ECS 175 OPEN BOOK (and open notes) Final Exam. Sat. December 18, 1999
1. Ray Tracing a sphere (9 points)
A sphere Sof radius 1.0 with center at (0., 0., -2.) is viewed in perspective from the viewpoint
(0., 0., 0.), with the view plane at z= -1., and the viewing direction along the negative zaxis. The
512 by 512 pixel window is mapped to the range -1. ≤x≤1., −1. ≤ y ≤ 1. on the view plane.
a) Given integers i and jrepresenting respectively the column and row of a pixel in the raster
image, show how to find the corresponding point (x,y, -1.) on the view plane. (Complete formula
required for full credit.)
b) Show how to determine whether the ray from the viewpoint through the point (x0,y0, -1.) inter-
sects the sphere S, and, if it does, the location of the first intersection point. (Complete formulas
required for full credit.)
c) Show how to shade (in black and white) a pixel (i,j) whose ray does intersect S, including the
contributions of ambient illumination, and of diffuse reflection of directional illumination from a
point light source “at infinity” in the direction (0., 1., 0.). (You may set any illumination and
reflectivity information not specified, or leave it as unspecified constants. Complete formula
required for full credit.)
2. Distributed Ray Tracing (4 points)
In distributed ray tracing, multiple ray trees are traced per pixel, and the resulting colors are
averaged. Describe how to vary the traced rays to produce the following effects:
a) anti-aliasing
b) motion blur
c) partial shadows from area light sources (penumbras).
d) “glossy” reflections from smooth, but not perfectly smooth, surfaces.
(See reverse side for questions 3 and 4.)
