Subdivision Surfaces

Peters-Reif Algorithm: 2/4
The original and new vertices has a
relationship as follows:
⎡1 1
⎢2 ⎢
2
⎤
0
⎥
⎥
'
⎡ v
⎤
1 1 1
⎡ 1
⎤
⎢ ' ⎥ ⎢0 0⎥
⎢ ⎥
v2
⎢
⎥ v2
⎢ ⎥ 2 2 ⎢ ⎥
⎢ ⎢
⎥
⎥ = ⎢ ⎥
⎢
⎥
⋅
⎢
'
⎥ ⎢ ⎥
⎢ v
1 1
n−1
⎥ ⎢ ⎥
1
0
⎢vn−
⎥
' ⎢
⎢ ⎥ ⎥
2 2 ⎢ ⎥
⎣ vn
⎦ ⎢ ⎥ ⎣ vn
⎦
⎢1 1⎥
⎢
0 0
⎣2 2⎥⎦
v
The limit of this process consists of a set of
regular planar polygons that are the tangent
planes of the limit surface, which is G 1 .
Peters-Reif algorithm was developed by J.
Peters and U. Reif in 1998.
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