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September1998

3DdrawinginVisualBasic

byNormBowler

Youcandownloadthisarticle'ssamplefilesfromourWebsiteaspartofthefilesept98.zip.Gotowww.zdjournals.com/ivb,thenclicktheSourceCodehyperlink.

IfyouaskedmewhetherornotVisualBasicwasagreatmultimediaplatform,myanswerwouldbe,"Yes,butnotrightoutofthebox."EvenwiththeMediaControlInterface(MCI)objectthatcomesintheprofessionalversionsofVB4and5,andtheGIFandJPGformatsupportinversion5,VisualBasicstilllacksmanyofthefeaturesthatwouldmakeitafirst-classmultimediadeliveryplatform.Gettingbettersupportforimages,animation,and3Drenderingwillcostyou--eitheryourtime(spentwritingcustomfunctionsinVBorWindowsC)oryourmoney(spentonprepackagedlibrariesandcontrolstodothecoolstuff).Ifit'scoolyouwant,wecanatleastsaveyousometime.Inthisarticle,we'll

introduceyoutotheconceptsbehind3Ddrawing.Then,we'llwalkyouthroughastraightforwardtechniquethatdraws3DlinesinaVBpicturebox,likethoseshowninFigureA.Nextmonth,we'lldemonstratehowtodraw3Dwireframesandfilledshapes.Onceyouhaveourcodeinhand,youcanuseittobuildcustom3Dgraphs,plots,andillustrations.Let'sbeginbyreviewingsomefundamentalaspectsof3Dspacethatareintegraltothisprocess.

FigureA:We'llshowyouhowtodrawlinesthatlookthree-dimensional.

Throughthelookingglass

Inordertomakeapictureboxactlikeawindowintoathree-dimensionalspace,you'llhavetousesomesortofperspective.Towardthisend,you'lldefineavanishingpointinthepicturebox.Then,you'llwriteanalgorithmthatdisplacespointstowardthevanishingpointastheymoveawayfromtheviewer.(Ifyoufindthisterminologyunfamiliar,you'llwanttoreadthearticle"SimplePerspective"inthismonth'sissue.)

Ofcourse,assoonasyoustartthinkingofaVBpictureboxasawindowinto3Dspace,you'llneedacoordinatesystemtodescribewhatyouseeanddraw.Thecoordinatesystemwillbefamiliartoalgebrastudents:Theorigin--the(0,0,0)point--willlieinthelower-leftcornerofthepicturebox.XvaluesincreaseastheymovetotherightandYvaluesincreaseastheymoveup.Forthethirddimension,you'lluseZ,whichincreasesasitmovesawayfromtheviewer

intothedepthsofthemonitor.Theplaneoftheboxitself,whichrepresentstheviewer'slocation,hasaZvalueof0.

FigureBshowsanexamplethatusesthiscoordinatesystem.Thelower-leftcornerofthepictureboxhasthe(X,Y,Z)coordinates(0,0,0);thelower-rightcornerliesat(100,0,0);theupper-leftcornerhasthecoordinates(0,100,0);andtheupper-rightcornerisat(100,100,0).Thefigurealsoshowsthevanishingpointinthecenterofthepicturebox,withcoordinates

drawing in Visual Basic http://kampol.htc.ac.th/web1/subject/programming2/sheet/vb6/vbarticl..

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(X,Y,1000).NotethatweusethevariablesXandYinsteadofnumbersbecausethevanishingpointrepresents allvaluesofXandYwhereZequals1000.We'vepositionedthepointinthecenterofthepictureboxasifitsXandYcoordinateswere(50,50).

FigureB:Ourcoordinatesystemactsasawindowinto3Dspace.

ThemostinterestingpartofFigureBisthelinethatrunsfromthelower-rightcorner(100,0,0)tothevanishingpoint(X,Y,1000).ThisisthelineofconvergencethatrepresentsallZvaluesbetween0and1000forpointswithanX,Ycoordinateof(100,0).Ourfiguredemonstratesthatinordertodrawapointinperspective,yousimplydeterminewhereitliesonthelinebetweenthevanishingpointandthepoint's(X,Y)locationonthepictureboxplanewhereZequals0.

Nowthatyouseethelineonwhichthepointmustfall,thequestionbecomes whereonthelineofconvergencedoyou

placeaparticularpoint?Thisiswheremyambitionexceedsmymathematicalunderstanding;butI'vedevelopedanalgorithmthatlooksgoodandappearstomakesense.Let'sseehowitworks.

Anangulara lgorithm

Therateofchangeinanobject'sapparentpositionisgreatestneartheviewerandbecomesprogressivelylessastheobjectsrecedeintothedistance.So,makingtheamountofconvergencedirectlyproportionaltoitsZdisplacementwon'twork.Instead,ouralgorithmtranslatesapoint'sconvergence backfromthevanishingpoint,proportionaltothesquareofitsZtraveloverthedistancebetweenthevanishingpointandtheplaneofthepicturebox.Whatamouthful!Here'showitworks,inpracticalterms,usingthecoordinatesystemshowninFigureB.

AnypointwithaZvaluegreaterthanorequaltothevanishingpointdistance(1000)willbeshownatthe

vanishingpoint.

ApointwithaZvalueof900hastraveled10percentofthedistancebetweenthevanishingpoint(Zequalto1000)andthepictureboxZplane(Zequalto0).Tenpercent(.10)squaredequals.01,or1percent.So,apointatZequalto900willbetranslated1percentalongthelinebetweenthevanishingpointandthepointonthepictureboxplane.Usingsimilarcalculations,pointswithZvaluesof500,100,and0willappearat25percent(.50squared),81percent(.90squared)and100percent(1.0squared),respectively,ofthedistance

fromthevanishingpointalongthelineofconvergence,respectively.

ApointwithaZvalueof-100hastraveled110percentofthedistancefromthevanishingpointtothepicture

boxplane.Squaring1.10yields1.21,sothepointwillbetranslated121percentalongthelineofconvergence.

Noticethatthealgorithmletsyoucalculatetranslatedcoordinatesforpointsthatare behindtheviewer'splaneofvision.You'llneedtodothistodrawlineswithoneormoreendpointsoffscreen.

Asyoucanseefromourexamples,thealgorithmappearstofitreality.The10percentofZtravelnearestthepicture


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boxplaneconverges18percent,whilethe10percentofZtravelnearestthevanishingpointconvergesonly1percent.

Setupcode

Now,let'stransformwhatyou'velearnedaboutperspectivedrawingintoasampleformandVBcode.You'llimplement3Ddrawingusingglobalvariablesandcodeattachedtotheform.(Packagingthecodeinaclasslibrarywouldbemoreelegant,butdoingsowouldaddsignificantlytothesizeofthecodeandthescopeofthisarticle.)We'llbeginworkontheprojectthismonthandaddtoitnextmonth.Tobegin,openanewVBproject.Namethedefaultform frm3d,andplaceonitapictureboxnamedpbandabuttonnamedbasic.AssigncaptionsasshowninFigureC.Savetheformasthreedee.frmandtheprojectas threedee.vbp.Nextyou'lladdthecode.

FigureC:Addapictureboxandabuttontoaforminanewproject.

Note:Commentreduction

Becauseofthelengthofourexample'scode,we'veomittedmanyofthecommentlines.However,thesamplefilesavailableatwww.zdjournals.com/ivbcontaincomprehensivecomments.

Declarations

ListingAcontainstheglobalvariabledeclarationsyouneedtoenterintofrm3d.Mostofthesevariableshavetodo

withimplementingthecoordinatesystemandvanishingpoint;theycontainvaluescalculatedfromthepicturebox'spropertiesduringcoordinatesetup.

ListingA:Globalvariabledeclarations

OptionExplicit

'windowconfiguration--pblleft(xmin),

`pbrright(xmax),pbbbottom(ymin),`pbttop(ymax),pbzzcoordDimpblAsDouble

DimpbrAsDoubleDimpbbAsDouble

DimpbtAsDoubleDimpbzAsDouble

'vanishingpoint--x,y,zcoordinates

DimvpxAsDoubleDimvpyAsDouble


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DimvpzAsDouble

'zdelta--zdistancefrompbplane'tovanishingpointDimzdAsDouble

Coordinatesetup

Thesubprocedureinit3dshowninListingBinitializesmostoftheglobalvariables;addthiscodetoyourform.This

procedureletsyouspecifytheXcoordinateoftheleftsideofthepicturebox,theYcoordinateofthebottomedge,thewidthofthepicturebox,itsZcoordinate,andhowfarintothescenethevanishingpointlies.Forthe

coordinatesystemdisplayedinFigureB,thecallwouldbeasfollows:

init3d0,0,100,0,1000

OurexampleformmakesthiscallinitsLoadeventcode,shownattheendofListingB.

ListingB:init3dandForm_Loadsubprocedures

Subinit3d(lAsDouble,bAsDouble,wAsDouble,zAsDouble,vpoffAsDouble)'l=left=xminimum.b=bottom=yminimum.

'w=width.l+w=xmaximum.z=zofpictureboxplane.vpoff=vanishingpointzoffset.

'Initializesvarsthatimplementcoordinatesystem.`Setsacustomscaleonpicturebox.

'pictureboxheightandwidth,inpixelsDimpbhpxAsSingleDimpbwpxAsSingle

pb.ScaleMode=3'pixelspbhpx=pb.ScaleHeight

pbwpx=pb.ScaleWidth

'setcoordinatesforwindow

pbl=lpbr=l+wpbt=b+((pbhpx/pbwpx)*w)

pbb=bpbz=z

'setpictureboxscalepb.ScaleLeft=pblpb.ScaleTop=pbt

pb.ScaleWidth=pbr-pblpb.ScaleHeight=pbb-pbt

zd=vpoff

'initvanishingptcoords,centeredhorizvert

vpx=(pbl+pbr)*(0.5)vpy=((pbt-pbb)*(0.5))+pbbvpz=pbz+zdEndSub

PrivateSubForm_Load()'initializecoordinatesysteminit3d0,0,100,0,1000

EndSub

Theinit3dproceduresetsacustomscaleforthepictureboxandcalculatesthemaximumYvalueforcorrectaspectratio.Ifyouspecifyawidthof100unitsandyourpictureboxishalfashighasitiswide,themaximumY

valuewillbe50.Thus,squareswillalwaysbesquare.


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Theargumentstoinit3dallowyoutosetadifferentcoordinatesystemthantheonewe'reusing,aswellasmakingtheperspectiveeffectmoreorlessobvious.Ourvanishingpointis10timesthewidthofthepicturebox.

DecreasingtheZoffsetwouldmaketheperspectiveeffectmorenoticeable,whichissimilartothelookproducedbyawide-anglelens.

Thecodealsoplacesthevanishingpointinthecenteroftheimage.Ifyouwishtomovethevanishingpointand

horizonlinehigheronthescreen,increasetheup/downmultiplier.Valuesgreaterthan.5raisethevanishingpointandmakeitappearthatyou'relookingdownonthescene,ratherthanlookingparalleltotheground.

3Dlines

NormallyinVB,you'ddrawalineinapicturebox(pb)byspecifyingtheXandYcoordinatesoftheendpoints,like

this:

pb.Line(x1,y1)-(x2,y2)

Todrawin3D,ontheotherhand,youneedaZcoordinateaswell.Enterintofrm3dthesubprocedureln3d,showninListingC,whosecallisasfollows:

ln3dx1,y1,z1,x2,y2,z2

Let'sseehowthissubprocedureworks.

ListingC:ln3dsubprocedureandcalledfunctions

Subln3d(ByValx1AsDouble,ByValy1AsDouble,ByValz1AsDouble,ByValx2AsDouble,_ByValy2AsDouble,ByValz2AsDouble)

`Drawsaperspectivecorrectedline

DimxaAsDouble

DimyaAsDoubleDimxbAsDoubleDimybAsDouble

xa=xtrans(x1,z1)

ya=ytrans(y1,z1)xb=xtrans(x2,z2)yb=ytrans(y2,z2)

pb.Line(xa,ya)-(xb,yb)EndSub

Functionxtrans(ByValxAsDouble,ByValzAsDouble)AsDouble

`Translates3Dxcoordinateinto2Dpicturebox

`coordinatebasedonitszdisplacement

DimzsAsDouble'zscratchDimcpAsDouble'correctionpercentage

DimsdAsDouble'scratchdelta

Ifz>=vpzThenxtrans=vpx

ExitFunctionElsezs=vpz-zcp=(zs/zd)*(zs/zd)sd=vpx-x

xtrans=vpx-(cp*sd)EndIfEndFunction

Functionytrans(ByValyAsDouble,ByValzAsDouble)AsDouble


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`Translates3Dycoordinateinto2Dpicturebox

`coordinatebasedonitszdisplacement

DimzsAsDouble'zscratch

DimcpAsDouble'correctionpercentageDimsdAsDouble'scratchdelta

Ifz>=vpzThen

ytrans=vpyExitFunction

Elsezs=vpz-zcp=(zs/zd)*(zs/zd)

sd=vpy-yytrans=vpy-(cp*sd)EndIf

EndFunction

Translationfunctions

Theactuallinethattheln3dprocedurewilldrawinthepictureboxwillbea2D(X,Y)line--infact,itwillcallpb.Line

todothejob.Butfirst,itmustcalculatetheconvergenceofthe3Dcoordinatesandtranslatetheminto2Dcoordinatesusingthealgorithmwedescribedearlier.Toperformthischore,ln3dcallstheproceduresxtransandytrans,asshowninListingC;addthemtoyourform.

Linefunction

Theln3dproceduredeclaresfourvariablestocontainthetranslated

(x1,y1)-(x2,y2)

endpoints,itcallsxtransandytranstoperformthecalculation,anditcallspb.Linetodrawtheline.Tosetthecolor

andwidthoftheline,modifytheForeColorandDrawWidthpropertiesofthepicturebox.

Anexample

Tosee3Dlinedrawinginaction,placethecodefromListingDintheClickeventoftheBasic3DDrawingbutton.Whenyouruntheproject,itwillgeneratethelinesshowninFigureA.

PrivateSubbasic_Click()'loopcounterDimlpAsDouble

'initializepictureboxvpy=(pbt+pbb)/2

pb.Clspb.ForeColor=QBColor(0)

pb.FillStyle=0pb.FillColor=QBColor(11)pb.DrawWidth=1

'constantsusedtodrawfloorgridConstxmin=-3000#

Constxmax=3000#Constzmin=0#Constzmax=1000#

Constgstep=50#

'horizonline

pb.Line(pbl,vpy)-(pbr,vpy)

'xlines

Forlp=xminToxmaxStepgstep


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ln3dlp,0,zmin,lp,0,zmaxDoEvents

Nextlp

'zlines

Forlp=zminTozmaxStepgstepln3dxmin,0,lp,xmax,0,lpDoEvents

Nextlp

pb.ForeColor=RGB(0,0,0)

EndSub

Youcandownloadthisarticle'ssamplefilesfromourWebsiteaspartofthefileoct98.zip.Gotowww.zdjournals.com/ivb,thenclicktheSourceCodehyperlink.

Thismonth,we'llexpandourprojecttodraw3Dspheres,cubes,andtriangles,aswellasfilledwireframeshapeslikethatshowninFigureA.We'llbuildonthecodewewrotelastmonth,andweassumeyou'veeitherdownloadedorcreatedthesampleproject.

FigureA:Nifty3Dimageslikethisonewilladdsophisticationtoyourapplications.

Setupsteps

Atpresent,thethreedeeforminthethreedeeprojectcontainsapicture boxtodisplay3Ddrawingsandasingle

commandbutton.Let'sbeginbyopeningtheprojectandaddingtwomorebuttonsnamedfilledandunfilled.GivethesebuttonsthecaptionsFilledWireframeandUnfilledWireframe.Nowwe'llgettoworkdrawing3Dcubesandspheres.

3Dcubesandspheres

Yourfirstnew3Dshapeisawireframecube.Ourcubeprocedure,showninListingA,usestheln3dprocedurewepresentedlastmonthtodrawarectangularprism.IttakesminimumandmaximumX,Y,andZvaluesasarguments,thendrawsthe12three-dimensionallinesrequiredtomakeacube.(Aswithlastmonth'scode,we'veremovedmostcommentlinestosavespace.However,thesamplefilescontaincomprehensivecomments.)

ListingA:Thecubeprocedure

Subcube(ByValxminAsDouble,ByValxmaxAs_Double,ByValyminAsDouble,ByValymaxAs_Double,ByValzminAsDouble,ByValzmaxAsDouble)

ln3dxmin,ymin,zmax,xmax,ymin,zmax'backface


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ln3dxmin,ymin,zmax,xmin,ymax,zmaxln3dxmax,ymin,zmax,xmax,ymax,zmax

ln3dxmin,ymax,zmax,xmax,ymax,zmax

ln3dxmin,ymin,zmax,xmin,ymin,zmin'sideedges

ln3dxmax,ymin,zmax,xmax,ymin,zminln3dxmin,ymax,zmax,xmin,ymax,zminln3dxmax,ymax,zmax,xmax,ymax,zmin

ln3dxmin,ymin,zmin,xmax,ymin,zmin'frontfaceln3dxmin,ymin,zmin,xmin,ymax,zmin

ln3dxmax,ymin,zmin,xmax,ymax,zminln3dxmin,ymax,zmin,xmax,ymax,zminEndSub

Next,you'llenterthecodetocreateasphere.Becausethisimplementationdoesn'tperformshading,representingasphereissimplyamatterofdrawingacirclewithatranslatedcenterpointandaperspective-correctedradius.Enterintothefrm3dformthesp3dsubprocedureshowninListingB,whichtakesfourarguments:theX,Y,andZ

coordinateofitscenter,anditsradius:

sp3dx,y,z,radius

ListingB:Thesp3dsubprocedure

Subsp3d(ByValx1AsDouble,ByValy1AsDouble,ByValz1AsDouble,ByValrAsDouble)

DimxaAsDouble'translatedxDimyaAsDouble'translatedyDimxbAsDouble'translatedxforradiusDimcrAsDouble'correctedradiuslength

xa=xtrans(x1,z1)ya=ytrans(y1,z1)xb=xtrans(x1+r,z1)

cr=xb-xa

pb.Circle(xa,ya),cr

EndSub

Theprocedureusesxtransandytranswecreatedlastmonthtotranslatethe3Dcenterpointtoa2Dcoordinate,thenaddstheradiustotheXcoordinateofthecenterpointtocalculateapointontherightedgeofthecircle.ThedifferencebetweenthetwotranslatedXcoordinatesistheperspective-correctedradius.

VBdeterminesthecircle'slinewidthandcolorfromthepicturebox'sDrawWidthandForeColorproperties.Similarly,thefillstyleandcolorcomefromthepicturebox'sFillStyleandFillColorproperties.

Let'supdatethecodeintheBasic3Ddrawingbuttontodisplay3Dcubesandspheresaswellaslines,asshowninFigureB.AddthecodeshownincolorinListingCatthebeginningandendoftheBasic3DDrawingbutton's

Clickevent.

FigureB:Ourcodegeneratesthesesamplespheres,cubes,andlines.


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ListingC:basic_click()

PrivateSubbasic_Click()DimlpAsDouble

Dimra(1To8,1To3)AsDoubleDimlp2AsInteger

DimxAsIntegerDimyAsIntegerDimzAsInteger

.

.

.

Forlp=700To100Step-100'spheressp3d0,10,lp,10DoEvents

Nextlp

pb.ForeColor=QBColor(12)`cubes

Forlp=0To900Step100cube140,180,100,140,lp,lp+40DoEvents

Nextlp

pb.ForeColor=RGB(0,0,0)

EndSub

3Dfilledtriangles

Foryourfinalprimitiveshape,you'llcreatefilledandunfilled3Dtriangles.Butfirst,youmustmakeacoupleof

additionstotheexistingcode.Addthefollowinglinetotheglobalvariablesintheform'sgeneraldeclarations:

DimsprAsDouble

Thisvariableprovidesascaleunit-to-pixelratioforthetrianglefillyou'llcreatelater.Now,addthislinetotheinit3dprocedure:

spr=(pbt-pbb)/pbhpx

Thiscodecalculatestheratioyoujustdefined.Thecodeforthetr3dprocedureappearsinListingD,alongwiththecodeforsimpleminandmaxfunctionstheprocedureuses.Thetr3dproceduretakesasargumentstheX,Y,and

Zcoordinatesofthethreecorners:

tr3dx1,y1,z1,x2,y2,z2,x3,y3,z3


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ListingD:Thetr3dprocedure

Subtr3d(ByValx1AsDouble,ByValy1AsDouble,_ByValz1AsDouble,ByValx2AsDouble,_ByValy2AsDouble,ByValz2AsDouble,_

ByValx3AsDouble,ByValy3AsDouble,_ByValz3AsDouble)

DimxaAsDouble'translatedcoordsfor3pointsDimyaAsDoubleDimxbAsDoubleDimybAsDoubleDimxcAsDoubleDimycAsDouble

DimcuryAsDouble'currentyDimyminAsDouble'minimumyfortriangle

DimymaxAsDouble'maxyfortriangleDimxminAsDouble'minxforscanlineDimxmaxAsDouble'maxxforscanline

DimstpAsDouble'ystepvalue

DimbAsBoolean'booleanflagforlinecomparisonDimiyAsDouble'scratchvarsforlinecomparisonDimayAsDoubleDimixAsDoubleDimaxAsDouble

DimxtmpAsDouble'xinterceptoncurrentline

'ifdens>1,scanlinestepwillbe


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ay=ybix=xa

ax=xbElseay=ya

ix=xbax=xaEndIf

If(cury>=iy)And(cury=iy)And(cury


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Nextcury

'outlines,justincase.(catchesroundingerrors)pb.Line(xa,ya)-(xb,yb),pb.FillColorpb.Line(xa,ya)-(xc,yc),pb.FillColor

pb.Line(xb,yb)-(xc,yc),pb.FillColorEndSub

Functionmin(ByValaAsDouble,ByValbAsDouble)IfabThen

max=aElse

max=bEndIfEndFunction

Thisprocedurewilldraweitherfilledorunfilledtriangles.Ifthepicturebox'sFillStylepropertyissetto1

(Transparent),theproceduretranslatesthethreeendpoints,drawsthethreelines,andexits.IfFillStyleissetto0(Solid)oranyothervalue,theproceduredrawsafilledtriangleinthepicturebox'sfillcolor.

Thefilledtrianglecodeusesascan-linefilltofilla2Dtriangleusingonlyhorizontallines.Thecodedeterminesthe

minimumandmaximumYvalueofthethreeendpoints,thenincrementsfromonetotheotherinone-pixelincrements.Atleasttwoofthelineswillhaveintersectionpointsoneachpixelrow.Allthreelineswillhaveapointonapixelrowonlywhenthetriangleincludesahorizontalline.

Thecodedeterminestheintersectionpoints,drawsahorizontallinefromtheminimumXpointtothemaximumXpoint,thencontinuestothenextpixelrow.WhenthecodereachesthelastYvalue,itwillhavefilledthetriangleusinghorizontallines,withnounfilledpixelsandnopixelfilledmorethanonce.

Whendevelopingthiscode,Inoticedslightroundingerrorsthatresultedinoccasionalunfilledpixelsattheedgeofthetriangle.Iaddedafewlinesofcodetodrawthetriangleedges,butbeawarethattheresultstillmissesasinglepixelonceinagreatwhile.

Beyondtriangles

Filledtrianglesarethebasisforallpolygonfills.Youcanbreakdownarectangleintotwotriangles;morecomplexshapesrequiremoretriangles.Ourfilledtriangleproceduretakesyououtoftheworldofwireframemodelsand

alittlebitcloserto3Drendering.Ifyou'recarefultodrawyourfilledshapesinreverseZ-order(drawingthefarthestshapefirst),youcanmakeyourwireframemodelsopaquebyperforminghiddensurfaceremoval.

FigureAshowsanexampleofafilledwireframemodel.Thelumpsandswoopsarethegraphoftheinteractionoftwosinewaves,varyingalongtheXandZaxes.ListingEcontainsthewireframe1procedurethatyieldsthis

result.

ListingE:Thewireframe1procedure

Subwireframe1()DimxAsIntegerDimzAsInteger

Constpi=3.14159265Constxmin=-400Constxmax=500

Constzmax=800Constzmin=375Conststp=20'gridsize


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Constfac1=250'factor1.sinrateofchangeConstfac2=120'factor2.sinmultiplier

Constfac3=-170'factor3.gridyoffset

pb.Cls

vpy=pbt'setvanishingpointtotopofpicturebox

pb.FillColor=QBColor(11)'setproperties

pb.ForeColor=QBColor(0)

pb.DrawWidth=1

Forz=zmaxTozminStep(stp*-1)_'drawfrombacktofrontForx=xminToxmaxStepstp_

'drawfromlefttorightIf(xzmin)And_(pb.FillStyle1)Then

tr3dx,(Sin(x*pi/fac1)+Sin(z*pi/fac1))_*fac2+fac3,z,x+stp,(Sin((x+stp)*pi/_fac1)+Sin(z*pi/fac1))*fac2+fac3,z,x,_

(Sin(x*pi/fac1)+_Sin((z-stp)*pi/fac1))*fac2+fac3,z-stp

tr3dx+stp,(Sin((x+stp)*pi/fac1)+_Sin(z*pi/fac1))*fac2+fac3,z,x,_(Sin(x*pi/fac1)+_

Sin((z-stp)*pi/fac1))*fac2+fac3,_z-stp,x+stp,(Sin((x+stp)*pi/fac1)+_Sin((z-stp)*pi/fac1))*fac2+fac3,z-stp

EndIfIfxzminThenln3dx,(Sin(x*pi/fac1)_+Sin(z*pi/fac1))*fac2_

+fac3,z,x,(Sin(x*pi/fac1)_+Sin((z-stp)*pi/_fac1))*fac2+fac3,z-stp

EndIfDoEventsNextx

Nextz

EndSub

Miscellaneousfunctions

Withthebasicframeworkinplace,it'seasytoextendyour3Ddrawingcapabilities.Forinstance,thesamplecodeavailablefromourWebsiteincludesasimpleextension.Thehorizonproceduretakes"groundcolor"and"skycolor"asarguments.Itclearsthepicturebox,thencolorseverythingabovethevanishingpoint'sYvalue"sky"andeverythingatorbelowthevanishingpoint"ground."You'llsoonfindyourselfdevelopingsimilartools.

Stonesleftunturned

Istherereallysuchathingasavanishingpoint?No--iftherewere,allthestarsinthenightskywouldconvergeto

asinglebrightpoint.Avanishingpointisjustaconvenientconstructiontousewhenimplementingperspective,anditworksonlywhenitliesbeyondthefarthestpointyoudraw.

Alsonotethatwedidn'tdiscusscolorinthesearticles.Oursamplecodeusesonlythestandard16colorsavailablethroughtheqbcolorfunction,butyoucanuseanycolors.However,youmaygetstrangeresultson16-or256-colorsystems,especiallywithlinewidthsof1.


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Conclusion

Afterworkingthroughourexamples,areyoureadytowriteyourownrenderingengine?Probablynot.Butyou'reboundtothinkofmanywaystousethetechniqueswe'vedemonstratedtodeliver3DgraphsandwireframesinyourVBapplications.Wehopeyou'lluseourexamplesasstartingpointstotakeyourapplicationstothenext

visuallevel.

1999MicrosoftCorporation.Allrightsreserved.Termsofuse

[email protected]

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