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February2011MasterofComputerApplication(MCA)Semester3

MC0072ComputerGraphics4Credits(BookID:B0810)AssignmentSet2

1. Writeashortnoteonthefollowings:A)Videomixing

Ans: Videocontrollerprovidesthe facilityofvideomixing. Inwhich itaccepts informationoftwo imagessimultaneously.Onefromframebufferandotherfromtelevisioncamera,recorderorothersource.

Thisisillustratedinfig2.7.Thevideocontrollermergesthetworeceivedimagestoformacomposite

image.

FrameBuffer VideoController

Monitor

VideoSignalSource

Videomixing

Therearetwotypesofvideomixing.Infirst,agraphicsimageissetintoavideoimage.Heremixingis

accomplishedwith hardware that treats a designated pixel value in the frame buffer as a flag to

indicatethatthevideosignalshouldbeshowninsteadofthesignalfromtheframebuffer,normally

thedesignatedpixelvaluecorrespondstothebackgroundcoloroftheframebufferimage.

Inthesecondtypeofmixing,thevideo image isplacedonthetopoftheframebuffer image.Here,

wheneverbackgroundcolorofvideo imageappears,theframebuffer isshown,otherwisethevideo

imageisshown.

B)FramebufferAns: Aframebufferisavideooutputdevicethatdrivesavideodisplayfromamemorybuffercontaininga

completeframeofdata.

Theinformationinthememorybuffertypicallyconsistsofcolorvaluesforeverypixel(pointthatcan

bedisplayed)on thescreen.Colorvaluesarecommonlystored in1bitbinary (monochrome),4bit

palettized, 8bit palettized, 16bit high color and 24bit true color formats. An additional alpha

channel issometimesusedtoretain informationaboutpixeltransparency.Thetotalamountof the

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memoryrequiredtodrivetheframebufferdependsontheresolutionoftheoutputsignal,andonthe

colordepthandpalettesize.

Framebuffersdiffersignificantlyfromthevectordisplaysthatwerecommonpriortotheadventof

the framebuffer.Withavectordisplay,only theverticesof thegraphicsprimitivesarestored.The

electronbeamof theoutputdisplay is thencommanded tomove fromvertex tovertex, tracingan

analog line across the areabetween thesepoints.With a framebuffer, the electronbeam (if the

display technologyusesone) is commanded to tracea lefttoright, toptobottompath across the

entirescreen,thewayatelevisionrendersabroadcastsignal.Atthesametime,thecolorinformation

for each point on the screen is pulled from the frame buffer, creating a set of discrete picture

elements(pixels).

Theterm"framebuffer"hasalsoenteredintocolloquialusagetorefertoabackingstoreofgraphical

information.Thekeyfeaturethatdifferentiatesaframebufferfrommemoryusedtostoregraphics

the

output

device

is

lost

in

this

usage.

DisplaymodesFramebuffersusedinpersonalandhomecomputingoftenhadsetsofdefined"modes"underwhich

the frame buffer could operate. These modes would automatically reconfigure the hardware to

outputdifferentresolutions,colordepths,memorylayoutsandrefreshratetimings.

IntheworldofUnixmachinesandoperatingsystems,suchconvenienceswereusuallyeschewed in

favorofdirectlymanipulatingthehardwaresettings.Thismanipulationwasfarmoreflexible inthat

anyresolution,colordepthandrefreshratewasattainablelimitedonlybythememoryavailableto

theframebuffer.

An unfortunate sideeffect of thismethodwas that thedisplay device couldbe driven beyond its

capabilities. In some cases this resulted inhardwaredamage to thedisplay.[3]More commonly, it

simplyproduced garbled andunusableoutput.ModernCRTmonitors fix thisproblem through the

introductionof"smart"protectioncircuitry.Whenthedisplaymodeischanged,themonitorattempts

toobtainasignallockonthenewrefreshfrequency.Ifthemonitorisunabletoobtainasignallock,or

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if the signal isoutside the rangeof itsdesign limitations, themonitorwill ignore the framebuffer

signalandpossiblypresenttheuserwithanerrormessage.

LCDmonitors tend to contain similar protection circuitry,but fordifferent reasons. Since the LCD

mustdigitallysamplethedisplaysignal(therebyemulatinganelectronbeam),anysignalthatisoutof

rangecannotbephysicallydisplayedonthemonitor.

ColorpaletteFramebuffershave traditionally supported awide varietyof colormodes.Due to the expense of

memory,mostearly framebuffersused1bit (2color),2bit (4color),4bit (16color)or8bit (256

color)colordepths.Theproblemwithsuchsmallcolordepthsisthatafullrangeofcolorscannotbe

produced.Thesolutiontothisproblemwastoaddalookuptabletotheframebuffers.Each"color"

stored in frame buffer memory would act as a color index; this scheme was sometimes called

"indexedcolor".

Thelookuptableservedasapalettethatcontaineddatatodefinealimitednumber(suchas256)of

differentcolors.However,eachofthose[256]colors,itself,wasdefinedbymorethan8bits,suchas

24 bits, eight of them for each of the three primary colors. With 24 bits available, colors can be

defined farmore subtlyandexactly,aswellasoffering the full rangegamutwhich thedisplaycan

show.Whilehavingalimitedtotalnumberofcolorsinanimageissomewhatrestrictive,nevertheless

theycanbewellchosen,andthisschemeismarkedlysuperiorto8bitcolor.

Thedata from the framebuffer inthisschemedeterminedwhichof the [256]colors in thepalette

wasforthecurrentpixel,andthedatastoredinthelookuptable(sometimescalledthe"LUT")went

tothreedigitaltoanalogconverterstocreatethevideosignalforthedisplay.

Theframebuffer'soutputdata,insteadofprovidingrelativelycrudeprimarycolordata,servedasan

indexanumbertochooseoneentry in the lookup table. Inotherwords, the indexdetermined

whichcolorandthedatafromthelookuptabledeterminedpreciselywhatcolortouseforthecurrent

pixel.

MemoryaccessWhile frame buffers are commonly accessed via a memory mapping directly to the CPUmemory

space,this

is

not

the

only

method

by

which

they

may

be

accessed.

Frame

buffers

have

varied

widely

inthemethodsusedtoaccessmemory.Someofthemostcommonare:

Mappingtheentireframebuffertoagivenmemoryrange.Portcommandstoseteachpixel,rangeofpixelsorpaletteentry.Mapping a memory range smaller than the frame buffer memory, then bank switching as

necessary.

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Theframebufferorganizationmaybechunky(packedpixel)orplanar.

VirtualframebuffersMany systems attempt to emulate the function of a frame buffer device, often for reasons of

compatibility.The

two

most

common

"virtual"

frame

buffers

are

the

Linux

frame

buffer

device

(fbdev)

andtheXVirtualFramebuffer(Xvfb).TheXVirtualFramebufferwasaddedtotheXWindowSystem

distribution toprovideamethod for runningXwithoutagraphical framebuffer.While theoriginal

reasonsforthisare losttohistory, it isoftenusedonmodernsystemstosupportprogramssuchas

the Sun Microsystems JVM that do not allow dynamic graphics to be generated in a headless

environment.

The Linux frame buffer device was developed to abstract the physical method for accessing the

underlying framebuffer into a guaranteedmemorymap that is easy forprograms to access. This

increasesportability,asprogramsarenotrequiredtodealwithsystemsthathavedisjointedmemory

mapsorrequirebankswitching.

PageflippingSinceframebuffersareoftendesignedtohandlemorethanoneresolution,theyoftencontainmore

memory than isnecessary todisplayasingle frameat lower resolutions.Sincethismemorycanbe

considerable insize,atrickwasdeveloped toallow fornew framestobewritten tovideomemory

withoutdisturbingtheframethatiscurrentlybeingdisplayed.Theconceptworksbytellingtheframe

buffertouseaspecificchunkofitsmemorytodisplaythecurrentframe.Whilethatmemoryisbeing

displayed, a completely separatepartofmemory is filledwith data for the next frame.Once the

secondarybufferisfilled(oftenreferredtoasthe"backbuffer"),theframebufferisinstructedtolook

atthesecondarybufferinstead.Theprimarybuffer(oftenreferredtoasthe"frontbuffer")becomes

the secondarybuffer, and the secondary bufferbecomes theprimary. This switch is usually done

during theverticalblanking interval toprevent thescreen from"tearing" (i.e.,half theold frame is

shown,andhalfthenewframeisshown).

Mostmodernframebuffersaremanufacturedwithenoughmemorytoperformthistrickevenathigh

resolutions.Asaresult,ithasbecomeastandardtechniqueusedbyPCgameprogrammers.

GraphicsacceleratorsAsthedemandforbettergraphicsincreased,hardwaremanufacturerscreatedawaytodecreasethe

amountofCPUtimerequiredtofilltheframebuffer.Thisiscommonlycalleda"graphicsaccelerator"

intheUnixworld.

Commongraphicsdrawingcommands(manyofthemgeometric)aresenttothegraphicsaccelerator

in their raw form.Theaccelerator then rasterizes the resultsof thecommand to the framebuffer.

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ThismethodcansavefromthousandstomillionsofCPUcyclespercommand,astheCPUisfreedto

dootherwork.

While early accelerators focusedon improving theperformanceof 2DGUI systems,mostmodern

acceleratorsfocusonproducing3D imagery inrealtime.Acommondesign istosendcommandsto

the graphics acceleratorusing a library such asOpenGL. TheOpenGL driver then translates those

commands to instructions for theaccelerator'sgraphicsprocessingunit (GPU).TheGPUuses those

microinstructionstocomputetherasterizedresults.Thoseresultsarebitblittedtotheframebuffer.

Theframebuffer'ssignalisthenproducedincombinationwithbuiltinvideooverlaydevices(usually

usedtoproducethemousecursorwithoutmodifyingtheframebuffer'sdata)andanyanalogspecial

effectsthatareproducedbymodifyingtheoutputsignal.Anexampleofsuchanalogmodificationwas

theantialiasing techniqueusedby the3dfxVoodoocards.Thesecardsadda slightblur tooutput

signalthatmakesaliasingoftherasterizedgraphicsmuchlessobvious.

Popular

manufacturers

of

3D

graphics

accelerators

are

Nvidia

and

ATI

Technologies.

C)ColortableAns: Incolordisplays,24 bitsperpixelare commonlyused,where8bits represent256 levels foreach

color. Here it is necessary to read 24bits for each pixel from frame buffer. This is very time

consuming. To avoid this video controller uses look up table (LUT) to store many entries of pixel

values inRGB format.With this facility,now it isnecessaryonly to read index to the lookup table

fromtheframebufferforeachpixel.Thisindexspecifiestheoneoftheentries inthe lookuptable.

ThespecifiedentryintheloopuptableisthenusedtocontroltheintensityorcoloroftheCRT.

Usually,lookuptablehas256entries.Therefore,theindextothelookuptablehas8bitsandhence

foreachpixel, the framebufferhas to store8bitsperpixel insteadof24bits. Fig.2.6 shows the

organizationofacolor(Video)lookuptable.

Organization of a Video look-up table

Thereareseveraladvantagesinstoringcolorcodesinalookuptable.Useofacolortablecanprovide

a "reasonable" number of simultaneous colors without requiring Iarge frame buffers. For most

applications,256or512differentcolorsaresufficientforasinglepicture.Also,tableentriescanbe

changedatanytime,allowingausertobeabletoexperimenteasilywithdifferentcolorcombinations

inadesign,scene,orgraphwithoutchangingtheattributesettingsforthegraphicsdatastructure.In

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visualizationand imageprocessingapplications,color tablesareconvenientmeans forsettingcolor

thresholdssothatallpixelvaluesaboveorbelowaspecifiedthresholdcanbesettothesamecolor.

Forthesereasons,somesystemsprovidebothcapabilitiesforcolorcodestorage,sothatausercan

electeithertousecolortablesortostorecolorcodesdirectlyintheframebuffer.

DisplaytechnologyThe image isshownonascreen (alsocalledamoniteur),which isanoutputperipheraldevice that

allowsavisual representation tobeoffered.This informationcomes from thecomputer,but inan

indirect way. Indeed, the processor does not directly send information to the monitor, but

processestheinformationcomingfromitsRandomaccessmemory(RAM),thensendsittoagraphics

cardthatconvertstheinformationintoelectricalimpulses,whichitthensendstothemonitor.

Computermonitorsareusuallycathodetubes,i.e.atubemadeoutofglassinwhichanelectrongun

emits electrons which are then directed by a magnetic field towards a screen on which small

phosphorescent elements (luminophores) are laid out, constituting points (pixels) that emit light

whentheelectronshitthem.

ThepixelconceptAn image consists of a set of points called pixels (the word pixel is an abbreviation of PICture

ELement)Thepixelisthusthesmallestcomponentofadigitalimage.Theentiresetofthesepixelsis

containedin

atwo

dimensional

table

constituting

the

image:

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Thescreensweepingiscarriedoutfromlefttorightandfromtoptobottom,itisusualtoindicatethe

pixellocatedatthetoplefthandcorneroftheimageusingthecoordinates[0,0],thismeansthatthe

directionsoftheimageaxesarethefollowing:

ThedirectionoftheXaxisisfromlefttoright Thedirectionof theYaxis is from top tobottom, contrary to the conventionalnotation in

mathematics,wherethedirectionoftheYaxisisupwards.

DefinitionandresolutionThenumberofpoints(pixels)constitutingtheimage,thatis,itsdimensions(thenumberofcolumns

ofthe imagemultipliedby itsnumberofrows) isknownasthedefinition.An image640pixelswide

and480pixelshighwillhaveadefinitionof640by480pixels,whichiswrittenas640x480.

Ontheotherhand,theresolution,atermoftenconfusedwiththedefinition,isdeterminedbythe

numberof

points

per

unit

of

area,

expressed

in

dots

per

inch

(DPI),

an

inch

being

equivalent

to

2.54

cm.Theresolutionthusmakesitpossibletoestablishtherelationshipbetweenthenumberofpixels

ofan imageand theactualsizeof itsrepresentationonaphysicalsupport.A resolutionof300dpi

thusmeans300columnsand300 linesofpixels inasquare inchwhichthusyields90000pixels ina

square inch.The72dpireferenceresolutiongivesusa1/72(an inchdividedby72)pixel,thatisto

say0.353mm,correspondingtoapica(AngloSaxontypographicalunit).

ColourmodelsAnimageisthusrepresentedbyatwodimensionaltableinwhicheachcellisapixel.Torepresentan

imageby

means

of

computer,

it

is

thus

enough

to

create

apixel

table

in

which

each

cell

contains

a

value.Thevaluestored inacell iscodedonacertainnumberofbitswhichdeterminethecolouror

the intensity of the pixel, This is called the coding depth (or is sometimes also called the colour

depth).Thereareseveralcodingdepthstandards:

Blackandwhitebitmap:bystoringonebitineachcell,itispossibletodefinetwocolours(blackorwhite).

Bitmapwith16

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FigureshowsthestarbustpatternsforcharactersAandM.thepatternsforparticularcharactersare

stored in the formof24bit code,eachbit representingone line segment.Thebit is set toone to

highlightthelinesegment;otherwiseitissettozero.Forexample,24bitcodeforCharacterAis0011

00000011110011100001andforcharacterMis000000110000110011110011.

Thismethodofcharactergenerationhassomedisadvantages.Theyare

1.The24bitsarerequiredtorepresentacharacter.Hencemorememoryisrequired2.Requirescodeconversionsoftwaretodisplaycharacterfromits24bitcode3.Characterqualityispoor.Itisworstforcurveshapedcharacters.C)BitmapmethodThethirdmethodforcharactergenerationisthebitmapmethod.Itisalsocalleddotmatrixbecause

inthis

method

characters

are

represented

by

an

array

of

dots

in

the

matrix

form.

It

is

atwo

dimensionalarrayhavingcolumnsandrows.An5x7arrayiscommonlyusedtorepresentcharacters

asshowninthebelowfigure.However7x9and9x13arraysarealsoused.Higherresolutiondevices

suchasinkjetprinterorlaserprintermayusecharacterarraysthatareover100x100.

CharacterAin5x7dotmatrixformatEachdotinthematrixisapixel.Thecharacterisplacedonthescreenbycopyingpixelvaluesfromthe

characterarray into someportionof the screens framebuffer.Thevalueof thepixelcontrols the

intensityofthepixel.

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3. Discussthehomogeneouscoordinatesfortranslation,rotationandscalingAns: For translation: The third 2D graphics transformation we consider is that of translating a 2D line

drawingbyanamount alongthe axisand alongthe axis.Thetranslationequationsmaybewrittenas:

(5)Wewish towrite theEquations5 as a singlematrixequation.This requires thatwe finda2by2

matrix,

Such

that

x

+

x

=

+

From this it is clear that a=1 and c=0, but there is no way to obtainthe term required in the first equation of Equations 5. Similarly we must have x + x = +

. Therefore, b=0 and d=1, and there is no way to obtain the term required in the second

equation of Equations 5.

ForRotation: Supposewewish to rotate a figure around theoriginofour 2D coordinate system.Belowfigureshowsthepoint beingrotated degrees(byconvention,counterclockwisedirection

ispositive)abouttheorigin.

RotatingaPointAbouttheOrigin

Theequations

for

changes

in

the

and

coordinates

are:

(1)

Ifweconsiderthecoordinatesofthepoint( )asaonerowtwocolumnmatrix[ ] andthematrix

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Then,giventheJdefinitionformatrixproduct,mp=:+/.*,wecanwriteEquations(1)asthematrix

equation

(2)

Wecandefinea Jmonad, rotate,whichproduces the rotationmatrix.Thismonad isapplied toan

angle, expressed in degrees. Positive angles are measured in a counterclockwise direction by

convention.

rotate=:monaddef'22$11_11*2112o.(o.y.)%180'

rotate90

01

_10

rotate360

`1_2.44921e_16

2.44921e_16 1

WecanrotatethesquareofFigure1by:

squaremprotate90

0 0

010

_1010

_10 0

0 0

producingtherectangleshowninbelowfigure.

TheSquare,Rotated90Degrees

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ForScaling:Nextweconsider theproblemof scaling (changing the sizeof)a2D linedrawing.Sizechangesarealwaysmadefromtheoriginofthecoordinatesystem.Theequationsforchangesin the

and coordinatesare:

(3)

Asbefore,weconsiderthecoordinatesofthepoint( ) asaonerowtwocolumnmatrix[ ] and

thematrix

then,wecanwriteEquations(3)asthematrixequation

(4)

WenextdefineaJmonad,scale,whichproducesthescalematrix.Thismonad isappliedtoa listof

twoscalefactorsfor and respectively.

scale=:monaddef'22$(0{y.),0,0,(1{y.)'

scale23

20

03

WecannowscalethesquareofFigure1by:

squarempscale23

0 0

20 0

2030

030

0 0

producingthesquareshowninbelowfigure.

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ScalingaSquare4. DescribethefollowingwithrespecttoProjection:

A)Parallel

Projection

Ans: Inparallelprojection,zcoordinateisdiscardedandparallel linedfromeachvertexontheobjectare

extendeduntiltheyintersecttheviewplane.Thepointofintersectionistheprojectionofthevertex.

Weconnecttheprojectedverticesbylinesegmentswhichcorrespondtoconnectionsontheoriginal

object.

Parallelprojectionofanobjecttotheviewplane

AsshownintheFigureabove,aparallelprojectionpreservesrelativeproportionsofobjectsbutdoes

notproducetherealisticviews.

B)PerspectiveProjectionAns: Theperspectiveprojection,ontheotherhand,producesrealisticviewsbutdoesnotpreserverelative

proportions. In perspective projection, the lines of projection are not parallel. Instead, they all

coverageata singlepointcalled the centerofprojectionorprojection referencepoint.Theobject

positionsaretransformedtotheviewplanealongtheseconvergedprojectionlinesandtheprojected

viewofanobjectisdeterminesbycalculatingtheintersectionoftheconvergedprojectionlineswith

theviewplane,asshownintheshownfigure

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PerspectiveprojectionofanobjecttotheviewplaneC)TypesofParallelProjections

Ans: Parallelprojectionsarebasicallycategorized intotwotypes,dependingontherelationbetweenthedirectionofprojection and thenormal to the viewplane.When thedirectionof theprojection is

normal(perpendicular)

to

the

view

plane,

we

have

an

orthographic

parallel

projection.

Otherwise,

we

haveanobliqueparallelprojection.Figureabove illustratesthetwotypesofparallelprojection.

OrthographicProjectionThe orthographic projection can display more than one face of an object. Such as orthographic

projectioniscalledaxonometricorthographicprojection.Itusesprojectionplanes(viewplanes)that

arenotnormaltoaprincipleaxis.Theyresembletheperspectiveprojectioninthisway,butdifferin

that the foreshortening is uniform rather than being related to the distance from the center of

projection.Parallelismoflinesispreservedbutanglesarenot.Themostcommonlyusedaxonometric

orthographic

projection

is

the

isometric

projection.

The isometric projection can be generated by aligning the view plane so that it intersects each

coordinateaxis inwhichtheobject isdefinedatthesamedistancefromtheorigin.Asshown inthe

shown figure, the isometricprojection isobtainedby aligning theprojection vectorwith the cube

diagonal. Itusesanusefulpropertythatallthreeprincipleaxesareequally foreshortened,allowing

measurementsalongtheaxestobemadetothesamescale(hencethename:isoforequal,metricfor

measure).

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Isometricprojectionofanobjectontoaviewingplane

ObliqueProjectionAnobliqueprojectionisobtainedbyprojectingpointsalongparallel linesthatarenotperpendicular

tothe

projection

plane.

Notice

that

the

view

plane

normal

and

the

direction

of

projection

are

not

the

same.Theobliqueprojectionsare furtherclassifiedasthecavalierandcabinetprojections.Forthecavalierprojection,thedirectionofprojectionmakesa450anglewiththeviewplane.Asaresult,the

projectionofalineperpendiculartotheviewplanehasthesamelengthasthelineitself;thatis,there

isnoforeshortening.

CavalierProjectionsoftheunitcubeWhen the direction of projection makes an angle of arctan (2)=63.40 with the view plane, the

resultingviewiscalledacabinetprojection.Forthisangle,linesperpendiculartotheviewingsurfaceare

projected

at

one

half

their

actual

length.

Cabinet

projections

appear

more

realistic

than

cavalier

projections because of this reduction in the length of perpendiculars. Figure below shows the

examplesofcabinetprojectionsforacube.

CabinetprojectionsoftheUnitCube