Past Midterm and Exam Questions (PDF) - Student.cs.uwaterloo.ca ...

CS488/688 Introduction to Computer Graphics 59
Write a short C function or give a matrix that takes normalized coordinates and outputs
PostScript coordinates.
19.2 Matrix Transformations [Last Used: Winter 2013 Final]
Let T be the matrix
T =
⎡
⎢
⎣
2 0 1
0 1 0
0 0 1
1. Suppose T represents a transformation mapping points specified relative to frame F w =
{w 1 , w 2 , O w } to points specified relative to frame F v = {v 1 , v 2 , O v }. In the figure below, draw
T (P ) where P ’s coordinates relative to F w are P = [1, 1, 1] T . Be sure to label T (P ) in the
figure.
2. Now suppose that T represents a change of coordinates from frame F w to a frame F q =
{q 1 , q 2 , O q }. In the figure below, draw and label the frame elements of F q .
⎤
⎥
⎦
v 2
w 2
P
O v
O w
w 1
v 1
19.3 Change of basis, geometric transformation [Last Used: Winter 1998
Midterm]
In the figure below are two coordinate frames, F W = {w 1 , w 2 , O W } and F V = {v 1 , v 2 , O V } with
v 1 = w 2 , v 2 = w 1 , and O V = O W + v 1 + v 2 (note the relationship between the basis vectors). Both
coordinate frames are orthonormal.
v 1
w 2
v
v
2
w
w 1