W7

Written Assignment 7

Due 12/5/2006, 9:30 am

Question 1

(note: this question is not meant to be tricky - its just hard to do subdivision by hand since we need to have a mesh that is big enough to have regular points. this question should be straightforward using the equations from the reading.)

Here is a house model made of triangles. There are 14 vertices. The bottom of the house is open, but the sides wrap around (so there is an edge from 4 to 1 and 4 to 5). There are 20 triangles (8 around each floor, 6 for the roof (2 "ends" and 2 "faces").

The vertices are places as follows:

1A: How many triangles will there be if we subdivide once (using either Loop or Modified Butterfly subdivision)?

1B: How many REGULAR vertices are there before subdivision? How many Extraordinary ones? (edge points are extraordinary)

1C: How Regular / Extraordinary vertices will there be after 1 subdivision?

1D: If we are doing modified butterfly subdivision with tension parameter (w) equal to zero, where will the following new points go:

• the vertex inserted between vertex 7 and vertex 8?
• between 2 and 3?
• between 2 and 7?
• between 13 and 14?

1E: If we are doing Loop subdivision where will the following new points go in the first step:

• the vertex inserted between vertex 7 and vertex 8?
• between 2 and 3?
• between 2 and 7?
• between 13 and 14?

1F: If we perform Loop subdivision, where will the following vertices move to in the first step:

• 2
• 7
• 13

Question 2:

If we have a bilinear patch with its vertices at (0,0,0), (10,0,0), (10,10,10), (0,0,10), where will the "center" point (u,v = .5,.5) be?