Minimal energy \(C^r\)-surfaces on uniform Powell-Sabin-type meshes for noisy data

DOI10.1016/j.cam.2008.01.015zbMath1148.65010OpenAlexW2078523710MaRDI QIDQ932747

B. E. Eshmatov

Publication date: 11 July 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2008.01.015

zbMATH Keywords

smoothingnoisy dataapproximationminimal energyvariational spline

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Spline approximation (41A15) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (9)

An approximation method based on MRA for the quasi-Plateau problem ⋮ Hole-filling techniques by using minimal energy surfaces ⋮ A coons patch spanning a finite number of curves tested for variationally minimizing its area ⋮ Preconditioned conjugate gradient method for finding minimal energy surfaces on Powell-Sabin triangulations ⋮ Filling polygonal holes with minimal energy surfaces on Powell-Sabin type triangulations ⋮ A hole filling method for surfaces by using \(\mathcal C^1\)-Powell-Sabin splines. Estimation of the smoothing parameters ⋮ Variational trivariate fitting using Worsey-Piper macro elements on tetrahedral partitions ⋮ Multiresolution Analysis for Minimal Energy C r -Surfaces on Powell-Sabin Type Meshes ⋮ Variationally improved Bézier surfaces with shifted knots

Uses Software

• BRENT

Cites Work

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• \(C^ r\)-finite elements of Powell-Sabin type on the three direction mesh
• Convergence rates for multivariate smoothing spline functions
• Approximation of method of regularization estimators
• Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
• Approximation order of bivariate spline interpolation for arbitrary smoothness
• Almost sure convergence of smoothing \(D^ m\)-splines of noisy data
• Approximation of surfaces by fairness bicubic splines
• Minimal energy \(C^r\)-surfaces on uniform Powell-Sabin type meshes. Estimation of the smoothing parameters
• Error Bounds for Hermite Interpolation by Quadratic Splines on an  -Triangulation
• Optimal Smoothing of Noisy Data Using Spline Functions
• Piecewise Quadratic Approximations on Triangles

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