Knot removal for parametric B-spline curves and surfaces
Computer Aided Geometric Design
Intrinsic parametrization for approximation
Computer Aided Geometric Design
Constrained B-spline curve and surface fitting
Computer-Aided Design
Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Parameter optimization in approximating curves and surfaces to measurement data
Computer Aided Geometric Design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Data point selection for piecewise linear curve approximation
Computer Aided Geometric Design
The NURBS book
Combinatorial optimization
Global reparametrization for curve approximation
Computer Aided Geometric Design
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)
Adaptive knot placement in B-spline curve approximation
Computer-Aided Design
A local fitting algorithm for converting planar curves to B-splines
Computer Aided Geometric Design
Coronal loop detection from solar images
Pattern Recognition
Cubic B-spline curve approximation by curve unclamping
Computer-Aided Design
B-spline surface fitting based on adaptive knot placement using dominant columns
Computer-Aided Design
Technical Section: An extended iterative format for the progressive-iteration approximation
Computers and Graphics
Efficient particle swarm optimization approach for data fitting with free knot B-splines
Computer-Aided Design
Geometric point interpolation method in R3 space with tangent directional constraint
Computer-Aided Design
A new iterative mutually coupled hybrid GA-PSO approach for curve fitting in manufacturing
Applied Soft Computing
An improved parameterization method for B-spline curve and surface interpolation
Computer-Aided Design
IGA-based point cloud fitting using B-spline surfaces for reverse engineering
Information Sciences: an International Journal
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In this paper, we present a new approach of B-spline curve fitting to a set of ordered points, which is motivated by an insight that properly selected points called dominant points can play an important role in producing better curve approximation. The proposed approach takes four main steps: parameterization, dominant point selection, knot placement, and least-squares minimization. The approach is substantially different from the conventional approaches in knot placement and dominant point selection. In the knot placement, the knots are determined by averaging the parameter values of the dominant points, which basically transforms B-spline curve fitting into the problem of dominant point selection. We describe the properties of the knot placement including the property of local modification useful for adaptive curve refinement. We also present an algorithm for dominant point selection based on the adaptive refinement paradigm. The approach adaptively refines a B-spline curve by selecting fewer dominant points at flat regions but more at complex regions. For the same number of control points, the proposed approach can generate a B-spline curve with less deviation than the conventional approaches. When adopted in error-bounded curve approximation, it can generate a B-spline curve with far fewer control points while satisfying the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.