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Scattered Data Interpolation with Multilevel Splines
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 1997
"... This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel Bsplines are introduced to compute a C²continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarsetofine hierarchy of control lattices to generate a sequen ..."
Abstract

Cited by 106 (9 self)
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This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel Bsplines are introduced to compute a C²continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarsetofine hierarchy of control lattices to generate a sequence of bicubic Bspline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using Bspline refinement to reduce the sum of these functions into one equivalent Bspline function. Experimental results demonstrate that highfidelity reconstruction is possible from a selected set of sparse and irregular samples.
Adaptive smooth scattereddata approximation for largescale terrain visualization
 IN PROCEEDINGS OF THE SYMPOSIUM ON DATA VISUALISATION 2003
, 2003
"... We present a fast method that adaptively approximates largescale functional scattered data sets with hierarchical Bsplines. The scheme is memory efficient, easy to implement and produces smooth surfaces. It combines adaptive clustering based on quadtrees with piecewise polynomial least squares app ..."
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Cited by 11 (5 self)
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We present a fast method that adaptively approximates largescale functional scattered data sets with hierarchical Bsplines. The scheme is memory efficient, easy to implement and produces smooth surfaces. It combines adaptive clustering based on quadtrees with piecewise polynomial least squares approximations. The resulting surface components are locally approximated by a smooth Bspline surface obtained by knot removal. Residuals are computed with respect to this surface approximation, determining the clusters that need to be recursively refined, in order to satisfy a prescribed error bound. We provide numerical results for two terrain data sets, demonstrating that our algorithm works efficiently and accurate for large data sets with highly nonuniform sampling densities.
A general method for overlap control in image warping
 Computers and Graphics
, 2001
"... Anewgeneral solution for the construction of onetoone image warping functions is presented. The algorithm takes a set of user speci ed translations and constructs a set of onetoone warps by interpolation and scaling. These are concatenated to produce a single onetoone warping function, which ..."
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Cited by 3 (0 self)
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Anewgeneral solution for the construction of onetoone image warping functions is presented. The algorithm takes a set of user speci ed translations and constructs a set of onetoone warps by interpolation and scaling. These are concatenated to produce a single onetoone warping function, which prevents overlap in the resultant warped image.