2011...d) Describe Mid-point circle drawing algorithm. 2 + 3 + 4 + 6 8. a) Derive the transformation matrix that rotates an object point θ about the origin. b) Explain the reflection

7302 [ Turn over

Name : ……………………………………………………………

Roll No. : ……………………………………………..…………..

Invigilator's Signature : ………………………………………..

CS/B.TECH(IT)/SEM-7/IT-703A/2011-12

2011

COMPUTER GRAPHICSTime Allotted : 3 Hours Full Marks : 70

The figures in the margin indicate full marks.

Candidates are required to give their answers in their own words asfar as practicable.

GROUP – A

( Multiple Choice Type Questions )

1. Choose the correct alternatives for the following :

10 × 1 = 10

i) After arbitary 2D transformation, a pair of parallel lines

a) become intersecting

b) become coincident

c) remain parallel

d) become circular arcs.


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ii) In Bresenham's circle rasterization algorithm, for the

first quadrant, if ( x, y ) is the current pixel position,

y-coordinate for the next position can be

a) y + 1 b) only y

c) y or y – 1 d) y + 1 or y – 1.

iii) Homogeneous coordinate ( 9, 6, 3, 3 ) is equivalent to

the Cartesian coordinate given by

a) ( 1, 2, 3 ) b) ( 9, 6, 3, 1 )

c) ( 9, 6, 3 ) d) ( 3, 2, 1 ).

iv) A rectangle is drawn at the centre of the display screen.

It is necessary to carry out a zoom-in process so that

the size of the rectangle is doubled and it remains at

the centre of the screen. The sequence of

transformations needed are

a) only scaling

b) scaling & then rotation

c) scaling & then shearing

d) translation, scaling and then translation again.


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v) For an order n Bezier curve with blending function

Jn i ( t ), 0 ≤ i ≤ n, 0 ≤ t ≤ 1,

∑i = 0

n

Jn i ( t ), for any arbitrary value of t in the range

0 to 1 is equal to

a) 0·5 b) 5·0

c) 0·1 d) 1·0.

vi) A 3D object is rotated about the y-axis, followed by

perspective projection of the rotated object on the x – y

plane from a centre of projection on the z-axis. This

sequence of transformations is equivalent to

a) Single point perspective projection

b) Two point perspective projection

c) Three point perspective projection

d) Oblique projection.

vii) In Sutherland-Cohen 2D line clipping, end-point-codes

for a line AB are ( 0101 ) and ( 0001 ). This line is

a) Partially visible b) Totally visible

c) Totally invisible d) None of these.


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viii) For filling a particular polygon, the run-time storage

requirement for the simple seed-fill algorithm, as

compared to the scan-line, seed-fill algorithm is

a) more b) same

c) less d) none of these.

ix) Raster refresh display systems use colour look-up

tables to

a) increase system speed

b) increase display resolution

c) increase number of colour shades

d) decrease bit-plane access time.

x) Two curves are said to be joined with first order

continuity if

a) end point of one curve is the same as starting

point of the other.

b) slopes at the end of first curve and start of the

second curve are equal.

c) curvatures at the end of first curve and start of

second curve are equal

d) both (b) and (c) conditions are true.


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GROUP – B

( Short Answer Type Questions )

Answer any three of the following. 3 × 5 = 15

2. A monochromatic graphics display system has 525 scan

lines with display screen height : width ratio of 9 : 16. Each

pixel is displaceable in 512 shades.

i) How many pixels are displayed on the screen ? 2

ii) What is the picture storage memory size ? 3

3. Changing the sequence of a given set of control points

results in different Bezier curves. Why ?

4. Show that the area of a 2D object after it is transformed

by an arbitrary 2 × 2 transformation matrix is

dependent only on the area of the original object and the

2 × 2 transformation matrix.

5. Write down the seed-fill algorithm to fill an eight-connected

region.

6. a) Is it possible to clip lines against a symmetric octagonal

window using Cohen-Sutherland's approach ? The

octagon is symmetrically placed with respect to the

coordinate axes and all its sides are equal. If your

answer is yes, how ? If it is no, why ? 3

b) Can the end-point-codes as used in regular-window

clipping be extended to Cyrus-Beck 2D window

clipping ? If yes, how ? It not, why ? 2

7. a) Show formally that parallel projection is actually a

special case of perspective projection. 3

b) What is an isometric projection ? 2


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GROUP – C

( Long Answer Type Questions )


8. a) Derive transformation matrix to rotate a 2D object about

origin by angle θ in the CCW direction. 5

b) Derive transformation matrix to reflect a 2D object

about a line y = mx + c. 5

c) Magnify the triangle given by vertices A ( 0, 0 ) , B

( 1, 1 ) and C ( 5, 2 ) to twice its size but keeping

position of vertex C fixed at ( 5, 2 ). 5

9. a) Give the mid-point rasterization algorithm for an ellipse.

8

b) Rasterize the first quadrant of an origin centered ellipse

with major axis 2 * 6 and minor axis 2 * 3. Both are

coincident with the coordinate axes. 7

10. a) Describe the Sutherland-Hodgman polygon clipping

algorithm. 7

b) A regular 2D clipping window has its lower-left and

upper-right corners at ( 100, 10 ) and ( 160, 40 )

respectively. Find visible portion of lines A ( 50, 0 ),

B ( 120, 30 ) and C ( 120, 20 ), D ( 140, 80 ) using

mid-point-subdivision algorithm. 8


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11. a) Derive transformation matrix to rotate a 3D object by an

angle θ ( CCW ) about a line passing through points

P ( x1 , y1 , z1 ), Q ( x2 , y2 , z2 ). 10

b) What is homogeneous coordinate system ? How is it

related to the Cartesian coordinate system. 2 + 3

12. a) Why are cubic polynomials extensively used to generate

space curves ? 3

b) Discuss the advantages and disadvantages of using

degree-2 and degree-4 polynomials for curve fitting. 3

c) Derive the conditions to be satisfied when joining two

Bezier curves with second order continuity at the join.

Discuss geometric interpretation for these conditions. 9

SS-325 [ Turn over

Name : …………………………………………….………………

Roll No. : …………………………………………...……………..

Invigilator’s Signature : ………………………………………..

CS/B.TECH(IT)/SEP.SUPPLE/SEM-7/IT-703A/2012

2012

COMPUTER GRAPHICS Time Allotted : 3 Hours Full Marks : 70


Candidates are required to give their answers in their own words

as far as practicable.

GROUP – A ( Multiple Choice Type Questions )

1. Choose the correct alternatives for any ten of the following : 10 × 1 = 10

i) The slope of the cubic Bezier curve at the start of the curve in controlled by a) first control point b) first two control points c) first three control points d) all four control points.

ii) A projection in which all three foreshortening factors are kept equal is called a) Isometric projection b) Diametric projection c) Trimetric projection d) none of these.

iii) If ( x, y, 0 ) is a point in the homogeneous coordinate system then it represents a) origin in 2D coordinate system b) origin in 3D coordinate system c) a point at infinity d) point ( x, y ) in 2D coordinate system.


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iv) In Bresenham's Circle generation algorithm, if ( x, y ) is the current pixel position, then the y value of the next pixel position is a) y or y + 1 b) y alone c) y + 1 or y – 1 d) y or y – 1.

v) In Cohen-Sutherland line clipping algorithm, if the codes of the two points P & Q are 0101 & 0001 then the line segment joining the points P & Q will be ................. the clipping window. a) totally outside b) partially outside c) totally inside d) none of these.

vi) .................... acts as anode in CRT. a) The phosphorous coating b) The glass panel

c) The deflector d) None of these.

vii) In the inside-outside test of polygon, if the winding number of a point is zero then the point lies ................. the polygon. a) inside b) outside c) on d) as vertex of.

viii) Sutherland-Hodgman algorithm is used for a) line clipping b) point clipping c) polygon clipping d) hybrid clipping.

ix) the blending functions of Bezier curves are a) Splines b) Bernstein polynomials c) Lagrangian polynomials d) Newton polynomials.

x) Z-buffer algorithm is used for a) frame buffer removal b) visible surface detection c) rendering d) animation.


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xi) Refresh rate is a) the rate at which the number of bit planes are

accessed at a given time b) the rate at which the picture is redrawn c) the frequency at which the aliasing takes place d) the frequency at which the contents of the frame

buffer is sent to the display monitor. xii) The Look up table technique ................. the number of

intensity levels. a) decreases b) increases c) removes d) gives no effect on.

GROUP – B ( Short Answer Type Questions )

Answer any three of the following. 3 × 5 = 15 2. Using Bresenham's line drawing algorithm, determine

successive pixel positions along the line path with end points ( 20, 10) and ( 30, 18 ).

3. Describe Bresenham's line generating algorithm. 4. Use the Cohen-Sutherland line clipping algorithm to clip two

lines with end points )45,75(),15,40( 21 pp and

)10,100(),20,70( 43 pp respectively; against a rectangular

window with vertices A ( 50, 10 ), B ( 80, 10 ), C (80, 40 ) and D ( 50, 40 ).

5. Perform a 45° rotation of triangle A ( 0,0 ), B ( 5, 2 ) and C ( 3, 7 ). a) about the origin and b) about P ( –1, –1 ).

6. Derive general parallel projection transformation matrix.

GROUP – C ( Long Answer Type Questions )


7. a) Why do we prefer incremental line drawing algorithm over DDA line drawing algorithm ?

b) What is homogeneous coordinate ? Why is a homogeneous coordinate system needed in transformation matrix ?


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c) How much memory is needed for the frame buffer to store a 640 × 400 display having 16 gray levels ?

d) Describe Mid-point circle drawing algorithm. 2 + 3 + 4 + 6 8. a) Derive the transformation matrix that rotates an object

point θ° about the origin. b) Explain the reflection of a 2D figure on y = mx + c.

Derive its transformation matrix. c) Magnify the triangle with vertices A ( 0,0 ), B ( 1, 1 ) and

C ( 5, 2 ) to twice its size while keeping C ( 5, 2 ) fixed. 5 + 5 + 5 9. a) Explain the term 'control points' in the context of curve

generation. b) Find equation of Bezier curve which passes through

points ( 0 , 0 ) and ( –2, 1 ) and is controlled through points ( 7, 5 ) and ( 2, 0 ).

c) Derive and plot Beizer blending functions for cubic curves ( n = 3 ). 3 + 7 + 5

10. a) Describe Depth-Buffer method of visible surface detection.

b) The pyramid defined by the coordinates A ( 0, 0, 0 ), B ( 1, 0, 0 ), C ( 0, 1, 0 ) and D ( 0, 0, 1) is rotated 45° about line L that has the direction V = J + K and passing through point C ( 0, 1, 0 ). Find the coordinate of the rotated figure.

5 + 10 11. Write short notes on any three of the following : 3 × 5 = 15 a) Window to view port coordinates transformation b) Gourad Shading c) Phong's Shading model d) CMY colour model e) Boundary fill algorithm f) Painter's algorithm g) Virtual reality.

=============

7305 [ Turn over

Name : ……………………………………………………………

Roll No. : ……………………………………………..…………..

Invigilator's Signature : ………………………………………..

CS/B.TECH(IT)/SEM-7/IT-703D/2011-12

2011

DISTRIBUTED COMPUTINGTime Allotted : 3 Hours Full Marks : 70


Candidates are required to give their answers in their own words asfar as practicable.

GROUP – A

( Multiple Choice Type Questions )

1. Choose the correct alternatives for the following :

10 × 1 = 10

i) Processes in distributed system normally communicate

by using

a) Shared data approach

b) Message-Passing approach

c) Both of these

d) None of these.


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ii) Cross-domain is associated with

a) RPC b) LRPC

c) WRPC d) none of these.

iii) What is used to detect deadlock in distributed system ?

a) Chandy-Misra-Hass algorithm

b) Active Time Server Algorithm

c) Ring Algorithm

d) Lamport Algorithm.

iv) Two events are said to be ............... if they are not

related by the happened before relation.

a) transitive b) concurrent

c) causal d) none of these.

v) Light weight RPC is made for

a) cross-domain communication

b) cross-machine communication

c) both (a) and (b)

d) none of these.


7305 3 [ Turn over

vi) Two events are said to be ............ if they are not

related by the happened before relation.

a) Concurrent b) Causal

c) Transitive d) Parallel.

vii) Non-blocking synchronization is implemented by using

the technique

a) polling b) interrupt

c) both (a) and (b) d) none of these.

viii) Process migration is advantageous because

a) it reduces average response time

b) utilizes resource effectively

c) reduces network traffic

d) all of these.

ix) UTC stands for

a) Universal Time for Communication

b) Coordinal Universal Time

c) Unique Time for Communication

d) None of these.

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2011...d) Describe Mid-point circle drawing algorithm. 2 + 3 + 4 + 6 8. a) Derive the transformation matrix that rotates an object point θ about the origin. b) Explain the reflection