Fast B-spline curve fitting by L-BFGS

DOI10.1016/j.cagd.2012.03.004zbMath1250.65022arXiv1201.0070OpenAlexW2154660120MaRDI QIDQ450235

Wenni Zheng, Pengbo Bo, Yang Liu, Wenping Wang

Publication date: 13 September 2012

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

Full work available at URL: https://arxiv.org/abs/1201.0070

zbMATH Keywords

numerical examplescurve fittingB-spline curvecontrol pointsquasi-Newton methodpoint cloudL-BFGS optimization

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical smoothing, curve fitting (65D10) Numerical mathematical programming methods (65K05) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (10)

Uncertainty quantification and estimation of closed curves based on noisy data ⋮ As-developable-as-possible B-spline surface interpolation to B-spline curves ⋮ Capturing outlines of generic shapes with cubic B´ezier curves using the Nelder–Mead simplex method ⋮ High speed machining for linear paths blended with \(G3\) continuous Pythagorean-hodograph curves ⋮ A limited-memory BFGS-based differential evolution algorithm for optimal control of nonlinear systems with mixed control variables and probability constraints ⋮ A general hybrid optimization strategy for curve fitting in the non-uniform rational basis spline framework ⋮ \(L_1C^1\) polynomial spline approximation algorithms for large data sets ⋮ Adjoint-based airfoil optimization with adaptive isogeometric discontinuous Galerkin method ⋮ A composite iterative procedure with fast convergence rate for the progressive-iteration approximation of curves ⋮ LSPIA, (stochastic) gradient descent, and parameter correction

Cites Work

• Curve and surface fitting and design by optimal control methods
• Capturing planar shapes by approximating their outlines
• Intrinsic parametrization for approximation
• Global reparametrization for curve approximation
• Optimal approximate conversion of spline surfaces
• An improved Hoschek intrinsic parametrization
• A second order algorithm for orthogonal projection onto curves and surfaces
• Curve Fitting with Conic Splines
• Numerical Optimization
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