Structured Exercises

8/2/2019 Structured Exercises

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COMPUTER GRAPHICS

Structured Questions

Computer Graphics

suraj

4/20/2012


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Q1

(a) What are homogeneous coordinates and why do we express coordinates inhomogeneous form in Computer Graphics?

[1 + 2 marks](b) A pyramid has the following coordinates: A(3,2,1), B(1,2,1), C(1,2,3) and D(1,3,1).(i) Graphically represent the pyramid on a diagram.

[2 marks]

(ii) What is the matrix for such a transformation?

[1 mark]

(iii) Determine the coordinates of the transformed pyramid.

[1 mark]

(c) The initial pyramid, with coordinates: A(3,2,1), B(1,2,1), C(1,2,3) and D(1,3,1) is to berotated by 30 degrees clockwise about the line with endpoints (-2, -2, 5) and (8, 8, 5).(i) What sequence of operations is required for this? Write it down in the order in

which the operations should be performed. [3 marks]

(ii) Write down the matrix for each transformation and combine the transformationsto form only one transformation matrix.

[7 marks]

(iii) Determine the coordinates of the pyramid after the rotation.

[3 marks]

Q2

(a) A drawing package uses scan conversion algorithms to display a number of primitiveshapes. The implementation of the algorithms must be computationally efficient.The shapes must not have any visual irregularities.Your answers to each section should include a diagram where appropriate.

(i) Two straight lines are drawn using a scan conversion algorithm. One has agradient of 0; the other has a gradient of 1. Both lines are drawn using 20pixels. Explain why the two lines appear to have different intensities andprovide TWO mechanisms by which this effect can be eliminated.

[2 + 2 + 2 marks]


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(ii) A quarter circle of Radius R is scan converted by incrementing the x coordinatein unit steps and calculating and rounding the y coordinate. Explain twodrawbacks of this scan conversion approach.

[2 marks]

(iii) Given that the pixel at co-ordinates (x, y) lies on a circle centred at (0, 0), usingconsiderations of symmetry state which other pixel co-ordinate points areknown to lie on the circle.

[2 marks]

Q3

Given in figure 4.1 is a 2D house-shaped object and a homogeneous transformation matrixM where


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Q4

Q5

Q6

(A)Explain the functioning of Liquid Crystal Displays (LCD). Give two advantages and twodisadvantages of LCDs over CRTs. [6 marks]

(B)Discuss the advantages and disadvantages of a vector system over a raster system.[5marks]

(C) Explain the functioning of any type of touch panel which is used as an input device.


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Q7

(a) Explain the DDA algorithm to plot a line. Discuss the disadvantages of the DDA

algorithm. [6 marks]

(b) Derive the midpoint circle drawing algorithm. [7 marks](c) Explain the steps involved in the scan-line algorithm to fill an area enclosed by a

polygon of any shape. [7 marks]

Q8

(a) Give the matrices for translation and scaling in three dimensions. Using the abovematrices, derive the matrix for a scaling about a fixed point (xf,yf,zf). [4 marks]

(b) Give the equations for rotations about the z-axis and hence derive the correspondingequations for the x and the y axes and hence write the corresponding matrices. [5marks]

(c) Explain the steps involved to obtain a view of a graphical object from an arbitrary pointin a three dimensional co-ordinate system. [6 marks]

(d) What do you understand by the term view volume? Discuss how you can transform theview volume for a perspective projection to allow for easier clipping. [5 marks]

Q9

(a) Historically, the CRT is a very important display device though its use is fading now.What do you understand by the following terms linked to CRTs?(i) Shadow mask; [2 marks]

(ii) Aspect ratio; [1 mark]

(iii) Persistence; [2 marks]

(iv) Random Scan. [2 marks](b) People are now shifting from CRTs to LCDs. Why is this so? [5 marks](c) What do you understand by the following terms related to LCDs?

(i) Reflective LCDs; [2 marks]

(ii) Backlit LCDs; [2 marks]

(iii) Active Matrix LCDs. [3 marks](d) Explain the operation of a plasma panel and how it produces colour.

[6 marks]


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Q10

(a) One of the simplest line drawing algorithms is the DDA. Derive this algorithm from the

line equation : y = mx + c. (m: gradient, c: y-intercept).[5 marks]

(b)

The basic circle algorithm is : x2

+ y2

= r2. One of the drawbacks of this approach is

considerable computation at each step.(i) What is the other major problem? Illustrate your answer with an example. [3 marks](ii) How can this problem be reduced? [2 marks]

Derive the Midpoint circle algorithm. [8 marks]

Q11

(a) With the aid of suitable diagrams explain the flood-fill algorithm. [5 marks](b) Devise a method to determine whether a line is completely inside, outside or partly

inside a rectangular area. [8 marks]

(c) Explain the meaning of the term clipping. Discuss how you can clip a solid area. [8marks]

(d) Explain the midpoint subdivision method used for clipping lines.[4 marks]


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Q12


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Q13


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Q14


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Q15


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Q16


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Q17


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Q18

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Structured Exercises