Nira Dyn

Subdivision Schemes in Geometric Modelling

Subdivision schemes are efficient computational methods for the design and representation of 3D surfaces of arbitrary topology. They are also the tool for the generation of refinable functions which are instrumental in the construction of wavelets. This talk presents various tastes of subdivision, flavored by the personal viewpoint of the speaker, which is mainly motivated by geometric modelling. Our starting point is the general setting of scalar multivariate non-stationary schemes on regular grids. We present several families of schemes from univariate stationary schemes to bivariate non-stationary ones, approximating schemes and interpolating schemes. Some of the major families of schemes are the spline and box-spline schemes, which link our talk to the work of Carl.
This talk is based on a review paper in Acta Numerica 2002, written jointly with D. Levin