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

CS488/688 Introduction to Computer Graphics 69
46. Given an affine transformation T who matrix representation for application to points and
vectors is
⎡ ⎤
2 0 0
⎢ ⎥
M = ⎣ 0 1 0 ⎦ .
0 0 1
Give the unnormalized coordinates resulting from applying T to the normal n = [1 1 0].
Assume M and n are specified relative to a common, orthonormal coordinate frame F .
47. Name two general guidelines for creating 3D models that help ensure proper hidden surface
removal and rendering of the objects.
48. Briefly describe, with any appropriate equations, the algorithm for removing (or “culling”)
backfacing polygons. Assume that the normal points out from the visible side of the polygon.
49. Which of the following polygons is making fun of you? Circle one.
(a) (b) (c) (d)
50. A ray (P, ⃗v) hits a surface S at a point Q, where the normal to S at Q is ˆn. Draw a picture
and give the formula for computing the reflected ray ⃗r emanating from Q.
51. There is one special situation where backfacing polygon removal, as in the part above, is a
reasonable hidden surface removal technique. What types of 3D models must we use in this
case?
52. Describe a situation in which backface culling is insufficient for hidden surface removal, and
a situation in which you might not wish to use backface culling.
53. What is the difference between polling an input device, and sampling an input device?
54. Is the multiplication of two 3D translation matrices commutative? Two scaling matrices?
Two rotation matrices?
55. If traversing a DAG structure applies a matrix M to a point p in a leaf node, what matrix
should be applied to a tangent vector? To a normal vector?
56. Does the basis represented by v x = [1, 0, 0, 0] T , v y = [1/ √ 2, 0, −1/ √ 2, 0] T , v z = [0, −1, 0] T , O v =
[0, 0, 0, 1] represent a right-handed or a left-handed coordinate system?
57. Describe in words or by an equation a cross-ratio, the quantity preserved by a projective
transformation.
58. For lighting calculations, a point x on a surface S is the origin of a normal vector n, a unit
vector l to the light source, and a unit vector v to the viewpoint. For specular reflections and
Phong shading, a unit vector r is reflected away from x in the same plane as l and n, and