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GRADE:

Final Exam -Computer Graphics (ECSE-4750) - Spring 2005 - RPI

1. (1 pt)) Does projection preserve straight lines?
   
   
   
   
2. (1 pt)) Does projection preserve angles?
   
   
   
   
3. (3 pt)) Here is a 2D transformations question that will take some thinking. I want to move an object as follows:
   1. First, translate by 2 in X.
   2. Then rotate by 180 degrees about the origin.
   3. Then translate by 2 in Y.
   4. Than rotate by another 180 degrees about the origin.

   These 4 combined operations could be simplified into one translation followed by one rotation about the origin. What would this translation and rotation be?
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

4. (4 pt)) Compute the 4x4 homogeneous transformation matrix to translate and uniformly scale a volume with corners (1,2,3) and (4,4,4) to be centered in a cube with corners (0,0,0) and (1,1,1), and to be as large as possible.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
5. (2 pt)) Can Gouraud shading produce a highlight in the interior of a face? Why (not)?
   
   
   
   
   
   
   
   
6. (2 pt)) Can the standard OpenGL pipeline easily handle light scattering from object to object? Why (not)?
   
   
   
   
   
   
   
   
   
   
   
   
7. (1 pt)) Can the rendering equation handle light scattering from object to object?
   
   
   
   
8. (2 pt)) How can a piece of red plastic look white when the light glances off it, but look red when the light hits it straight on? In both cases, the incident light is white.
   
   
   
   
   
   
   
   
   
   
   
   
9. (1 pt)) Find a normal vector to the plane thru the 3 points: (0,0,0), (1,1,1), (3,3,3).
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
10. (1 pt)) Why does OpenGL requires you explicitly to enable shading, instead of having it on all the time?
    
    
    
    
    
    
    
    
11. (2 pt)) Normalize the following vector: (3,4,0).
    
    
    
    
    
    
    
    
    
    
12. (1 pt)) How can you use successive applications of XOR to swap the numbers in 2 different registers?
    
    
    
    
    
    
    
    
    
    
13. (1 pt)) Cohen-Sutherland clipping is efficient when most of the input lines have what property?
    
    
    
    
    
    
    
    
    
    
    
    
14. (2 pt)) Find the intersection point between the plane x+y+2z=1 and the line x=y=z=t (t is a parameter).
    
    
    
    
    
    
    
    
    
    
    
    
15. (1 pt)) What is the Mach band effect?
    
    
    
    
    
    
    
    
16. (2 pt)) What is the backward mapping problem in texture mapping?
    
    
    
    
    
    
    
    
17. (1 pt)) What is a big problem with the painters algorithm?
    
    
    
    
    
    
    
    
18. (1 pt)) When is Binary Space Partitioning useful?
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
19. (3 pt)) Do the Bresenham circle algorithm for a circle of radius 12.
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
20. (1 pt)) What property of the eye allows us to represent a color with 3 values?
    
    
    
    
    
    
    
    
21. (4 pt)) Give 4 reasons why color printers have black ink, even though printing cyan, magenta, and yellow on top of each other produces a form of black.
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
22. (1 pt)) Gamma describes what property of a CRT?
    
    
    
    
    
    
23. (3 pt)) Give the relative advantages and disadvantages of explicit, implicit, and parametric curves.
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
24. (3 pt)) Transform this parametric curve into an implicit one. It will take some creative thinking.

    x = 2t/(t²+1)
    
    y = (t²-1) /(t²+1)
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    

25. (2 pt)) The figure below shows two examples of spline curves, each with one joint, marked by an arrow. What degree of continuity is there at each joint? The choices are C-1, C0, C1, and C2.

    
    
    
    
    
    
    
    
    

26. (2 pt)) What is local control? Do CAD designers like it or hate it?
    
    
    
    
    
    
    
    
    
    
27. (2 pt)) Interpolate a quadratic explicit polynomial through these points: (0,0), (1,0), (2,2).
    
    
    
    
    
    
    
    
    

    Total: 50