Scattered Data Fitting



Poster

The following papers describe a recently developed approach to the problem of scattered data fitting suitable for efficient approximation of very large data:

O. Davydov and F. Zeilfelder, Scattered data fitting by direct extension of local polynomials to bivariate splines , Advances in Comp. Math. 21 (2004), 223-271.

J. Haber, F. Zeilfelder, O. Davydov and H.-P. Seidel, Smooth approximation and rendering of large scattered data sets, in  ``Proceedings of IEEE Visualization 2001,'' (Th.Ertl, K.Joy and A.Varshney, Eds.), pp.341-347, 571, IEEE Computer Society, 2001.

O. Davydov, On the approximation power of local least squares polynomials, in  "Algorithms for Approximation IV," (J.Levesley, I.J.Anderson and J.C.Mason, Eds.), pp.346-353, University of Huddersfield, UK, 2002.

O. Davydov, R. Morandi and A. Sestini, Local hybrid approximation for scattered data fitting with bivariate splines, Comput. Aided Geom. Design 23 (2006), 703-721.

Ch. Rössl, F. Zeilfelder, G. Nürnberger and H.-P. Seidel, Spline approximation of general volumetric data, ACM Solid Modeling 2004.

O. Davydov, R. Morandi and A. Sestini, Local RBF approximation for scattered data fitting with bivariate splines, in  "Trends and Applications in Constructive Approximation," (M. G. de Bruin, D. H. Mache, and J.Szabados, Eds.), pp.91--102, ISNM Vol.151, Birkhäuser, 2005.

O. Davydov, Error bound for radial basis interpolation in terms of a growth function, Strathclyde Mathematics Research Report (2006), No. 24.

O. Davydov and L. L. Schumaker, Scattered data fitting on surfaces using projected Powell-Sabin splines, Strathclyde Mathematics Research Report (2007), No. 3.

O. Davydov and L. L. Schumaker, Interpolation and scattered data fitting on manifolds using projected Powell-Sabin splines, Strathclyde Mathematics Research Report (2007), No. 6.

Software package TSFIT available under GPL, including our test data.

Richard Franke's Test Data can be downloaded following instructions at this link

Talk at the University of Sussex, November 2006.

Talk at the Foundations of Computational Mathematics Conference in Minneapolis, August 2002.



Homepage