Homework 5
CSCI-4967: Three-Dimensional Computer Graphics
Fall 2004
Due: Monday, November 22, 2004
Homeworks are due at the beginning of lecture on Monday, November 22. Late homeworks
will receive no credit. Homeworks are to be done individually and will be graded on the basis of
correctness, clarity, and legibility. Show the steps in your work where appropriate. Each question
is worth 10 points, for a total of 50 points.
Be sure to write your name and RPI email address on your homework submission.
1. (a) Consider a polygonal face fwith outward normal vector ~n = (5,−3,2) and a viewing
vector ~v = (2,1,3) from the camera towards the polygon. Is face fa front or back face?
(b) Consider any two methods for visible surface detection and state an advantage and
disadvantage of each method.
2. Suppose that visible surface detection is performed using a 8-bit integer depth buffer. Suppose
that the nearest object to be displayed is xunits away from the viewer and the furthest object
is 10xunits away from the viewer. Assume the near clipping is set at a distance x, but the
far clipping plane is set at distance 1000x. What (if any) are some of the dangers of setting
the far clipping plane at this unnecessarily large distance from the viewer?
3. Consider mapping a texture onto a cylinder. The cylinder is aligned with the Zaxis and has
a radius of runits and a height of hunits with its base at z= 0. You are given a texture
map whose scoordinate ranges from 0 to 1, and whose tcoordinate ranges from 0 to 1. You
are to wrap three copies of this texture around the cylinder (so they are not overlapping and
their vertical join lines are parallel to the Zaxis). Assume the first texture copy starts at
the positive Xaxis. Give the inverse mapping function, which maps a point (x, y, z) on the
cylinder to the corresponding point (s, t) on the texture.
4. (a) Texture mapping significantly increases the memory bandwidth required per rendered
pixel. Consider a simplified model of the memory bandwidth required due to texture
reads when we perform 2D texture mapping with multitexturing. Consider a display
with 1280×1024 pixels, and assume each pixel has two textures applied to it, where
each texel is represented as a 32 bit RGBA value. Additionally assume that bilinear
interpolation is performed at each pixel (that is, a linear average of the 2 ×2 array of
texels nearest the center of the pixel must be computed). Finally, assume an average
depth complexity of 3. (The depth complexity refers to the number of times each pixel
is rendered, and depends on the number of surfaces that cover each pixel).
