I found an interesting visualization of the Catmull-Clark algorithm here: https://www.youtube.com/watch?v=lU8f0hnorU8
andrewdcampbell
From reading further about this rule, I learned the formula was chosen by Catmull and Clark based on the aesthetic appearance of the results rather than any mathematical properties. However, they justify the formula by rigorously showing that the method converges to bicubic B-spline surfaces in the original paper.
john-b-yang
I'm not sure whether this was covered in lecture, but what is the valence of a vertex? I googled online and saw that it seems to mean the same thing as the degree, which would be the number of edges connected to that vertex.
If that is correct, would the valence of a vertex in Catmull-Clark be 4 most of the time? Similar to extraordinary points in loop subdivision, would the valence be different for those points?
orkun1675
@john-b-yang thats exactly right. As far as I understand its just another term for degree used for graphics. Yes, an extraordinary vertex in a quad mesh is shown in slide 49.
I found an interesting visualization of the Catmull-Clark algorithm here: https://www.youtube.com/watch?v=lU8f0hnorU8
From reading further about this rule, I learned the formula was chosen by Catmull and Clark based on the aesthetic appearance of the results rather than any mathematical properties. However, they justify the formula by rigorously showing that the method converges to bicubic B-spline surfaces in the original paper.
I'm not sure whether this was covered in lecture, but what is the valence of a vertex? I googled online and saw that it seems to mean the same thing as the degree, which would be the number of edges connected to that vertex. If that is correct, would the valence of a vertex in Catmull-Clark be 4 most of the time? Similar to extraordinary points in loop subdivision, would the valence be different for those points?
@john-b-yang thats exactly right. As far as I understand its just another term for degree used for graphics. Yes, an extraordinary vertex in a quad mesh is shown in slide 49.