Knot removal for parametric B-spline curves and surfaces
Computer Aided Geometric Design
The NURBS book
Some characterizations of families of surfaces using functional equations
ACM Transactions on Graphics (TOG)
Swarm intelligence
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
An Introduction to Genetic Algorithms
An Introduction to Genetic Algorithms
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Comparison between Genetic Algorithms and Particle Swarm Optimization
EP '98 Proceedings of the 7th International Conference on Evolutionary Programming VII
Evolutionary Optimization Versus Particle Swarm Optimization: Philosophy and Performance Differences
EP '98 Proceedings of the 7th International Conference on Evolutionary Programming VII
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
An error-bounded approximate method for representing planar curves in B-splines
Computer Aided Geometric Design
Breeding swarms: a GA/PSO hybrid
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
Hybrid Evolutionary Algorithm Based on PSO and GA Mutation
HIS '06 Proceedings of the Sixth International Conference on Hybrid Intelligent Systems
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
A hybrid genetic algorithm and particle swarm optimization for multimodal functions
Applied Soft Computing
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
Tool path generation for a surface model with defects
Computers in Industry
IEEE Computational Intelligence Magazine
A new differential approach for parametric-implicit surface intersection
ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
Information Sciences: an International Journal
Efficient particle swarm optimization approach for data fitting with free knot B-splines
Computer-Aided Design
The particle swarm - explosion, stability, and convergence in amultidimensional complex space
IEEE Transactions on Evolutionary Computation
A hybrid of genetic algorithm and particle swarm optimization for recurrent network design
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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Fitting data points to curves (usually referred to as curve reconstruction) is a major issue in computer-aided design/manufacturing (CAD/CAM). This problem appears recurrently in reverse engineering, where a set of (possibly massive and noisy) data points obtained by 3D laser scanning have to be fitted to a free-form parametric curve (typically a B-spline). Despite the large number of methods available to tackle this issue, the problem is still challenging and elusive. In fact, no satisfactory solution to the general problem has been achieved so far. In this paper we present a novel hybrid evolutionary approach (called IMCH-GAPSO) for B-spline curve reconstruction comprised of two classical bio-inspired techniques: genetic algorithms (GA) and particle swarm optimization (PSO), accounting for data parameterization and knot placement, respectively. In our setting, GA and PSO are mutually coupled in the sense that the output of one system is used as the input of the other and vice versa. This coupling is then repeated iteratively until a termination criterion (such as a prescribed error threshold or a fixed number of iterations) is attained. To evaluate the performance of our approach, it has been applied to several illustrative examples of data points from real-world applications in manufacturing. Our experimental results show that our approach performs very well, being able to reconstruct with very high accuracy extremely complicated shapes, unfeasible for reconstruction with current methods.