Computer Graphics Q n A's

5/24/2018 Computer Graphics Q n A's

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Computer Graphics and Visualization 10CS65

VTU QUESTION PAPER SOLUTION

UNIT -1

INTRODUCTION

1. Briefly explain any t! appli"ati!n# !f "!$p%ter &rap'i"#. ()%ne *+1*, Ans: Applications of computer graphics are:

Display f !nformation Design Simulation " Animation #ser !nterfaces

*. Explain t'e "!n"ept !f pin'!le "a$era !f an i$a&in& #y#te$. Al#! /eri0e t'e

expre##i!n f!r an&le !f 0ie. ()%ne *+1*,

Ans :

#se trigonometry to find pro$ection of point at

%&'y'z(xp= -x/z/d yp= -y/z/d zp= d

)hese are e*uations of simple perspecti+e

2. Di#"%## t'e &rap'i"# pipeline ar"'ite"t%re3 it' t'e 'elp !f a f%n"ti!nal #"'e$ati"/ia&ra$. ()%ne *+1*, 1+

A

ns : Graphics ,ipeline :

,rocess o-$ects one at a time in the order they are generated -y the application

All steps can -e implemented in hard.are on the graphics card

Verte& ,rocessor

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uch of the .or2 in the pipeline is in con+erting o-$ect representations from one coordinatesystem to another

3 -$ect coordinates

3 Camera %eye( coordinates

3 Screen coordinates

+ery change of coordinates is e*ui+alent to a matri& transformation Verte& processor also computes +erte& colors

,rimiti+e Assem-ly

Vertices must -e collected into geometric o-$ects -efore clipping and rasterization can ta2eplace

3 4ine segments

3 ,olygons

3 Cur+es and surfaces

Clipping

ust as a real camera cannot see7 the .hole .orld' the +irtual camera can only see part of the.orld or o-$ect space

3 -$ects that are not .ithin this +olume are said to -e clippedout of the scene

8asterization :

!f an o-$ect is not clipped out' the appropriate pi&els in the frame -uffer must -e assigned colors

8asterizer produces a set of fragments for each o-$ect 9ragments are potential pi&els7

3 a+e a location in frame -ufffer

3 Color and depth attri-utes Verte& attri-utes are interpolated o+er o-$ects -y the rasterizer

9ragment ,rocessor:

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9ragments are processed to determine the color of the corresponding pi&el in the frame -uffer

Colors can -e determined -y te&ture mapping or interpolation of +erte& colors 9ragments may -e -loc2ed -y other fragments closer to the camera

. 4it' a neat /ia&ra$3 explain t'e "!$p!nent# !f a &rap'i"# #y#te$. (De" *+11,

An# 5 A Graphics system has 5 main elements :

!nput De+ices

,rocessor

emory

9rame


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!n simple systems the C,# does -oth normal and graphical processing/

Graphics processing ? )a2e specifications of graphical primiti+es from application program and

assign +alues to the pi&els in the frame -uffer !t is also 2no.n as 8asterization or scan

con+ersion/

6. 4it' a neat /ia&ra$3 explain t'e '%$an 0i#%al #y#te$. (De" *+11, An#5

8ods are used for : monochromatic' night +ision

Cones Color sensiti+e

)hree types of cones

nly three +alues %the tristimulus+alues( are sent to the -rain

@eed only match these three +alues

3 @eed only threeprimarycolors

6/ De#"ri7e t'e !r8in& !f an !%tp%t /e0i"e it' an exa$ple. ()%ly*+11, 6An# 5 )he most predominant type of display has -een the Cathode 8ay )u-e %C8)(/

Various parts of a C8):

lectron Gun 3 emits electron -eam .hich stri2es the phosphor coating to emit light/

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Deflection ,lates 3 controls the direction of -eam/ )he output of the computer is con+erted -ydigital?to?analog con+erters o +oltages across & " y deflection plates/

8efresh 8ate 3 !n order to +ie. a flic2er free image' the image on the screen has to -e

retraced -y the -eam at a high rate %modern systems operate at=5z( ; types of refresh: @oninterlaced display: ,i&els are displayed ro. -y ro. at the refresh rate/

!nterlaced display: dd ro.s and e+en ro.s are refreshed alternately/

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UNIT -*

T9E OPEN:L

1. 4it' t'e 'elp !f a /ia&ra$3 /e#"ri7e t'e !pen :L interfa"e. ()%n*+1*,

An#5 penG4 pro+ides a po.erful -ut primiti+e set of rendering commands' and all higher?le+el

dra.ing must -e done in terms of these commands/

)he penG4 #tility 4i-rary %G4#( contains se+eral routines that use lo.er?le+el penG4

commands to perform such tas2s as setting up matrices for specific +ie.ing orientations and

pro$ections' performing polygon tessellation' and rendering surfaces/ )his li-rary is pro+ided

as part of e+ery penG4 implementation/

9or e+ery .indo. system' there is a li-rary that e&tends the functionality of that .indo.

system to support penG4 rendering/ 9or machines that use the B indo. System' the

penG4 &tension to the B indo. System %G4B( is pro+ided as an ad$unct to penG4/

G4B routines use the prefi& &l;/ 9or icrosoft indo.s' the G4 routines pro+ide the

indo.s to penG4 interface/

)he penG4 #tility )ool2it %G4#)( is a .indo. system?independent tool2it' .ritten -y

ar2 ilgard' to hide the comple&ities of differing .indo. system A,!s/

;/ 4rite explanat!ry n!te# !n5 i, R:B "!l!r $!/el< ii, in/exe/ "!l!r $!/el. ()%n*+1*,

An#5 Colors are indices into ta-les of 8G< +alues

8e*uires less memory

3 indices usually = -its

3 not as important no. emory ine&pensi+e



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@eed more colors for shading

!n inde&ed mode' colors are stored as indices/ !f there are 2 indices then there can -e 2n?1 colors

that could -e got -y com-ining red' green and -lue/ )his yields a huge color palette as compared

to the normal 8G< mode/

2. 4rite an !pen :L re"%r#i0e pr!&ra$ f!r *D #ierpin#8i &a#8et it' rele0ant "!$$ent#.

()%n*+1*, 1+

An#5 Einclude Fstdaf&/hF

Einclude G4Hglut/hI

typedef float

pointJ>KL HM initial

tetrahedron MH

point +JK NOO0/0' 0/0' 1/0P'

O0/0' 1/0' ?1/0P' O?1/0'

?1/0' ?1/0P' O1/0' ?1/0'

?1/0PPL

static G4float thetaJK N O0/0'0/0'0/0PL

int nL

+oid triangle% point a' point -' point c(

HM display one triangle using a line loop for .ire frame MH

O

glf+%a(L

glVerte&>f+%-(L

glVerte&>f+%c(L


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glnd%(L

P

+oid di+ideQtriangle%point a' point -' point c' int m(

O

HM triangle su-di+ision using +erte& num-ers

righthand rule applied to create out.ard pointing faces MH

point +1' +;'+>L int $L

if%mI0(

O

for%$N0L $>L $TT( +1J$KN%aJ$KT-J$K(H;L

for%$N0L $>L $TT( +;J$KN%aJ$KTcJ$K(H;Lfor%$N0L $>L $TT( +>J$KN%-J$KTcJ$K(H;L

di+ideQtriangle%a' +1' +;' m?1(L

di+ideQtriangle%c' +;' +>' m?1(L

di+ideQtriangle%-' +>' +1' m?1(L

P

HM dra. triangle at end of recursion MHelse%triangle%a'-'c((L

P

+oid tetrahedron% int m(O

HM Apply triangle su-di+ision to faces of tetrahedron/Gi+ea different color to each face of the tetrahedronMH

glColor>f%1/0'0/0'0/0(L

di+ideQtriangle%+J0K' +J1K' +J;K' m(L

glColor>f%0/0'1/0'0/0(L

di+ideQtriangle%+J>K' +J;K' +J1K' m(L

glColor>f%0/0'0/0'1/0(L

di+ideQtriangle%+J0K' +J>K' +J1K' m(L

glColor>f%0/0'0/0'0/0(L

di+ideQtriangle%+J0K' +J;K' +J>K' m(L

P

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+oid display%+oid(

O

glClear%G4QC48Qtetrahedron%n(L

gl9lush%(L

P

+oid my8eshape%int .' int h(

O

glVie.port%0' 0' .' h(L

glatri&ode%G4Q,8C)!@(L

gl4oad!dentity%(L

HM code to maintain the aspect

ratioMH HM hen .idth -ecomes lessthan height' ad$ust the -ottom'top parameters

to maintain the aspect ratioMH

if %. N h(

glrtho%?;/0' ;/0' ?;/0 M %G4float( h H %G4float(.' ;/0 M %G4float( h H %G4float( .' ?10/0' 10/0(L

HM hen height -ecomes less

than .idth' ad$ust the left'right parameters tomaintain the aspect ratioMH

else

glrtho%?;/0 M %G4float( . H %G4float( h';/0 M %G4float( . H %G4float( h' ?;/0' ;/0'

?10/0' 10/0(L

glatri&ode%G4QD4V!(L

glut,ost8edisplay%(L

P

+oid main%int argc' char MMarg+(

O

printf%Fenter the no of di+ision :F(L scanf%FdF'"n(L

glut!nit%"argc' arg+(L

glut!nitDisplayode%G4#)QS!@G4 U G4#)Q8G< U G4#)QD,)(Lglut!nitindo.Size%60' =0(L

glutCreateindo.%F>D Gas2etF(L

glut8eshape9unc%my8eshape(L

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glutDisplay9unc%display(L

glna-le%G4QD,)Q)S)(L

glClearColor %1/0' 1/0' 1/0' 1/0(Lglutain4oop%(L

P

. 4it' a neat /ia&ra$3 /i#"%## t'e "!l!r f!r$ati!n. Explain t'e a//iti0e an/ #%7tra"ti0e

"!l!r#3 in/exe/ "!l!r an/ "!l!r #!li/ "!n"ept. (De"*+11, 1*

An#5

A +isi-le color can -e characterized -y the function C%X(

)ristimulus +alues 3 responses of the > types of cones to the colors/

> color theory 3 !f ; colors produce the same tristimulus +alues' then they are +isually

indistinguisha-le/7

Additi+e color model 3 Adding together the primary colors to get the percie+ed colors/

/g/ C8)/

Su-tracti+e color model 3 Colored pigments remo+e color components from light that is

stri2ing the surface/ ere the primaries are the complimentary colors : cyan' magenta and

yello.

R:B "!l!r

ach color component is stored separately in the frame-uffer #sually = -its per component in -uffer

@ote in &lC!l!r2fthe color +alues range from 0/0 %none( to 1/0 %all(' .hereas in

&lC!l!r2%7 the +alues range from 0 to ;55

)he color as set -y &lC!l!r-ecomes part of the state and .ill -e used until changed



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3 Colors and other attri-utes are not part of the o-$ect -ut are assigned .hen the

o-$ect is rendered

e can create conceptual vertex colors-y code such as

&lC!l!r

&lVertex

&lC!l!r

&lVertex

8G

An#5 indo.3A rectangular area of our display/

odern systems allo. many .indo.s to -e displayed on the screen %multi.indo.en+ironment(/



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)he position of the .indo. is .ith reference to the origin/ )he origin %0' 0( is the top leftcorner of the screen/

&l%tInit(,

allo.s application to get command line arguments and initializes system/)he function is

-asically used for initializing the glut li-rary and also to initiate a session .ith the .indo.s

system/ )he function does not ta2e any arguments and should -e the first function to -e

called .ithin the main program/

&l%InitDi#play!/e(, re*uests properties for the .indo. %therendering context(

8G< color? specified -y the argument G4#)Q8G color modeneeds to -e used/

Single -uffering 3 G4#)QS!@G4: specifies that the images are static and only asingle frame -uffer is re*uired to store the pi&els

G4#)QD#KL HM initial

tetrahedron MH

point +JK NOO0/0' 0/0' 1/0P'

O0/0' 1/0' ?1/0P' O?1/0'

?1/0' ?1/0P' O1/0' ?1/0'

?1/0PPL

static G4float thetaJK N O0/0'0/0'0/0PL

int nL

+oid triangle% point a' point -' point c(


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HM display one triangle using a line loop for .ire frame MH

O

glf+%a(L

glVerte&>f+%-(L

glVerte&>f+%c(L

glnd%(L

P

+oid di+ideQtriangle%point a' point -' point c' int m(

O

HM triangle su-di+ision using +erte& num-ers

righthand rule applied to create out.ard pointing faces MH

point +1' +;'+>L int $L

if%mI0(

O

for%$N0L $>L $TT( +1J$KN%aJ$KT-J$K(H;L

for%$N0L $>L $TT( +;J$KN%aJ$KTcJ$K(H;L

for%$N0L $>L $TT( +>J$KN%-J$KTcJ$K(H;L

di+ideQtriangle%a' +1' +;' m?1(L

di+ideQtriangle%c' +;' +>' m?1(L

di+ideQtriangle%-' +>' +1' m?1(L

P

HM dra. triangle at end of recursion MHelse%triangle%a'-'c((L

P

+oid tetrahedron% int m(

O

HM Apply triangle su-di+ision to faces of tetrahedron/Gi+ea different color to each face of the tetrahedronMH

glColor>f%1/0'0/0'0/0(L

di+ideQtriangle%+J0K' +J1K' +J;K' m(L

glColor>f%0/0'1/0'0/0(L

di+ideQtriangle%+J>K' +J;K' +J1K' m(L

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glColor>f%0/0'0/0'1/0(L

di+ideQtriangle%+J0K' +J>K' +J1K' m(L

glColor>f%0/0'0/0'0/0(L

di+ideQtriangle%+J0K' +J;K' +J>K' m(L

P

+oid display%+oid(

O

glClear%G4QC48Qtetrahedron%n(L

gl9lush%(L

P

+oid my8eshape%int .' int h(O

glVie.port%0' 0' .' h(L


gl4oad!dentity%(L

HM code to maintain the aspectratioMH HM hen .idth -ecomes less

than height' ad$ust the -ottom'top parametersto maintain the aspect ratioMH

if %. N h(

glrtho%?;/0' ;/0' ?;/0 M %G4float( h H %G4float(.' ;/0 M %G4float( h H %G4float( .' ?10/0' 10/0(L

HM hen height -ecomes less

than .idth' ad$ust the left'right parameters tomaintain the aspect ratioMH

else

glrtho%?;/0 M %G4float( . H %G4float( h'

;/0 M %G4float( . H %G4float( h' ?;/0' ;/0'

?10/0' 10/0(L

glatri&ode%G4QD4V!(L

glut,ost8edisplay%(L

P

+oid main%int argc' char MMarg+(

O

printf%Fenter the no of di+ision : F(L



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scanf%FdF'"n(Lglut!nit%"argc' arg+(L

glut!nitDisplayode%G4#)QS!@G4 U G4#)Q8G< U G4#)QD,)(Lglut!nitindo.Size%60' =0(L

glutCreateindo.%F>D Gas2etF(L

glut8eshape9unc%my8eshape(L

glutDisplay9unc%display(L

glna-le%G4QD,)Q)S)(L

glClearColor %1/0' 1/0' 1/0' 1/0(L

glutain4oop%(L

P

@. Cla##ify t'e $a!r &r!%p# !f API f%n"ti!n# in !pen :L. Explain any f!%r !f t'e$.

()%ly*+11,

Ans:

,rimiti+e functions: Defines lo. le+el o-$ects such as points' line segments' polygons

etc/

Attri-ute functions : Attri-utes determine the appearance of o-$ects

o Color %points' lines' polygons(

o Size and .idth %points' lines(

o ,olygon mode

Display as filled

Display edges

Display +ertices

Vie.ing functions: Allo.s us to specify +arious +ie.s -y descri-ing the cameraYs

position and orientation/

)ransformation functions: ,ro+ides user to carry out transformation of o-$ects li2e

rotation' scaling etc/

!nput functions : Allo.s us to deal .ith a di+erse set of input de+ices li2e 2ey-oard'

mouse etc

Control functions: na-les us to initialize our programs' helps in dealing .ith any errorsduring e&ecution of the program/

Zuery functions: elps *uery information a-out the properties of the particular

implementation/



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>. 4'at i# an attri7%te it' re#pe"t t! &rap'i"# #y#te$= Li#t attri7%te# f!r line# an/

p!ly&!n#. ()%ly*+11,

An#5 Attri-ute functions : Attri-utes determine the appearance of o-$ects

Color %points' lines' polygons(

Size and .idth %points' lines(

,olygon mode

Display as filled

Display edges

Display +ertices

,olygons : -$ect that has a -order that can -e descri-ed -y a line loop " also has a .ell definedinterior

. Li#t !%t /ifferent !pen :L pri$iti0e#3 &i0in& exa$ple# f!r ea"'. ()an*+1+, 1+

Ans: penG4 supports ; types of primiti+es:

Geometric primiti+es %+ertices' line segments/( 3 they pass through the geometricpipeline



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8aster primiti+es %arrays of pi&els( 3 passes through a separate pipeline to the frame -uffer/4ine segments

G4Q4!@S

G4Q4!@QS)8!,

G4Q4!@Q4,

1+. Briefly explain t'e !rt'!&rap'i" 0iein& it' Open:L f%n"ti!n# f!r */ an/ 2/ 0iein&.In/i"ate t'e #i&nifi"an"e !f pr!e"ti!n plane an/ 0iein& p!int in t'i#. ()an*+1+, 1+

An#5 !n the default orthographic +ie.' points are pro$ected for.ard along theza&is onto theplanez=0

Tran#f!r$ati!n# an/ Viein& )he pipeline architecture depends on multiplying together a num-er of transformation matrices to

achie+e the desired image of a primiti+e/ ).o important matrices :

odel?+ie.

,ro$ection

)he +alues of these matrices are part of the state of the system/

!n penG4' pro$ection is carried out -y a pro$ection matri& %transformation(

)here is only one set of transformation functions so .e must set the matri& modefirst &latrix!/e (:LPRO)ECTION,

)ransformation functions are incremental so .e start .ith an identity matri& and alter it .ith apro$ection matri& that gi+es the +ie. +olume

&lL!a/I/entity(,


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glVerte&;f%0/ M cos%angle(T0/5' 0/ M sin%angle(T0/5(glVerte&;f%0/5 M cos%angle(T0/5' 0/5 M sin%angle(T0/5(

P

glnd%(L

-rea2L

P

P

. Explain Pi"8in& !perati!n in !pen:L it' an exa$ple. ()%l*+11, 6

An# 5 !dentify a user?defined o-$ect on the display

!n principle' it should -e simple -ecause the mouse gi+es the position and .e should -ea-le to determine to .hich o-$ect%s( a position corresponds

,ractical difficulties,ipeline architecture is feed for.ard' hard to go from screen -ac2 to.orld Complicated -y screen -eing ;D' .orld is >D

o. close do .e ha+e to come to o-$ect to say .e selectedit[ +oid mouse %int -utton' int state' int &' int y(

O

G4#int name


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HM same clipping .indo. as in reshape call-ac2MH glurtho;D%&min'&ma&'ymin'yma&(L

dra.Qo-$ects%G4QS4C)(L


HM restore +ie.ing matri&MH gl,opatri&%(L

gl9lush%(L

HM return -ac2 to normal render mode MH

hits N gl8enderode%G4Q8@D8(L

HM process hits from selection mode renderingMH

processits%hits' namef%1/0'0/0'0/0(gl8ectf%?0/5'?0/5'1/0'1/0(L

if %mode NN G4QS4C)(gl4oad@ame%;(L

glColor>f%0/0'0/0'1/0(gl8ectf%?1/0'?1/0'0/5'0/5(L

P

+oid processits%G4int hits' G4#int -ufferJK(

O

unsigned int i'$L

P

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UNIT

:EOETRIC OB)ECTS AND TRANSKORATIONS-1

1. Explain t'e "!$plete pr!"e/%re !f "!n0ertin& a !rl/ !7e"t fra$e int! "a$era !r eye

fra$e3 %#in& t'e $!/el 0ie $atrix. ()%n*+1*, 1+

An#5 4!rl/ Spa"e

-$ect space for a particular o-$ect gi+es it no spatial relationship .ith respect to other o-$ects/

)he purpose of world space is to pro+ide some a-solute reference for all the o-$ects in your

scene/ o. a .orld?space coordinate system is esta-lished is ar-itrary/ 9or e&ample' you may

decide that the origin of .orld space is the center of your room/ -$ects in the room are then

positioned relati+e to the center of the room and some notion of scale %!s a unit of distance a foot

or a meter[( and some notion of orientation %Does the positi+e y?a&is point FupF[ !s north in the

direction of the positi+ex?a&is[(/

T'e !/elin& Tran#f!r$

)he .ay an o-$ect' specified in o-$ect space' is positioned .ithin .orld space is -y means of a

modeling transform/ 9or e&ample' you may need to rotate' translate' and scale the >D model of a

chair so that the chair is placed properly .ithin your room_s .orld?space coordinate system/ ).o

chairs in the same room may use the same >D chair model -ut ha+e different modeling

transforms' so that each chair e&ists at a distinct location in the room/

Rou can mathematically represent all the transforms in this chapter as a & matri&/ #sing theproperties of matrices' you can com-ine se+eral translations' rotations' scales' and pro$ections

into a single & matri& -y multiplying them together/ hen you concatenate matrices in this

.ay' the com-ined matri& also represents the com-ination of the respecti+e transforms/ )his

turns out to -e +ery po.erful' as you .ill see/

!f you multiply the & matri& representing the modeling transform -y the o-$ect?space position

in homogeneous form %assuming a 1 for the wcomponent if there is no e&plicit wcomponent('

the result is the same position transformed into .orld space/ )his same matri& math principle

applies to all su-se*uent transforms discussed in this chapter/

Eye Spa"e

#ltimately' you .ant to loo2 at your scene from a particular +ie.point %the FeyeF(/ !n the

coordinate system 2no.n as eye space%or view space(' the eye is located at the origin of the

coordinate system/ 9ollo.ing the standard con+ention' you orient the scene so the eye is loo2ing

do.n one direction of thez?a&is/ )he FupF direction is typically the positi+eydirection/

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ye space' .hich is particularly useful for lighting' .ill -e discussed in Chapter 5/

T'e Vie Tran#f!r$

)he transform that con+erts .orld?space positions to eye?space positions is the view transform/

nce again' you e&press the +ie. transform .ith a & matri&/

)he typical +ie. transform com-ines a translation that mo+es the eye position in .orld space to

the origin of eye space and then rotates the eye appropriately/ 'G4Q94A)' 0' Vertices(L

glColor,ointer %>'G4Q94A)' 0' C48(L

2. Explain $!/elin& a "!l!r "%7e in /etail. (De"*+11, 1+

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An#5 e can use the +erte& list to define a color cu-e/ e can define a function *uad to dra.

*uadrilaterals polygons specified -y pointers into the +erte& list/ )he color cu-e specifies the si&

faces' ta2ing care to ma2e them all out.ard facing as follo.s/

G4floatVertices J=K J>K N OO?1/0' ?1/0' ?1/0P' O1/0' ?1/0' ?1/0P' O1/0' 1/0' ?1/0P' O?1/0' 1/0' ?1/0P O?

1/0' ?1/0' 1/0P' O1/0' ?1/0' 1/0P' O1/0' 1/0' 1/0P' O?1/0' 1/0' 1/0PPG4float color J=K J>K N OO0/0' 0/0' 0/0P' O1/0' 0/0' 0/0P' O1/0' 1/0' 0/0P' O0/0' 1/0' 0/0P' O0/0' 0/0'1/0P' O1/0' 0/0' 1/0P' O1/0' 1/0' 1/0P' O0/0' 1/0' 1/0PPL

+oid *uad %int a' int -' int c' int d(

O

glf+ %colorsJaK(L

glVerte&>f+%+erticesJaK(L

glcolor>f+%colorsJ-K(LglVerte&>f+%+erticesJ-K(L

glcolor>f+%colorsJcK(L

glVerte&>f+ %+erticesJcK(L

glcolor>f+ %colorsJdK(L

glVerte&>f+%+erticesJdK(L

glnd%(L

P

Void colorcu-e %(

O *uad %0'>';'1(L *uad

%;'>''6(L *uad

%0' ''>(L *uad

%1' ;' 6' 5(L *uad

%' 5' 6' (L *uad

%0' 1' 5' (L

. Explain affine tran#f!r$ati!n#. (De"*+11, 1+

An#5 An affine transformation is an important class of linear ;?D geometric transformations

.hich

maps +aria-les %e.g.pi&el intensity +alues located at position in an input image( into ne.

+aria-les %e.g. in an output image( -y applying a linear com-ination of translation'

rotation' scaling andHor shearing %i.e.non?uniform scaling in some directions( operations/

Dept of CS' CC ,age ;=


31/57


)he general affine transformation is commonly .ritten in homogeneous coordinates as sho.n-elo.:


32/57


)he origin %or displacement +ector(

)he -asis +ectors ? )he direction and distance for T1 mo+ement along each a&is

)his definition is relati+e

)o plot a point


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UNIT 6

:EOETRIC OB)ECTS AND TRANSKORATIONS-II

1. Define an/ repre#ent t'e f!ll!in& *-D tran#f!r$ati!n# in '!$!&en!%# "!!r/inate

#y#te$.

a. Tran#lati!n

7. R!tati!n

". S"alin&

/. Refle"ti!n ()%n*+1*, 1*

Ans: Tran#lati!n

+oid gl)ranslateOfdP %)R, &' )R, y' )R, z(L

ultiplies the current matri& -y a matri& that mo+es %translates( an o-$ect -y the gi+en&' y' and z +alues

R!tati!n

+oid gl8otateOfdP%)R, angle' )R, &' )R, y' )R, z(L

ultiplies the current matri& -y a matri& that rotates an o-$ect in acountercloc2.ise direction a-out the ray from the origin through the point %&' y' z(/)he angle parameter specifies the angle of rotation in degrees/

S"alin& +oid glScaleOfdP %)R,&' )R, y' )R,z(L

ultiplies the current matri& -y a matri& that stretches' shrin2s' or reflects an o-$ect alongthe a&es/

Dept of CS' CC ,age >1


34/57


*uations :

)ranslation: ,f N ) T ,&fN &oT d&

yfN yoT dy

8otation: ,f N 8 ` ,

&fN &oM cos ? yoMsin

yfN &oM sin T yoMcos

Scale: ,f N S ` ,

&fN s& M &o

yfN sy M yo

*. 4'at i# "!n"atenati!n tran#f!r$ati!n= Explain r!tati!n a7!%t a fixe/ p!int. ()%n*+1*,

>

Ans: 8otate a house a-out the origin

8otate the house a-out one of its corners

translate so that a corner of the house is at the origin

rotate the house a-out the origin

translate so that the corner returns to its original position

Dept of CS' CC ,age >;


35/57


2. 4'at are J%aterni!n#= 4it' an exa$ple3 explain it# $at'e$ati"al repre#entati!n#.

(De"*+11, 1+

Ans: A *uaternion is an element of a dimensional +ector?space/ !t_s defined as . T &i T y$ T

z2 .here i' $ and 2 are imaginary num-ers/ Alternati+ely' a *uaternion is .hat you get .hen

you add a scalar and a >d +ector/ )he math -ehind *uaternions is only slightly harder than the

math -ehind +ectors/

void Camera::movex(float xmmod)

{

pos +=rotation *Vector3(xmmod,0.0f,0.0f);

void Camera::move!(float !mmod)

{

pos.!"=!mmod;

void Camera::move#(float #mmod)

{

pos +=rotation *Vector3(0.0f,0.0f, "#mmod);

void Camera::rotatex(float xrmod)

{

$%aternion nrot(Vector3(&.0f,0.0f,0.0f),xrmod *'V&0);rotation =rotation *nrot;

void Camera::rotate!(float !rmod)

{

$%aternion nrot(Vector3(0.0f,&.0f,0.0f),!rmod *'V&0);rotation =nrot *rotation;

void Camera::tic-(float seconds)

{if (xrot=0.0f)rotatex(xrot*seconds*rotspeed);

if (!rot=0.0f)rotate!(!rot*seconds*rotspeed);

if (xmov = 0.0f) movex(xmov * seconds * movespeed);

if (!mov = 0.0f) move!(!mov * seconds * movespeed);

if (#mov=0.0f)move#(#mov*seconds*movespeed);

Dept of CS' CC ,age >>


36/57


. Explain t'e 7a#i" tran#f!r$ati!n# in 2D an/ repre#ent t'e$ in $atrix f!r$. ()%n*+1+,

1+

Ans: )ranslation:

Scaling:

8otation:

6. 4'at are t'e a/0anta&e# !f J%aterni!n= ()%n*+1+, *

Ans: Zuaternions ha+e some ad+antages o+er other representations of rotations/

Zuaternions don_t suffer from gim-al loc2' unli2e uler angles/

)hey can -e represented as num-ers' in contrast to the W num-ers of a rotations matri&/

)he con+ersion to and from a&isHangle representation is tri+ial/

Smooth interpolation -et.een t.o *uaternions is easy %in contrast to a&isHangle or

rotation matrices(/

After a lot of calculations on *uaternions and matrices' rounding errors accumulate' so

you ha+e to normalize *uaternions and orthogonalize a rotation matri&' -ut normalizing a

*uaternion is a lot less trou-lesome than orthogonalizing a matri&/

Similar to rotation matrices' you can $ust multiply ; *uaternions together to recei+e a

*uaternion that represents -oth rotations/

Dept of CS' CC ,age >


37/57


UNIT -

VIE4IN:

1. 4it' neat #8et"'e#3 explain t'e 0ari!%# type# !f 0ie# t'at are e$pl!ye/ in "!$p%ter

&rap'i"# #y#te$#. ()%n*+1*, 1+

An#5

Per#pe"ti0e an/ parallel pr!e"ti!n# 5

,arallel +ie.ing is a limiting case of perspecti+e +ie.ing

,erspecti+e pro$ection has a C, .here all the pro$ector lines con+erge/

,arallel pro$ection has parallel pro$ectors/ ere the +ie.er is assumed to -e present atinfinity/ So here .e ha+e a Direction of pro$ection %D,(7 instead of center of

pro$ection%C,(/



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Ort'!&rap'i" Pr!e"ti!n# 5

,ro$ectors are perpendicular to the pro$ection plane/ ,ro$ection

plane is 2ept parallel to one of the principal faces/

A +ie.er needs more than ; +ie.s to +isualize .hat an o-$ect loo2s li2e from itsmulti+ie. orthographic pro$ection/

*. Briefly /i#"%## t'e f!ll!in& al!n& it' t'e f%n"ti!n# %#e/ f!r t'e p%rp!#e in !pen :L

i, Per#pe"ti0e pr!e"ti!n#

ii, Ort'!&!nal pr!e"ti!n# ()%n*+1*, 1+

An#5 i, ,erspecti+e pro$ection has a C, .here all the pro$ector lines con+erge/

T'e f!ll!in& f%n"ti!n# 'a0e t! 7e %#e/ t! "reate per#pe"ti0e pr!e"ti!n#5



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gl4oad!dentity%(L

glu,erspecti+e%f9V' fAspect ' f@ear,lane' f9ar,lane(L

Ort'!&!nal pr!e"ti!n#

,ro$ectors are perpendicular to the pro$ection plane/ ,ro$ection

plane is 2ept parallel to one of the principal faces/

A +ie.er needs more than ; +ie.s to +isualize .hat an o-$ect loo2s li2e from its multi+ie.orthographic pro$ection/

+oid glrtho% G4dou-le left'

G4dou-le right'

G4dou-le -ottom'

G4dou-le top'G4dou-le nearVal'

G4dou-le farVal(L

,arameters

left' right

Specify the coordinates for the left and right +ertical clipping planes/

-ottom' top

Specify the coordinates for the -ottom and top horizontal clipping planes/

nearVal' farVal

Specify the distances to the nearer and farther depth clipping planes/

)hese +alues are negati+e if the plane is to -e -ehind the +ie.er/

2. Explain t'e 0ari!%# type# !f ax!n!$etri" pr!e"ti!n#. (De"*+11, @

Dept of CS' CC ,age >


40/57


An#5 ,ro$ectors are orthogonal to the pro$ection plane ' -ut pro$ection plane can mo+e relati+e too-$ect/

Classification -y ho. many angles of a corner of a pro$ected cu-e are the same none: trimetric t.o: dimetric

three: isometric

. 4'at i# "an!ni"al 0ie 0!l%$e= Explain t'e $appin& !f a &i0en 0ie 0!l%$e t! t'e"an!ni"al f!r$. (De"*+11, @

An#5 )he diagram sho.s the normalization process

9irst the +ie. +olume specified -y the glortho function is mapped to the canonical form

Canonical 9orm : default +ie. +olume centerd at the origin and ha+ing sides of length ;/

)his in+ol+es ; steps :

3 o+e center to origin

)%?%leftTright(H;' ?%-ottomTtop(H;'%nearTfar(H;((3 Scale to ha+e sides of length ;

S%;H%left?right(';H%top?-ottom(';H%near?far((

)he resultant matri& is a product of the a-o+e ; matrices i/e/ , N S) N

;0 0

right left

right left right left

0;

0top ottom

top ottom top ottom0 0

; far near

near far far near 0 0 0 1

Dept of CS' CC ,age >=


41/57


6. Deri0e eJ%ati!n# f!r per#pe"ti0e pr!e"ti!n an/ /e#"ri7e t'e #pe"ifi"ati!n# !f aper#pe"ti0e "a$era 0ie in !pen :L. ()%n*+11, >

An#.5 )he ne. coordinate system is specified -y a translation androtation.ith respect to the old coordinate system:

+N 8 %+ ? +0( +0 is displacement+ector 8 is rotation matri&

8 may -e decomposed into

> rotations a-out the

coordinate a&es:

By $%ltiplyin& t'e 2 $atri"e# Rx3 Ry an/ R?3 !ne &et#

K!r f!r$%la $anip%lati!n#3 !ne trie# t! a0!i/ t'e tri&!n!$etri" f%n"ti!n#an/ ta8e#

@ote that the coefficients of 8 are constrained:

A rotation matri& is orthonormal: 8 8) N ! %unit matri&(

Dept of CS' CC ,age >W


42/57


UNIT @

LI:9TIN: AND S9ADIN:

1. Explain p'!n& li&'tin& $!/el. In/i"ate t'e a/0anta&e# an/ /i#a/0anta&e#. ()%n*+1*,

1+

An#5 ,hong de+eloped a simple model that can -e computed rapidly !t considers three components

3 Diffuse

3 Specular

3 Am-ient And #ses four +ectors

3 )o source represented -y the +ector l

3 )o +ie.er represented -y the +ector +

3 @ormal represented -y the +ector n

3 ,erfect reflector represented -y the +ector r

e need W coefficients to characterize the light source .ith am-ient' diffuse and specularcomponents/)he !llumination array for the ith

light source is gi+en -y the matri&:4ira 4iga 4i-a

4iN 4ird 4igd 4i-d

4irs 4igs 4i-s

)he intensity for each color source can -e computed -y adding the am-ient'specular and diffusecomponents/

/g/ 8ed intensity that .e see from source !:

!irN 8ira4iraT 8ird4irdT 8irs4irsN !raT!rdT!rs

Since the necessary computations are same for each light

source' ! N !aT!dT!s

*. 4'at are t'e /ifferent $et'!/# a0aila7le f!r #'a/in& a p!ly&!n= Briefly /i#"%## any *!f t'e$. ()%n*+1*, 1+

An#5 P!ly&!nal S'a/in&



43/57


Klat #'a/in&

!n case of flat shading there are distinct -oundaries after color interpolation

> +ectors needed for shading are: l'n'+ /)he openG4 function to ena-le flat shading is :

glShadeodel%G4Q94A)(

9or a flat polygon'n is constant as the normal nis same at all points on the polygon/Also if .e

assume a distant +ie.er' the +ector 0is constant and if .e consider a distant light source then the

+ector l is also a constant/ere all the > +ectors are constant and therefore the shading

calculations needs to -e done only once for an entire polygon and each point on the polygon is

assigned the same shade/ )his techni*ue is 2no.n as 9lat shading/

Disad+antage :


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O

glClearColor%1/0'1/0'1/0'1/0(L

glColor>f%1/0'0/0'0/0(L

gl,ointSize%5/0(L


gl4oad!dentity%(L

glurtho;D%0/0'WW/0'0/0'WW/0(L

glut,ost8edisplay%(L HH re*uest redisplay

P

+oid display%+oid(

O

HM clear .indo. MH

glClear%G4QC48QglColor>f%0/0' 0/0' 1/0(L HH set color to -lueHM dra. rectangles MH

for%iN0Lima&&LiTT(

&JiKN&0TiMd&L HH compute &JiK

for%$N0L$ma&yL$TT(

yJ$KNy0T$MdyL HH compute yJiK

glColor>f%0/0' 0/0' 1/0(L

for%iN0Lima&&?1LiTT(

for%$N0L$ma&y?1L$TT(

O

glColor>f%0/0' 0/0' 1/0(Lgl


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glut!nitDisplayode%G4#)QS!@G4 U G4#)Q8G


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/* ec%rsive s%division of tetra1edron (C1apter 2). 1reedispla! modes: 4ire frame, constant, and interpolative s1adin5 */

/*'ro5ram also ill%strates definin5 materials and li51tso%rces in m!iit() */

/* mode 0 = 4ire frame, mode & = constants1adin5, mode 6 = interpolative s1adin5 */

/* 7pdated ctoer &2, 6000, ! Car! 8axer to convert / to C++. */

9incl%de stdli.19incl%de mat1.19incl%de iostream9incl%de ;

/* initial tetra1edron */

point v>={{0.0, 0.0, &.0, {0.0, 0.?@60?, "0.33333,

{"0.&2@?A, "0.@A&@0B, "0.333333, {0.&2@?A, "0.@A&@0B," 0.333333;

static = {0.0,0.0,0.0;

int n;int mode;

void trian5le (point a, point , pointc); void normal (point p);

void dividetrian5le (point a, point , point c, intm); void tetra1edron (int m);void displa! (void);

void m!es1ape (int 4, int1); void m!init ();

%sin5 namespace std;

void main(int ar5c, c1ar **ar5v){

co%t Dnter n%mer of levels of rec%rsion:D; cin n;5l%tnit (Ear5c, ar5v);

5l%tnitFispla!Gode (


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{

if (mode==0) 5lHe5in(; d=sPrt(d);if(d0.0) for(i=0; i3; i++) pi>/=d;

void dividetrian5le (point a, point , point c, intm) /* trian5le s%division %sin5 vertex n%mersri51t1and r%le applied to create o%t4ard pointin5 faces */{

point v&, v6,v3; int Q;if(m0){

for(Q=0; Q3; Q++) v&Q>=aQ>+Q>; normal(v&);

for(Q=0; Q3; Q++) v6Q>=aQ>+cQ>; normal(v6);

for(Q=0; Q3; Q++) v3Q>=Q>+cQ>; normal(v3);dividetrian5le (a, v&, v6, m"&);dividetrian5le (c, v6, v3, m"&);dividetrian5le (, v3, v&, m"&);dividetrian5le (v&, v3, v6, m"&);

else

trian5le (a,,c); /* dra4 trian5le at end of rec%rsion */

void tetra1edron (int m)/* Rppl! trian5le s%division to faces of tetra1edron */{

dividetrian5le (v0>, v&>, v6>, m);dividetrian5le (v3>, v6>, v&>, m);dividetrian5le (v0>, v3>, v&>, m);dividetrian5le (v0>, v6>, v3>, m);

void displa! (void)/* Fispla!s all t1ree modes, side ! side */{



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5lClear (


49/57


UNIT ->

IPLEENTATION

1. Di#"%## t'e Bre#en'a$M# ra#teri?ati!n al&!rit'$. 9! i# it a/0anta&e!%# 'en

"!$pare/ t! !t'er exi#tin& $et'!/#= De#"ri7e. ()%n*+1*, 1+

An#5 Consider dra.ing a line on a raster grid .here .e restrict the allo.a-le slopes of the line to

the range /

!f .e further restrict the line?dra.ing routine so that it al.ays incrementsxas it plots' it -ecomes

clear that' ha+ing plotted a point at !x"y#' the routine has a se+erely limited range of options as to

.here it may put the nextpoint on the line:

!t may plot the point !x$%"y#' or:

!t may plot the point !x$%"y$%#/

So' .or2ing in thefirst positive octantof the plane' line dra.ing -ecomes a matter of deciding-et.een t.o possi-ilities at each step/

e can dra. a diagram of the situation .hich the plotting program finds itself in ha+ing plotted

!x"y#/

!n plotting !x"y#the line dra.ing routine .ill' in general' -e ma2ing a compromise -et.een .hat it

.ould li2e to dra. and .hat the resolution of the screen actually allo.s it to dra./ #sually the

plotted point !x"y#.ill -e in error' the actual' mathematical point on the line .ill not -e addressa-le

on the pi&el grid/ So .e associate an error' ' .ith eachyordinate' the real +alue of

y should -e / )his error .ill range from ?0/5 to $ust under T0/5/

Dept of CS' CC ,age


50/57


!n mo+ing from x to x$%.e increase the +alue of the true %mathematical( y?ordinate -y an

amount e*ual to the slope of the line' m/ e .ill choose to plot !x$%"y#if the difference -et.een

this ne. +alue andyis less than 0/5/

ther.ise .e .ill plot !x$%"y$%#/ !t should -e clear that -y so doing .e minimise the total error-et.een the mathematical line segment and .hat actually gets dra.n on the display/

)he error resulting from this ne. point can no. -e .ritten -ac2 into ' this .ill allo. us to

repeat the .hole process for the ne&t point along the line' at x$&/

)he ne. +alue of error can adopt one of t.o possi-le +alues' depending on .hat ne. point isplotted/ !f !x$%"y#is chosen' the ne. +alue of error is gi+en -y:

ther.ise it is:

)his gi+es an algorithm for a DDA .hich a+oids rounding operations' instead using the error

+aria-le to control plotting:

)his still employs floating point +alues/ Consider' ho.e+er' .hat happens if .e multiply across

-oth sides of the plotting test -y and then -y ;:

Dept of CS' CC ,age =


51/57


All *uantities in this ine*uality are no. integral/

Su-stitute for / )he test -ecomes:

)his gi+es an integer-onlytest for deciding .hich point to plot/

)he update rules for the error on each step may also -e cast into form/ Consider the floating?

point +ersions of the update rules:

ultiplying through -y yields:

.hich is in form/

#sing this ne. bberror__ +alue' ' .ith the ne. test and update e*uations gi+es


52/57


!nteger only ? hence efficient %fast(/

ultiplication -y ; can -e implemented -y left?shift/

)his +ersion limited to slopes in the first octant' /

*. Explain t'e "!'en-#%t'erlan/ line "lippin& al&!rit'$ in /etail. ()%n*+1*, 1+

An#5


53/57


!f .e further restrict the line?dra.ing routine so that it al.ays incrementsxas it plots' it -ecomes

clear that' ha+ing plotted a point at !x"y#' the routine has a se+erely limited range of options as to

.here it may put the nextpoint on the line:

!t may plot the point !x$%"y#' or:

!t may plot the point !x$%"y$%#/

So' .or2ing in thefirst positive octantof the plane' line dra.ing -ecomes a matter of deciding-et.een t.o possi-ilities at each step/

e can dra. a diagram of the situation .hich the plotting program finds itself in ha+ing plotted

!x"y#/

!n plotting !x"y#the line dra.ing routine .ill' in general' -e ma2ing a compromise -et.een .hat

it .ould li2e to dra. and .hat the resolution of the screen actually allo.s it to dra./ #sually theplotted point !x"y#.ill -e in error' the actual' mathematical point on the line .ill not -e

addressa-le on the pi&el grid/ So .e associate an error' ' .ith eachyordinate' the real +alue of

y should -e / )his error .ill range from ?0/5 to $ust under T0/5/

!n mo+ing from x to x$%.e increase the +alue of the true %mathematical( y?ordinate -y an

amount e*ual to the slope of the line' m/ e .ill choose to plot !x$%"y#if the difference -et.een

this ne. +alue andyis less than 0/5/

ther.ise .e .ill plot !x$%"y$%#/ !t should -e clear that -y so doing .e minimise the total error-et.een the mathematical line segment and .hat actually gets dra.n on the display/

)he error resulting from this ne. point can no. -e .ritten -ac2 into ' this .ill allo. us to

repeat the .hole process for the ne&t point along the line' at x$&/



54/57


)he ne. +alue of error can adopt one of t.o possi-le +alues' depending on .hat ne. point isplotted/ !f !x$%"y#is chosen' the ne. +alue of error is gi+en -y:

ther.ise it is:

)his gi+es an algorithm for a DDA .hich a+oids rounding operations' instead using the error

+aria-le to control plotting:

)his still employs floating point +alues/ Consider' ho.e+er' .hat happens if .e multiply across

-oth sides of the plotting test -y and then -y ;:

All *uantities in this ine*uality are no. integral/

Su-stitute for / )he test -ecomes:

)his gi+es an integer-onlytest for deciding .hich point to plot/

)he update rules for the error on each step may also -e cast into form/ Consider the floating?

point +ersions of the update rules:

Dept of CS' CC ,age 5;


55/57


ultiplying through -y yields:

.hich is in form/

#sing this ne. bberror__ +alue' ' .ith the ne. test and update e*uations gi+es


56/57


intersecting lines' -oth aliased and antialiased/ )he pictures ha+e -een magnified to sho. the

effect/

6. Explain Lian& Bar#8y line "lippin& al&!rit'$ in /etail. ()%n*+1+, 1+

Ans:



57/57


Dept of CSE, CEC Page 55

Computer Graphics Q n A's

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Transcript of Computer Graphics Q n A's