Computer Graphics Algorithms Quiz 1 Study Questions

William Shoaff

Notes on studying and answering tests (with thanks to Dr. Kaner):

• You may not use any reference materials during the test (closed book test).
• I recommend that you study with one or more partners. 3-6 people is a good sized group. 15 is too many.
• I strongly recommend that you read the questions carefully before the test, and that you attempt an answer to each one. AFTER you have tried your own answers, compare notes with your friends.
• Working with others will help you discover and work through ambiguities before you take the test. If a question is unclear, send me a note before the test. If you tell me early enough, I can fix it. If a question takes too long to answer, send me a note about that too.
• When you write the test, keep in mind that I am reading your answer with the goal of finding reasons to give you points:
  • If the question contains multiple parts, be sure to give me a separate answer for each part.
  • If a question asks about “some”, that means at least two. I normally expect three items in response to a “some”. Similarly if the question asks for a list, it is probably expecting a list of at least three.
  • Be aware that different words in questions have different meanings. For example, each of the following words calls for a different answer: identify, list, define, describe, explain, compare, contrast. If I ask you to list and describe some things, give me a brief identification (such as a name) of each and then a description for each one.
  • If you find it hard to define or describe something, try writing your answer around an example.
  • If you are asked to describe the relationship among things, you might find it easiest to work from a chart or a picture. You are not required to use a diagram or chart (unless I ask for one), but feel free to use one if it will help you get across your answer.
  • If I ask you to describe or define something that is primarily visual (such as a table or a graph), your answer will probably be easier to write and understand if you draw an example of what you are defining or describing.
• The test is time-limited 75 minutes. Plan to spend no more than 5 minutes on any definition, no more than 10 minutes on any short answer, and no more than 15 minutes on any long answer. Spend less on most answers. Suppose the test has 4 definitions (20 points), 2 short answers (20 points), and 3 long answers (60 points). You should plan to spend, on average, about 3 minutes per definition, about 8 minutes per short answer, and about 12 minutes per long answer (total = 64 minutes). Use the remaining 11 minutes to check your work.
• Pick the order of your answers. If you spend too long on definitions, start writing your long answers first. If you are nervous, start with the questions you find easiest to answer.
• Be aware of some factors that, in general, bias markers. These are generalizations, based on research results. I try, of course, to be unbiased, but it's a good idea to keep these in mind with ANY grader for ANY exam:
• Exams that are hard to read tend to get lower grades. Suggestions: Write in high contrast ink (such as black, medium). Write in fairly large letters. Skip every second line. Don't write on the back of the page. If your writing is illegible, print.
• Answers that are well-organized tend to be more credible. Suggestions: If the question has multiple parts, start each part on a new line, and identify each part at its start. In a list, start each list item on a new line maybe bullet the list.
• Don't answer what has not been asked. For example, if I ask you to define one thing, don't define that and then give me the definition of something related to it. If you do, (a) I won't give you extra credit, (b) I'll think that you don't know the difference between the two things, and (c) if you make a mistake, I'll take off points.

Study Questions

(This is not complete at the moment: Thursday, February 7, 2002, 6:30 pm)

1.

Define ``model space''

2.

Define ``world space''

3.

Define ``view space''

4.

Show the general 3 dimensional translation matrix and use it to translate the unit cube [vertices (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,1,1), (1,1,1), (1,0,1), (0,0,1)] along the direction vector $\langle2,\,3,\,-4\rangle$.

5.

Show the general 3 dimensional scale matrix and use it to scale the unit cube [vertices (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,1,1), (1,1,1), (1,0,1), (0,0,1)] by factors S_x=2, S_y=3, and S_z=-4 in x, y, and z, respectively.

6.

Show how to use a 3 dimensional matrix to rotate the unit cube [vertices (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,1,1), (1,1,1), (1,0,1), (0,0,1)] about the axis defined by vector $\langle 1, 1, 1 \rangle$.

7.

Given an eye point at e=(3, 0, 0) a look-at point a=(3, -1, 0) and an up-vector $\vec{v}_{\mbox{up}}=\langle 1, 0, 0\rangle$ determine the view space coordinates of the following world space points. 

• (3,0,0)
• (3,-1,0)
• (4,0,0)
• (4,-1,1)
• (0,0,0)

8.

Construct the view transformation matrix for question 7 and show that it maps the world points given in the problem to the view points you gave as an answer to question 7.

9.

Find a representation of the achromatic color line from black (0,0,0) to white (1,1,1) in RGB color space.

10.

Find a representation of the chromatic color line from cyan (0,1,1) to yellow (1,1,0) in RGB color space.

11.

Using the following simplified illumination model:

$$I=k_aI_a+I_p[k_d(\vec{N}\cdot \vec{L})+ k_s(\vec{R}\cdot \vec{V})]$$

answer the following questions.

• What parameter would you vary from midnight on a new moon to noon? How would that parameter vary? State assumptions you may need to make.
• What parameter would you vary as you use a rheostat to change the intensity of a single light bulb hanging in a room from off to on? How would that parameter vary? State assumptions you may need to make.

12.

Find the parametric equation (parameters s and t) for the bi-linear surface defined by points P₀=(0,0,0), P₁=(1,0,0), P₂=(1,1,1), and P₃=(0,1,0). Find point on the surface at s=0.75 and t=0.25.