Smoothness equivalence properties of univariate subdivision schemes and their projection analogues

DOI10.1007/s00211-009-0231-9zbMath1173.65013OpenAlexW2036881824MaRDI QIDQ841114

Philipp Grohs

Publication date: 14 September 2009

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-009-0231-9

zbMATH Keywords

subdivision schemesprojectionsmoothnessnonlinear perturbationproximity conditionequivalence properties

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items (17)

Approximation order of interpolatory nonlinear subdivision schemes ⋮ Stability of manifold-valued subdivision schemes and multiscale transformations ⋮ Single basepoint subdivision schemes for manifold-valued data: time-symmetry without space-symmetry ⋮ On a New Proximity Condition for Manifold-Valued Subdivision Schemes ⋮ Optimal a priori discretization error bounds for geodesic finite elements ⋮ Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces ⋮ Point-normal subdivision curves and surfaces ⋮ Embedding-Based Interpolation on the Special Orthogonal Group ⋮ Invariance property of proximity conditions in nonlinear subdivision ⋮ De Casteljau's algorithm on manifolds ⋮ Subdivision schemes with general dilation in the geometric and nonlinear setting ⋮ Geometric Subdivision and Multiscale Transforms ⋮ A necessary and sufficient proximity condition for smoothness equivalence of nonlinear subdivision schemes ⋮ Scattered manifold-valued data approximation ⋮ Stability of nonlinear subdivision and multiscale transforms ⋮ Interpolatory wavelets for manifold-valued data ⋮ $C^1$ Analysis of Hermite Subdivision Schemes on Manifolds

Cites Work

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• Interpolatory wavelets for manifold-valued data
• Smoothness analysis of subdivision schemes by proximity
• Convergence and \(C^1\) analysis of subdivision schemes on manifolds by proximity
• How Data Dependent is a Nonlinear Subdivision Scheme? A Case Study Based on Convexity Preserving Subdivision
• Smoothness Properties of Lie Group Subdivision Schemes
• Smoothness Equivalence Properties of Manifold‐Valued Data Subdivision Schemes Based on the Projection Approach
• Stationary subdivision
• Smoothness of interpolatory multivariate subdivision in Lie groups

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