Interpolating nets of curves by smooth subdivision surfaces
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Polynomial reproduction by symmetric subdivision schemes
Journal of Approximation Theory
Convergence and C1 analysis of subdivision schemes on manifolds by proximity
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Blending based corner cutting subdivision scheme for nets of curves
Computer Aided Geometric Design
A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Interpolatory blending net subdivision schemes of Dubuc-Deslauriers type
Computer Aided Geometric Design
| Hi-index | 7.29 |
In this paper we develop tools for the analysis of net subdivision schemes, schemes which recursively refine nets of bivariate continuous functions defined on grids of lines, and generate denser and denser nets. Sufficient conditions for the convergence of such a sequence of refined nets, and for the smoothness of the limit function, are derived in terms of proximity to a bivariate linear subdivision scheme refining points, under conditions controlling some aspects of the univariate functions of the generated nets. Approximation orders of net subdivision schemes, which are in proximity with positive schemes refining points are also derived. The paper concludes with the construction of a family of blending spline-type net subdivision schemes, and with their analysis by the tools presented in the paper. This family is a new example of net subdivision schemes generating C^1 limits with approximation order 2.