3D Interpolation and Approximation

  • Hebert Montegranario
  • Jairo Espinosa
Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)


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.


Radial Basis Function Cloud Point Fundamental Solution Null Space Interpolation Problem 
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© The Author(s) 2014

Authors and Affiliations

  1. 1.Mathematics InstituteUniversidad de AntioquiaMedellínColombia
  2. 2.Facultad de MinasUniversidad Nacional de ColombiaMedellínColombia

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