Abstract
Subdivision schemes are efficient computational methods for the design, representation and approximation of surfaces of arbitrary topology in ℝ3. Subdivision schemes generate curves/surfaces from discrete data by repeated refinements. This paper reviews some of the theory of linear stationary subdivision schemes and their applications in geometric modelling. The first part is concerned with "classical" schemes refining control points. The second part reviews linear subdivision schemes refining other objects, such as vectors of Hermite-type data, compact sets in ℝn and nets of curves in ℝ3. Examples of various schemes are presented.
Original language | English |
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Pages | 1201-1226 |
Number of pages | 26 |
State | Published - 2006 |
Event | 25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain Duration: 22 Aug 2006 → 30 Aug 2006 |
Conference
Conference | 25th International Congress of Mathematicians, ICM 2006 |
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Country/Territory | Spain |
City | Madrid |
Period | 22/08/06 → 30/08/06 |
Keywords
- Approximation order
- Arbitrary topology
- Compact sets
- Curves
- Geometric modelling
- Nets of curves
- Nets of points
- Refinements
- Smoothness
- Subdivision schemes
- Surfaces