Nonlinear subdivision schemes on irregular meshes

DOI10.1007/s00365-009-9063-1zbMath1247.65018OpenAlexW2017499683MaRDI QIDQ975343

Andreas Weinmann

Publication date: 9 June 2010

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-009-9063-1

zbMATH Keywords

irregular meshnonlinear subdivisionextraordinary point

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Computer-aided design (modeling of curves and surfaces) (65D17) Classical differential geometry (53A99) Continuity properties of mappings on manifolds (58C07)

Related Items (10)

A second-order TV-type approach for inpainting and denoising higher dimensional combined cyclic and vector space data ⋮ Wavelet Sparse Regularization for Manifold-Valued Data ⋮ Point-normal subdivision curves and surfaces ⋮ Old problems and new challenges in subdivision ⋮ Subdivision schemes with general dilation in the geometric and nonlinear setting ⋮ Non-smooth Variational Regularization for Processing Manifold-Valued Data ⋮ Geometric Subdivision and Multiscale Transforms ⋮ A necessary and sufficient proximity condition for smoothness equivalence of nonlinear subdivision schemes ⋮ Total Generalized Variation for Manifold-Valued Data ⋮ Clothoid fitting and geometric Hermite subdivision

Cites Work

• Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces
• A unified approach to subdivision algorithms near extraordinary vertices
• Interpolatory wavelets for manifold-valued data
• Smoothness of subdivision surfaces at extraordinary points
• Smoothness of stationary subdivision on irregular meshes
• Subdivision surfaces
• Convergence and \(C^1\) analysis of subdivision schemes on manifolds by proximity
• Smoothness Analysis of Subdivision Schemes on Regular Grids by Proximity
• Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence
• Stationary subdivision
• Riemannian center of mass and mollifier smoothing
• Analysis of Algorithms Generalizing B-Spline Subdivision
• A Method for Analysis ofC¹-Continuity of Subdivision Surfaces
• Multiscale Representations for Manifold-Valued Data
• A unified framework for primal/dual quadrilateral subdivision schemes

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