Code: C-15                                                                             Subject: COMPUTER GRAPHICS

Time: 3 Hours                                                            June 2006                                          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 a pixel is accessed in 100 nano seconds and the frame buffer is of        640 640 pixels, then the refresh rate is  

 

(A)    30                                                (B)  60

                   (C) 24                                                 (D)  20                                                                

 

b.      Half toning is a technique using ________number of intensity levels

 

(A) maximum                                       (B)  minimum

(C) average                                         (D)  large

            

             c.   For a 8 8 pixel grid where each pixel can to be upto four intensity levels, the total number of overall intensity levels is

                  

(A)    512.                                             (B)  193.

(C) 256.                                              (D)  195

 

             d.   For scan-converting a line, using DDA algorithm and having slope between 45 and - 45, which one is required

 

(A)                         (B) 

(C)                        (D) 

 

             e.   The matrix  defines shearing transformation. When will it represent shearing along x-axis?              

                  

(A)     When q = 0                                 (B)  when p = 0

(C)  when p = 0 = q                            (D)  when  p  0

 

             f.    With respect to the rectangular window (-2, 2) (-2, 8), (3, 2) and (3, 8), what is the outcode of  (-3, 9)? Given outcode format as left, right, bottom, top.

 

(A)     1000                                            (B)  1001

(C)  0001                                            (D)  0000

            

 

             g.   In a 4  4 homogeous transformation, the submatrix  cannot represent

                    

 

(A)     translation.

(B)     shearing.

(C)     rotation.

(D)    reflection.

             h.   A face is called a back face with respect to  if the angle between the normal vector  to the face satisfies

 

(A)    .                                    (B)  does not exist

(C) .                                     (D)

 

             i.    The sequence  where  are complex numbers, C is a fixed complex number gives Mandelbort set. Given C=0, Zn  will converge to 0 if

 

(A)                                          (B)

(C)                                         (D)

             j.    For which of the curves it is easier to compute basis functions.

 

(A)  Bezier curves.                               (B)  open B-spline.

(C)  Uniform B-spline.                         (D) periodic B-spline

 

 

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

 

  Q.2     a.   What do you mean by control dials? How are these used for track balls?            (5)

       

             b.   What do you mean by aliasing? How can we avoid aliasing? Write modified Bresenham’s line drawing algorithm with antialiasing.                    (8)

            

             c.  What are the different filtering methods for antialiasing? Enumerate only.               (3)

 

  Q.3     a.   Using 4 bit code for the nine regions, clip the lines P1 P2 and P3 P4 given below:-                 (8)

                

 

             b.   The following transformations are performed on a triangle in 2 D: scaling along both axes, rotation through an angle about a point (xc, yc) followed by translation. Give the composite matrix for performing these operations in the given order.                                                                              (8)

                  

  Q.4     a.   Define perspective and parallel projection. Give the hierarchy of the plane geometric projections.                                                               (5)

 

             b.   What do you mean by vanishing points? Draw a diagram to show three vanishing points, using 2 D-plane.                                                              (4)

 

             c.   Write Cyrus Beck algorithm for clipping lines with respect to a rectangular region.               (7)

       

  Q.5     a.   In Z-buffer algorithm how do you find the depth of one plane of the polygon? What are the drawbacks of z-buffer algorithm?                                  (6)

 

             b.   With respect to floating horizon algorithm define the following:-

(i)                  Upper horizon.

(ii)                Lower horizon.

(iii)               Function interpolation.                                                                            (6)

 

             c.   Write the matrix for parallel projection onto xy plane. Under what conditions does that matrix represent orthographic parallel projection.           (4)

 

Q.6   a.    Describe briefly Warn model for simulating studio lighting.                                  (5)

       

             b.   Why are hidden-surface detection algorithms needed?                                        (2)

 

             c.   Develop an illumination model for a scene with one light source. Take into account effect of ambient light as well.                                                    (9)

            

  Q.7     a.   What are the main characteristics of a fractal?                                                     (3)   

 

             b.   Derive the formula for the dimension of a fractal.                                                 (3)          

 

             c.   What is Mandelbort set? Describe the construction of the set.                             (7)

 

             d.  In computer graphics, why do we prefer parametric representation of curves?                      (3)

 

  

  Q.8     a.   What do you mean by knot vector? What are various types of knot vectors?       (4)

                  

             b.   Give the general expression for B-spline curve defined by Cox-de-Boor. Give also the characterstics of B-spline curve.                                        (6)

 

             c.   Write the blending functions of cubic Bezier curves. Draw their curves also.                        (6)

 

  Q.9     a.   What do you mean by morphing? What are the rules for equalizing key frames for morphing?                                                                     (6)

 

             b.   Describe various steps for designing on animation sequence.                               (5)

 

             c.  What is an octree? Describe briefly how can an octree be generated for an object.               (5)