:'\' ' ~6

Time. J.oo I Irs

Note : Attempt any five questions.

QL

by Explain all the steps in 3D viewing pipeline

t o.f .... ;

' i _-ju....--, "~ ""Jl ! ---;

7)/Dcfi B . . . . ... 2. 1nc czrcr CUrves. DI.SO..LSS thCJr propcrocs aod lurul:ltons

b/Wruu is the rcbtionship among!'t the fo llowing

."'- -.{ 1. : c 4o l ' -:c~ ... rv~ . o . ,)l::: r I l

l .. L'-' )/ ,- {:/) _:) ' l '\).._,' D/ ~ '~ \.!" ... ...... I . I / ~\)v ' '..; ~ ,J ..,.~V'/

J'-l n'-"' fl

~ J ':: I ~ .... ,. ~ #

l 'l \ J

. :

II[ (ICf I

M , M ork 10

.,., ( I (

8

I I ... I

,, .

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L - :::-.~ : .: i~ .. - :-:h.f' ::: . ::h'h~~ ~! : ~.J.n li.nc p(,l ~ !.!(.~ :-~ :i ! t:r: ~ ~.ftit~ ;;~s.o ::. wh)St: ,-~rfl t:c..~ m ihc: ci ~::. '' l s ;:--d : rtX:lwn :!.r~ .sn .. orhd ow: -- - -

.-\( 1. 1). nn.4). C(--1.8). 0(6,7). E(7,3),"F(5,2) 8

I -7 t !1 E-q:J..ain th~ Sutherland Hodgman algorithm for clipping polygons. 6

~~.' L~ th < ; l f ob" ~--- L-. A -;r a.._ uo ,,.. c transOrmall()n matnx .or rO!atlo!! o an ~ea auuu any arbnrary axes, ...... JS

J, par.illel to one of the coordiDalc axes. I 1 ., . f (

b). Fine the transformation matrix for oblique p~ojcction onto the XY pl311ny one JD ctipping algonthm. cy Wl12I do you mean by homogeneous coordinate system w 20 and JD

~ 6 a) PcrfQml a 45' rotation of a triangle A(O,O). B(l,l) and C(5,2) about P(-t.-1)

(2+4)_

4

~ o b) List tbc steps in clipping the following lines using the Cyrus beck line clipping algorithm against a rccungular window "hose coordinates arc (10,10) and (100, 100).

L Pl(-10,-20) and p2(50,40)

b. PJ(70,20) and p

Total No. of Page(s): 3 Roll No .... . ... FOURTH SEMESTER B.E. (ICE)

B.E. END SEM. EXAMINATION, Mal'-2008 IC~214: PRINCIPLES OF COMPUTER GRAPHICS Tim~ : 3:00 fl ro. Mux. MArk o: 70 NOte: AttemPt any FIVE questions. All questions carnJ equnl mnrr<

Assiline suitabls mts.'iin data i nnr . -- 1.

[a] Develop the 'Integer version of .Bresenhom '" l.onr dra11~ algorithm for Unei In thJrd quadrant ... , . ) 51

[b] .A:>er!ve the transformation matrix (i n horJ>ogcneou s ;,_;/ eoordJnotea) to rotate A 30 Obj ect by an Allt:le '1\ AbO \It nn

arbi trAl)' axia parallel to but not colncide.n ,With z-nxis . ([>) (c) Draw the Bezler eurve delintd by thee rol pints!? , 1). (3 . ~ 1 .

(5,0) nnd (6,2). By properly chooa an other ct or control point draw a bezi.er cubic cui"'V such th at the !'ccon 1 c: u rvc

::1 . . is joined smoothly with the t curve. /1) (~) Consider a rectangle the following com er coorclin:.r r . . p, (3,1,3), 2 (3,5,3), Po .(5,5,3) o.nd p, (5,1 ,3} : . .an.d a triangle the follO>!Ing coordinate:

. Tr (4 ,4J , .. T2 (3,3, 1}, To (5,2,1) . , Colour or e recblngle Ia black and tria ngle is r',r" t'lo

Apply y h,idden s urface removal Algorithm "' ~hu,, "'tuh'~ surf cs. . ;,,1

(b) W at is Hermlte Spline? l"ind the coc(licio::t "" . :, ' ,. .. ermite spJlne . . ' ~.

Derive the transformation ma trix for n~ Ocr.liun :1( ~~~ ' .I nbo ut an aroi trary line aa shown in Pis .- 1.

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I ' ' q,'l,~ I ..

(aJ Vc~!or /I ;mull ar1. Jcflltcu as l .' i l k a1:ci 2i+J k. ,\ i ! II ,crlor /, --~~tvr ll. Gi1~ th, ihaltr~nslimua t i n mu1rix. ~(Pcn~1.m Wi~uow ,_. \'iewpon l ran~formution for u P~ n l

\L 5,30) 111 a wmdow. rhe Window descri be~.i cr cubic cun~ sucj1tha1 1hc second curve is j.oind smooth!, with 1hc (j rst l urvc. (h) Ex pl~in thf;![vie~:i n)O pipcl i;;: (C) F ~ ~ l ::~ i :-: !h: ~~~ vf C.mapl.! h.:r gra ptllcs in Engineering icld .

[ 5,5, .:j Q.i . (a) A Pyramid A( I, 1,1), 13(2, 1,1 ), C( I ,2, I j and D( I, I ,2) i:: housed inside a cube of 5 unit length. Ptrfom1 normalized trans formal ion 1n a t:;,i1 ct:ht... Gi v.: 1hc ll':tnsfonn .. d coordin:ucs cJf pyl':: tn;d. (h l

. ' {....

. ll ,,.

'J'ucal No. oj l:'ugc:(s): :J FOURTH SEMESTER B E.. (ICE)

B .E. END SEM. EXAMINATIO , Mo.; 2009 IC-214: COMPUTER GRAPHICS

Time: 3:00 Hrs . Max ~larks 7() I No te: Attempt ANY FNE questions . All questions carnt equal rnorks I 1.

[a] Modify Bresenham's Line drawing a\gonthm 'o that 1t / _.- will produce

/ !) Dashed lin~ - . The d~sh len gth should be independent of slope

/ !!) A line of thickness ~::pl;uls . ,6) (b) Use the midpoint method and symme try cun"dc r.tH>n'

/ to scan convert a parabola y = 1 00x 2 {51

)] Derive the transformation matrix for sco.l!nfl an ol:JcCt

by u scaling factors in a descrip tion 'fJCCifll'd by lhc direction an gles a, 13 and y. \JI

.J [;>:f Thc _coord ina tes of the vcrtic~s of a poi\'J~'"' .trc ~l.uw: ._/ - Ill f"'1g .-1 .

..,, (~,1) -. . ( CI' ,~) B(i;e) ..... , (.'l.,~) " :J t~ . ~, )

L-------;>-'f Ftg - 1 Us ing solid ar~a scan conversion a lgonthm -;how h > v the interior of the polygon is filled . 1-~Briefly explain the viewing pipeline wh1k cli~l''"):''"g .JD. objects on a 2D screen . 1:11

,j91Prove that the multiplication of thccc-d>mc ,-, 10nill transformation matrices for each of I!H folt J\o,;ng sequence of operations is commut ative

.___.,-(Y,Any two s uccessive translations \.,l1) Any two successive rotations a bout dny

rnrHt lin : \1~ ::.v,...._

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3. [,.0Vhat IS the s~q.ucncc of, transformations required to

.,/ chanr,c the positiOn of obJeCt shown 1n F'ig. -2 to Fig.-3 .

1~,7 c. ~ .. )(

l~ig.-2

c~ ; -~ t

Tot-dl No. of Pages: 3 Roll No. __ _

FOURTH SE.MSTR BE (ICE)

END SEMESTER EXAMINATION, May -2011 ICE-214: PRINCIPLE OF COMPUTER GRAPHICS

Time: 3 Hrs. Max. Marks: 70

Note: Question 1 i~ Compulsory and Attempt QIIY FOUR Quest/oM from the rest

QI.

All Questions carry equal marks Assume suitable missing data, if any.

(a) Compute the size of a 1 024X768 image at 480 pixels per inch. (b) 1fan image has a height of 4 inches and an aspect ratio of'!., what

is its width? (c) What are the major adverse side effects of scan conversion? (d) What are the new coordinates of the point P( -4, 2) after the

rotation by 30 about Q( I, 3). (e) Find a normalization transformation from the window whose

lower left corner is at ( 1, 1) and upper right comer is at (5, 4) onto the nonnalized device screen so that aspect ratios are preserved.

(I) Give the transformation matrix for mirror reflection with respect to tl1e Y -Z plane.

(g) Find tl1e transformation for cabinet projections with 8 =30. [7X2]

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Q2. (a) ruur poiniS Po( a, b), 1' ,(20, 50), P1(40, 40). 1'3(70, 6) "'f' available

for drawing a B- pline curve segment. ornpute the values of a, b, c such that Lhe curve s tariS from tho point (2 1, 43) and termi nates with s lope (- !12).

b) Deve lop the integer versio n of Brescnham's circle drawing algorithm fo r c ircle arc in the third quadran!.

(c) What is the Convex Hull property of Bezier curves? How is it satisfied? (6, 4, 4]

~ A cube has its vertices located at A(O, 0, 5), B(S, 0, 5), C{5, 5, 5), D(O, 5, 5), E(O, 0. 0), F(S, 0 ,0), G(S, 5, 0), H(O, 5, 0). The Y axis is vertical and positive z axis is oriented towards the viewer. The cube is viewed from the point (0, I 0, 40). Work out the perspective view of the cube on the XY plane.

Q4.

b) Explain Polygon filling approach through VERTICAL SCANN ING on a given polygon whose vertices are PI (2, 8), 1'2(6, 14), P3 (8, 10), 1'4(4, 2). Give the data structure that describes the edge.

L Construct the Global Edge Table 11. Traverse the Active Edge Table in filling the given

polygon. c) The reflection along the line y = x is equivalent to the reflection

along the X axis fo llowed by counter clockwise rotation by e

(a)

degrees. Find the value of e. (6, 6. 2]

A clipping window ABCD is specified as A(30. 60), 8(70, 60), C(90. 20), D( 1 O, 20). We want to clip two lines P(S, 25) Q(95, 45) and R(2, 45) 5(40, 0) against the window. Use a suitable li~e clipping algorithm to find visi ble portion of the lines. Explam your approach clearly.

(b) D1scuss the nature of blending function used in Bezior curve formu l3tion .

(c) Why arc homogeneous coord inates used for transformation / com putation in Compuler Graphics? [7, 4, 3)

fl5 . (a) What is oblique projection? Provide orne example of oblique

projection. (b) State the reason why we prefer unit x interval or urut y interval

for corresponding s lopes m :S I and m ;:: I in line drawing a lgorithm.

(c) Given points P1 (2, 4, 0), P2 (6, 12, 40) and 1'3 (4, 8, 12) and a view point C{O, 0, -20), determine which points obscure the ~ n / others when viewed from C. [5, 5, 4)

v Write short notes on the followmg (a) Principle Vanishing Point (b) Weighted and Un-Weighted Area Sampling in Anti-Aliasing

(~ Painter Algorithm of Hidden Surface ('a) Weiler Atherton of Polygon clipping

(J Y,X 4J

----Y----

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