Code: AC15                                                                            Subject: COMPUTER GRAPHICS

Time: 3 Hours                                                                                                     Max. Marks: 100

NOTE: There are 9 Questions in all.

· Question 1 is compulsory and carries 20 marks. Answer to Q. 1. must be written in the space provided for it in the answer book supplied and nowhere else.

· Out of the remaining EIGHT Questions answer any FIVE Questions. Each question carries 16 marks.

· Any required data not explicitly given, may be suitably assumed and stated.

Q.1       Choose the correct or best alternative in the following:                                         (2x10)

a. If it takes 50 microseconds to display a scan line and 40 frames are displayed per second each frame having k scan lines then the value of k is    

(A) 400                                              (B)  500

                   (C) 600                                               (D)  700                                                              

b.

Which of the points in the following are considered to have one point of intersection 

(A) 1, 4                                              

(B)  2, 3, 5, 6

(C) None                                           

(D)  All

             c.   The Cyrus-Beck algorithm require the region to be

(A) Convex                                        (B)  Concave

(C) Open                                            (D)  None

             d.   If an area is represented by 4096 pixels then octree has k levels, where k is    

(A) 8                                                  (B)  6

(C) 4                                                  (D)  2

             e.   Cubic Bezier curve has __________ blending functions

(A) 1                                                  (B)  2

(C)  3                                                  (D)  4

             f.    Direction of projection is required for

(A) Parallel projection                        (B)  Perspective projection

(C)  Both (A) & (B) (D)  None

g.   The dimension of the fractal with

                   is 

(A) 3                                                  (B)  2.5

(C)  1.5                                               (D)  None

             h.   Which of the following function is best as attenuation function?

(A) (B)

(C)  (D)  None

             i.    A B-spline curve has (n+1) control points, then it will have _________ blending functions.

(A)	n	(B)	n + 1
(C)	n + 2	(D)	n – 1

             j.    Z Buffer algorithm is

(A)  Image space method                     (B)  Object space method

(C)  scan conversion method                (D)  None

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

Q.2     a.   Describe briefly physical interactive device tablets.                                              (3)

             b.   Describe the scan line seed fill algorithm.                                                             (7)

             c.   Give the advantage and disadvantages of z-Buffer visible surface algorithm.                         (6)

Q.3     a.   Explain Binary Space Partitioning tree method.                                                   (7)

             b.   Derive the intensity equations for Phong’s shading model.  How is it different from Gouraud model?                                                                       (8)

             c.   Give the homogenous co-ordinate for a point (2, 3, 4) in 3D.                              (1)

Q.4     a.   Give the technique for drawing octree.  (5)

b.   Using Cyrus Beck algorithm find the line visible in the rectangular window (0, 0), (0, 6), (8, 0), (8, 6).  The line end points are , .   (6)

             c.   What is a light pen?  How does it work?                                                             (5)

  Q.5     a. Derive the basis matrix for cubic Bezier curve.                                                    (6)

             b.   Give the general expression for B-spline curves defined by Cox-de-Boor.           (5)

c.   Give advantages of homogenous co-ordinates.  What are its disadvantages?        (5)

  Q.6     a.    What are various types of projections?  Derive the transformation matrix for a typical perspective projection.                                                                                                                         (8)

     b.   Derive the transformation matrix for shearing operation along the line        y = k, k > 0.                   (4)

c. What is the perspective projection of line joining (–1, –1, –10) and

                                                                       (2, –2, 0) onto plane z = –5.                             (4)

Q.7     a.   Show that rotation is commutative in 2D.                                                            (3)

b.   Write DDA algorithm for drawing a line.                                                             (5)

             c.   What do you mean by fractal?  Give an example.  How do we compute the dimension of a fractal?  Give an example.                                              (8)

Q.8     a.   Derive the floating horizon algorithm.    (10)

             b.   Derive the expression for specular reflection.                                                      (6)

Q.9     a.   Briefly explain the following B-splines

                   (i)   Uniform, periodic

                   (ii)  Cubic, periodic

                   (iii) Open, uniform

                   (iv) Non-uniform                                                                                                (8)

b.   Describe Cyrus-Beck line clipping algorithm.                                                      (8)