Point data reconstruction and smoothing using cubic splines and clusterization

DOI10.1016/j.matcom.2020.04.002OpenAlexW3016685638MaRDI QIDQ1998043

Marco Frego, Francesco Biral, Enrico Bertolazzi

Publication date: 6 March 2021

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2020.04.002

zbMATH Keywords

least squarescubic splinepath reconstructiongeneralised cross-validation

Mathematics Subject Classification ID

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Numerical methods for mathematical programming, optimization and variational techniques (65Kxx)

Related Items (2)

Implicit reconstructions of thin leaf surfaces from large, noisy point clouds ⋮ Applied scientific computing XV: innovative modeling and simulation in sciences

Uses Software

• TSPACK
• pchip
• Algorithm 547
• Clothoids

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Symbolic-numeric indirect method for solving optimal control problems for large multibody systems
• Polynomial cubic splines with tension properties
• Planar point set fairing and fitting by arc splines
• Geometric Hermite interpolation
• Constrained approximation by splines with free knots
• On the deviation of a parametric cubic spline interpolant from its data polygon
• Modifying the shape of FB-spline curves
• A fast compact algorithm for cubic spline smoothing
• New spline spaces with generalized tension properties
• The BS class of Hermite spline quasi-interpolants on nonuniform knot distributions
• Geometric spline curves
• High accuracy geometric Hermite interpolation
• A shape preserving interpolant with tension controls
• The use of Cornu spirals in drawing planar curves of controlled curvature
• Choosing nodes in parametric curve interpolation
• Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
• \(\mathbb{P}_1\)-reproducing shape-preserving quasi-interpolant using positive quadratic splines with local support
• Shape-preserving knot removal
• A general scheme for shape preserving planar interpolating curves
• Spatial shape-preserving interpolation using \(\nu\)-splines
• Flexible smoothing with \(B\)-splines and penalties. With comments and a rejoinder by the authors
• Total least squares fitting of Bézier and B-spline curves to ordered data
• Semi-analytical minimum time solutions with velocity constraints for trajectory following of vehicles
• Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics
• Spline approximation by quasiinterpolants
• Shape-preserving \(C^3\) interpolation: The curve case
• Algorithms for shape preserving local approximation with automatic selection of tension parameters
• On the \(G^2\) Hermite interpolation problem with clothoids
• Geometric construction of spline curves with tension properties
• The family of biarcs that matches planar, two-point \(G^{1}\) Hermite data
• Shape-preserving, first-derivative-based parametric and nonparametric cubic \(L_{1}\) spline curves
• Minimizing B-spline knots in representative road axis from GPS points cloud
• Optimum smoothing parameter selection for penalized least squares in form of linear mixed effect models
• Formulation and optimization of cubic polynomial joint trajectories for industrial robots
• Semianalytical minimum-time solution for the optimal control of a vehicle subject to limited acceleration
• Chordal cubic spline interpolation is fourth-order accurate
• Fitting noisy data using cross-validated cubic smoothing splines
• A COMPARISON OF MIXED MODEL SPLINES FOR CURVE FITTING
• On geometric interpolation by planar parametric polynomial curves
• Monotone Piecewise Cubic Interpolation
• Algorithm 547: Fortran Routines for Discrete Cubic Spline Interpolation and Smoothing [E1, [E3]]
• Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
• Towards a Generalized Singular Value Decomposition
• Generalizing the Singular Value Decomposition
• Approximation to Data by Splines with Free Knots
• The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems
• Algorithm 716: TSPACK: tension spline curve-fitting package
• The Singular Value Decomposition: Anatomy of Optimizing an Algorithm for Extreme Scale
• Interpolating clothoid splines with curvature continuity
• On Geometric Interpolation by Polynomial Curves
• Shape-preserving interpolation by G1 and G2 PH quintic splines
• Shape-preserving interpolation of spatial data by Pythagorean-hodograph quintic spline curves
• Point-Clothoid Distance and Projection Computation
• G¹ fitting with clothoids
• Smoothing noisy data with spline functions
• On shape preserving \(C^2\) Hermite interpolation
• Shape-preserving approximation by space curves
• A practical guide to splines.

This page was built for publication: Point data reconstruction and smoothing using cubic splines and clusterization