• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.8
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• pp.921-931
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• 2011

This paper presents a data-fitting technique in which a B-spline hypervolume is used to approximate a given data set of scattered data samples. We describe the implementation of the data structure of a B-spline hypervolume, and we measure its memory size to show that the representation is compact. The proposed technique includes two algorithms. One is for the determination of the knot vectors of a B-spline hypervolume. The other is for the control points, which are determined by solving a linear least-squares minimization problem where the solution is independent of the data-set complexity. The proposed approach is demonstrated with various data-set configurations to reveal its performance in terms of approximation accuracy, memory use, and running time. In addition, we compare our approach with existing methods and present unconstrained optimization examples to show the potential for various applications.