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

64 CS488/688 Introduction to Computer Graphics
19.15 Window to Viewport Transformation [Last Used: Winter 2009 Final]
After projection, suppose we have a triangle appearing in our window as shown in the following
diagram:
Sketch how this triangle will map to each of the following viewports on our output device (the
large rectangle is the output device, with two of its corners labeled with pixel coordinates; the small
rectangle is the viewport on our output device).
1600,1200 0,0
612,792
0,0
1600,1200
(a) (b) (c)
0,0
19.16 Change of Coordinates [Last Used: Winter 2006 Midterm]
Suppose we have two coordinate frames F w = { ⃗w 1 , ⃗w 2 , O w } and F v = {⃗v 1 , ⃗v 2 , O v } as shown below,
with
√ √ √ √
2 2
2 2
⃗v 1 =
2 ⃗w 1 −
2 ⃗w 2, ⃗v 2 =
2 ⃗w 1 +
2 ⃗w 2, O v = O w + 3 ⃗w 1 + ⃗w 2
⃗v 2
⃗w 2
⃗w 1
⃗v 1
P
O v
O w