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UNIT I

INTRODUCTION TO GRAPHICS

DEFINITION

Graphics are visual presentations on some surface such as wall, canvas,

computer screen or paper.

Eg: Photographs, rawings, line art, graphs, iagrams, s!m"ols, maps, geometric esigns

# engineering rawings.

Graphics can "e functional, artistic, realistic or imaginar!.

$I%TO&'

The earliest graphics (nown to anthropologists stu!ing of prehistoric perios are cave

painting # mar(ings on "oulers, "one, antlers uring the upper Paleolithic perio from

)*,***+*,*** -.

&ecors from Eg!pt preate graphics # Pap!rus was use "! the Eg!ptians as a materialfor planning the "uiling of P!ramis.

Gree(s pla!e a ma/or role in geometr!. Gree(s use graphics to represent mathematical

memories.

Eg: ircle Theorem, P!thagorean Theorem.

In 01*, one first computer 2 riven ispla! was attache to 3IT4s 5hirlwin I

computer generate simple pictures.

In 067, Ivan %utherlan invente %(etch pa , an innovative program that influence

alternative forms of interaction with computers.

In the mi 06*4s large computer graphics research pro/ects were "egun at 3IT, General

3otors, -ell 8a"s # 8oc(hee 9ircraft.

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In 06, &a! Tracing was invente "! 9ppel.

During the late 0;*4s personal computers were capa"le of rawing "asic # compleGraphical =ser

Interface?.

@D graphics "ecame more popular in the 00*4s in Gaming, 3ultimeia an 9nimation.

i? Graphics is one of the fire (e! elements of 3ultimeia Technolog!.

ii? Aua(e 2 one of the first full! @D game.

iii? 001, the first full! animate film B TO' %TO&' B was release in inemas

worlwie.

=%E% OF G&9P$I%

Graphics are often use to point reaers an viewers to particular information.

The practical areas where graphics are applie are given "elow :

i? -usiness

ii? 9vertising

iii? Political News

iv? Eucation

v? Film # 9nimation

vi? Graphics Eucation

PICE8

DEFINITION :

9 pior?

9 pior? information element is not reall! a ot, nor a suare.

Piots per inch? >or? ppi >pi

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$I%TO&'

The term Pi

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Eg: 716 colours 7, "pp

76 611@6 colours 6 "pp > highcolour or thousans?

77) 6,;;;,76 colours 7) "pp > truecolour or millions ?

7) ) "pp > for all practical purposes # in flat"e scanners ?

716 colours

%tore in the computers vieo memor!.

E

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The phosphor then emit a small spot of light at each position contacte "! the electron

"eam.

-ecause the light emitte "! the phosphor faes ver! rapil! some metho is neee for

maintaining the screen picture.

One wa! is to reraw the picture repeatel! "! uic(l! irecting the electron "eam "ac(

over the same points.

This t!pe of ispla! is calle a refresh &T.

5O&LING

The primar! component of an electron gun are heate metal cathoe an a control gri.

$eat is supplie to the cathoe "! irecting a current through a coil of wire calle the

filament insie the c!linrical cathoe structure.

This causes electrons to "e "oile off

In the vaccum insie the &T envelope the free negativel! charge electrons are then

accelerate towar the phosphor coating "! a high positive voltage.

The accelerating voltage can "e generate with a Mvel! charge metal coating on the

insie of the &T near the phosphor screen.

E8ET&O%T9TI DEF8ETION

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Deflection of the electron "eam can "e controlle either with electric fiels or with

magnetic fiels.

athoe ra! tu"es constructe with magnetic eflection coils mounte on the outsie of

the &T envelope.

Two pairs of coils are use.

One pair is mounte on the top # "ottom of the nec(.

Other pair is mounte on the opposite sies of the nec(.

The magnetic fiels prouce "! each pair is of coils results in transverse eflection force

that is perpenicular "oth to the irection of the magnetic fiel # to the irection of travel

of the electron "eam.

&9%TE& %9N D%IP89'%

The most common t!pe of graphics monitor emplo!ing a &T is the &aster scan ispla!.

5O&LING P&INIP8E

In a raster scan s!stem the electron "eam is swept across the screen one row at a time

from top to "ottom.

5hen the electron "eam moves across each row the "eam intensit! is turne on an off

to create a pattern of illuminate spots.

Picture efinition is store in memor! area calle &efresh "uffer >or? Frame "uffer.

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The frame "uffer hols the set of intensit! values for all the screen points.

The store intensit! values are then retrieve from the refresh "uffer an painte on the

screen one row at a time.

One row is also referre to as %can 8ine.

Each screen point is referre to as Pior? Pel.

-IT PE& PICE8

Intensit! range for pior? off.

Onl! one "it per pi

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&EF&E%$ING

&efreshing of &aster scan ispla!s is carrie out as the rate of 6* to * frames per secon.

&efresh rates are escri"e in units of c!cles per secon or $ert.

c!cle 2 frame

9t the en of each scan line the electron "eam returns to the left sie of the screen to

"egin ispla!ing the ne

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9 refresh "uffer is use to store picture efinition. The line rawing commans are store

in the refresh "uffer.

To ispla! a specifie picture the s!stem processes the set of rawing commans.

&anom scan ispla!s are esigne to raw all the components lines of a picture @* to 6*

times each secon.

&anom scan s!stem are esigne for line rawing applications an cannot ispla!

realistic shae scenes.

&anom scan ispla!s prouce smooth line rawings "ecause the &T "eam irectl!

follows the line path.

O8O& &T 3ONITO&%

9 &T monitor ispla!s color pictures "! using a com"ination of phosphors that emit

ifferent colore light.

Two "asic techniues are use for proucing color ispla! with a &T namel!

i? -eam penetration metho.

ii? %haow mas( metho.

-E93 PENET&9TION 3ET$OD

This metho is use with ranom scan monitors .

$ere two la!ers of phosphor namel! re # green are coate onto the insie of the &T

screen.

The ispla!e color epens on how far the electron "eam penetrates into the phosphor

la!ers.

9 slow "eam of electrons penetrates through the screen # ecom"inations of re an green lights?

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The spee of the electrons # hence the screen color at an! point is

controlle "! the "eam acceleration voltage.

%$9DO5 39%L 3ET$OD%

This metho is commonl! use in &aster scan s!stems.

9 shaow mas( &T has three phosphor color ots at each pi

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9nother configuration for the electron guns is an in+line arrangement where the @

electron "eams are aligne to a single scan line.

-! var!ing the intensit! of levels of the three electron "eams various color variations are

o"taine.

The color got epens on the amount of re, green an "lue phosphors.

9 white area inicates that all the three electron "eams are with the same

intensit!.

O8O& O3-IN9TION%

'ellow 2 green # re "eams

3agenta + "lue # re "eams

!an 2 "lue # green "eams

3ore sophisticate s!stems can set intermeiate intensit! levels for the electron "eams.

DI&ET KIE5 %TO&9GE T=-E%

9n alternative metho for maintaining a screen image is to store the picture information

insie the &T instea of refreshing the screen.

Two electron gns are use in DK%T

DK%T stores the picture information as a change istri"ution /ust "ehin the phosphor

coate screen.

The primar! electron gun stores the picture pattern.

The floo gun maintains the picture ispla!.

9DK9NT9GE%

i? No refreshing is neee.

ii? Ker! comple< pictures can "e ispla!e at ver! high resolutions without

flic(er.

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DI%9DK9NT9GE%

i? %electe parts of a picture cannot "e erase.

ii? The! orinaril! o not ispla! color.

F89T P9NE8 DI%P89'

INT&OD=TION

The term refers to a class of vieo evices that have reuce volume, weight # power

reuirements.

9 significant feature of that panel ispla!s is that the! are thinner than &T4s.

Flat panel ispla!s are availa"le as poc(et notepas.

=ses of flat panel ispla!s are

TK monitors

alculators

Poc(et vieo games

8aptop computers

9rmrest viewing of movies on airplanes.

9vertisement "oar in elevators

9TEGO&IE%

There are two ma/or categories of flat panel ispla!s

i? Emissive ispla!s

ii? Non emissive ispla!s

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i? Emissive ispla!s

onvert electrical energ! into light.

E

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5hen a high voltage is applie to a pair of crossing electroes the phosphor "ecomes a

conuctor in the area of intersection of the electroes.

The manganese atoms a"sor" the electrical energ! as a spot of light.

Electroluminescent ispla!s reuire more power than plasma panels.

Goo color # gra! scale ispla!s are har to achieve.

8IG$T E3ITTING DIODE > 8ED ?

9 matri< of ioes is arrange to form the pi

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Polarie light passing through the material is twiste so that it will pass through the

opposite polarier.

The light is then reflecte "ac( to the viewer.

This t!pe of flat panel evice is referre to as a passive matri< 8D.

9nother metho for constructing 8D4s is to place te transistor at each pi

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The two views of a scene are generate from a viewing irection corresponing to each

e!e > left # right ?.

%imultaneous viewing of each view merges into a single image.

The screen is viewe with glasses > speciall! esigne ?

%tereoscopic viewing is also a component in virtual+realit! s!stems where users can step

into a scene # interact with the environment.

9 heaset containing an optical s!stem to generate the stereoscopic views is commonl!

use in con/unction with interactive ip evices to locate # manipulate o"/ects in the

scene.

9 sensing s!stem in the heaset (eeps trac( of the viewers position so that the front #

"ac( of o"/ects can "e seen as the viewer wal(s through.

INP=T DEKIE%

Karious evices are availa"le for ata input on graphics wor(stations.

3ost s!stems have a (e!"oar # one or more aitional evices speciall! esigne for

interactive input.

The various input evices that are iscusse in this section are

i? (e!"oars

ii? mouse

iii? trac("all # space"all

iv? /o!stic(s

v? ata glove

vi? igitiers

vii? image scanners

viii? touch panels

i

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The (e!"oar is an efficient evice for inputting such nongraphic ata as picture la"els

associate with a graphic ispla!.

9lphanumeric (e!"oar

Le!"oars are provie with features to facilitate entr! of screen co+orinates , menu

selections or graphics functions.

The common features on general purpose (e!"oars are

i? cursor+control (e!s

ii? function (e!s

i? cursor control (e!s:

can "e use to select ispla!e o"/ects or co+orinate

positions "! positioning the screen cursor.

ii? functional (e!s:

allow users to enter freuentl! use operations in a single

(e!stro(e. 9itionall! a numeric (e!pa is often inclue

on the (e!"oar for fast entr! of numeric ata.

3O=%E

9 mouse is a small han hel evice use to position the screen cursor.5heels or rollers on the "ottom of the mouse can "e use to recor the amount #

irection of movement.

9nother metho for etecting mouse movements is with an optical sensor.

One,two or three "uttons are usuall! inclue on the top of the mouse for signaling the

e

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5ith the +mouse , one can pic( up an o"/ect , rotate it an move it in an! irection or the

navigation of one4s viewing position # orination through a @D scene.

9pplication of +mouse are

virtual realit!

9D

9nimation

T&9L-988 9ND %P9E-988

T&9L-988

Trac("all is a "all that can "e rotate with thr fingers or palm of the han to prouce

screen cursor movements.

Potentiometers attache to the "all measure the amount # irection of rotation.

The! are often mounte on (e!"oar or +mouse.

%P9E-988

9 space"all provies sie egrees of freeom.

9 space"all oes not actuall! move. %train gauges measure the amount of pressure

applie to the space"all.

9pplications where space"alls are use are

i? @D positioning

ii? Kirtual realit! s!stems

iii? 3oeling

iv? 9nimationv? 9D

O'%TIL%

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9 /o!stic( consists of a small vertical lever calle the stic(

The stic( is mounte on a "ase which steers the screen aroun.

There are 7 t!pes of /o!stic(

i? mova"le stic( /o!stic(

ii? non+mova"le stic( /o!stic(

3OK9-8E %TIL O'%TIL

The stic( is actuall! place in the center position.

%creen cursor movement is achieve "! moving the stic( in an! irection from the center.

Potentiometers also mounte at the "ase of the /o!stic( # the! measure the amount of

movement.

Potentiometers also return the stic( to the center position when release.

In another t!pe of mova"le /o!stic( the stic( is use to activate switches that cause the

screen cursor to move at a constant rate in the selecte irection.

NON 3OK9-8E %TIL O'%TI(

These /o!stic(s are also calle isometric /o!stic(s.

The! have a non mova"le stic( # pressure applie on the /o!stic( is measure "! strain

gauges # converte to the movement of the cursor in the specifie irection.

D9T9 G8OKE

Data glove can "e use to grasp a virtual o"/ect

The glove has a series of sensors that etect han # finger movements.

Electromagnetic coupling "etween transmitting antennas # receiving antennas is use ot

provie information a"out the position # orientation of the screen.

Input from the glove can "e use to position or manipulate o"/ects in a virtual scene.

9 7D pro/ection of the scene can "e viewe using vieo monitor.

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9 @D pro/ection can "e viewe with a heaset.

DIGITIE&%

9 igitier is a common evice for rawing , painting or interactivel! selecting co+

orinating positions on an o"/ect.

Digitiers are use to input co+orinate values in either a 7D or @D space.

9 igitier is use to scan over a rawing or o"/ect # to input a set of iscrete co+

orinate positions.

Graphics ta"let is an e

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OPTI98 TO=$ P9NE8%

These panels emplo! a line of infrare light emitting ioes > 8ED4s? along one vertical

ege # along one horiontal ege of the frame.

The opposite vertical ege # horiontal ege contain light etectors.

5hen the panel is touche these light etectors recor which "eams are interrupte.

The 7 crose "eams that are interrupte ientif! the horiontal # vertical co+ornates of

the screen position selecte.

Positions can "e selecte with an accurac! of a"out Q inch.

The 8ED4s operate at infrare freuencies so that the light is not visi"le to a user.

E8ET&I98 TO=$ P9NE8

These plates are constructe with 7 transparent plates separate "! a small istance.

One plate is coate with a conucting material # the other with resistive material.

Touching the outer plate forces it into contact with the inner plate.

This contact creates a voltage rop across the resistive plate that is converte into co+

orinate values of the selecte screen position.

9O=%TI98 TO=$ P9NE8

$ere high freuenc! soun waves are generate "! the horiontal # vertical irections

across a glass plate.

Touching the screen causes part of each wave to "e reflecte from the fingers to the

emitters.

The screen position is calculate from a measurement of the time interval "etween the

transmission of each wave # its reflection to the emitter.

8IG$T PEN

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8ight pens are pencil+shape evices use to select screen positions "! etecting the light

coming fro points on the &T screen.

8ight pens are sensitive to short "urst of light emitte from the phosphor coating of the

&T.

Other light sources are not usuall! etecte "! a light pen.

9n activate light pen pointe at a spot on the screen as the electron "eam lights up that

spot generates an electric pulse that causes the co+orinate position of the electron "eam

to "e recore.

The recore light pen co+orinates can "e use to position an o"/ect or to select a

processing option.

DI%9DK9NT9GE%

i? %creen image o"scure "! han # light pen

ii? Prolonge use causes arm fatigue

iii? 8ight pen reuire special implementation for some applications.

iv? %ometimes light pens give false reaings ue to "ac(groun lighting in room.

KOIE %'%TE3%

%peech recogniers are use in some graphics wor(stations as input evices to accept

voice commans.

The voice s!stem input can "e use to initiate graphics operations or to enter ata.

These s!stems operate "! matching an input against a preefine ictionar! of wors an

pharses.

DITION9&'

9 ictionar! is set up for a particular operator

The operator spea( the comman wors to "e use into the s!stem

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Each wor is spo(en several times # the s!stem anal!es the wor # esta"lishes a

freuenc! pattern for that wor in the ictionar!.

8ater when a voice comman is given the s!stem searches the ictionar! for a freuenc!

pattern match

Koice input is t!picall! spo(en into a microphone mounte on a heaset.

The microphone is esigne to minimie input of other "ac(groun souns.

$9&D+OP' DEKIE%

$ar cop! output for images can "e o"taine in several formats

=sers can put pictures on paper "! irecting graphics output to a printer or plotter.

The ualit! of pictures o"taine from a evice epens on the ot sie # ot per inch or

lines per inch.

%mooth characters can "e prouce in printe te

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Dot matri< printers have a ot matri< print hea containing a rectangular arra! of

protruing pins

The no. of pins epens on the ualit! of the printer

Iniviual characters or graphic patterns are o"taine "! retracting certain pins so that the

remaining pins form the pattern to "e printe

NON I3P9T DEKIE%

Non impact plotters an printers use laser techniues , in( /et spra!s , pi?

INL ET P&INTE&

These printers prouce output "! suirting in( in horiontal rows across a roll of paper

wrappe on a rum.

The electricall! charge in( stream is eflecte "! an electric fiel to prouce ot matriP$IG%?

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P$IG% is an e

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UNIT II

DISPLAY PRIMITIVES AND ATTRIBUTES

LINE DRAWING ALGORITHM

8ine rawing is our first aventure into the area of scan conversion. The nee for scan

conversion, or rasteriation, techniues is a irect result of scanning nature of raster

ispla!s

The goal of an! line rawing algorithm is to construct the "est possi"le appro

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The common conventions that pi! U !*? >

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In the following pseuocoe sample plot(x,y)plots a point an abs returns a"solute

value:

function line>

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%o, wor(ing in the first positive octant of the plane, line rawing "ecomes a matter of

eciing "etween two possi"ilities at each step.

5e can raw a iagram of the situation which the plotting program fins itself in having

plotte >

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The new value of error can aopt one of two possi"le values, epening on what new

point is plotte. If >

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This gives an integer+onl! test for eciing which point to plot.

The upate rules for the error on each step ma! also "e cast into form. onsier the

floating+point versions of the upate rules:

3ultipl!ing through "! !iels:

which is in form.

=sing this new YYerrorVV value, , with the new test an upate euations gives

-resenhamVs integer+onl! line rawing algorithm:

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Integer onl! + hence efficient >fast?.

3ultiplication "! 7 can "e implemente "! left+shift.

This version limite to slopes in the first octant, .

98GO&IT$3 FO& GENE&9TING I&8E

3an! incremental methos e

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5e can set eight s!mmetric pipi?. 5e can use

s!mmetr! to improve the eu? an cos>u?.

are generating a circle from the origin with raius *. This woul impl! the following

ta"le of values:

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u Crcos>u? 'rsin>u?

* * *

. 0.01 .000

.7 0. .00

.@ 0.11 7.06

.) 0.7 @.0

.1 .; ).;0

.6 .71 1.61

.; ;.61 6.))

. 6.0; ;.; >Note: pi) .;1)?

....

.1;* * * >Note: pi7 .1;*?

7? &otation 3etho + this metho consists of using the point >u?+'sin>u?

'rot Csin>u? M 'cos>u?

To use the rotation metho, we assign >C*,'*? eual to >r,*?. 5e can then use the

following euations to generate successive points:

CnMCncos>u?+'nsin>u?

'nM Cnsin>u? M 'ncos>u?

E88IP%E GENE&9TING 98GO&IT$3

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7a is the length of the ma/or a7+7!pM7?

In region 7, choices are % an %E

Initial conition: init "7>>!+?7+"7?

For a move to %, new olMDeltas with Deltas a7>+7!pM@?

For a move to %E, new olMDelta%E with

Delta%E "7>7+7!pM@?

%top in region 7 when the ! value is ero.

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9&E9 FI88ED 9TT&I-=TE%

It is an area fille with the foregroun color, "ut it epens on the current interior st!le.

The %O8ID st!le epens onl! on the foregroun color. The $9T$ an %TIPP8E st!le

epen on the foregroun color, "ac(groun color an on the "ac( opacit! attri"ute. The

hatch lines rawn with this st!le o not epen on the other line attri"utes. The

P9TTE&N st!le epens onl! on glo"al canvas attri"utes.

The fille area inclues the line at the ege of the area. %o if !ou raw a fille rectangle,

sector or pol!gon on top of a non fille one using the same coorinates, no st!le an

pi

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Note that when a Filling 9ttri"ute is moifie, the active filling st!le is now that of the

moifie attri"ute >hatch, stipple or pattern?. Notice that this is not true for the clipping

area. 5hen the clipping area is moifie, the clipping is onl! affecte if it is active.

Fills the arc of an ellipse aligne with the a

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8ine color is set using the routine plcol*.The argument is ignore for evices which can

onl! plot in one color, although some terminals support line erasure "! plotting in color

ero.

8ine with is set usingplwi. This option is not supporte "! all evices.

8ine st!le is set using the routine plst!lorpllst!. 9 "ro(en line is specifie in terms of a

repeate pattern consisting of mar(s >pen own? an spaces >pen up?. The arguments to

this routine are the num"er of elements in the line, followe "! two pointers to integer

arra!s specif!ing the mar( an space lengths in micrometers. Thus a line consisting of

long an short ashes of lengths ) mm an 7 mm, separate "! spaces of length .1 mm

is specifie "!:

mar(]*^ )***J

mar(]^ 7***J

space]*^ 1**J

space]^ 1**J

plst!l>7, mar(, space?J

To return to a continuous line, /ust call plst!lwith first argument set to ero. 'ou can use

pllst!to choose "etween ifferent preefine st!les.

8ines an line segments

In mathematics, lines are infinite 2 that is, the! have no ens. It is not often, in the real

worl, that we eal with such lines. 5hen people use the wor VlineV to tal( a"out the

lines of a tennis court, for e

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UNIT III

TWO DIMENSIONAL TRANS%ORMATIONS AND VIEWING

TRANS%ORMATION TYPES

9 two imensional transformation is an! operation on a point in space >

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This is accomplishe "! aing a translation factor T< to the C coorinate an T! to the

' coorinate of each verte

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If an o"/ect that is scale is not positione at the origin, the scale figure will also "e

translate. This change in position can "e compensate for "! scaling a"out an ar"itrar!

point, usuall! a corner or the center of the o"/ect.

Rotation

&otation is a transformation that causes a point p to "e move relative to a central point,

without changing the istance of p from that point. This transformation is accomplishe

"! appl!ing the rotation euation to each verte< of the o"/ect. 9 rotation is specifie "!

proviing an angle, -, inicating how man! egrees of rotation are esire. This angle

ma! "e either positive or negative. 9 positive angle inicates a counter+cloc(wise

rotation a"out the origin.

The transformation euations for rotation are:

CVCcos-+'sin-

'V C sin- M ' cos-

These euations can "e easil! erive from the figure a"ove, in which a rotation "! -

transforms P>C,'? into P7>CV,'V?. -ecause the rotation is a"out the origin, the istance

from the origin to P an P7 la"ele r in the figure, are eual.

-! simple trigonometr!, we fin that

Crcos9

' r sin9

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an

sin>9M-?'Vr

cos>9 M -? CVr

%u"stitution using the ou"le angle formula

sin>9M-?sin9cos-Mcos9sin-

cos>9M-? cos9 cos- + sin9 sin-

5e see that

CVr>Cr?cos-+>'r?sin-

'Vr >'r? cos- M >Cr? sin-

an then

CVCcos-+'sin-

'V ' cos- M C sin-

Thus,

CVCcos-+'sin-

'V C sin- M ' cos-

39T&IC &EP&E%ENT9TION

It is more reasona"le to fin a consistent wa! to hanle all three transformations. This can

"e one "! eC,',5?, instea of >C,'?. Triples of coorinates t!picall!

represent points in @+space, "ut here it is use to represent points in 7+space. =suall! 5 is

fi

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Translation

The matri< for translation is:

an the euations for the translation transformation "ecome

Scale

The matri< for scaling is:

an the euations for the scaling transformation relative to the origin "ecome

Rotation

The matri< for rotation is:

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an the euations for the rotation transformation a"out the origin "ecome

CONCATENATION

We use matrix composition to produce any series of transformations that are desired.

The transformation seuence is then defined !y multiplying the transformation

matrices together. The order of the multiplication seuence is important.Remem!er matrix multiplication is not commutati"e.

Rotation or Scaling a!out an ar!itrary point

The scaling an rotation transformations are efine a"out the origin. The user might

wish to rotate or scale a"out an ar"itrar! point. This can "e one using a com"ination of

transformations we alrea! (now a"out.

To scale a"out P >+

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To rotate a"out P >+_?

@.Translate the o"/ect "! >T

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9 shear parallel to the < a

is not ifficult to see that "etween a point >

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Therefore, if a line has an euation 9< M -! M *, after plugging the formulae for 9cosa + -sina?9sina M -cosa?!V M *

Translations an rotations can "e com"ine into a single euation li(e the following:

The a"ove means that rotates the point >

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8et & "e a transformation matri< sening

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5ith this set of euations, letting a "e 0* egree rotates >,*,*? to >*,,*? an >*,,*? to >+

,*,*?. Therefore, the < : ! : : w?. Theplane at infinit! is usuall! ientifie with the set of points

with w *. 9wa! from this plane we can use >

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If we tr! to intersect the two planes efine "! euations < w an < 7w then we

clearl! will erive first w * an then < *. That tells us that the intersection is

containe in the plane at infinit!, an consists of all points with coorinates >* : ! : : *?.

It is a line, an in fact the line /oining >* : : * : *? an >* : * : : *?. The line is given "!

the euation

>*:!::*? > U `?>*::*:*? M `>*:*::*?

where is a scaling factor. The scaling factor can "e a/uste to normalie the

coorinates >* : ! : : *?, there"! eliminating one of the two egrees of freeom. The

result is a set of points with onl! one egree of freeom, as is e

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'wma< + 'wmin 'vma< + 'vmin

5e can rewrite a"ove as

Cv ]>Cvma< + Cvmin?>Cwma< + Cwmin?^ >Cw + Cwmin? M Cvmin %< >Cw + Cwmin? M Cvmin %< Cw M 'vma< + 'vmin? >'wma< + 'wmin?^ >'w + 'wmin? M 'vmin

%! >'w + 'wmin? M 'vmin %! 'w M !

Note that %

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Isotropic an Non+Isotroptic Transformations

8et the real worl co+orinate "e represente "! >C, '? an its euivalent co+orinate in

ispla! space "e >

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It is esira"le to restrict the effect of graphics primitives to a su"region of the canvas, to

protect other portions of the canvas. 9ll primitives are clippe to the "ounaries of this

clipping rectangleJ that is, primitives l!ing outsie the clip rectangle are not rawn.

The efault clipping rectangle is the full canvas > the screen ?, an it is o"vious that we

cannot see an! graphics primitives outsie the screen.

9 simple eC,'? to "e insie the clipping rectangle:

Cmin [ C [ Cma%G?

%5EEP &EP&E%NT9TION

%pecif!ing a 7D shape an a sweep that moves the shape through a region of space.

5e perform a sweep "! moving the shape along a path. 9t intervals along this path, we

replicate the shape an raw a set of connectiong line in the irection of the sweep to

o"tain the wireframe reprensentation.

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E

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KI%=98I9TION

The use of graphical methos to ai in anal!sis, often of atasets so large or complean pieces of o"/ects? that are not visi"le

in the image

Ne

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* * 2*

* * *

P&OETION%

9fter the worl coorinate escriptions of the o"/ects in a scene are converte to viewing

coorinates , we can pro/ect the @D o"/ect onto the 7D view plane.

There are 7 t!pes of pro/ection methos

. parallel pro/ection metho

7. perspective pro/ection metho

. P9&988E8 P&OETION 3ET$OD

Parallel pro/ections catagorie one of two ma/or su"classes of planar geometric

pro/ections. Pro/ections within this su"class have two characteristics in common. The

first characteristic concerns the placement of the center of pro/ection >P&P? which

represents the camera or viewing position. In a parallel pro/ection, the camera is locate

at an infinite istance from the viewplane . -! placing the camera at an infinite istance

from the viewplane, pro/ectors to the viewplane "ecome parallel >the secon

characteristic of a parallel pro/ection? in result forming a parallelepipe view volume.

Onl! o"/ects within the view volume are pro/ecte to the viewplane. Figure shows the

pro/ection of line 9- to the viewplane. In this case, the measurement of line 9- is

maintaine in the pro/ecte line 9V-V. 5hile the measurements of an o"/ect are not

preserve in all parallel pro/ections, the parallel nature of pro/ectors maintains the

proportion of an o"/ect along a ma/or a

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There are two ifferent t!pes of parallel pro/ections:If the irection of pro/ection is

perpenicular to the pro/ection plane then it is an orthographic pro/ection. If the irection

of pro/ection is not perpenicular to the pro/ection plane then it is an o"liue pro/ection.

8oo( at the parallel pro/ection of a point >Note the left hane coorinate

s!stem?. The pro/ection plane is at *.

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Orthographic pro/ections that show more than sie of an o"/ect are calle a

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The pro/ectors are not perpenicular to the pro/ection plane "ut are parallel from the

o"/ect to the pro/ection plane The pro/ectors are efine "! two angles 9 an where:

9 angle of line >

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-? tan9 7, 9 6@.)*, 8 7

8ines which are perpenicular to the pro/ection planeare pro/ecte at 7 length . This is

a a"inet pro/ection.

7. PE&%PETIKE P&OETION

=se for:

o avertising

o presentation rawings for architecture, inustrial esign, engineering

o fine art

Pros:

o gives a realistic view an feeling for three imensional form of o"/ect

ons:

o oes not preserve shape of o"/ect or scale >e

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o parallel lines not parallel to the pro/ection plane converge

o sie of the o"/ect is iminishe with istance

o foreshortening is not uniform.

Perspective Pro/ections

8i(e parallel pro/ections, perspective pro/ections efine a ma/or su"class of planar

geometric pro/ections. Divisons within perspective pro/ections are consistent in that the

center of pro/ection >P&P? is place at a finite istance from the viewplane. -ecause of

this finite istance "etween the camera an the viewplane, pro/ectors are no longer

parallel. -! placing the camera near the viewplane, as shown for the perspective

pro/ection in Figure @, pro/ectors from the P&P to the eges of the pro/ection winow,

locate on the u+, v+plane, efine a p!ramial view volume. 9s shown in Figure the

pro/ectors from the center of pro/ection to line 9- form a much shorter line 9V-V in the

viewplane. The reuction in length of the pro/ecte line is attri"ute to the ecreasing

istance "etween the two pro/ectors as the viewing surface "ecomes nearer to the center

of pro/ection.

In comparison to parallel pro/ections, perspective pro/ections often provie a more

natural an realistic view of a three+imensional o"/ect. -! comparing the viewplane of a

perspective pro/ection with the view seen from the lens of a camera, the unerl!ing

principals of a perspective pro/ection can "e easil! unerstoo. 8i(e the view from a

camera, lines in a perspective pro/ection not parallel to the viewplane converge to a

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istant point >calle a vanishing point? in the "ac(groun. 5hen the e!e or camera

position is close to the o"/ect, perspective foreshortening occurs with istant o"/ects

appearing smaller in the viewplane than closer o"/ects of the same sie.

Perspective pro/ections are t!picall! separate into three classes: one+point, two+point,

an three+point pro/ections. Each class iffers in the orientation of the viewplane an the

num"er of vanishing points the unit cu"e has.

In a one+point perspective, lines of a three+imensional o"/ect along a ma/or a

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>n

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5e can also animate o"/ects along two+imensional motion paths using the color+ta"le

transformlions. $ere we preefine the o"/ect at successive positions along the

motion path, an set the successive "loc(s of piin arra! P.&? of current critical point.

P.9ET 2 active ege ta"le of pol!gon P. Note that each pol!gon has its own 9ET.

9n! other ata relevant to the application, such as the pol!gon4s @+imensional ata,

lighting information, etc. The scanline epth "uffer is a +imensional arra! % whose sie

is eual to the num"er of pi

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will "e referre to as P.DET&, etc. In aition, P.F I88 is moifie so that it reners a

pii,$? onl! if its epth is less than the current value of %]i^, an the value of %]i^ is

upate. The %+"uffer algorithm is specifie "elow. The scanline generation of the image

is o"taine "! an outer loop on the scanlines an an inner loop on the pol!gons which

calls on P.PO8INE for ever! pol!gon P. PO8INE reners a single scanline of a single

pol!gon an the %+"uffer uses it in a ovetail fashion on all the pol!gons. There e

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Figure . &a! trace image

A)*an$a"es #+ ra, $racin"

&a! tracingVs popularit! stems from its "asis in a realistic simulation of lighting over

other renering methos >such as scanline renering or ra! casting?. Effects such as

reflections an shaows, which are ifficult to simulate using other algorithms, are a

natural result of the ra! tracing algorithm. &elativel! simple to implement !et !ieling

impressive visual results, ra! tracing often represents a first fora! into graphics

programming.

Disa)*an$a"es #+ ra, $racin"

9 serious isavantage of ra! tracing is performance. %canline algorithms an other

algorithms use ata coherence to share computations "etween pi

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Tracing ra!s from the light source to the e!e. 8ots of ra!s are waste "ecause the! never

reach the e!e.

Figure ). 5e trace a new ra! from each ra!+o"/ect intersection irectl! towars the light

source

In the figure we see two ra!s, a an ", which intersect the purple sphere. To etermine

the color of a, we follow the new ra! aV irectl! towars the light source. The color of a

will then epen on several factors, iscusse in olor an %haing"elow. 9s !ou can

see, " will "e shaowe "ecause the ra! "V towars the light source is "loc(e "! the

sphere itself. &a! a woul have also "een shaowe if anot

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3O&P$ING

3orphing is aspecial effectinmotion picturesan animationsthat changes >or morphs?

one imageinto another through a seamless transition. 3ost often it is use to epict one

person turning into another through some magical or technological means or as part of a

fantas! or surreal seuence. Traitionall! such a epiction woul "e achieve through

cross+faing techniues on film. %ince the earl! 00*s, this has "een replace "!

computer software to create more realistic transitions. 3orphing was use in the film &un

-en -unn! run to have the humans an the cartoon animals communicating in the same

picture.

Early Morphing Techniques

In earl! feature films a morph woul "e achieve "! cross+faing from the motion picture

of one actor or o"/ect to another. -ecause of the limitations of this techniue the actors or

o"/ects woul have to sta! virtuall! motionless in front of a "ac(groun that i not

change or move in the frame "etween the "efore an after shots.

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Later Morphing Techniques

8ater more sophisticate cross+faing techniues were emplo!e that fae ifferent

parts of one image to the other grauall! instea of faing the entire image at once. This

st!le of morphing was perhaps most famousl! emplo!e in the vieo former *cc

mem"ers Levin Gole! an 8ol reme >performing as Gole! # reme? prouce in

01for their song r!. It consiste of a series of "lac( an white close+up shots of faces

of man! ifferent people that grauall! fae from one to the ne