Introduction to computer graphics - Copy.pdf

Introduction to computer graphics

1. CSC 407 Computer
Graphics
Olufemi AKINYEDE, PhD

2. Course Description
ComputerGraphics:ApplicationofComputer
Graphics,InteractiveandPassiveGraphics;
GraphicSystems:DisplayProcessor,CathodeRay
Tube(CRT),RandomScanvsRasterScan,Color
CRTMonitors,DirectViewStorageTubes,Flat
PanelDisplayopenlink;Input-OutputDevices:
InputDevices,OutputDevices;ScanConversiona
line:ScanConversionDefinition,ScanConverting
aPoint,ScanConvertingaStraightLine,DDA
Algorithm,Bresenham'sLineAlgorithm;Scan
ConversionCircle:DefiningaCircle,Defininga
CircleusingPolynomialMethod.

3. Lecture 1

4. Introductionandoverview
•Computergraphicsisanartofdrawing
picturesoncomputerscreenswiththehelpof
programming.
•Itinvolvescomputations,creation,and
manipulationofdata.
•Inotherwords,wecansaythatcomputer
graphicsisarenderingtoolforthegeneration
andmanipulationofimages.
•Renderingorimagesynthesisistheprocessof
generatingaphotorealisticornon-
photorealisticimagefroma2Dor3Dmodel
bymeansofacomputerprogram.

5. Whycomputergraphicsisimportant
•Computergraphicsisresponsiblefor
displayingartandimagedataeffectivelyand
meaningfullytotheconsumer.
•Itisalsousedforprocessingimagedata
receivedfromthephysicalworld,suchas
photoandvideocontent
Why?
•Weneedtoproduceappealingpictures.
•Humansrespondbettertopictorial
information.
•Humanbrainrecognizesvisualpatterns.

6. Computergraphicstools…
CGtoolsincludehardwareandsoftwaretools.
•Thehardwaredevicesusedforthecomputer
graphicsare:
•InputDevices:Keyboard,Mouse,Datatablet,
Scanner,Lightpen,Touchscreen,Joystick
•OutputDevices:RasterDevices-CRT,Liquid
CrystalDisplay(LCD),Light-EmittingDiode
display(LED),Plasmascreens,Printers,
VectorDevices-Plotters,Oscilloscopes.

7. Computergraphicstools…
Softwaretools.
•Operatingsystem.graphics-basedoperating
systeminterfaceusesicons,menusandamouse
tomanageinteractionwiththesystem
•Complier.Ithelpstocompilesourcecodeand
executeit.
•Editor.Itallowsuserstoeditandmanipulate
graphicalimagesthroughavarietyofmethods.
Thesetypesofeditorprogramsaretypically
dividedintooneoftwodifferenttypes:either
rastergraphicseditorsorvectorgraphicseditors.

8. Computergraphicstools…
Softwaretools…
•Debuggers.Itisacomputerprogramusedtotest
anddebugotherprograms.
•Graphicslibrary.Itisaprogramlibrarydesigned
toaidinrenderingcomputergraphicstoa
monitor.

9. Applicationsofcomputergraphics?
Theareasinwhichcomputergraphicsisusedinclude:
•ComputerArt.Usingcomputergraphicswecan
createfineandcommercialartwhichinclude
animationpackages,paintpackages.
•ComputerAidedDrawing.Designingof
buildings,automobile,aircraftisdonewiththe
helpofcomputeraideddrawing,thishelpsin
providingminutedetailstothedrawingand
producingmoreaccurateandsharpdrawings
withbetterspecifications.
•Visualization.Itisanytechniqueforcreating
images,diagrams,oranimationstocommunicate
messages.

10. •Medicaldiagnostics.Theuseofcomputer
graphicsformedicaldiagnosishasprovidedan
extraordinaryabilitytovisualize,measureand
evaluatestructuresinanon-intrusivemanner.
•Draftingandcomputerdesign.Computer-aided
draftinganddesignorCADD,istheuseof
softwaretodrawanddesignphysical
componentsortolayoutprocesses.It'san
importantpartofmanyindustries,including
architectureandengineering,becauseit
providespreciseinstructiononhowthings
shouldbemade.
Applicationsofcomputergraphics?…

11. •ImageProcessing.Processingofexisting
imagesintorefinedonesforbetter
interpretationisoneofthemanyapplications
ofCGs.
•MachineDrawing.Computergraphicsisvery
frequentlyusedfordesigning,modifyingand
creationofvariouspartsofmachineandthe
wholemachineitself,themainreasonbehind
usingCGforthispurposeistheprecisionand
claritywegetfromsuchdrawingisultimateand
extremelydesiredforthesafemanufacturingof
machineusingthesedrawings.
Applicationsofcomputergraphics?…

12. •Education.Usingcomputergraphicsmany
educationalmodelscanbecreatedthrough
whichmoreinterestcanbegeneratedamong
thestudentsregardingthesubject.
•Entertainment.Computergraphicsfindsa
majorpartofitsutilityinthemovieindustry
andgameindustry.Usedforcreatingmotion
pictures,musicvideo,televisionshows,cartoon
animationfilms.
•GraphicalUserInterface.Theuseofpictures,
images,icons,pop-upmenus,graphicalobjects
helpsincreatingauserfriendlyenvironment.
Applicationsofcomputergraphics?…

13. Lecture 2

14. Displaydevices
Themostcommonlyuseddisplaydeviceisa
videomonitor.Theoperationofmostvideo
monitorsbasedonCRT(CathodeRayTube).
Thefollowingdisplaydevicesareused:
•RefreshCathodeRayTube
•RandomScanandRasterScan
•ColorCRTMonitors
•DirectViewStorageTubes
•FlatPanelDisplay
•LookupTable

15. CathodeRayTube
•CRTstandsforCathodeRayTube.CRTisa
technologyusedintraditionalcomputer
monitorsandtelevisions.TheimageonCRT
displayiscreatedbyfiringelectronsfromthe
backofthetubeofphosphoruslocated
towardsthefrontofthescreen.
•Oncetheelectronheatsthephosphorus,they
lightup,andtheyareprojectedonascreen.
Thecoloryouviewonthescreenisproduced
byablendofred,blueandgreenlight.

16. CathodeRayTube…
MainComponentsofCRTare:
1.ElectronGun:Electrongunconsistingofa
seriesofelements,primarilyaheatingfilament
(heater)andacathode.Theelectrongun
createsasourceofelectronswhicharefocused
intoanarrowbeamdirectedatthefaceofthe
CRT.

17. CathodeRayTube…
2.ControlElectrode/Grid:Itisusedtoturn
theelectronbeamonandoff.
3.Focusingsystem/coil:Itisusedtocreatea
clearpicturebyfocusingtheelectronsinto
anarrowbeam.

18. CathodeRayTube…
4.Deflectionyoke/coil:Itisusedtocontrolthe
directionoftheelectronbeam.Itcreatesanelectric
ormagneticfieldwhichwillbendtheelectronbeam
asitpassesthroughthearea.InaconventionalCRT,
theyokeislinkedtoasweeporscangenerator.The
deflectionyokewhichisconnectedtothesweep
generatorcreatesafluctuatingelectricormagnetic
potential.

19. CathodeRayTube…
5.Phosphorus-coatedscreen:Theinsidefront
surfaceofeveryCRTiscoatedwith
phosphors.Phosphorsglowwhenahigh-
energyelectronbeamhitsthem.
Phosphorescenceisthetermusedto
characterizethelightgivenoffbyaphosphor
afterithasbeenexposedtoanelectron
beam.

20. Thereare2kindsofredrawing
mechanisms:Random-Scanand
Raster-Scan

21. RandomScanDisplay:
•RandomScanSystemusesanelectronbeam
whichoperateslikeapenciltocreatealine
imageontheCRTscreen.Thepictureis
constructedoutofasequenceofstraight-line
segments.Eachlinesegmentisdrawnonthe
screenbydirectingthebeamtomovefromone
pointonthescreentothenext,whereitsx&y
coordinatesdefineeachpoint.Afterdrawing
thepicture.Thesystemcyclesbacktothefirst
lineanddesignallthelinesoftheimage30to
60timeeachsecond.Theprocessisshownin
fig:

22. RandomScanDisplay…
•TheprocessofRandomScanDisplayisas
shownbelow.
Random-scan
monitorsarealso
knownasvector
displaysorstroke-
writingdisplaysor
calligraphicdisplays.

23. Advantages:
•ACRThastheelectronbeamdirectedonly
tothepartsofthescreenwhereanimageis
tobedrawn.
•Producesmoothlinedrawings.
•HighResolution
Disadvantages:
•Random-Scanmonitorscannotdisplay
realisticshadesscenes.
RandomScanDisplay…

24. •ARasterScanDisplayisbasedonintensity
controlofpixelsintheformofarectangular
boxcalledRasteronthescreen.Information
ofonandoffpixelsisstoredinrefreshbuffer
orFramebuffer.
•TelevisionsinourhousearebasedonRaster
ScanMethod.Therasterscansystemcan
storeinformationofeachpixelposition,soit
issuitableforrealisticdisplayofobjects.
RasterScanprovidesarefreshrateof60to
80framespersecond.
Raster-ScanDisplay.

25. •FrameBufferisalsoknownasRasterorbit
map.InFrameBufferthepositionsarecalled
pictureelementsorpixels.Beamrefreshingis
oftwotypes.Firstishorizontalretracingand
secondisverticalretracing.Whenthebeam
startsfromthetopleftcornerandreaches
thebottomrightscale,itwillagainreturnto
thetopleftsidecalledatverticalretrace.
Thenitwillagainmovehorizontallyfromtop
tobottomcallashorizontalretracingshown
infig:
Raster-ScanDisplay….

26. Raster-ScanDisplay….
InInterlacedscanning,eachhorizontallineofthescreenis
tracedfromtoptobottom.Duetowhichfadingofdisplayof
objectmayoccur.ThisproblemcanbesolvedbyNon-
Interlacedscanning.Inthisfirstofalloddnumberedlinesare
tracedorvisitedbyanelectronbeam,theninthenextcircle,
evennumberoflinesarelocated.
Fornon-interlaceddisplayrefreshrateof30framesper
secondused.Butitgivesflickers.Forinterlaceddisplayrefresh
rateof60framespersecondisused.

27. Raster-ScanDisplay….
TypesofScanningortravellingofbeaminRaster
Scan
1.InterlacedScanning
2.Non-InterlacedScanning
•InInterlacedscanning,eachhorizontallineof
thescreenistracedfromtoptobottom.Dueto
whichfadingofdisplayofobjectmayoccur.
ThisproblemcanbesolvedbyNon-Interlaced
scanning.Inthisfirstofalloddnumberedlines
aretracedorvisitedbyanelectronbeam,then
inthenextcircle,evennumberoflinesare
located.

28. Raster-ScanDisplay….
•Fornon-interlaceddisplayrefreshrateof
30framespersecondused.Butitgives
flickers.Forinterlaceddisplayrefreshrate
of60framespersecondisused.

29. Raster-ScanDisplay….
Advantages:
•Realisticimage
•MillionDifferentcolorstobegenerated
•ShadowScenesarepossible.
Disadvantages:
•LowResolution
•Expensive

30. DifferentiatebetweenRandomandRaster
ScanDisplay:

31. Lecture 3

32. ColorCRTMonitors
TheCRTMonitordisplaybyusinga
combinationofphosphors.Thephosphorsare
differentcolors.
Therearetwopopularapproachesfor
producingcolordisplayswithaCRTare:
1.BeamPenetrationMethod
2.Shadow-MaskMethod

33. ColorCRTMonitors
1.BeamPenetrationMethod:Thishasbeenused
withrandom-scanmonitors.Inthismethod,the
CRTscreeniscoatedwithtwolayersof
phosphor,redandgreenandthedisplayedcolor
dependsonhowfartheelectronbeampenetrates
thephosphorlayers.Thismethodproducesfour
colorsonly,red,green,orangeandyellow.Abeamof
slowelectronsexcitestheouterredlayeronly;
hencescreenshowsredcoloronly.Abeamof
high-speedelectronsexcitestheinnergreenlayer.
Thusscreenshowsagreencolor.

34. ColorCRTMonitors…
BeamPenetrationMethod
Advantages
1.Inexpensive
Disadvantages
1.Onlyfourcolorsarepossible
2.Qualityofpicturesisnotasgoodaswithanother
method.

35. ColorCRTMonitors…
2.Shadow-MaskMethod:.
•ShadowMaskMethodiscommonlyusedinRaster-
ScanSystembecausetheyproduceamuchwider
rangeofcolorsthanthebeam-penetrationmethod.
•ItisusedinthemajorityofcolorTVsetsand
monitors.
•Construction:AshadowmaskCRThas3phosphor
colordotsateachpixelposition.
•Onephosphordotemits:redlight
•Anotheremits: greenlight
•Thirdemits: bluelight
•ThistypeofCRThas3electronguns,oneforeach
colordotandashadowmaskgridjustbehindthe
phosphorcoatedscreen.

36. ColorCRTMonitors…Shadow-Mask
Method
•Shadowmaskgridispiercedwithsmallround
holesinatriangularpattern.
•Figureshowsthedelta-deltashadowmask
methodcommonlyusedincolorCRTsystem.

37. ColorCRTMonitors…Shadow-MaskMethod
Advantage:
•Realisticimage
•Milliondifferentcolorstobegenerated
•Shadowscenesarepossible
Disadvantage:
•Relativelyexpensivecomparedwiththe
monochromeCRT.
•Relativelypoorresolution
•ConvergenceProblem

38. DirectViewStorageTubes(DVST).
•DVSTterminalsalsousetherandom
scanapproachtogeneratetheimageon
theCRTscreen.
•Theterm"storagetube"referstothe
abilityofthescreentoretaintheimage
whichhasbeenprojectedagainstit,thus
avoidingtheneedtorewritetheimage
constantly.

39. DirectViewStorageTubes(DVST).
Functionofguns:Two
gunsareusedinDVST
1.Primaryguns:Itis
usedtostorethe
picturepattern.
2.Floodgun or
Secondarygun:Itis
usedtomaintain
picturedisplay.

40. DirectViewStorageTubes(DVST).
Advantage:
•Norefreshingisneeded.
•HighResolution
•Costisveryless
Disadvantage:
•Itisnotpossibletoerasetheselectedpartof
apicture.
•Itisnotsuitablefordynamicgraphics
applications.
•Ifapartofpictureistomodify,thentimeis
consumed.

41. FlatPanelDisplay
•TheFlat-Paneldisplayreferstoaclassof
videodevicesthathavereducedvolume,
weightandpowerrequirementcompareto
CRT.
•Example:SmallT.V.monitor,calculator,
pocketvideogames,laptopcomputers,an
advertisementboardinelevator.

42. FlatPanelDisplay…
1.EmissiveDisplay:Theemissivedisplaysare
devicesthatconvertelectricalenergyinto
light.ExamplesarePlasmaPanel,thinfilm
electroluminescentdisplayandLED(Light
EmittingDiodes).
2.Non-EmissiveDisplay:TheNon-Emissive
displaysuseopticaleffectstoconvert
sunlightorlightfromsomeothersource
intographicspatterns.ExamplesareLCD
(LiquidCrystalDevice).

43. Emissive-FlatPanelDisplay
PlasmaPanelDisplay:Plasma-Panelsarealso
calledasGas-DischargeDisplay.Itconsistsof
anarrayofsmalllights.Lightsarefluorescent
innature.
Theessentialcomponentsoftheplasma-paneldisplay
are:
1.Cathode:Itconsistsoffinewires.Itdelivers
negativevoltagetogascells.Thevoltageis
releasedalongwiththenegativeaxis.

44. FlatPanelDisplay…
Theessentialcomponentsoftheplasma-paneldisplay
are:
2.Anode:Italsoconsistsoflinewires.It
deliverspositivevoltage.Thevoltageis
suppliedalongpositiveaxis.
3.Fluorescentcells:Itconsistsofsmall
pocketsofgasliquidswhenthevoltageis
appliedtothisliquid(neongas)itemits
light.
4.GlassPlates:Theseplatesactascapacitors.
Thevoltagewillbeapplied,thecellwillglow
continuously.

45. FlatPanelDisplay…
•Thegaswillslowwhenthereisasignificant
voltagedifferencebetweenhorizontaland
verticalwires.Thevoltageleveliskept
between90voltsto120volts.Plasmalevel
doesnotrequirerefreshing.Erasingisdoneby
reducingthevoltageto90volts.
•Eachcellofplasmahastwostates,socellis
saidtobestable.Displayablepointinplasma
panelismadebythecrossingofthe
horizontalandverticalgrid.Theresolutionof
theplasmapanelcanbeupto512*512pixels.

46. FlatPanelDisplay…
Advantage:
•HighResolution
•Largescreensizeisalsopossible.
•LessVolume
•Lessweight
•FlickerFreeDisplay
Disadvantage:
•PoorResolution
•Wiringrequirementanodeandthecathodeis
complex.
•Itsaddressingisalsocomplex.

47. Emissive-LED(LightEmittingDiode)
InanLED,amatrixofdiodesisorganizedto
formthepixelpositionsinthedisplayand
picturedefinitionisstoredinarefreshbuffer.
Dataisreadfromtherefreshbufferand
convertedtovoltagelevelsthatareappliedto
thediodestoproducethelightpatterninthe
display.

48. NonEmissive-LCD(LiquidCrystalDisplay)
LiquidCrystalDisplaysarethedevicesthat
produceapicturebypassingpolarizedlight
fromthesurroundingsorfromaninternal
lightsourcethroughaliquid-crystalmaterial
thattransmitsthelight.
LCDusestheliquid-crystalmaterialbetween
twoglassplates;eachplateistherightangle
toeachotherbetweenplatesliquidisfilled.
Oneglassplateconsistsofrowsof
conductorsarrangedinverticaldirection

49. NonEmissive-LCD(LiquidCrystalDisplay)
Anotherglassplateisconsistingofarowof
conductorsarrangedinhorizontaldirection.
Thepixelpositionisdeterminedbythe
intersectionofthevertical&horizontal
conductor.Thispositionisanactivepartof
thescreen.
Liquidcrystaldisplayistemperature
dependent.Itisbetweenzerotoseventy
degreeCelsius.Itisflatandrequiresverylittle
powertooperate.

50. NonEmissive-LCD(LiquidCrystalDisplay)
Advantage:
1.Lowpowerconsumption.
2.SmallSize
3.LowCost
Disadvantage:
1.LCDs aretemperature-
dependent(0-70°C)
2.LCDsdonotemitlight;asa
result,theimagehasverylittle
contrast.
3.LCDshavenocolorcapability.
4.Theresolutionisnotasgoodas
thatofaCRT.

51. Lecture 4

52. Scan
Conversion a
line

53. ScanConversion
•Theprocessofrepresentingcontinuous
graphicsobjectasacollectionofdiscrete
pixelsisknownasscanconversion.Each
pixelcanhaveeitheronoroffstate.
•Thecircuitryofthevideodisplaydeviceof
thecomputeriscapableofconvertingbinary
values(0,1)intoapixelonandpixeloff
information.
•0isrepresentedbypixeloff.
•1isrepresentedusingpixelon.

54. ScanConversion…
Theprocessofscanconversionrequiressomebasicrules
andguidelines:
1.Alltheobjectsdrawnonthegraphicsscreen
shouldbeofuniformbrightness.The
brightnesscontentmustbethesameforevery
pointsothattheconversionismadeeasy.
2.Theobjectsdrawnonthegraphicsscreen
shouldbefreefromanyorientationand
independentoflengthandsize.

55. ScanConversion…
•Pixels.Apixelisthesmallestunitofa
graphicsimageorreferredtoasaphysical
pointinaraster.Thisisthecomponentof
theoriginalgraphicsimagewhichprovides
evenmoreclearrepresentationthanthe
originalimage.
•Theintensityofeachpixelmayvaryasit
dependsontheimagerepresentedinthe
graphicsimageandthecolorcombinationis
representedbythethreebasiccolorsthatare
red,greenandblue.

56. ScanConversion…
•Pixelsarealsodefinedasthesmallest
addressableunitorelementofthescreen.
Eachpixelcanbeassignedanaddressas
showninfig:

57. ScanConversion…Pixel
•Differentgraphicsobjectscanbegenerated
bysettingthedifferentintensityofpixelsand
differentcolorsofpixels.Eachpixelhas
someco-ordinatevalue.Thecoordinateis
representedusingrowandcolumn.
•P(5,5)usedtorepresentapixelinthe5th
rowandthe5thcolumn.Eachpixelhassome
intensityvaluewhichisrepresentedin
memoryofcomputercalledaframebuffer.
FrameBufferisalsocalledarefreshbuffer.

58. ScanConversion…Pixel
•Thismemoryisastorageareaforstoringpixels
valuesusingwhichpicturesaredisplayed.Itis
alsocalledasdigitalmemory.
•Insidethebuffer,imageisstoredasapattern
ofbinarydigitseither0or1.Sothereisan
arrayof0or1usedtorepresentthepicture.
•Inblackandwhitemonitors,blackpixelsare
representedusing1'sandwhitepixelsare
representedusing0's.Incaseofsystems
havingonebitperpixelframebufferiscalleda
bitmap.Insystemswithmultiplebitsperpixel
itiscalledapixmap.

59. ScanConversion…
Scanconversionisdoneusingtwomethodsortechniques.
1.Analogmethods:Thisconversionisdone
forlargenumbersofdelaycellsandis
appropriateforananalogvideo.Itmaybe
performedalsousingaparticularspecialized
scanconvertervacuumtube.Inthiscase,all
polarcoordinatesi.e.(Angleanddistance)
datafromasourcesuchasaradarreceiver,
sothatitcanbedisplayedonanyrasterscan
display.

60. ScanConversion…
Scanconversionisdoneusingtwomethodsortechniques.
2.Digitalmethods:Inthisparticularmethod,
anypictureisstoredinalineorframebuffer
withn1speed(datarate)andisreadwithn2
speed,severalpictureprocessingtechniques
areapplicablewhenthepictureisstoredin
buffermemoryincludingkindsof
interpolationfromsimpletosmarthigh
ordercomparisons,motiondetectionandto
improvethepicturequalityandpreventthe
conversioncomplications.

61. ScanConversion…
Scanconversionisdoneusingtwomethodsortechniques.
2.Digitalmethods:Inthisparticularmethod,
anypictureisstoredinalineorframebuffer
withn1speed(datarate)andisreadwithn2
speed,severalpictureprocessingtechniques
areapplicablewhenthepictureisstoredin
buffermemoryincludingkindsof
interpolationfromsimpletosmarthigh
ordercomparisons,motiondetectionandto
improvethepicturequalityandpreventthe
conversioncomplications.

62. ScanConversion…
Needofscanconversionalgorithms
•Thishelpsinacceleratingtheprocessofscan
conversionandcangenerategraphicobjects
atafasterratecomparatively.Usingthese
algorithmsmemoryisalsousedefficiently
andtheproductionqualityoftheobjectson
thescreenisalsoimproved.

63. ScanConversion…
Needofscanconversionalgorithms….
•Wecanusearandomscansystemforthis
process.Itusesabeamofelectronsthatare
acceleratedthroughthepotentialdifference
andoperateslikeapencilonthescreenof
thecathoderaytubethusproducingobjects
onthescreen.Theseareconstructedthrough
aparticularsequenceoflinesdrawn.
•TheScanConvertingrateisatechniquethat
isusedinvideoprocessing.Inthistechnique,
wecanchangethehorizontalandvertical
frequenciesfordifferentpurposes.

64. ScanConversion…
Wecanapplythescanconversionalgorithmfor
variousobjectsthatare
Point,Line,Polygon(examplerectangle,
triangleandmanymore),Circle,Arc,
Sector,Anyfilledregion.

65. ScanConversion…
AdvantagesofScanConversion
1.Algorithmscangenerategraphicsobjectsat
afasterrate.
2.Usingalgorithmsmemorycanbeused
efficiently.
3.Algorithmscandevelopahigherlevelof
graphicalobjects.

66. ScanConversion…
DisadvantagesofScanConversion
1.Whiledigitalscanconversion,theanalog
videosignalgetsconvertedintodigital
signalsofdata.
2.WecanapplyscanconversionwithonlyLSI
(LargeScaleIntegration)andVLSI(Very
LargeScaleIntegration)integratedcircuits.

67. ScanConvertingaStraightLine
•Astraightlinemaybedefinedbytwo
endpoints&anequation.Infigthetwo
endpointsaredescribedby(x
1,y
1)and(x
2,y
2).
Theequationofthelineisusedtodetermine
thex,ycoordinatesofallthepointsthatlie
betweenthesetwoendpoints.

68. ScanConvertingaStraightLine
•Usingtheequationofastraightline,y=mx
+b
•wherem=ScanConvertingaStraightLine&
•b=theyinterrupt,wecanfindvaluesofy
byincrementingxfromx=x
1,tox=x
2.
•Byscan-convertingthesecalculatedx,y
values,werepresentthelineasasequenceof
pixels.

69. Lecture 5

70. ScanConvertingaStraightLine
AlgorithmforlineDrawing:
1.DirectMethod
2.Bresenham'sAlgorithm
3.DDA(DigitalDifferentialAnalyzer)

71. ScanConvertingaStraightLine
1.DirectMethod.Itisthesimplestmethodof
this.Inthisalgorithm,wehavetwoendpoints.
Wefindtheslopeofthelinebyusingboth
thepointsandweputtheslopeintheline
equationY=MX+C.Thenwefindthe
valueofCbyputtingXandYisequalto0.
Afterthis,wehavearelationbetweenXand
Y.NowweincreasethevalueofXandfind
thecorrespondingvalueofY.Thesevalues
willbetheintermediatepointsoftheline.
Afterfindingtheintermediatepointswe'll
plotthosepointsanddrawtheline.

72. ScanConvertingaStraightLine
Algorithmfordrawinglineusingequation:
Step1:StartAlgorithm
Step2:Declarevariablesx1,x2,y1,y2,dx,dy,m,b,
Step3:Entervaluesofx1,x2,y1,y2.
The(x1,y1)areco-ordinatesofastartingpointoftheline.
The(x2,y2)areco-ordinatesofaendingpointoftheline.
Step4:Calculatedx=x2-x1
Step5:Calculatedy=y2-y1
Step6:Calculatem=
Step7:Calculateb=y1-m*x1
Step8:Set(x,y)equaltostartingpoint,i.e.,lowestpointandxend
equaltolargestvalueofx.
Step9: Check whether the complete line has been drawn if x=xend, stop
Step10: Plot a point at current (x, y) coordinates
Step11: Increment value of x, i.e., x = x+1
Step12: Compute next value of y from equation y = mx + b
Step13: Go to Step9.

73. Scan Converting a
Straight Line …
Program to draw a line using LineSlopeMethod
1
#include<graphics.h>
#include<stdlib.h>
#include<math.h>
#include<stdio.h>
#include<conio.h>
#include<iostream.h>
classbresen
{
floatx,y,x1,y1,x2,y2,dx,dy,m,c,xend;
public:
voidget();
voidcal();
};
voidmain()
{
bresenb;
b.get();
b.cal();
getch();
}
Voidbresen::get() 2
{
print("Enterstart&endpoints");
print("enterx1,y1,x2,y2");
scanf("%f%f%f%f",sx1,sx2,sx3,sx4)
}
voidbresen::cal()
{
intgdriver=DETECT,gmode,errorcode;
initgraph(&gdriver,&gmode,"");
errorcode=graphresult();
if(errorcode!=grOK)

74. ScanConvertingaStraightLine
{
printf("Graphicserror:%s\n",grapherrormsg(errorcode);
3
printf("Pressanykeytohalt:");
getch();
exit(1);
}
dx=x2-x1;
dy=y2-2y1;
m=dy/dx;
c=y1-(m*x1);
if(dx<0)
{
x=x2;
y=y2;
xend=x1;
}
else 4
{
x=x1;
y=y1;
xend=x2;
}
while(x<=xend)
{
putpixel(x,y,RED);
y++;
y=(x*x)+c;
}
}

75. 2.Bresenham'sAlgorithm.Thismethodofline
drawingisveryeffectivebecauseitincludes
integeraddition,subtraction,and
multiplication.Thecalculationisveryfastin
thismethodthat'swhythelineisdrawnvery
quicklyinthis.We'llneedthetwoendpointsin
thisandthenwehavetofindthedecision
parameters.Letassumethat(x
1,y
1)and
(x
2,y
2)arethetwopoints.So,dx=x
2-x
1and
dy=y
2-y
1.
•Theformulaforthedecisionparameteris:di=
2dy-dx
ScanConvertingaStraightLine

76. ScanConvertingaStraightLine..
Bresenham'sAlgorithm
•Thisisthewaywe
can findthe
intermediatepoint
andafterfinding
thesepointswecan
plotallthepointson
thescreenusing
programming.

77. ... Bresenham's
Algorithm

78. ... Bresenham's
Algorithm

79. ... Bresenham's
Algorithm

80. ... Bresenham's
Algorithm
Similarly,Step-03isexecuteduntiltheendpointis
reachedornumberofiterationsequalsto4times.
(Numberofiterations=ΔX–1=5–1=4)

81. ... Bresenham's
Algorithm
X
k+1
Y
k+1

82. ... Bresenham's
Algorithm

83. ... Bresenham's
Algorithm

84. ... Bresenham's
Algorithm
X
k+1
Y
k+1

85. Bresenham'sAlgorithm
Advantages
•Itiseasytoimplement.
•Itisfastandincremental.
•ItexecutesfastbutlessfasterthanDDAAlgorithm.
•Thepointsgeneratedbythisalgorithmaremore
accuratethanDDAAlgorithm.
•Itusesfixedpointsonly.
Disadvantages
•Thoughitimprovestheaccuracyofgeneratedpoints
butstilltheresultedlineisnotsmooth.
•Thisalgorithmisforthebasiclinedrawing.
•Itcannothandlediminishingjaggies

86. Lecture 6

87. DDAAlgorithm
DDAstandsforDigitalDifferentialAnalyzer.
Itisanincrementalmethodofscan
conversionofline.Inthismethodcalculation
isperformedateachstepbutbyusingresults
ofprevioussteps.

88. DDA Algorithm
….

89. DDAAlgorithm….

90. DDAAlgorithm….

91. DDAAlgorithm….
Example:Ifalineisdrawnfrom(2,3)
to(6,15)withuseofDDA.Howmany
pointswillneededtogeneratesuchline?

92. DDAAlgorithm….
Example:Calculatethepointsbetween
thestartingpoint(5,6)andending
point(8,12).

93. DDAAlgorithm….
X
p+1
Y
p+1

94. DDAAlgorithm….
Example:Calculatethepointsbetween
thestartingpoint(5,6)andending
point(13,10)

95. DDAAlgorithm….
Example:Calculatethepoints
betweenthestartingpoint(5,6)
andendingpoint(13,10)
X
p+1
Y
p+1

96. DDAAlgorithm….
Example:Calculatethepoints
betweenthestartingpoint(1,7)
andendingpoint(11,17).

97. DDAAlgorithm….
Example:Calculatethepoints
betweenthestartingpoint(1,7)
andendingpoint(11,17).
X
p+1
Y
p+1

98. DDAAlgorithm….
The advantagesof DDA Algorithm are-
•It is a simple algorithm.
•It is easy to implement.
•It avoids using the multiplication operation which is
costly in terms of time complexity.
ThedisadvantagesofDDAAlgorithmare-
•Thereisanextraoverheadofusingroundoff()
function.
•Usingroundoff()functionincreasestime
complexityofthealgorithm.
•Resultedlinesarenotsmoothbecauseofround
off()function.
•Thepointsgeneratedbythisalgorithmarenot
accurate.

99. Next time:
begins examination