Knot removal for parametric B-spline curves and surfaces
Computer Aided Geometric Design
Curve and surface fitting with splines
Curve and surface fitting with splines
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
The NURBS book
Swarm intelligence
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Numerical Methods, Software, and Analysis
Numerical Methods, Software, and Analysis
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
The particle swarm optimization algorithm: convergence analysis and parameter selection
Information Processing Letters
Automatic Knot Placement by a Genetic Algorithm for Data Fitting with a Spline
SMI '99 Proceedings of the International Conference on Shape Modeling and Applications
Capturing Outline of Fonts Using Genetic Algorithm and Splines
IV '01 Proceedings of the Fifth International Conference on Information Visualisation
An error-bounded approximate method for representing planar curves in B-splines
Computer Aided Geometric Design
Spline curve approximation and design by optimal control over the knots
Computing - Geometric modelling dagstuhl 2002
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
Fundamentals of Computational Swarm Intelligence
Fundamentals of Computational Swarm Intelligence
B-spline curve fitting based on adaptive curve refinement using dominant points
Computer-Aided Design
Automatic knot adjustment using an artificial immune system for B-spline curve approximation
Information Sciences: an International Journal
Adaptive knot placement in B-spline curve approximation
Computer-Aided Design
Industrial geometry: recent advances and applications in CAD
Computer-Aided Design
The particle swarm - explosion, stability, and convergence in amultidimensional complex space
IEEE Transactions on Evolutionary Computation
Latent nonuniform splines for animation approximation
SIGGRAPH Asia 2012 Technical Briefs
A new iterative mutually coupled hybrid GA-PSO approach for curve fitting in manufacturing
Applied Soft Computing
Hi-index | 0.00 |
Data fitting through B-splines improves dramatically if the knots are treated as free variables. However, in that case the approximation problem becomes a very difficult continuous multimodal and multivariate nonlinear optimization problem. In a previous paper, Yoshimoto et al. (2003) [18] solved this problem for explicit curves by using a real-code genetic algorithm. However, the method does not really deal with true multiple knots, so the cases of data with underlying functions having discontinuities and cusps are not fully addressed. In this paper, we present a new method to overcome such a limitation. The method applies the particle swarm optimization (PSO) paradigm to compute an appropriate location of knots automatically. Our scheme yields very accurate results even for curves with singularities and/or cusps. Several experiments show that our proposal is very efficient and improves previous results (including those by Yoshimoto et al. (2003) in [18]) significantly in terms of data points error, AIC and BIC criteria. Furthermore, the important case of true multiple knots is now satisfactorily solved.