Linear subdivision schemes for the refinement of geometric objects
Nira Dyn
Tel Aviv University, Israel
Download Chapter PDF
A subscription is required to access this book chapter.
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.