The following papers describe a two-stage 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.
Talk at the University of Sussex,
November 2006.
Talk at the Foundations of Computational Mathematics
Conference in Minneapolis, August 2002.
Poster