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Lecture notes of the week: W4

# QS4: Week 4 Survey Questions

📗 Enter your ID (the wisc email ID without @wisc.edu) here: and click (or hit the "Enter" key) 1,2,3,4,5,6,7,8,9,10 2 q4

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📗 Question 0

📗 Question 1

Question 2

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Question 4

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Question 6

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Question 8

📗 Question 9

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📗 [1 points] Which of the following are parameterizations of the line segment from [0, 0] to [1, 1] with the unit parameter u between 0 and 1?

[u, u]
[u2, u2]
[2 * u, 2 * u]
[u, u2]
[Math.sin(u), Math.sin(u)]
None of the above.

📗 [1 points] Which of the following parameterizations trace the curve faster at the beginning (speed is faster at u = 0 than u = 1)? Do not include the ones with constant speed.

📗 Note: the answer [-u2, 0] has speed 0 at the beginning and -2 as the end, and technically -2 is "faster" than 0, so the answer is incorrect.

[Math.sqrt(u), 0]
[Math.log(1 + u), 0]
[-u2, 0]
2, 0]
[-u, 0]
None of the above.

📗 [1 points] Which of the following parameterizations traces the line segment [a * (1 - u) + b * u, 0] where u is the unit parameter from 0 to 1? Choose the ones that work for any values of a and b.

[b * (1 - u) + a * u, 0]
[a + (b - a) * u, 0]
[b + (a - b) * u, 0]
[a + b * u, 0]
[a + b * (1 - u), 0]
None of the above.

📗 [1 points] Which two of the following are endpoints of the polynomial segment [1 + 2 * u + 3 * u2, u]?

[1, 0]
[6, 1]
[6, 0]
[1, 1]
[3, 1]
None of the above.

📗 [1 points] What is the derivative (rate of change) of the quadratic curve segment [1 + u2, u] at [1, 0]?

[0, 1]
[2, 1]
[2, 0]
[0, 0]
[1, 0]
None of the above.

📗 [1 points] What is the point at u = 0.5 from the De Casteljau construction of the quadratic Bezier curve with endpoints [0, 0], [1, 1] and the middle control point [1, 0]?

[0.75, 0.25]
[0.5, 0]
[1, 0.5]
[0.25, 0.75]
[0.5, 0.5]
None of the above.

📗 [1 points] Given a quadratic Bezier curve with endpoints [0, 0], [1, 1] and derivative [0, 1] at the first point, which three of the following points are the control points of the Bezier curve?

📗 Note: not covered during lecture, the answer is [0, 0], [0, 0.5], [1, 1].

[0, 0]
[1, 1]
[0, 0.5]
[0, 1]
[0, 2]
None of the above.

📗 [1 points] Given a cubic Bezier curve with endpoints [0, 0], [1, 1] and derivatives at those points [0, 1] and [1, 0] respectively, which two of the following points are the second and third control points of the Bezier curve?

📗 Note: not covered during lecture, the answer is [0, 1/3], [2/3, 1].

[0, 1/3]
[2/3, 1]
[4/3, 0]
[0, 3]
[-2, 1]
None of the above.

📗 [1 points] Please provide additional comments, questions, or feedback:

📗 [1 points] Why are you submitting this survey?

Did not attend one or both of the lectures this week.
Attended both lectures but missed some questions on TopHat.
Attended the lectures but TopHat did not work.
Want to submit anonymous feedback.
Note: if you selected the third (please also email me) or forth choice, you only have to complete the last question.

Last Updated: September 11, 2025 at 10:55 PM