?Whether itwill be visible in your viewdepends on (a) how close you are standing to the structure, and (b) howhightheconeandthetankactuallyare.Somepossibilitiesareshown.

5.Assumethelegsandbracesareallroundpipeswithnoactualtaper.(They'lltapersome,ofcourse,whenshowninperspective.)

Inclines

I'minclinedtothinkthereareslantedsurfaceseverywhereyoulook.Nexttomeisaprinterwithacoupleofslants,above.Downthestreetattheshoppingcenteraresidewalkramps,right.

Andthentherearetheslopingroofsofhousesandbarns,lotsoftiltedroadsandstreets,fieldsthatdon'tlielevel,andagreatvarietyofstairways.Includinginclined surfaces in a drawing very often provides the spark that revives anotherwisecomatosepicture.Inclinessometimesbedeviltheartist,butthey'renotso hard to do if (you guessed it) you start offwith plain, old-fashioned linearperspective.

The simplest kind of incline is a wedge-shaped object that looks like thiswhenviewedfromtheside.

Thatsameinclinelookslikethiswhenseeninperspective.

Thewedgealsocanbeseenashalfarectangularbox.

Inclines

Drawingmost inclines is as straightforward as drawing the sloping roof of ahouse–somethingwe'vealreadycovered.Ifyouforgetabouttheslopinglinesforthetimebeing,andfirstdraw(inperspective)therectangularshapeintowhichtheinclinewillfit,thenyoucaneasilyslicetherectangularshapeinhalf,erasethepartoftherectangularboxyoudon'twant,andwhat'sleftisawedgeshape.Don't forget that the sloping edges of an incline will have a vanishing point,providedtheinclineisactuallyofuniformwidth.

Hereisacombinationof inclinesata loadingdock.I'vedrawnthebuildingand the platforms in one-point linear perspective (remember Part One?). Thevanishingpoint towhich allhorizontal receding lines retreat isVP. It's on theeye level. The distant ramp, however, is not horizontal, not parallel to the

ground,soitsvanishingpointisnotateyelevel,but,inthiscase,aboveitatVPramp. The boards in the nearer ramp recede to VP because they are ordinaryhorizontal lines,eachparallel to theground.Thesideedgesof this rampdon'thave a vanishing point because all points along either of these lines are, forpracticalpurposes,equallydistantfromtheviewer.

Exercise:BuildingaRamp

ConstructarampgoingfromlevelAtolevelBandasecondrampfromlevelBtolevelC.Maketheirwidthsapproximatelyasindicatedbywandw',andtheirlengthswhateveryouwish.

Hint:Thissceneisdrawninone-pointperspective,withthevanishingpointattheupperleft.LocatetheVP.Thenconstructtworectangularboxes,onefittingup againstw and the other againstw'.When you slice awedge from each oftheseboxesyou'llbeleftwithsomethingsimilartowhatisshownaboveright.


Although a roador path leadingup to a buildingmay seemaminor part of apicture,properlydone itcanbeveryeffective insuggestingdepth in thesceneand indescribing the flatnessorhillinessof the landscape.Atright isascenewithnoobviousmeansofgetting to thehouse,built by thebozowhodidmyhouse,nodoubt.Belowthatarethreealternativepathsonemightusetoleaduptothehouse.

Take a small piece of tracing paper and trace the lines of the three paths.Overlaythehousesketchwiththefirstpath.It'sclearlynoteffective.Itsuggeststhatthepathhasthesamewidthalltheway,whichinturnsuggeststhatthepathisverticaltotheviewer'seye–eitherthatorthishousesitsonacliffandthepathisreallyaladdertogetupthecliff!

Trythesecondpath.Ithaswhatthefirstpathlacks:linearperspective.Usingthispath,onewouldconcludethatthegroundleadinguptothehouseismoreorlessflat.Thispathintroducesdepth.

Trysketchingasimilarpath,butonethatdoesnotappeartobroadenquiteasmuch as the second path–a path somewhere between the first and secondexamples.Notice that narrowing thepath tends tomake thedistant house feelmoreasthoughit'sonariseandthepathisclimbingupwardtogettothehouse.Theextremeofthis,ofcourse,isthefirstpath,wherethehillleadinguptothehouseindeedseemstobeverysteep.Themoreyoubroadenthepathasitcomesforward,themorethelandseemstoflatten,uptoapoint.Whenthebroadeningbecomes too pronounced, the perspective will simply seem exaggerated. Youneedtoplaywithvariouswidthstofindwhatfeelsright.

Thepathswe'veconsideredsofararepretty rigid.Thatmightservewell insome pictures, but often you'll want to introduce some zigzag in the path toeffectmore interest. Overlay the scenewith the third example.Whatwe findhereareacoupleofperspectivetechniquesatwork.Notonlyareweusinglinearperspective,asinthesecondexample,butsizevariation,aswell.Thepathcanbe thoughtof as a seriesof segmentshaving similar shapes,butdecreasing insizeastheyrecede,bottom.


Anothereffectofthezigzaggypathisthatitpullstheeyeintothepicturealongamore scenic route. The straight path just zaps you right up to the house, nofoolingaroundalongtheway.

Paths, roads, and streets are effective elements in conventional landscapes.They provide a thread around which buildings and other elements may be

woven;theyofferaneasymeansofsuggestingdepth;andtheyprovideaterrificmeans of focusing attention. Drawing them is sometimes tricky, but if you'llthinkofthemasthinslabsinperspectiveandbeawareofthetilteachsegmentmighthave, thedrawingwillcomemoreeasily.Studywhat'shappening in thesceneabove.

Thinkofthisroadascomprisingseveralsegments,1,2,3,andsoonthroughsegment7,below.

I've shown perspective lines (they're only rough approximations) andvanishing points for some of the segments. Segment 3 appears to be fairlyhorizontalasitspansabubblingbrook.Itcanbeseenasarectanglehavingitsvanishing points as shown. Segment 1 is also roughly level; we know thisbecause itsvanishingpoint (ithappens toappear inone-pointperspective) lieson theeye level.The remainingsegmentsare inclineshavingvanishingpointsabove or below the eye level, as in the case of roofs we discussed earlier.Estimateforyourselfwherethevanishingpointsforsegments4and5mightlie.You'llfindthemquitehighabovetheeyelevel.

Ifyouhaveaproblemmakingaroad(orpathorstreet)dowhatyouwantittodo, try visualizing it in rectangular segments, someofwhichmaybe inclines.Draw in the level, establishvery roughlywhere thevanishingpointsmight liewhen the sides of the segments are extended, and vary the positions of thesevanishing points to get the degree of tilt you want. But as always, SKETCHFIRSTand resort tovanishingpointsandconstruction linesonly tohelpsolveproblems.


Often theeffectivedrawingofaroadorstreetdependsoncluesother than thelines representing the edges. We just discussed the value of graduallydiminishing sizes of segments as a zigzagging road recedes.Another effectiveperspective technique is to pay attention to details of things along the road.Above,forinstance,thefencepostsandutilitypolesdomoretodefinetheroadthanthelinesoftheroaditself.

Ifyou lookcloselyyou'll see the topsof thepostsbeyond thehill–they tellyouthattheroaddipsasitgoesoverthecrestofthehillandthatitturnssometoward the right. Some subtle detail can bemore interesting and enlighteningthanatonofmoreobviousinformation.

Onemoreexample.In thesketchcenterrightweknowthere isadownhillsegmentofthisroadthatisinvisibleinthisview.Howdoweknow?

The discontinuity between the nearest road segment and the more distantsegmenttellsus.Thefactthatwidthbissomuchlessthanwidthatellsusthatsomethingsneakyishappeningbetweenaandb,andintuitionfillsinwhatthatsomethingmustbe.Thefactthatthedistantsegmentisalsooutoflinewiththenear one helps, too, but even if the segments were all neatly lined up as atbottomright,we'dstillknowwewerelookingatarollercoasterroad.

Exercise:WhichPath?

Hereareseveralpaths,anyoneofwhichmightbeusedtoleaduptothehouse.Usingerasablesoftpencilorcharcoal,placeeachoftheseroadsinthescenetogetafeelforsomeoftheoptionsyouhave.Thereisno“correct”answer,onlyavarietyfromwhichtochoose.Seewhateachchoicedoesforthefeelingofdepthinthepicture.

FieldsandStreams

Ifyouweretopaintflatcountryfields,youmighthavesomethinglikethefirstdrawingatright.

Onrollingterrain,plowedfurrowsorrowsofcornwillfollowthecurvesofthegroundandmaybeyou'llseeasceneliketheseconddrawingatright.

You can find all kinds of perspective in such scenes.Youwill see rows ofcorn or plow marks getting closer together in the distance, just as linearperspective says they ought to; near stalks are tall and distant ones are pip-

squeaks; near stalks are full of luscious detail, distant ones fuzz and blendtogether; near ones are strong-colored greens and yellows and browns, distantones are paler and cooler. It seems that such fields really are putting on aperspective show forus! Ifyoucangetout and sketch such seemingly simplescenes,you'lllearnalotaboutperspective.

Therearesomethingsyou'llobserveinthesescenesthat,ifcopiedexactlyasobserved, may not work in the painting. Often, for example, there will be anearby field of very strong blue-green (a field of rye, perhaps) and in thedistancestrongwarmcolors(newlyplowedearth,ripehayfields).Thepatternofcolorsmaylookgreatoutthere,butonyourcanvasthewarmdistantcolorsmayscream to come forward and the cool nearby colors may retreat into thebackground.

Suchapparentanomaliesoccurallthetime.Don'tbeboundbyrulessuchas,“Warm colors advance, cools recede.” Sounds like amilitarymarching order.Onlyuse the“rules”asguidelines tohelpsmoothoverproblems. If thecolorsaren'tworkingonyour canvas, then takewhatever liberties youmust tomakethemwork, but don't blindly interchange the green fieldwith the yellow one!Simply play with the colors gently until they no longer complain.Maybe allyou'llneedinthisexampleistowarmupthegreenalittleanddulltheyellow.

It may be that you can leave the colors alone, but play with the otherperspectivetechniquesyouknowandusethemtohelpgetthedepthyouwant,ignoring the apparent inconsistency between the forward cool area and thedistantwarms.Itmaybethatincludingfencepostswhosesizesdiminishrapidlyastheygobackintothepicture,ortreesorhedgerowsthatdothesame,willhelpalot.Anddetailupclose,fuzzinessinthedistance,willcertainlyhelp.Youmayeven have a strong layer of clouds overhead which you can paint asprogressively smaller blobs as they recede into the picture. Add to this someoverlappingobjects,andprettysoonyou'llhaveapicturewhosecolorreversalsareinconsequential.

FieldsandStreams

Sometimesyou'llhaveastreammeanderingthroughyourfields.Youcanprettymuchtreatastreamasifitwerearoadonflatground,withappropriatecurvesorzigzags,butwithawidthmorelikelytovarythanthatofmostroads.Iftherearerocksorwaveletsorotherdetailsyouwant to include,make thenearerdetailsmoreevidentthanthedistantones,justasyouwoulddrawanythingelse.ThereisonecautionIwouldmention:bodiesofwater,other thanfallsor rapids,areflat.Youcanenhancetheirflatnessbyafewwell-placedhorizontalstrokes,asat

top left, but youmay have to invent some of these horizontal strokes. If youpainttoomanyoftheactualripplesyousee,asatbottomleft,andtheyarenothorizontal, you may destroy the feeling of flatness. This is one time whenpaintingfaithfullywhatyouseemaynotbeagoodidea.

Stairs

Stairwayslookcomplicated,butbasicallytheyareavariationofasimpleinclinewhich in turn is a rectangular block sliced diagonally in half, right, like thecheesewedgeinanearliersketch.Aboveisabasicsetofstairs.

Stairs

ThisisasketchthatIintendedtoworkupasafinisheddrawing,butneverdid.EverythingsaggedintheoldHarper'sFerrybuilding,anditslinearperspectiveisfarfromperfect.Myeyelevelwasaboutinthemiddleoftheright-handsteps.Theupperlandingsaggedsomuchthatinsteadofseeingslightlyupunderit,Icouldseethetopsofitsboards.

I'lltakeyoustepbystepthroughtheprocessIusedtodrawthestairsinthisscene.

Stairs

Todrawthehighersetofsteps,Ididn'tdrawawedge,orincline,inperspective,althoughIkeptsuchanimageinmind.WhatIdrewfirstwereacoupleoflightlinesrepresentingthedirectionandouterboundsofmysteps,asinFigure1.

Those lineskeptmystairsaimed in the rightdirectionanddefined theareatheywould occupy on the drawing. Then I drew in essentially horizontal andvertical lines showing the shape of the near side of the stringer (the longsawtooth-shaped support for the steps). This located all the individual steps,Figure2.

Next I drew the “horizontal” lines for the top edge of each step,Figure3.ThenIaddedtheverticalfaredges(thesawtoothshapeontheothersideofthesteps),Figure4.

After that itwas a simplematter to add the step thicknesses and to tilt thestepsgraduallyastheydescendedbelowmyeyelevel.

BelowisanothersetofstepsIpaintedwithconsciousattentiontoperspective.I've overlaid the painting with a few perspective lines. Notice, first, that in asubjectsuchasthis,thingssagandperspectiveisnotperfect.It'senoughthattherightandleftslantsofappropriatelinesaregenerallycorrect.

Thesetofstepsinthepictureisadjacenttotheshed,and,ifbuilt“correctly”and not ravaged by age, would share the same vanishing points as the shed.Indeed,ifyouprojectlinesfarenoughtotheright,theydoseemaimedtowardthe same vanishing point, but left-leaning lines do not. The lines I've shownheadedleftfromthestepsmeettheeyelevelroughlywheretheoldtreestandsattheleftofthepicture.Inaproperstructure,however,thoselineswouldmeettheeye levelmuch farther left, in fact at the samepoint as the line from the roofedge,linea.Thefactis,thestepshavesagged(haven'tweall),andfurthermore,theyweren'tmadeallthatperfectlyinthefirstplace.

Thereareotherperspectivetechniquesatworkhere.Thedetailinthecenterof the picture helps focus the eye there; the suggested path, wider in theforegroundthanatthesteps,leadstheeyetothesteps;thereissomefuzzinessinthe distant background; the sudden change in value at the doorwaymakes theinsideoftheshedseemdeeper,fartheraway,thanthefaceoftheshed;andmanyobjectsoverlaponeanotherandpusheachotherback.

Figure1

Figure2

Figure3

Figure4

FarmyardSteps,PhilMetzger,watercolor,28″×36″

Exercise:DrawingStairs

Here's an exercise showing oneway (there aremany different approaches) ofdrawingsteps.Ifyou'lldotheexercisealongwithmebyfollowingtheapproachI'veoutlined,Ithinkyou'llfindtheconstructionnotallthatbaffling.Iwouldn'twanttokidyou,though–drawingasetofstepstofitaparticularspace(thekindof job an architect might face) can be tricky. But it can also be fun. If you

understandthebasicsoflinearperspectivepresentedinthisbook,youcanfigureoutmoststepproblems.Ifyougetintoweirdsituationsinvolving,say,circularstairways,thingsgetmuchmorecomplicated,buteventhereyoucanbuildyourstepswithinperspectivecylinders.

Usetheworksheetandfollowalongwithme.Thejobistodrawasetofstairsbetween line a and the doorway on the raised floor. This is an approximatemethod.Therearebooksfullofexactarchitecturalmethodsforbuildingstairs,but that'snotour interesthere.Youknow theold saying…“goodenough forgovernmentwork!”

Startwiththeknowledgethatthewidthofthestairsatthetopisb.Sincethetopofthestairswillbealittlefartherawayfromyouthanthebottom,bshouldbea little shorter than the footof the stairs.Howmuchshorter?Dropverticallinesfromeachendofbtothefloor.Wherethoseverticalshitthefloor,followthe floorboard lines out toa.Where the two floorboard lines chop offa, youhavethewidthandlocationofthefootofthestairs.(Yourealize,ofcourse,thatthefloorboardlinesgototheleftvanishingpoint.)

Lightly draw the two lines between a and b which define the incline, orwedgeshape,ofthestairs.

Decidehowmanystepstherearetobe.We'llassumeit'seight,includingthetopstepatb.Divideoneoftheverticalsyoudrewearlierintoeightequalparts.


Draw light construction lines through thesepoints towardVPL.Nowwehavetheslopesofthesteps.

DrawconstructionlinesfromVPRtothepointswheretheslopesofthestepshittheinclineofthesteps.Nowyouhavethefrontedgeofeachstep.

Drawtheshortvertical linesdefiningthenearendof therisers(theverticalpiecesbetweensteps).Darkentheresultingsawtoothshape.


Draw lines toVPR from each of the low points on the sawtooth. Those linesdefine the rear edges of the steps.Drop short verticals tomark the right-handedgesoftherisers.

Completetheright-handsawtoothwithlinesdrawntoVPL.

Thebasic stairs are complete, ready for details.Thesedetails can easily bedonefreehand,butasyousee,theystillfollowtherulesofperspective,thesirencallsofthosesexyvanishingpoints!

Fordirections,seeExercise:DrawingStairs.

BeyondEyeballing

Sometimes we get involved in subjects that demand more accuracy than ispossible with casual eyeballing or thumb-and-pencil measurement. Here is amethodofdetermininghowevenlyspacedobjectsofequalsizediminishinsizeandspacingastheyrecede.

UprightObjects

Supposeyou'redrawinganeatrowofutilitypolesstretchingacrossaflatpieceof land. The poles are all the same size and the spaces between them are allequal.Howdoyouproceed?

First establish the eye level, and then draw the first pole. Draw guidelinesfromthetopandbottomofthepoletoavanishingpointontheeyelevel.Thendrawasecondpolebetweentheguidelines,guessingataboutwhereitshouldbeplaced.

Crossdiagonalstofindtheperspectivecenterofthefour-sidedshapeyou'veformedanddrawalinefromthatpointtothevanishingpoint.

Nowdrawadiagonallinefromthetopofthefirstpolethroughthe“middle”

of the secondpole. Itwillhit the lowerguidelineat the footof the thirdpole.Drawthethirdpole.

Drawadiagonalfromthetopofthesecondpolethroughthe“middle”ofthethirdpole.Itwillhitthebottomconstructionlineatthefootofpole4…and,asWalterCronkiteused tosay, that's thewayit is.Youcangoall thewayto thehorizon in thismanner and have a perfectly orderly set of poles when you'redone.

BeyondEyeballing

ATileFloor

Perhapsmoreusefulwouldbe an example such as a tile floor. Sometimesweincludethemininteriorpaintingsorstilllifes,andifthey'renotrightthey'llruinthepaintingbymakingthefloorseemtotilttoomuchornotenough.

Supposeyou'redrawingatilefloorfromavantagepointsomethinglikethis.You've chosen your viewing position a little right of center (but it could havebeenatcenterorleftofcenter).

We'llfirstdrawthisfloorinone-pointlinearperspective.Thevanishingpointwillbedirectlyaheadofyou–ontheeyelevel,ofcourse.

Thereasonforchoosingone-pointisthis:whenyouaresoclosetoasubject(you'restandingrightonthetilefloor,let'ssay),asecondvanishingpointwouldbe so far to your right or left that the lines converging toward thatVPwouldhavenegligibleslant. Inotherwords,one-pointperspectivemaybeconsideredtwo-point perspective with one of the vanishing points out aroundMars. Forpracticalpurposes,thelinesinthetilesrunningrighttoleftacrossthesceneareparallel to the picture plane. If the floor were large enough – that is, if itstretchedfarenoughawayfromtheviewer– in thatcase theremightbesomediscernibletwo-pointperspective.Anexamplealittlelaterwillillustratethis.

Asyoucan see in the sketchright, I'vedrawn in the lines representing therowsof tiles(theycouldbefloorboardsat thispoint).Howdoyoumakethemfan out properly? The easiest way, and accurate enough, is tomark off equalwidths along the edge where the floor meets the far wall. Then draw linesthroughthosepointsandtheVP.

Next,pickapairofhorizontallinesneartoyouandsketchthemintodefineyourfirsttile.Thesearelikethefirsttwopolesintheearlierexample;onceyouestablish them, everything else becomes pretty mechanical. You may need toexperimentalittletogettheselinesfeelingright.

Drawrighton this sketchand followalongwithme through the restof thesteps.

BeyondEyeballing

Locatetheperspectivemidpointofthetilebycrossingitsdiagonals,anddrawaconstructionlinethroughittotheVP.

Drawalinefromoneendoftheneartileedgethroughthe“midpoint”ofthefartileedge.Wherethatlinehitslinea,drawhorizontallineb.

Continue thisprocessuntilyouhit the farwall. If the last tiledoesn't comeoutexactlywherethefarwallbegins,movethewallalittle.Nobodywilltell.

CommonGoofs

Certain errors in perspective occur frequently. The following three sketcheshighlightsomeofthem.Seehowmanyyouspotandcompareyourfindingstomine. I hope you don't findmore than I intended! (Answers are on CommonGoofs.)

CommonGoofs

CommonGoofs

CommonGoofs

Conclusion

Be a little careful in applying the “rules” of perspective. Although theperspective techniques are powerful tools, they have their limitations. What's“right”mathematicallyortheoreticallymaynotbe“right”foryourpainting.

Earlier,forexample,wediscussedanaccuratewaytospaceobjects,suchaspoles, in such a way that they would recede properly. Although the methoddiscussed will give you an accurate division of spaces, the result might notalwaysbepleasing.

Several scholars have experimented with this very example by presentingpeoplewithpicturesofrecedingpolesinwhichperspective(linearperspective,tobemoreprecise)wasusedrigidlyandaskingthemtochoosebetweenthosepicturesandonesinwhichcertainlibertiesweretaken.Inthelatter,therecedingpoleswere notmade to bunch together quite as rapidly as perspective “rules”woulddictate.Peoplechosestronglyinfavorofthelatter.

It's not that linear perspective is wrong – it prettymuch duplicateswhat agood camera would record – it's just that there's no denying certainpsychologicalurgespeoplehaveforarrangingthingsincertainways.Inthecaseofthepoles,peopleseemednottowantthemtorecedequiteasprecipitouslyastheyreallydid.Iwon'tpretendtoanalyzewhatmakesthosethingshappen–I'monlysuggestingthatyouneedtoknowwhena toolhasdoneall itcanforyouandneedstobeabandonedinfavorofgutfeeling.

Anotherexample:linearperspectiveisonlyusefulwithinthenormalhuman“cone of vision” – that is, the area you can see ahead, left and right, up anddown, without moving your head or eyes. Beyond that space, in peripheralvision,thingsgetprettydistorted.Andbeyondthatspace,linearperspectivealsogetsdistortedandineffective.

Agoodexampleofa failingof linearperspective is inpaintingavery longmural, or perhaps an ornamented frieze along the top edge of a building. It'squite impossible to view such long scenes without actually moving yourselfphysicallyandstrollingalongthelengthof thepicture,orstandingsofarbackthatyoucanseeeverythingatoncebutcandiscernlittleofthepicture'sdetail.Whatmanyartistshaveresortedtoinsuchsituationsistobreakthepictureintoa seriesof scenes, eachwith itsownvanishingpoints, rather thanattemptonelongscenewithasinglesetofvanishingpoints.

Despitesuchlimitations,perspectiveworkswellforthevastmajorityofthescenesmostofusdrawandpaint.

Nowthatyou'vewadedthroughthisbookandassimilatedeverything,letmeplead one final time formoderation in the application ofwhatwe've covered.Perspectiveisatoolforhelpingtogainasenseofdepthinadrawingorpainting,nothing more. Perspective is not an end in itself. Too rigidly applied, thetechniquesofperspectivecouldsmotheranotherwiseexpressivepainting.Don'tletthemtieyoudown.

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Perspective Without Pain (North Light 20th Anniversary Classic Editions)