Subdivision Surfaces

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Simple Corner Cutting: 2/5 Suppose we have a polyline P 0 . Divide its edges with the above scheme, yielding a new polyline li P 1 . Dividing P 1 yields P 2 , …., and so on. What is P ∞ = Limit i P i i→∞ The u’s and v’s do not have to be the same for every edge. Moreover, the u’s and v’s used to divide P i do not have to be equal to those u’s s andv’s v used to divide P i+1 . 4
Simple Corner Cutting: 3/5 1/4 P 0 u = 1/3 and v = 1/4 P P 1 P 2 1/3 5
Page 1 and 2: Subdivision ision Techniqueses Spri
Page 3: Simple Corner Cutting: 1/5 On each
Page 7 and 8: Simple Corner Cutting: 5/5 1/2 v 1
Page 9 and 10: Facts about Subdivision Surfaces Su
Page 11 and 12: Regular Quad Mesh Subdivision: 1/3
Page 13 and 14: Regular Quad Mesh Subdivision: 3/3
Page 15 and 16: Doo-Sabin Subdivision: 1/6 Doo and
Page 17 and 18: Doo-Sabin Subdivision: 3/6 Most fac
Page 19 and 20: Doo-Sabin Subdivision: 5/6 1 2 3 4
Page 21 and 22: Catmull-Clark Algorithm: 1/10 Catmu
Page 23 and 24: Catmull-Clark Algorithm: 3/10 Comp
Page 25 and 26: Catmull-Clark Algorithm: 5/10 For e
Page 27 and 28: Catmull-Clark Algorithm: 7/10 Afte
Page 29 and 30: Catmull-Clark Algorithm: 9/10 1 2 3
Page 31 and 32: Loop’s Algorithm: 1/6 Loop’s (i
Page 33 and 34: Loop’s Algorithm: 3/6 Let a trian
Page 35 and 36: Loop’s Algorithm: 5/6 Doo-Sabin C
Page 37 and 38: Peters-Reif Algorithm: 1/4 This is
Page 39 and 40: Peters-Reif Algorithm: 3/4 39
Page 41 and 42: √3-Subdivision of Kobbelt: 1/8
Page 43 and 44: √3-Subdivision of Kobbelt: 3/8 St
Page 45 and 46: √3-Subdivision S ision of Kobbelt
Page 47 and 48: √3-Subdivision of Kobbelt: 7/8 1
Page 49: The End 49

Subdivision Surfaces

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