Linear subdivision schemes for the refinement of geometric objects

• Autores: Nira Dyn
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé , Javier Soria de Diego , Juan Luis Varona Malumbres , Joan Verdera , Vol. 3, 2006, ISBN 978-3-03719-022-7, págs. 1201-1226
• Idioma: inglés
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• Resumen

  • 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.