Code: C-15                                                                             Subject: COMPUTER GRAPHICS

Time: 3 Hours                                                                                                     Max. Marks: 100

NOTE: There are 11 Questions in all.

· Question 1 is compulsory and carries 16 marks. Answer to Q. 1. must be written in the space provided for it in the answer book supplied and nowhere else.

· Answer any THREE Questions each from Part I and Part II. Each of these questions carries 14 marks.

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

Q.1       Choose the correct or best alternative in the following:                                           (2x8)

a. Which of the following statements is true?

(A) (B)

(C) (D)

            b.   The perspective projections are classified into 1-point, 2-point and 3-point on

                   the basis of

(A) vanishing points.                            (B)  principal vanishing points.

(C)  centre of projection.                      (D)  principal axes.

             c.   Which of the following is false for Bezier curves?

(A) It passes through all the control points.                                                                      

(B) It passes through first and last control points only.

(C) It lies within the convex hull of the control points.       

(D) The slope at the beginning of the curve is along the line joining the first two control points and slope at the end of the curve is along the line joining the last two control points.

             d.   Non-zero winding number rule is used to

(A) find how many lines are there in clockwise direction in a self    

                          intersecting polygon.                     

                   (B) find how many lines are there in anticlockwise direction in a self  

                          intersecting polygon.

(C) find whether it is possible to unwind a self intersecting polygon.                                   

                   (D) identify the interior regions of a self intersecting polygon.

             e.   ___________ uses set operations to model solid objects.

(A) Swept solids                                (B)  Cubic splines

(C)  CSG models                                (D)  Cubic Bezier curves   

             f.    Mandelbrot set is an example of 

(A) self affine fractals.                         (B)  self similar fractals.

(C)  self inverse fractals.                       (D)  self squaring fractals.

             g.   It is necessary to compute the points for only the following portion of a circle using Bresenhem’s algorithm and the remaining entire circle can be generated by symmetry.

(A)   octant                                          (B)  quadrant

(C)  half                                               (D)  none of these

             h.   In halftone approximations, let pixels grid patterns be used to display an image in 512  512 pixels screen area, then the number of intensity points in the image are

(A) .                              (B) .

(C) .                                 (D)  .

PART I

Answer any THREE Questions. Each question carries 14 marks.

Q.2     a.   Describe beam penetration method of color generation.  What are its advantages and disadvantages over shadow mask method to generate colors?                                                                          (7)

             b.   Derive the necessary equations for circle generation using Bresenhem’s method.                 (7)

Q.3     a.   Clip using Cyrus Beck algorithm.  Given : line with end points A (2, -1) and B (5, 10); and the clipping rectangle with diagonally opposite end points as X (1, 1) and Y (6, 8).                               (10)

             b.   Consider the following two line segments AB and  and the clipping rectangle LMNO:

                   Between Cohen Sutherland and Cyrus Beck, which algorithm will you prefer to clip AB and? Why?                                                                (4)

Q.4           Briefly explain the seed fill algorithm and apply it on a polygon with vertices: (2, 3) (2, 5) (3, 5) (3, 6) (5, 6) (5, 5) (6, 5) (6, 3) (5, 3) (5, 2) (3, 2) (3, 3) (2, 3) and seed S(4, 4).                                  (14)

Q.5           Find the transformation matrix that rotates a pyramid defined by the coordinates A (0, 0, 0), B (1, 0 , 0), C (0, 1, 0) and D (0, 0, 1) by about the line passing through P1 (0, 1, 0) and P2 (0, 2, 1).  Also find the coordinates of the rotated figure.                                                                      (14)

  Q.6     a. Differentiate between the following :

      (i)   parallel and perspective projections.

                   (ii)  DDA algorithm and Bresenhem’s algorithm for line drawing.                     (4+4)

     b. What do you understand by fractal dimension?  Calculate the fractal dimension for the following self similar fractal, after one iteration.

                   Initiator           _________                   Generator

                   (segment length: )                              (segment length: )                                (6)

PART II

Answer any THREE Questions. Each question carries 14 marks.

Q.7           Describe the following methods for visible surface detection:

(i) BSP tree.

(ii) Scan line z-buffer algorithm.                                                        (7+7)

Q.8     a.   Briefly explain the gourand shading model.                                                          (7)

             b.   Derive the matrix for parallel projection onto xy plane.                                        (7)

Q.9     a.   What are B-spline curves?  State three important properties of B-spline curves.  What are the advantages of B-splines over Bezier curves?              (8)

b.   What are uniform, periodic B-splines?  Give an example of such splines.             (6)

Q.10           a.                                                        What do you understand by constructive geometry methods to generate solids?  Explain with the help of examples.                                            (7)

             b.   What are octrees?  How can scaling and rotation be carried out on an object represented by an octree?                                                                (7)

Q.11     Write short notes on (any FOUR):-

(i) Digitizers.

(ii) Half toning.

(iii) Animation.

(iv) Vanishing Points.

(v) Shearing transformations.                                               (3.4 x 4 = 14)