**UNIVERSITY EXAMINATIONS: 2018/2019**

**EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE IN**

**INFORMATION TECHNOLOGY**

**BIT 2301A: COMPUTER GRAPHICS**

**FULL TIME/PART TIME/DISTANCE LEARNING**

**DATE: APRIL, 2019 TIME: 2 HOURS**

**INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.**

**QUESTION ONE (30 MARKS)**

a) The architecture of a raster-graphics system is partly made up of the components listed below.

Briefly explain the function of the following components and terms as used in image

formation and display in the display device.

i. Display processor

ii. Frame Buffer

iii. Scan Conversion

iv. Video Controller

v. Display Processor Memory

(2 Marks Each)

b) Why are matrix representations used to describe point transformations in computer graphics?

(4 Marks)

c) Describe how to represent three different 2D transformations as matrices. (4 Marks)

d) Explain how to derive a sequence of transformations to achieve the overall effect of

performing a 2D rotation about an arbitrary point. (4 Marks)

e) Consider the following figure:

2010 Paper 4 Question 4

Computer Graphics and Image Processing

(a) Homogeneous coordinates are often used to represent transformations in 3D:

**QUESTION TWO (20 MARKS)
**The most popular technique used in computer animation is the key frame interpolation technique or

in-betweening.

Consider an object with its local origin at an initial position Pin = (Xin,Yin,Zin) at key frame KFin,

which then attains the final position of Pfin =(Xfin, Yfin’ Zfin) at keyframe KFfin.

Assuming that you want one in between frame as in figure (a), using linear interpolation what

is the position of Y(f).

(5 Marks)

b) Now suppose we needed two in-between frames, Fi and Fj as shown in figure (b), Determine

the coordinates of the two in- between frames.

(5 Marks)

c) If we were to extend the above to a total of N frames (including the initial and final key

frames), we would have N-2 in-between frames. Give the equation of the position of any

frame J .

(10 Marks)

Linear Interpolation

The simplest type of interpolation is linear interpolation. In linear interpolation,

the values of a given property is estimated between two known values on a

straight-line basis (hence the term linear). In simpler terms, linear interpolation

takes the sum of the property values in the two key frames and divides by the

number of frames needed to provide as many equally spaced in-between frames

as needed. For example, consider a model P, with a position along the y-axis of

Yi, at the initial key frame Kin. At the final key frame, Kfin, they position has

moved to Yfin. Now, say we want only one in-between frame f. This frame would

be midway between the two key frames, and P would be located midway

between the positions Yi, and Yfin as shown in Fig.9.3.

Fig.9.3: Linearly interpolating the Y position

Mathematically, the position Y(f) at Frame f, is given by

YO = Yin + (Ylin – Yi,J / 2 = + YiJ / 2

Now, suppose we want two in-between frames, fl and f2. The model would

then be defined such that at fly it occupies a position, Y(fl), which is one third

the distance from Yin; and at frame f2, it occupies a position Y(f2), which is two

thirds the distance from Yin.

**QUESTION THREE (20 MARKS)**

a) EXPLAIN 2 (Two) ways that Linear Algebra is used in Computer Graphics discipline.

(4 Marks)

b) OUTLINE the key stages in the processes involved in the production of a 3D full feature

animated movie.

(10 Marks)

c) EXPLAIN ways by which these steps differ between production of animated Movie and

Computer Game development.

(6 Marks)

**QUESTION FOUR (20 MARKS)**

Three-dimensional objects can be grouped together to create structures that define how these models

are transformed and how they relate to one another. Grouping of these models creates structures

called hierarchical structures, because within these structural groupings some objects are always more

dominant than others. The components of the structure are commonly referred to as nodes.

The figure below shows a conceptual snowman. It has the following components; the base, tummy,

and head are of course all spheres. The hands are cylinders, the eyes are disks, and the carrot-shaped

nose is a simple cone.

Using a diagram, DEFINE the hierarchy of the Snowman.

**QUESTION FIVE (20 MARKS)**

a) Briefly DISCUSS each of the following concepts. Clearly explaining its relevance in

computer graphics image formation.

i. Lighting

ii. Shading

iii. Illumination

iv. Ray Tracing

(3 Marks each)

b) Using a flow chart, EXPLAIN the DDA line drawing algorithm