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

12 CS488/688 Introduction to Computer Graphics
5.4 Exact Colour [Last Used: Fall 1990]
Suppose that we are designing a modelling program for a museum that will use images generated
by our software to evaluate architectural and lighting proposals for the interior of a new building,
and that it is particularly important to model accurately the appearance of the paintings that will
hang in the building. Explain why representing object colour by RGB triplets would probably not
be satisfactory.
6 Geometry
6.1 Affine combination [Last Used: Fall 2011 Final]
Which of the following are valid expressions in affine geometry, where P, Q, R are points, ⃗v is a
vector, and B n i (t) = ( n
i) (1 − t) n−i t i .
Expression Valid? Expression Valid? Expression Valid?
(P + Q)/2 2P − Q Q − 2P
P − 2Q + R P − 20⃗v P − 2Q + ⃗v
(1 − t)P + tQ cos 2 (t)P + sin 2 ∑
(t)R
ni=1
Bi n(t)P i
(P + Q)/R R/(P · Q) ⃗v × (P − Q)
6.2 Spaces [Last Used: Winter 2007 Midterm]
Here, in alphabetic order, are the four kinds of spaces we constructed to understand the geometry
of computer graphics:
1. Affine space
2. Cartesian space
3. Euclidean space
4. Vector space
Write them in order so that each space is an extension of the previous one. Between every two
spaces, write down what was added to the first space to get the second one.
Which of these spaces is the simplest one in which we can talk about parallel lines?
Which of these spaces is the simplest one in which we can talk about perpendicular lines?
6.3 Planar Polygon Test [Last Used: ?]
Given a sequence of n points P 1 , . . . , P n in in three dimensions, describe a boolean function
Planar(P 1 , . . . , P n ) that returns true if and only if the points lie in a common plane. If you give
pseudo-code, comment the code to indicate what it is doing.