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MCS318: Computer Graphics


Revision Questions 31

September 2004



1.

Define ray tracing.

2.

What does backward direction tracing mean.

3.

Explain the following:

(a)

coordinate refence fr
ame and draw a demonstrative labelled example to
support your answer.

(b)

object geometrical specifications, giving example in two
-
dimensional and
three
-
dimensional.

(c)

Write down the OpenGL window command statements which define the
coordinate frame for the scre
en display window for 2
-
dimension and 3
-
dimension.


4.

What is an
input mode
? What is the purpose of the following glut callback functions:

(a)

glutDisplayFunc

(b)


glutKeyboardFunc

(c)

glutMouseFunc

5.

Input procedures are handled as callback functions that interact wi
th the system
software. Such functions specify what actions are to be taken by a program when an
input event occurs. List the three typical input events:

6.

Representations of schemes for solid objects are often divided into two broad
categories: Boundary r
epresentations (B
-
reps) and Space
-
partitioning representations.
Define, giving the difference and example of each of these categories.

7.

There are ten GLUT Regular Polyhendron functions provided; five generating wire
-
frame objects and five which display face
ts fill areas. List any
four
of the five regular
polyhedra and write down their respective wire
-
frame and solid
-
frame glut function.
Sketch each of your polyhedras (where possible).

8.


Name any three Non
-
Polygonal Representation model giving their GLUT fun
ctions
and parameters required.

9.

How is a 3
-
dimensional n inverse rotational matrix obtained?

10.


Prove that the multiplication of transformation matrices for each of the following
sequences is commutative.

(a)

Two successive rotations.

(b)

Two successive translation
s.

(c)

Two successive scalings.

11.

Transformations: Scale, Rotate, Translate

(a)

What are the transformation equations/matrices for scale, rotate
(clockwise vs counterclockwise), and translate? Write your answer in 3
-
D
transformation form.

(b)

E
xpress positions above in

Homogenous coordinates
form

(c)

Apply rotational transformations. If the point P(3,5) and is rotated
through 30
o

about the origin, determine its image when the rotation is (i)
anti
-
clockwise, (ii) clockwise

(d)

Why set up
a sequence of transformations as
ma
trices/composite matrices?
Does it matter in which order you apply the transformations?

Revision Questions

MCS318: Computer Graphics



2

12.

Write down the 4x4 matrix for rotating an object by 90
o

around the z axis.

13.

Draw houseA and houseB, transformed by the appropriate OpenGL commands. The
untransformed

house is below.


glIdentity( );

glTranslate(1, 0, 0);

glRotate(90, 1, 0, 0);

glTranslate(0, 2, 0);

drawHouseA( );

glTranslate(
-
1, 0, 0);

drawHouseB( );

















14.

Show that the composition of two rotations is add
itive by concatenating the matrix
representations for
R

1
) and
R

2
) to obtain


R

1
)
.

R

2
) =
R

1
+ θ
2
)




15.

Derive the following equations for transforming a coordinate point
P

= (x,y) in one
two
-
dimensional Cartesian system to the coordinate values (x',y') in another Cartesian
system that is rotated
counterclockwise by an angle
θ

relative to the first system.
Projecting point P onto each of the four axes and analysing the resulting right
triangles can obtain the transformation equations.


x' = x cosθ + ysin θ

y' = x sinθ + ycos θ


16.

Show that two suc
cessive reflections about either the x
-
axis or the y
-
axis is equivalent
to a single rotation in the xy plane about the coordinate origin.

17.

There are two general methods of 3D viewing projections: Parallel and Perspective.
With a help of a suitable diagram,
describe each of these projection methods.


18.

Write a few notes on the following and show the
OpenGL viewing
-
transformation
function implementation.

(a)

GlMatrixMode

0
1

1

2

3

4

1

2
1

3
1

4

Revision Questions

MCS318: Computer Graphics



3

(b)

GL_MODELVIEW



19.

What is difference between "local illumination model" and "global illumination
m
odel"? Give one use of lighting model.

20.

List the properties of a

light source specification.

21.

OpenGL provides two types of light sources:
directional

and
positional
. Explain each
of these light sources supporting with a sketch diagram.

22.

What do you understa
nd by the following:


(a)

Output primitives

(b)


OpenGL primitive constant

(c)

Output attributes giving citing two appropriate attribute examples to support
your answer.