AMIETE – CS (OLD SCHEME)

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 the best alternative in the following:                                 (2 10)

a. The size of frame buffer for a VDU with resolution  with 3 bit plane is   

(A)  bits.                                       (B)  bits.

                   (C) bits.                                    (D)  bits.                                                  

b. The time taken for the display of each scan line for a system having 525 lines / frame and 30 frames are displayed per second is

(A)  seconds.                              (B)  micro seconds.

(C)  milli seconds.                        (D)  nano seconds.

             c.   Which of the points in the following is considered to have two points of intersection with scan lines

(A) 1, 4                                              (B)  2, 3, 5, 6

(C) none of the points                          (D)  all the points

             d.   The location of the third pixel for the line joining the points (0, 0) to (6, 6) using Bresenham’s  algorithm is   

(A) (0, 0).                                          (B)  (1, 1).

(C) (2, 2).                                           (D)  (3, 3).

             e.   The code of the point P in the following is sign bit of                      

(A) (B) 

(C)  (D)  None

             f.    In an Octree each node is labelled as

(A) full, empty                                    (B)  full, partially full

(C)  empty, partially full                        (D)  full, empty, partially full

             g.   The equation of plane is .  On the scan line y = k, the depth of the pixel at  is given by  

(A) (B)

(C)  (D)  None

             h.   The following curve is the blending function given by

(A)

(B)

(C) 

(D) 

             i.    The dimension of a fractal with scaling factor ,  number of segments in the generator 8 is given by 

(A)	1.5	(B)	.66
(C)	2	(D)	3

             j.    To model decreasing speed between the frames of an animation the trigonometric expression used is

(A)  (B)

(C) (D) 

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

Q.2     a.   Write the name of most commonly used locator device.                                      (1)

             b.   Write the integer Bresenham’s algorithm for a lines with slope < 1.                      (4)

             c.   Give the pixel locations of the circle with centre at origin and radius equal to 15 units.  Use Bresenham’s algorithm and give first five pixels.         (5)

             d.   Write Cyrus Beck algorithm for clipping line with respect to a polygon.               (6)

Q.3     a.   Describe sample seed fill algorithm for four connected boundary region.              (3)

             b.   How are codes of points obtained in Cohen-Sutherland line clipping algorithm?                   (2)

             c.   What do you mean by an Octree?  Write an algorithm to display an Octree.        (5)

d.   Describe the following terms with respect to floating horizon algorithm with diagram lower horizon and upper horizon.                                               (6)

Q.4     a.   Describe Pointers algorithm for hidden surface removal.                                      (8)

b.   Derive the following equation for an illumination model .  Where symbols have their own meaning.                               (8)

  Q.5     a. Derive the transformation matrix for reflection about the line y = mx + c, c> 0.                    (6)

             b.   What do you mean by vanishing points?  Give an example of each.                      (5)

c.   If the projector to the plane z = 6 is inclined at an angle .  What will be the co-ordinates of oblique projection of the point (1, 1, 1) on to the plane?                                                  (5)

  Q.6     a.   Give the transformation matrix for inverse of shearing i.e. .            (3)

     b.   What are the boundary conditions for periodic cubic B-splines with consecutive four control points  and .  Give the blending functions also.                                                         (6)

             c.   Bezier curved sections with control points  and  are joined together (at ).  Derive the conditions, in terms of control points for the first order and second order connectivity at .                                                           (7)

Q.7     a.   Using generalized Bresenham’s algorithm give the pixel locations of line joining (1, 1) and (10, 5).  Give first four pixels.                                           (6)

b.   Find the perspective projection of point (11, 12, 13) onto the plane z = 6, when the projection reference point is (0, 0, 1).                                  (10)

Q.8     a.   Give the transformation matrix for an object to double the size of a triangle, keeping co-ordinates of any one vertex fixed.  Give the new        co-ordinates of the vertices also.                                       (8)

             b.   Describe the steps for designing an animation.                                                     (8)

Q.9     a.   Describe B-rep model of solid representation using a set of surface polygons.                    (8)

b.   Briefly explain specular reflection.                                                                       (4)

c. Differentiate between random and raster scan display devices.                            (4)