When computing the total grade, I followed the syllabus, except for lowering some of the letter grade cutoffs. The reason is that I felt that the class had earned higher grades. The new cutoffs are:

I enjoyed teaching the class, and hope that you enjoyed taking it. Comments about how to improve it are welcome.

I am available in the future, including after you graduate, to talk about any legal ethical topic.

I wish you success in the rest of your time at RPI, and after.

Name, RCSID:

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Rules:

1. You have 180 minutes.
2. You may bring in two 2-sided 8.5"x11" papers with notes.
3. You may not share material with each other during the exam.
4. No collaboration or communication (except with the staff) is allowed.
5. There are 25 questions. Check that your copy of this test has all the pages.

Questions:

1. (2 pts) Put these graphics pipeline components in the correct order:

   1. fragment-shader
   2. primitive-assembly
   3. rasterizer
   4. vertex-shader

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2. (2 pts) Name an advantage and a disadvantage of standards.

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3. (2 pts) If you do not tell OpenGL to do hidden surface removal, and two objects overlap the same pixel, then what color is that pixel?

   1. OpenGL throws an error.
   2. the closer object
   3. the farther object
   4. the first object to be drawn there
   5. the last object to be drawn there

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4. (2 pts) Why can the following not possibly be a 3D Cartesian rotation matrix?

   \(\begin{pmatrix} 1& 0 &1\\1 & 0 &0\\0& 0 &1\end{pmatrix}\)

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5. (2 pts) What is the purpose of vPosition in this line of code?

   var vPositionjs = gl.getAttribLocation( program, "vPosition" );

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6. (2 pts) There is an aliasing problem when raytracing objects that are so small that one ray sent through the center of a pixel might go to the left of the object, and the next ray, through the center of the next pixel, go to its right. Give two ways to modify ray tracing to lessen this problem.

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7. (2 pts) Consider a 2D cubic Bezier curve with control points (0,0), (1,1), (2,2), (3,3). What is the point at t=0.5?

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8. (2 pts) Describe what the curve in the previous question looks like.

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9. (2 pts) Bezier curves do not generally go through the their control points, except for the first and last control points. It would be quite easy to design a curve fitting system so that the curve goes through all the control points. However the CAD community has decided that they don't want this. Why?

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10. (2 pts) When designing a curve with many control points, the CAD community has decided to use a sequence of low degree curves instead of one high degree curve. Give two reasons why.

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11. (2 pts) In a fragment shader, a sampler2D does something more than a simple array lookup like you have in most programming languages. What?

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12. (2 pts) Tell me about view normalization. What is it? What is good about it?

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13. (2 pts) Is ray tracing an object-space or an image-space algorithm?

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14. (2 pts) The last big update in the OpenGL standard removed many things from the standard. Name two things that we've discussed in class that we now have to implement ourselves if we wish to use.

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15. (2 pts) Give two reasons why OpenGl removed many things from the standard.

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16. (2 pts) What rotation does the quaternion k represent?

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17. (2 pts) Consider this 2D homogeneous point: (2,3,4). Translate it by 1 in the x direction. What is the resulting point, in a Cartesian representation?

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18. (2 pts) What is the 3x3 2D homogeneous matrix for a translation by 1 in the x direction?

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19. (2 pts) Here are two possible ways to calculate the color of each pixel of a curved triangle: 1) Compute the color at each vertex of the triangle, and then interpolate the color. 2) Compute the surface normals at the vertices, interpolate the normal at each pixel, and use that to compute the color.

    Method (2) produces more realistic lighting. Give one effect that it can render that (1) cannot.

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20. (2 pts) Describe what bump mapping is, and tell why it is useful.

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21. (2 pts) Compute the projection equations when the viewpoint is at (0,0,0) and the projection plane is 3x+2y+z=4. Use Cartesian coordinates. You do not need to put the result into a matrix form, but simplify your result as much as possible.

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22. (2 pts) Using homogeneous coordinates for spline control points gives the designer an extra tool. What happens to the curve when the designer changes the weight in a homogeneous control point?

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23. (2 pts) What is Constructive Solid Geometry?

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24. (2 pts) Why are the Bresenham line and circle drawing algorithms less useful now?

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25. (2 pts) What texture mapping problem does the mipmap solve?

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End of final exam

No questions from slide sets 9_5, 10_1, 10_2 (we spent enough time on those topics).

1. When you add many images together to blend them, there may be problems: (10_3)
   1. Loss of accuracy if each color has only 8 bits.
   2. You can't do this at all in WebGL.
   3. This requires using a color buffer of at least 4096x4096.
   4. This requires a stencil buffer.
   5. This requires that the A component be set to 0.0.
2. Fog has been removed from OpenGL, and is not in WebGL, because: (10_3)
   1. The several possible fog factors (linear, exponential, gaussian) were too confusing.
   2. With cleaner air, we no longer want to model smog.
   3. It executed too slowly.
   4. Removing it simplified the standard, and anyway you can implement it yourself.
   5. It wasn't removed; it's still part of WebGL.
3. What does sampler2D do? (10_4)
   1. Return a sample random variable from a probability distribution.
   2. Return one specific texel from a texture map.
   3. Return a point on a bezier curve by interpolating control points.
   4. Interpoint a texture value from nearby texels.
   5. Compute a phong-shaded color.
4. Rendering a scene by computing which pixels are colored by each object is called (12_5)
   1. Image space approach
   2. Modelview space approach
   3. Object space approach
   4. Pixel space approach
   5. Viewport space approach
5. Rendering a scene by computing which objects are behind each pixel is called (12_5)
   1. Image space approach
   2. Modelview space approach
   3. Object space approach
   4. Pixel space approach
   5. Viewport space approach
6. Cohen-Sutherland clipping (13_1)
   1. Clips faces fast by doing concave faces properly.
   2. Clips faces fast by normalizing the projection first.
   3. Clips lines fast by eliminating many simple cases quickly.
   4. Clips lines fast by using the fact the current CPUs do division fast.
   5. Clips textures fast with a mipmap.
7. View normalization (13_1)
   1. Makes the clip region into a cube but changes object cubes into parallelepipeds.
   2. Preserves angles and distances.
   3. Preserves angles but not distances.
   4. Preserves distances but not angles.
   5. Was obsoleted by fast CPUs.
8. About polygon clipping: (13_2)
   1. A polygon might gain vertices.
   2. A polygon might gain area.
   3. If a polygon's vertices are all outside the clip region, then it may be deleted.
   4. Using a 6-stage pipeline keeps the latency the same.
   5. Concave polygons become convex.
9. From his profits from SGI, Netscape, and other startups, Jim Clark bought the world's XXX largest yacht.
   1. 1st
   2. 2nd
   3. 3rd
   4. 4th
   5. 5th
10. Which hidden surface algorithm sorts objects back-to-front? (13_2)
    1. BSP tree
    2. depth (Z) buffer
    3. image space
    4. painter's
    5. scan line
11. Which hidden surface algorithm preprocesses objects into a tree so that you can change the viewpoint and then render by traversing the tree in a different order? (13_2)
    1. BSP tree
    2. depth (Z) buffer
    3. image space
    4. painter's
    5. scan line
12. Which hidden surface algorithm might send its output straight to a display like a CRT w/o ever storing the whole image? (13_2)
    1. BSP tree
    2. depth (Z) buffer
    3. image space
    4. painter's
    5. scan line
13. Some colors that you can see on your display cannot be printed, and vv. Why? (13_4)
    1. Purple is not a pure spectral color.
    2. The UV emitted by the display fades the printer paper.
    3. The display and printer's gamuts don't match.
    4. The printer has 4 inks but the display only 3 primaries.
    5. There's no such thing as a standard display - different manufacturers have different notions of red.