Flowchart: Alternate Process: MARCH 2010Code: CS40                                                                            Subject: COMPUTER GRAPHICS

Time: 3 Hours                                                                                                     Max. Marks: 100



·      Question 1 is compulsory and carries 28 marks. Answer any FOUR questions from the rest.  Marks are indicated against each question.

·      Parts of a question should be answered at the same place.




             a.  Write the transformation matrix to get top view of an object on the XY plane of the screen.


             b.  Given four control points P1(x1,y1), P2(x2, y2), P3(x3, y3), P4(x4, y4), work out the starting slope of a cubic Bezier curve.


             c.  While performing polygon scan conversion, how do you treat the case when a scan line passes through a vertex of the polygon?


             d.  Define the terms:

                  (i)   foreshortening factor                                                                                                   

                  (ii)  floating Horizon

                  (iii) B-spline curve


             e.  Discuss the relative merits and demerits of Z-buffer hidden surface elimination algorithm over scan line Z-buffer algorithm.


             f.   Describe the diffuse and specular light reflection modelling in computer graphics.


             g. Write short notes on:

                  (i)  half-toning                                  (ii) CSG models                                                (74)


Q.2       a.  Describe the Boundary fill algorithm.


             b.  Using the parametric approach of Cyrus-Beck line clipping algorithm compute the visible portion of the line segment joining P(15, 0) and Q(15, 40) for the window area given by: P0(10,10), P1(20, 10), P2(20, 30) and P3(10,30). Show all the calculations.                                                                       (8+10)


  Q.3     a.  A triangle ABC is given with vertices being A(3, 5), B(7, 5) and C(5, 10). Find the transformation to obtain its reflection about the line y = 4x. Also find the coordinates of the reflected triangle.


             b.  A unit cube located at the origin is rotated about the X-axis by 45 degrees counter clockwise direction and then projected on the z = 0 plane with centre of projection at

                  ( 0, 0, –10 ). Find the matrix transformation of the above projection?                       (8+10)


  Q.4     a.  Using integer Bresenham circle generation algorithm determine the coordinates of the points on the arc of the circle in the 1st octant with centre at (0, 0) having radius 7 units. Show all the calculations.


             b.  Derive the transformation matrix to obtain isometric projection of an object. Use this to obtain the screen coordinates of a rectangular box. Work out XY screen points corresponding to object coordinates A(0, 0, 10), B(0, 20, 10), and C(30, 10, 0)                                                                                 (9+9)


  Q.5     a.  Explain in detail depth-buffer hidden surface removal algorithm. What are its advantages and disadvantages in comparison with scan line z-buffer algorithm?                                                                 


             b.  Describe the method of constructing terrain model as an example of fractals?           (10+8)


  Q.6     a.  Control points for a cubic Bezier curve are given by:

                            p0=(10, 0), p1=(20, 20), p2=(40, 20) and p3=(50, 0). Find the parametric equations of the curve. Draw a rough sketch of the curve.


             b.  Explain briefly how are the vanishing points obtained in perspective projection.


             c.  Discuss the method of choosing the root node of a Binary Space Partitioning Tree. (6+6+6)


  Q.7     a.  Describe in detail the Gouraud shading algorithm. Also state its advantages over the Phong’s shading algorithm.


             b.  State the components of the traditional animation.


             c.  Explain a method of simulating acceleration at the beginning followed by de-acceleration at the end between two given key frames in an animation clip.                                                                    (8+4+6)