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

CS488/688 Introduction to Computer Graphics 29
where I(a, b) is the final itensity of the pixel, and a and b represent distances along the ray to the
nearest and farthest voxels of the volume, respectively. Assuming we collect samples of the volume
along the ray from i = 1 near the viewer to i = n, giving a voxel intensity I i and opacity α i at each
sample:
a) Write an equation approximating the integral I in terms of the samples I i and α i , for i =
1, . . . , n.
b) Assuming sample i = 1 is nearest the viewer, why is summing the equation from “back to
front” (from i = n to i = 1) fast to evaluate?
c) Why could summing the equation from “front to back” (from i = 1 to i = n) allow an even
faster approximation of I than in part (b)?
d) Given a light source L, if we want to compute an illumination equation for each I i , what
vector should we use as a normal in the equations? Precomputing this vector for all voxels
can save rendering time; however, what is the main disadvantage of precomputing this vector?
e) If we don’t precompute the normal vector described in (e) above, in a simple, unoptimized
implementation of volume rendering, how many evaluations of the illumination equation typically
contribute to each sample I i on the ray
– for Gouraud-style lighting?
– for Phong-style lighting?
f) If I i is computed by interpolating the voxel intensities in the volume, nearest neighbour and
trilinear interpolation are two possible methods. Give an advantage for each method.
g) For rendering purpoess, storing a volume as a large 3D array makes inefficient use of cache
memory. Suggest a better storage method and briefly describe why it is more efficient.
13.6 Bounding Boxes [Last Used: Fall 2000 Midterm]
Bounding boxes are one method of increasing the speed of a ray tracer. Typically, the bounding
boxes are aligned with the coordinate axes.
1. Discuss the benefits/costs of axis aligned bounding boxes vs bounding boxes that are not axis
aligned.
2. Discuss the benefits/costs of using bounding spheres instead of bounding boxes.
14 Perspective
14.1 Perspective Matrix [Last Used: ?]
(a) Give the equations for the clipped 3-D coordinates (x1 ′ , y1 ′ , z1 ′ ) and (x2 ′ , y2 ′ , z2 ′ ) in terms
of the unclipped 3-D homogeneous coordinates (x1, y1, z1, 1) and (x2, y2, z2, 1) plus the two
clipping parameters α1 and α2 that are computed by the clipper. You may assume that
α1 < α2.