Subdivision Surfaces and Mesh Data Structures

Subdivision Matrix
• Compute the new positions/vertices as a linear
combination of previous ones.
• To find the limit position of p 0, repeatedly apply the
subdivision matrix.
0
B
@
p (n)
0
p (n)
1
p (n)
2
p (n)
1
C
A
= 1
16
0
B
@
10 1 1 1 1 1 1
6 6 2 0 0 0 2
6 2 6 2 0 0 0
6 0 2 6 2 0 0
6 0 0 2 6 2 0
6 0 0 0 2 6 2
6 2 0 0 2 2 6
1n
0
If, after a change of basis we have M=A-1DA, where D is a
diagonal matrix, then:
3
p (n)
4
p (n)
5
p (n)
p3
p4
M p5
p6
6
n =A-1DnA, Since D is diagonal, raising D to the n-th power just amounts to
raising each of the diagonal entries of D to the n-th power.
Monday, November 19, 12
C
A
B
@
p0
p1
p2
1
C
A