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

CS488/688 Introduction to Computer Graphics 51
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17.7 Ray tracing a paraboloid [Last Used: Spring 2000 Final]
A paraboloid surface is given by the equation z = (x − 1) 2 + 3y 2 . We want to ray-trace this surface.
a) Give a rough sketch of this surface.
b) Write the paraboloid equation as a parametric equation in u and v, that is, as [x(u, v), y(u, v), z(u, v)] T .
c) Given a ray at the origin [0, 0, 0] T and in the direction [1, 0, 1] T , write a parametric equation
for the ray as [x(t), y(t), z(t)] T .
d) Compute the first point of intersection of the ray with the paraboloid. (Hint: this is really a
2D problem.)
e) For ray-tracing, we need a normal at the intersection point above. Compute this normal vector
(you may want to make use of the hint above).
17.8 CSG and Ray Tracing [Last Used: Winter 2013 Final]
In Constructive Solid Geometry (CSG), it is difficult to explicitly represent the boundaries of the
modeled objects. Briefly explain why this isn’t an issue when ray tracing, indicating how the
ray-intersect-scene calculation is performed on a CSG model.
17.9 Recursive Ray Tracing [Last Used: Fall 2002 Final]
You just bought a commerical raytracing package, but you didn’t buy the source code. You’ve been
told that the termination criteria for tracing rays is either (a) to always trace rays to a recursive
depth of 4, or (b) to adaptively terminate based on ray contribution. Describe a scene that can be
used to discern which method is used.
Be specific about the scene itself, and what you would look for in the resulting image to determine
which termination method is used. Draw a sketch of your scene if possible.
17.10 Rays, rays, rays [Last Used: Fall 2010 Final]
For each of the following types of rays, describe the start position of the ray, where they go, and
what they’re used for.