ALCCS

**NOTE: **

· **Question 1 is compulsory and
carries 28 marks. Answer any FOUR questions from the rest. Marks are indicated against each question.**

· **Parts of a question should be
answered at the same place.**

**Q.1 **

** **a.** **Write the transformation matrix to get top view of an object
on the XY plane of the screen.

** **b.** **Given four control points P_{1}(x_{1},y_{1}),
P_{2}(x_{2}, y_{2}), P_{3}(x_{3}, y_{3}),
P_{4}(x_{4}, y_{4}), work out the starting slope of a
cubic Bezier curve.

c. While performing polygon scan conversion, how
do you treat the case when a scan line passes through a vertex of the polygon?

d. Define the terms:

(i)
foreshortening factor

(ii) floating Horizon

(iii)
B-spline curve

e. Discuss the relative merits and demerits of
Z-buffer hidden surface elimination algorithm over scan line Z-buffer
algorithm.

f. Describe the diffuse and specular light
reflection modelling in computer graphics.

g.
Write short notes on:

(i) half-toning (ii) CSG
models **(7****4)**

**Q.2 **a.** **Describe the Boundary fill algorithm.

** **

b. Using the parametric approach of Cyrus-Beck
line clipping algorithm compute the visible portion of the line segment joining
P(15, 0) and Q(15, 40) for the window area given by: P0(10,10), P1(20, 10),
P2(20, 30) and P3(10,30). Show all the calculations. **(8+10)**

**Q.3** a. A
triangle ABC is given with vertices being A(3, 5), B(7, 5) and C(5, 10). Find
the transformation to obtain its reflection about the line y* = *4*x*.
Also find the coordinates of the reflected triangle.

** **

b. A unit cube located at the origin is rotated
about the X-axis by 45 degrees counter clockwise direction and then projected
on the *z = *0 plane with centre of
projection at

(
0, 0, –10 ). Find the matrix transformation of the above projection? **(8+10)**

** Q.4 **a. Using integer Bresenham circle generation algorithm determine the
coordinates of the points on the arc of the circle in the 1^{st} octant
with centre at (0, 0) having radius 7 units. Show all the calculations.

** **

b. Derive the transformation matrix to obtain
isometric projection of an object. Use this to obtain the screen coordinates of
a rectangular box. Work out XY screen points corresponding to object
coordinates A(0, 0, 10), B(0, 20, 10), and C(30, 10, 0) **(9+9)**

**Q.5** a. Explain
in detail depth-buffer hidden surface removal algorithm. What are its
advantages and disadvantages in comparison with scan line z-buffer algorithm?

b. Describe the method of constructing terrain
model as an example of fractals? **(10+8)**

**Q.6** a. Control
points for a cubic Bezier curve are given by:

** p0**=(10, 0), **p1**=(20, 20), **p2**=(40, 20)
and **p3**=(50, 0). Find the parametric
equations of the curve. Draw a rough sketch of the curve.

b. Explain briefly how are the vanishing points
obtained in perspective projection.

c. Discuss the method of choosing the root node
of a Binary Space Partitioning Tree. **(6+6+6)**

**Q.7** a. Describe
in detail the Gouraud shading algorithm. Also state its advantages over the Phong’s
shading algorithm.

b. State the components of the traditional
animation.

c. Explain a method of simulating acceleration at
the beginning followed by de-acceleration at the end between two given key
frames in an animation clip. **(8+4+6)**