CS559
Fall 2005
Written Assignment 4:
Surfaces, Lighting, and Rendering
Due Tuesday, December 6th, 9:30am
Question 1: Light Paths
For each of the following light paths, describe a real-world situation where it is important. (by real world, think of something that you might see in your house)
1A: LSE
1B: LSDE
1C: LDSE
1D: LDDSE
Question 2: (Catmull Clark Subdivision)
For the following figure (with 4 quads, a triangle, and a pentagon):
Draw the topology after 2 subdivision steps using Catmull Clark subdivision rules.
How many polygons will there be?
How many vertices will there be? How many will be ordinary?
Question 3: (Butterfly Subdivision)
Consider a unit cube with its faces divided into 4 triangles (by placing a point in the center of each face) as follows:
(note: there are a total
of 24 triangles)
The cube is placed with a corner at the origin and is axis aligned, so that one of the edges goes from (0,0,0) to (1,0,0).
If the cube is subdivided once using the butterfly scheme (or the modified butterfly scheme with w=0), where does the new point on the edge (0,0,0)->(1,0,0) end up?
If the top and bottom (the faces with y=0 and y=1) are removed, where would this point have gone? (hint: just because a vertex has 6 edges, doesn't mean its ordinary)
Question 4: (Lighting)
A single polygon at the origin is viewed from above (0,10,0). A single point light source is placed at (10,10,0). The light has intensity 1, and the polygon has diffuse and specular reflectance of 1. The specular exponent is 5.
For the 3 points on the polygon (0,0,0) (5,0,0) (10,0,0), compute the amount of specular and diffuse lighting.