Intrinsic parametrization for approximation
Computer Aided Geometric Design
Modifying the shape of rational B-splines. part 1: curves
Computer-Aided Design
Automatic fairing algorithm for B-spline curves
Computer-Aided Design
Matrix computations (3rd ed.)
Global reparametrization for curve approximation
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
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
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
IGA-based point cloud fitting using B-spline surfaces for reverse engineering
Information Sciences: an International Journal
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In [1] Optimal Control methods over re-parametrization for curve and surface design were introduced. The advantage of Optimal Control over Global Minimization such as in [16] is that it can handle both approximation and interpolation. Moreover a cost function is introduced to implement a design objective (shortest curve, smoothest one etc...). The present work introduces the Optimal Control over the knot vectors of non-uniform B-Splines. Violation of Schoenberg-Whitney condition is dealt naturally within the Optimal Control framework. A geometric description of the resulting null space is provided as well.