Please Note :

1. Make justifiable assumptions where necessary. Trivialising assumptions will attract trivial credit.
2. No credit shall be given w/o correct justifications.

1. Give short answers for the following -
   
   
   1. A'B' is the parallel projection of the line AB onto some plane. When is the length of A'B' = length of AB ?
   2. Give five factors in order of decreasing priority, that influence the rendering speed of a scene.
   3. Give the fundamental difference between Local and Global illumination models.
   4. By looking at the two specular objects kept in the same lighting conditions, can you tell which one has a higher specular exponent? Justify? Why will your method work?
   5. Is Environment mapping a view independent algorithm? Justify.
   6. Can variation of transparency help in achieving a texture? How? Give one example which proves your point.
   7. Give two applications of Degree Elevation.
   8. Enumerate five properties of piecewise bezier spline curves.
2. Justify true/false -
   
   
   1. Gouraud shading will never miss specular highlights completely.
   2. We can not have reflections within reflections in Environment mapping.
   3. B-spline curve will never pass through start and end control points.
   4. In Phong spcular reflection model, angle between halfway vector and surface normal is always half the angle between reflected ray vector and viewing vector.
   5. Intensity discontinuities can occur in Flat Shading, not in Gouraud Shading.
   6. Colour of specular highlight on the object is independent of object colour.
   7. With planar mapping (slide projector effect), there is always one direction in which a pattern will degenerate into stripes.
   8. MIP mapping requires 33% more space to store texture information, than usual texture mapping.
   9. A Z-buffer algorithm can help in rendering transparent objects, but it can not simulate refraction.
3. Give the transformation matrix for scaling a cube by Sx, Sy and Sz along X, Y and Z axis respectively, such that the centroid of the cube stays at same point. Explain, how you obtained the transformation matrix.
4. Given the pixel coordinates of the endpoints of a line segment as (5,15) and (80,25), give the pixel coordinates for the values of x in the interval [35,37] for this line, using Bresenham's line drawing algorithm. Give decision variable's value at all the pixels corresponding to x values in the interval. Also label the selected pixels as NE/N/E wrt to previous one selected, except for the start point in the interval. State and justify any assumptions you made in solving this problem.
5. Equation of a sphere is --
   

   x = r * cos(theta) * cos(phi)
   y = r * sin(theta) * cos(phi)
   z = r * sin(phi)

   where -
   

   theta = [0, 2*PI]
   phi = [-(PI/2), (PI/2)]

   If you polygonalise the sphere by varying theta and phi, then you will have problem of thin triangles at the poles and broader triangles at the equator. How can you polygonalise the sphere so that you get (more or less) equal sized triangles everywhere?
6. You are given the pixels corresponding to a filled square in scanline order. Devise a fast scanline algorithm to obtain the square when sheared by a factor of K along the X direction. Extend your fast solution to handle shearing along Y direction also. Modify/Change your algorithm to handle the case of an arbitrary convex quadrilateral.
7. Model the spray emanating from (coming out of) a typical spray painting gun filled with HOLI color. Neglect the effect of any breeze/wind. Also model the effect of this spray on the objects in the world.
8. Consider the situation when view point and point light source are diametrically opposite to each other and are hidden from each other by the object. What is the effect you see in real life? How will you generate the effect in your scene rendering.
9. Given the control points b0, ... , b4 for a bezier curve of degree 4, find the conditions that lead to middle control point also falling on the curve. Give a solution other than five collinear control points.
10. Describe the difference in appearance you would expect between a Phong illumination model that used (N.H)^n and one that used (R.V)^n .
11. In the rendering pipeline for z-buffer and Gouraud shading, we folow the order "... -> lighting -> viewing transformation -> clipping -> ...". Why should/should not lighting be done before clipping?
12. You are modelling a lawn lit up under sunlight. You have modelled grass leaves consisting of small triangles. What will be your approach, if you have to render the lawn as fast as possible.