Nonlinear subdivision through nonlinear averaging

DOI10.1016/j.cagd.2007.07.003zbMath1172.65347OpenAlexW2010498540MaRDI QIDQ735462

D. Kharzeev

Publication date: 22 October 2009

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cagd.2007.07.003

Mathematics Subject Classification ID

Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (21)

Non-uniform interpolatory subdivision schemes with improved smoothness ⋮ On the Geometry and Kinematics of Smoothly Distributed and Singular Defects ⋮ A nonlinear generalized subdivision scheme of arbitrary degree with a tension parameter ⋮ A shape-preserving variant of Lane-Riesenfeld algorithm ⋮ Subdivision schemes for positive definite matrices ⋮ Single basepoint subdivision schemes for manifold-valued data: time-symmetry without space-symmetry ⋮ Hölder regularity of geometric subdivision schemes ⋮ On the smoothness of real-valued functions generated by subdivision schemes using nonlinear binary averaging ⋮ Convergence and smoothness of nonlinear Lane-Riesenfeld algorithms in the functional setting ⋮ Point-normal subdivision curves and surfaces ⋮ Geometric Hermite interpolation in \(\mathbb{R}^n\) by refinements ⋮ A generalized curve subdivision scheme of arbitrary order with a tension parameter ⋮ On a family of non-oscillatory subdivision schemes having regularity \(C^r\) with \(r > 1\) ⋮ A new variant of Lane-Riesenfeld algorithm with two tension parameters ⋮ A class of nonlinear four-point subdivision schemes ⋮ Nonlinear weighted average and blossoming ⋮ High order smoothness of non-linear Lane-Riesenfeld algorithms in the functional setting ⋮ A global approach to the refinement of manifold data ⋮ Two open questions relating to subdivision ⋮ A six-point variant on the Lane-Riesenfeld algorithm ⋮ On the use of generalized harmonic means in image processing using multiresolution algorithms

Cites Work

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• On the smoothness of real-valued functions generated by subdivision schemes using nonlinear binary averaging
• A unified approach to subdivision algorithms near extraordinary vertices
• A 4-point interpolatory subdivision scheme for curve design
• Symmetric iterative interpolation processes
• Nonlinear corner-cutting
• Quasilinear subdivision schemes with applications to ENO interpolation.
• Interpolatory subdivision schemes and wavelets
• Nonlinear subdivision using local spherical coordinates
• Convergence and \(C^1\) analysis of subdivision schemes on manifolds by proximity
• Three Families of Nonlinear Subdivision Schemes
• Smoothness Equivalence Properties of Manifold‐Valued Data Subdivision Schemes Based on the Projection Approach
• A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces

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