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UNIVERSITY OF MAURITIUS

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UNIVERSITY OF MAURITIUS

    UNIVERSITY OF MAURITIUS

    FACULTY OF ENGINEERING

    PAPER NO EXAMINATION DATE

     First Semester

    BECSE/01F/9 BEng (Hons) Computer Thursday

     Science & Engineering 29 November 2001

     Level 3

    SERIES PAPER TIME

    Nov/Dec 2001 Computer Graphics 13.30 15.30

     (CSE 3102)

    EXAMINERS:

    MR R RAMDHANY

    MR A RAMLOWAT

This paper contains SIX (6) Questions. Students are requested to

    answer ANY TWO (2) Questions from Section A and ANY TWO (2) Questions from Section B.

    Each Question is worth 25 marks.

    SECTION A

Answer ANY TWO (2) Questions from this Section

Question 1

    (a) The following diagram shows the organization of a raster system:

     Display-Frame Video Processor Controller Monitor Buffer Memory

    CPU System Display Memory Processor

    System Bus

     I/O Devices Explain briefly the function of the following components in the raster

    system organization:

     Frame Buffer

     Display Processor

     Display Processor Memory

     Video Controller. [4 marks]

    (b) How do raster-scan systems and random-scan systems differ? Which

    one is more commonly used and why? [4 marks]

(c) The goal of any line algorithm is to construct the best approximation of

    an ideal line given the inherent limitations of a raster display.

    (i) What are the line qualities that are considered when evaluating

    a line-drawing algorithm? [4 marks]

    (ii) What technique(s) could be used to optimise the performance of

    a line-drawing algorithm? [4 marks]

(d) Explain how the DDA-line drawing algorithm works.

    Illustrate your answer by calculating using DDA, the intermediate

    points of a line with end points (20, 10) and (25, 20). [7 marks]

    What are the drawbacks of this algorithm? [2 marks]

    Page 1 of 8

    Question 2

    (a) When line segments are scan-converted for display, frame buffer

    positions must be calculated.

     ymaxscreen

    (x,y) scan-lines

    3

    2

    1

    x 0 max

    pixels

    

    ,y) (xmaxmax(0,0) (1,0) (2,0) (x,y) (0,1) (1,1) (2,1) (x,0) (x,1) max(0,2) max

    Addr(x,y) Addr(0,0)

Assuming the frame buffer address for the pixel at (0,0) is given by

    Addr(0,0), derive expressions for the frame-buffer bit address for pixel

    positions,

(i) (x,y)

    (ii) (x+1, y)

    (iii) (x+1, y+1).

    [6 marks]

    (b) What do you understand by the following terms: (i) Run-Length Encoding

    (ii) Cell Encoding?

    [4 marks]

    (Continued on next page)

    Page 2 of 8

    Question 2 (Continued)

    (c) The bresenham midpoint circle algorithm uses a decision parameter p

    to determine the pixel position closest to the circumference of the circle.

    A rough pseudo-code of the midpoint circle algorithm is given below:

    midptcircle(xcentre, ycentre, radius)

     {

    x=0

    y=radius

    plot_points(xcentre,ycentre,x,y) ;

    initialize p ;

    while (x<y) {

     if ( p > 0 ) ++x;

    else{

     ++x;

    y ; --

    }

    if (p<0) p += E;

     else p += NE;

    plot_points(xcentre,ycentre,x,y);

    }

    }

    (i) Derive expressions for the following:

    a. P [3 marks]

    b. E [4 marks]

    c. NE [4 marks]

    (ii) What properties of circles could you use to reduce the computation of

    points on the circular path? Illustrate your answer by writing the

    implementation of the function plotpoints().

    [4 marks]

    Page 3 of 8

Question 3

(a) The Ellipse Midpoint algorithm uses the ellipse function, f(x,y) as a

    decision parameter to determine which pixel to choose for points on

    the elliptical path.

     222222f(x,y) = r + r y rr xyxxy

     y Region1 Q

     r yRegion2

     rxx

    ; We start at (0,r) taking unit steps along the x-axis and compute the y

    decision parameter for Region1 each time.

    ; We switch to unit steps in the y-direction when the slope on the

    elliptical curve is less than 1 (at point Q). The decision parameter for

    Region2 is now used to determine the pixel position.

    (i) Calculating the slope of the ellipse at each unit x-interval is time

    consuming. How can you improve this decision of where exactly to

    change the sampling direction? Show your calculation.

    [4 marks]

    (ii) Derive the decision parameter for Region1.

    [8 marks]

    (b) In scan-line filling, points of intersection of each scan-line with the

    polygon edges are determined and the pixels in between, filled with

    the specified fill color.

    (i) Show how you can use incremental calculation to compute the

    points of intersection of scan-lines along a polygon edge. Derive

    any equations involved.

    [4 marks]

    (Continued on next page)

    Page 4 of 8

Question 3 (Continued)

     B yb

    C

     y c

    E yE

     yDD y AA

    (ii) Sketch the sorted-edge table for the polygon shown above, filled

    using the scan-line filling algorithm. Explain how this

    information is used to scan-convert a polygon.

    [6 marks]

    (iii) Use the Non-Zero Winding Number Rule to identify the interior

    regions of the polygon shown below.

    A D

     C G

     E

     F

     B

    [3 marks]

    Page 5 of 8

    SECTION B

Answer ANY TWO (2) Questions from this Section

Question 4

    (a) Transformation matrices are expressed in homogeneous coordinates.

    (i) Explain the advantages of using homogeneous coordinates.

    [3 marks]

    (ii) Illustrate your answer by obtaining the transformation matrix for

    the following series of two-dimensional transformations:

    ; a translation by [10,20] followed by,

    ; a rotation about the origin given by the non-unit upwards

    orientation vector [4,5], followed by

    [4,5]

    ; a scaling transformation about the origin by scale factor=2 along

    both axes. [7 marks]

    (b) How does the Cohen-Sutherland line clipping algorithm use region

    codes to clip lines against the viewport? Explain all the steps involved

    and illustrate your answer by considering the lines in the figure below:

     P3

     P6

     P5 P 1

     Clipping P 2 window

     P 4[6 marks]

(c) (i) What is the Nyquist Frequency? [2 marks]

     (ii) What is pixel phasing? What graphics problem does it address?

    [3 marks]

    (iii) Describe briefly two other methods which can be used to

    address the same problem. [4 marks]

    Page 6 of 8

null

Question 6

(a) What are the two basic characteristics of fractals? [4 marks]

    (b) Calculate the Fractal dimension D for the following fractal:

     ?

     ?

     ?

    [4 marks]

    (c) To investigate the effect of hotel construction sites on underwater

    marine life, you have been requested by the Ministry of Fisheries to

    build a three-dimensional model of a lagoon. The three-dimensional

    scene should be as realistic as possible and will be used for simulation

    purposes. A simplified 3D model of a lagoon is shown below:

    Sea

    surface

    Fern-corals

    Discuss how you would produce realistic displays of the following:

     (Specify which modeling structure you would use in each case and

    describe methods you would use to generate that structure)

    (i) Sea surface,

    (ii) Fern-corals,

    (iii) Water spray.

    [12 marks]

    (d) Explain the depth buffer algorithm for removing surfaces hidden by

    other opaque surfaces. [5 marks]

    END OF QUESTION PAPER

    Page 8 of 8

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