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

CS488/688 Introduction to Computer Graphics 23
Describe the ray tracing process discussed in the paragraph above on a ray (p, ⃗v) as it is traced
in this scene. Assume that the transformed ray strikes the simple primitive at point q and that the
primitive has normal ˆn at q, where both q and ˆn are specified relative to the modeling coordinates
of the simple primitive.
Be sure to note what geometric entities get transformed and what transformation they get
transformed by, what ray is used in the object intersection calculation, and what geometric surface
information is used in the actual shading calculation.
9.7 Ray Tracing and Hierarchical Transformations [Last Used: Winter 2000
Midterm]
Suppose you are given the following parameters for viewing a scene relative to a left handed world
frame:
View direction: (0, -3, 4)
Up vector: (0, 1, 0)
Eye point: (0, 10, -10)
Field of view: 90 degrees
a) Define a left handed orthonormal view frame with respect to the world frame. The z-axis should
point in the view direction, the y-axis should be in the same plane as the view direction and
the up vector, and the origin should be at the eye point.
b) Give a change of basis matrix from coordinates relative to the view frame to coordinates relative
to the world frame.
c) Suppose you are given the following DAG. Transformation matrices V, M, and L represent
change of basis transformations from child space to parent space. We have found a ray-object
intersection point and normal in model space and wish to perform a lighting calculation in
light space. Indicate the required transformation to convert E V , P M and N M into light space
(fill in the blanks below).
World Space
V M L
View Space Model Space Light Space
EV
P M
E
=
L
EV
N M
P
=
L
P M
N =
L
N M
?
?
?
9.8 Hierarchical Transformations [Last Used: Winter 2006 Final]
Suppose you are given the following two-dimensional CSG scene hierarchy