Abstract
In this chapter we extend to n dimensions the spline theory developed in Chap. 4 on cubic splines for interpolation and approximation of functions; in particular we deal with 3D data. As a consequence of interpolation and smoothness conditions we obtain by a constructive proof, the Thin Plate Spline (TPS), whose explicit expression is given in terms of a convolution with the fundamental solutions of the biharmonic differential operator. In this construction no geometry on data is assumed. Thus, the data do not have to conform a regular grid, so we speak about reconstruction from scattered data.
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Montegranario, H., Espinosa, J. (2014). 3D Interpolation and Approximation. In: Variational Regularization of 3D Data. SpringerBriefs in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0533-1_7
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DOI: https://doi.org/10.1007/978-1-4939-0533-1_7
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-0532-4
Online ISBN: 978-1-4939-0533-1
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