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.

Linear subdivision schemes for the reﬁnement of geometric objects

Nira Dyn

Abstract