Midterm Exam

CS 248: Introduction to Computer Graphics

Pat Hanrahan

Grader: Reid

1. In the following, assume we are working in 2D and that S(a,b) scales by a in x, b in y,; that R(a) rotates by the angle a, and T(t,s) translates t in x and s in y.

1A. (5 points) Which of the following pairs of transforms can be reversed without effecting the result(that is, applied in reverse order)? Write Yes if they can be reversed and No if they cannot.

T(1,2)T(2,3)
- Yes.
S(2,1)R(45)
- No.
R(45)T(1,1)
- No.
R(10)R(20)
- Yes.
S(2,2)R(45)
- Yes.

Scoring:

1 point for each correct answer.

1B. (5 points) Write down a sequence of transformations that has the effect of rotating an object by 45 degrees about the point (1,1).

Step 1: T(-1,-1)
Step 2: R(45)
Step 3: T(1,1)

Scoring:

5 points for the right answer. 2 points for the first two steps.