Code: C-15                                                                             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 the refresh rate of a picture is 10 frames per second and the size of frames buffer is 1024 1024 then what is time required to access a pixel.

(A) 100 nano seconds.                       (B)  100 micro seconds.

                   (C)  200 nano seconds.                       (D)  1200 nano seconds.                                      

b. Halftoning is a technique used for obtaining ______visual resolution. 

(A) maximum                                       (B)  minimum

(C) increased                                       (D)  spatial

             c.   If the out codes of two end points of line are non zero but their AND operation gives (0000) then the line is

(A) completely invisible.                      (B)  completely visible.

(C)  partially visible.                             (D)  incomplete data.

             d.   The 4  4 matrix represents case of

(A)  translation.                                  (B)  shearing along all axis.

(C)  scaling.                                        (D)  none of the above.     

             e.   Two-principal vanishing point projection occurs when                   

(A) the projection plane intersects exactly two of its principal axes.

(B) The  projection plane is perpendicular to two axes.

(C) the projection plane is perpendicular to one axis.

(D) The projection  plane intersects all the three axis.

             f.    BSP tree represents a

(A) Recursive, hierarchical partitioning.

(B) Recursive, networked partitioning.

(C) Recursive, hierarchical partitioning of n dimensional space into convex subspaces.

(D) Recursive, hierarchical partitioning of n dimensional space into concave subspaces.

             g.   The size of an image of 640  480 pixels at 160 pixels per inch is

(A)  10 inches² (B)  12 inches²

(C)  14 inches² (D)  192 inches²

             h.   We can construct a closed B-spline curve by taking knot values  such that

(A)

(B)

(C)

(D)

             i.    If the scaling factor is  and each line segment in the initiator is replaced with 8 equal length segments at each step then the dimension of the object so obtained is

(A) 2.5                                               (B) 1

(C) 2                                                   (D) 1.5

             j.    Motion path in animation can be given with

(A)  key frame description.                  (B)  a set of spline curves.

(C)  transformation of object shapes.    (D) degrees of freedom.

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

Q.2     a.   What do you mean by interlacing? How is it useful in displaying the frames having (say) 525 scan lines?                                                                  (3)

             b.   How is optical mouse better than mechanical mouse? Describe briefly.                (3)

             c.  Using Cyrus-Beck algorithm clip the line joining P₁(-1, 1) and P₂ (9, 3) in the rectangular window with diagonally opposite vertices (0, 0) and (6, 4).                                                   (10)

Q.3     a.   What do you mean by half toning? Describe briefly.                                            (3)

             b.   Using seed fill algorithm for 4-connected boundary defined region fill the polygon with vertices (2, 2), (2,7), (5, 7) and (5, 2). Given seed as (4, 6). (8)

             c.   Write the circle generation Bresenham’s algorithm for an octant.                          (5)

Q.4     a.   What are the advantages and disadvantages of homogenous co-ordinate system?                (5)

b.   Describe briefly the term ‘affine transformation”.                                                 (4)

             c. Define perspective and parallel projections. Give various types of perspective and parallel projections.                                                                     (7)

  Q.5     a. Compute the composite transformation matrix to perform the following transformations in sequence in 3D:  (i)Translate by (3, 2, 4), (ii) Rotate about x axis by  (iii) Scale by (1.5, -2, 2)  (iv)  Rotate about y axis by .                                                                                                             (8)

             b.   Bezier curves can be considered as a special case of a particular type of B-spline. Give the justification.                                                                 (4)

             c.   Draw a Bezier curve by hand passing through the control points  so that  are collinear.                 (4)

Q.6   a.   Give the transformation steps only for obtaining rotation of a point about

an arbitray axis, the axis not parallel to any of the principal axis.                          (6)

     b.   Describe the CSG method for generating valid solids.                                         (6)

             c.   What  are the different types of sweep methods? Give an example of each.         (4)

Q.7     a.   Write a pseudo code for constructing a BSP tree for a solid.                               (8)

b.   Consider a unit cube with vertices (0, 0, 0), (0, 0, 1), (1, 0, 0), (0, 1, 0),         (1, 1, 0), (0,1, 1), (1, 0, 1) and (1, 1, 1). Compute the transformation matrix with centre of projection at x = -5 and y = 5 and projection done onto plane z = 0.                                                                                      (8)

Q.8     a.   Describe briefly and scan line Z-buffer algorithm.                                                (8)

             b.   Given that vector to the eye is S [1, 1 , 1] and single point light source is located at positive infinity of z axis giving right vector L [0, 0, 1]. Use the phong’s model to find the intensity of light at point P on the plane.                                                           (8)

                   -2x +3y+10z-25 = 0.

                    Given: d =0, K=1, I_a =1, I_l = 10, n = 2, k_s = 0.8, k_a = k_d = 0.15

Q.9     a.   Describe briefly the self-squaring transformations, which can generate fractals.                    (6)

b.   Describe briefly how can we simulate zero acceleration, positive acceleration and deceleration between two key frames an animation.                      (6)

c.  How can we generate real time animation using raster operations?                        (4)