Intrinsic parametrization for approximation
Computer Aided Geometric Design
Optimal approximate conversion of spline surfaces
Computer Aided Geometric Design
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Surface fitting with hierarchical splines
ACM Transactions on Graphics (TOG)
Global reparametrization for curve approximation
Computer Aided Geometric Design
Curve Fitting with Conic Splines
ACM Transactions on Graphics (TOG)
Smooth approximation and rendering of large scattered data sets
Proceedings of the conference on Visualization '01
Curve-fitting with piecewise parametric cubics
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Approximation with Active B-Spline Curves and Surfaces
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
Automatic Knot Determination of NURBS for Interactive Geometric Design
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
An improved Hoschek intrinsic parametrization
Computer Aided Geometric Design
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
A second order algorithm for orthogonal projection onto curves and surfaces
Computer Aided Geometric Design
Capturing planar shapes by approximating their outlines
Journal of Computational and Applied Mathematics
A revisit to least squares orthogonal distance fitting of parametric curves and surfaces
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
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We propose a fast method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two alternating time-consuming steps in every iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the L-BFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to solve a linear system of equations or performing foot point projection in every iteration. As a result, the proposed method is much faster than existing methods.